tribology in industry 1-2013.pdf

tribology in industry 

ISSN 0354-8996 

1 

VOLUME 35 

2013.

Vol. 35, Nº 1 ( 2013) 

Tribology in Industry 

Journal of the 

Serbian 

Tribology Society 

www.tribology.fink.rs 

EDITOR IN CHIEF: 

MANAGING EDITOR: 

EDITORIAL BOARD: 

TECHNICAL EDITOR: 

ISSN: 

Published by: 

Financially supported by: 

M. BABI Ć, Faculty of Engineering, University of Kragujevac, Serbia 

B. IVKOVI Ć, Faculty of Engineering, University of Kragujevac, Serbia 

S. MITROVI Ć, Faculty of Engineering, University of Kragujevac, Serbia 

B. BHUSHAN, The Ohio State University, Columbus, USA 

K.-D. BOUZAKIS, Aristotle University of Thessaloniki, Thessaloniki, Greece 

M.D. BRYANT, The University of Texas at Austin, Austin, USA 

M.A. CHOWDHURY, Dhaka University of Engineering & Technology, Gazipur, 

Bangladesh 

M. KANDEVA, Technical University of Sofia, Sofia, Bulgaria 

G. MANIVASAGAM, VIT University, Vellore, India 

N. MANOLOV, Technical University of Sofia, Sofia, Bulgaria 

M. MILOSAVLJEVI Ć, Vinča Institute of Nuclear Sciences, Belgrade, Serbia 

N. MYSHKIN, Metal-Polymer Research Institute of National Academy of Sciences 

of Belarus, Gomel, Belarus 

S. PYTKO, AGH University of Science and Technology, Krakow, Poland 

A. RAC, Faculty of Mechanical Engineering, University of Belgrade, Serbia 

S. SEKULI Ć, Faculty of Technical Sciences, University of Novi Sad, Serbia 

A.I. SVIRIDENOK, The Research Center of Resources Saving Problems of the 

National Academy of Sciences of Belarus, G rodno, Belarus 

A. TUDOR, University Politehnica of Bucharest, Bucharest, Romania 

A. VENCL, Faculty of Mechanical Engineering, University of Belgrade, Serbia 

S. MITROVIĆ, 

Faculty of Engineering, University of Kragujevac, Serbia 

0354-8996 (print version) 

2217-7965 (electronic version) 

Tribology Center, Faculty of Engineering, University of Kragujevac 

Sestre Janjić 6, 34000 Kragujevac, Serbia 

Ministry of Education, Science and Technological Development 

Republic of Serbia 

Nemanjina 22-26, 11000 Belgrade, Serbia 

Published quarterly


Vol. 35, Nº 1 ( 2013) 


Contents 

RESEARCH 

B. CHATTERJEE, P. SAHOO: Shakedown Behavior in Multiple Normal 

Loading-Unloading of an Elastic-Plastic Spherical Stick Contact . . . . . . . . . 

M. IANCU, R.G. RIPEANU, I. TUDOR: Heat Exchanger Tube to Tube Sheet 

Joints Corrosion Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

K.K. ALANEME, B.O. ADEMILUA, 

M.O. BODUNRIN: Mechanical 

Properties and Corrosion Behaviour of Aluminium Hybrid Composites 

Reinforced with Silicon Carbide and Bamboo Leaf Ash . . . . . . . . . . . . . . . . . 

A. TODIĆ, D. ČIKARA, V. LAZIĆ, T. TODIĆ, I. ČAMAGIĆ, A. SKULIĆ, 

D. ČIKARA: Examination of Wear Resistance of Polymer – Basalt 

Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

M.A. CHOWDHURY, D.M. NURUZZAMAN: Experimental Investigation 

on Friction and Wear Properties of Different Steel Materials . . . . . . . . . . . . 

R.R. RAO, K. GOUTHAMI, J.V. KUMAR: Effects of Velocity-Slip and 

Viscosity Variation in Squeeze Film Lubrication of Two 

Circular Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

S.A. ADNANI, S.J. HASHEMI, A. SHOOSHTARI, M.M. ATTAR: 

The Initial Estimate of the Useful Lifetime of the Oil in Diesel Engines 

Using Oil Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

S. ILAIYAVEL, A. VENKATESAN: Investigation of Wear Coefficient of 

Manganese Phosphate Coated Tool Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

A. SONTHALIA, C.R. KUMAR: The Effect of Compression Ring Profile on 

the Friction Force in an Internal Combustion Engine . . . . . . . . . . . . . . . . . . 

S.K. ROY CHOWDHURY, K. MALHOTRA, H. PADMAWAR: Effect of Contact 

Temperature Rise During Sliding on the Wear Resistance of TiNi Shape 

Memory Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

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ISSN 0354-8996 

VOLUME 33 

2011. 

3

Vol. 35, No. 1 (2013) 3‐18 



RESEARCH 

Shakedown Behavior in Multiple Normal 

Loading‐Unloading of an Elastic‐Plastic 

Spherical Stick Contact 

B. Chatterjee a , P. Sahoo a 

a Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India. 

Keywords: 

Shakedown 

Multiple loading‐unloading 

Strain hardening 

Spherical contact 

ANSYS 

Corresponding author: 

Prasanta Sahoo 

Department of Mechanical 

Engineering, Jadavpur University, 

Kolkata 700032, India 

E‐mail: psjume@gmail.com 

A B S T R A C T 

The effect of strain hardening and hardening rule on shakedown behavior is 

studied in a multiple normal interaction process of an elastic plastic sphere 

against a rigid flat using finite element software ANSYS under full stick contact 

condition. Seven to ten repeated loading cycles are considered in the 

interference controlled multiple normal loading unloading depending upon the 

maximum interference of loading. Emphasis is placed on wide range of tangent 

modulus by varying the hardening parameter within the range as found for 

most of the practical materials with both the kinematic and isotropic hardening 

model, which has not yet been investigated. It is found that with small tangent 

modulus, the cyclic loading process gradually converges into elastic shakedown 

with both kinematic and isotropic strain hardening laws; similar to recently 

published finite element based normal loading unloading results. The effect of 

strain hardening laws on shakedown behavior is pronounced at higher tangent 

modulus. The higher dimensionless interference of loading and higher tangent 

modulus increase the dimensionless dissipated energy with kinematic 

hardening rule. The load‐interference hysteretic response with varying tangent 

modulus using both kinematic and isotropic hardening laws is interpreted in 

the context of elastic and plastic shakedown. 

© 2013 Published by Faculty of Engineering 

1. INTRODUCTION 

When a material is subjected to repeated normal 

loading‐unloading, its deformation depends on 

the extent of the amplitude of the maximum 

stress with respect to the yield stress of the 

material. When contact stress exceeds yield 

stress, plastic flow of the material occurs beyond 

the elastic limit loading. Residual stresses, 

developed after complete unloading, are 

protective in nature as they reduce the tendency 

of plastic flow in the subsequent loading. Strain 

hardening of the material strongly affects the 

development of residual strain after complete 

unloading. The cyclic response may be perfectly 

elastic and reversible, stabilized and closed cycle 

of plastic strain or consists of repetitive 

accumulation of incremental unidirectional 

plastic strain [1‐3] depending on the intensity of 

loading, elastic and plastic properties of the 

3

B. Chatterjee and P. Sahoo, Tribology in Industry Vol. 35, No. 1 (2013) 3‐18 

materials and the tribological system parameters 

like friction, wear etc. [4]. Thus the modeling of 

cyclic response is quite complex. The repeated 

cyclic loading promotes fatigue of the deformable 

or softer materials. Non‐conforming bodies when 

brought into contact without deformation, either 

point or line contact may occur [5]. The type of 

relative motion between mating surfaces 

produces sliding, rolling contact. The prominent 

contact damages encountered due to the sliding 

and rolling contact fatigues are galling, surface 

distress, spalling, pitting etc. [6]. Fretting fatigue 

is observed owing to the relative cyclic motion 

with small amplitude between two oscillating 

surfaces [7]. 

The basic step of investigating the cyclic 

response of rough surfaces involves the study 

with single asperity contact. Cattaneo [8] and 

then Mindlin [9] independently published the 

solutions for pure elastic sliding contact. Both of 

them assumed a central stick region surrounded 

by a slip annulus in the contact area. The local 

Coulomb’s friction law governs the slip annulus 

region and it increases with the increase in 

tangential loading. The local Coulomb’s friction 

law couples normal stress with local shear stress 

and the central stick region gets eliminated at 

the point of sliding inception. Mindlin et al. [10, 

11] offered first analytical solutions for the 

problem of oscillating tangential loading. The 

derived force‐displacement hysteretic loop by 

Mindlin et al. is concerned about the energy 

dissipation due to partial frictional sliding 

between the contacting surfaces during the 

loading cycles. The fretting models, which are 

based on the assumptions of Cattaneo‐Mindilin 

[8,9], ignored the formation of junction growth. 

The authors of fretting models [12,13] also made 

simplified assumption that the normal contact 

pressure and the contact area, which resulted 

from the normal loading alone, remain 

unchanged during application of the tangential 

loading. Bowden and Tabor [14] described the 

sliding inception and static friction as a failure 

mechanism, which are functions of material 

properties. The approach of Bowden and Tabor 

was different from Cattaneo‐Mindlin in the sense 

that in the former the static friction coefficient is 

not known a priori. Bowden and Tabor was also 

successful to completely decouple the maximum 

shear stresses at the contact interface from the 

normal stresses. Based on the assumptions of 

Bowden and Tabor, Tabor [15] further 

presented the concept of junction growth in 

metallic friction. Recently, Ovcharenko et al. [16] 

investigated the junction growth in elastic 

plastic spherical contact. The materials deform 

elastically following Hooke’s law within elastic 

limit. Above elastic limit the deformation follows 

certain strain‐hardening rule. No bodies are 

perfectly elastic, so during cyclic loadingunloading 

even within elastic limit some energy 

is dissipated. Tabor [17] reported the resistance 

to rolling of bodies of imperfectly elastic 

material, which can also be expressed in terms 

of their hysteresis loss factor. The model of 

rolling friction provided by Tabor was well 

supported by Greenwood et al. [18] in their 

experimental work with rubber. Tabor inferred 

that the theory of rolling friction does not hold 

good for metals. Actually hysteresis loss factor, 

fraction of loss of maximum strain energy 

stored, is not generally a material constant. 

Hysteresis loss is common phenomena for both 

stress controlled (Constant load during cyclic 

loading) and strain controlled (Constant 

interference) fatigue. The respective strain 

amplitude and stress amplitude during stress 

controlled and strain controlled cyclic loading 

unloading attains a stable saturation value after 

an initial shakedown period. This saturation 

provides a stable hysteresis loop. 

Depending up on the nature of hysteresis loop, 

many authors identified the type of shakedowns 

in sliding contact, fretting contact, adhesive 

contact apart from the literatures discussed 

above. In the recently published research works, 

shakedown has been simulated in elastic plastic 

loading level with the use of finite element 

software, which can provide an accurate result 

of interfacial parameters during elastic plastic as 

well as in plastic contact. Kadin et al. [19] found 

plastic shake down with kinematic hardening 

while elastic shake down with isotropic 

hardening for a cyclic loading of an elasticplastic 

adhesive spherical micro contact with the 

use of finite element software ANSYS. They also 

inferred that the plasticity parameter, a function 

of yield strength, of the material plays an 

important role on the shakedown behavior. Song 

and Komvopoulos [20] performed the finite 

element simulation for the adhesive contact of 

an elastic plastic half space with a rigid sphere 

using finite element software ABAQUS. They 

concluded that the elastic and plastic shakedown 

might occur even with elastic perfectly plastic 

4


materials, depending on the plasticity 

parameter. They found elastic shakedown for a 

low plasticity parameter even under large 

maximum normal displacement while plastic 

shakedown for a high plasticity parameter under 

very small maximum normal displacement. 

Based on the fundamental of Bowden and Tabor 

[14], Zolotarevskiy et al. [21] simulated elastic 

plastic spherical contact under cyclic tangential 

loading in pre‐sliding using ANSYS. They found 

that the friction‐displacement loops of isotropic 

hardening materials exhibited elastic 

shakedown whereas materials with kinematic 

hardening shows plastic shakedown following 

the second cycle. The experimental results by 

Ovcharenko and Etsion [7] report elastic 

shakedown with 2.5% hardening steel spheres 

and plastic shakedown with elastic perfectly 

plastic copper spheres for elastic plastic 

spherical contact fretting. 

The type of hardening model and the intensity of 

strain hardening greatly affect the interfacial 

parameters of a spherical contact during 

repeated normal loading unloading. It is 

pertinent to mention here that the changes in 

contact geometry are more pronounced in 

purely normal loading rather than during rolling 

or sliding contact. Most of the theoretical studies 

on normal loading unloading of a spherical 

contact assumed frictionless contact with 

bilinear isotropic hardening or with the elastic 

perfectly plastic material. Kral et al. [22] inferred 

that the effect of strain hardening on the contact 

parameters during loading unloading in the 

elastic plastic region is severe in comparison 

with the less significant effect of elastic 

properties of the material. They simulated the 

repeated normal indentation of an elastic plastic 

half space by a rigid sphere assuming a 

hardening power law, where the strainhardening 

exponent was varied up to 0.5, to 

study the effect of strain hardening. They also 

observed that the hardening materials reached a 

shakedown in respect to accumulation of plastic 

strain after three to four repeated normal 

loading unloading under perfect slip contact 

condition with isotropic hardening. Chatterjee 

and Sahoo [23] offered a model for loading 

unloading of a deformable sphere against a rigid 

flat to study the effect of strain hardening under 

perfect slip contact condition assuming a 

hardening parameter which enabled them to 

study the effect of tangent modulus as high as 

33% of modulus of elasticity. They found that 

the higher strain hardening caters less 

resistance to full recovery of the original shape. 

They noted that the load interference path for 

the second loading coincides with the first 

unloading path for the elastic perfectly plastic 

material as well as the materials with high 

tangent modulus under perfect slip contact 

condition with bilinear isotropic hardening. 

Thus the multiple loading unloading of a 

deformable sphere against a rigid flat under 

perfect slip contact condition is reversible. Then 

Chatterjee and Sahoo [24] extended their study 

to investigate the effect of strain hardening in 

elastic plastic loading of a deformable sphere 

against a rigid flat under full stick contact 

condition. They also considered both the 

isotropic and kinematic hardening rules. The 

only finite element based multiple loading 

unloading of a deformable sphere against a rigid 

flat under full stick contact condition with 

isotropic and kinematic hardening is available so 

far in the literature is the simulation generated 

by Zait et al. [25]. They considered only 2% 

bilinear hardening and their load displacement 

loop exhibited vanishing dissipated energy, 

which resulted in elastic shakedown for both 

isotropic and kinematic hardening. The same 

result of hysteresis loop with both the hardening 

model provides a ground to study the effect of 

strain hardening with varying tangent modulus 

using the model of Zait et al. [25]. Hence the 

main goal of the present study is to investigate 

the effect of strain hardening on the hysteretic 

behavior of repeated normal loading unloading 

of a deformable sphere against a rigid flat under 

full stick contact condition considering both the 

isotropic and kinematic hardening models. 

2. MULTIPLE NORMAL LOADING‐UNLOADING 

MODEL 

The deformable sphere with a rigid flat is shown 

in Fig. 1. The dashed and solid lines in the figure 

show the position of sphere and the rigid flat 

before and after the loading respectively. The 

interference (), the contact radius (a) of the 

deformable sphere of radius R, correspond to an 

external load (P) applied to the contact are 

presented in the Fig. 1. The expressions of 

critical interference, c , which initiates the yield 

inception at first loading and the corresponding 

critical load Pc under full stick condition are 

5


given by Brizmer et al. [26], which are used to 

normalized the contact parameters. 

2 

(1 

 

) Y 2 

2 

c ( C v ( )) R(6.82 

7.83( 0.0586)) (1) 

2 E 

3 

Y 3 

2 Y 2 

2 

P C ( R(1 

 

)( )) (8.88 

10.13( 

0.089)) 

(2) 

c v 

6 

E 

Where C v 1.234 

1.256 

. The parameters Y, E, 

and are the virgin yield stress, the Young 

modulus, and Poisson’s ratio of the sphere 

material, respectively and R is the radius of the 

sphere. The sphere size used for this analysis is 

R = 1 m. The material properties used here are 

Young’s Modulus ( E ) = 70 GPa, Poisson’s Ratio 

( ) = 0.3 and Yield stress (Y) = 100 MPa. 

Fig. 1. A deformable sphere pressed by a rigid flat. 

Multiple normal loading unloading cycle consists 

two stages. First the rigid flat gradually loads the 

deformable sphere to a dimensionless interference 

max / c , which results a dimensionless loading 

P max /P c . The plastic zone evolves within contact 

region inside the sphere. During the second stage 

of unloading, the interference () is gradually 

reduced. At the completion of the unloading, under 

zero contact load and contact area, the sphere has 

locked‐in residual stresses and strain. 

The residual stresses and strains, which remain 

locked in the sphere results in a deformed unloaded 

sphere and the amount depends on the hardening 

ratio (E t /E) [27]. Therefore the original undeformed 

spherical geometry is not fully recovered. 

The normal loading unloading cycle, to the same 

max / c , is performed seven to ten times 

considering both isotropic and kinematic hardening 

models to study the effect of strain hardening as 

well as hardening rule on the hysteretic behavior 

under full stick contact condition. 

3. THE FINITE ELEMENT MODEL 

The commercial finite element software ANSYS 

11.0 is used to get the response of the repeated 

normal loading unloading of the elastic plastic 

sphere against a rigid flat. The sphere is modeled 

as quarter of a circle due to the advantage of 

simulation of axisymmetric problems. A line 

models the rigid flat. Six node triangular 

axisymmetric elements (plane183) are used in 

the present model. Plane183 has plasticity, 

hyperelasticity, creep, stress stiffening, large 

deflection, and large strain capabilities along with 

the capability for simulating deformations of 

nearly incompressible elastoplastic materials, and 

fully incompressible hyperelastic materials [28]. 

The mesh consists of maximum 18653 six node 

triangular axisymmetric elements (plane183) 

comprising 37731 nodes. The resulting ANSYS 

mesh is presented in Fig. 2. The mesh density at 

the bottom of the sphere is coarsest one and is 

made gradually finer towards the sphere summit. 

The finest mesh density near the contact region 

simultaneously allows the sphere’s curvature to 

be captured and accurately simulated during 

deformation with a reduction in computation 

time. Window 2 of Fig. 2 presents the enlarged 

view of the finest mesh density at sphere summit. 

The sphere surface is modeled with the contact 

elements CONTA172 and the rigid flat is modeled 

by a single, non‐flexible two‐node target surface 

element TARGE169. The nodes lying on the axis 

of symmetry of the hemisphere are restricted to 

move only in the radial direction. Likewise the 

nodes in the bottom of the hemisphere are fixed 

in both the axial and radial direction. For full stick 

contact condition, infinite friction condition is 

adopted. Both the bilinear kinematic hardening 

(BKIN) and bilinear isotropic hardening (BISO) 

options are considered to study the effect of 

hardening rule on the hysteretic loop during the 

repeated normal loading unloading. The rate 

independent plasticity algorithm incorporates the 

von Mises criterion. The mesh density is 

gradually doubled until the contact force and 

contact area differed by less than 1% between the 

iterations. In addition to mesh convergence, the 

model also compares well with the Hertz elastic 

solution at interferences below the critical 

interference for perfect slip contact condition. 

This work uses Lagrangian multiplier method. 

The tolerance of current work is set to 1% of the 

element width. 

6


Fig. 2. Finite element mesh of a sphere generated by ANSYS. 

Engineering stress‐strain curves are used within 

elastic limit. The dimension of the specimen 

changes substantially in the region of plastic 

deformation. The increment of strain in 

conjunction with true stress can be termed as 

strain hardening. Strain hardening causes an 

increase in strength and hardness of the metal. 

Strain hardening is expressed in terms of 

tangent modulus (E t ), which is the slope of the 

stress‐strain curve. Below the proportional limit, 

the tangent modulus is the same as the Young’s 

modulus (E). Above the proportional limit, the 

tangent modulus varies with the strain. The 

tangent modulus is useful in describing the 

behaviour of materials that have been stressed 

beyond the elastic region. In elastic perfectly 

plastic cases, the tangent modulus becomes zero. 

Very few materials exhibit elastic perfectly 

plastic behaviour, generally all the materials 

follow the multi‐linear behaviour with some 

tangent modulus. This multi‐linear behaviour 

can be modelled as bilinear behaviour for 

analysis purpose in elastic‐plastic cases. In this 

analysis a bilinear material property, as shown 

in Fig. 3, is provided for the deformable sphere. 

Fig. 3. Stress‐strain diagram for a material with 

bilinear properties. 

7


4. RESULTS AND DISCUSSIONS 

It is already stated that the aim of the present 

study is to investigate the influence of strain 

hardening and the hardening model on the 

hysteretic loop. Shankar and Mayuram [29] 

mentioned that the tangent modulus for the 

most practical materials is less than 0.05 E, 

whereas Kadin et al. [27] found the tangent 

modulus for most practical materials below 0.02 

E. However both the authors used tangent 

modulus up to 0.1E for analytical purpose. On 

the other hand, Ovcharenko et al. [30] used 

stainless steel specimen with tangent modulus 

of 0.26 E (Fig. 6(b)) in their in‐situ 

investigation). It is also available in literature 

that structural steel, aluminum alloys have 

significant amount of strain hardening. Zait et al. 

[25] found elastic shakedown with two percent 

kinematic hardening. Thus first multiple normal 

loading‐unloading is simulated with elastic 

perfectly plastic material and the elastic plastic 

sphere with 2.5 and 5 percent bilinear hardening 

using both isotropic and kinematic hardening. 

Figure 4 presents dimensionless normal contact 

load as a function of dimensionless normal 

interference during ten multiple loadingunloading 

cycles for maximum dimensionless 

interference, max =100. 

Fig. 4. Dimensionless normal contact load vs. 

dimensionless interference hysteretic loop for 

maximum loading, * max =100. 

The sphere material is considered as elastic 

perfectly plastic. Interference controlled 

multiple loading unloading is adopted. It is 

found that the response of the elastic perfectly 

plastic materials during multiple loadingunloading 

with both the isotropic and kinematic 

hardening is identical. The area bounded by 

dimensionless interference and dimensionless 

contact load after first unloading under full stick 

contact condition, the quantity of dissipated 

energy, clearly indicates elastic shakedown. 

Figure 5 shows the load interference hysteretic 

loop during ten repeated loading unloading. The 

maximum dimensionless interference for 

loading is * max =100, with tangent modulus, E t = 

0.025E using kinematic hardening. 


dimensionless interference hysteretic loop for maximum 

loading, * max =100 with kinematic hardening. 

The elastic shakedown with vanishing dissipated 

energy even with kinematic hardening is 

prominent from the figure. Zait et al. [25] 

furnished the results (Fig. 4) with maximum 

dimensionless interference of 60 using kinematic 

hardening. They have shown that with small 

tangent modulus the materials result in elastic 

shakedown even under the influence of kinematic 

hardening. The present simulated results are in 

good agreement with the findings of Zait et al. 

[25]. The right top figure (a) here, enlarged view 

of contact load after each loading cycle, shows the 

decrease of contact load during ten repeated 

loading cycles, using 2.5% bilinear kinematic 

hardening, under full stick contact condition. The 

bottom right figure (b), detailed view of residual 

interferences after each unloading cycles, 

presents the increase of residual interferences 

during ten repeated loading unloading cycles 

with 2.5% bilinear kinematic hardening under 

full stick contact condition. 

8


Figure 6 represents the load interference 

hysteretic loop during ten repeated loadingunloading 

cycles under full stick contact 

condition. The simulation used 2.5% bilinear 

isotropic hardening for the maximum 

dimensionless loading up to * max =100. Here 

also the elastic plastic deformable sphere yields 

in elastic shakedown. The right top figure (a) 

indicates the decrease of dimensionless contact 

load during ten repeated loading cycles. The 

bottom right figure (b) presents the increase of 

residual interferences after each unloading 

cycles during ten loading unloading cycles. 

Comparing the results of Figs. 5 and 6, it is 

observed that the decrease of contact load after 

tenth loading cycles and increase of residual 

interference after ten loading unloading cycles 

with both hardening rule is almost identical with 

vanishing dissipated energy. 

(a) 

(b) 



maximum loading, * max =100 with (a) isotropic 

hardening (b) kinematic hardening. 



maximum loading, * max =100 with isotropic hardening. 

Figure 7(a) presents the hysteretic loop of the 

dimensionless normal contact load with respect 

to dimensionless interference during ten 

repeated loading unloading cycles under full 

stick contact condition with 5% bilinear 

isotropic hardening. The maximum 

dimensionless interference of loading is 

* max =100. The figure reveals the elastic 

shakedown with vanishing dissipated energy as 

expected for isotropic hardening. Figure 7(b) is 

the plot of the hysteretic loop under full stick 

contact condition with 5% bilinear kinematic 

hardening. The maximum dimensionless 

interference of loading during ten repeated 

loading unloading cycles is * max =100. 

Here also the figure indicates the elastic 

shakedown even with kinematic hardening. Zait 

et al. [25] also observed that under full stick 

contact condition the deformable sphere 

resulted in elastic shakedown with 2% bilinear 

kinematic hardening for normal repeated 

loading. They attributed the similar shakedown 

behavior with both hardening models to the 

small variation of the von Mises stress. 

As can be seen from Figs. 4 to 7, the deformable 

sphere shows elastic shakedown with both the 

hardening models for repeated normal loading 

unloading under full stick contact condition. The 

results show excellent agreement with the 

results of Zait et al. [25]. Zait et al. did not 

consider the effect of high tangent modulus on 

the multiple normal loading‐unloading of a 

deformable sphere against a rigid flat. Kral et al. 

9


[22] used strain‐hardening exponent to study 

the effect of strain hardening on the deformation 

of an elastic plastic half space against a rigid 

sphere during repeated loading unloading. They 

reported that the hardening materials (strain 

hardening exponent up to 0.5) reached to a 

shakedown in light of accumulation of plastic 

strain after three to four repeated normal 

loading unloading cycles under perfect slip 

contact condition with isotropic hardening. The 

tangent modulus of stainless steel, structural 

steel, aluminum alloys etc. are 15% or above the 

modulus of elasticity of the respective materials. 

Thus in the next part of present analysis, the 

tangent modulus (E t ) is varied according to a 

hardening parameter (H). The hardening 

parameter is defined as: 

H 

E 

t 

. 

E Et 

The present analysis considered four different 

values of H, covering wide range of tangent 

modulus to depict the effect of strain hardening 

in single asperity multiple loading unloading 

contact analysis with other material properties 

being constant. The values of H used in this 

analysis are within range 0 H 0. 5 as most of 

the practical materials falls in this range [31]. 

The value of H equals to zero indicates elastic 

perfectly plastic material behavior, which is an 

idealized material behavior. The hardening 

parameters used for this analysis and their 

corresponding E t values are shown in Table 1. 

shakedown. Figure 8(b) shows the resulted 

hysteretic loop of the dimensionless normal 

contact load versus dimensionless interference 

under full stick contact condition for the elastic 

perfectly plastic material. Here the maximum 

dimensionless interference of loading in the 

interference controlled repeated loading 

unloading is 200. It is clear from Figs. 8(a) and 

8(b) that the increase of the loading interference 

exhibits no effect on the shakedown behaviour 

as hysteretic loop in both the figure indicate 

vanishing dissipated energy. 

(a) 

Table 1. Different H and E t values used for the study 

of strain hardening effect. 

H E t in %E E t (GPa) 

0 0.0 0.0 

0.1 9.0 6.3 

0.3 23.0 16.1 

0.5 33.0 23.1 

Figure 8(a) is the plot of hysteretic loop of 

dimensionless normal contact load versus 

dimensionless interference under full stick 

contact condition for the elastic perfectly plastic 

material. The maximum dimensionless 

interference of loading in this interference 

controlled repeated normal loading unloading is 

* max =50. The figure indicates vanishing 

dissipated energy, which resulted in elastic 

(b) 



maximum loading, (a) * max =50 (b) * max =200. 

Figure 9 presents the dimensionless contact load 

as a function of dimensionless interference 

during ten normal loading unloading cycles 

under full stick contact condition for the sphere 

material with hardening parameter, H=0.1. The 

hysteretic loop considering bilinear isotropic 

10


hardening with tangent modulus (E t ) equals to 

9% of elastic modulus clearly converged into 

elastic shakedown. The right top figure (a) 

shows the slight decrease of dimensionless 

contact load in interference controlled repeated 

normal loading with maximum interference of 

loading equals to * max =50 while bottom right 

figure (b) presents the increase of residual 

interferences after each unloading cycles. 

(a) 



maximum loading, * max =50. 

Hysteretic loop of repeated normal loading 

unloading for the deformable sphere with 

hardening parameter, H=0.1 considering 

kinematic hardening under full stick contact 

condition is plotted in Fig. 10(a). The figure 

reveals more dissipated energy with kinematic 

hardening compared to the dissipated energy 

with isotropic hardening. 

The top Fig. of 10 (b) shows the evolution of 

contact load after each loading cycles during ten 

repeated loading unloading cycles with tangent 

modulus, E t =0.09E. The maximum dimensionless 

interference of loading is 50. 

The bottom Fig. of 10(b) exhibits the residual 

interference after each unloading cycles. 

Comparing the results with two different 

hardening models, it is found that the contact 

load at the end of maximum dimensionless 

interference with kinematic hardening is greater 

than the contact load with isotropic hardening. 

Similar behaviour is also observed elsewhere 

[24]. On the other hand, the residual 

interference with kinematic hardening is lesser 

than that of with isotropic hardening. 

(b) 

Fig. 10. (a) Dimensionless normal contact load vs. 


maximum loading, * max= 50 with kinematic hardening 

(b) Decrease of contact load and increase of residual 

interferences during ten loading unloading cycles. 

The dimensionless normal contact load as a 

function of the dimensionless normal interference is 

presented in Fig. 11(a). The hysteretic loop, area 

bounded by unloaded cycle and loading cycle after 

first loading, with maximum dimensionless 

interference of 200 shows that the value of the 

bounded area subsequently decreasing in nature. 

