Fracture Mechanics and Crack Growth

by Recho, Naman

• ISBN13: 9781848213067
• ISBN10: 1848213069
• Edition: 1st
• Format: Hardcover
• Copyright: 2015-01-12
• Publisher: Wiley-ISTE

Summary

The aim of the book is to present the recent advances related to the following two topics: how to determine the mechanical fields close to the material or geometrical singularities such as cracks? and how failure criteria can be established as function of the singularity degrees related to these discontinuities? Concerning the determination of the mechanical fields close to crack tip , a presentation of most traditional methods is done in order to classify them into two major categories. The first one is based on the stress field such as Airy function and the second one resolves the problem going from functions related to displacement fields. Then, a new method based on the hamiltonian system will be deeply presented. The second part of the book describes methodologies to establish the critical fracture loads. Singular fields for homogeneous and non-homogeneous problems near crack tips, v-notches, corners, interfaces...associated to stress concentrations allow to determine the basis of failure criteria.

Author Biography

Naman Recho is Professor at the University Blaise Pascal in Clermont Ferrand, France. He is also head of the ERMESS-Research laboratory (Equipe de Recherche on Mcanique et Scurit des Structures) at the EPF Engineering school in Sceaux, France. He has worked extensively with conceptual and applied aspects of fracture mechanics, with welded offshore structures and reliability analysis of cracked structures. He also teaches at Centre des Hautes Etudes de la Construction, Paris, and is guest Professor at Hefei University of Technology in China.

