Tensile Cracks in Creeping Solids

Abstract

The aim of the paper is to answer the question: which loading parameter determines the stress and strain fields near a crack tip, and thereby the growth of the crack, under creep conditions? As candidates for relevant loading parameters, the stress intensity factor KI, the path-independent integral C*, and the net section stress σnet have been proposed in the literature. The answer, which is attempted in this paper, is based on the time-dependent stress analysis of a stationary crack in Mode I tension. The material behavior is modeled as elastic-nonlinear viscous, where the nonlinear term describes power law creep. At the time t = 0, load is applied to the cracked specimen, and in the first instant the stress distribution is elastic. Subsequently, creep deformation relaxes the initial stress concentration at the crack tip, and creep strains develop rapidly near the crack tip. These processes may be analytically described by self-similar solutions for short times t. An important result of the analysis is that small-scale yielding may be defined. In creep problems, this means that elastic strains dominate almost everywhere except in a small “creep zone” which grows around the crack tip. If crack growth ensues while the creep zone is still small compared with the crack length and the specimen size, the stress intensity factor governs crack growth behavior. If, however, the calculated creep zone becomes larger than the specimen size, the stresses become finally time-independent and the elastic strain rates can be neglected. In this limiting case, the stress field is the same as in the fully-plastic limit of power law hardening plasticity that has been treated in the literature. The loading parameter that determines the near tip fields uniquely is then the path-independent integral C*. It should be emphasized that KI and C* characterize opposite limiting cases. Which case applies in a given situation can be decided by comparing the creep zone size with the specimen size and the crack length. Criteria for small-scale yielding are worked out in several alternative forms. Besides several methods of estimating the creep zone size, a convenient expression for a characteristic time is derived also, which characterizes the transition from small-scale yielding to extensive creep of the whole specimen.