Thus the repeated ten loading unloading cycles 

under full stick contact condition with isotropic 

hardening converges into elastic shakedown even 

with large interference. The area of the hysteretic 

loop between the unloading curve and the 

subsequent loading curve of dimensionless contact 

load and dimensionless interference under full stick 

contact condition presents the amount of dissipated 

energy. The Fig. 11(b) indicates a constant 

dissipation of energy after first unloading cycle. 

Thus it is evident that the material with high 

tangent modulus and kinematic hardening resulted 

11


in plastic shakedown. It can also be seen from the 

figure that the area of the hysteretic loop increases 

with the increase in maximum dimensionless 

interference of loading in the interference 

controlled repeated loading unloading. 

curve and loading curve on and from first unloading 

cycle of load displacement figure, shows no 

remarkable dissipation of energy. The vanishing 

nature of dissipated energy resulted in elastic 

shakedown. These findings are in good agreement 

with Kadin et al. [19] where the authors concluded 

that the elastic shakedown is associated with 

isotropic hardening. 

(a) 

(a) 

(b) 



maximum loading,* max =200 with (a) isotropic 

hardening (b) kinematic hardening. 

Figure 12(a) to 12(c) presents the dimensionless 

elastic plastic load displacement results during 

repeated normal loading unloading process in 

terms of P* vs. * under full stick contact condition. 

The simulations have done with the hardening 

parameter of the sphere material, H=0.3 (tangent 

modulus, E t =0.23E) using isotropic hardening. The 

maximum dimensionless interferences of loading 

for Figs. 12(a), 12(b) and 12(c) are 50, 100 and 200 

respectively. We have considered ten repeated 

loading unloading cycles for the maximum loading 

interference of 50 and 100 while seven loading 

unloading cycles for the loading interference of 200. 

The hysteretic loop, the area between the unloading 

(b) 

(c) 



loading, (a) * max =50, (b) * max =100, (c) * max =200. 

12


The dimensionless normal contact loads as a 

function of normal dimensionless interferences 

under full stick contact condition are plotted in 

Fig. 13 (a) to 13(c). The hardening parameter 

chosen for these simulations is, H=0.3 (tangent 

modulus, E t =0.23E) using kinematic hardening. It 

reveals from the figures that the unloading curves 

and the loading curves are identical on and from 

second cycle exhibiting constant dimensionless 

energy dissipation (the area of the hysteretic 

loop) during each repeated cycle. Here also we 

have used ten repeated cycles for the maximum 

interference loading of 50 and 100, whereas 

seven repeated cycles for the maximum 

interference loading of 200. The constant 

dimensionless energy dissipation indicates plastic 

shakedown as would be expected for kinematic 

hardening. It is also observed from Fig. 13(a) to 

13(c) that the dissipated energy increases with 

the increase in maximum interference of loading. 

Figure 14, the details of Fig. 13(c), presents the 

evolution of dimensionless contact load and 

dimensionless residual interferences during 

repeated loading unloading. It is found from the 

figure (a) that the dimensionless contact load is 

almost identical from second loading cycles and 

figure (b) indicates that the increase in 

dimensionless residual interference is also 

negligible after repeated unloading cycles. 

Comparison of two hardening model also reveals 

that the dimensionless contact load for the same 

dimensionless interference is larger with isotropic 

hardening than that of with kinematic hardening. 

However the effect of hardening model is more 

pronounced during unloading, the materials with 

kinematic hardening offer less resistance to 

recovery of original shape compared to the 

materials associated with isotropic hardening. 

(b) 

(c) 




Fig. 14. Evolution of contact load and residual 

interferences during repeated loading unloading of 

plastic shakedown process. 

(a) 

Figure 15(a) to 15(c) presented the effect of 

maximum dimensionless interference of loading 

13


in interference controlled repeated loading 

unloading on the evolution of dimensionless 

normal contact load versus dimensionless 

normal interference for repeated loading 

unloading cycles. Ten repeated loading 

unloading cycles are considered when the 

maximum dimensionless interferences are 50 

and 100. Seven repeated loading unloading 

cycles are simulated for maximum 

dimensionless interference loading of 200. The 

load displacement loop of the sphere material 

with hardening parameter, H=0.5 (tangent 

modulus, E t =0.33E) using isotropic hardening 

exhibiting convergence to an elastic shakedown 

irrespective of the extent of maximum 

interference of loading. Thus the shakedown 

behavior in case of normal repeated loading 

unloading depends predominantly on the 

hardening rule and tangent modulus of the 

deformable sphere rather than the extent of 

loading in the interference controlled repeated 

loading unloading. 

(a) 

(b) 

(c) 




The dimensionless normal contact load versus 

dimensionless normal interference in repeated 

loading unloading for a deformable sphere with a 

rigid flat under full stick contact condition using 

kinematic hardening are shown in Fig. 16(a) to 

16(c). The maximum dimensionless interferences 

of loading for the sphere material with tangent 

modulus, E t =0.33E (Hardening parameter, H=0.5) 

are 50,100 and 200 respectively. Ten repeated 

loading unloading cycles are used for the 

maximum dimensionless loading interferences of 

50 and 100 although seven such repeated cycles 

are used foe the maximum loading interference of 

200. It reveals from the figures that the loaddisplacement 

hysteretic loops, irrespective of the 

maximum dimensionless interferences of loading, 

exhibited constant dissipated energy indicating 

plastic shakedown. 

From the several simulations it was found that in 

order to enable a common basis for the comparison 

of the dimensionless dissipated energy, the energy 

transferred to the deformable sphere during first 

loading is to be kept constant. Thus the dissipated 

energy is normalized with the product P of elastic 

perfectly plastic materials. The dissipated energy is 

calculated by numerically integrating the area 

enclosed within the hysteretic load‐displacement 

loop. The effects of strain hardening (E t /E) on the 

constant dissipated energy at plastic shakedown are 

shown for maximum dimensionless loading 

interference of 50, 100 and 200 in Figs. 17(a), 17(b) 

and 17(c) respectively. As can be observed from the 

figures, the constant dissipated energy during 

plastic shakedown increases with the increase in 

14


the tangent modulus of the deformable sphere. 

Comparing the results for the different maximum 

dimensionless interference of loading, it is evident 

that the constant dissipation energy during plastic 

shakedown is increasing with the increase in 

maximum dimensionless interference of loading for 

a specific tangent modulus of the sphere material. 

Zolotarevskiy et al. [21] found that the constant 

dissipated energy during plastic shakedown 

increases with the increase in dimensionless 

normal load while simulating under tangential 

loading in pre‐sliding under full stick contact 

condition. Our results for repeated normal loading 

unloading under full stick contact condition 

correlate well with Zolotarevskiy et al. [21] in 

regards to the effect of normal load on constant 

dissipated energy during plastic shakedown. 

(c) 



maximum loading, (a) * max =50, (b) * max =100, (c) 

* max =200. 

(a) 

(a) 

(b) 

(b) 

15


(c) 

Fig. 17. Dimensionless dissipated energy vs. E t /E at 

(a) * max =50, (b) * max =100, (c) * max =200. 

The present study considers the shakedown 

behavior in full stick contact condition for varying 

tangent modulus. However, there are other 

material parameters like Poisson’s ratio, work 

hardening, ratio of elastic modulus to yield 

strength etc. that need to be considered [32]. Also 

other contact conditions like pure slip and stickslip 

need to be considered in future studies. The 

present study assumes non‐adhesive contact 

situation but a realistic contact analysis should 

include the presence of adhesion [33]. Future 

work will consider such contact situations. 

5. CONCLUSIONS 

The elastic plastic spherical contact subjected to 

repeated normal loading unloading under full 

stick contact condition with varying tangent 

modulus was analyzed using commercial finite 

element software ANSYS. Both the isotropic and 

kinematic hardening rules were studied. The 

elastic shakedown for isotropic hardening and 

plastic shakedown for kinematic hardening was 

predicted for most of the published results of 

sliding, fretting and rolling contact repetitive 

loading. Recently published finite element based 

multiple normal loading unloading of a 

deformable sphere against a rigid flat converged 

into elastic shakedown with both 2% bilinear 

isotropic and kinematic hardening. The present 

results within 5% hardening were found 

qualitatively similar elastic shakedown with 

both isotropic and kinematic hardening as 

inferred in recently published finite element 

based results. The sphere material with high 

tangent modulus (from 9% to 33% of elastic 

modulus), as observed in stainless steel, 

structural steel and different aluminum alloys, 

exhibited constant dissipated energy (plastic 

shakedown) following the second loading cycles 

with kinematic hardening and converges into 

elastic shakedown with isotropic hardening. It 

was also found that elastic plastic spherical 

contact with isotropic hardening produced more 

dimensionless contact load than the elastic 

plastic spherical contact with kinematic 

hardening particularly for high tangent modulus. 

The residual interferences with kinematic 

hardening after complete unloading is less 

compared to the residual interferences 

simulated with isotropic hardening, which, in 

turn, offers less resistance to full recovery of the 

original shape with kinematic hardening. The 

results from present simulation also revealed 

that the higher dimensionless interference of 

loading and higher tangent modulus increase the 

dimensionless dissipated energy. 

NOMENCLATURE 

a Contact area radius 

E Modulus of elasticity of the sphere 

Y Yield Strength of the sphere material 

A Real contact area 

R Radius of the sphere 

P Contact load 

Interference 

Poisson’s ratio of sphere 

p Mean contact pressure 

E t Tangent modulus of the sphere 

P* Dimensionless contact load, P/P c in stick 

contact 

A* Dimensionless contact area, A/A c in stick 

contact 

* Dimensionless interference,/ c in stick 

contact 

Subscripts 

c critical values 

res Residual values following unloading 

max Maximum values during loadingunloading 

process 

Superscripts 

* Dimensionless 

16


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18

Vol. 35, No. 1 (2013) 19‐24 



RESEARCH 

Heat Exchanger Tube to Tube Sheet 

Joints Corrosion Behavior 

M. Iancu a , R.G. Ripeanu b , I. Tudor b 

a OMV PETROM S.A., Brazi, Trandafirilor, No.65, 107080, Romania. 

b Petroleum‐Gas University of Ploiesti, Blvd. Bucuresti, No.39, 100680, Romania. 

Keywords: 

Tube to tube sheet fittings 

Stress 

Corrosion rate 

Hydrofining oil 

Temperature 


Razvan George Ripeanu 

Petroleum‐Gas University of Ploiesti, 

Blvd. Bucuresti, No.39, 100680, 

Romania 

E‐mail: rrapeanu@upg‐ploiesti.ro 


Paper presents the studies made by the authors above the tube to tube sheet 

fittings of heat exchanger with fixed covers from hydrofining oil reforming 

unit. Tube fittings are critical zones for heat exchangers failures. On a device 

made from material tube and tube sheet at real joints dimensions were 

establish axial compression force and traction force at which tube is 

extracted from expanded joint. Were used two shapes joints with two types 

of fittings surfaces, one with smooth hole of tube sheet and other in which on 

boring surface we made a groove. From extracted expanded tube zones 

were made samples for corrosion tests in order to establish the corrosion 

rate, corrosion potential and corrosion current in working mediums such as 

hydrofining oil and industrial water at different temperatures. The 

corrosion rate values and the temperature influence are important to 

evaluate joints durability and also the results obtained shows that the 

boring tube sheet shape with a groove on hole tube shape presents a better 

corrosion behavior then the shape with smooth hole tube sheet. 



Shell and tube heat exchangers are most 

commonly used in the process refinery 

industries due to a large ratio of heat transfer 

area to volume and weight. The tubes are the 

basic component of the heat exchanger, 

providing the heat transfer surface between one 

fluid flowing inside the tube and the other fluid 

flowing across the outside of the tubes. The 

tubes are held in place by being inserted into 

holes in the tube sheet and there either 

expanded into grooves cut into the holes or 

welded to the tube sheet were the tube 

protrudes from the surface. The main failures of 

heat exchangers are: corrosion of tubes and 

jacket, tubes blockage and failures of tube to 

tube sheet joints. Paper presents the studies 

made by authors above the tube to tube sheet 

fittings of heat exchanger, type BEM as classified 

of Tubular Exchanger Manufacturers 

Association, with fixed covers from hydrofining 

oil reforming unit, [1]. In Fig. 1 is presented the 

catalytic reforming unit of hydrofining oil 

schema were heat exchanger has position “121‐ 

S1”. Weldings between tubes and tube sheet is 

not recommended [2,3,4]. At studied heat 

exchanger the tube to tube sheet are expanded 

19

M. Iancu et al., Tribology in Industry Vol. 35, No. 1 (2013) 19‐24 

joints. The tubes and tube sheet, in addition to 

mechanical requirements, must withstand 

corrosive attack by both fluids in the heat 

exchanger and must be electrochemically 

compatible with the tube and all tube‐side 

material [1,2,3]. 

Fig. 1. Catalytic reforming unit schema. 

At heat exchanger analyzed through the jacket is 

circulating hydrofining oil and through the tubes 

is circulating industrial water. In Table 1 are 

presented the main working conditions. 

Table 1. Main working conditions 

Parameter Jacket Tubes 

Maximum working 

pressure, MPa 

1.15 0.65 

Maximum 

temperature, 0 C 

70 38 

Minimum 

temperature, 0 C 

50 30 

Working medium 

Danger 

Hydrofining 

oil 

Toxic, 

inflammable 

Industrial 

water 

The mechanical process of expanding of tube 

comprises two distinct phases, [4]: 

a) pre expanding of tube, that preliminary 

flexible flare or / and elastic‐plastic the tubular 

element (TE) until it comes in contact with the 

wall tube sheet hole (TP); 

b) proper expanding of tube, additional 

enlargement mainly concerned elastic‐plastic, 

residual TE, while broadening mainly flexible, 

reversible, the holes in TP as shown in Fig. 2, [4]. 

‐ 

Fig. 2. Typical characteristic curves of TE materials 

and, respectively, TP regarded as joint materials 

building plastic linear hardening. 

Pre expanding of tube phase corresponds to full 

depletion clearance of assembly δ 0 = 2δ (Fig.3), [4]. 

Fig. 3. Tube to tube sheet schema 

The main requirement of a tube‐to tube sheet 

joint is better to resist the axial stress, 

compressive or tensile, applied to tube. This 

happens if tube to tube sheet joints, where 

tubes and tube sheet are made of steel, when 

the hoop stress in tube sheet is higher than in 

tubes [4]. 

In order to better respect conditions of tension 

and compression in expanded tube to tube sheet 

joints the paper propose a different geometry of 

tube sheet which on boring surface we made a 

groove. 

20


2. EXPERIMENTS 

2.1 Tension and compression tests 

To simulate the tube to tube sheet expanded 

joints were prepared samples at real joint 

dimensions. In Fig. 4 is presented the tube sheet 

sample with smooth hole tube sheet and in Fig. 5 

the tube sheet sample which on boring surface 

we made a groove. 

The obtained assemblies were tested at tension 

and at compression. In Fig. 7 it is shown the 

tension variation vs. tube displacement in 

expanded joint with smooth hole tube sheet. 

Fig. 7. Tension variation vs. tube displacement in 

expanded joint with smooth hole tube sheet. 

In Fig. 8 it is presented the tension variation vs. 

tube displacement in expanded joint with a 

grove on tube sheet boring surface. 

Fig. 4. Tube sheet with smooth hole tube sheet. 

Fig. 5. Tube sheet with a groove on boring surface. 

In Fig. 6 it is shown the tube samples 

dimensions. 

Fig. 6. Tube sample construction. 

Tube sheet samples were made of steel type P355 

NH, EN 10028 – 2:2009 and tubes of steel type 

P265 GH, SR EN 10217‐5. The samples were 

extruded in similar conditions as real components. 

Fig. 8. Tension force variation vs. tube displacement 

in expanded joint with a groove on boring surface. 

From Figs. 7 and 8 could be observed that the 

tension values were grater at expanded joint 

with tube sheet with a grove on boring surface. A 

similar behaviour was obtained at compression 

test. The maximum compression value obtained 

at expanded joint with smooth hole tube sheet 

was 3280 daN and at joint with a grove on tube 

sheet boring surface was 3350 daN. 

The tension and compression results obtained 

confirm that model with a grove on tube sheet 

boring has an efforts better behavior. 

Measuring the samples surfaces microgeometric 

parameters initial and after disassembling 

extruded joints by tension and by compression 

21


for the tubes that was in tube sheet with smooth 

hole tube sheet the roughness rise after 

compression and after tension than initial 

roughness. In Table 2 are presented the 

roughness modifications for tubes. 

Table 2. Tubes surface roughness modification. 

Type of 

extruded joint Disassembling 

type 

Tubes for 

joint with 

smooth hole 

tube sheet 

Tubes for 

joint with a 

grove on tube 

sheet boring 

surface 

Roughness 

parameter 

modification, m 

Ra Rz Rt 

Tension 1.765 13.4 14.67 

Compression 0.445 ‐0.22 0.37 

Tension ‐0.051 ‐0.04 0.78 

Compression ‐0.281 ‐1.96 ‐2.24 

For the tubes that was in tube sheet with a 

groove on boring surface the roughness was 

smaller after compression and after tension than 

initial roughness. The tube sheet surface 

roughnesses were greater in case of 

disassembling by tension than in case of 

disassembling by compression for both tested 

geometries. 

2.2 Corrosion tests 

From both types expanded joints with tube 

sheet with smooth hole and with a grove on tube 

sheet boring surface were extracted samples 

from tube tubes active surfaces for corrosion 

tests. The samples were of steel type P265 GH, 

SR EN 10217‐5. Also were tested samples 

extracted from tubes not used for expanded 

joints. Samples were named: 

“I” extracted from tubes not used for 

expanded joints: 

“5A” extracted from tubes from expanded 

joint with smooth hole tube sheet; 

“1A” extracted from tubes from expanded 

joint with a grove on tube sheet boring 

surface. 

Working medium were industrial water with 

pH=7.18, conductivity=1524 S/cm, total solid 

deposition TDS=42 mg/l and hydrofining oil with 

pH=5.55, conductivity=80pS/m, sulphur=1 ppm. 

Testing medium temperatures were 20, 40, 60 

and 70 0 C. 

Samples have parallelepiped shapes and were 

machined without affecting tubes active surface. 

At immersion corrosion tests the corrosion rate 

was obtained with relation, [5]: 

m 

f 

mi 

vcor 8 . 76 , mm/year (1) 

A 

m f ‐ sample final mass, g; 

m i ‐ initial sample mass, g; 

A ‐ sample area, m 2 ; 

‐ time, hours; 

γ ‐ specific weight, g/cm 3 . 

In Fig. 9 is it presented the corrosion rate 

variation in time at temperature of 20 0 C for 

tube samples immersed in industrial water. 

Corrosion rate, Vcor [mm/an] 

0.055 

0.05 

0.045 

0.04 

0.035 

0.03 

I 1A 5A 

120 135 150 165 180 195 210 225 240 255 270 

Time [hours] 

Fig. 9. Corrosion rate at 20 0 C in industrial water. 

In Fig. 10 it is shown the corrosion rate vs. time 

at temperature 40 0 C, in Fig. 11 at 60 0 C and in 

Fig. 12 at 70 0 C in industrial water. 


0.07 

0.065 

0.06 

0.055 

0.05 

0.045 

0 5 10 15 20 25 

Time [hours] 


From Figs. 9‐12 could be observed that corrosion 

rate rise with temperature. Also the samples 

made from tube expanded joint with smooth hole 

tube sheet have a better corrosion behavior than 

samples made of tube with joint expanded having 

a grove on tube sheet boring surface. 

1A 

5A 

22



0.075 

0.07 

0.065 

0.06 

0.055 

0.05 

0.045 

0 5 10 15 20 25 

Time [hours] 



0.075 

0.07 

0.065 

0.06 

0.055 

0.05 

0.045 

0 5 10 15 20 25 

Time [hours] 


In Fig. 13 it is presented the corrosion rate 

variation in time at temperature of 70 0 C for 

tube samples immersed in hydrofining oil. 


0.012 

0.01 

0.008 

0.006 

0.004 

0 5 10 15 20 25 

Time [hours] 

Fig. 13. Corrosion rate at 70 0 C in hydrofining oil. 

At temperatures of 20, 40 and 60 0C was 

observed a similar behaviour of corrosion rate 

as shown in Fig. 13. Could be observed that in 

hydrofining oil a better corrosion behaviour 

presents samples extracted from tube expanded 

joint with smooth hole tube sheet than samples 

extracted from tube expanded joint with a grove 

on tube sheet boring surface. 

To establish electrochemical parameters, 

corrosion potential E corr , corrosion current I corr 

and corrosion rate v corr, were extracted samples 

1A 

1A 

5A 

1A 

5A 

5A 

from tubes none extruded similar as from 

immersion corrosion tests. Specimens were 

machined with small cutting conditions and with 

cutting fluid in order to avoid the influence 

above metallographic structure at dimensions 

16 ‐0.1 x3 mm. Active samples surface was 

polish with 500 Mesh abrasive papers. 

There are several electrochemical techniques 

that can be used to evaluate the behavior of 

materials in aggressive medium such as [5,6,9]: 

potentiodynamic anodic, cathodic or both 

polarization measurements, galvanic corrosion 

measurements, potentiostatic measurements, 

linear polarization, pitting scans, Tafel plots 

measurements etc. Tafel plots technique quickly 

yields corrosion rate information. The linear 

portion of the anodic or cathodic polarization 

logarithm current vs. potential plot is 

extrapolated to intersect the corrosion potential 

line. This permits rapid, high accuracy 

measurement of extremely low corrosion rates. 

For this reason to determine electrochemical 

parameters we used this technique. 

According to the mixed potential theory [5,6,9], any 

electrochemical reaction can be divided into two or 

more oxidation and reduction reactions, and can be 

no accumulation of electrical charge during the 

reaction. In a corroding system, corrosion of the 

metal and reduction of some species in solution is 

taking place at same rate and the net measurable 

current, i meas is zero. Electrochemically, corrosion 

rate measurement is based on the determination of 

the oxidation current, i ox at the corrosion potential, 

E corr . This oxidation current is called the corrosion 

current, i corr . 

i meas = i corr ‐i red =0 at E corr (2) 

The corrosion measurement system used was 

EG&G Princeton, New Jersey‐ model 350 that 

works together with compensator IR 351, 

[6,7,8,9]. 

Corrosion cell works with a saturated calomel 

reference electrode and specimen holder 

exposes 1 cm 2 of the specimen to the test 

solution. Using Tafel plots technique were 

determined the electrochemical parameters 

presented in Table 3. Electrochemical tests were 

made according to ASTM G5‐94, [7] and ASTM 

G1‐90, [8]. The reference electrode was Calomel 

(Pt/Hg/Hg 2 Cl 2 ). For tests at 40 and 60 0 C was 

used a thermometer and a thermostatic plate 

were placed corrosion cell. 

23


In Fig. 14 it is presented the electrochemical 

parameters obtained by Tafel technique sample 

“I” in industrial water at 20 0 C. 

roughness is smaller than in case of disassembling 

extruded joints by compression. 

Because the tube sheet with a grove on boring 

surface rise the stress in joints, more than smooth 

tube sheet surface, this modify the corrosion 

potential and the corrosion rate is greater. 

The differences between corrosion rates for two 

models is not significant, nevertheless the number 

of groves and groves dimension must be 

reconsidered in order to obtain a uniform stress 

on the entire contact surface in the extruded joint. 

Fig. 14. Electrochemical parameters obtained by Tafel 

technique sample “I” in industrial water at 20 0 C. 

In Table 3 are presented electrochemical 

parameters obtained for specimens extracted 

from non extruded tubes in industrial water. 

Table 3. Electrochemical parameters. 

Temperature 

T, 0 C 

Corrosion 

potential 

Ecor, V 

Corrosion 

current 

Icor, A 

Corrosion 

rate 

vcor, mm/year 

20 0.154 1.466 0.017 

40 0.143 3.133 0.053 

60 0.137 5.981 0.070 

From values presented in Table 3 we could 

observe that the corrosion current and 

corrosion rate rise with temperature. The 

obtained corrosion rate values by immersion are 

proximate with values obtained by 

electrochemical method. 

3. CONCLUSION 

Tube to tube extruded joints at heat exchangers 

represents a critical zone for stress and corrosion. 

The tension and compression tests show that 

proposed model of tube sheet with a grove on 

boring surface improve the tube to tube sheet joint. 

It is recommended to disassembling the extruded 

joints by tension because the obtained surfaces 

REFERENCES 

[1] Wolverine Engineering Data Book II, available at 

www.wlv.com/products/databook/databook.p 

df, accessed: 20.05.2011. 

[2] Η.Μ. Τawancy: Failure of hydrocracker heat 

exchanger tubes in an oil refinery by polythionic 

acid‐stress corrosion cracking, Engineering Failure 

Analysis, Vol. 16, No. 7, pp. 2091–2097, 2009. 

[3] Y. Gong, J. Zhong, Z.G. Yang: Failure analysis of 

bursting on the inner pipe of a jacketed pipe in a 

tubular heat exchanger, Materials & Design, Vol. 

31, No. 9, pp. 4258‐4268, 2010. 

[4] M. Iancu, A. Pupazescu, I. Tudor: Study on the 

state of stress and strain in tube‐to tubular plate 

joints, Petroleum – Gas University of Ploieşti 

Bulletin, Technical Series, Vol. LXII, No. 4B, pp. 

61‐66, 2010. 

[5] I. Tudor, R.G. Ripeanu: Corrosion engineering, 

Petroleum ‐ Gas, Ploiesti, 2002. 

[6] AN 140‐10M‐5: Application note 140, 

Princetown Applied Research Corporation, 

Princetown, 1978. 

[7] ASTM G5‐94(2011)e1: Standard Reference Test 

Method for Making Potentiostatic and 

Potentiodynamic Anode Polarization 

Measurements, 2011. 

[8] ASTM G1‐90(1999)e1: Standard Practice for 

Preparing, Cleaning and Evaluating Corrosion 

Test Specimens, 1999. 

[9] NACE Publication: Electrochemical Techniques 

for Corrosion, Houston, U.S.A. 77027, 1978. 

24

Vol. 35, No. 1 (2013) 25‐35 



RESEARCH 

Mechanical Properties and Corrosion Behaviour of 

Aluminium Hybrid Composites Reinforced with 

Silicon Carbide and Bamboo Leaf Ash 

K.K. Alaneme a , B.O. Ademilua a , M.O. Bodunrin a 

a Department of Metallurgical and Materials Engineering, Federal University of Technology, Akure, P.M.B 704, Nigeria. 

Keywords: 

Hybrid composites 

Bamboo leaf ash 

Al‐Mg‐Si alloy 

Corrosion 

Stir casting 

Mechanical properties 

Silicon carbide 


Kenneth K. Alaneme 

Department of Metallurgical and 

Materials Engineering, 

Federal University of Technology, 

Akure, P.M.B 704, Nigeria 

E‐mail: kkalaneme@gmail.com 


The viability of developing low cost – high performance Al matrix hybrid 

composites with the use of bamboo leaf ash (an agro waste ash) and silicon 

carbide as complementing reinforcements was investigated. Silicon carbide 

(SiC) particulates added with 0, 2, 3, and 4 wt% bamboo leaf ash (BLA) were 

utilized to prepare 10 wt% of the reinforcing phase with Al‐Mg‐Si alloy as 

matrix using two‐step stir casting method. Microstructural characterization, 

mechanical properties evaluation and corrosion behaviour were used to 

assess the performance of the composites. The results show that the 

hardness, ultimate tensile strength, and percent elongation of the hybrid 

composites decrease with increase in BLA content. The fracture toughness of 

the hybrid composites were however superior to that of the single reinforced 

Al ‐ 10 wt% SiC composite. Only the 2 wt% BLA containing hybrid composite 

had specific strength value comparable to that of the single reinforced 

composite. In 5wt% NaCl solution, it was observed that the 2 and 3 wt % 

BLA containing hybrid composites had higher corrosion resistance in 

comparison to the single reinforced Al ‐ 10 wt% SiC composite but the 

reverse trend was observed in 0.3 M H 2 SO 4 solution where the single 

reinforced had superior corrosion resistance. 



The synthesis and characterization of a wide 

range of Aluminium based composites has 

continued to generate a lot of interest judging 

from the large volume of publications in this area 

of materials science and engineering for the past 

thirty years [1‐3]. This is due to the versatile 

applications Al based composites have been 

successfully utilized in and the huge prospects it 

has for so many other new applications [3‐4]. 

From the development of high performance 

components for automobile, aerospace, defense, 

marine and other notable industrial applications 

to the development of facilities for sports and 

recreation [5‐7], the areas of application of Al 

based composites is expected to still continue to 

grow. This is possible by virtue of the attractive 

property spectrum possessed by AMCs and the 

lower cost of production in comparison with 

other competing MMCs or engineering materials 

for similar applications [8‐9]. 

25

K.K. Alaneme et al., Tribology in Industry Vol. 35, No. 1 (2013) 25‐35 

The selection of reinforcing material for Al 

matrices is very important in ensuring that 

desired property combinations are harnessed 

[10]. The target for most developing countries 

involved in AMCs development is optimizing 

cost reduction and performance levels by 

consideration of industrial and agro wastes as 

reinforcing materials. This philosophy is 

informed by the relatively high cost of 

purchasing the commonly used synthetic 

reinforcements such as silicon carbide and 

alumina from abroad [11]. Fly ash, silica, and 

graphite are a few examples of 

industrial/inorganic materials that have been 

used as reinforcement in AMCs [12‐14]. Rice 

hush ash, bagasse ash, and coconut shell ash are 

a few agro waste products which have also been 

tested as potential reinforcing material [11, 

15,16]. Though literatures on the potentials of 

agro‐waste ashes are still scanty (compared to 

the synthetic reinforcement), the available 

results show that Al based composites 

reinforced with synthetic ceramics such as 

silicon carbide and alumina have superior 

properties in comparison to the agro waste ash 

reinforced grades [17]. An approach which will 

seek to harness the clearly superior strength 

levels of the synthetic reinforcements and the 

lower cost and density advantages of the agro 

wastes have not received much attention in 

literature. This research work is motivated by 

the prospect of developing high performance Al 

matrix hybrid composites using silicon carbide 

and bamboo leaf ash as complementing 

reinforcements. Bamboo trees are found in large 

quantities in Nigeria and likewise so many other 

parts of the world; and the leaves often liter the 

environments where they are found [18]. 

