HT-TMF-Conference - TMF-Workshop

Christian-Doppler-Laboratory 

for Fatigue Analysis 

RIEDLER_TMF-Workshop_BAM-Berlin_TMF-Energy_Presentation_2005.ppt 

HT-TMF-Conference – Berlin 

22/23 Sept., 2005 

University of Leoben 

Department Product Engineering 

Chair of Mechanical Engineering 

Applicability of hysteresis energy criteria for simulating 

lifetime under thermo-mechanical thermo mechanical fatigue 

University of Leoben, Austria 


Institut für Allgemeinen 

llgemeinen Maschinen aschinenBau au 

Dipl.-Ing. Dr.mont. Martin Riedler (Martin.Riedler@mu-leoben.at), 

Dipl.-Ing. Robert Minichmayr, Dipl.-Ing. Gerhard Winter, 

Univ.Prof. Dipl.-Ing. Dr.techn. Wilfried Eichlseder 

1



Engine Components: 

Identification of the 

loading cond. 

HCF, LCF, 

TMF 

1 



22/23 Sept., 2005 

Simulation of the 

component, component, 

Interpretation 

55 




Thermo-mechanical 

Thermo mechanical fatigue: fatigue lifetime estimation 

4 

Simulation of the lifetime 

behaviour 

Simulation at specimens and 

comp. near specimens 

Taking into account relevant 

influences on lifetime and 

deformation beh., 

Experiments 

2 

3 

Simulation of the cyclic 

deformation behaviour 

2





22/23 Sept., 2005 

Fatigue Analysis Laboratory 




Part of the servo hydraulic fatigue testing laboratory. Left side: Self-designed thermomechanical 

fatigue testing machines, behind: Instron servo hydraulic testing machines, in the 

front: multi-axial test rig. 

3





22/23 Sept., 2005 

TMF-test TMF test benches: benches: 

2 Concepts 




1) Temperature controlled specimen in a stiff load frame 

2) Additional strain control (servo-hydraulic TMF-test-rig) 

Self-designed 

• 10 kW Induction heating 

• Planetoid coil 

• Typ-K-sheath-TC 

• HT-Extensometer 

• Water cooled clamping device 

• Pressed air 

• Controller system 

• Data acquisition system 

Riedler (2003, 2004) 

Minichmayr (2004, 2005) 

4





22/23 Sept., 2005 




LCF-/HCF LCF HCF-test test benches: benches servo-hydraulic 

servo hydraulic 

• 10/100/250 kN servohydraulic 

Instron test 

machines 

• Temperature chamber 300 °C 

• Furnace heating 1000 °C 

• 10 kW induction heating 

1000 °C 

• Planetoid coil 

• Type-K-sheath-thermocouple 

• HT-Extensometer 

• Water-cooled clamping 

device 

• Controller 

• Data acquisition system 

5





22/23 Sept., 2005 




Approaches for a TMF lifetime assessment 

� Strain based (Manson-Coffin + modifications) 

� Damage parameters 

� �J – fracture mechanical view 

� Energy based approaches 

� Cumulative, much computing time 

� Accumulation of damage parts (pure fatigue, creep, oxidation, e.g. 

Miller, Sehitoglu) 

� Strain Range Partitioning 

� Microstructural approaches 

6





22/23 Sept., 2005 

TMF LCF HCF 

Maximum 

temperature 

Quasistatic - 

Creep 

Temperature Temperature Tensile Tests 




Metallo- 

graphic 

Dwell time Dwell Time LCF-HCF Creep Chem. analysis 

Pre-ageing Pre-ageing Pre-ageing 

Mean strain Mean strain 

Rigid clamped - 

controlled 

Strain 

constraining 

HCF interaction 

Strain rate 

Strain 

amplitude 

Argon 

atmospere 

Phase shift Incr. Step Test 

Experimental investigations 

1,E+011,E+03 

1,E+02 

6 

Stress � [N/mm 2 ] 

Plastische 

Dehnungsamplitude Spannung � [N/mm� a,p [‰] 

2 therm. bzw. mech. Dehnungsamp. 

