A finite element study of the residual stress and deformation in hemispherical contacts

This work presents a finite element model (FEM) of the residual stresses and strains that are formed after an elastoplastic hemispherical contact is unloaded. The material is modeled as elastic perfectly plastic and follows the von Mises yield criterion. The FEM produces contours for the normalized axial and radial displacements as functions of the removed interference depth and location on the surface of the hemisphere. Contour plots of the von Mises stress and other stress components are also presented to show the formation of the residual stress distribution with increasing plastic deformation. This work shows that high residual von Mises stresses appear in the material pileup near the edge of the contact area after complete unloading. Values are defined for the minimum normalized interference, that when removed, results in plastic residual stresses. This work also defines an interference at which the maximum residual stress transitions from a location below the contact region and along the axis of symmetry to one near to the surface at the edge of the contact radius (within the pileup).