Management of most agro wastes could be 

overwhelming and the best approach remains to 

explore more recycling techniques; and then 

applications where recycled wastes can be 

productively utilized. This work is part of current 

efforts aimed at considering the potentials of a 

wide range of agro waste ashes for the 

development of low cost‐high performance 

Aluminium based hybrid composites. These low 

cost hybrid composites could have potentials for 

use in stress bearing and wear applications 

among others [15]. In this paper, the processing, 

microstructural features, mechanical and 

corrosion behavior of an Al matrix composite 

reinforced with varied weight ratios of bamboo 

leaf ash and silicon carbide is reported. 

2. MATERIALS AND METHOD 

2.1 Materials 

Al‐Mg‐Si alloy with chemical composition presented 

in Table 1 was selected as Al matrix for the 

investigation. Chemically pure silicon carbide (SiC) 

particles having average particle size of 30 µm and 

processed ash (


2.3 Production of Composites 

Two steps stir casting process performed in 

accordance with Alaneme and Aluko [19] was 

adopted for the production of the composites. 

Charge calculation was used to determine the 

amount of bamboo leaf ash (BLA) and silicon 

carbide (SiC) required to prepare 10 wt% 

reinforcements (in the Al matrix) consisting of 

0:10, 2:8, 3:7, and 4:6 bamboo leaf ash and 

silicon carbide weight percents respectively. The 

bamboo leaf ash and silicon carbide particles 

were initially preheated separately at a 

temperature of 250 o C to remove moisture and 

to help improve wettability with the molten Al‐ 

Mg‐Si alloy. The Al‐Mg‐Si alloy billets were 

charged into a gas‐fired crucible furnace (fitted 

with a temperature probe), and heated to a 

temperature of 750 o C ± 30 o C (above the 

liquidus temperature of the alloy) to ensure the 

alloy melts completely. The liquid alloy was then 

allowed to cool in the furnace to a semi solid 

state at a temperature of about 600 o C. The 

preheated bamboo leaf ash and Sic particles 

along with 0.1 wt% magnesium were then 

charged into the melt at this temperature and 

stirring of the slurry was performed manually 

for 5‐10 minutes. The composite slurry was 

superheated to 800 o C ± 50 o C and a second 

stirring performed using a mechanical stirrer. 

The stirring operation was performed at a speed 

of 400 rpm for 10 minutes before casting into 

prepared sand moulds inserted with chills. 

2.4 Density Measurement 

The densities of the composites were 

determined by comparing the experimental and 

theoretical densities of each composition of the 

BLA‐SiC reinforced composites produced [19]. 

The experimental density was determined by 

dividing the measured weight of a test sample by 

its measured volume; while the theoretical 

density was evaluated by using the rule of 

mixtures given by: 

ρ Al‐Mg‐Si / BLA‐SiCp = wt. Al‐Mg‐Si × ρ Al‐Mg‐Si + wt. BLA × 

ρ BLA + wt. SiC × ρ SiC (2.1) 

Where, ρ Al‐Mg‐Si / BLA‐SiCp = Density of Composite, 

wt. Al‐Mg‐Si = Weight fraction of Al‐Mg‐Si alloy, ρ Al‐ 

Mg‐Si = Density of Al‐Mg‐Si alloy, wt. BLA = Weight 

fraction BLA, ρ BLA = Density of BLA, wt. SiC = 

Weight fraction SiC, and ρ SiC = Density of SiC. 

The percent porosity of the composites was 

evaluated using the relations [20]: 

% porosity = {(ρ T – ρ EX ) ÷ ρ T } × 100% (2.2) 

where, ρ T = Theoretical Density (g/cm 3 ), ρ EX = 

Experimental Density (g/cm 3 ). 

2.5 Tensile test 

Tensile tests were performed on the composites 

produced in accordance with the specifications 

of ASTM 8M‐91 standards [21]. The samples for 

the test were machined to round specimen 

configuration with 6 mm diameter and 30 mm 

gauge length. The test was carried out at room 

temperature using an Instron universal testing 

machine operated at a strain rate of 10 ‐3 /s. 

Three repeat tests were performed for 

composite composition to guarantee reliability 

of the data generated. The tensile properties 

evaluated from the stress‐strain curves 

developed from the tension test are ‐ the 

ultimate tensile strength (σ u ), the 0.2% offset 

yield strength (σ y ), and the strain to fracture (ε f ). 

2.6 Fracture Toughness Evaluation 

The fracture toughness of the composites was 

evaluated using circumferential notch tensile 

(CNT) specimens in accordance with Alaneme 

[22]. The effectiveness of CNT testing for 

fracture toughness determination has been well 

reported in literature [23‐24]. The composites 

were machined for the CNT testing with gauge 

length, specimen diameter (D), notch diameter 

(d), and notch angle of 30, 6, 4.5 mm, and 60 o C. 

The specimens were then subjected to tensile 

loading to fracture using an instron universal 

testing machine. The fracture load (P f ) obtained 

from the CNT specimens’ load – extension plots 

were used to evaluate the fracture toughness 

using the empirical relations by Dieter [25]: 

K 1C =P f /(D) 3/2 [1.72(D/d)–1.27] (2.3) 

where, D and d are respectively the specimen 

diameter and the diameter of the notched 

section. The validity of the fracture toughness 

values was evaluated using the relations in 

accordance with Nath and Das [26]: 

D≥(K 1C /σ y ) 2 (2.4) 

Three repeat tests were performed for each 

composite composition and the results obtained 

were taken to be highly consistent if the 

27


difference between measured values for a given 

composite composition is not more than 2%. 

2.7 Hardness Test 

The hardness of the composites was evaluated 

using an Emco TEST DURASCAN Microhardness 

Tester equipped with ecos workflow ultra 

modern software. Prior to testing, test 

specimens cut out from each composite 

composition were polished to obtain a flat and 

smooth surface finish. A load of 100 g was 

applied on the specimens and the hardness 

profile was evaluated following standard 

procedures. Multiple hardness tests were 

performed on each sample and the average 

value taken as a measure of the hardness of the 

specimen. 

2.8 Microstructural Examination 

A Zeiss Metallurgical Microscope with 

accessories for image analysis was used for 

optical microscopic investigation of the 

composites produced. The specimens for the test 

were metallographic ally polished and etched 

with 1HNO3: 1HCl solution before microscopic 

examination was performed. A JSM 7600F Jeol 

ultra‐high resolution field emission gun 

scanning electron microscope (FEG‐SEM) 

equipped with an EDS (courtesy of the 

Department of Chemical and Metallurgical 

Engineering, Tshwane University of Technology, 

Pretoria, South Africa) was used for detailed 

study of the microstructural features and 

elemental compositions of the composites. 

2.9 Corrosion Test 

The corrosion behaviour of the composites was 

studied by weight loss method using mass loss 

and corrosion rate measurements as basis for 

evaluating the results generated. The corrosion 

test was carried out by immersion of the test 

specimens in 0.3M H 2 SO 4 (pH 1.3) and 5wt% 

NaCl (pH 8.37) solutions which were prepared 

following standard procedures [7]. The 

specimens for the test were cut to size 

15×15×10 mm and then mechanically polished 

with emery papers from 220 down to 600 

grades to produce a smooth surface. The 

samples were de‐greased with acetone, rinsed in 

distilled water, and then dried in air before 

immersion in still solutions of 0.3M H 2 SO 4 and 

5wt% NaCl at room temperature (25 o C). The 

solution‐to‐specimen surface area ratio was 

about 150 ml cm ‐2 , and the corrosion setups 

were exposed to atmospheric air for the 

duration of the immersion test. The weight loss 

readings were monitored on two day intervals 

for a period of 22 days. The mass loss (mg/cm 2 ) 

for each sample was evaluated in accordance 

with ASTM G31 standard recommended practice 

[27] following the relation: 

m. l = CW/A (2.5) 

where m.l is the mass loss (mg/cm 2 ), CW is the 

cumulative weight loss (mg), and A is the total 

surface area of the sample (cm 2 ). 

Corrosion rate for each sample was evaluated 

from the weight loss measurements following 

the relation [7]: 

C.R = KW/ρAt (2.6) 

Where C.R is corrosion rate (mmy), W is weight 

loss (g), D is the density (g/cm 3 ), A is the area 

(cm 2 ), T is time (hours), and K is a constant 

equal to 87500. 

W = W i ‐ W f (2.7) 

where W is the weight loss (g), W i is the initial 

weight (g) and W f is the final weight (g). 

Three repeat tests were carried out for each 

composition of the composite, and the 

reproducibility and repeatability were found to 

be good as there were no significant differences 

between results from triplicates. 

3.0 RESULTS AND DISCUSSION 

3.1 Microstructure 

Representative optical and scan electron 

photomicrographs; and the EDAX profiles of the 

BLA‐SiC reinforced Aluminium hybrid 

composites produced are presented in Figs 1‐2. 

Figure 1 shows the optical photomicrographs of 

the Al‐Mg‐Si/2wt%BLA‐8wt%SiC hybrid 

composite. It is observed that the reinforcing 

particles (BLA and SiC) are visible and clearly 

delineated in the microstructure. The particles 

are fairly well distributed in the Al‐Mg‐Si matrix 

and signs of particle clusters are minimal. Figure 

2 shows secondary electron image and EDAX 

profile of the Al‐Mg‐Si/ 2wt% BLA‐8wt%SiC 

28


hybrid composite. From Fig. 2(a) the reinforcing 

particles can be easily identified; the EDS profile 

of the composite (Fig. 2b) shows peaks of 

aluminium (Al), oxygen (O), carbon (C), iron 

(Fe), and silicon (Si). The presence of these 

elements confirms the presence of silicon carbide 

(SiC); silica (SiO 2 ), alumina (Al 2 O 3 ), and ferric 

oxide (Fe 2 O 3 ) in the composite. It is noted that 

silica (SiO 2 ), alumina (Al 2 O 3 ), and ferric oxide 

(Fe 2 O 3 ) observed in the EDAX profile are primary 

constituents found in bamboo leaf ash [18]. 

(a) 

(b) 

(c) 

(d) 

Fig. 1. Photomicrograph showing (a) Al‐Mg‐Si/10 wt% SiC composite with the SiC particles dispersed in the Al‐ 

Mg‐Si matrix, (b) Al‐Mg‐Si/2wt% BLA‐8 wt% SiC hybrid composite with the BLA‐SiC particles dispersed in the 

Al‐Mg‐Si matrix, (c) Al‐Mg‐Si/3wt% BLA‐7 wt% SiC hybrid composite showing the BLA‐SiC particles dispersed in 

the Al‐Mg‐Si matrix, and (d) Al‐Mg‐Si/4wt% BLA‐6 wt% SiC hybrid composite showing the BLA‐SiC particles 

dispersed in the Al‐Mg‐Si matrix. 

29


with the single reinforced Al ‐ 10 wt% SiC 

composite. Porosity levels not above 4% have 

been reported to be acceptable in cast 

Aluminium matrix composites [19]. 

3.2 Mechanical Behaviour 

(a) 

The mechanical properties of the composites 

presented in Figs. 3 ‐ 8. The hardness (Fig. 3), 

ultimate tensile strength (Fig. 4) and yield 

strength (Fig. 5) of the composites are observed 

to decrease with increase in BLA content in the 

composites. 4.58, 8.14, and 10.94% reduction in 

hardness , and 7.97, 15.6, and 23.29% reduction 

in ultimate tensile strength were observed for 

the hybrid composites having respectively 2, 3, 

and 4 wt% BLA in comparison with the single 

reinforced Al‐Mg‐Si matrix ‐10wt% SiC 

composite. This trend is due to the composition 

of the BLA which consists mainly of silica which 

is noted to have lower hardness and strength 

levels in comparison with silicon carbide [28]. 

(b) 

Fig. 2. (a) representative SEM Photomicrograph of the 

Al‐Mg‐Si/2wt% BLA‐8 wt% SiC hybrid composite 

showing particles dispersed in the Al‐Mg‐Si matrix, and 

(b)EDAX profile obtained from the Al‐Mg‐Si/2wt% BLA‐ 

8 wt% SiC hybrid composite confirming the presence of 

SiC, Al 2 O 3 , SiO 2 , Fe 2 O 3 , K 2 O, and CaO. 

Table 3. Composite density and estimated percent porosity. 

Sample 

Weight Ratio 

of BLA and 

SiC 

Theoretical 

Density 

Experimental 

Density 

% Porosity 

A 0:10 2.745 2.714 1.14 

B 2:8 2.694 2.670 0.89 

C 3:7 2.668 2.638 1.24 

D 4:6 2.643 2.615 1.06 

The results of the percent porosity of the 

composites are presented in Table 3. It is 

observed from comparison of the theoretical and 

experimental densities of the composites that 

slight porosities (less than 1.5%) exist in the 

produced composites. The use of BLA and SiC as 

complementing reinforcements in the Al matrix 

did not arise in any significant rise in porosity 

level of the hybrid composites when compared 

Fig. 3. Variation of Hardness for the single reinforced 

Al‐Mg‐Si/10 wt% SiC and hybrid reinforced Al‐Mg‐ 

Si/BLA‐SiC composites. 

Fig. 4. Variation of Ultimate Tensile Strength for the 

single reinforced Al‐Mg‐Si/10 wt% SiC and hybrid 

reinforced Al‐Mg‐Si/BLA‐SiC composites. 

30


Fig. 5. Variation of Yield Strength for the single 

reinforced Al‐Mg‐Si/10 wt% SiC and hybrid reinforced 

Al‐Mg‐Si/BLA‐SiC composites. 

The specific strength (Fig. 6) and percent 

elongation (Fig. 7) are equally observed to 

decrease with increase in BLA content. In the case 

of the specific strength, it is noted that the margin 

of difference between the specific strength of the 

single reinforced Al‐Mg‐Si/10wt%SiC and the Al‐ 

Mg‐Si/2wt%BLA‐8wt%SiC is less than 2%. Also, 

the fracture toughness of the composites (Fig. 8) is 

observed to increase with increase in the BLA 

content, which is encouraging considering that 

MMCs are noted to have poor fracture toughness 

values. The fracture toughness values obtained 

were reported as plain strain fracture toughness 

because it meets the conditions specified by Das 

and Nath [26] and Alaneme and Aluko [5].The 

improvement in fracture toughness with increase 

in BLA content may be attributed to the increased 

presence of silica which is a softer ceramic in 

comparison with SiC. It is also noted that for most 

engineering materials fracture toughness scales 

inversely with yield strength [29] which is the case 

observed for the composites. 

Fig. 6. Variation of Specific Strength for the single 

reinforced Al‐Mg‐Si/10 wt% SiC and hybrid reinforced 

Al‐Mg‐Si/BLA‐SiC composites. 

Fig. 7. Variation of Percent Elongation for the single 

reinforced Al‐Mg‐Si/10 wt% SiC and hybrid 


Fig. 8. Variation of Fracture Toughness for the single 

reinforced Al‐Mg‐Si/10 wt% SiC and hybrid 


3.3 Corrosion Behaviour 

Figure 9 show the variation of mass loss and 

corrosion rate with exposure time for composite 

samples immersed in 3.5% NaCl solution. From 

Fig. 9(a), it is observed that compared to sample 

A (Al‐Mg‐Si/10wt%SiC), sample B (Al‐Mg‐ 

Si/2wt% BLA‐8 wt% SiC) and sample C (Al‐Mg‐ 

Si/3wt% BLA‐7wt% SiC ) had negative mass loss 

values for virtually the entire period of 

immersion in the 3.5% NaCl solution. The 

negative mass loss is indicative of weight gain 

during the period of immersion‐ suggesting that 

the passive film formed on sample B and C are 

very stable in comparison to that of sample A. 

Thus sample B (Al‐Mg‐Si/2wt% BLA‐8 wt% SiC) 

and sample C (Al‐Mg‐Si/3wt% BLA‐7wt% SiC) 

exhibits a higher resistance to corrosion in 

comparison to the single reinforced (Al‐Mg‐ 

Si/10wt%SiC) composite. This trend in 

corrosion behaviour is supported by the 

31


corrosion rate profiles presented in Fig. 9(b). It 

is observed from the plot that peak corrosion 

was observed on the 3 rd day of immersion with 

the 2 and 3 wt% BLA containing composites 

exhibiting the least susceptibility to corrosion. 

Bobic et al. [30] have reported on the corrosion 

susceptibility of Al matrix‐SiC reinforced 

composites in marine (chloride) environments. 

The improvement in corrosion resistance 

observed by the addition of 2‐3 wt% BLA is 

attributed to the presence of silica which is the 

primary constituent of BLA. Silica has been 

reported to inhibit the formation of Al 4 C 3 phase 

which forms from interfacial reaction between 

the matrix and SiC during the production 

process [31]. The Al 4 C 3 phase has been reported 

to have adverse effect on the corrosion 

resistance of aluminium based composites [32]. 

reinforced Al‐Mg‐Si/10 wt% SiC composite 

(sample A). This is in contrast with the trend 

observed in 3.5% NaCl solution (Fig. 9). In 

addition, the mass loss increases with increase in 

exposure time. This is an indication that the 

passive film formed on the composites was unable 

to give adequate protection to the substrates; and 

the addition of BLA promoted corrosion of the 

composites. Furthermore it is observed that 

among the hybrid composites, the mass loss is 

more pronounced for the Al‐Mg‐Si/4wt%BLA‐ 

6wt%SiC composition. This same trend was also 

observed in 3.5% NaCl environment – an 

indication that the Al‐Mg‐Si/4wt%BLA‐6wt%SiC 

composite composition may not be suitable for use 

in marine and acidic environments. Figure 10(b) 

shows that the corrosion rate behaviour of the 

composites is in agreement with the trends 

observed in Fig. 10(a). 

(a) 

(a) 

(b) 

Fig. 9. Variation of (a) mass loss and (b) corrosion 

rate with exposure time for the single reinforced Al‐ 

Mg‐Si/10 wt% SiC and hybrid reinforced Al‐Mg‐ 

Si/BLA‐SiC composites in 5wt% NaCl solution. 

Figure 10 shows the plots of variation of mass 

loss and corrosion rate with exposure time for 

the composites immersed in 0.3 M H 2 SO 4 

solution. From Fig. 10(a), it is observed that the 

hybrid composites exhibit inferior corrosion 

resistance in comparison with the single 

(b) 

Fig. 10. Variation of (a) mass loss and (b) corrosion 

rate with exposure time for the single reinforced Al‐ 

Mg‐Si/10 wt% SiC and hybrid reinforced Al‐Mg‐ 

Si/BLA‐SiC composites in 0.3M H 2 SO 4 solution. 

Figure 11 shows that the corrosion mechanism 

of the hybrid composites in H 2 SO 4 solution is 

most likely to be galvanic corrosion as a result of 

the preferential dissolution of the Al matrix 

which exposed the BLA‐SiC reinforcements. In 

32


this regards the Al matrix is known to have a 

higher electrochemical potential in comparison 

with BLA‐SiC (ceramic particle) which have 

higher resistivity [33]. Thus at the Al 

matrix/reinforcement interfaces, micro galvanic 

corrosion cells are created which results in the 

dissolution of Al (anode) in preference to BLA‐ 

SiC (which serves as the cathode) [34‐35]. 

resistance in comparison to the single 

reinforced Al ‐ 10 wt% SiC composite but 

the reverse trend was observed in 0.3M 

H2SO4 solution where the single 

reinforced Al ‐ 10 wt% SiC composite had 

superior corrosion resistance. 

5. The 4 wt % BLA containing hybrid 

composite composition was observed to 

be the least satisfactory in achieving the 

goal of reduced cost while maintaining 

high performance levels of the composites. 

Acknowledgement 

The authors acknowledge the assistance of Dr. P.A. 

Olubambi of the Department of Chemical and 

Metallurgical Engineering, Tshwane University of 

Technology, South Africa in carrying out 

microstructural and compositional characterization 

of the composites produced. 

Fig. 11. SEM photomicrograph showing secondary 

electron image of the corroded surface of the Al‐Mg‐ 

Si/3wt% BLA‐7 wt% SiC hybrid composite. 

3. CONCLUSION 

The microstructures, mechanical properties and 

corrosion behaviour of Al‐Mg‐Si matrix 

composites containing 0:10, 2:8, 3:7, and 4:6 wt 

% bamboo leaf ash and silicon carbide as 

reinforcement was investigated. The results 

show that: 

1. The hardness, ultimate tensile strength, 

and percent elongation of the hybrid 

composites decreased with increase in 

BLA content. 

2. The fracture toughness of the hybrid 

composites was observed to be superior to 

that of the single reinforced Al ‐ 10 wt% 

SiC composite. 

3. The specific strength of the 2 wt % BLA 

containing hybrid composite was 

comparable to that of the single reinforced 

Al ‐ 10 wt% SiC composite while the 3 and 

4 wt % BLA containing hybrid composites 

had lower specific strength values. 

4. In 5wt% NaCl solution, it was observed 

that the 2 and 3 wt % BLA containing 

hybrid composites had higher corrosion 

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[7] K.K. Alaneme, M.O. Bodunrin: Corrosion behaviour 

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Characterisation and Engineering, Vol. 10, No. 2, 

pp. 1153‐65, 2011. 

33


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Miloradović, M. Pantić, D. Džunić: Tribological 

Potentials of Hybrid Composites Based on Zinc 

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57–65, 2010. 

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Garcia: Synthesis and microstructural 

characterization of Al‐Mg alloy‐SiC particulate 

composite, Materials Letters, Vol. 62, No. 17‐18, 

pp. 2623‐2625, 2008. 

[11] P.B. Madakson, D.S. Yawas, A. Apasi: 

Characterization of Coconut Shell Ash for 

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for Automotive Applications, International 

Journal of Engineering Science and Technology 

(IJEST), Vol. 4, No. 3, pp. 1190‐1198, 2012. 

[12] K.V. Mahendra, A. Radhakrisna: Characterization 

of stir cast Al‐Cu‐(fly ash + SiC) hybrid Metal 

Matrix Composites, Journal of Composite 

Materials, Vol. 44, No. 8, pp. 989‐1005, 2010. 

[13] H. Zuhailawati, P. Samayamutthirian, C.H. Mohd 

Haizu, Fabrication of Low Cost Aluminium Matrix 

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[15] K.K. Alaneme, I.B. Akintunde, P.A. Olubambi, T.M. 

Adewale: Mechanical Behaviour of Rice Husk Ash – 

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34


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Vol. 31, No. 3 & 4, pp. 44‐54, 2009. 

35

Vol. 35, No. 1 (2013) 36‐41 



RESEARCH 

Examination of Wear Resistance of 

Polymer – Basalt Composites 

A. Todić a , D. Čikara a , V. Lazić b , T. Todić a , I. Čamagić a , A. Skulić, D. Čikara c 

a University of Priština, Faculty of Technical Sciences, Kneza Milosa 7, 38220 Kosovska Mitrovica, Serbia. 

b Universitu of Kragujevac, Faculty of Engineering, Sestre Janjić 6, 34000 Kragujevac, Serbia. 

c University of Belgrade, Faculty of Technology and Metalurgy, Karnedžijeva 4, 11000 Belgrade, Serbia. 

Keywords: 

Wear 

Basalt 

Composite 

Polymers 


V. Lazić 

Universitu of Kragujevac, 

Faculty of Engineering, 

Sestre Janjić 6, 

34000 Kragujevac, Serbia 

E‐mail: vlazic@kg.ac.rs 


Olivine basalt, as a natural material, has excellent physical and mechanical 

properties such as hardness, compressive strength, wear resistance, color and 

gloss. On the other hand it is difficult for processing, because of its high values of 

mechanical properties. Retention of physical and mechanical properties of basalt 

and its formation is only possible by mixing basalt powder with polymers which 

would enable the composite material that can be formed by the casting process 

into complex shapes. The mechanical properties of the obtained composites and 

production technologies are, to a great extent, unknown in both, local and foreign 

literature. Researchers conducted and presented in this paper show an overview 

of tribological behavior of the basaltic composite material and some 

technological parameters of the production process. Based on the obtained 

results, it can be determine the best ratio of components in the composite. These 

data are important for the development of new composite materials based on 

basalt, which will have significant application in the future. 



Research in this work is aimed to create a new 

composite material, which consists of basalt, 

polymers and additives. 

The main goal of this research is to obtain a 

basalt‐polymer base composite that has 

properties of basalt (good strength, hardness 

and toughness) and is also suitable for forming 

by casting process that is practically impossible 

for the pure basalt. The combination of these 

two materials should allow the obtaining of a 

new material that will keep the characteristics of 

basalt (primarily high hardness, color, etc.) and 

polymers that allow its easy forming. 

The long geological, mining and technological 

research tends to show that the basalt ore can be 

cost‐effective for production of various products of 

basalt aggregates such as: basalt composites, 

basaltic glass, cast basalt, basalt fibers, and even 

jewelry whose value is similar to values of jewelry 

made of semi‐precious stones. These researches 

included defining of the parameter of the process 

for obtaining composites of basalt and polyester 

resin (Polipol 357‐C, 383, Polipol, BRE‐325, etc.), 

by casting methods. 

36

A. Todić et al., Tribology in Industry Vol. 35, No. 1 (2013) 36‐41 

The process parameters to be determined are: the 

granulometric compo‐sition of basaltic aggregates, 

type and amount of the resin and additives, elements 

of casting and pressing process, etc. 

2. PREPARATION OF THE COMPONENTS AND 

MOLDS 

Basalt is very strength and hard alumo‐silicate 

rock, which belong to wild group of granites. For 

the purposes of this research, the basalt is taken 

from the locality of „Vrelo”, situated on the 

slopes of Kopaonik Mountain in the South‐west 

of Serbia. 

From the mineralogical analyses of basalt 

samples Vrelo locality, we can see that these 

rocks are very compact. Porphyry structure with 

distinctly marked fenocrystals, 1‐3 mm size, was 

easily noted. Rock mass is very fine‐grained, 

crypto crystalline and mat‐black colored. 

Mineral composition appears on two ways: in 

olivine fenocrystals that is predominating and 

pyroxene that is inferior. Physical and 

mechanical properties of the basalt from Vrelo 

locality are given in Table 1. 

Table 1. Physical and mechanical properties of basalt 

from Vrelo locality. 

Density (kg/m 3 ) 2600 – 2630 

Melting point ( °C) 1150 – 1170 

Compression strength (dry state) (MPa) 240 – 260 

Compression strength (hydrosaturated 210 – 225 

state) (MPa) 

Compression strength (after freezing) 190 – 195 

(MPa) 

Wear resistance (method Bohme) 

4.1 – 4.5 

(cm 3 /50 cm 3 ) 

Wear resistance (method Los Angeles) (%) 11.5 – 12.0 

Raw basalt grain size was 3 to 5 mm. This basalt 

aggregate was milled and micronized in 

tungsten‐carbide vibrating mill. Milling lasted 30 

minutes, and after that basalt powder was 

centrifugally sifted into the following granulations: 

100 μm 

150 + 50 μm 

300 + 100 μm 

500 + 300 μm i 

1000 + 500 μm. 

For making the composites, polyester resin BRE 

325 (manufacturer BOYTEK ‐ Turkey) was used 

[3]. This is orthophthalic unsaturated polyester 

resin with low reactivity and medium viscosity. 

It is used for the construction of sanitary 

elements and figurines by casting process. After 

curing, it has high elongation, nice color and very 

good soaking of fillers. Manufacturer of these 

polyester resins declared characteristics shown 

in Table 2 and 3 [3]. 

Table 2. Physical properties of liquid resin at 20 °C. 

Viscosity (cp) 700 – 900 

Acid number (max.) (mg KOH/g) 30 

Styrene content (% mass) 32 – 38 

Exothermic peak ( °C) 130 – 140 

Time of gelation 1% Co (minutes) 5 – 10 

Storage stability (months) 6 

Table 3. Mechanical and physical properties of resin 

in the fully matured state. 

Tensile strength (MPa) 55 

Modulus of elasticity (MPa) 2800 

Elongation (%) 

65 

Bending strenght (MPa) 110 

Flexural modulus (MPa) 3100 

Hardness (Barkola) 35 

Heat distortion temperature ( °C) 55 

As the catalyst and initiator high active Methylethyl‐ketone‐peroxide 

was used. The catalyst is 

added in an amount of 2% of the mass of resin 

used. As an accelerant we used Co (6%) at a 

concentration between 0.2% and 0.6% of the 

amount of the polyester resin [456]. Pattern for 

making molds are made of metal alloy in 

standard sizes for this type of testing. 

Moulds are made of high tackiness silicone 

(poliysilosan). This is a two‐component silicone 

where the first component is pure silicone and the 

second component is a hardener. Mixing silicone 

and hardener is performed by mixing up to 30 s at 

23 °C, until color become homogenous. Molds 

making is performed by pressing of pattern in the 

formed mass and for full curing of molds a period 

of about 72 h is required [78]. 

This silicone mass is used because it does not glue 

to polyester resin, and allows easy extraction of 

test specimens from the mold. The disadvantage is 

that the silicone molds, do not allow high 

pressures, because they will elastically deform. 

Therefore, it is necessary to pour a mixture at low 

pressure just enough that the excess of material be 

extruded from the mold [9]. 

37


3. PREPARATION OF THE COMPOSITE 

MIXTURE 

This silicone mass is used because it does not glue 

to polyester resin, that allows easy extraction of 

test specimens from the mold. The disadvantage 

is that the silicone molds, do not allow high 

pressures, because they will elastically deform. 

Therefore, it is necessary to cast a mixture at low 

pressure just enough that the excess of material 

be extruded from the mold [9]. 

