Predictions of Fatigue Crack Growth and Residual Strength in Plane and Shell Structures using Numerical Methods without Remeshing
- 주제(키워드) Structural Engineering
- 발행기관 고려대학교 대학원
- 지도교수 Zi Goangseup
- 발행년도 2011
- 학위수여년월 2011. 8
- 학위구분 박사
- 학과 일반대학원 건축·사회환경공학과
- 원문페이지 188 p
- 실제URI http://www.dcollection.net/handler/korea/000000026702
- 본문언어 영어
- 제출원본 000045670262
초록/요약
The extended finite element method (XFEM) and a phantom-node method are used to predict fatigue life and residual strength in two-dimensional plane and shell structures containing through-the-thickness cracks. These methods can model arbitrary cracks independent of the mesh and crack growth without remeshing. In the XFEM, the displacement approximation is locally enriched by a step function to represent discontinuities across cracks. Furthermore, the approximated displacement is incorporated basic functions of the asymptotic near-tip solutions in the linear elastic fracture mechanics to improve accuracy. A phantom-node method is developed for three-node shell elements to describe cracks. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Fatigue time is analyzed in the linear elastic fracture mechanics frame. The fatigue crack growth follows the Paris law or the NASGRO equation. Residual strength is determined by simulating a process of stable crack growth under a monotonic increase of applied loads in the elastoplastic fracture mechanics. The process is characterized by the J2 model with linear isotropic hardening and the crack tip opening angle (CTOA) criterion. The XFEM is applied to calibrate fracture properties known as fatigue constants and the critical value of CTOA from the middle-tension M(T) tests. The XFEM is also used to numerically simulate fatigue crack growth in thin-sheet plates with multiple cracks. Stress intensity factors and J-integral of several benchmark examples are calculated to demonstrate the phantom-node method. The method is also employed to predict fatigue life and residual strength of pressurized cylinders.
more목차
Acknowledgements ix
1 Introduction 1
1.1 Overview ............................................................... 1
1.2 Objectives ............................................................. 4
1.3 Outline .................................................................. 6
2 Extended Finite Element Method for Two-dimensional Plane Fracture 8
2.1 Approximation of discontinuous displacement field ..... 8
2.2 Weak form and discretized equilibrium equations ...... 13
2.3 Numerical implementations .................................... 16
2.3.1 Numerical integration .......................................... 16
2.3.2 Crack description ............................................... 17
2.4 Calculation of stress intensity factors ...................... 18
2.5 Benchmark examples ............................................ 21
2.5.1 Plate with an edge crack under tension ................. 22
2.5.2 Plate with an edge crack under shear ................... 24
2.5.3 Plate with an angled crack ................................... 25
3 Phantom-node Method for Shell Fracture 28
3.1 Three-node isotropic triangular MITC shell elements for uncracked elements ................................................... 28
3.1.1 6 degrees of freedom nodes ................................ 32
3.2 Overlapping paired elements for cracked elements ... 33
3.3 Constrained overlapping paired elements for tip elements ................................................................... 35
3.4 Equilibrium equations and numerical integration ....... 39
3.4.1 Discretized equilibrium equations ......................... 39
3.4.2 Numerical integration .......................................... 40
3.5 Calculation of fracture parameters ........................... 41
3.5.1 Domain form for J-integral calculation ................... 41
3.5.2 Extraction of mixed-mode stress intensity factors .. 44
3.6 Numerical examples ............................................. 48
3.6.1 Central cracked plate under pressure ................... 48
3.6.2 Pressurized cylinder with an axial crack ............... 50
3.6.3 Cylinder with a circumferential crack under tension 51
3.6.4 Pressurized cylinder with an inclined crack ........... 53
4 Phantom-node Method for Geometrically Nonlinear Analysis of Shell Fracture 56
4.1 Geometrically nonlinear MITC3 shell elements for uncracked part ........................................................... 56
4.2 Overlapping paired elements for cracked part ........... 63
5 Constitutive Model of Elastoplastic Materials 64
5.1 J2 model with linear isotropic/kinematic hardening ... 64
5.1.1 Yield function ..................................................... 65
5.1.2 Associative flow rule ........................................... 66
5.1.3 Linear isotropic and kinematic hardening rule ........ 67
5.2 J2 model for plane stress problems ........................ 69
5.2.1 Governing equations ........................................... 69
5.2.2 Implicit integration algorithm:
Return-mapping method ............................................. 71
5.3 J2 model for shell problems ................................... 73
5.3.1 Governing equations ........................................... 73
5.3.2 Implicit integration algorithm:
Return-mapping method ............................................. 75
6 Simulations of Fatigue Crack Growth 78
6.1 Review of fatigue laws ........................................... 78
6.1.1 Crack growth under constant amplitude cyclic
loading ..................................................................... 78
6.1.2 Paris law ........................................................... 80
6.1.3 NASGRO equation .............................................. 81
6.2 Strategy for modeling fatigue crack growth ............... 82
6.2.1 Length of new crack increment ............................ 83
6.2.2 Direction of new crack increment ......................... 84
6.2.3 Numerical implementations ................................. 84
6.3 Numerical simulations of multiple-crack growth in thin plates ....................................................................... 87
6.3.1 Experimental work .............................................. 87
6.3.2 Fitting of parameters in fatigue laws ...................... 89
6.3.3 Simulations of fatigue growth in multiple-crack
specimens ................................................................ 92
7 Prediction of Residual Strength 99
7.1 Residual strength .................................................. 99
7.1.1 Stable crack growth ............................................ 99
7.1.2 Crack tip opening angle (CTOA) criterion ............. 100
7.2 Strategy for prediction of residual strength .............. 103
7.2.1 Residual strength prediction for two-dimensional problems ................................................................. 106
7.2.2 Residual strength prediction for shell problems ..... 110
7.3 Numerical examples ............................................ 112
7.3.1 Middle-tension M(T) specimen .......................... 112
7.3.2 Specimen with a 45^0-incline crack .................... 116
7.3.3 Pressurized cylinder with tear straps ...................117
8 Conclusions and Future Work 120
8.1 Conclusions ....................................................... 120
8.2 Future work ......................................................... 121
A Computer Program 123
A.1 Introduction ........................................................ 123
A.2 Pre-processor .................................................... 123
A.3 Solver ................................................................ 129
A.4 Post-processor ................................................... 129
B Asymptotic Fields near a Crack Tip in LEFM 132
B.1 Two-dimensional problems ................................. 132
B.2 Shell problems ................................................... 133
C Details of Governing Equations and Integration Algorithm for Plane Stress J2 Model 136
C.1 Basic governing equations of plane stress J2 model ..................................................................... 136
C.2 Integration algorithm for the basic governing equations of plane stress J2 model ........................................... 138
D Line-search Algorithm 146
E Algorithm to Solve an Augmented System of Equations148
F Miscellaneousness 151
F.1 Shape functions .................................................. 151
F.2 Angle of crack growth based on the maximum hoop stress criterion ........................................................ 152
