On the determination of residual stress distribution in plane elasticity

Abstract

Problem of the distribution of incompatibilities in elastic solid in a quasi-plane stress state is discussed. It is assumed that the stress distribution can be measured at the boundary of a simply connected subregion of the body. Residual stress, field must satisfy static equilibrium equations but, in general, the corresponding elastic strain field does not satisfy strain compatibility conditions. Taking the measured values of the stress components at the boundary of the region as the external boundary tractions and solving the corresponding boundary value problem of elasticity (including strain compatibility conditions), one can obtain a unique stress field, which, in general, differs from the actual one. It is reasonable to treat their difference as the residual stress field assigned to the region under consideration. Obviously, the values of residual stress defined in such a way (at given point of the region) depend on the choice of the region and do not depend on the external loading of the elastic body. Fourier series integral technique of determining such residual stress fields for simply connected circular regions are proposed. Some quantitative integral characteristics of residual stress fields are discussed.