4 - Small-Scale Yielding versus Exact Linear Elastic Solutions

Abstract

This chapter discusses the differences among exact linear elastic solutions for crack problems and small-scale yielding solutions, using as examples the solutions of the three fundamental modes of fracture for infinite plates. The linear elastic solution to the plane strain, mode I crack problem for an infinite plate subjected to a biaxial tensile traction applied at an infinite distance from an internal crack is proposed. The plots of comparisons among the small-scale yielding stresses and exact linear elastic stresses are analyzed. It is found that the deviations between the exact and approximate solutions increase with distance from the crack tip. For the stresses, the exact solution tends toward the remote traction, whereas the small-scale yielding solution tends toward zero. It is observed that if the plastic deformation is extensive, the purely linear elastic solutions may not characterize the problem at all, owing to elastic unloading and a redistribution of the stresses. The elastic-plastic loci as predicted by linear elastic fracture mechanics are also elaborated.