Testing samples are made of composites with the 

different ratios of basalt powder and polyester 

resin, different granulation and different content 

of accelerators. Samples designations with values 

of their masses are given in Table 4. Designation 

of samples consists of three ascendants (Fig. 1) 

where the first ascendant indicates the basalt 

grain size, the second amount of basalt in the 

mixture, and the third, the content of the 

accelerator in the mixture. 

Basalt mixture made of these components are 

uniformly mixed to homogeni‐sation about 10 

min and then poured into the mold. Poured 

mixture solidifies at room temperature and the 

curing time is 30 to 50 minutes, depending on 

the percentage of basalt powder in it. After 

curing samples, together with molds, 

transferred into the furnace and heated to a 

temperature of 60 °C for 3 hours. In the next 

stage, the samples will be removed from the 

mold and reheated at temperature of 100 °C for 

one hour. Completion of the polymerization 

process continues after removing the samples 

from the furnace in the next 24 hours. Samples 

for wear resistance testing are made by this 

method. Figure 2 shows one of the test samples. 

In the Fig. 3 is given photos of the wear 

resistance testing device. 

Table 4. Samples for testing resistance wear 

Samples 

designation 

Sample mass m0 

(g) 

I3a 11.36 

I3b 10.29 

I4a 10.64 

I4b 10.93 

I5a 12.60 

I5b 11.50 

I6a 12.71 

I6b 11.87 

I8a 13.70 

I8b 13.57 

II6a 12.16 

II6b 12.96 

III6a 12.20 

III6b 12.64 

IV6a 12.37 

IV6b 12.54 

V6a 13.42 

V6b 13.52 

X Y Z 

I 

II 

III 

IV 

V 

Basalt grain size 

150+50 μm 

100 μm 

300+100 μm 

500+300 μm 

1000+500 μm 

Propor. of basalt 

3 

4 

5 

6 

8 

30% 

40% 

50% 

60% 

80% 

Prop. of accelerator 

a 0.2% 

b 0.6% 

Fig. 1. Schematic presentation of samples designation. 

38


4. TEST RESULTS 

Fig. 2. Wear resistance test sample. 

Fig. 3. Tribological and Wear resistance testing device. 

The procedure for wear resistance testing is the 

following: rotary abrasive disc made of steel 

with a diameter of 148 mm overlaps the 

prepared sample. The disc rotates with speed of 

0.05 RPM with 200 revolutions on one sample 

(Fig. 3). The higher speed is not possible because 

the samples are quickly heated and burn. Wear 

resistance is defined as the loss of mass per unit 

of wear surface. Wear surface in this case is a 

semi‐spherical, so it can be calculated by the 

expression: 

r 

 

2 

P al 

a 

10.0037, 

cm 

o 

180 

where: 

a ‐ width of the sample (which is 3.1 cm) 

l ‐ length of the port (which is 3.227 cm) 

φ ‐central angle (angle which covers the length 

of the arc which is 0.43633 rad). 

The loss of mass per surface unit can be 

calculated using the following equation: 

m 1 g 

O , 

2 

P cm 

The values of mass loss are shown in Table 5. 

Table 5. Test results of wear resistance. 

Sample 

designation 

Mass before 

testing m0 (g) 

Mass after 

testing m (g) 

Mass loss 

m1 (g) 

I3a 11.36 11.330 0.030 0.00299 

I3b 10.29 10.270 0.020 0.00199 

I4a 10.64 10.610 0.030 0.00299 

I4b 10.93 10.895 0.035 0.00349 

I5a 12.60 12.585 0.015 0.00249 

I5b 11.50 11.480 0.020 0.00199 

I6a 12.71 12.695 0.015 0.00149 

I6b 11.87 11.855 0.015 0.00149 

I8a 13.70 13.675 0.025 0.00249 

I8b 13.57 13.560 0.010 0.00299 

II6a 12.16 12.140 0.020 0.00199 

II6b 12.96 12.950 0.010 0.00099 

III6a 12.20 12.180 0.020 0.00199 

III6b 12.64 12.620 0.020 0.00199 

IV6a 12.37 12.360 0.010 0.00099 

IV6b 12.54 12.530 0.010 0.00099 

V6a 13.42 13.400 0.020 0.00199 

V6b 13.52 13.510 0.010 0.00099 

Mass loss reduced to wear 

surface O (g/cm 2 ) 

4.1. Discussion of the results 

Table 5 shows the values of the mass of samples 

before and after wear mass loss and mass loss 

reduced to wear surface. Based on the results in 

Table 5 a histogram of mass loss per wear 

surface is made (Fig. 4). 

From the above histogram can be concluded that 

the least amount of lost material are on the 

samples with the designation I6a and I6b 

containing 60% basalt powder and grain size 

150+50 μm. Content of accelerator in the first 

sample is 0.2%, and in the second 0.6%. 

39


direction of its application for the production of 

parts in the automotive industry and food 

production [1011]. 

Fig. 4. Histogram of samples mass loss. 

Since these samples showed the best wear 

resistance we continued to test samples with a 

60% of basalt powder, but with different grain 

size. Figure 5 shows histogram the mass loss per 

wear surface. 

Samples generally showed very uniform values 

of wear resistance. However a certain number 

of samples have reduced value of mass loss per 

wear surface, which is especially noticeable on 

the samples: I6a I6b, IV6a and IV6b. This means 

that the wear resistance of these samples is the 

best, and in future work should use these 

technological parameters. A broader view of all 

these results is given in the papers [789]. 

Technology of the production and design of 

these composites is now less known in the 

world. For the production of such composites 

should define in more detail the technological 

parameters, equipment, tools, etc. It will 

probably be the task of future research. 

REFERENCES 

Fig. 5. Histogram of samples mass loss. 

On the diagram it is evident that the best values 

of wear resistance have the samples IV6a and 

IV6b. These samples contain 60% basalt powder 

with a grain size of 500+300 μm. Content of 

accelerator in the first case is 0.2%, and in the 

second 0.6%. This clearly indicates that the 

specified granulation of basalt powder gives the 

highest wear resistance. 

5. CONCLUSION 

Good characteristics of basalt qualify them for the 

final works in construction and manufacturing of 

basalt wool, used as insulating material. During the 

research, the technological parameters of the 

production of polymer matrix composites with 

basalt as reinforcements are established. Further 

development of these materials will go in the 

[1] K. Flinn R. Trojan: Engineering materials and 

their applications 4‐th edition John Wiley & 

Sons New York 1995. 

[2] Study on reserves and quality of basalt as raw 

materials for technical ‐ building stone and 

petrology “Geozavod‐nemetali” Beograd 1999. 

[3] Catalog of polyester resins manu‐facturers 

Boytek. 

[4] Lowe: Composite materials Depart‐ment of 

Engineering Australian National University 

Canberra 2001. 

[5] Iulian‐Gabriel Birsan Circium Adrian Bria 

Vasile Ungureanu Victor: Tribological and 

electrical properties of filled epoxy reinforced 

composites Tribologly in Industry Vol. 31 No. 

1‐2 pp. 33‐36, 2009. 

[6] Capitanu Lucian Onişoru Justin Iarovici Aron: 

Tribological aspects for injection processing of 

thermoplastic composite materials with glass 

fiber Tribologly in Industry Vol. 26, No. 1‐2 pp. 

32‐41, 2004. 

[7] A. Todic B. Nedeljkovic D. Cikara and I, Ristovic: 

Particulate basalt‐polymer composites 

characteristics investigation Materials Design 

Vol. 32, No. 3, pp. 1677 – 1683, 2011. 

[8] Todić R. Aleksić D. Čikara T. Todić: Research of 

particulate composites based on polyester resins 

and basalt, IMK – 14 Oktobar Research and 

development (28‐29)1‐2/2008. pp. 37‐42. 

40


[9] Todić D. Čikara, T. Todić B. Ćirković: Toughness 

testing of particulate composites based on basalt 

polymer and silane IMK – 14 Oktobar Research 

and development (32‐33)3‐4/2009. pp. 25‐28. 

[10] William F. Hosford Mechanical behavior of 

materials University of Michigan Cambridge 

University press 2005. 

[11] Jovičić Gordana and Milosavljević Dragan: The 

equivalent macro ‐ mechanical characteristics of 

composite laminate Tribologly in Industry Vol. 

24 No. 3‐4 pp. 57‐60, 2002. 

41

Vol. 35, No. 1 (2013) 42‐50 



RESEARCH 

Experimental Investigation on Friction and Wear 

Properties of Different Steel Materials 

M.A. Chowdhury a , D.M. Nuruzzaman b 

a Department of Mechanical Engineering, Dhaka University of Engineering and Technology, Gazipur‐1700, Bangladesh. 

b Faculty of Manufacturing Engineering, University Malaysia Pahang, Malaysia. 

Keywords: 

SS 314 

SS 202 

Mild steel 

Friction coefficient 

Wear rate 


Mohammad Asaduzzaman Chowdhury 

Professor 


Engineering 

Dhaka University of Engineering and 

Technology, Gazipur 

Gazipur‐1700, Bangladesh 

E‐mail: asadzmn2003@yahoo.com 


Friction coefficient and wear rate of different steel materials are 

investigated and compared in this study. In order to do so, a pin on disc 

apparatus is designed and fabricated. Experiments are carried out when 

different types of disc materials such as stainless steel 314 (SS 314), 

stainless steel 202 (SS 202) and mild steel slide against stainless steel 314 

(SS 314) pin. Experiments are conducted at normal load 10, 15 and 20 N, 

sliding velocity 1, 1.5 and 2 m/s and relative humidity 70%. At different 

normal loads and sliding velocities, variations of friction coefficient with the 

duration of rubbing are investigated. The obtained results show that 

friction coefficient varies with duration of rubbing, normal load and sliding 

velocity. In general, friction coefficient increases for a certain duration of 

rubbing and after that it remains constant for the rest of the experimental 

time. The obtained results reveal that friction coefficient decreases with the 

increase in normal load for all the tested materials. It is also found that 

friction coefficient increases with the increase in sliding velocity for all the 

materials investigated. Moreover, wear rate increases with the increase in 

normal load and sliding velocity for SS 314, SS 202 and mild steel. In 

addition, at identical operating condition, the magnitudes of friction 

coefficient and wear rate are different for different materials depending on 

sliding velocity and normal load. 



Study of mechanics of friction and the 

relationship between friction and wear dates 

back to the sixteenth century, almost 

immediately after the invention of Newton’s law 

of motion. It was observed by several 

researchers [1‐13] that the variation of friction 

depends on interfacial conditions such as normal 

load, geometry, relative surface motion, sliding 

velocity, surface roughness of the rubbing 

surfaces, type of material, system rigidity, 

temperature, stick‐slip, relative humidity, 

lubrication and vibration. Among these factors 

normal load and sliding velocity are the two 

major factors that play significant role for the 

variation of friction. In the case of materials with 

surface films which are either deliberately 

applied or produced by reaction with 

environment, the coefficient of friction may not 

42

M.A. Chowdhury and D.M. Nuruzzaman, Tribology in Industry Vol. 35, No. 1 (2013) 42‐50 

remain constant as a function of load. In many 

metal pairs, in the high load regime, the 

coefficient of friction decreases with load. 

Bhushan [14] and Blau [15] reported that 

increased surface roughening and a large 

quantity of wear debris are believed to be 

responsible for decrease in friction at higher 

loads. It was observed that the coefficient of 

friction may be very low for very smooth 

surfaces and/or at loads down to micro‐to 

nanonewton range [16,17]. The third law of 

friction, which states that friction is independent 

of velocity, is not generally valid. Friction may 

increase or decrease as a result of increased 

sliding velocity for different materials 

combinations. An increase in the temperature 

generally results in metal softening in the case of 

low melting point metals. An increase in 

temperature may result in solid‐state phase 

transformation which may either improve or 

degrade mechanical properties [13]. The most 

drastic effect occurs if a metal approaches its 

melting point and its strength drops rapidly, and 

thermal diffusion and creep phenomena become 

more important. The resulting increased 

adhesion at contacts and ductility lead to an 

increase in friction [13]. The increase in friction 

coefficient with sliding velocity due to more 

adhesion of counterface material (pin) on disc. 

Friction coefficient and wear rate of metals and 

alloys showed different behavior under different 

operating conditions [18‐25]. In spite of these 

findings, the effects of normal load and sliding 

velocity on friction coefficient of different types 

steel materials, particularly SS 314, SS 202 and 

mild steel sliding against SS 314 are yet to be 

investigated. Therefore, in this study, an attempt 

is made to investigate the effect of normal load 

and sliding velocity on the friction coefficient of 

these materials. The effects of duration of 

rubbing on friction coefficient are observed in 

this study. The effects of normal load and sliding 

velocity on wear rate of SS 314, SS 202 and mild 

steel are also examined. 

2. EXPERIMENTAL 

A schematic diagram of the experimental set‐up 

is shown in Fig. 1 i.e. a pin which can slide on a 

rotating horizontal surface (disc). 

In this set‐up a circular test sample (disc) is to 

be fixed on a rotating plate (table) having a long 

vertical shaft clamped with screw from the 

bottom surface of the rotating plate. The shaft 

passes through two close‐fit bush‐bearings 

which are rigidly fixed with stainless steel plate 

and stainless steel base such that the shaft can 

move only axially and any radial movement of 

the rotating shaft is restrained by the bush. 

These stainless steel plate and stainless steel 

base are rigidly fixed with four vertical round 

bars to provide the rigidity to the main structure 

of this set‐up. The main base of the set‐up is 

constructed by 10 mm thick mild steel plate 

consisting of 3 mm thick rubber sheet at the 

upper side and 20 mm thick rubber block at the 

lower side. A compound V‐pulley above the top 

stainless steel plate was fixed with the shaft to 

transmit rotation to the shaft from a motor. An 

electronic speed control unit is used to vary the 

speed of the motor as required. A 6 mm 

diameter cylindrical pin whose contacting foot is 

flat, made of SS 314, fitted on a holder is 

subsequently fitted with an arm. The arm is 

pivoted with a separate base in such a way that 

the arm with the pin holder can rotate vertically 

and horizontally about the pivot point with very 

low friction. Sliding speed can be varied by two 

ways (i) by changing the frictional radius and (ii) 

by changing the rotational speed of the shaft. In 

this research, sliding speed is varied by changing 

the rotational speed of the shaft while 

maintaining 25 mm constant frictional radius. To 

measure the frictional force acting on the pin 

during sliding on the rotating plate, a load cell 

(TML, Tokyo Sokki Kenkyujo Co. Ltd, CLS‐10NA) 

along with its digital indicator (TML, Tokyo Sokki 

Kenkyujo Co. Ltd, Model no. TD‐93A) was used. 

The coefficient of friction was obtained by 

dividing the frictional force by the applied normal 

force (load). Wear was measured by weighing the 

test sample with an electronic balance before and 

after the test, and then the difference in mass was 

converted to wear rate. To measure the surface 

roughness, Taylor Hobson Precision Roughness 

Checker (Surtronic 25) was used. Each test was 

conducted for 30 minutes of rubbing time with 

new pin and test sample. Furthermore, to ensure 

the reliability of the test results, each test was 

repeated five times and the scatter in results was 

small, therefore the average values of these test 

results were taken into consideration. 

43


2 

19 

1 

15 

16 

17 

14 

3 

5 

6 

13 

4 

11 

12 

7 

8 

9 10 

1 Load arm holder 

2. Load arm 

3. Normal load (dead weight) 

4. Horizontal load (Friction 

force) 

5. Pin sample 

6. Test disc with rotating table 

7. Load cell indicator 

8. Belt and pulley 

9. Motor 

10. Speed control unit 

11. Vertical motor base 

12. 3 mm Rubber pad 

13. Main shaft 

14. Stainless steel base 

15. Stainless steel plate 

16. Vertical square bar 

17. Mild steel main base plate 

18. Rubber block (20 mm thick) 

19. Pin holder. 

18 

Fig. 1. Block diagram of the experimental set‐up. 

The detail experimental conditions are shown in 

Table 1. 

Table 1. Experimental Conditions. 

Sl. 

No. 

Parameters Operating Conditions 

1. Normal Load 10, 15, 20 N 

2. Sliding Velocity 1, 1.5, 2 m/s 

3. Relative Humidity 70 ( 5)% 

4. Disc materials (i) Stainless steel 314 

(ii) Stainless steel 202 

(iii) Mild steel 

5. Pin material Stainless steel 314 

6. Average surface 0.35‐0.45 m 

roughness of disks (Ra 

) 

7. Average surface 0.3‐0.4 m 

roughness of pin (Ra ) 

8. Surface Condition Dry 

9. Duration of Rubbing 30 minutes 

3. RESULTS AND DISCUSSION 

Figure 2 shows the variation of friction 

coefficient with the duration of rubbing at 

different normal loads for SS 314. During 

experiment, the sliding velocity and relative 

humidity were 1.5 m/s and 70% respectively. 

Curve 1 of this figure is drawn for normal load 

10 N. From this curve, it is observed that at the 

initial duration of rubbing, the value of friction 

coefficient is 0.215 and then increases very 

steadily up to 0.27 over a duration of 24 minutes 

of rubbing and after that it remains constant for 

the rest of the experimental time. At the initial 

stage of rubbing, friction is low and the factors 

responsible for this low friction are due to the 

presence of a layer of foreign material on the 

disc surface. 


0.5 

0.4 

0.3 

0.2 

0.1 

10 N 

15 N 

20 N 

0.0 

0 4 8 12 16 20 24 28 32 

Duration of rubbing (min) 

Fig. 2. Friction coefficient as a function of duration of 

rubbing at different normal loads (sliding velocity: 

1.5 m/s, relative humidity: 70%, test sample: SS 314, 

pin: SS 314). 

This layer on the disc surface in general 

comprises of (i) moisture, (ii) oxide film (iii) 

deposited lubricating material, etc. At initial 

duration of rubbing, the oxide film easily 

separates the two material surfaces and there is 

little or no true metallic contact and also the 

oxide film has low shear strength. After initial 

1 

2 

3 

44


rubbing, the film (deposited layer) breaks up 

and clean surfaces come in contact which 

increase the bonding force between the 

contacting surfaces. At the same time due to the 

ploughing effect, inclusion of trapped wear 

particles and roughening of the disc surface, the 

friction force increases with duration of rubbing. 

After certain duration of rubbing, the increase of 

roughness and other parameters may reach to a 

certain steady state value and hence the values 

of friction coefficient remain constant for the 

rest of the time. Curves 2 and 3 of this figure are 

drawn for normal load 15 and 20 N respectively 

and show similar trends as that of curve 1. From 

these curves, it is also observed that time to 

reach steady state value is different for different 

normal loads. Results show that at normal load 

10, 15 and 20 N, SS 314 takes 24, 20 and 17 

minutes respectively to reach steady friction. It 

indicates that the higher the normal load, the 

time to reach steady friction is less. This is 

because the surface roughness and other 

parameter attain a steady level at a shorter 

period of time with the increase in normal load. 

The trends of these results are similar to the 

results of Chowdhury and Helali [26,27]. 

Figure 3 shows the effect of the duration of 

rubbing on friction coefficient at different 

normal loads for SS 202 at velocity of 1.5 m/s 

and 70% of relative humidity. 


0.5 

0.4 

0.3 

0.2 

0.1 

10 N 

15 N 

20 N 

0.0 

0 4 8 12 16 20 24 28 32 




1.5 m/s, relative humidity: 70%, test sample: SS 202, 


Curve 1 of this figure drawn for normal load 10 

N, shows that during initial rubbing, the value of 

friction coefficient is 0.32 which rises for few 

minutes to a value of 0.38 and then it becomes 

1 

2 

3 

steady for the rest of the experimental time. 

Almost similar trends of variation are observed 

in curves 2 and 3 which are drawn for load 15 

and 20 N respectively. From these curves, it is 

found that time to reach steady friction is 

different for different normal loads. At normal 

loads 10, 15 and 20 N, SS 202 takes 22, 19 and 

15 minutes respectively to reach steady friction. 

It means that higher the normal load, SS 202 

takes less time to stabilize. 

Experiments are conducted to observe the effect 

of duration of rubbing on friction coefficient 

under different normal loads for mild steel and 

these results are shown in Fig. 4. 


0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

10 N 

15 N 

20 N 

0.0 

0 4 8 12 16 20 24 28 32 




1.5 m/s, relative humidity: 70%, test sample: mild 

steel, pin: SS 314). 

Curve 1 of this figure drawn for normal load 10 N 

shows that during initial rubbing, the value of 

friction coefficient is 0.44 which increases almost 

linearly up to 0.51 over a duration of 21 minutes of 

rubbing and after that it remains constant for the 

rest of the experimental time. Curves 2 and 3 of 

this figure are drawn for normal load 15 and 20 N, 

respectively. These curves also show similar trend 

as that of curve 1. Results show that at normal load 

10, 15 and 20 N, mild steel takes 21, 18 and 16 

minutes respectively to reach constant friction. It 

means that the higher the normal load, the time to 

reach constant friction is less. The possible reason 

is the surface roughness and other parameter 

attains a steady level at a shorter period of time 

with the increase in normal load. 

Figure 5 shows the comparison of the variation of 

friction coefficient with normal load and curves of 

this figure are drawn for SS 314, SS 202 and mild 

steel. 

1 

2 

3 

45



0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

SS 314 

SS 202 

Mild steel 

0.0 

5 10 15 20 25 

Normal load (N) 

Fig. 5. Variation of friction coefficient with the 

variation of normal load for different materials 

(sliding velocity: 1.5 m/s, relative humidity: 70%, pin: 

SS 314). 

These results are obtained from the steady 

values of friction coefficient of Figs. 2‐4. It is 

shown that friction coefficient varies from 

0.27 to 0.21, 0.38 to 0.31 and 0.51 to 0.45 with 

the variation of normal load from 10 to 20 N 

for SS 314, SS 202 and mild steel respectively. 

All of these results show that friction 

coefficient decreases with the increase in 

normal load. Increased surface roughening 

and a large quantity of wear debris are 

believed to be responsible for the decrease in 

friction [14,15] with the increase in normal 

load. 

Similar behavior is obtained for Al–Stainless 

steel pair [28] i.e friction coefficient decreases 

with the increase in normal load. From the 

obtained results, it can also be seen that the 

highest values of the friction coefficient are 

obtained for mild steel and the lowest values of 

friction coefficient are obtained for SS 314. The 

values of friction coefficient of SS 202 are found 

in between the highest and lowest values. It was 

found that after friction tests, the average 

roughness of SS 314, SS 202 and mild steel discs 

varied from 1.15‐1.32, 1.45‐1.7 and 2.1‐2.45 m 

respectively. 

Figures 6, 7 and 8 show the variation of friction 

coefficient with the duration of rubbing at 

different sliding velocities for SS 314, SS 202 and 

mild steel respectively at 15 N normal load. 


0.0 

0 4 8 12 16 20 24 28 32 



rubbing at different sliding velocities (normal load: 

15 N, relative humidity: 70%, test sample: SS 314, 



0.0 

0 4 8 12 16 20 24 28 32 




15 N, relative humidity: 70%, test sample: SS 202, 



0.5 

0.4 

0.3 

0.2 

0.1 

0.5 

0.4 

0.3 

0.2 

0.1 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

1 m/s 

1.5 m/s 

2 m/s 

1 m/s 

1.5 m/s 

2 m/s 

1 m/s 

1.5 m/s 

2 m/s 

0.0 

0 4 8 12 16 20 24 28 32 




15 N, relative humidity: 70%, test sample: mild steel, 

pin: SS 314) 

3 

2 

1 

3 

2 

1 

3 

2 

1 

46


Curves 1, 2 and 3 of Fig. 6 are drawn for sliding 

velocity 1, 1.5 and 2 m/s respectively. Curve 1 of 

this figure shows that initially the value of friction 

coefficient is 0.14 which increases almost linearly 

up to 0.2 over a duration of 25 minutes of rubbing 

and after that it remains constant for the rest of the 

experimental time. Curves 2 and 3 show that for the 

higher sliding velocity, the friction coefficient is 

more and the trend in variation of friction 

coefficient is almost the same as for curve 1. The 

obtained results show that at sliding velocity 1, 1.5 

and 2 m/s, time to reach constant friction 25, 21 

and 19 minutes respectively. From Figs. 7 and 8, it 

can be observed that the trends in variation of 

friction coefficient with the duration of rubbing are 

very similar to that of Fig. 6 but the values of friction 

coefficient are different for different disc materials. 

Figure 9 shows the comparison of the variation 

of friction coefficient with sliding velocity and 

the curves of this figure are drawn for SS 314, SS 

202 and mild steel. These results are obtained 

from the steady values of friction coefficient of 

Figs. 6‐8. It is shown that friction coefficient 

varies from 0.2 to 0.29, 0.3 to 0.395 and 0.44 to 

0.53 with the variation of sliding velocity from 1 

to 2 m/s for SS 314, SS 202 and mild steel 

respectively. These results indicate that friction 

coefficient increases with the increase in sliding 

velocity. Sliding contact of two materials results 

in heat generation at the asperities and hence 

increases in temperature at the frictional 

surfaces of the two materials. The resulting 

increased adhesion at contacts and ductility lead 

to an increase in friction [13]. The increase in 

friction coefficient with sliding velocity due to 

more adhesion of counterface material (pin) on 

disc. From the obtained results, it can also be 

seen that the highest values of the friction 

coefficient are obtained for mild steel and the 

lowest values of friction coefficient are obtained 

for SS 314. The values of friction coefficient of SS 

202 are found in between the highest and lowest 

values. After friction tests it was found that the 

average roughness of SS 314, SS 202 and mild 

steel discs varied from 1.2‐1.34, 1.52‐1.85 and 

2.23‐2.62 m respectively. 

Figure 10 shows the variations of wear rate with 

normal load for SS 314, SS 202 and mild steel. 

Results show the variation of wear rate from 

2.262 to 3.544, 1.956 to 3.187 and 6.524 to 

10.354 mg/min with the variation of normal 

load from 10 to 20 N for SS 314, SS 202 and mild 

steel respectively. From these curves, it is 

observed that wear rate increases with the 

increase in normal load for all types of materials 

investigated. When the load on the pin is 

increased, the actual area of contact would 

increase towards the nominal contact area, 

resulting in increased frictional force between 

two sliding surfaces. The increased frictional 

force and real surface area in contact causes 

higher wear. This means that the shear force and 

frictional thrust are increased with increase of 

applied load and these increased in values 

accelerate the wear rate. Similar trends of 

variation are also observed for mild steel–mild 

steel couples [29], i.e wear rate increases with 

the increase in normal load. 


0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

SS 314 

SS 202 

Mild steel 

0.0 

0.5 1.0 1.5 2.0 2.5 

Sliding velocity (m/s) 

Fig. 9. Variation of friction coefficient with the variation 

of sliding velocity for different materials (normal load: 15 

N, relative humidity: 70%, pin: SS 314). 

Wear rate (mg/min) 

14 

12 

10 

8 

6 

4 

2 

SS 314 

SS 202 

Mild steel 

0 

5 10 15 20 25 

Normal load (N) 

Fig. 10. Variation of wear rate with the variation of 

normal load for different materials (sliding velocity: 

1.5 m/s, relative humidity: 70%, pin: SS 314). 

From the obtained results, it can also be seen 

that the highest values of wear rate are obtained 

for mild steel and the lowest values of wear rate 

are obtained for SS 202. The values of wear rate 

47


of SS 314 are slightly higher than that of SS 202. 

It is very clear that within the observed range of 

normal load, the magnitudes of wear rate of mild 

steel are significantly higher than that of SS 314 

and SS 202. 

The variations of wear rate with sliding 

velocity for above mentioned materials are 

also observed in this study and the results are 

presented in Fig. 11. These results indicate 

that wear rate varies from 2.956 to 4.826, 

2.642 to 4.495 and 6.934 to 11.862 mg/min 

with the variation of sliding velocity from 1 to 

2 m/s for SS 314, SS 202 and mild steel 

respectively. It is observed that wear rate 

increases with the increase in sliding velocity 

for all types of materials investigated. This is 

due to the fact that duration of rubbing is same 

for all sliding velocities, while the length of 

rubbing is more for higher sliding velocity. The 

reduction of shear strength of the material and 

increased true area of contact between 

contacting surfaces may have some role on the 

higher wear rate at higher sliding velocity. 

Wear rate (mg/min) 

14 

12 

10 

8 

6 

4 

2 

SS 314 

SS 202 

Mild steel 

0 

0.5 1.0 1.5 2.0 2.5 

Sliding velocity (m/s) 

Fig. 11. Variation of wear rate with the variation of 

sliding velocity for different materials (normal load: 

15 N, relative humidity: 70%, pin: SS 314). 

At different sliding velocities, the highest values 

of wear rate are obtained for mild steel and the 

lowest values of wear rate are obtained for SS 

202. Wear rates of SS 314 are slightly higher 

than that of SS 202. It is apparent that within the 

observed range of sliding velocity, wear rates of 

mild steel are remarkably higher than that of SS 

314 and SS 202. 

4. CONCLUSION 

Normal load and sliding velocity indeed affect 

the friction coefficient and wear rate of SS 314, 

SS 202 and mild steel considerably. Within the 

observed range, the values of friction coefficient 

decrease with the increase in normal load while 

friction coefficients increase with the increase in 

sliding velocity. Friction coefficient varies with 

the duration of rubbing and after certain 

duration of rubbing, friction coefficient becomes 

steady for the observed range of normal load 

and sliding velocity. The highest values of 

friction coefficient are obtained for mild steel 

and the lowest values of friction coefficient are 

obtained for SS 314. 

The values of friction coefficient of SS 202 are 

found in between the highest and lowest values. 

Wear rates of SS 314, SS 202 and mild steel 

increase with the increase in normal load and 

sliding velocity. Wear rates of mild steel are 

significantly higher than that of SS 314 and SS 

202. For the observed range, the values of wear 

rates of SS 314 are slightly higher than that of 

SS 202. 

Therefore, maintaining an appropriate level of 

normal load, sliding velocity as well as 

appropriate choice of sliding pair, friction and 

wear may be kept to some optimum value to 

improve mechanical processes. 