Table of Contents

Preamble	p. xiii
Preface	p. xv
Notations	p. xix
	p. 1
Stress Field Analysis Close to the Crack Tip	p. 5
Review of Continuum Mechanics and the Behavior Laws	p. 7
Kinematic equations	p. 9
Equilibrium equations in a volume element	p. 16
Behavior laws	p. 20
Modeling the linear elastic constitutive law	p. 22
Definitions	p. 24
Modeling of the elastic-plastic constitutive law	p. 35
Modeling the law of perfect plastic behavior in plane stress medium	p. 45
Energy formalism	p. 50
Principle of virtual power	p. 51
Potential energy and complementary energy	p. 54
Stationary energy and duality	p. 59
Virtual work principle - two-dimensional application	p. 60
Solution of systems of equations of continuum mechanics and constitutive behavior law	p. 63
Direct solution method	p. 63
Solution methods using stationary energies	p. 64
Solution with other formulation devices (Airy function)	p. 68
Review of the finite element solution	p. 72
The displacements	p. 74
The strains	p. 75
The stresses	p. 76
Minimum potential energy principle	p. 76
Assembly	p. 78
Overview of Fracture Mechanics	p. 81
Fracture process	p. 83
Basic modes of fracture	p. 84
Fracture Mechanics	p. 87
Determination of stress, strain and displacement fields around a crack in a homogeneous, isotropic and linearly elastic medium	p. 90
Westergaard Solution	p. 90
William expansion solution	p. 101
Solution via the Mushkelishvili analysis	p. 106
Solution of a three-dimensional fracture problem in mode I	p. 110
Solution using energy approaches	p. 115
Plastic zone shape around a crack	p. 137
Plastic analysis around a crack in an isotropic homogeneous medium	p. 144
Irwin's approach	p. 145
Dugdale's (COD) solution	p. 146
Direct local approach of the stress state in a cracked elastic-plastic medium	p. 151
Determination of the J-integral in an elastic-plastic medium	p. 161
Asymptotic stress fields in an elastic-plastic medium: the Hutchinson, Rice and Rosengren solution	p. 162
Case of a heterogeneous medium: elastic multimaterials	p. 164
New modeling approach to singular fracture fields	p. 165
The fracture Hamiltonian approach	p. 165
Integral equations approach	p. 174
Case of V-notches	p. 179
Introduction to the Finite Element Analysis of Cracked Structures	p. 187
Modeling of a singular field close to the crack tip	p. 188
Local method from a "core" element	p. 192
Local methods from enhanced elements	p. 198
Energetic methods	p. 200
Finite variation methods	p. 201
Contour integrals	p. 203
Other integral/decoupling modes	p. 205
Nonlinear behavior	p. 208
Case of a power law	p. 209
Case of a multilinear law	p. 209
Relationship between COD and the J-integral	p. 212
Specific finite elements for the calculation of cracked structures	p. 213
Barsoum elements and Pu and Hussain	p. 213
Verification of the strain field form	p. 214
Study of a finite elements program in a 2D linear elastic medium	p. 216
Definition and formulation of the conventional QUAD-12 element	p. 217
Definition and formulation of the conventional TRI-9 element	p. 220
Definition of the singular element or core around the crack front	p. 221
Formulation and resolution by the core element method	p. 222
The evaluation of stress intensity factor (K) as a function of the radius (r)	p. 223
Application to the calculation of the J-integral in mixed mode	p. 224
Partitioning of J in JI and JII	p. 227
Different meshing fracture monitoring techniques by finite elements	p. 229
The eXtended finite element modeling method	p. 231
Crack box technique (CBT)	p. 232
Crack Growth Criteria	p. 235
Crack Propagation	p. 237
Brittle fracture	p. 239
Stress intensity factor criteria	p. 240
Criterion of energy release rate, G	p. 242
Crack opening displacement (COD) criterion	p. 242
J-integral criterion	p. 243
R-curve criterion	p. 244
Feddersen's concept	p. 246
Two criteria approach	p. 248
Electro Power Research Institute Method	p. 250
Leguillon's criterion	p. 250
Tensile/shear transition criterion	p. 255
Crack extension	p. 265
Maximum circumferential stress criterion	p. 266
Minimum local strain energy density criterion	p. 268
Maximum energy release rate criterion	p. 269
Discussion of criteria	p. 271
Crack extension criterion in an elastic plastic medium	p. 272
Crack extension criterion for tensile fractures	p. 273
Crack-extension criterion for shear fracture	p. 273
Crack-extension criterion from V-notches	p. 275
Fracture following crack growth under high-cycle number fatigue	p. 277
Crack propagation laws	p. 279
Closure of the crack lips	p. 284
Crack propagation laws in mixed mode	p. 285
Approaches used for the calculation of fatigue lifetime	p. 286
Standard approach by means of (S-N) curves	p. 286
Approach by means of linear fracture mechanics	p. 288
Quick calculation of the stress intensity factor in mode I	p. 291
Case of the variable amplitude loading	p. 296
Physical definitions of the damage law giving the fatigue resistance	p. 296
Physical definitions of the cumulative damage law	p. 298
Considered definitions of the damage and cumulative damage laws	p. 298
Several types of associations of damage laws to cumulative damage laws	p. 299
Fatigue dimensioning methodology of a mechanical component subjected to variable loading	p. 301
Cycle-counting methods	p. 302
Principle of the cumulative damage theories	p. 305
Miner's rule	p. 306
Drawbacks of Miner's rule	p. 308
Mean lifetime	p. 308
Other more complex theories	p. 309
Crack retardation effect due to overloading	p. 312
Phenomenon of crack closure	p. 314
Cyclic strain hardening of the material at the crack tip	p. 315
Phenomenon of residual compressive stresses at the crack tip	p. 315
"Reliability-failure" in the presence of random variables	p. 318
Reliability elements	p. 320
Damage indicating integral	p. 322
Case of random variable loading	p. 324
Damaging cycles	p. 325
Effect of the application sequence of solicitation	p. 329
Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue	p. 331
Significance and analysis by calculation of stresses around the local effect	p. 333
Tubular joints, geometry and position of the problem	p. 335
First numerical local effect (the intersection of finite elements)	p. 337
Second and third local effects: inertia of the weld bead and weld toe	p. 338
Fourth local effect (defects at the weld toe)	p. 342
Crack initiation under fatigue	p. 343
Crack initiation fatigue	p. 344
Initial crack size in angle welds	p. 356
Localization and sensitivity to rupture of cracks	p. 367
Definitions and position of the problem in cruciform welded joints	p. 368
First approach	p. 369
Count data and compare with the experimental results	p. 371
Load-carrying cruciform welded joint submitted to bending	p. 372
Conclusions relative to localization and sensitivity to rupture of cracks	p. 375
Extension of the initiated crack under fatigue	p. 375
Preliminary test campaign	p. 376
Crack monitoring in an elastic-plastic medium	p. 384
Simulation of crack propagation in mixed-mode test configurations	p. 386
Potential Use of Crack Propagation Laws in Fatigue Life Design	p. 395
Calculation of the crack propagation fatigue life of a welded-joint	p. 395
Case of a welded cruciform joint	p. 396
Study of the influence of different parameters on fatigue life	p. 402
Statistical characterization of the initial crack size according to the welding procedure	p. 404
Crack propagation and a proposed relationship between n and C	p. 406
Statistical approach and calculation of the initial crack depth, a0	p. 408
Initiation/propagation coupled models: two phase models	p. 410
Propagation period	p. 411
Initiation period	p. 414
S-N curve analysis from the coupled model	p. 415
Coupled model application in the case of variable amplitude loading	p. 417
Development of a damage model taking into account the crack growth phenomenon	p. 419
Numerical determination of the number of cycles according to crack length or vice versa	p. 422
Taking into account the presence of residual welding stresses on crack propagation	p. 423
Distribution of residual stresses	p. 423
Method for calculating the energy release rate, G	p. 425
Numerical simulation	p. 426
The influence of welded residual stresses on crack growth rate	p. 428
Consideration of initial crack length under variable amplitude loading	p. 430
Method description	p. 431
Propagation of short cracks in the presence of a stress gradient	p. 433
Parametric study of a sample in mode I opening of a notch	p. 436
Application in the case of a welded joint	p. 438
Conclusion and future extensions	p. 439
Probabilistic approach to crack propagation fatigue life: reliability-failure	p. 440
Modeling of crack retardation effect due to overloading	p. 445
Evolution of the probability of failure	p. 446
Study of sensitivity in terms of reliability	p. 447
Inspection and reliability/failure	p. 448
Conclusion	p. 451
Bibliography	p. 455
Index	p. 477
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