Page 14 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

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2.7 Relationship between K and G ..............................................................................................58
2.8 Crack-Tip Plasticity................................................................................................................61
2.8.1 The Irwin Approach ...................................................................................................61
2.8.2 The Strip-Yield Model ...............................................................................................64
2.8.3 Comparison of Plastic Zone Corrections...................................................................66
2.8.4 Plastic Zone Shape .....................................................................................................66
2.9 K-Controlled Fracture.............................................................................................................69
2.10 Plane Strain Fracture: Fact vs. Fiction ..................................................................................72
2.10.1 Crack-Tip Triaxiality ................................................................................................73
2.10.2 Effect of Thickness on Apparent Fracture Toughness .............................................75
2.10.3 Plastic Zone Effects..................................................................................................78
2.10.4 Implications for Cracks in Structures.......................................................................79
2.11 Mixed-Mode Fracture.............................................................................................................80
2.11.1 Propagation of an Angled Crack ..............................................................................81
2.11.2 Equivalent Mode I Crack..........................................................................................83
2.11.3 Biaxial Loading.........................................................................................................84
2.12 Interaction of Multiple Cracks...............................................................................................86
2.12.1 Coplanar Cracks........................................................................................................86
2.12.2 Parallel Cracks ..........................................................................................................86
Appendix 2: Mathematical Foundations of Linear Elastic
Fracture Mechanics..................................................................................................88
A2.1 Plane Elasticity.............................................................................................88
A2.1.1 Cartesian Coordinates ....................................................................89
A2.1.2 Polar Coordinates...........................................................................90
A2.2 Crack Growth Instability Analysis...............................................................91
A2.3 Crack-Tip Stress Analysis ............................................................................92
A2.3.1 Generalized In-Plane Loading .......................................................92
A2.3.2 The Westergaard Stress Function ..................................................95
A2.4 Elliptical Integral of the Second Kind.......................................................100
References ......................................................................................................................................101

Chapter 3
Elastic-Plastic Fracture Mechanics ...............................................................................................103
3.1 Crack-Tip-Opening Displacement........................................................................................103
3.2 The J Contour Integral.........................................................................................................107
3.2.1 Nonlinear Energy Release Rate ...............................................................................108
3.2.2 J as a Path-Independent Line Integral .....................................................................110
3.2.3 J as a Stress Intensity Parameter .............................................................................111
3.2.4 The Large Strain Zone .............................................................................................113
3.2.5 Laboratory Measurement of J..................................................................................114
3.3 Relationships Between J and CTOD ...................................................................................120
3.4 Crack-Growth Resistance Curves ........................................................................................123
3.4.1 Stable and Unstable Crack Growth..........................................................................124
3.4.2 Computing J for a Growing Crack ..........................................................................126
3.5 J-Controlled Fracture............................................................................................................128
3.5.1 Stationary Cracks......................................................................................................128
3.5.2 J-Controlled Crack Growth......................................................................................131
3.6 Crack-Tip Constraint Under Large-Scale Yielding..............................................................133
3.6.1 The Elastic T Stress..................................................................................................137
3.6.2 J-Q Theory................................................................................................................140