Plasticity model for simulation, description and evaluation of vibratory stress relief

A plasticity model for simulation and description of the phenomenon of vibratory stress relief (VSR) is presented. The model is based on the premise that the external vibratory force induces cyclic stresses that interact with the residual stresses existing in the material. Residual stress relief thus occurs when the sum of induced cyclic stress and residual stress exceeds the local yield stress of the material. Since residual stresses are self-equilibrating, local stress relief results in the occurrence of stress redistribution towards achieving equilibrium. By means of Matlab/Simulink Software Program, it is shown that VSR is a localized cyclic plasticity phenomenon that combines aspects of cycle-dependent stress relaxation and cyclic-creep processes, in that the peak stress decreases while the elapsed strain increases with cycle. Simulated stress-strain, stress-cycle and strain-cycle curves are similar to those observed experimentally by other investigators. Based on these similarities, a stress relaxation model is proposed for vibratory stress relief. The effect of loading/material parameters, such as vibration frequency, stress amplitude, strain amplitude, yield stress and initial strain hardening rate on the effectiveness of the VSR treatment may be explained/analysed in the light of this model. It is shown that the strain-cycle curve due to VSR process is an important data for the quantitative evaluation of the effectiveness of VSR, and also provides a practical means of determining residual stress reduction in real-time. From such data reduction in residual stress may be determined as the product of the elastic modulus of the material and the change in mean strain. (C) 2009 Published by Elsevier B.V.