Compressible Ideal Elastic-plastic Crack Steady Expansion Of State-of-the-art Field,

The solution of near-tip fields for crack growing quasi-statically and steadily in elastic perfectly-plastic compressible (v<1/2) materials is a difficult problem unresovled for a long time in Fracture Mechanics. This paper gives correct formulations of the problem, and the correct solution is obtained by using three different methods. In the first method, which is initiated by present author, the perturbations expansions with ∈=1/2-v as a small parameter are proposed. Based on the solution for incompressible materials, the asymptotic solution of the order up to ∈~2 is obtained. In the second and third methods, the Near-tip solutions are obtained based on the frames of theoretical formulations by Rice, and Gao and Hwang, respectively. It turns out that the upper plane of the near-tip field is divided into 5 sectors for compressible materials. As ∈→ o , the 5-sector solutions degenerate to the well-known 4-sector solutions for incompressible materials. It is pointed out that, in the solutions by Drugan et al., the plastic flow factor turns out to be negative in part of the plastic sector, hence the plastic flow law is violated.