Analysis of Residual Stress Fields Using Linear Elasticity Theory

Abstract

In one of the most comprehensive books on mieroplasticity, Mura[l] defines residual stresses as the “self-equilibrating internal stresses existing in a free body which has no external forces or constraints acting on its boundary”. These stresses arise from the elastic response of the material to an inhomogeneous distribution of nonelastic strains such as plastic strains, precipitation, phase transformation, misfit, thermal expansion strains, etc. For example, mechanical deformation processes that cause plastic deformation in the surface layers of the material, such as shot-peening, grinding, machining, etc., cause residual stresses in these layers because of the constraining effect of the bulk, where plastic deformation is minimal. These stresses are called macrostresses. Since the surface layers will also constrain the bulk in return, the bulk material will also have residual stresses even though it may not have suffered deformation. It is also possible to have residual stresses when a multi-phase body, where the phases have different yield points, is pulled in uniaxial tension. The macrostress field in the deformed material will be negligible since the material will have the same plastic strains at all depths. The inhomogeneous distribution of yield points in the material volume, however, causes an inhomogeneous partitioning of the plastic strains between the phases, which, due to the constraining effect of the stronger phases on the weaker ones, causes a residual stress field to form. Residual stresses of this type are called microstresses.