A semi-analytical model for elastoplastic stress fields induced by sharp polygonal indenters

Abstract Analytical descriptions of indentation-induced stress fields are essential for interpreting deformation and crack initiation in brittle materials. Conventional point-load solutions generate axisymmetric stress fields and therefore cannot resolve the non-axisymmetric contact conditions produced by Vickers and Berkovich indenters. A semi-analytical elastoplastic stress-field model is developed for sharp indenters with regular polygonal cross-sections acting on approximately isotropic brittle materials. The contact region is discretized into rectangular elements, and the elastic contributions generated by the normal and tangential stress on each element are evaluated using closed-form influence functions and superposed in the global coordinate system. The resulting contact field is combined with the ECD residual field through one-way superposition. For Vickers and Berkovich indentations of BK7 glass, the calculated tensile-stress concentrations are consistent with the reported locations of median-, radial-, and lateral-crack initiation. A discretization analysis shows that M = N = 100gives the monitored stress and depth quantities within approximately 0.5% of the M = N = 200results while requiring approximately one quarter of the computation time. For the n = 50 conical approximation, the present model and Yoffe’s solution predict comparable peak stress magnitudes near their respective plastic zones and similar far-field decay, although their plastic-zone depths and near-field stress profiles differ. Increasing the indenter edge count or edge inclination angle increases the normalized maximum tensile stress beneath the indenter and reduces the critical load predicted by Lawn’s median-crack initiation criterion.