In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the shaft's angle of twist doesn't revert to its original state after the torque removal, indicating the presence of residual stress. This behavior is graphically represented on a torque versus angle of twist diagram, where the shaft unloading process is depicted as a linear path.

The methodology to calculate these residual stresses incorporates the principle of superposition. It involves two steps: initially evaluating the stresses induced by the applied torque during the loading phase, followed by assessing the stresses generated by applying an equal and opposite torque to unload the shaft. The distribution of residual stresses within the shaft is ascertained by aggregating these two stress responses. A further analysis, plotting stress against radial distance, reveals that residual stresses may align with the original stress direction or counteract it. This insight is crucial for assessing materials' resilience and structural integrity under stress.