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50

Vol. 35, No. 1 (2013) 51‐60 



RESEARCH 

Effects of Velocity‐Slip and Viscosity Variation in 

Squeeze Film Lubrication of Two Circular Plates 

R.R. Rao a , K. Gouthami a , J.V. Kumar b 

a Department of Mathematics, K L University, Green Fields,Vaddeswaram,Guntur‐522502., Andhra Pradesh, India. 

b Department of Mathematics, Vasireddy Venkatadri Institute of Technology, Nambur‐522508, Andhra Pradesh, India. 

Keywords: 

Reynolds equation 

Velocity‐slip 

Viscosity variation 

Squeeze film lubrication 

Load capacity 

Squeezing time 


R.Raghavendra Rao 

Department of Mathematics, 

K.L.University, Green Fields, 

Vaddeswaram, Guntur, ‐522502. 

Andhra Pradesh, India. 

E‐mail: rrrsvu@sify.com 


A generalized form of Reynolds equation for two symmetrical surfaces is 

taken by considering velocity‐slip at the bearing surfaces. This equation is 

applied to study the effects of velocity‐slip and viscosity variation for the 

lubrication of squeeze films between two circular plates. Expressions for 

the load capacity and squeezing time obtained are also studied 

theoretically for various parameters. The load capacity and squeezing 

time decreases due to slip. They increase due to the presence of high 

viscous layer near the surface and decrease due to low viscous layer. 



In general, most of the lubricated systems can 

be considered to consist of moving 

/stationary surfaces (plane/curve, 

loaded/unloaded) with a thin film of an 

external material (lubricant) between them. 

The presence of such a thin film between 

these surfaces not only helps to support 

considerable load but also minimizes friction. 

The characteristics such as pressure in the 

film, frictional force at the surface, flow rate 

of the lubricant etc. of the system depend 

upon the nature of the surfaces, the nature of 

the lubricant film boundary conditions etc. 

The equation governing the pressure generated 

in the lubricant film can be obtained by coupling 

the equations of motion with the equation of 

continuity and was first derived by Reynolds [1] 

in 1886 and is known as ``Reynolds Equation’’. 

In deriving this equation, the thermal, 

compressibility, viscosity variation, slip at the 

surfaces, inertia and surface roughness effects 

were ignored. Later this Reynolds equation is 

modified in 1949 by Cope [2] including viscosity 

and density variation along the fluid film. In 

1957‐58 the viscosity variation across the film 

thickness has been considered by Zienkiewicz 

and Cameron [3,4] who also pointed out that 

51

R.R. Rao et al., Tribology in Industry Vol. 35, No. 1 (2013) 51‐60 

temperature gradient and viscosity variation with the following usual assumptions of 

across the film may not be ignored. In the year lubrication theory: 

1962, Dowson [5] unified the various attempts 

in generalizing the Reynolds Equation by 

considering the variation of fluid properties 

across as well as along the fluid film thickness by 

neglecting the slip effects at the bearing surfaces. 

Since then many workers including myself have 

studied the effects of viscosity variation in 

lubricated systems by considering Reynolds 

Equation with energy equation [6‐13]. R.M.Patel 

et.al [14] studied the performance of a magnetic 

fluid based squeeze film between transversely 

rough triangular plates. Also M.E.Shimpi , 

G.M.Dehari [15] studied surface roughness and 

elastic deformation effects on the behaviour of the 

magnetic fluid based squeeze film between 

rotating porous circular plates with concentric 

circular pockets and improved in 2012 to the 

rotating curved porous circular plates [16].In this 

study the effects of velocity‐slip and viscosity 

variation in squeeze film lubrication of two 

circular plates has been discussed. 

2. BASIC EQUATIONS 

Consider the laminar flow of a fluid between two 

symmetric surfaces, whose physical Fig. 1. Coordinate System. 

configuration is as shown in the Fig. 1. 

Considering the variation of fluid properties 1) Inertia and body force terms are negligible 

across as well as along the film thickness, the compared with the pressure and viscous 

basic equations of motion and equation of terms. 

continuity in their general form for a newtonian 

2) There is no variation of pressure across the 

fluid can be written as: 

 

fluid film, which means 

 

=0. 

Dv P 

2 v 

u 

2 v 

w 

Y 

 

 

 

 

 

 

z 

Dt y 

3 y 

y 

x 

 

3 y 

y 

z 

 

3) There is no slip in the fluid‐solid 

boundaries. 

w 

v 

 

v 

u 

 

4) No external forces act on the film. 

 

 

 

 

 

 

z 

y 

z 

 

x 

x 

y 

 

5) The flow is viscous and laminar. 

6) Due to the geometry of fluid film the 

derivatives of u and v with respect to z are 

Dw P 

2 w 

u 

 

2 w 

v 

 

Z 

 

 

 

 

3 

3 

 

 

much larger than other derivatives of 

Dt z 

z 

z 

x 

 

z 

z 

y 

 

velocity components. 

7) The height of the film h is very small 

compared to the bearing length l. 

u 

w 

w 

v 

 

 

 

 

 

 

(1) A typical value of h/l is about 10 ‐3 . 

x 

z 

x 

 

y 

y 

z 

 

The Navier–Stokes equation (1) can be 

( u) 

+ ( v) 

+ ( w) 

=0 (2) 

t x y 

z 

simplified by Dowson [5] as follows 

52


P u 

 

= 

x 

z 

 

z 

 

 

P v 

 

= 

y 

z 

z 

 

(3) 

 

where P = P (x,y) is the pressure in the film and 

is the viscosity. 

The boundary conditions considering slip at the 

surfaces [17] are: 

u 

 

u = (u) 1 = ( ) 1 

 

U1 

z 

 

 

v 

v = (v) 1 = ( ) 1 

 

V1 

z 

 

 

1 

1 

at Z = H 1 

u 

 

u = (u) 2 = ‐ ( ) 2 

 

U 

2 

z 

2 

at Z = H 2 

v 

v = (v) 2 = ‐ ( ) 2 

 

V2 

z 

 

 

2 

(4) 

where ( ) 1 ( ) 2 denote the value at z = H 1 

and z = H 2 . Here ’s and ’s are molecular 

mean free path for gas lubrication and depend 

upon the lubricant temperature, pressure and 

viscosity. In liquid lubrication and depend 

on viscosity and the coefficient is sliding friction. 

However, with porous bearings and are 

functions of slip coefficient at the wall and the 

permeability parameter of the porous facing. 

Integrating equation (3) and using boundary 

conditions (4) expressions for the fluid film 

velocities are obtained. 

 

u=U 1 + 

1H 

 

 

U 

 

 

2 

U 

F 

0 

1 

 

v=V 1 + 1H 

 

1 

z 

 

H1 

F 

 

F 

1 

1 

0 

zdz 

P 

 

 

x 

P 

 

 

1 

x 

 

z 

zdz 

 

 

H1 

 

P 

y 

z 

 

H1 

dz 

 

 

V2 

V 

 

1 

 

F0 

1 

F 

 

F 

1 

1 

1 

0 

P 

 

z 

dz 

1 

 

y 

 

(5) 

 

 

 

H1 

 

where: 

z 

z 

dz 1 

zdz 

F 0 = 

1 

 

2 

, F0 

1 

 

2 

, 

 

 

H1 

H 

H1 

2 

z 

F 1 = 

zdz 

 

1H1 

 

2H 

2 

, 1 

zdz 

F1 1H1 

 

2H 

2 

, 

 

 

 

1 

 

( ) 

1 

, 

( ) 

1 

( ) 

H1 

2 

2 

, 

( ) 

2 

 

( ) 

( ) 

H1 

1 

2 

1 

, 

2 

(6) 

( ) 

1 

( ) 

2 

Integrating the equation of continuity (2) w.r.t. 

z. and taking limits from z = H 1 to z = H 2 gives 

H 2 

 

H1 

H 2 

H2 

 

 

dz 

t 

( u) 

dz x 

( ) ( ) H2 

v dz w 

0 (7) 

H1 

y 

H1 

H1 

The integrals of ( u) 

and ( v) 

are evaluated by 

partial integration. Introducing the expressions 

for ( u) 

and ( v) 

and their derivatives in 

equation (7) gives: 

 

 

 

 

x 

P 

1 1 

F 

G F 

G 

 

x 

 

 

y 

 

P 

 

 

y 

 

= 

2 1 

2 1 

 

H ( u) 

2 

( v) 

2 H1 

( u) 

1 

( v 

x 

y 

x 

y 

2 

) 

1 

H 

2 

 

H 

+ 

dz ( w) H 

y 

H1 

where 

2 

1 

H2 

z 

F 

F 2 = 

 

1 

z dz 

 

H F0 

 

F 

1 

H 2 

1 

1 z 

F 

 

1 

2 

z 

1 dz, 

 

H1 

F0 

 

H 2 

 

 

 

z 

zdz 

F 

3 

 

H 2 

 

H1 

z 

dz 

 

dz 

 

dz 

G 1 = 1 

z 

 

 

 

1 

H1 

 

1 

 

z 

F 

H1 

 

H1 0 

 

H1 

 

 

H2 

z 

z 

1 

G 

1 

= 

zdz F dz 

z H 

dz 

z 

1 

1 

H 

F 

1 1 

1 1 

 

 

 

 

 

 

 

 

 

1 H1 0 H 

 

 

 

 

 

 

 

 

 

1 

 

 

F 

 

z 

 

 

 

(8) 

53


G 2 = 

G 2 1 = 

H 2 

 

 

 

z 

 

z 

 

 

1 

H1 H1 

H 2 

 

 

 

 

 

z 

 

dz 

 

dz 

 

 

dz 

 

 

H3 

z 

1 

dz, 

G3 

z 

z 

 

H1 H1 

z 

H1 

 

dz 

z 

(9) 

Equation (8) represents a generalized form of 

Reynolds equation for compressible fluid film 

lubrication considering slip velocities at the 

bearing surfaces. The two sets of functions F and 

G depend upon the variation of fluid properties 

both along as well as across the film and on the 

slip conditions at the surfaces. 

i.e., ( ) 

1 

( ) 

2 

( ) 

1 

( ) 

2 

0 

0 

1 2 1 2 

 

The velocity of the lubricant can vary across the 

film and may be different near the bearing 

surfaces owing to the reaction of additives and 

surfactants with the surfaces [18‐20]. 

Considering a reasonable case where the density 

and viscosity of the lubricant near the bearing 

surfaces may be different from the central 

region, we can have 

1 ( x, y), 1 

(x, y) H 1 < z < H 1 + h 1 

 

2 

( x, y), 2 

(x, y) 

H 1 + h 1 < z < H 1 + h 1 + h 2 

3 ( x, y), 3 

(x, y) 

H 1 + h 1 + h 2 < z < H 1 + h 1 + h 2 + h 3 (10) 

This introduces the concept of multiple‐layer 

lubrication. By taking 

U 1 = U U 2 = V 1 = V 2 = 0 

 

1 

1 

 

2 

 

2 

 

i 

0 i 1,2,3, 

............ 

z 

(11) 

The generalized equation with slip reduces to 

the following form. 

P 

P 

 

 

F2 

 

F2 

 

x 

 

x 

y 

y 

 

 

H 

2 ( u) 

2 

( v) 

2 

x 

y 

 

 

H1 

( u) 

1 

( v) 

1 

x 

y 

 

F3 

 

H2 

U [ w] 

(12) 

H1 

x 

F0 

 

where: 

h1 

h 

2 

h 

3 

F 0 = 1 

 

2 

 

1 

2 

3 

F 1 = 

h1 

(2H1 

h1) 

h 

2 

(2H1 

2h1 

h 

2 

) 

1 

H1 

 

2 

H 

2 

 

 

2 

1 

2 

2 

+ 

h 

3 

(2H1 

2h1 

2h 

2 

h 

3) 

2 

2 

F 2 = 

1 

3 3 

2 

3 

H 

 

 

3 

1 

h1 

H1 

H1 

h1 

h 

2 

(H1 

h1) 

3 

3 

1 

 

3 

3 

3 F1 

F3 

H 

2 

(H1 

h1 

h 

2 

) 

3 

3 

F0 

1 

h1 

 

2 

h 

2 

F 3 = (2H1 

h1 

) (2H 1 + 2h 1 + h 2 ) 

2 

2 

1 

+ 

3 

2 

h 

2 

3 

3 

 

2 

(2H 1 + 2h 1 + 2h 2 + h 3 ) 

F 

1 P 

 

( u) 

1 

= 1 

1 

1 

H1 

 

1U 1 

F0 

x 

F0 

 

F 

1 P 

 

2 

( u) 

2 

= 3 

 

2 H 

2 

 

3U 

F0 

x 

F0 

F 

1 P 

( v) 

1 

= 1 

1 

H1 

 

F0 

y 

F1 

P 

( v) 

2 

= ‐ 3 

 

2 H 

2 

 

F0 

y 

(13) 

H 

2 

[ w] H 

= (u) 

H 2 

H 

1 2 ( v) 

2 

2 

x 

y 

H1 

H1 

( u) 

1 

( v) 

1 

V s 

x 

y 

54


here V s is the resultant velocity towards the film. 

To see the effect of slip, consider three 

symmetrical incompressible layers between two 

solid boundaries. 

1 2 

1 

2 

3 

H 1 = 0 

 

 

H 2 =(h+a)=h, h 1 = h 3 = a/2, h 2 = (h‐a) 

1/ 

 

(14) 

1 2 1 2 

 

may be considered. The Reynolds equation can 

be written from equation (12) as follows: 

P 

P 

 

F4 F4 

U (h) V 

x x y 

 

y 

 

(15) 

 

 

x 

where 

3 3 2 

2 2 

(h a) a 3a (h a) 3a(h a) h 

F 4 = 

 

12 2 

12 

1 

2 

 

taking 

1 

as the slip parameter. 

 

3. SQUEEZE FILM LUBRICATION OF TWO 

CIRCULAR PLATES: 

Consider the squeeze film lubrication between two 

parallel circular plates as shown in Fig. 2. Let the 

film thickness of the lubricant present between the 

two plates be `h’ and squeeze velocity be `V’. 

Fig. 2. Squeeze film between two Circular Plates. 

The governing equation of flow of the lubricant 

in the case of squeeze film lubrication is given by 

equation [15] as: 

d 

dx 

dP 

 

F4 

V 

dx 

 

(16) 

where h is the total film thickness, a is the 

thickness of the peripheral layer, k is the ratio of 

the viscosities, be the viscosity of the base 

lubricant i.e., the middle layer, be the slip 

parameter. 

The equation (16) can be written in the 

following form: 

where 

and 

F 

4 

d 

dx 

dP 

 

F4 V 

dx 

(17) 

 

3 

l ( 

h a) 

 

12 

 

a 

a ; 

l 

3 

h 

h ; 

l 

( k 1) 

h 

k 

 

 

 

l 

 

 

 

3 

2 

6h 

 

 

 

 

 

(18) 

 

The flow flux, Q of the lubricant is given by 

equation (17) as 

dP 

Q 2 b 

 

F 

(19) 

4 

dx 

where F 

4 

is given by the equation(18) and b is 

the width of the bearing. In the case of circular 

plates b is equal to 2 r . 

The flux Q obtained from the equation of 

continuity is given by 

2 

Q 4r 

V 

(20) 

Now from equations (19) and (20), we obtain 

dP Vr 

(21) 

dr 

F 4 

The boundary condition for equation (21) is 

P 0 at r R 

Now using the above condition and integrating 

equation (21), we get 

P 

V 

 

 

2 2 

R r 

(22) 

2F4 

where R is the radius of the approaching 

surfaces. 

where 

F 

4 

3 

3 2 

1 ( 

h a) 

( k 1) 

h 6h 

 

 

 

12 

k 

 

The load capacity W is given by 

55


W 

 

R 

 

0 

 

2 rPdr 

(23) 

substituting equation (22) in (23), we get 

4 

R 

W V 

(24) 

F 4 

4 

The squeezing time,T is given from (24) as 

4 

R 

T 

4W 

h 

i 

 

h 

f 

F dh 

where h 

i 

is the initial film thickness and 

the final film thickness and F 

4 

is given by 

4 

(25) 

h 

f 

is 

3 

3 2 

1 ( 

h a) 

( k 1) 

h 6h 

 

F 

4 

 

 

12 

k 

 

Now the equations (24) and (25) are nondimensionalised 

as given below and numerically 

analyzed to see the effects of velocity‐slip and 

viscosity variation. Similar results can be 

expected for the case of parallel plates. 

Equations (24) and (25) are nondimensionalised 

in the following manner: 

Thus 

and 

where 

a 

a ; 

l 

h 

f 

h 

f 

 

 

l 

h 

h ; 

l 

 

; 

 

0 

V 

; V ; 

P0 

l 

 

l 

F4 

F ; 

hi 

 

h 

4 

i 

 

3 

l l 

 

12 

 

W V 

W 4 (26) 

P l F 

T 

T 

4l 

 

h 

f 

W 

 

4 

h i 1 

 

dh 

F 

1 4 

(27) 

3 

3 2 

( h a) 

( k 1) 

h 6h 

 

F 

4 

 

(28) 

k 

 

 

equations (26) and (27) are analyzed 

numerically and graphs have been plotted. 


a) Load Capacity: 

The parameters considered here are , k and 

a . So represents the slip, k represents the 

ratio of the viscosities of the peripheral layer to 

the middle layer and a be the thickness of the 

peripheral layer. represents the nondimensionalised 

slip parameter. Low values of 

indicates high slip at the surfaces and as 

increases the slip decreases and it tends to zero 

for high values of . Thus an increases in 

indicates decreasing the slip at the surfaces. 

In Figs. 3‐5, the load capacity, W is plotted w.r.t 

for various values of k treating a as constant. All 

these graphs coincides for k 1. 

It is seen from these figures that the load 

capacity increases as increases indicating 

that the load capacities decrease due to slip and 

decreases further as the slip parameter 

increases. It is also seen from these graphs that 

the load capacities increase due to increase in 

the value of k that is the peripheral layer 

viscosity i.e., the capacity increase as the 

peripheral layer viscosity increases. 

3.556 

3.048 

2.540 

2.032 

1.524 

1.016 

0.508 

__ 

w 

0.000 

0 100 200 300 400 500__ 

600 700 800 900 1000 

k=0.4 

 

k=0.5 

k=0.6 

k=0.7 

k=0.8 

k=0.9 

Fig. 3. Variation of W with for various values of k . 

56


10.08 

8.64 

7.20 

5.76 

4.32 

2.88 

1.44 

__ 

w 

0.00 

0 100 200 300 400 _ 500 600 700 800 900 1000 

 

k=1.5 k=2.0 k=2.5 

k=3.0 k=3.5 k=4.0 


10.22 

8.76 

7.30 

5.84 

4.38 

2.92 

1.46 

__ 

w 

0.00 

0 100 200 300 400 500 __ 600 700 800 900 1000 

 

k=1.5 k=2.0 k=2.5 

k=3.0 k=3.5 k=4.0 


__ 

w 

6.951 

5.958 

4.965 

3.972 

2.979 

1.986 

0.993 

0.000 

0 100 200 300 400 __ 500 600 700 800 900 1000 

_ _ 

_ 

_ a=0.01 _ a=0.02 a=0.03 _ 

a=0.04 a=0.05 a=0.06 

Fig. 6. Variation of W with for various values of a . 

3.234 

2.772 

2.310 

1.848 

1.386 

0.924 

0.462 

_ 

w 

0.000 

0.000 0.005 0.010 0.015 0.020 0.025 _ 0.030 0.035 0.040 0.045 0.050 0.055 

a 

k=0.4 k=0.7 k=1.0 

k=1.3 

k=1.7 

Fig. 7. Variation of W with a for various values of k . 

In Fig. 6, the load capacity is plotted with 

for various values of a (for k 1). It is seen 

from these figures that the load capacity 

decreases as the slip increases and they 

increase as the peripheral layer increases. 

In Fig. 7, the load capacity is plotted with a for 

various k . It is seen from the graph that for 

k 1 , it is parallel to x‐axis. That is when the 

peripheral layer viscosity is same as the middle 

layer viscosity, the effect of increase in the 

peripheral layer is nil as expected. It is also seen 

from the graph, that whenk 

1, the load 

capacity decrease as the peripheral layer 

viscosity increases i.e., as a increases. 

That is when the peripheral layer viscosity is less 

than the middle layer viscosity, the load capacity 

decreases as the thickness peripheral layer 

increases. It is also seen from the graph that when 

k 1 , the load capacity increase as the 

peripheral layer viscosity increases indicating 

that when the peripheral layer viscosity is higher 

than the middle layer, the load capacity increases 

and this increase is enhanced as the thickness 

of the peripheral layer increases. It is in 

agreement with the experimental reports 

observed by various works of Cameron etc. [17] 

that when high polymer additives are added to 

the base lubricant, the lubricant properties 

improved. The high polymer additives due to 

their affinity towards the surface attach 

themselves to the surface and form a high viscous 

layer near the surface, that is the case of k 1 , 

where we observed increase in the load capacity. 

57


In Figs. 8 and 9, the load capacity is plotted with 

k for various a . It is found these figures, that 

the load capacity increases, as k increases for 

k 1 and it is more for higher values of a as 

expected from the previous results. 

543.2 

465.6 

388.0 

310.4 

232.8 

155.2 

77.6 

_ 

w 

0.0 

0 1 2 3 4 5 6 7 8 9 10 11 

_ 

k 

_ 

_ 

_ a=0.01 a=0.02 _ 

a=0.03 _ 

a=0.04 a=0.05 a=0.06 

Fig. 8. Variation of W with k for various values of a . 

__ 

w 

5.495 

4.710 

3.925 

3.140 

2.355 

1.570 

0.785 

0.000 

0 1 2 3 4 5 6 7 8 9 10 11 12 

_ 

k _ 

_ 

_ a=0.01 _ a=0.02 _ a=0.03 

a=0.04 a=0.05 a=0.06 

Fig. 9. Variation of W with k for various values of a . 

b) Squeezing Time: 

Equation (27) is integrated numerically for 

various values of , k , a and graphs have been 

plotted for squeezing time with various values 

of these parameters in Figs. 10‐14. 

In the Figs. 10 and 11, squeezing time, T is 

plotted with for various k . It is found from 

these figures that the squeezing time increases 

as increases, that as slip parameter increase. 

It is mentioned earlier that the slip decreases as 

increases. Thus due to slip the squeezing time 

decreases and decreases further as the slip 

increases. It is also observed from these figures 

that the squeezing time is more for higher values 

of k showing that the squeezing time increases 

as the viscosity of the peripheral layer increases. 

_ 

T 

889 

762 

635 

508 

381 

254 

127 

0 

0 100 200 300 400 500__ 

600 700 800 900 1000 1100 

 

k=0.4 k=0.5 k=0.6 

k=0.7 k=0.8 k=0.9 

Fig. 10. Variation of T with for various values of k . 

_ 

T 

2548 

2184 

1820 

1456 

1092 

728 

364 

0 

0 100 200 300 400 500 _ 600 700 800 900 1000 1100 

 

k=1.5 k=2.0 k=2.5 

k=3.0 k=3.5 k=4.0 

Fig. 11. Variation of T with for various values of k . 

In Fig. 12, the squeezing time,T is plotted with 

for various values of a taking k 2. 0 . It is 

seen from these graphs that the squeezing time 

increases as increases, i.e., as the slip 

decreases and it has more value for higher 

58


values of a , showing that the squeezing time 

decreases as the slip increases. It is also 

observed that for k 1 , the squeezing time has 

more value for higher values of a , that is when 

the viscosity of the peripheral layer is more than 

the middle layer, the squeezing time increases and 

this increase is enhanced as its thickness increases. 

_ 

T 

1736 

1488 

1240 

992 

744 

496 

248 

0 

0 100 200 300 400 500 _ 600 700 800 900 1000 1100 

_ 

_ 

_ 

_ a=0.01 _ a=0.02 a=0.03 _ 

a=0.04 a=0.05 a=0.06 

Fig. 12. Variation of T with for various values of a . 

In Figs. 13 and 14, the squeezing time, T is 

plotted with a for various values of k .It is seen 

from this figure that when k 1 , the graph is 

parallel to the x‐axis, that is when the viscosity 

of the peripheral layer and middle layer are 

equal, it has no effect on squeezing time as the 

peripheral layer thickness increases. It is also 

observed that when k 1, the squeezing time 

decreases, as a increases for k 1 and 

increases for k 1 . 

1044 

928 

812 

696 

580 

464 

348 

232 

116 

_ 

T 

0 

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 

_ 

a 

k=0.4 k=0.7 k=1.0 

k=1.3 

k=1.6 

Fig. 13. Variation of T with a for various values of k . 

1372 

1176 

980 

784 

588 

392 

196 

_ 

T 

0 

0 1 2 3 4 5 6 7 8 9 10 11 12 

_ 

k _ 

_ 

_ a=0.01 a=0.02 _ 

_ a=0.03 

a=0.04 a=0.05 a=0.06 

Fig. 14. Variation of T with k for various values of a 

That is when the viscosity of the peripheral layer 

is less than the viscosity of the middle layer, the 

squeezing time decreases as its thickness 

increases. 

On the other hand, when the viscosity of the 

peripheral layer is more than the viscosity of the 

middle layer, the squeezing time increases as its 

thickness increases. It is in agreement with the 

experimental reports observed by various 

workers. 

4. CONCLUSION 

A generalized form of Reynolds equation 

applicable to fluid film lubrication was derived 

considering the variation of fluid properties, 

both across and along the film thickness, with 

velocity‐slip at the bearing surfaces. The 

effects of velocity‐slip and viscosity variation 

in squeeze film lubrication of two circular 

plates have been studied. The beneficial result 

for hydrodynamic lubrication due to the 

presence of increased viscosity near the 

bearing surface was indicated. 

However, although the effects of velocity‐slip 

at the bearing is to decrease both the frictional 

force and the load capacity, the coefficient of 

friction increases, which leads to an 

unfavorable results. For a gas‐lubricated 

hydrostatic bearing, the gas film pressure and 

load decrease with increasing molecular mean 

free path. 

59



The author would like to thank Prof J. B. Shukla, 

Indian Institute of Technology, Kanpur for his 

valuable help and encouragement during the 

completion of this study. 

Nomenclature 

h Total film thickness 

h 

f 

Final film thickness 

k Ratio of the viscosities 

l Length of the bearing 

P Hydrodynamic Pressure 

R Radius of the surfaces in case of circular 

plates 

T Squeezing time of for stiff surfaces 

V Squeeze Velocity 

W Load capacity for stiff surfaces 

Viscosity of the purely hydrodynamic zone 

References 

[1] O. Reynolds: On the theory of lubrication and its 

application to Mr. Beauchamp Tower’s 

experiment, Phil. Trans. R. Soc. London, Vol. 177, 

No. 1, pp. 157‐234, 1886. 

[2] W.F. Cope: The hydrodynamic theory of film 

lubrication, Proc. R. Soc. London Ser. A, Vol. 197, 

pp. 201‐217, 1949. 

[3] O.C. Zienkiewiez: Anote on theory of Hydrodynamic 

lubrication of parallel surface thrust 

bearings, in: Proc. 9 th Int. Conf. On Applied 

Mechanics, Brussels, University of Brussels, 

Brussels, Vol. 4, pp. 251‐258, 1957. 

[4] A. Cameron: The viscous wedge, Trans. ASME, 

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[5] D. Dowson: A generalized Reynolds equation for 

fluid film lubrication, Inst. J. Mech. Sci., Vol. 4, pp. 

159‐170, 1962. 

[6] J.B. Shukla: Theory for the squeeze film for power 

law lubricants, Trans. ASME, Paper No. 64‐lub‐4, 

1964. 

[7] J.B. Shukla, K.R. Prasad and Peeyush Chandra: 

Effects of consistency variation of power law 

lubricants in squeeze films, Wear, Vol. 76, No. 3, 

pp. 299‐319, 1982. 

[8] P. Sinha, C. Singh and K.R. Prasad: Viscosity 

variation considering cavitation in a journal 

bearing lubricant containing additives, Wear, 

Vol. 86, No. 1, pp. 43‐56, 1983. 

[9] J. Prakash: Theoritical effects of solid particles 

on the lubrication of journal bearings considering 

cavitation, Wear, Vol. 41, No. 2, pp. 233‐249, 

1977. 

[10] R. Raghavendra Rao, K.R. Prasad: Effects of 

velocity ‐ slip on the elasto – hydrodynamic 

lubrication of heavily loaded Rollers, Bulletin of 

pure and applied sciences, Vol. 20E, No. 2, pp. 

277‐295, 2001. 


velocity‐slip and viscosity variation in Rolling and 

Normal motion, Journal of Aeronautical Society 

of India, Vol. 54, No. 4, pp. 399‐407, 2002. 


velocity ‐ slip and viscosity variation for 

lubrication of Roller Bearings, Defence Science 

Journal, Vol. 53, No. 4, pp. 431‐442, 2003. 


velocity‐slip and viscosity variation on Journal 

Bearings, ANZIAM Journal, Vol. 46, pp. 143‐ 155, 

2004. 

[14] R.M. Patel, G.M. Dehari, P.A. Vadhar: Performance 

of a Magnetic Fluid Based Squeeze film between 

Transversely Rough Triangular plates, Tribology 

in Industry, Vol. 32, No. 1, pp. 33‐38, 2010. 

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Elastic Deformation Effects on the behavior of the 

Magnetic Fluid Based squeeze film between 

rotating porous circular plates with concentric 

circular pockets, Tribology in Industry, Vol. 32, 

No. 2, pp. 21‐30, 2010. 

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squeeze Film Performance in Rotating curved 

porous circular plates: The effects of Deformation 

and Surface roughness, Tribology in Industry,Vol. 

34, No. 2, pp. 57‐67, 2012. 

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a naturally permeable wall, J. Fluid Mech., Vol. 

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[18] T.C. Devenport: The Rheology of Lubricants, 

Wiley, New York, 1973. 

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studies of the oil film in lubricated point contacts, Proc. 