� a,x bei N] B/2 [‰] 

Plastische Dehnungsamplitude 

Plastic strain amplitude � a,p [‰] 

Stress � a,p � [N/mm [‰] 

2 Stress � [N/mm 

] 

2 Strain amplitude 

] 

� a,x at N f/2 [‰] 

Spannung � [N/mm 


Strain amplitude � a,x at N f/2 [‰] 

Dehnung � [‰] 

Totaldehnungsamplitude � a,t 

bei NB/2 [‰] 

2 ] 

5 

4 

Stress 

relaxation 

Microstructure, 

fract. surface 

SAXS, REM, 

TEM 

Thermal vs. mechanical strain hysteresis loops 

Zyklisches dependent Verformungsverhalten, on the dwell at OP-TMF thermischer at Nf/2 vs. 

mechanischer 300 plastischer Dehnungsanteil 

AlCuBiPb 

OP-TMF � R = -1 

200 

tHo = Tmax 144 s = 250 °C 

� tDmax = 8 / 24 / 144 s 

100 

0 

-100 

-200 

tD1: Compensated thermal strain tD1: Mechanicall strain 

tD2: Compensated thermal strain tD2: Mechanical strain 

tD3: Compensated thermal strain tD3: Mechanical strain 

-300 

Strain � [‰] 

Lastwechsel N [-] 

mech AlCuBiPb 

TMF-OP - R = -1 

To = 250 °C 

a,p 

tHo= 8 / 24 / 144 s 

tHo = 8 s 

� th tHo = 8 s 

� 

a,p 

mech tHo = 24 s 

a,p 

� th tHo = 24 s 

� 

a,p 

mech a,p 

tHo = 144 s 

� th Einfluss Influence der Gegenüberstellung lokalen of pre-aging Dehnungen on the der bei mono-cyclic Zugversuche 

AlCuBiPb and bei 

500 

OP-TMF Influences LCF bei deformation verschiedenen on the LCF lifetime behaviour Haltezeiten behaviour 

Einfluss AlCuBiPb/2 Influences 

Deformation der on Vorauslagerung the plastic 

behaviour 

LCF auf of 

deformation die the Hysteresen plastic part 

450 

Einfluss Influence Lifetime 

des Dehnungsverhältnisses of pre-aging behaviour on (Manson-Coffin-Basquin) behaviour 

12 30,0 

the AlCuBiPb LCF 

500 

auf hysteresis den - plastischen 

LCF loops 

1,E+02 AlCuBiPb T = 25/200/250 - LCF AlCuBiPb Incremental Step Test 

Vorschlag °C zur Überführung von Spannungswöhlerlinien 

12 

500 

AlCuBiPb 11 (1) T Dehnungsanteil - = LCF 25 °C - R = -1 in Abhängigkeit - der Schwingspiele 

12 

TMF-OP 0 h T = 25 / 200 

T 

AlCuBiPb 

= 25 °C - R 

LCF 

= -1 

- tHo = 8 / 24 AlCuBiPb AlCuBiPb/2 °C 

300 

400 Vorausl.: 0 / M500 anson-Coffin-Basquin hin 

Dehnungswöhlerlinien: AlCuBiPb/2 HCF-Bereich 

/ 144 s - LCF 

1,E+01 

400 

T = 25 (2) °C T - = R 25 = °C -1 - R = -1 - 

11 (1) T = 25 °C - R = -1 R 

500 400 

- 0 � h-� 

h 

- 

at 250 R = 

Tu = 40 

°C-1 

/ 0 

10 pre-aged: � a,t 

T = 25 °C 

0 = 

- 

h 30,00 

M anson-Coffin-Basquin 

R 

vs. ‰ 

hole Comparison 

AlCuBiPb °C T = without 25 / - 200 with drilling 

LCF°C 

- 

350 l0 = 12,5 mm= 

-1 

Vorausl.: 500 (3) AlCuBiPb 8T 

0 = h 25 vs. °C - R = 0 300 - 0 h 

10 9 pre-aged: 

h at 250 Cu 

(2) T = 25 0 °C h 

°C Fe Pb Bi Si Manson-Coffin-curve 25 °C 

without Zn 

- R = 0 - 0 h T = R 25 = 

T 

°C -1 

= Mn drilled / 

25 

0 

°C AlCuBiPb/2 

Mg hole Cr 200 Ni Sn Ti 

300 

Basquin-curve 25 °C 

1,E+01 vs. 

