ABSTRACT
In the previous chapters, the primary emphasis of our discussion was on identifying a single parameter that uniquely characterizes the crack tip stress fields independent of the specimen size and geometry. This discussion led us to characterize stable and unstable fracture in terms of K if the small-scale yielding (SSY) conditions were met, and if an elastic–plastic or fully plastic condition prevailed by the J-integral. Both K and J characterize the amplitudes of the first and only singular term in a series expansion consisting of several higher-order terms that describe the stress field ahead of the crack tip. It is argued that very near the crack tip where the fracture process develops, the singular term is dominant. The contribution of the second-order terms depends on the distance from the crack tip, r, the geometry and size of the specimen, and the extent of crack tip plasticity. As one approaches the crack tip, r → 0, the singular term dominates the magnitude of the stress and the contribution from other terms can be neglected.