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60

Vol. 35, No. 1 (2013) 61‐68 



RESEARCH 

The Initial Estimate of the Useful Lifetime of the Oil 

in Diesel Engines Using Oil Analysis 

S.A. Adnani a , S.J. Hashemi b , A. Shooshtari c , M.M. Attar d 

a Department of Engineering, Hamedan Branch, Islamic Azad University, Science and Research Campus, Hamedan, Iran. 

b Petroleum University of Technology, Department of Engineering, Iran. 

c Bu‐Ali Sina University, Department of Engineering, Iran. 

d Department of Mechanics, Hamedan Branch, Islamic Azad University, Hamedan, Iran. 

Keywords: 

Diesel engine 

Oil analysis 

Oil life 

Oil properties 

Wear 


S.A. Adnani 

Department of Engineering, 

Hamedan branch, Islamic Azad 

University, Science and Research 

Campus, Hamedan, Iran 

E‐mail: ah_adnani@yahoo.com 


In this paper the Initial lifetime of the lubricating oil in 70 Diesel 

engines model E6‐350 ECONODYNE 4VH has been estimated using oil 

analysis. The engines have been installed on the super heavy vehicles. This 

method is used to change the used oil based on oil operating hours, 

odometer and taking samples before that. Next, the samples are sent to the 

laboratory for analysis and obtaining the results. In order to be able to 

determine the overall condition of the engine, we have to study various 

parameters, such as wear elements, pollutants, elements correlation 

coefficients, viscosity, base number, acid number, type and the amount of 

engine wear in the same condition of the engine model, oil consumption and 

operating condition and therefore, the useful oil life is determined (100 

hours). At last, a formula for silicon and aluminum elements is found. If the 

number of samples increases then the error rate will be reduced. So, the 

results are only based on the number of taken samples. 



Today, machines and equipment condition 

monitoring through oil analysis as a method of 

effective maintenance program is known. 

Nevertheless, the application of this technology to 

the various types of industry and user equipment 

is still very broad to a certain extent [1]. 

The best performance engine oil is important in 

two aspects: 1) the economy 2) in terms of its 

effect on engine life. The economic aspects 

should be emphasized the probability that the 

engine oil should be changed sooner is very high 

and it is not economically. On the other hand, it 

may be late to oil change because this is the 

probable cause engine damage and wear. So, the 

use of oil analysis is the best method for 

achieving this goal. Among the important factors 

that could affect the oil life reduction as follows: 

Improper storage and contamination 

before use, 

Incorrect oil selection and mixed oils that 

are not compatible with each other (for 

example, when overflow), 

61

S.A. Adnani et al., Tribology in Industry Vol. 35, No. 1 (2013) 61‐68 

Lack of adequate consumer appliances (air 

filter, oil filter and etc.), 

Fuel, water and dust contaminations, 

Not regulated engine, 

Existence of excessive metal particles in oil, 

Oil clean reduction in sensitive mechanical 

systems (turbines, compressors and 

hydraulic) [2]. 

2. ENGINES SPECIFICATIONS 

Model: E6‐350 ECONODYNE 4VH 

Horsepower maximum BHP@1800 rpm: 

350 (261 Kw) 

Compression Ratio (pressure@1000 rpm): 

15:1(31.72 bar) 

Bore & Stroke: 123.8 mm × 152.4 mm 

Cylinder: 6 

Year: 1990 

Manufactured by Mack Co. in U.S.A [3]. 

3. EXPERIMENTAL WORK 

Sampling procedure has been done when 

changing the engine oil and after laboratory tests, 

test results have been evaluated (see Table 1). 

Table 1. The number of engines and samples. 

Tested engines 

70 

Table 2. The new oil properties [4]. 

Oil name 

Manufacturer 

Performance grade(API) 

Grade (SAE) 

T.B.N (mgKOH/g) 

T.A.N (mgKOH/g) 

Viscosity index(Min) 

Viscosity at 40 ° C (cSt) 

Viscosity at 100 ° C (cSt) 

Open flash point (° C) 

Oil samples number 

160 

Sepahan 

Generator speedy 

CD/SF 

40 

14.5 

1.1 

99 

163.91 

15.84 

241 

Sampling has been done so that each engine has 

been sampled in two or three times. Since all 

engines have the same oil, model and work 

conditions, so variables are low. If oil samples 

increases, errors in results will be less. In addition 

to the regular test and verification of new oil, 

specifications in terms of quality and standards of 

the new oil have been tested in accordance with 

Table 2. The results are based on the number of 

oil samples in accordance with Table 1. 

4. OIL USEFUL LIFE ESTIMATION 

For engine oil life estimation, items should 

include physical and chemical properties of oil, 

such as acid number, base number, viscosity, oil 

pollution, and wear parameters can be analyzed 

at various functions. Then we should compare 

the figures obtained from physical and chemical 

properties of oil. As we know, the new oil 

properties go away from its ideal operating 

conditions and incurred loss. So in first step, we 

evaluate the wear and pollutants elements that 

play important role in oil life reduction. 

4.1 Wear elements 

Metallic particles in engine oil are mainly due to 

wear. If wear rate arises then the rate of metal 

in the oil will be higher. The most wear 

elements and their origins are according to 

Table 3 [5]: 

Table 3. Wear elements and origins [2,6]. 

Wear 

elements 

Fe 

Cr 

Al 

Cu 

Pb 

Origins 

Cylinder bush – Piston rings –Pins – 

Cylinder block – Nuts 

Rings – Liners – Valves – Cooling 

system 

Cylinder – Piston – Blowers 

Piston pin bushes – Crank case – Oil 

cooler 

Bearings 

4.2 Determination of maximum concentration 

limit for wear elements 

To determine the limit of wear, pollution and 

silicon boundary between normal and abnormal 

wear on engine components, the formula for the 

standard deviation formula (1) can be used: 

σ = S.D. = (1) 

Where σ, the standard deviation values, Xi, wear 

and pollutant elements, μ, wear and pollutant 

element values, N, the number of values [1]. 

According to oil analysis results, we can have 

the data on Table 4. 

62


Table 4. Maximum concentration limits for different 

elements of wear in engines (ppm) [7]. 

4.3 Correlation coefficient 

One of the basic definitions of statistics is 

correlation between two variables. Dependence 

between two variables is defining correlation. 

The correlation coefficient changes between ‐1 

and 1. Relationship between two variables can 

be positive or negative. However, a closer 

correlation between the two variables, then the 

dependency rate is higher [8]. Here, by using 

Pearson's correlation and statistical analysis 

software (s.p.s.s), we can calculate correlation 

coefficients between wear and pollutant 

elements. The results can be seen in Table 5. 

Table 5. Correlation coefficient between wear elements. 

Fe 

Al 

Cr 

Cu 

Pb 

Si 

Elements Si Pb Cu Cr Al Fe 

Average 8.1 2.8 2.7 2.8 3.2 26 

Standard deviation 5.6 2 2.4 2.4 1.8 16 

Maximum 

concentration 

limits 

14 5 5 5.5 5 42 

Fe 

1 

0.626 

0.474 

0.369 

0.541 

0.526 

Al 

0.626 

1 

0.632 

0.334 

0.439 

0.869 

Cr 

0.474 

0.632 

1 

0.217 

0.442 

0.544 

Cu 

0.369 

0.334 

0.217 

1 

0.274 

0.208 

Pb 

0.541 

0.439 

0.442 

0.274 

1 

0.367 

Si 

0.526 

0.869 

0.544 

0.208 

0.367 

1 

According to Table 5, aluminum and silicon 

have the most correlation, while silicon and 

copper have the lowest correlation. In fact, with 

the arrival of silicon in oil, erosion effects occur 

in parts which are made of aluminum, such as 

pistons. According to the correlation rate, 

effects of erosion vary in different parts of the 

engine. Next, a higher correlation is between 

aluminum and chromium. In fact, wear in each 

of these two elements has a direct effect on 

other wear. For example, if silicon entrance 

causes erosion on the pistons then the rings that 

made of chrome and the piston grooves will 

wear. Other elements that are correlated 

influence on erosion of engine components. 

Since the aluminum and silicon have the most 

correlation between each other, therefore, 

according to Fig. 1 and equation (2) the exact 

relationship between them is found. 

Fig. 1. Silicon and aluminum profile (ppm). 

Y = 0.2733X + 1.0379 (2) 

Here, X and Y are amount of silicon and 

aluminum in ppm, respectively. 

So if x = 14 ppm then y = 4.86 ppm. So the 

results in Table 4 are correct. 

4.4 Engine wear process 

According to (Fig. 2) and plotted points, operating 

hours by increasing iron concentration was 

increased. Points that have gone beyond the 

maximum concentration limit for iron element 

(42 ppm) will appear up to 100 hours. So this time 

is the warning border for iron. 

Fig. 2. Operating hours and iron wear debris 

concentration. 

Figure 3 shows that up to 100 hours, the copper 

has exceeded its maximum limit (5 ppm). So, 

100 hours is determined as a warning border 

for it. According to scatter of points in Fig. 4, 

with increasing operating hours, chromium 

concentration has also increased. Since up to 

100 hours points that have gone beyond the 

limit 5.5 ppm are strongly, so, 100 hours is 

determined as a warning border for chromium. 

63


Fig. 3. Operating hours and copper wear debris 


Fig. 5. Operating hours and aluminum wear debris 


Fig. 6. Operating hours and lead wear debris 


Fig. 4. Operating hours and chromium wear debris 


Figure 5 is related to the aluminum element. 

With increasing operating hours, aluminum 

concentration has also increased. Thus, 

according to the plotted points, up to 100 hours, 

the limit points of these elements have exceeded 

from 5 ppm. So, for this element, 100 hours is a 

warning border too. Figure 6 is related to lead 

element. With increasing operating hours, lead 

concentration has also increased. According to 

the plotted points, up to 100 hours, the limit 

points of these elements have exceeded from 5 

ppm. So, for this element, 100 hours is a warning 

border. But beside the wear elements, pollutants 

also play a main role in loss of life and oil 

properties. Based on oil analysis, the only 

pollutant in oil samples is silicon that is in the 

form of dust into the oil. Therefore, according to 

(Fig. 7) we investigate this pollutant. 

Figure 7 shows the limit points of these 

elements have exceeded from 14 ppm. So, for 

this pollutant, 100 hours is a warning border. 

Oil quality and its life are affected by silicon. 

Fig. 7. Operating hours and silicon wear debris 


The analysis conducted can be summarized 

bordered warned on wear elements as 

presented in Table 6. 

64


Table 6. Warning border for wear elements. 

Elements and pollutants 

Fe 

Al 

Cr 

Cu 

Pb 

Si 

Warning border 

100 

100 

100 

100 

100 

100 

Here, wear elements of oil were studied. But in 

addition to these cases, the properties of the oil 

play main role in oil life. That is why in this step, 

we will study the physical and chemical 

properties of the oil. 

investigate the viscosity of the oil in different hours 

and conditions. According to (Fig. 9), the viscosity of 

oil declined from 164 cSt. In normal conditions, i.e. 

without pollutants, due to the increase in oil hour, 

viscosity trend has become decreased and 

approximately remains at 150 cSt. But the greatest 

loss of viscosity is after 120 hours. In (Fig. 10), the 

viscosity of the oil due to the presence of the 

contaminant is 150 cSt. Up to 200 hours, maximum 

viscosity loss is seen. So, 120 hours is determined as 

warning border for viscosity. 

4.5 Wear index 

One of the most important factors in engine 

wear is wear index of iron particles in oil so 

called P.Q. [2]. According to (Fig. 8), with 

increasing operating hours, iron particles have 

also increased. According to focal points, up to 

150 hours, points are separated from each other 

and even we see points that reached to 250 

ppm. This matter indicates sudden increase in 

the number of iron particles. So, 150 hours is 

determined as an warning border for P.Q, So at 

this step, we investigate other oil properties. 

Fig. 9. Operating hours and viscosity without 

pollution. 

Fig. 10. Operating hours and viscosity with pollution. 

4.7 Base number 

Fig. 8. The variation of wear rate on engines. 

Base number is a kind of oil properties. By 

reducing the oil base number, oil ability in the face 

of acid entering from combustion get weak. It 

indicates the need to replace or add new oil 

[1,2,10,11]. On the base of tested samples, oil base 

numbers in different status were evaluated and 

the results are in accordance with Fig. 11. 

4.6 Viscosity 

Viscosity as a one of oil properties, affect on 

reduction of bearings friction and oil film thickness. 

Therefore, evaluation of viscosity in oil analysis 

program is sensitive. Any change in the viscosity of 

the lubricant indicates oil degradation, the presence 

of thermal stresses in the oil and oxidation [1,9]. So 

after analyzing the wear index, we desire to 

Fig. 11. Operating hours and base number. 

65


According to the (Fig. 11), standard limit of base 

number is 14.5 mg (KOH) but maximum loss is 7.5 

mg (KOH) and it is happened on 160 hours. It is 

very natural because with increasing operating 

hours, oil properties and its life losses. So by 

increasing operating hours, the oil life decreased 

as a result of oil properties. So, 120 hours is 

determined as a warning border for base number. 

4.8 Acid number 

Acid number is a kind of oil properties that is used 

for industrial oil. Acid number is used for 

measuring of oil acidity. Increasing acid value 

indicates the end of the useful life of oil and its 

replacement is necessary. Acid value higher than 

4 mg (KOH) is highly corrosive and bearings and 

other metal substances can be invaded [1,2,11]. 

According to (Fig. 12), with increasing operating 

hours, the amount of acid number has also 

increased. According to focal points, up to 180 

hours, the acid number has exceeded its limit (4 

mg (KOH)). So, 180 hours is determined as a 

warning border for acid number. 

Table 7. Warning border for oil properties. 

Oil properties 

Base number 

Acid number 

Viscosity 

P.Q 

Warning boundary 

120 hours 

180 hours 

120 hours 

150 hours 

4.9 The engine oil life in kilometer 

Now we intend to equivalency the oil by other 

factors such as the amount of kilometer unit, 

kilometers were recorded at each sampling. 

According to the Figs. 13 to 15, we can also 

estimate oil life in hour and kilometer. Since the 

operation of heavy vehicles in terms of workplace 

is different, so we classify vehicles into 

three categories respectively, "Tandem", 

"Keshande" and "Jean Paul". 

4.10 "Tandem" engine 

Figure 13 shows the correlation between 

operating hours and the distance traveled by 

the vehicle "Tandem". This vehicles move in a 

limited area. As in previous discussions of the 

oil life was 100 hours, now, with respect to (Fig. 

13), we want to get the maximum distance 

traveled by vehicle after 100 hours. So 100 

hours is equal to 3000 km. 

Fig. 12. Operating hours and acid number. 

So, the properties of the oil and its 

corresponding warning limits can be 

summarized as described in Table 7. 

At this stage of the investigation carried out on 

erosion, pollution, and finally the physical and 

chemical properties of oil and according to the 

results in Table 6 and 7, and based on the 

number of samples, look carefully and errors, 

initial engine oil life is estimated 100 hours. 

Based on figures obtained after 100 hours, we 

can see the presence of contaminants, the 

sudden drop in oil properties and wear on 

engine parts and it is necessary to oil change. 

Fig. 13. Operating hours and distance. 

4.11 "Keshande" engine 

According to data from oil analysis, Fig. 14 

shows the relationship between distance 

traveled by these vehicles and operating 

hours. It is worth mentioning that these 

vehicles are more mobile and have road 

traffic. Therefore, according to the 100 hours, 

the maximum distance traveled by these 

vehicles is 5,900 km. 

66


Oil laboratory equipment error 

Error in the type of oil used in an engine oil 

(two types) 


4.12 "Jean paul" engine 

Based on data from oil analysis, Fig. 15 is obtained. 

This vehicles move in a limited area. Based on 

points in (Fig. 15), for 100 hours, maximum 

distance traveled by these vehicles is 900 km. 


Correspond to the useful life of oil per hour with 

maximum distance traveled by all vehicles; we 

can summarize the results presented in Table 8. 

Table 8. Primary and useful life of the oil in all vehicles. 

Vehicle 

Jean paul 

Tandem 

Keshande 

5. CONCLUSION 

Operating hours 

100 

100 

100 

Km 

900 

3000 

5900 

As was mentioned to achieve the oil life should 

be a lot of things are considered, including the 

following: 

Wear elements 

Pollutants 

Physical and chemical properties of oil 

Sampling error 

Reading operating hours indicator error 

Based on the above, we investigated wear 

elements, pollutants, their allowable limitations 

and correlation coefficients. The highest 

correlation was between silicon and aluminum 

element. We introduced a relation between 

them and we got a formula about it. According 

to the resulting curves, we noticed that in what 

time abnormal abrasion of engine parts occurs. 

Therefore, we chose warning boundary that will 

have minimal wear on engine parts. The 

physical and chemical properties of the oil 

studied and according to the figures the 

warning boundary (100 hours) is determined in 

order to prevent sudden and sharp changes in 

oil properties. Finally, considering the results of 

wear elements, silicon and physical and 

chemical oil properties, the useful life of oil in 

hour and kilometer is determined. It is 

important that the results are only based on oil 

samples taken from the vehicles. So if we 

increase the number of oil samples, surely, 

better results can be obtained. That is why a 

title as "Early Life" for the oil life is selected. If, 

we provide the ideal conditions for engines, oil 

life of 100 hours goes beyond. These conditions 

are as follows: 

Replace air filters (every 4 months), 

Choosing the right oil, 

Choosing the right fuel, 

Proper using in accordance with the 

recommendations of vehicle manufacturers 

Check to make sure no oil pollutants 

including aerosols, fuel, water and silicon 

into engine, 

To ensure the quality and authenticity of 

replacement parts for engines. 

6. REFERENCES 

[1] A. Masoudi: Oil Analysis Basics, Doost Mehraban, 

Tehran, 2011. 

[2] A.T. Khouzestan: Machinery condition 

monitoring, Series of technology articles, Vol. 2, 

No. 28, pp.17‐20, 2009. 

[3] M.T.S. Manual: Mack Engine Tune up 

Specifications, Service, Pennsylvania, 1990. 

[4] Oil Analysis Services Reports. 

67


[5] G. Hamidi: Condition Monitoring Services Using 

Oil Analysis, Wear Elements and a Case Study for 

Wearing Iron, in: 6 rd Condition Monitoring and 

Fault Diagnosis Conference, 28.02.2012, Tehran, 

Iran, pp. 1‐12. 

[6] B. Nedic, S. Peric, M. Vuruna: Monitoring physical 

and chemical characteristics oil for lubrication, 

Tribology in Industry, Vol. 31, No. 3&4, pp. 59‐ 

61, 2009. 

[7] H. Kaleli, E. Yildirim: Determination of oil drain 

period in naval ship Diesel engine, Tribology in 


[8] M. Najibi: Correlation Coefficients and Calculations, 

Statistical Science Group, Tehran, 2009. 

[9] A. Toms, L. Toms: Oil Analysis and Condition 

Monitoring, in: Chemistry and Technology of 

Lubricants, Springer, Netherlands, pp.459‐495, 

2010. 

[10] S. Peric, B. Nedic: Monitoring lubricant 

performance in field application, Tribology in 


[11] A.T. Khouzestan: Machinery condition 

monitoring, Series of technology articles, 

Vol.1, No.17, pp. 4‐6, 2009. 

68

Vol. 35, No. 1 (2013) 69‐73 



RESEARCH 

Investigation of Wear Coefficient of Manganese 

Phosphate Coated Tool Steel 

S. Ilaiyavel a , A. Venkatesan a 

a Mechanical Engineering Department, Sri Venkateswara College of Engineering, Sriperumbudur, Tamil Nadu, India. 

Keywords: 

Wear Testing 

Sliding Wear 

Lubricated Wear including Scuffing 

Lubricant additives 

Boundary Lubrication 

Surface analysis 


Sivakumaran Ilaiyavel 

Mechanical Engineering 

Department, Sri Venkateswara 

College of Engineering, 

Sriperumbudur, Tamil Nadu, India 

E‐mail: ilaiyavel@svce.ac.in 


In recent years the properties of the coating in terms of wear resistance is 

of paramount importance in order to prevent the formation of severe 

damages. In this study, Wear coefficient of uncoated, Manganese 

Phosphate coated, Manganese Phosphate coated with oil lubricant, Heat 

treated Manganese Phosphate coated with oil lubricant on AISI D2 steels 

was investigated using Archard’s equation. The wear tests were performed 

in a pin on disk apparatus as per ASTM G‐99 Standard. The volumetric 

wear loss and wear coefficient were evaluated through pin on disc test 

using a sliding velocity of 3.0 m/s under normal load of 40 N and 

controlled condition of temperature and humidity. Based on the results of 

the wear test, the Heat treated Manganese Phosphate with oil lubricant 

exhibited the lowest average wear coefficient and the lowest wear loss 

under 40 N load. 



The Principal aim of conversion coating is confer 

anti‐welding characteristics although it may also 

cause a slight increase in the surface hardness 

[1]. High carbon high chromium steels are used 

in application requiring tremendous wear 

resistance in tool and die making industries. 

Phosphating is chemical conversion treatments 

which produce a porous surface layer of 

crystalline phosphate [2]. This process relating a 

reaction between a solution and a metal surface 

such that the coating derives partly from the 

solution and partly from the substrate [3]. 

Phosphate coatings are normally formed by 

immersing iron into an aqueous solution of 

phosphoric acid and manganese carbonate [4]. 

Manganese Phosphate coating are produced by 

chemical conversion and the main component of 

the film is hureaulite (Mn Fe) 5 .H 2 (PO 4 ) 2 . Due to 

its economy, speed of operation, ability to afford 

excellent corrosion resistance, wear resistance, 

adhesion and lubricative properties, it plays a 

significant role in the industries [5‐9]. To 

understand the wear properties of different 

types of coating wear test are carried out with 

suitable wear testing techniques. The pin on disc 

test is the established method universally used 

for wear experiment. To assist the measurement 

the pin is usually the wearing member that has 

lesser hardness. Wear coefficient is superior 

parameter though wear loss and Friction 

69

S. Ilaiyavel and A. Venkatesan, Tribology in Industry Vol. 35, No. 1 (2013) 69‐73 

coefficient are frequently used for studying the 

wear characteristics of test specimen. It is so 

because the wear coefficient takes into account 

not only the wear rate, but also the applied load, 

and the hardness of the pin [10]. L.J. Yang [11] 

proposed new moving pin technique that is 

allowed to move across most of the disc space 

during testing at the same time maintaining the 

constant speed by varying the distance and 

rotational speed. The wear coefficient values 

obtained is not varying with the disc materials 

used. The variation is about 4% and 17% of the 

mean value obtained from the moving pin and 

stationary pin tests, respectively. Therefore 

more reliable wear coefficient values are 

obtained from the moving pin test than from the 

stationary pin test. Reasonably, the moving pin 

technique has given to a higher wear rate and a 

slightly higher wear coefficient. This is due to a 

enhanced work‐hardening effect with the use of 

more virgin disc surface area in the wear testing. 

C.S. Ramesh [12] investigated on wear 

coefficient of Al6061–TiO2 composites. Based on 

the result Al 6061–TiO2 composites exhibited 

higher hardness, lower wear coefficient when 

compared with matrix alloy. M.A. Chowdhury et 

al [13] observed that the presence of normal 

load and sliding velocity affects the co effect of 

friction considerably. The values of friction 

coefficient decrease with the increase in normal 

load for copper‐copper, copper‐brass, brassbrass 

and brass‐copper pairs. V. Bria et al [14] 

explained that the role of aramids fibers in the 

composite on increasing the wear resistance of 

materials while the graphite particles appearing 

from carbon fibers breaking acts as dry 

lubricant. The aim of this paper is to find the 

volumetric wear loss and wear coefficient of 

uncoated, Manganese Phosphate coated, 

Manganese Phosphate coated with oil lubricant 

and heat treated Manganese Phosphate coating 

with oil lubricant on AISI D2 steel substrate. 

2. EXPERIMENTAL PROCEDURE 

2.1 Materials 

The High carbon and high chromium tool steel 

was used as substrates. The chemical 

composition of the materials is given in Table1. 

2.2 Specimen 

The specification, initial hardness values and 

surface roughness for the pin and disc are listed 

in Table 2. The four types of pins were prepared 

such as uncoated, Manganese Phosphate coated, 

Manganese Phosphate coated with oil lubricant 

and heat treated Manganese Phosphate coating 

with oil lubricant for the comparison of the wear 

coefficient parameter. 

2.3 Manganese Phosphate Coating 

The Manganese Phosphatation consists of 

three basic sequences are cleaning, refining 

and phosphating. The refining bath consisting 

of Mn Phosphate solutions favours the deposit 

of a fine layout of metallic salts onto the steel 

surface. S. Ilaiyavel et al [15] explained the 

details of Manganese Phosphate coating 

procedure used in this present study. The 

coating thickness is around 1.5 to 2 g/m 2 by an 

immersion process. The coatings produced are 

single phase and the only coating forming 

mineral is hurealite i.e. mixed iron‐manganese 

orthophosphate, having the chemical formula 

as: ‐(Mn,Fe) 3 (PO 4 ) 2 .2(Mn,Fe)HPO 4 .4H 2 O. 

Table 1. Chemical composition of the material [wt. %] analysed by optical emission vacuum spark spectrometer. 

Elements C Si Mn Cr Ni Mo V Ti S P Fe 

Percentage 1.50 0.41 0.74 12.01 0.01 1.01 0.27 0.01 0.03 0.03 Balance 

Table 2. Specification, hardness and surface finish for pin and disc. 

Description Material 

Surface Roughness 

Hardness HRc 

(Ra) Microns 

Pin (8 mm dia, 15 mm long) D2 Steel (As received) 20 0.1 

Disc (Dia 60 mm, Thickness 10mm) D2 Steel Hardened and Tempered 60 0.1 

70


71 

2.4 Heat treatment after the Coating 

The coated steel substrate is heated slowly up to 

450 0 C and kept around 15 mins duration. It is 

then cooled in the furnace to reach room 

temperature. The steel substrate surface is not 

affected by the heating and furnace cooling. 

2.5 Lubrication 

In this experiment 20W40 oil is used as a 

lubricant. Table 4 shows the properties of the 

lubricant. After coating prior to wear testing 

both coated and heat treated and only coated 

pins are dipped into oil lubricant for around 15 

to 20 mins at room temperature. Lubricating oil 

creates a thin separating film between surfaces 

of adjacent moving parts [16] .This minimizes 

direct contact between them, decreases heat 

caused by friction and reduces wear. 

Table 4. Properties of lubricant. 

Kinematic Viscosity at 100 0 C 13.5‐15.5 

Viscosity Index, Min. 110 

Flash point (COC), o C Min. 200 

Pour point, o C Max. (‐)21 

causes the heavy deformation at higher sliding 

distance. Manganese Phosphate coated pins shows 

slight higher volumetric loss after 600 m sliding 

distance, because of partly removal of coating after 

longer sliding distances at constant load 40 N. Both 

Manganese Phosphate coated with oil lubricant and 

Heat treated Manganese Phosphate coated with oil 

lubricant show lowest volumetric loss, because of 

very less coefficient of friction achieved by the 

presences of oil lubricant. S. Ilaiyavel et al [8] 

expressed that Manganese Phosphate coated with 

oil lubricant pins show very low coefficient of 

friction about 0.1 to 0.2. Heat treated Manganese 

Phosphate coated with oil lubricant pins show the 

same coefficient of friction even at higher the loads 

and longer sliding distances. Because of heat 

treatment more micro cracks present in the crystal 

which are perpendicular to the substrate surface. 

Fig. 2 shows micro graph of heat treated Manganese 

Phoshate coated AISI D2 steel. These cracks occur 

due to the loss of water and when the dehydration 

is completed, the maximum oil retaining capacity 

also improved. 

2.6 Wear testing 

Wear performance of materials are commonly 

obtained from testing carried out in pin‐on‐disk 

equipment to ASTM G99 standard procedure. It 

gives a laboratory standard method to carry out 

sliding and abrasion wear tests. The tests were 

carried out under 40 N applied load and for 

sliding velocity of 3.0 m/s for a constant sliding 

radius of 15 mm. During testing the tangential 

force was measured by a set of load cell and 

monitored by Computerised data acquisition 

system. In all the cases the friction coefficient 

and volumetric wear loss of the pin were 

estimated by taking three pins average value. 

Fig. 1. Volumetric wear loss vs sliding distance at 

velocity of 3.0 m/s. 

3. RESULTS AND DISCUSSION 

3.1 Volumetric Wear loss 

The variation of volumetric wear loss with sliding 

distance is shown in Fig. 1. With increase in sliding 

distances there is higher volumetric loss for 

uncoated pins, at longer sliding distance higher rise 

in temperature on both the sliding surfaces. This 

Fig. 2. Micro graph of heat treated manganese 

phosphate coated AISI D2 steel.


3.2 Wear Coefficient 

Steady state wear was proposed by Archard V= 

KsPL/3H where V is the volumetric loss of 

material after sliding for a distance L and load P 

normal to the wear surface. H is the Brinell 

hardness number of the pin while Ks a 

dimensionless standard wear coefficient. For 

known values of V, P, L and H the standard wear 

coefficient can be calculated from the equation 

Ks=3HV/PL. Volumetric wear loss can be 

calculated from the weight loss W and the 

density. L.J. Yang [10] expressed that the higher 

initial running – in wear rate, has a higher value 

initially in the transient wear regime and will 

reach a steady – state value when the wear rate 

become constant. Figure 3 shows the variation 

of wear coefficient with sliding distance. It is 

observed that wear coefficient decreased with 

increased sliding distance. However under the 

same conditions Heat treated Manganese 

Phosphate coated with oil lubricant shows 

lowest wear coefficient. The major reason is the 

lowest volumetric loss is recorded. The 

annealing treatment increase the micro cracking 

and also increases oil retention. Oil can react at 

the grain boundaries of the Heat treated coating 

to form a beneficial adherent film, increasing the 

wear resistance under oil lubricating conditions. 

P.H. Hivart et al [17] also expressed that the 

dehydrated and transformed new coating 

surface has a better reactivity towards 

lubrication than the initial Huralite. 

phosphate coated with oil lubricant pins were 

examined under 40 N loads at sliding velocity of 

3.0 m/s using pin on disk apparatus and the 

results are summarized as follows: 

Increased sliding distance resulted in 

higher volumetric loss and lowered the 

wear coefficient for, un coated, Manganese 

phosphate coated, Manganese phosphate 

coated with oil lubricant and Heat treated 

Manganese phosphate coated with oil 

lubricant pins. 