300 500 h (4) Charge 

at 250 T = 1, 

°C 

Mechanische M.-C.-Basquin-model (=thermische + 25 °C 

20,0 200 °C - R = -1 - 0 h 

89 

200 

R Manson-Coffin-curve T 

= pre-aged: = 25 � m,t °C, = 0,0 � 

T = 

-1 / 0 R 0 m,t h ‰ 

= 0= 

25 

vs. 0,0 

°C 

‰ 

500 LCF103 h at 250 °C 

lokale) Dehnungen 

� a,t = 10 ‰ elastic part 

200 

Basquin-curve R = 0 R = -1 

250 

500 h at 250 °C 

78 

�Charge 4 

a,t= 3.75 

2, 

M.-C.-Basquin-model R = 0 100 

elastic / 10 part ‰ hole 100 � a,t = 10 ‰ (2) Manson-Coffin-curve 200 °C 

LCF107 

67 

� a,t = 100 10 ‰ (4) Basquin-curve Dehnungswöhlerlinie � a,t = 3.75 200 °C/ 

10 ‰ mit dem 

2001,E+00 

M.-C.-Basquin-model �� a,t 200 = 5,00 °C ‰ 

plastic strain 0 

6 

� a,t = amplitude 10 � a,t ‰ = (2) 10 0‰ 

(3) plastic 

kombinierten 

part 

Modell nach 

0 � a,t = 15,00 ‰ 

�� a,t = 5,00 ‰ 0 

150 5 

elastic strain amplitude 

Manson-Coffin-Basquin 

0 

-15 

510,0 

-10 total 2�a,t strain = 15,00 -5 amplitude 4 ‰ 6 8 

a,p -100 � a,t = 10 ‰ 0 plastic 10 

Thermische Dehnungen 

� (1) 5 �� part 12 

a,t hole = 103,75 ‰ 14 

15 

a,t = 10 ‰ (1) 

4 LCF data plastic points strain 0 h ampl. (model) 

-100 Tensile test 0 h 

100 

elastic strain Argon 

ampl. (model) 

4 

plastic part 0 h (model) elastic part 0 h (model) �� a,t 

a,t = 3,75 =3,75 ‰ ‰ 

-4 ��Manson-Coffin-Basquin Spannungswöhlerlinie 

(2) 

a,t = 10,00 ‰ 

-100 

3 1,E-01 Ramberg-Osgood-model plastic -200 0 �h LCF data points 500 h 

�a,t = 

a,t -200 = 10,00 7,5 ‰ (2) 

�� a,t 

Datenpunkte 3 Tensile � a,t = 3,75 ‰ (1) 

TMF tHo1 

Test mit 500 vorgeschlagenem 

strain ampl. hole 

= 3,75 1 x‰ 

50 

T101 25 elastic °C - 0 Datenpunkte strain h ampl. hole TMF tHo3 

plastic 

Datenpunkte T117 part 25 �500 h 


(model) 

a,t °C = - 3,30 500 tHo2 h ‰ bei LCF+HCF 250 3 x°C 

2 � elastic 

a,t T114 = 5 ‰ part 200 total linearelastischen (1) 500 °C strain - h 0 �(model) ha,t ampl. = -300 7,50 hole Ansatz ‰ Ramberg-Osgood-model � a,t = 7,5 ‰ (1) 500 h 

� a,t = 7,50 T121 ‰ 200 °C - 500 h bei 200 °C 

2 

plastic strain ampl.hole � a,t = 3,75 ‰ (4) 

-300 

(model) 

