Semi-analytical expressions to describe stress fields near the tip of Mode-I crack under plane-strain conditions

Abstract

In this study, the stress distribution near a mode-I crack tip under plane-strain conditions for power-law hardening materials and its semi-analytical expression are investigated. The analytical equations to express the equivalent stress and strain of the representative volume element are derived based on energy density equivalence and dimensional arguments. After acquiring the correspondence between the equivalent stress and the derived J-integral for fully plastic materials, the present work proposes a mathematical formula to characterize the stress fields near the crack tip that is closely related to the Hutchinson–Rice–Rosengren asymptotic fields. Furthermore, semi-analytical expressions are proposed to describe the stress fields in the close vicinity of the crack tip. The findings of this study will be useful in structural safety assessment and can promote theoretical advancement in the field of fracture mechanics.