Heat treated Manganese phosphate coated 

with oil lubricant pins exhibited the lower 

coefficient friction and lower wear 

coefficient as compared with uncoated, 

Manganese phosphate coated, Manganese 

phosphate coated with oil lubricant pins. 

The heat treatment may increase the 

quantity of oil retained through the micro 

cracking phenomenon which increases oil 

retention. Oil can react at the grain 

boundaries of the Heat treated coating to 

form a beneficial adherent film, which 

increase the wear resistance under oil 

lubricating conditions resulting lower the 

wear coefficient. 


The Authors are thankful to Sri Venkateswara 

college of Engineering for providing the 

continuous support. 

REFERENCES 

Fig. 3. Wear coefficient vs sliding distance at velocity 

of 3.0 m/s. 


The Wear coefficient of uncoated, Manganese 

phosphate coated, Manganese phosphate coated 

with oil lubricant and Heat treated Manganese 

[1] J.C. Gregory: Chemical conversion coatings of 

metals to resist scuffing and wear, Tribol. int., Vol. 

105, pp.105‐112, 1978. 

[2] J. Perry, T.S. Eyre: The effect of Phosphating on 

the Friction and wear properties of Grey cast iron, 

Wear, Vol. 43, No. 2, pp. 185‐197, 1977. 

[3] Jose Daniel B. De Mello, Henara L. Costa, Roberto 

Binder: Friction and wear behavior of steamoxidized 

sintered iron components coated with 

manganese Phosphate, Wear, Vol. 263, No. 1‐6, pp. 

842‐848, 2007. 

[4] Simon C. Tung, Donald J. Smolenski, SU‐Chee S. 

Wang: Determination of differences in tribological 

behavior and surface Morphology between 

Electrodeposited and Traditional Phosphate 

72


73 

Coatings, Thin Solid Films, Vol. 200, No. 2, pp. 

247‐261, 1991. 

[5] S. Jaganathan, T.S.N Sankara Narayanan, K. 

Ravichandran, S. Rajeswari: Formation of Zinc 

phosphate coating by anodic electrochemical 

treatment, Surface and Coatings Technology, Vol. 

200, No. 20‐21, pp. 6014‐6021, 2006. 

[6] D.B. Freeman: Phosphating and Metal 

Pretreatment: A Guide to Modern Process and 

Practice, Industrial Press Inc., New York, 1986. 

[7] W. Raush: The Phosphating of Metals, Finishing 

Publication Ltd, London, 1990. 

[8] S. Ilaiyavel, A. Venkatesan, N. Nallusamy, T. 

Sornakumar: Wear characteristics of Manganese 

Phosphate coating with oil lubricant, Applied 

Mechanic and Materials, Vol. 110‐116, pp. 616‐ 

620, 2012. 

[9] T.S.N. Sankara Narayanan: Surface Pretreatment by 

Phosphate conversion coatings, Advanced 

Materials Science, Vol. 9, No. 2, pp. 130‐177, 2005. 

[10] L.J. Yang: Wear coefficient equation for 

aluminium–based matrix composites against steel 

disc, Wear, Vol. 253, pp. 579‐592, 2003. 

[11] L.J. Yang: Pin‐on‐disc wear testing of tungsten 

carbide with a new moving pin technique, Wear, 

Vol. 225–229, pp. 557–562, 1999. 

[12] C.S. Ramesh, A.R. Anwar Khan, N. Ravikumar, P. 

Saravanprabhu: Prediction of wear coefficient o 

Al6061‐Tio2 Composites, Wear, Vol. 259, pp. 602‐ 

608, 2005. 

[13] M.A. Chowdhury, D.M. Nuruzzaman, A.H. Mia, 

M.L. Rahaman: Friction Coefficient of Different 

Material Pairs Under Different Normal Loads and 

Sliding Velocities, Tribology in Industry, Vol. 34, 

No. 1, pp. 18‐23, 2012 . 

[14] V. Bria, D. Dima, G. Andrei, I.G. Birsan, A. 

Circiumaru: Tribological and Wear Properties of 

Multi‐Layered Materials, Tribology in Industry, 

Vol. 33, No. 3, pp. 104‐109, 2011. 

[15] S. Ilaiiyavel, A. Venkatesan: Experimental 

investigation of manganese phosphate coated AISI 

D2 steel, Int. j. of Pre. Eng and Manu, Vol. 13, pp. 

581‐586, 2012. 

[16] S. Ilaiyavel, A. Venkatesan: The wear 

characteristics of heat treated Manganese 

Phosphate coating applied to AISI D2 steel with 

oil lubricant, Tribology in Industry, Vol. 34, No. 4, 

pp. 247‐254, 2012. 

[17] Ph. Hivart, B. Hauw, J. Crampon, J.P. Bricout: 

Annealing improvement of tribological properties 

of manganese phosphate coatings, Wear, Vol. 219, 

No. 2, pp. 195‐204, 1998.

Vol. 35, No. 1 (2013) 74‐83 



RESEARCH 

The Effect of Compression Ring Profile on the 

Friction Force in an Internal Combustion Engine 

A. Sonthalia a , C.R. Kumar a 

a VIT University, India. 

Keywords: 

Friction 

Ring profile design 

Simulation 

Floating liner method 


C. Ramesh Kumar 

VIT University, India 

E‐mail: crameshkumar@vit.ac.in 


In an internal combustion engine piston, piston ring and cylinder are the 

most important assembly for transmitting the forces produced by the 

combustion process. The friction between piston ring pack and cylinder 

accounts for major portion of friction in an internal combustion engine and 

it also significantly affects the mechanical efficiency of the engine. In the 

piston ring pack, friction is mainly due to the compression ring, especially at 

the top dead centre and bottom dead centre where boundary lubrication 

exists. This paper provides a detailed study on the effect of ring profile on 

ring friction using MATLAB code. Three different ring profiles were selected 

and analysed for lubricant film thickness, ring twist angle, ring friction and 

friction coefficient. Out of these three, friction force and friction coefficient of 

one ring profile design was found minimum. The ring design with minimum 

friction force and friction coefficient was manufactured and assembled in a 

low speed SI engine. The engine liner was modified to float and friction of 

the ring was studied using motoring test method. The experimental results 

were compared with the simulation result, it was found that simulation 

result was in agreement with the experimental result. 



Reducing fuel consumption in IC engine is 

important from viewpoints of both effective use 

of oil resources and prevention of global 

warming. For realizing a better heat balance in 

engines it is desirable that not only combustion 

efficiency but also mechanical efficiency is 

improved. Reduction of friction loss is a proper 

measure of the improvement in mechanical 

efficiency as pointed out by many engine 

developers and researchers [1]. 30‐50 % of total 

friction losses in an internal combustion engine 

occur at the interfaces of piston cylinder, piston 

ring‐cylinder, and piston‐piston ring. Even small 

reduction in friction at piston ring‐cylinder liner 

interface may contribute in significant fuel 

saving and reduction in emissions [2,3]. The 

piston rings move freely in its grooves and these 

movements depends on the forces acting on the 

piston ring system, like, the ring tension due to 

the placement of the piston ring in cylinder, the 

gas pressure forces due to combustion and 

blow‐by, the hydrodynamic force due to 

lubricant film, the inertia forces due to the ring 

mass, the engine speed and asperity contact 

74

A. Sonthalia and C.R. Kumar, Tribology in Industry Vol. 35, No. 1 (2013) 74‐83 

forces between the ring and cylinder walls [4]. 

The study of piston ring motion leads to a better 

understanding of these mechanisms and many 

researchers have attempted to understand the 

same through experimental studies. For 

example, the investigation of the friction force 

exerting on the piston ring using floating liner 

test rig [5], and the investigation of oil film 

thickness was done using ultraviolet light [6] 

and using differential voltage drop method [7]. 

Similarly, piston ring motions have also been 

studied, through simulation method [6‐10]. The 

model used by these researchers were similar 

for each mechanism, but with different 

procedures and assumptions. However, they did 

not revealed the detailed steps of simulation. 

The present work aims to analytically study the 

effect of piston ring profile on the friction force. 

Three different ring profiles were analyzed for 

lubricant film thickness, ring twist angle, ring 

friction and friction coefficient using the MATLAB 

code. The ring with the minimum friction force 

was manufactured and tested using non firing 

floating liner method. The friction force 

computed from the theoretical analysis was 

compared with the experimental results. 

2. THEORETICAL ANALYSIS OF PISTON RING 

Initially, the dimensionless parameters that 

characterize the operation of a piston ring and 

its friction were identified. Next an analytical 

model describing the dynamics surrounding 

ring’s performance was developed. Using this 

model in numerical simulation, the operational 

behavior of ring was predicted. The in‐cylinder 

pressure which is one of the inputs for the 

MATLAB code was simulated using the first law 

of thermodynamics. 

2.1 Assumptions 

focus in only on interaction between ring, the 

piston and the wall. The ring is much wider in its 

relaxed state but when installed in the cylinder 

the ring was squeezed to fit in the cylinder. 

The ring deflects inwards and it exerts a local 

elastic pressure on the cylinder wall. In this study 

it is assumed that the ring contracts and expands 

equally round the circumference. It was assumed 

that the ring rests on a single point, as shown in 

Fig. 1, with a rolling contact on the topland or the 

bottomland of the groove. The angle of tilt is used 

to determine the contact point. It is assumed that 

the contact points seal the pressure on one side 

from the other so that there is a step change in 

the pressure across this contact point. Due to 

reciprocating motion of the piston in the cylinder, 

the velocity of the piston is maximum at the midstroke 

and zero at the dead centers. 

The change in piston speed changes the 

lubrication regime in the cylinder, which in turn 

changes the friction between the ring and the 

liner during the entire stroke of the piston. The 

frictional patterns which the piston ring would 

experience can be classified into different modes 

based on this lubrication regime [11]. In this 

study hydrodynamic lubrication was assumed i.e. 

the ring always rides on full fluid film. 

The friction force peaks at the midpoint, 

where the speed is at its maximum, i.e. it is 

proportional to the instantaneous piston 

speed in mid‐stroke. If the engine speed or oil 

viscosity is high, a thick oil film is formed that 

would not be completely squeezed out even at 

dead centers where the piston velocity falls to 

zero [11]. Also, the effect of temperature on oil 

viscosity was not considered. Using these 

assumptions a model for theoretical analysis 

of piston rings was made using cosine method 

[12] and the governing equations were solved 

by bisection method. 

The following assumptions were considered for 

the analytical model: 

Side thrust force is the largest cause of friction in 

an internal combustion engine, this force is 

transmitted to the cylinder wall on the thrust 

side, resulting in noticeable wear on the wall 

near the top dead centre position of first ring. 

This force is neglected in this work since our 

Fig. 1. Ring pivot position. 

75


2.2 The governing equations 

The Reynolds’ equation [13], for a fully 

lubricated gap; which indicates the relationship 

the pressure and film shape as a function of 

viscosity and velocity, can be used, which is 

given by (1). 

3 P P 3 

 

h h 6U dh 6V dh 12 

dh 

(1) 

x x y 

 

y 

 

dx dy dt 

Assuming axis symmetry along the cylinder axis, 

at each instant of time [1] can be written in one 

dimensional form for piston and ring liner 

contact: 

3 P 

dh dh 

h 

6U 12 

(2) 

x 

x 

dx dt 

To produce pressure in the oil film, the film 

thickness under the ring changes with respect to 

time, is given by (3) 

h( x, 

t) 

hp ( x) 

hr 

( t) 

a( 

t). 

x (3) 

Using classical slit flow theory, the shear stress 

between two parallel plates is given by Eq.4 

h P U 

Shear 

(4) 

2 x 

h 

The piston ring in the piston fits loosely in the 

ring groove, thus leaving room axially and 

behind the ring. Due to this the ring can move 

axially in its groove, from topland to bottomland, 

depending upon operating conditions [12]. It can 

thus be assumed that ring operates in two 

modes (Fig. 2) it is either on topland or 

bottomland. The ring can be considered a free 

body which is influenced by outside forces: On 

the front surface, there is a normal oil pressure 

distributed over the axial width, which produces 

a normal force as well as a moment on the ring 

surface. When the ring is resting on the 

bottomland, the pressure above and behind the 

ring is assumed to be the combustion chamber 

pressure (Fig. 3). However, the pressure below 

is the crankcase pressure and the combustion 

pressure before the contact point thus a step in 

pressure can be seen in Fig. 3. 

direction. The inertial properties of the ring 

exerts a d’ Alembert force axially on the ring, as 

it is moving along with the piston. 

Fig. 2. Ring modes. 

Fig. 3. Pressure distributions about ring. 

Composite Secant method [12] was used to find 

the ring friction, ring twist angle and the film 

height. The above equations were normalized, 

and then a MATLAB code was written to find the 

effects of ring movement in the cylinder liner. 

The normalized equations are given below. 

The dimensionless radial force acting on the ring 

is given by [5]. 

2 

2 2 

P 6U 

L1 1 L2 

1 z2 sin z2 

1 

1 

2 

 

2 

Pe 

hr' L 

 

e 

1 z 

 

PWh 2 4 4 

2 

sec 

sin 

z2 

 

2cosz2 2 C2z2 

F 

 

 

3 2 

 

2 2 2 

1 z1 sin z1 sec 


z1 

 

2cosz 

2 

12C1z1 

z1 

4 4 3 2 

 

(5) 

The dimensionless moment equation for the oil 

is given by [6]. 

On the other hand when the ring is resting on 

topland the pressure step is on the top surface 

and the pressure behind and below the ring is 

assumed to be same as that of the crankcase. The 

elastic properties of the ring also exert an 

effective elastic pressure on the ring in radial 

76


F 

2 ' 

' 

PB 1 

P EBW 

1 

2 2 

' 1 

2 

4PW 

e 

P 6 

0 e 

PR 

e cyl 

2 

BY 

ULB 

1 1 sinz1 L2 

sinz2 

 

2 ' 

PW PW 

e 

 

 

m e 

h 

 

h 

 

L 

r 

z 

 

1 1 z2 

3 sec 

sec 

 

sin z1 z1 sin 2z1 

z 

 

 

2 4 

1 

 

 

 

 

 

3 

3 L2 

sec 

sec 

sin z2 z2 sin 2z2 

z L 

 

2 1 

2 4 

 

 

 

2 

2 

12U 

L L 2 2 

1 

L 1 z sin z 

2 

2 

'2 2 

PW h L 

e 

h 

r 1 z 

2 4 4 

1 2 2 2 2 

2 

sec 


z 

 

2 

2cosz2 

2 Cz 

2 2 

3 

 

 

2 

 

2 2 

 

2 

z1 z1 z 

 

1 

2cosz1 

2 

 

1 4 4 3 

 

2 

1 sin sec sin 

z 

 

12U 

L 1 1 z sin 2z 

 

 

3 

3 

1 1 1 

1 1 

2 

 

2 '2 3 

PW 

e 

h 

 

hr 

z 

1 6 16 

Cz 

z1 2sec 

sin 2z1 

cos2z1 

 

z1cos z1sin 

z1 

8 3 

16 

3 

2 3 

1 L 

1 1 2 

2 

sin 2 

2 

cos2z1 C1 

 

 

3 

z 

L 

 

 

2 1 

z z z z 

 

8 2 6 16 

z2 2sec 

sin 2z2 

cos2z2 

 

z2cos z2 sin z2 

 

8 3 

16 

2 

z2 z 

2 

cos2z2 C2 

 

8 2 

The dimensionless axial force is given by [7]. 

' 

PBh 

1 

L1sin 

z1 L2sin 

z2 

F3 1 

' ' ' 

2UW 

 

 

 

 

0 Wz1hr 

Wz2hr 

3UL 

sec 

sec 

UWz h 

1 

' sin z1z1 sin 2z1 

1 r 2 4 

3UL 

sec 

sec 

UWz h 

YBh 

U 

2 

' sin z2 z2 sin 2z2 

2 r 2 4 

 

 

 

 

 

 

 

 

(6) 

(7) 

1 

C 

2 

z sin z cos z sec 

sin z 2 cos z 

(9) 

2 2 2 2 2 

2 

Ph W L sin z cos z L sin z cos z 

 

6U 

2 2z1 2z2 

sec 

 

L1sin z1 2 cosz1 2 2 

2 

 

3z 

3z 

2 

1 r 

1 1 1 2 2 2 

L sin z 2 

cosz 

 

1 2 

2.3 Simulation Algorithm 

(10) 

A step wise procedure was used for simulating 

the piston and piston ring mechanisms at any 

instant of time during the engine cycle. The ring 

inclination angle α 1 was assumed initially. α 1 was 

substituted into the force equation (F 1 (5)) and 

the film thickness h r1 was calculated by the 

bisection method. α 1 and h r1 were then 

substituted into the moment equation (F 2 (6)) 

and the residue of F 2 (α 1 , h r1 ) was calculated. 

The algorithm then assumes another α 2 , and 

solves for h r2 , α 2 and h r2 were then substituted 

into F 2 (6), and the residue of F 2 (α 2 , h r2 ) was 

calculated. If the residues were of opposite sign, 

a solution exists between α 1 and α 2 . For each 

crank angle, the values of the state variables α, h r 

and the friction was calculated. 

2.4 Input for the Program 

Simulated cylinder pressure with respect to 

crank angle was used as input. Three ring 

profiles were considered, as shown in figure 4 

and their profiles were normalized to form two 

secant curves joined back to back. This shape 

approximates the ring more closely and its 

associated oil pressure distribution also 

resembles the actual moment distribution. The 

physical and operating properties that are 

required are given in Table 1. The ring profile 

properties are given in Table 2. 

C1, C2 and sec is given by Eq. 8, 9 and 10 

respectively. 

Pz1h 1 

C1 r 

z1 

sin z1cos 

z1 

6U 

L1 

2 

(8) 

sec 

sin z 2 cos z 

 

1 1 

 

Fig. 4. Different ring profiles. 

77


Table 1. Input parameter for simulation program. 

Parameters 

Connecting Rod Length 

Crank Radius 

Ring Axial Width 

Ring Radial Width 

Piston Bore Diameter 

Value 

127 mm 

28.7 mm 

1.63mm 

2.63 mm 

70 mm 

Oil Density 881.5 kg/m 3 

Oil Viscosity 

0.008736 Pa‐s 

Ring Density 7900 kg/m 3 

Ring Modulus of Elasticity 

2.05 e11 Pa 

Ring Elastic Pressure 93539 N/m 2 

Engine Speed 

Compression Ratio 6.67 

Table 2. Ring profile property. 

3000 rpm 

Property Type I Type II Type III 

Ring Surface Crest 0.5 cm 0.5 cm 0.5 cm 

Position 

Ring Surface Upper 1.63 µm 3.26 µm 6.52 µm 

Profile Height 

Ring Surface Lower 

Profile Height 

1.63 µm 3.26 µm 6.52 µm 

3. EXPERIMENTAL SETUP 

A single cylinder 4‐stroke spark ignition engine 

was coupled to a DC motor cum generator on a 

test rig. Engine specification is given in Table 3. 

sketch shown in Fig. 5 describes the setup of the 

test rig onto which the engine and motor are 

being mounted. 

Fig. 5. Test setup. 

A simplified floating liner was designed and 

fabricated for this experiment. The liner was 

constrained to move only in the vertical 

direction using the mounting guide studs. A 

piezoelectric force sensor was mounted on a 

support stand and it was attached to the liner as 

shown in Fig. 6. When the piston is moving 

towards TDC, the rubbing friction between the 

piston and liner imparts a force which tends to 

move the liner along with the piston in the 

vertical direction. The force sensor restricts the 

movement of the liner and converts the 

movement into voltage signals. Using a charge 

amplifier, cathode ray oscilloscope (CRO) and 

data acquisition system, the voltage signal was 

transferred to a personal computer. A crank 

angle encoder was used to measure the crank 

angle, which gives voltage peaks when the 

piston reaches the TDC. 

Table 3. Engine specification. 

Parameters 

Make 

Type 

Engine Capacity 

Bore 

Value 

Greaves MK‐25 

Stroke 

66.7 mm 

Compression Ratio 6.67 

Maximum Power 

Maximum Torque 

Cooling System 

Lubrication 

4‐stroke, side valve 

256 cc 

70 mm 

2.5 kW @ 3000 rpm 

14Nm @ 1700 rpm 

Forced Air Cooling 

Splash type 

Ammeter and voltmeter were used for power 

measurements. The prime mover, a DC shunt 

motor, was chosen in order to keep the speed 

constant and precise without fluctuation. Using a 

Ward Leonard system the motor was connected 

and speed was varied from zero to 2000 rpm. 

Using diodes AC power was converted to DC 

power to run the prime mover. The tests were 

performed using non firing condition. A simple 

Fig. 6. Test setup. 


The piston position, velocity and acceleration 

needed for ring dynamics model were found 

using the piston kinematics equations (Appendix 

I) and were plotted as shown in Figs. 7‐9. 

Simulated cylinder pressure is shown in figure 

10. The piston axial position is considered with 

78


respect to Bottom Dead Centre (BDC) where 

piston’s axial position is zero. 

The simulated result for non‐dimensional ring 

twist angle is shown in Fig. 11. The positive 

values of the twist angle refer to the ring’s back 

(inner diameter) moving down and the ring’s 

face moving up. The largest twist will take place 

just after Top Dead Centre (TDC) following 

compression, since it is necessary to generate 

the lift force as the piston speed is low at the 

TDC. It can be seen that Type 3 has the smallest 

ring twist angle, and Type 1 having the largest 

ring twist angle. 

Fig. 7. Piston axial location. 

Fig. 11. Ring twist angle. 

Fig. 8. Piston axial speed. 

Fig. 9. Piston acceleration. 

Fig. 10. Simulated cylinder pressure. 

Figure 12 shows the non‐dimensional lubricant 

film thickness with respect to crank angle. The 

compression and power stroke has lower film 

thickness contributing to increase friction. The 

exhaust stroke is similar to the intake stroke, as 

the cylinder gas pressure is closer to 

atmospheric pressure. At both the dead center 

the film is very thin, especially at the TDC after 

compression stroke; this may result in heavy 

wear of the cylinder wall due to surface to 

surface contact. Type 1 ring profile has highest 

oil film thickness and type 3 the lowest. 

In order to validate the film thickness values 

obtained through simulation, data collected from 

literature was utilized, as shown in Fig. 13. 

Takiguchi et al. [8] conducted experiments on a 

four‐ stroke engine and found the film thickness. 

The same engine parameters were used as input 

for the MATLAB code to find the oil film thickness. 

Since some data were not available, few 

assumptions were made as inputs of the program, 

like the ring radial width which was assumed to be 

0.4 times the bore [15], ring material properties 

where the ring density was 7600 kg/m 3 and 

modulus of elasticity was taken to be 1.2e +11 . The 

output of the simulation code is almost matching 

with the work done by Takiguchi et al. [8]. The 

79


small variations could be due to the assumptions 

that were made for the input. 

Fig. 12. Lubricant film thickness. 

friction force. At TDC the film thickness for type 3 

profile is found to be lowest. It is expected that 

the friction due to lubricant viscosity was 

minimum which is in line with [14]. 

The total force acting between the ring and the 

liner is shown in figure 15, it comprises of the 

friction force acting because of the lubricant oil 

viscosity and the combustion mixture in the 

axial direction, and the ring elastic pressure 

force acting in radial direction. Type 3 ring 

designs has minimum total force acting on it, 

followed by type 2 with type 1 having the 

highest force acting on it at the TDC after 

compression. 

From Fig. 16 friction coefficient was found 

minimum for type 3 rings, which is 1.82e ‐2 and it 

was found to be maximum for type 1 ring (2.8e ‐ 

2). The reason for minimum friction coefficient 

for type 3 ring was due to the minimum force 

acting between the ring and the cylinder liner. 

The total force can be reduced by using tribopads 

inserted into the piston and tribo‐inserts 

inserted into the cylinder liner [16]. 

Fig. 13. Comparison of film thickness. 

Fig. 14. Total force. 

Fig. 14. Friction force. 

Figure 14 shows the friction force acting between 

the ring and the cylinder liner, it can be seen that 

friction is maximum at point of maximum 

cylinder pressure. It can be attributed to the fact 

that there is an increase in asperity contact near 

the top and bottom dead center due to the mixed 

lubrication regime, whereas hydrodynamic 

lubrication exists for most part of the stroke. The 

friction was found maximum for type 1 ring 

profile, on the other hand type 3 has minimum 

Fig. 16. Friction coefficient. 

80


Type 3 ring profiles were then manufactured 

and the original compression ring was replaced 

by type 3 ring profile in the engine piston. 

Experiments were performed on the engine 

using motored floating liner method. Figure 17 

and 18 shows the friction force acting on the 

liner. From the experimental result it can be 

seen that with the increase in speed, the friction 

force reduces, because of the increase in film 

thickness and better lubrication. On the other 

hand, as it was assumed to be hydrodynamic 

lubrication, the friction force obtained through 

simulation increases with the increase in speed. 

A high friction force was observed for simulated 

curve during power stroke. This is attributed to 

the fact that the engine was motored during 

experiments and no combustion took place, as a 

result the friction force during power stroke is 

less. The difference in the force during the 

combustion period was found to be 156.23 N 

and 267.72 N for 1500 rpm and 2000 rpm 

respectively. The force was calculated by 

subtracting the area under the curve of friction 

force acquired from the tests from the simulated 

friction force. 

Fig. 17. Friction force at 1500 rpm. 

5. CONCLUSION 

In this study a ring dynamics model was 

simulated for the analysis of ring film thickness, 

the ring twist angles, the friction force and the 

friction coefficient using Secant method, for the 

compression ring. Three different ring profiles 

were chosen for the analysis purpose. Results 

indicate that hydrodynamic lubrication occurs 

for most part of the stroke except at the dead 

center where mixed lubrication regime was 

found due to reduced film thickness resulting in 

increased friction force. 

Type 3 ring profiles was found to have the 

lowest friction coefficient and the lowest friction 

force, this would result in increase in fuel 

economy since the work done by the engine 

against the friction force would be reduced. On 

the other hand the oil film thickness was found 

to be minimum for type 3 profile, this could be a 

cause for concern since there can be direct 

contact between the ring and the cylinder liner 

thus increasing the wear rate of the liner. 

Type 3 ring profile was manufactured and 

experimental work was carried out on the 

engine using floating liner method. The result 

from the experiment and the simulation were 

found to have a similar trend. The oil film 

thickness was validated by comparing the 

output of the MATLAB code (using the same data 

as given in literature) with literature and it was 

found to be in situ. This shows that whenever a 

change in ring design is needed this model can 

be used before going for actual manufacturing of 

the ring, thus saving time and expenses involved 

in ring manufacturing. 

Further improvements can be done in this model 

by taking into consideration blow‐by and finding 

its effect on hydrocarbon emissions and also 

finding the ring movement in the piston groove. 

REFERENCES 

Fig. 18. Friction force at 2000 rpm. 

[1] Y. Wakuri, M. Soejima, Y. Ejima, T. Hamatake, T. 

Kitahara: Studies on friction characteristics of 

reciprocating engine, SAE 952471, 1995. 

[2] R.C. Singh, R. Chaudhary, R.K. Pandey, S. Maji: 

Experimental Studies for the role of piston rings’ 

face profile on performance of a diesel engine 

fueled with diesel and jatropha based biodiesel, 

81


Journal of Scientific and Industrial Research, Vol. 

71, pp. 57‐62, 2012. 

[3] Y. Wakuri, T. Hamatake, M. Soejima, T. Kitahara: 

Piston ring friction in internal combustion 

engines, Tribology International, Vol. 25, No. 5, 

pp. 299‐308, 1992. 

[4] K. Wannatong, S. Chanchaona, S. Sanitjai: 

Simulation algorithm for piston ring dynamics, 

Simulation Modelling Practice and Theory, Vol. 

16, pp. 127–146, 2008. 

[5] Bryan O’Rourke, Rudolf Stanglmaier, Donald 

Radford: Development of a floating ‐ liner engine 

for improving the mechanical efficiency of high 

performance engines, SAE 2006‐01‐3636, 2006. 

[6] Kwang‐soo Kim, Thom Godward, Masaaki 

Takiguchi, & Shuma Aoki: Part 2: The effects of 

lubricating oil film thickness distribution on 

gasoline engine piston friction, SAE 2007‐01‐ 

1247, 2007. 

[7] Philipe Saad, Lloyd Kamo, Milad Mekari, Walter 

Bryzik, Victor Wong, Nicolas Dmitrichenko, 

Rudolf Mnatsakanov: Modeling and measurement 

of tribological parameters between piston rings 

and liner in turbocharged diesel engine, SAE 

2007‐01‐1440, 2007. 

[8] Y. Harigaya, M. Suzuki, M. Takiguchi: Analysis of 

oil film thickness on a piston ring of diesel engine: 

effect of oil film temperature, J. Eng. Gas Turbines 

Power Vol. 125, pp. 596–603, 2003. 

[9] T. Eduardo, & F.E.B. Nigro: Piston Ring Pack and 

Cylinder Wear Modeling, SAE 2001‐01‐0572, 2001. 

[10] T. Tian: Modelling the performance of the piston ringpack 

in internal combustion engines, PhD Thesis, 

Massachusetts Institute of Technology, 1997. 

[11] Sung‐Woo Cho, Sang Min Choi, Choong‐Sik Bae: 

Frictional modes of barrel shaped piston rings 

under flooded condition, Tribology International, 

Vol. 33, No. 8, pp. 545‐551, 2000. 

[12] C.T. Chang: Piston Ring Friction, Master of 

Science Thesis, Massachusetts Institute of 

Technology, 1982. 

[13] H. Rahnejat, P.C. Mishra, P.D. King: Tribology of 

the ring–bore conjunction subject to a mixed 

regime of lubrication, Proc. IMechE, Part C: J. 

Mechanical Engineering Science, Vol. 223, pp. 

987‐998, 2009. 