� a,t = 3,30 ‰ 

-8 T129 250 °C - 0 h 

elastic strain ampl.hole (model) Hysteresen 

T120 250 

0 

°C 

h 

- 500 h bei 250 °C 

0 

in Dehnungswöhlerlinie transformiert Low 1,E-01 1 

Hysteresen Hysteresis 500 not h bei 250 °C 

1 � a,t = 3,75 ‰ (1) 1,E+00 

-400 

1,E+01 � a,t = strain 3,00 

� 

Zugversuche a,t = 5 ‰ (2) 

�pre-aged a,t = ‰ 3,75 LCF+HCF rate -200 

1,E+02 ‰ (3) 

1,E+00 00,0 1,E+01 50 

Manson-Coffin-Basquin 

1,E+02 100 LCF Datenpunkte 1,E+03 

hole 

150 1,E+04 Hysteresis 200 T101/103 pre-aged 1,E+05 Dehnungswöhlerlinie 

250 0 500 h h 1,E+06 at 250 °C 300 

1,E-02 

0 

-400 

Zugversuch 500 h � a,t bei 

= 

250 

3,75 

°C 

‰ (2) 

0 

1,E+00 Bruchschwingspielzahl 1,E+01 1,E+02 HCF Strain Dehnung Datenpunkte � [‰] 1,E+03 NB � [‰] [-] Tensile 1,E+04 test not pre-aged Spannungswöhlerlinie 

1,E+05 1,E+06 

1,E+00 1,E+01 Tensile test pre-aged 500 h at 250 °C 

1,E+00-12 1,E+00 

1,E+01 Number 1,E+02 of -500 1,E+02 cycles 1,E+03 to failure 1,E+04 

1,E+03Nf [-] 1,E+05 1,E+06 1,E+07 

1,E+04 1,E+05 -300 

1,E+00 1,E+04 1,E+01 Number 1,E+02 1,E+05-500of cycles 1,E+03 1,E+06 N [-] 1,E+04 1,E+07 1,E+05 1,E+08 

Number Dehnung Number of � of cycles [‰] cycles to N failure [-] Nf [-] 

Schwingspiel Bruchschwingspielzahl Strain Zeit � [s] [‰] Ni [-] NB [-] 

1,E+02 1,E+01 

-10 

3 

-8 -6 -4 -2 0 2 4 6 8 10 

-15 

2 

-10 -5 0 5 10 15 

1 

3,64 0,35 0,97 0,02 0,17 0,05 0,63 0,89




LCF hysteresis loops 

Influence of pre-aging on the LCF hysteresis loops 

AlCuBiPb - LCF 

T = 25 °C - R = -1 

pre-aged: 0 h vs. 

500 h at 250 °C 

� a,t= 3.75 / 10 ‰ 


500 

400 

300 

200 

100 

0 

-200 

-300 

-400 

-500 


22/23 Sept., 2005 

-15 -10 -5 0 5 10 15 

-100 


E.g.: E.g.: 

Influence of pre-aging pre aging 

Hysteresis not pre-aged 

Hysteresis pre-aged 500 h at 250 °C 

Tensile test not pre-aged 

Tensile test pre-aged 500 h at 250 °C 


1,E+03 

1,E+02 

1,E+01 




LCF cyclic deformation 

behaviour 

Influence of pre-aging on the mono-cyclic and 

LCF deformation behaviour 


T = 25 °C - R = -1 


500 h at 250 °C 

LCF data points 0 h Tensile test 0 h 

plastic part 0 h (model) elastic part 0 h (model) 

Ramberg-Osgood-model 0 h LCF data points 500 h 

Tensile Test 500 h plastic part 500 h (model) 

elastic part 500 h (model) Ramberg-Osgood-model 500 h 

1,E-01 1,E+00 1,E+01 1,E+02 


pre-aging: 

stress parts decrease, plastic strain parts increase 

8




1,E+02 

1,E+01 

1,E+00 



22/23 Sept., 2005 

E.g.: E.g.: 

