Abstract
In this paper, a mathematical analysis of residual stress is proposed, by which the plastic strain is calculated from an already known total strain distribution without cutting process for relieving the elastic strain. In order to confirm the analysis, numerical calculations are carried out on the following two subjects.
First, the differential equation and boundary condition are derived from the condition of compatibility and the equation of equilibrium on the assumption of incompressibility, plane stress state and nonphase transformations. The differential equation is applied to find the plastic strain value in the case that the total strain distribution for an arbitrarily assumed plastic strain distribution has been known by the analyses of inherent strain method. The resultant values of the plastic strain are in well agreement with the assumed ones.
Second, the equation is applied to analyze the residual stress and distortion resulting from spot heating of aluminum alloy thin plate. The results coincide with the experimental data except around the heating point where swelling deformation occurs and the stress state is three dimensional.
