Plasticity and failure behavior of solids: Memorial volume dedicated to the late Professor Yuriy Nickolaevich Rabotnov(3 Fatigue and Fracture)

More than six years ago, several of Rabotnov's close friends and colleagues from the USSR and USA decided to contribute a volume on Plasticity and Failure of Solids in honor of his 70th birthday. The celebration was interrupted unexpectedly by his death on May 13, 1985 at which time another decision was made still to publish the work, but as a memorial volume. As in any field of scientific endeavor, research confronts the scientists with anomalies; our chosen area is no exception. The ways in which failure criteria and plasticity theory are combined can differ widely among the researchers; they will never yield quite the same results. Each of the invited contributors has, therefore, been encouraged to express his views and to expound on his personal opinion. The contributors are free of enumeration from the authority and/or consensus of any scientific society or community. What impedes scientific process is the esoteric tradition of accepting ideas and theories by consensus among members of societies and communities. The absence of such a trend is refreshing; the collaboration between the authors from the USSR and the USA had to be one of the contributing factors. Finally, the editors wish to acknowledge the authors who have made the publication of this volume possible. a. c. Sib S. T. Mileiko AJ. Ishlinsky xi The late Professor Yuriy Nickolaevich Rabotnov (February 24, 1914 - May 13, 1985) xii Scientific biography of the late academician Yu. N.

Table of Contents:
1 Past and possible future directions in plasticity.- 1.1 Introduction.- 1.2 The beginning of plastic stress-strain relations.- 1.3 Isotropic hardening as a next step.- 1.4 Computers and the very limited experimental information obtainable.- 1.5 The stability postulate for small displacements.- 1.6 Perfect plasticity and the limit theorems.- 1.7 Stress invariants and further remarks on idealization and reality.- 1.8 Finite elastoplasticity for small incremental displacements.- 1.9 On some future directions and other concluding comments.- References.- 2 Physical theory of plasticity: a multicrystal model.- 2.1 Introduction.- 2.2 Requirements of multicrystal model.- 2.3 Multicrystal model.- 2.4 Some numerical results using this model.- 2.5 Conclusions.- References.- 3 Creep theories in metal forming.- 3.1 Introduction.- 3.2 One-dimensional problems.- 3.3 Reduction from two to one dimension.- 3.4 Two-dimensional problems.- 3.5 Damage in metal forming.- References.- 4 Failure of inelastic solids.- 4.1 Introduction.- 4.2 Load bearing capacity of an ideal elastic-plastic solid under plane strain.- 4.3 Stationary tensile crack in elastic-plastic material.- 4.4 Dynamics of longitudinal shear crack in elastic-plastic medium.- 4.5 Fracture of viscoelastic solids.- 4.6 Constitutive instability.- References.- 5 Plastic deformation and crack growth behavior.- 5.1 Introduction.- 5.2 Classical theory of plasticity.- 5.3 Macroplastic deformation and crack growth.- 5.4 Inhomogeneous deformation: change in local strain rates.- 5.5 Limitations of plasticity and possible alternatives.- References.- 6 Nonexistence of higher order discontinuities across elastic/plastic boundary in elastic-plastic wave propagation.- 6.1 Introduction.- 6.2 Basic equations for longitudinal waves in a thin rod.-6.3 Discontinuities of first order.- 6.4 Discontinuities of second order at M, first order on T.- 6.5 Discontinuities of second order at M and on T.- 6.6 Discontinuities of third and higher order at M, first order on T.- 6.7 Discontinuities of third and higher order at M, second order on T.- 6.8 Impossibility of third and higher order discontinuities on T.- 6.9 Improbability of second and higher order discontinuities on a loading boundary.- 6.10 Concluding remarks.- References.- 7 Engineering mechanics of composites.- 7.1 Introduction.- 7.2 Visco-elastic properties of constituents.- 7.3 Creep of unidirectionally reinforced plastic.- 7.4 Creep of bidirectional reinforced plastics.- 7.5 Stress-rupture under sustained load.- References.- 8 Interaction of macro- and microcracks in a nonhomogeneous solid.- 8.1 Introduction.- 8.2 Delamination of inclusion from matrix.- 8.3 Fibre/matrix delamination and stress-strain response.- 8.4 Fracture toughness.- 8.5 Conclusion.- 8.6 Appendix: Matrix/fibre interface fracture under longitudinal shear.- References.- 9 Energy balance for elastoplastic fracture: static and cyclic loading.- 9.1 Introduction.- 9.2 Energy balance.- 9.3 Heat conduction and generation.- 9.4 Static and cyclic loading.- 9.5 Local mechanical energy.- 9.6 Analytical method.- 9.7 Local thermal energy.- References.- 10 Stability of materials and structures.- 10.1 Introduction.- 10.2 Stability of elastic-plastic structures.- 10.3 Stability of visco-elastic structures.- 10.4 Stability of a strip.- 10.5 Macroscopic material stability.- References.