Matched asymptotic expansions in nonlinear fracture mechanics.

Abstract

This thesis is concerned with the analysis of two-dimensional cracked specimens at load levels which induce significant plastic yielding near the crack tip. The differences between the solutions discussed here and the well known linear elasto-static ones are confined to the effects of this yielding. Small load expansions of the elastic-plastic response are constructed by the method of matched asymptotic expansions. These give the small scale yielding estimate of linear fracture mechanics as a first approximation, and provide systematic refinements which take account of the nonlinear interaction between the elastic and plastic regions. Besides providing an insight into the unknown elastic-plastic solutions, these expansions can be used directly as useful approximations in the 'medium scale yielding' range. The first half of the thesis is concerned with longitudinal shear problems in which only the out of plane displacement is non-zero. The comparative simplicity of the governing equations allows a completely analytic development. The second half deals with the technically more important problems in which both in-plane displacements are present. Their general structure is first discussed and illustrated by analysis of the simple Dugdale yielding model. A more realistic model, which admits incremental plastic flow, is then incorporated into the analysis by means of a finite element computation. Details of the elastic-plastic response of any specimen are expressed in terms of a set of standard computations that can, in principle, be performed once and for all.

Date of Award	1977
Original language	English
Awarding Institution	University of Bath