Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
Residual Strength and Fatigue Lifetime of ... - Solid Mechanics Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
For the specimens with H250 core the crack first propagated in the core due to the initial crack location after pre-cracking. The crack consequently kinked into the interface due to the presence of negative mode-mixity phase angle and large fracture toughness of the H250 core. The interface crack eventually kinked into the face sheet, which resulted in large-scale fibre bridging. A 2D finite element model of the STT specimen was developed to determine the mode-mixity phase angle and the energy release rate at the crack tip of the STT specimens. To characterise the interface fatigue behaviour of the STT specimens, fatigue tests were conducted on Mixed Mode Bending (MMB) specimens at a mode-mixity phase angle similar to that of the STT specimens. The resulting da/dN vs. G relations generated by the MMB fatigue tests were utilised in the developed crack growth finite element routine to simulate fatigue crack growth in the STT specimens. To choose appropriate control parameters, simulations with different control parameters were performed. A convergence analysis was conducted and an appropriate control parameter was chosen. Simulations of the H45 STT specimens showed a very high dependency on the control parameters. During the initial cycles, simulations using different control parameters showed small differences, but as the unstable crack growth zone was approached the deviation became larger. This dependency is attributed to the extrapolations in the transition from stable to unstable crack growth zone and the extreme non-linearity of this transition, which implies the importance of appropriate choice of control parameters in the case of highly nonlinear problems. With smaller control parameters the crack growth diagrams converged to one diagram since the cycle jump scheme was able to extrapolate accurately the stable-unstable crack transition zone by performing small or no jumps. H100 specimens, due to less non-linearity and stable crack growth, showed much less dependency to the control parameters. The developed finite element models were validated against the conducted fatigue tests. Simulations of the specimens with H100 core showed fair accuracy compared to the fatigue experiments. However, the simulation of the H45 specimens was much less accurate due to unstable crack growth observed in the fatigue experiments of the H45 STT specimens. Since the interface fatigue characterisation using the MMB specimens was only conducted for the stable linear part of the crack growth rates diagram (Paris’ regime), the resulting da/dN vs. G relation was not valid for unstable crack growth observed during the experiment of the H45 STT specimens and produced incorrect results. To validate the 3D fatigue crack growth numerical scheme, it was used to simulate fatigue crack growth in sandwich panels with a circular debond. Fatigue tests were carried out on a limited number of debonded sandwich panel specimens with a circular face/core debond at the centre with H45 PVC core and glass/polyester face sheets. It was observed that the crack initially kinks into the core and continues to propagate below the resin-rich core cells at the core. Because of a similar mode-mixity at the crack tip and similar face/core materials, da/dN vs. G relations from the MMB tests obtained previously were employed as input to the crack growth routine. A convergence analysis was conducted for different control parameter values to choose appropriate 132
control parameters. Simulations of the debonded sandwich panels showed fair accuracy compared to the fatigue experiments with a maximum deviation of 7 mm in determination of the debond diameter. This deviation can be attributed to the crude crack length measurement technique using the DIC technique, which was based on out-of-plane deflections of the debond and scatter of the input crack growth rates data. The presented 2D and 3D accelerated fatigue crack growth schemes proved to be reliable tools for the simulation of stable fatigue crack growth. However, for highly non-linear problems the presented method should be used more carefully. To reduce the uncertainties concerning the simulation of highly non-linear problems, a convergence sensitivity analysis must be carried out due to a strong dependency of the accuracy of the cycle jump method on the control parameters. 6.4 Future Works This thesis was an effort to develop different methodologies for studying with the residual strength and fatigue lifetime of debonded sandwich composites. The study was carried out at two main levels: 1) A material level by characterisation of face/core interface behaviour of foam cored sandwich composites under static or cyclic loading. 2) A structural level by finite element modelling and testing of debonded sandwich columns, panels, and X-joints. At the material level different types of PVC foam/GFRP interfaces were characterised under static or cyclic loading at different mode-mixities. The fracture toughness of different foam/GFRP interfaces was determined by use of TSD and MMB specimens for a full range of negative mode-mixity phase angles. However, the fatigue characterisation of the face/core interface was only conducted for one negative mode-mixity phase angle. A full fatigue characterisation of a face/core interface for a large range of mode-mixities is necessary for a general use of the proposed fatigue crack growth simulation scheme. Furthermore, in this thesis only linear elastic fracture mechanics was employed for determination of fracture parameters, which is not valid where the fracture process zone is large compared to the dimensions of the specimen, e.g. when fibre bridging occurs, which was often observed in the testing of interfaces with heavier foams. Cohesive zone modelling utilising cohesive laws along with a kinking criterion can be incorporated in the developed fatigue crack growth scheme to simulate kinking and fatigue crack growth in the presence of fibre bridging. In Chapter 4 a very short analysis of the distribution of the mode III energy release along the debond front in debonded sandwich panels was presented. Results showed that in some cases the mode III effects are significant and need to be taken into account. However, there have not been many studies addressing the mode III loading problem at the crack tip in a bimaterial interface. 133
- Page 104 and 105: Figure 4.18 (a) presents the deflec
- Page 106 and 107: Debond radius (mm) 100 90 80 70 60
- Page 108 and 109: using the cycle jump method, more t
- Page 110 and 111: Chapter 5 Face/Core Interface Fatig
- Page 112 and 113: of this chapter, sandwich panels wi
- Page 114 and 115: H250 Specimen H100 Specimen H45 Spe
- Page 116 and 117: Figure 5.5: Test setup. Initially,
- Page 118 and 119: H100 Specimen Fibre bridging Figure
- Page 120 and 121: propagation, the crack continues to
- Page 122 and 123: Figure 5.14: Kinking of the crack i
- Page 124 and 125: Crack length [mm] Crack length [mm]
- Page 126 and 127: mode-mixity phase angle was chosen
- Page 128 and 129: should be taken into account for a
- Page 130 and 131: Figure 5.25: Kinking of the crack i
- Page 132 and 133: log (da/dN) (mm/cycle) 10 log G (J/
- Page 134 and 135: erroneous extrapolations in the tra
- Page 136 and 137: compared to the 65% efficiency obta
- Page 138 and 139: the case of uneven debond growth, t
- Page 140 and 141: Load (kN) 2 1.5 1 0.5 0 Panel 1 Pan
- Page 142 and 143: Figure 5.42: Zero and ninety degree
- Page 144 and 145: G(J/m 2 ) 180 150 210 120 150 100 5
- Page 146 and 147: 110 q=qG=0.4 Test #1 100 Test #2 Te
- Page 148 and 149: panels were determined for differen
- Page 150 and 151: Chapter 6 Conclusion and Future Wor
- Page 152 and 153: toughness using MMB fracture toughn
- Page 156 and 157: Development of testing methods for
- Page 158 and 159: This page is intentionally left bla
- Page 160 and 161: Bezazi A., Mahi A. E., Berthelot J.
