A Simple Method to Estimate Numerically the Residual Stresses in Bodies Subjected to Cyclic Loads

Abstract

Abstract Residual stresses in metallic materials may arise during the manufacturing process as a byproduct of the process itself, or they may be introduced on purpose to enhance the behavior of the product in service (for instance the compressive hoop stress in railroad vehicle wheels). Depending on the service regimen, the residual stresses in a body subjected to cyclic loads may either attain the stable (time-independent) state, thus leading to elasto-plastic shakedown of the body to the given loading program, or may not stabilize, resulting in the destruction of the body because of the ratcheting (alternating plasticity). The residual stresses in a considered body may be calculated using the standard incremental approach, where the final state is found through following step by step the actual loading program, or they may be estimated by the application of plastic shakedown theorems. The first approach, although yielding precise information on body behavior, may be extremely time consuming in the case of cyclic loads. The second approach, although yielding only an estimate of the final residual stress distributions, is much more time efficient. The numerical approach discussed in this article is based on Melan’s theorem and allows for a reasonably accurate estimate of residual stresses induced in an elastic plastic body made of strain hardening material as long as an upper bound of the loading program is known. The tests performed on an autofrettage problem exhibit excellent agreement with an exact analytical solution. The results for the calculations of the residual stresses in railroad rails subjected to simulated service loads are provided.