Inherent-Strain-Based Theory of Measurement of Three-Dimensional Residual Stress Distribution and Its Application to a Welded Joint in a Reactor Vessel

Abstract

The stress that exists in a body under no external force is called the inherent stress. The strain that is the cause (source) of this stress is called the inherent strain. This study proposes a general theory of an inherent-strain-based measurement method for the residual stress distributions in arbitrary three-dimensional bodies and applies the method to measure the welding residual stress distribution of a welded joint in a reactor vessel. The inherent-strain-based method is based on the inherent strain and the finite element method. It uses part of the released strains and solves an inverse problem by a least squares method. Thus, the method gives the most probable value and deviation of the residual stress. First, the basic theory is explained in detail, and then a concrete measurement method for a welded joint in a reactor vessel is developed. In the method, the inherent strains are unknowns. In this study, the inherent strain distribution was expressed with an appropriate function, significantly decreasing the number of unknowns. Five types of inherent strain distribution functions were applied to estimate the residual stress distribution of the joint. The applicability of each function was evaluated. The accuracy and reliability of the analyzed results were assessed in terms of the residuals, the unbiased estimate of the error variance, and the welding mechanics. The most suitable function, which yields the most reliable result, was identified. The most reliable residual stress distributions of the joint are shown, indicating the characteristics of distributions with especially large tensile stress that may produce a crack.