[14] V.D’ Agostino, P. Maresca, A. Senatore: 

Theoretical analysis for friction losses 

minimization in piston rings, Proceedings of the 

International Conference on Tribology, Parma, 

Italy, 20‐22.09.2006. 

[15] A. Kolchin, V. Demidov: Design of Automotive 

Engines, MIR Publishers, Moscow, 1984. 

[16] R. Pesic, A. Davinic, S. Veinovic: Methods of 

tribological improves and testing of piston 

engines, compressors and pumps, Tribology In 

Industry, Vol. 27, No. 1&2, pp. 38‐47, 2005. 

NOMENCLATURE 

η dynamic Viscosity of oil (Ns/m 2 ) 

L 1 width of ring above profile crest (m) 

ρ ring density (kg/m 3 ) 

L 2 width of ring below profile crest (m) 

constant of integration 

ΔP pressure difference across the ring (N/m 2 ) 

characteristic ring tilt angle 

P e ring elastic pressure (N/m 2 ) 

a ring inclination angle (°) 

R cyl cylinder bore radius (m) 

a’ normalized ring tilt angle 

R crank radius (m) 

a o ’ normalized maximum ring tilt angle 

Al 

V 

B 

W 

x 

h 

Y 

h p 

Z 1 

h r 

h r ’ 

Z 2 

normalized piston speed 

connecting rod length (m) 

circumferential ring speed 

ring radial width (m) 

ring axial width (m) 

characteristic film height 

axial coordinate between ring and wall 

local film height (m) 

piston axial location (m) 

ring profile height (m) 

transformed coordinate at the top edge of the ring 

ring reference distance (m) 

normalized ring reference film height 

transformed coordinate at the bottom edge of 

the ring 

APPENDIX I 

The piston acceleration, speed and piston 

position is calculated using the below equations 

Position of piston 

Y R cos 

Al cos 

Al R 

Velocity of the piston 

V DthetaRsin 

DphiAl sin 

 

82


Acceleration of piston 

A 

2 

DDthetaR sin 

Dtheta R cos 

 

DDphiAl sin 

 

Where 

1 sin 


R 

 

Al 

2 

Dphi Al 

cos 

 

R cos 

Dphi Dtheta Al cos 

 

2 2 sin 

 

DDtheta Dtheta R cos 

Dtheta R Al sin 

 

 

cos 

 

R cos 

2 2 R sin 

DDphi DDtheta Dphi tan 

Dtheta 

Al cos 

Al cos 

Dtheta 

Rpm 

9.54928 

83

Vol. 35. No. 1 (2013) 84‐94 



RESEARCH 

Effect of Contact Temperature Rise During Sliding on 

the Wear Resistance of TiNi Shape Memory Alloys 

S.K. Roy Chowdhury a , K. Malhotra a , H. Padmawar a 

a Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302, India. 

Keywords: 

TiNi alloy 

Wear resistance 

Phase transformation 

Contact temperature 

Pseudoelasticity 

Corresponding Author: 

S.K. Roy Chowdhury 

Professor 


Engineering, Indian Institute of 

Technology, Kharagpur 721 302, 

India 

E‐mail: skrc@mech.iitkgp.ernet.in 


The high wear resistance of TiNi shape memory alloys has generally been 

attributed to its pseudoelastic nature. In the present work the hardening 

effect due to its phase transformation from martensite to austenite due to 

frictional heating during sliding has been considered. Based on existing 

constitutive models that represent the experimental results of TiNi shape 

memory alloys a theoretical model of the dependence of wear‐resistance on 

the contact temperature rise has been developed. 

The analysis was further extended to include the operating and surface 

roughness parameters. The model essentially indicates that for these alloys 

wear decreases with the rise in contact temperature over a wide range of 

load, speed and surface roughness combination during sliding. This means 

that the wear resistance of these alloys results from the very cause that is 

normally responsible for the increased wear and seizure of common 

engineering materials. 

Preliminary wear tests were carried out with TiNi alloys at varying ambient 

temperature and varying load‐speed combinations and the results agree 

well with the theoretical predictions. 



Titanium‐Nickel (TiNi) alloys are widely known 

for their shape memory effect and 

pseudoelasticity. These effects are due to the fact 

that these alloys can exist in two different 

temperature‐dependent crystal structures: 

martensite at low temperatures and austenite at 

high temperatures. When a TiNi alloy in 

martensite phase is heated the phase changes to 

austenite and if it is cooled after complete 

transformation it reverts back to martensite phase 

with some hysteresis. The phase transformation 

can also be induced by change in stress level and 

the initial phase can be recovered with the 

removal of the stress. Here a decrease in stress is 

equivalent to increase in temperature resulting in 

nucleation of martensite. This gives rise to 

basically three different forms from the practical 

application point of view: martensite, stress 

induced martensite and austenite. In the 

martensitic form the material is soft and ductile 

and can be easily deformed. In the stress induced 

martensitic form it is highly elastic and it can 

return to its original shape on unloading even 

after substantial deformation. This form is known 

84

S.K. Roy Chowdhury et al., Tribology in Industry Vol. 35, No. 1 (2013) 84‐94 

as pseudoelasticity. In the austenitic form it is 

strong and hard [1,2]. 

A good deal of research has been carried out on 

the shape memory effect of TiNi alloys and their 

applications [3‐8]. These alloys have also been 

found to be extremely resistant to wear in sliding, 

fatigue, abrasion and erosion modes [9‐14]. Some 

Ti based alloys have also been widely used in 

biomedical engineering [15]. The high wear 

resistance of TiNi alloys has generally been 

attributed not to the increase in hardness but to 

the pseudoelastic nature of the alloys. The 

argument here is that in the pseudoelastic state, 

contact between the sliding pair would be largely 

elastic and wear is likely to be small since in 

pseudoelastcity recoverable strain may reach up 

to 8% or more [16]. Li [10] proposed that the 

excellent wear resistance of these alloys is 

influenced by their hardness too. According to this 

proposition wear resistance is partly influenced by 

pseudoelasticity and partly by hardness 

depending on the material state. High hardness 

contributes to wear resistance when the 

pseudoelasticity is of low order. Some authors 

attributed the wear resistance of TiNi alloys to 

causes other than pseudoelasticity, for example, 

work hardening [17], erosion resistance [18]. 

Abedini et al. [19] observed decrease in wear with 

the increase in temperature and attributed this 

effect to both pseudoelasticity and higher strength 

of the alloy in the austenitic state at higher 

temperatures. Some attempts have been made to 

develop a model that shows increase in hardness 

of these alloys with the increase in temperature in 

micro level [20]. 

However the effect of frictional heat generated 

at the contact area between a sliding pair on the 

wear resistance of these alloys has not been 

considered hitherto. The present work explores 

the possibility of attributing wear resistance of 

TiNi alloys to the hardening effect due to phase 

transformation from martensite to austenite 

due to contact temperature rise during sliding. 

The deformation during wear process is mostly 

not recoverable and therefore it is likely that the 

wear resistance would be more influenced by 

hardness than pseudoelasticity that occurs in a 

narrow temperature zone near the austenitic 

transformation temperature. In tribological 

contacts the temperature rise due to frictional 

heat generated at the peaks of the asperities can 

be of very high order of magnitude and under 

normal circumstances for most engineering 

materials this has an adverse effect on the life of 

rubbing components due to increased wear and 

friction. If, however, the wear resistance of near 

equi‐atomic TiNi alloys is indeed due to 

hardening during the martensite to austenite 

phase transformation due to frictional heat then 

this would mean that the wear resistance of 

these alloys results from the very cause that is 

normally responsible for the increased wear and 

seizure of engineering components. 

The paper attempts to develop a simple 

theoretical model to relate contact temperature 

rise during sliding and wear resistance of TiNi 

alloys in the macroscopic level. Some 

elementary experiments were also carried out 

in support of the theoretical predictions. 

2. A THEORETICAL MODEL OF TEMPERATURE 

DEPENDENCE OF HARDNESS AND WEAR 

RESISTANCE OF TiNi ALLOYS 

In order to develop a theoretical model we first 

consider a 1‐D constitutive model that 

represents the existing experimental results of 

TiNi shape memory alloys. Several such models 

exist and they all basically couple a 

phenomenological macro‐scale constitutive law 

relating stress to strain temperature and phase 

fraction with a kinetic law that describes the 

evolution of the phase fraction as a function of 

stress and temperature [8,21,22]. Here we use 

the model proposed by Liang and Rogers [8]. 

In a typical martensitic phase change as a 

function of temperature there are four 

important temperatures: martensitic start 

temperature (M s ) , martensitic finish 

temperature (M f ), austenitic start temperature 

(A s ) and austenitic finish temperature (A f ). Liang 

and Rogers [8] described the martensitic 

fraction () vs. temperature (T) relation as a 

cosine function for a shape memory alloy where 

A s >M s and the equation describing the phase 

transformation is given as: 

1 

[cos{ a 

A( 

T AS 

)} 1] (1) 

A 

2 

M 

where is the martensite volume fraction, T is 

the alloy specimen temperature and the 

constant a is given by: 

A 

85


aA 

/( Af 

As 

) 

(2) 

Since we are interested in the hardening effect 

of the shape memory alloys with rise in contact 

temperature only the phase transformation 

between martensite to austenite needs to be 

considered. It has been shown [8] that the phase 

changes temperatures are linearly related to the 

applied stress and within the range between 

austenite start and finish temperatures we may 

write: 

 

0 

A0 As 

(3) 

C 

where A 0 s is the austenite start temperatures in 

stress free state and C is a constant. Combining 

equations (1) and (3) we have: 

1 

' o 

[cos( aA( 

T As 

)) 1] 

(4) 

M A 2 

C 

Here a 

A 

will change to: 

0 0 

a C 

/( A A ) 

A 

0 

A 

f 

being the austenite finish temperature in 

stress free state. Since in the present case we 

consider that the phase transformation will be 

complete when all the martensite changes into 

austenite we may set to zero and this gives: 

M A 

f 

o 

' C( 

T As 

) (5) 

A 

a 

M 

In many cases hardness is taken as three times 

the yield stress and therefore the temperature 

dependent hardness variation during 

martensite to austenite transformation can be 

given by: 

Here C, 

H 

M A 

A and 

o 

s 

A 

 

3C[ 

T A 

a 

A 

s 

o 

s 

] 

(6) 

a 

A 

are all constants and 

therefore hardness varies only with 

temperature. In general in sliding wear 

hardness plays an important role and this is 

given by Archard’s wear law: 

Wx 

V K 

(7) 

w 

H 

M A 

Here K w is the wear coefficient, W is the load, x 

the sliding distance and H the hardness of the 

softer of the two rubbing materials. Combining 

equations (6) and (7) a simple temperature 

dependent wear equation can be written as: 

o 

where B ( As 

) . 

a 

K 

wWx 

V (8) 

3C( 

T B) 

Defining non‐dimensional wear volume 

_ 

non‐dimensional temperature T as: 

_ 

V 

V 

Wx 

CB 

A 

and 

_ 

T 

T 

B 

_ 

V and 

we may rewrite equation (8) in nondimensional 

form as: 

_ 

V 

 

K 

w 

3 _ 

( T 1) 

(9) 

Variation of non‐dimensional wear with nondimensional 

temperature with the experimental 

value of K w from section‐5(b) is shown in Fig. 1. 

Fig. 1. Variation of non‐dimensional wear with nondimensional 

temperature with the average K 

w value of 

2.5E‐5 from the experimental results in section 5 (b). 

Clearly this shows decrease in wear with 

increase in temperature and this supports the 

argument that with the increase in contact 

temperature is likely to cause the austenitic 

phase transformation of TiNi alloy leading to 

increased wear resistance due to increase in 

hardness. 

86


3. INFLUENCE OF TRIBOLOGICAL OPERATING 

AND MATERIAL PARMETERS THAT 

AFFECT CONTACT TEMPERATURE RISE 

The total contact temperature at the sliding 

interface is the sum of the bulk temperature 

T bulk and the contact temperature rise . 

T=+T bulk (10) 

In general T bulk may be taken as atmospheric 

temperature and therefore the effective 

temperature at the sliding interface is mainly 

dominated by the contact temperature rise . 

The contact temperature rise between sliding 

bodies has been researched widely ever since 

Block [23] and Jaeger [24] reported their 

pioneering works on flash temperature in 1937 

and 1942 respectively. Subsequently, Archard 

[25] proposed the following set of handy 

equations to predict the mean contact 

temperature rise for different speed and 

deformation conditions: 

 

 

 

 

mhe 

mhp 

mle 

mlp 

* 

WvE 

 

0.41 

 

KcR 

 

H 

0.8 

Kc 

 

3 

4 

2 

3 

W E v 

0.142 

1 

3 

KR 

1 

2 

W vH 

0.125 

K 

 

1 

2 

W 

1 

2 

1 

4 

* 1/3 

v 

1 

2 

 

1 

2 

(11) 

Here mhe, mhp ,mle and mlp indicate mean high 

speed elastic, mean high speed plastic, mean low 

speed elastic and mean low speed plastic 

respectively and v is the sliding speed, E * the 

equivalent elastic modulus, K the thermal 

conductivity, ρ the density, c specific heat and R 

the protrusion radius. These equations are widely 

used even today for their simplicity even though 

they essentially refer to continuous area of contact 

and disregard the discrete nature of rough 

surfaces. The deformation conditions for rough 

surfaces with typically Gaussian distribution of 

surface heights are ideally determined using the 

plasticity index (ψ) given by: 

* 

E 

(12) 

H r 

where the equivalent elasticity modulus E * is 

2 

2 

given by 

1 1 1 

, σ is the standard 

* 

E E1 

E2 

deviation of the surface height distribution and r 

is the asperity radius. A contact is considered to 

be elastic if ψ< 0.6 and plastic if ψ > 1.5. Speed 

criterion (L) is given by: 

L = vaρc/2K (13) 

where a is the contact radius. A contact is 

considered to be fast if L > 5 and slow if L < 0.5. 

However, since Archard’s contact temperature 

formulations are essentially for single contact 

area we consider the bulk deformation and 

therefore we would consider the deformation to 

be plastic if P/ (πa 2 ) > H. Taking T≈ and 

combining equations (8) and (11) we may write 

the wear volumes for different speed and 

deformation conditions in terms of operating and 

material parameters in non‐dimensional form as: 

_ 

V 

_ 

V 

_ 

V 

_ 

V 

mhe 

mpe 

mle 

mlp 

 

 

 

 

3(0.41 

W 

_ 1/ 4 

3(0.8 

H 

K 

w 

_ 1/ 2 

3(0.142 

E 

3(0.125 

H 

K 

K 

w 

_ 1/ 4 

W 

w 

_ 2/ 3 _ 2/ 3 

K 

w 

_ 1/ 

2 

_ 1/ 2 

v 

e 

W 

1) 

_ 1/ 2 

p 

_ 1/ 2 

W 

v 

_ 

v 

e 

_ 

1) 

1) 

v p 1) 

(14) 

_ 

where non‐dimensional wear volume V , nondimensional 

load W , non‐dimensional 

_ 

velocity 

in elastic case 

_ 

v , non‐dimensional velocity in 

e 

_ 

plastic case v 

p 

, non‐dimensional elastic 

_ 

modulus E and non‐dimensional hardness 

_ 

H are given by : 

_ 

_ 

VCB K _ 

w 

V ; W ; v 

2 v ; 

Wx BCR 

e 

 

* 

( BK / E R) 

_ 

_ * 

v v E 

; E 

p 

( BK / HR) 

BC 

; 

_ 

H 

H 

BC 

87


Non-dimensional Wear volume 




1 

0.8 

0.6 

0.4 

0.2 

W 22.510 3 

W 4510 3 

W 67.510 3 

0 

20 40 60 80 100 

-3 

Non-dimensional velocity v×10 

 

6 

4 

2 

(a) 

W 22.510 3 

W 4510 3 

W 67.510 3 

0 

60 80 100 120 140 160 180 200 

1.5 

1 

0.5 

Non-dimensional velocity v 

 

(b) 

W 1210 2 

W 2410 2 

W 3610 2 

0 

20 40 60 80 100 

-3 

Non-dimensional velocity v×10 

 

(c) 

2 

1.5 

1 

0.5 

W 3 

W 6 

W 9 

0 

50 100 150 200 

Non-dimensional velocity v 

 

(d) 

Fig. 2. Plots of non‐dimensional wear against nondimensional 

velocity for (a)High Speed Elastic (b) 

High Speed Plastic (c) Low Speed Elastic (d) Low 

Speed plastic contacts over a range of nondimensional 

load with experimental value of 

K =2.5E‐5 and =0.3, E =555 and H =6. 

w 

Non‐dimensional wear calculated with the 

average value of experimental wear coefficient 

from section‐5(b) plotted against nondimensional 

velocity over a range of nondimensional 

load for different speed and load 

conditions are shown in Fig. 2. 

4. INFLUENCE OF SURFACE ROUGHNESS 

PARAMETERS THAT AFFECT CONTACT 

TEMPERATURE RISE. 

A good deal of work [26‐29] has also been carried 

out to include the multiple heat inputs in contact 

temperature analysis. Based on Archard’s model a 

set of equations that takes into account the surface 

roughness parameters for both Gaussian and 

exponential distributions of surface heights can be 

written [29]. The average flash temperature 

equations in terms of material and roughness 

parameters and with exponential surface height 

distributions may be given by: 

 

 

 

 

av. 

he 

av. 

hp 

av. 

le 

av. 

lp 

EV 

1.149 

( KC) 

HV 

1.72 

( KC) 

EV 

0.368 

K 

VH 

0.5 r 

K 

1/ 2 

1/ 2 

1/ 2 

1/ 2 

1/ 2 

 

 

 

r 

 

1/ 2 

3/ 4 

1/ 4 

r 

. 

1/ 4 1/ 4 

(15) 

Since exponential distribution represents the 

upper reaches of the asperities this may be used 

as a first approximation. There are at least two 

issues which need to be addressed here. Firstly, 

from operating conditions and other 

considerations we need to identify the equation 

among the four that needs to be used in a 

particular application. This can be determined 

using equations (12) and (13) for rough 

surfaces and for single contact elementary 

plasticity condition P/(πa 2 ) > H may be 

used.The other important issue is that the 

contact temperatures in equation (15) appear to 

be independent of load but depends on the 

roughness parameters σ and r. The explanation 

lies in the fact that the total real area of contact 

per unit area A r , total elastic load per unit area 

W e and total plastic load per unit area W p are 

given by [30]: 

88


 

 

d 

z 

2 

Ar N a 

dz 2rn 

W 

(16) 

* 1/ 2 

e 

0.8Ar 

E ( / r) 

(17) 

W p 

2rnH 

(18) 

Here N is the total number of asperities per unit 

area, φ(z) is the surface height distribution, n 

number of asperities in contact , A r is the real 

area of contact. This clearly shows the 

dependence of load on real area of contact 

which in turn depends on the roughness 

parameters σ and r. Now combining equations 

(8), (15) and the non‐dimensional scheme used 

in equation(14) we may write the wear volumes 

for different speed and deformation conditions 

in terms of operating and material parameters 

in non‐dimensional form as: 

_ 

V 

_ 

V 

_ 

V 

_ 

V 

avhe 

avhp 

avle 

avlp 

 

 

 

 

3(1.149 

v 

3(1.72 

v 

3(0.368 

v 

_ 

3(0.5 

v 

_ 

K 

K 

_ 1/ 2 

w 

_ 

w 

K 

w 

_ 1/ 

2 

_ 

1) 

_ 1/ 2 

 

K 

H 

w 

_ 1/ 

2 

E 

1) 

_ 3/ 4 

 

_ 3/ 4 

 

1) 

1) 

(19) 

 

where . 

r 

Non‐dimensional wear calculated with the 

average value of the wear‐coefficient from 

section‐5(b) plotted against non‐dimensional 

roughness over a range of non‐dimensional load 

for different load and speed conditions are 

shown in Fig. 3. 

Figs. 2 and 3 essentially show that the wear 

decreases with the increase in velocity over a 

range of load and with the increase in 

roughness over a range of velocity. This in 

turn indicates that wear decreases with 

contact temperature and clearly this is 

because, contrary to the behaviour of normal 

engineering materials hardness of this class of 

TiNi alloys increases with contact 

temperature rise. 





0.02 

0.015 

0.01 

0.005 

0.3 

0.2 

0.1 

3 

v 1010 

3 

v 2010 

v 3010 

2 4 6 8 10 

2 

Non-dimensional roughness σ×10 

 

(a) 

v 60 

v 80 

v 120 

0 

2 4 6 8 10 

2 


 

(b) 

0.04 

0.03 

0.02 

0.01 

3 

2 

1 

3 

v 1010 

3 

v 2010 

3 

v 3010 

0 

2 4 6 8 10 

2 


 

(c) 

v 60 

v 80 

v 120 

0 

2 4 6 8 10 

2 


 

(d) 

Fig. 3. Plots of non‐dimensional wear against nondimensional 

roughness for (a)High speed Elastic (b) 

High speed Plastic (c) Low speed Elastic (d) Low 

speed plastic contacts over a range of nondimensional 

load with experimental value of 

K =2.5E‐5 and =0.3, E =555 and H =6. 

w 

3 

89


5. EXPERIMENTAL DETAILS 

Two preliminary sliding wear tests were carried 

out with TiNi alloys one at a constant load and 

speed but at varying specimen temperature and 

the other at a constant load and ambient 

temperature but at varying sliding speed. 

(a) Sliding wear test with TiNi alloy at a 

constant load and speed but at varying 

specimen temperature. 

This set of tests was aimed at determining the 

dependence of wear resistance of these alloys on 

specimen temperature. A near equi‐atomic TiNi 

(Ti‐51at‐%Ni) alloy was prepared in a vacuum 

induction melting furnace. A disc specimen of 

42mm diameter and 10mm thickness was then 

prepared with the alloy. Wear tests were carried 

out in a commercially available high‐temperature, 

high‐vacuum Tribometer, initially using a 10 mm 

diameter tungsten carbide ball rubbing against the 

alloy disc at a normal load of 1.1 kg and a disc 

rotational speed of 200 rpm for 300 seconds in 

water media. Tungsten carbide balls of relatively 

high hardness were chosen so that the wear 

characteristics of the alloy disc alone could be 

observed. The water temperature was varied 

between 20 0 C to 80 0 C in order to obtain different 

specimen temperatures. The weight loss of the 

specimen was measured using a high precision 

balance. The results with the tungsten carbide 

balls are shown in Fig. 4. 

Fig. 4. Plot of wear volume of a TiNi alloy disc, 

rubbing against a tungsten carbide ball, against the 

specimen temperature. 

(b) Sliding wear test of TiNi alloy at a constant 

load and ambient temperature but at 

varying sliding speed. 

Another TiNi (Ti‐51at‐%Ni) specimen was 

prepared following similar procedure and 

sliding tests were carried out using the same 

Tribometer, a steel pin of 5mm radius pressed 

against the TiNi alloy disc specimen under a 

constant normal load of 5 N and at varying 

sliding speeds of 20 mm/s, 40 mm/s, 80 mm/s 

and 150 mm/s so that different contact 

temperatures could be generated. The contact 

temperatures for each load and speed 

combination were calculated using Archard’s 

flash temperature equations, reproduced in a 

convenient form in equation (10). The 

deformation conditions were determined using 

the elementary plasticity condition P/ (πa 2 ) > H, 

a being the contact radius. The speed conditions 

were determined using equation (13). With 

these constraints all the test conditions turned 

out to be high speed elastic. The weight loss of 

the specimen was again measured using a high 

precision balance and the plot of experimental 

wear volume against calculated specimen 

temperature is shown in Fig. 5. 

Fig. 5. A plot of wear volume against contact 

temperature during sliding experiments with TiNi 

alloy disc pressed against a steel pin at a normal load 

of 5N and different sliding speeds. 

It can be seen that the trend of wear vs. 

temperature plots in Fig. 4 for tests under 

constant load and speed but at varying 

specimen temperature is similar to this plot. 

This supports our argument that the rise in 

contact temperature during sliding due to 

frictional heat itself may be sufficient to cause 

the initial martensite to austenite phase 

transformation and the associated increase in 

hardness that leads to decrease in wear with 

increasing sliding velocity. 

It is now necessary to consider the phase 

transformation due to the frictional heat 

generated during the sliding process. The X‐ray 

diffraction signatures of the sample in the constant 

load and speed test were recorded before and 

90


after the wear test. The signature of the initial 

unworn surface is shown in Fig. 6. This indicates 

rhombohedral and monoclinic crystal structures 

which indicate the presence of martensite phase. 

Presence of some Ni 4 Ti 3 was also observed. This 

may be due to the presence of excess Ni while 

preparing the sample. In general formation of 

Ni 4 Ti 3 is favoured in case of excess aging of sample 

but in the present case no excess aging was done 

and therefore this cannot be the reason for its 

presence. The X‐ray analysis of the worn surface is 

shown in Fig. 7 and this indicates cubic crystal 

structure which is responsible for the highest 

peak. Cubic crystal structure indicates the 

presence of austenite phase in worn surface. The 

analysis also indicates the presence of small 

amount of TiO 2 and this may partly contribute to 

the wear resistance of TiNi alloy as suggested by 

Korshunov [31]. 

presence of high elastic stresses in austenitic or 

pseudoelastic state repeated cyclic loading 

during sliding may introduce surface or 

subsurface cracks that eventually lead to 

formation of large cracks on the surface as seen 

in Fig. 8. Severe plastic deformation needed for 

ploughing wear in martensitic state could not be 

detected. 

Fig. 8. SEM micrograph of the worn surface. 

These preliminary tests therefore indicate that 

TiNi alloy specimens with the initial martensitic 

phase transformed to austenitic phase during 

wear process and this supports the basic claim 

in this work. 


Fig. 6. X‐ray diffraction signature of the initial 

surface of TiNi alloy. 

Fig. 7. X‐ray diffraction signature of the worn surface 

of TiNi alloy. 

SEM micrograph of the worn surface is shown in 

Fig. 8. The micrograph generally indicates 

fatigue fracture in the worn surface. In the 

The high wear resistance of TiNi alloy has 

traditionally been attributed to its pseudoelastic 

nature alone but the present work indicates that 

the contact temperature rise due to frictional heat 

generated during sliding plays an important role. 

Based on Liang and Rogers [8] and others 

[21,22,25,29,30] works a simple theoretical model 

to relate the wear resistance of TiNi alloys to 

contact temperature rise during sliding against 

other materials has been proposed in equations 

(9) and (14). A realistic contact temperature 

model [29] for rough sliding bodies has been 

incorporated and the resulting wear model that 

takes into account multiple heat source at the 

sliding contact is proposed in equation (19). The 

model again predicts an increase in wear 

resistance with temperature. 

Preliminary sliding tests were carried out with a 

near equi‐atomic TiNi alloy both at (a) a 

constant load and speed combination but at 

varying specimen temperature and (b) a 

91


constant load and ambient temperature but at 

varying sliding speed. In both cases wear level 

fell with the increase in temperature and the 

results agree well with the theoretical 

prediction. The results are of importance in 

industrial practice where contact temperature 

rise is considered to be detrimental to smooth 

sliding for most engineering materials whereas 

here it seems that the temperature rise may 

prove to be tribologically useful for TiNi alloys. 

However more work is needed to establish the 

range of temperature rise where the effect is of 

practical use. 

NOMENCLATURE 

a Contact radius, 

0 0 

aA 

Material constant ( C /( A f 

A s 

) ), 

A f Austenitic phase finish temperature, 

A r Total real area of contact per unit area, 

A s Austenitic phase start temperature, 

A o f Austenitic phase start temperature in stress free state, 

A o s Austenitic phase finish temperature in stress free state, 

o 

B Material constant ( ), 

A 

c Specific heat, 

C Constant, 

E Elastic modulus, 

E * Equivalent elastic modulus, 

_ 

s 

 

a 

E Non‐dimensional elastic modulus, 

H Hardness of the softer of the two rubbing material, 

H Non‐dimensional hardness, 

K Thermal conductivity, 

K w Wear coefficient, 

L Non‐dimensional Speed Parameter, 

M f Martensitic phase finish temperature, 

M s Martensitic phase start temperature, 

n Number of asperities in contact per unit area , 

N Total number of asperities per unit area, 

P Normal Load, 

r Asperity radius, 

R Protrusion radius, 

T Alloy specimen temperature, 

T bulk Bulk temperature, 

_ 

T Non‐dimensional temperature, 

v Sliding Speed, 

v 

e 

Non‐dimensional velocity in elastic case, 

A 

v 

p 

V 

_ 

V 

V _ 

avhe 

V _ 

avhp 

V _ 

avle 

V _ 

avlp 

Non‐dimensional velocity in plastic case, 

Wear volume, 

Non‐dimensional wear volume, 

Non‐dimensional average wear volume for 

high speed elastic case, 

Non‐dimensional average wear volume for 

high speed plastic case, 

Non‐dimensional average wear volume for low 

speed elastic case, 

Non‐dimensional average wear volume for low 

speed plastic case, 

W Normal load, 

W e Total elastic load per unit area, 

W p Total plastic load per unit area, 

_ 

W Non‐dimensional Load, 

x Sliding distance, 

Coefficient of friction, 

 

 

ξ 

υ 

ψ 

Density, 

Martensite volume fraction, 

Poisson’s ratio, 

Plasticity index, 

zSurface height distribution, 

σ 

σ' 

_ 

Standard deviation of the surface height distribution, 

Applied Stress, 

Non‐dimensional roughness, 

θ Contact temperature rise, 

 

avhe 

avhp 

Average flash temperature for high speed 

elastic case, 

Average flash temperature for high speed 

plastic case, 

 

avle 

Average flash temperature for low speed elastic 

case, 

avlp 

Average flash temperature for low speed plastic 

case, 

 

mhe 

Mean contact temperature rise for high speed 

elastic case, 

 

mhp 

Mean contact temperature rise for high speed 

plastic case, 

 

mLe 

Mean contact temperature rise for low speed 

elastic case, 

 

mlp 

Mean contact temperature rise for low speed 

plastic case. 

92


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94


ISSN 0354-8996 

VOLUME 33 

2011. 

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ISSN 0354-8996 

VOLUME 33 

2011. 

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