Unified theoretical solutions for describing the crack-tip stress fields of finite specimens with mode-I crack under fully plastic conditions

Abstract

The analytical equation to express the equivalent stress of the representative volume element (RVE) is derived from the energy density equivalence. Based on the analytical expression for equivalent stress of the RVE, extensive analyses are conducted for the stress fields in the forward sector near the crack-tip of finite specimens with mode-I crack for pure power-law hardening materials. Further, unified theoretical solutions with various special functions for describing the stress fields are proposed under fully plastic and plane-strain conditions. Comparisons of radial stress distributions in various angles, angular stress distributions, and contour lines of the equivalent stress between the results predicted by the finite element analysis, HRR (Hutchinson and Rice and Rosengren) solutions, and the proposed unified theoretical solutions are performed. The excellent capability of the proposed unified theoretical solutions for predicting the crack-tip stress fields is verified.