||Estimation of the stress intensity factors of cracks and notches in anisotropic, multi-material and inclusion material
||Department of Civil Engineering
Stress intensity factors
Finite element method
Cracks and notches often occur in engineered objects, and failures can then initiate from these critical regions due to the resulting discontinuities in geometry and material properties. This can occur with large items, such a the beam-column joints of steel structures, welding members, and in aerospace, vessel and automobile components, as well as smaller items, such as those found in electronic packaging, semiconductor packaging and solar panels. While there are many studies that examine problems related to homogenous cracks and notches, relatively few consider the stress intensity factors (SIFs) of cracks and notches in anisotropic, multi-material and inclusion problems. This study thus estimated the notch-tip and crack-tip coordinates, as well as the SIFs, using image-correlation experiments with the least-squares method. In this approach the complex displacement functions are deduced into a least-squares form, and then displacement fields from the image-correlation experiments are substituted into the least-squares equation to obtain the SIFs. The results of the experiments are compared using H-integral and finite element analyses, and this reveals that the SIFs obtained using the proposed method are acceptably accurate. The major advantage of this approach is that it is easy, simple and systematic, and the experimental data required for it do not need to include that near the notch tip or specimen boundaries. In addition, it is not necessary to smooth the experimental data, since the least-squares method can average the deviations in this. The proposed method thus provides a very simple and convenient tool for researchers to obtain the SIFs of notch and crack problems.
List of Figures vii
List of Tables xi
Chapter 1 Introduction 1
1.1 Background 1
1.2 Objectives and Scope of research 2
1.3 Organization of Dissertation 3
Chapter 2 Literature Review 5
2.1 Research correlated with determination of SIFs, crack-tip coordinates and crack angle in composite materials 5
2.2 Research correlated with determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments 7
2.3 Research correlated with determination of stress intensity factors for multi-material junctions 10
Chapter 3 Details of the image-correlation experiment 13
3.1 Introduction 13
3.2 Theory of image correlation method 14
3.3 Optical system 18
3.4 The procedures of the image correlation program CCD82 19
3.5 Summary 21
Chapter 4 Determination of notch SIFs, crack-tip coordinates and crack angle in composite
4.1 Introduction 24
4.2 Displacements near the crack tip 24
4.3 Least-squares method to find KI and KII 27
4.4 Linear search and Powell methods to find crack-tip coordinates and angle b 28
4.5 Validations using the finite element method 30
4.5.1 Studing the accuracy of the crack-tip coordinates and angle b using equation (4.15) 31
4.5.2 Studing the accuracy of the SIFs using equation (4.17) 33
4.6 Validations using image correlation experiments 34
4.7 Conclusion 35
Chapter 5 Calculation of V-notch SIFs in multi-material notches 46
5.1 Introduction 46
5.2 Displacement and stress fields of notches 46
5.3 Definition of Notch SIFs 50
5.4 Evaluation of g using the H-integral 52
5.5 Evaluation of g using the least-squares method 54
5.6 Illustration of experiments 55
5.7 Results and comparisons 57
5.8 Conclusions 59
Chapter 6 Determination of stress intensity factors for multi-material junctions 66
6.1 Introduction 66
6.2 Displacement and stress fields of multi-material junctions 67
6.3 Junction-tip SIFs 70
6.4 Least-squares method to find inclusion tip coordinates and g 72
6.5 H-integral to find g using finite element results 74
6.6 Numerical validations 76
6.7 Validation using image correlation experiments 79
6.8 Conclusions 82
Chapter 7 Error and limitations study of generalized plane-strain least-squares method 90
7.1 Introduction 90
7.2 3D J-integral and least-squares method 92
7.3 Numerical examples 93
7.3.1 A plate with a central horizontal crack (case 1) 93
7.3.2 A plate with a central slant crack (case 2) 94
7.3.3 Finite Element results and discussions 94
Chapter 8 Conclusions and Recommendations 100
8.1 Conclusions 100
8.2 Recommendations for Further Research 102
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