Page 15 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_FM.fm Page xiii Tuesday, May 3, 2005 5:49 PM

3.6.2.1 The J-Q Toughness Locus.........................................................................142
3.6.2.2 Effect of Failure Mechanism
on the J-Q Locus.......................................................................................144
3.6.3 Scaling Model for Cleavage Fracture ......................................................................145
3.6.3.1 Failure Criterion ........................................................................................145
3.6.3.2 Three-Dimensional Effects........................................................................147
3.6.3.3 Application of the Model..........................................................................148
3.6.4 Limitations of Two-Parameter Fracture Mechanics.................................................149
Appendix 3: Mathematical Foundations
of Elastic-Plastic Fracture Mechanics ...................................................................153
A3.1 Determining CTOD from the Strip-Yield Model ......................................153
A3.2 The J Contour Integral...............................................................................156
A3.3 J as a Nonlinear Elastic Energy Release Rate...........................................158
A3.4 The HRR Singularity..................................................................................159
A3.5 Analysis of Stable Crack Growth
in Small-Scale Yielding..............................................................................162
A3.5.1 The Rice-Drugan-Sham Analysis ................................................162
A3.5.2 Steady State Crack Growth..........................................................166
A3.6 Notes on the Applicability of Deformation Plasticity
to Crack Problems......................................................................................168
References ......................................................................................................................................171

Chapter 4
Dynamic and Time-Dependent Fracture........................................................................................173
4.1 Dynamic Fracture and Crack Arrest ....................................................................................173
4.1.1 Rapid Loading of a Stationary Crack......................................................................174
4.1.2 Rapid Crack Propagation and Arrest.......................................................................178
4.1.2.1 Crack Speed...............................................................................................180
4.1.2.2 Elastodynamic Crack-Tip Parameters.......................................................182
4.1.2.3 Dynamic Toughness ..................................................................................184
4.1.2.4 Crack Arrest ..............................................................................................186
4.1.3 Dynamic Contour Integrals .....................................................................................188
4.2 Creep Crack Growth ............................................................................................................189
4.2.1 The C * Integral ........................................................................................................191
4.2.2 Short-Time vs. Long-Time Behavior.......................................................................193
4.2.2.1 The C Parameter ......................................................................................195
t
4.2.2.2 Primary Creep ...........................................................................................196
4.3 Viscoelastic Fracture Mechanics..........................................................................................196
4.3.1 Linear Viscoelasticity...............................................................................................197
4.3.2 The Viscoelastic J Integral.......................................................................................200
4.3.2.1 Constitutive Equations ..............................................................................200
4.3.2.2 Correspondence Principle..........................................................................200
4.3.2.3 Generalized J Integral ...............................................................................201
4.3.2.4 Crack Initiation and Growth .....................................................................202
4.3.3 Transition from Linear to Nonlinear Behavior........................................................204
Appendix 4: Dynamic Fracture Analysis....................................................................................206
A4.1 Elastodynamic Crack Tip Fields ................................................................206
A4.2 Derivation of the Generalized Energy
Release Rate ...............................................................................................209
References ......................................................................................................................................213