Closed form solutions of the differential equations governing the plastic fracture field in a power-law hardening material with low strain-hardening exponent

Abstract

In this paper closed form solutions for the evaluation of the stress and strain-fields are estimated for a power-law hardening, plastically incompressible material, cracked under plane-strain conditions. A convenient decoupling methodology, concerning a strongly non-linear ordinary differential system given by Rice and Rosengren [1], leads to a modified higher-order non-linear differential equation which for the case of low strain-hardening behaviour, using appropriate analytical treatments, is integrated in a closed form. Applications of the derived solutions for low hardening exponents yield results which are in excellent agreement with those derived numerically by other investigators. The solutions obtained herein cover a large class of problems in the mathematical theory of plasticity and fracture mechanics, and may be proved powerful in application .