Application of the Linear Matching Method to Cracked Bodies Available to Purchase

The purpose of this paper is to demonstrate the application of the Linear Matching Method (LMM) to cracked bodies subjected to cyclic histories of loads and temperatures. The method [1,2,3], related to the methods of Elastic Compensation and Gloss r-node, used in design calculations for a number of years, involves matching the behaviour of a non-linear material to that of a linear material. The significance of the developed programming methods, in engineering design, is then discussed for two applications. The first is in the identification of ratchet limits for cracked structures subjected to variable loads and temperatures. Solutions are presented for both perfect plasticity and complete cyclic hardening conditions, for differing values of crack lengths, for the classical axisymmetric Bree problem. The other is in the investigation of the relationship between the near crack-tip fields and the cyclic loading histories. The analysis reveals the strong influence of the elastic stresses, immediately outside the stress singularities, allowing an understanding of the behaviour of mechanically and thermally induced crack-tip fields to be developed.