Influence of pre-aging pre aging, dwell time 




LCF lifetime behaviour TMF stress-cycle 

stress cycle behaviour 

Influence of pre-aging on the LCF lifetime behaviour 


T = 25 °C - R = -1 


500 h at 250 °C 

plastic strain amplitude 0 h elastic strain amplitude 0 h 

total strain amplitude 0 h 

Basquin-curve 0 h 

plastic strain amplitude 500 h 

total strain amplitude 500 h 

Manson-Coffin-curve 0 h 

M.-C.-Basquin-model 0 h 

elastic strain amplitude 500 h 

Manson-Coffin-curve 500 h 

Basquin-curve 500 h M.-C.-Basquin-model 500 h 

1,E-01 

1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 

Number of cycles to failure Nf [-] 

pre-aging: 

lifetime decrasing effect in the lower 

strained area, lifetime increasing effect 

in the upper strained area possible 


400 

350 

300 

250 

200 

150 

100 

Influence of pre-aging on the OP-TMF deformation 

behaviour 

144 s, 0 h 

144 s, 500 h 8 s, 0 h 

8 s, 500 h 

50 

0 

�m 

1,E+00 

-50 

1,E+01 1,E+02 1,E+03 1,E+04 

Number of cycles N [-] 

AlCuBiPb - OP-TMF 

Tmax = 250 °C - R = -1 

pre-aged: 0 h 

vs. 500 h at 250 °C 

tDmax = 8 / 144 s 

�max 

pre-aging / dwell time: 

influence of dwell time disappears in 

face of the lifetime and the cyclic 


9






22/23 Sept., 2005 




E.g.: E.g.: 

Influence of temperature, temperature mean strain 

Isothermal temperature at LCF, maximum temperature at TMF 

Alternating vs. pulsating tests 

LCF plastic strain-cycle 

strain cycle behaviour 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

Influences on the plastic LCF deformation behaviour 

(1) T = 25 °C - R = -1 - 0 h 

(2) T = 25 °C - R = -1 - 500 h at 250 °C 

(3) T = 25 °C - R = 0 - 0 h 

(4) T = 200 °C - R = -1 - 0 h 

� a,t = 10 ‰ (2) 

� a,t = 10 ‰ (4) 

� a,t = 10 ‰ (3) 

� a,t = 10 ‰ (1) 

0 

1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 

Number of cycles N [-] 


T = 25 / 200 °C 

R = -1 / 0 


500 h at 250 °C 

� a,t = 3.75 / 10 ‰ 

� a,t = 3,75 ‰ (2) 

� a,t = 3,75 ‰ (1) 

� a,t = 3,75 ‰ (4) 

� a,t = 3,75 ‰ (3) 


1,E+02 

1,E+01 

LCF lifetime behaviour 

Influences on the LCF lifetime behaviour 


T = 25 / 200 °C 

R = -1 / 0 

1,E+00 

1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 


Manson-Coffin-curve 25 °C 


M.-C.-Basquin-model 25 °C 

Manson-Coffin-curve R = 0 

Basquin-curve R = 0 

M.-C.-Basquin-model R = 0 

Manson-Coffin-curve 200 °C 


M.-C.-Basquin-model 200 °C 

Mean strain: small influence on lifetime and cyclic deformation behaviour 

Temperature: in general lifetime decreasing effect 

10

Strain amplitude � mech a,t at 

1,E+01 



Nf/2 [‰] 

1,E+00 


LCF-data correlates with TMF-data, if: 



22/23 Sept., 2005 

Strain-life Strain life curves 

Comparison of the mechanical TMF- 

with relevant isothermal LCF strain-life curves 


LCF 250 °C 


AlCuBiPb 

TMF-OP - LCF 

LCF 25 °C / preaged 

500 h bei 250 °C 

data points LCF 25 °C, preaged Manson-C.-B. LCF 25 °C, preaged 

data points LCF 250 °C Manson-Coffin-Basquin LCF 250 °C 

data points TMF tHo1 Manson-Coffin-Basquin TMF tHo1 



data points TMF tHo1 preaged data points TMF tHo1 mean strain 

data points TMF tHo2 mean strain data points TMF tHo3 preaged 

1,E+02 1,E+03 1,E+04 


• Temperature- and ageing loading are comparable 

AlCuBiPb - R = -1 

TMF-OP - tHo = 24 s 

LCF - 250 °C 




Disadvantage of Manson-Coffin- 

Basquin: 

