Tensile cracks in creeping solids

Abstract

The loading parameter determining the stress and strain fields near a crack tip, and thereby the growth of the crack, under creep conditions is discussed. Relevant loading parameters considered are the stress intensity factor K/sub I/, the path-independent integral C*, and the net section stress sigma/sub net/. The material behavior is modelled 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. 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 the calculated creep zone becomes larger than the specimen size, the stresses become finally time-independent and the elastic strain rates can bemore » neglected. In this case, the stress field is the same as in the fully-plastic limit of power law hardening plasticity. The loading parameter which determines the near tip fields uniquely is then the path-independent integral C*.K/sub I/ and C* characterize opposite limiting cases. The case applied in a given situation is decided by comparing the creep zone size with the specimen size and the crack length. Besides several methods of estimating the creep zone size, a convenient expression for a characteristic time is derived, which characterizes the transition from small scale yielding to extensive creep of the whole specimen. « less

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