The Improved Irwin's Model for Crack Problems in Power-Law Hardening Materials

In this paper, an improved Irwin's model for power-law hardening materials is established through the static equivalence between the linear elastic stress solution and the stress redistribution in the plasticity-affected zone (PAZ) under small-scale yielding (SSY) conditions. HRR solution is adopted to describe the stress field within the crack-tip plastic zone (CTPZ). Analytical expressions of the effective stress intensity factor (SIF) and the size of PAZ are derived to illustrate the effect of CTPZ on the fracture behavior for power-law hardening materials. Influences of external load and hardening exponent on fracture behavior are explored. The proposed model can assess the toughening effect of CTPZ accurately using the SIF ratio, which is always smaller than 1. This model can be applied to various materials obeying power-law hardening constitutive equations. It will reduce to the extended Irwin's model for elastic-perfectly plastic materials in the limiting case.