• 4 parameter per influence 

• Interactions not considered 

Advantage: global understanding 

3 0 0 

2 0 0 

1 0 0 

0 

-1 0 -8 -6 -4 -2 0 2 4 6 8 1 0 

-1 0 0 

-2 0 0 

-3 0 0 

TMF-Hysteresen 

LCF-Hysteresen 

11




1,E+01 � ref,m ax 

Nf/2 [‰] 

� ref,m in 

1,E+00 

Comparsion of mechanical TMF- with relevant 

isothermal LCF strain-life curves 

LCF 250 °C 

TM F tD1 

TMF tD3 

TM F tD2 



22/23 Sept., 2005 

1,E+02 1,E+03 1,E+04 


Correlation LCF-TMF LCF TMF 

AlCuBiPb 


LCF 25 °C / pre-aged 

500 h at 250 °C 


1,E+01 � ref,max 

Nf/2 [‰] 

� ref,m in 

1,E+00 




Comparison of mechanical TMF- with relevant 

isothermal LCF strain-life curves 

LCF 250 °C 

TM F tD3 


AlSi7MgCu0,5 


LCF 25 °C / preaged 

500 h at 250 °C 


1,E+02 1,E+03 1,E+04 


Correlation at: 

• Mechanical strain-life curves according to Manson-Coffin-Basquin 

• Cyclic stress-strain curves according to Ramberg-Osgood 

• Stress-strain-hysteresis 

• Energy based damage parameter 

12

Calculated lifetime N cal 

[-] 



1,E+08 

1,E+07 

1,E+06 

1,E+05 

Estimation of LCF and TMF lifetime according to the 

specific parameter sets according to M.-C.-Basquin 

AlCuBiPb 

LCF - TMF-OP 

all investigated influences 

Basis: 44 parameter 



22/23 Sept., 2005 

1,E+04 

1,E+03 

1,E+02 

1,E+01 

1,E+00 




LCF 25 °C R=-1 Var.1 

LCF 25 °C R=-1 Ch.1 

LCF 25 °C R=-1 Var.2 

LCF 25 °C R=-1 with drill. 

LCF 25 °C R=0 

LCF 25 °C R=-1 pre-aged 

LCF 200 °C R=-1 

LCF 250 °C R=-1 

1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 

i 

a, 

t 

Experimental lifetime Nexp [-] 

i 

� ' f i 

i i 

b 

� � a, 

e � � a, 

p � ( ) � N f � �' 

E 

i 

f 

�N 

i 

c 

f 


[-] 

1,E+07 

1,E+06 

1,E+05 

1,E+04 




Lifetime estimation with the specific parameter sets of 

Manson-Coffin 

Manson Coffin-Basquin Basquin 

� 

Estimation of LCF and TMF lifetime according to the 

specific parameter sets according to M.-C.-Basquin 

±2,5 ±2,5 

AlSi7MgCu0,5 


all investigated influences 

Basis: 52 parameters 




1,E+03 

1,E+02 

1,E+01 

1,E+00 

TMF tHo2 sek. 

LCF 25 °C R=-1 Var.1 

LCF 25 °C R=-1 sek. 

LCF 25 °C R=-1 Var.2 

LCF 25 °C R=-1 w. drill. 

