Discrete analysis of actual residual stresses resulting from cyclic loadings

Abstract

The problem of calculating actual residual stresses induced in cyclically loaded bodies at loads up to and including the maximal shakedown limit is considered. A novel theoretical approach based on minimization of a total complementary energy objective function under nonlinear yield constraints is summarized. The numerical implementation is well suited for application to practical problems, for example the evaluation of residual stress in railroad rails created by means of rolling contact. Alternative formulations based on the hybrid finite element, finite difference, and boundary element methods are presented. Numerical studies of several test problems with independently known solutions are presented to illustrate the accuracy, convergence, and computational efficiency of the analysis. The study examples include loading conditions at and below the shakedown limit, combined loads, and bodies with initial stresses.