- Page 162 and 163: Kanny K. and Mahfuz H. (2005), Flex
- Page 164 and 165: Ratcliffe J. and Cantwell W. J. (20
- Page 166 and 167: This page is intentionally left bla
- Page 168 and 169: Out-of-plane displacement (mm) 1 0.
- Page 170 and 171: Out-of-plane displacement (mm) 3 2
- Page 172 and 173: A.5 Out-of-plane deflection of Debo
- Page 174 and 175: (a) Figure A.14: Out-of-plane defle
- Page 176 and 177: (a) (b) Figure A.18: Out-of-plane d
- Page 178 and 179: Load (kN) 250 200 150 100 50 250 30
- Page 180 and 181: Displacement (mm) 4 3 2 1 0 8 9 (a)
- Page 182 and 183: (a) (b) Figure B.11: Out-of-plane d
- Page 184 and 185: (a) (b) Figure B.15: Out-of-plane d
- Page 188: DTU Mechanical Engineering Section
control parameters. Simulations <strong>of</strong> the debonded s<strong>and</strong>wich panels showed fair accuracy<br />
compared to the fatigue experiments with a maximum deviation <strong>of</strong> 7 mm in determination <strong>of</strong> the<br />
debond diameter. This deviation can be attributed to the crude crack length measurement<br />
technique using the DIC technique, which was based on out-<strong>of</strong>-plane deflections <strong>of</strong> the debond<br />
<strong>and</strong> scatter <strong>of</strong> the input crack growth rates data.<br />
The presented 2D <strong>and</strong> 3D accelerated fatigue crack growth schemes proved to be reliable tools<br />
for the simulation <strong>of</strong> stable fatigue crack growth. However, for highly non-linear problems the<br />
presented method should be used more carefully. To reduce the uncertainties concerning the<br />
simulation <strong>of</strong> highly non-linear problems, a convergence sensitivity analysis must be carried out<br />
due to a strong dependency <strong>of</strong> the accuracy <strong>of</strong> the cycle jump method on the control parameters.<br />
6.4 Future Works<br />
This thesis was an effort to develop different methodologies for studying with the residual<br />
strength <strong>and</strong> fatigue lifetime <strong>of</strong> debonded s<strong>and</strong>wich composites. The study was carried out at two<br />
main levels:<br />
1) A material level by characterisation <strong>of</strong> face/core interface behaviour <strong>of</strong> foam cored<br />
s<strong>and</strong>wich composites under static or cyclic loading.<br />
2) A structural level by finite element modelling <strong>and</strong> testing <strong>of</strong> debonded s<strong>and</strong>wich<br />
columns, panels, <strong>and</strong> X-joints.<br />
At the material level different types <strong>of</strong> PVC foam/GFRP interfaces were characterised under<br />
static or cyclic loading at different mode-mixities. The fracture toughness <strong>of</strong> different<br />
foam/GFRP interfaces was determined by use <strong>of</strong> TSD <strong>and</strong> MMB specimens for a full range <strong>of</strong><br />
negative mode-mixity phase angles. However, the fatigue characterisation <strong>of</strong> the face/core<br />
interface was only conducted for one negative mode-mixity phase angle. A full fatigue<br />
characterisation <strong>of</strong> a face/core interface for a large range <strong>of</strong> mode-mixities is necessary for a<br />
general use <strong>of</strong> the proposed fatigue crack growth simulation scheme. Furthermore, in this thesis<br />
only linear elastic fracture mechanics was employed for determination <strong>of</strong> fracture parameters,<br />
which is not valid where the fracture process zone is large compared to the dimensions <strong>of</strong> the<br />
specimen, e.g. when fibre bridging occurs, which was <strong>of</strong>ten observed in the testing <strong>of</strong> interfaces<br />
with heavier foams. Cohesive zone modelling utilising cohesive laws along with a kinking<br />
criterion can be incorporated in the developed fatigue crack growth scheme to simulate kinking<br />
<strong>and</strong> fatigue crack growth in the presence <strong>of</strong> fibre bridging.<br />
In Chapter 4 a very short analysis <strong>of</strong> the distribution <strong>of</strong> the mode III energy release along the<br />
debond front in debonded s<strong>and</strong>wich panels was presented. Results showed that in some cases the<br />
mode III effects are significant <strong>and</strong> need to be taken into account. However, there have not been<br />
many studies addressing the mode III loading problem at the crack tip in a bimaterial interface.<br />
133