LCF 25 °C R=0 

LCF 25 °C pre-aged 

LCF 150 °C R=-1 

LCF 200 °C R=-1 

LCF 250 °C R=-1 

1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 


4 parameter per influence 

� 44 resp. 52 parameters 

Standard deviation 0,22-0,25 

too many parameters, interactions are not considered 

Aim: Parameter reduction, Considering of the interactions 

13





22/23 Sept., 2005 

Energy based damage parameters 




14





22/23 Sept., 2005 

Energy based damage parameters 

Representative for cyclic loading (� AND �) (Morrow, Halford) 1960 




Associated with macroscopic crack initiation (Dowling, Tomkins, Heitmann, 

Riedel, Schmitt, Nitta, Kuwabara) 1980 

3D-applications (Constantinescu, Charkaluk, Lederer, Verger) 2000 

Multiaxial (Sermage, Lemaitre, Desmorat, Gasiak, Pawliczek) 2000 

Independent of the temperature, material specific (Charkaluk et al.) 2000 

TMF: ageing effect dominant (T, t D, pre-aging, ageing 

in operation time), Interplay of stress and plastic 

strain values 

�W � W '�N 

W 

p 

p 

� W 

f 

B 

'�N 

b�c 

f 

1�b�c 

f 

mech 1 

� a, 

p, 

N � f / 2 � 

a, 

N f 

/ 2 

15

Specific energy � W 

[10 -3 J/mm 3 ] 





22/23 Sept., 2005 

TMF (out-of-phase) and LCF (250 °C) results based on 

a plastic energy criterion 

1,E+04 

1,E+03 

1,E+02 

1,E+01 

1,E+00 

1,E-01 

1,E-02 

1,E-03 

120 

Damage parameter based on energy 

AlCuBiPb 


TMF dwell time 8 s, rigid clamped 



TMF dwell time 24 s, closed-loop controlled 

LCF 250 °C 

LCF: Slope: 0,39 

TMF: Slope: 0,09 

TMF Slope: -0,91 

LCF: Slope: -0,61 

1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 





mech 

a, 

p, 

N 

mech 

� , � , N 

Describes TMF-influences: dwell time, ageing in service, pre-aging, mean 

strain, local strain 

1,E+04 

1,E+03 

1,E+02 

1,E+01 

1,E+00 

1,E-01 

1,E-02 

1,E-03 

Accumulated energy 

W [10 -3 J/mm 3 ] 

N 

f 

� 

� 

W 

p 

f 

/ 2 

a 

�� 

Proposed energy 

criteria: 

1-2 parameter 

f 

/ 2 

a, 

N 

f 

/ 2 

16

Specific plastic hysteresis 

energy �W H,p [MPa] 



5 

4 

3 

2 

1 

0 

TMF energy-cycle 

energy cycle behaviour 

Cycle dependency of the specific hysteresis energy 

Tmax=300°C, tD=24s, eps,m=0, PA=0h 


Tmax=250°C, tD=24s, eps,m=0,5%, PA=0h 


Tmax=250°C, tD=24s, eps,m=0,225%, PA=0h 


Tmax=225°C, tD=24s, eps,m=-0,225%, PA=0h 

Tmax=225°C, tD=8s, eps,m=0, PA=500h at 250°C 


Tmax=212,5°C, tD=24s, eps,m=0, PA=0h 

0 200 400 600 800 1000 

Cycle number Ni [-] 



22/23 Sept., 2005 

Energy criterions 

AlCuBiPb 

TMF-OP 

1200 

5600 

AlCuBiPb: Accumulated plastic 

energy W [MPa] 

1,E+05 

1,E+04 

1,E+03 

1,E+02 

1,E+01 

1,E+00 

AlCuBiPb 





LCF/TMF accumulated 

energy 

Accumulated plastic energy W 

LCF 25 °C / pre-aged 

500 h at 250 °C 

LCF 250 °C 

AlSi7MgCu0,5 


1,E-01 

1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 


Amplitude 

values at N f/2 Accumulated energy: 

mech 

a N 

� �� 

, p, 

f / 2 a, 

N f 

/ 2 

slope depending on 

material, LCF/TMF 


AlSi7MgCu0,5: Accumulated plastic 

energy W [MPa] (scaled on the 

intersection point at N f=100) 

17


[-] 



1,E+05 

1,E+04 

1,E+03 

1,E+02 

1,E+01 



22/23 Sept., 2005 




Material dependent TMF energy criterions 

Estimation of TMF lifetime based on the materialspecific 

best suited energy based approach 

AlCuBiPb: 1 Par. 

AlSi7MgCu0,5: 2 Par. 

AlSi6Cu4: 2 Par. 

AlSi8Cu3: 2 Par. 

1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 


1-2 parameters per material 

Standard deviation: 0.227 

Even longer dwell times are considered 

±2,5 

TMF-OP: all 

investigated 

influences 

AlSi8Cu3 PSWT2 V=0,01 

AlCuBiPb W1 V=0,10 

AlSi6Cu4 Tomkins V=0,10 

AlSi7MgCu0,5 PSWT1 V=0,22 

AlCuBiPb: 

P SWT1 

� � max �� 

a, 

t 

� � � �� 

max 

a 

m 

N 

f 

� 

Riedler (2004) 

� 

W 

mech 

� p , � a , N f / 2 

mech 

a, 

p, 

N �� 

f / 2 a, 

N f / 2 

AlSi7MgCu0,5, AlSi8Cu3: 

P � a � 

SWT 

� � * 

c 

N 

PSWT 2 � � max �� 

a, 

t 

Smith, Watson, Topper (1970) 

AlSi6Cu4: 

Tomkins (1978) 

2 �� 

�� 

max 

�J 

� a �� 

� � 

� E 

� 

N � A� 

( �J 

/ a) 

f 

B 

2 max 

f 

� E 

� �� 

�� 

p � 

� 

� 

1� 

n' 

� 

18



General description for all materials: 

�W 

� ce 

� f ( �We 

) � c p � f ( �W 

p ) 

N 

f 

� 

c 

5 

� �W 

�c6 

u 



22/23 Sept., 2005 

Unified energy approach 

z 

z 

� � f �� ;� � � � f �� ;� � 

W e x x, 

y 

W p x x, 

y 

Minimization processes for the materials investigated with 

different possibilities and combinations 

Unified energy criterion: 

� 

c u in correlation 

with the tensile 

Standard deviation s [-] 

0,30 

0,28 

0,26 

0,24 

0,22 

0,20 

stresses 0,18 

�� 

�� 

� 

W u � cu 

� �Wu, 

e � �Wu, 

p � cu 

� max a, 

e a a, 

p 

AlCuBiPb - TMF-OP 

0,0 1,0 2,0 3,0 

Specific elastic energy parameter c u [-] 




N f 

� 

f 

��W� 19


[-] 



1,E+05 

1,E+04 

1,E+03 

1,E+02 

Comparison of the TMF lifetime estimation based on the 

material dependent and the unified energy approach 

Investigated influences: 

M aximum temperature 

Dwell time 

Mean strain 

Pre-aging 

Aging in service time 



22/23 Sept., 2005 

Unified approach 

1,E+01 

1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 

� 


Unified energy approach 

±2,5 

Investigated materials: 

AlCuBiPb, AlSi7MgCu0,5, 

AlSi6Cu4, AlSi8Cu3 

Material dependent approach 

Number of specimens in the 

given scatter [%] 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 




Thermo-mechanical fatigue: Lifetime estimation based 

on the unified hysteresis energy approach 

0 

Specimens 1 in Specimens 2 in Specimens 3 in 

scatter +/- 2,5 scatter +/- 2,0 scatter +/- 1,5 

Quality of lifetime estimation 

�� 

�� 

� 

W u � cu 

� �Wu, 

e � �Wu, 

p � cu 

� max a, 

e a a, 

p 

Standard deviation: 0.225 with the unified hysteresis energy criterion 

AlCuBiPb 

AlSi7MgCu0,5 

AlSi6Cu4 

AlSi8Cu3 

Basis: 

100 TMF tests 

More than 50% of the specimens can be predicted within a scatter of 1.5, more 

than 80% within a scatter of 2.0 and more than 90% within a scatter of 2.5 

20



Engine Components: 

Identification of the 

loading cond. 

HCF, LCF, 


1 



22/23 Sept., 2005 

Simulation of the 

component, component, 

Interpretation 

55 




Thermo-mechanical 

Thermo mechanical fatigue: fatigue lifetime estimation 

4 

Simulation of the lifetime 

behaviour 

Simulation at specimens and 

comp. near specimens 

Taking into account relevant 

influences on lifetime and 

deformation beh., 

Experiments 

2 

3 

Simulation of the cyclic 


21

HT-TMF-Conference - TMF-Workshop

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?