The Localized Eigenstrain Method for Determination of Triaxial Residual Stress in Welds

This paper discusses the localized eigenstrain method, a new technique for the determination of triaxial residual stresses deep within long welded joints. The technique follows from the " Inherent Strain Method " developed by Ueda, which uses a combined experimental and analytical approach to determine the source of residual stress (i.e., " eigenstrain " or, equivalently, " inherent strain ") by sectioning and strain measurement. Once the eigenstrain field is found, it is used to deduce residual stress in the original body prior to sectioning. The main advantage of this method is that residual stress is estimated within the entire welded joint. On the other hand, the localized technique focuses on finding residual stress only in the bead region of the joint, often a critical region with respect to fracture and fatigue. Because the method focuses only on near-bead residual stress, the required experimental effort is greatly reduced in comparison with Ueda's original formulation. In the paper, we begin by presenting the eigenstrain method in general and then describe localization of the technique. A model problem is then developed and used to investigate the accuracy of the technique through numerical modeling. Finally, the advantages and drawbacks of this new method are discussed. NOMENCLATURE eigenstrain tensor individual component of eigenstrain stress tensor individual component of stress assembled vector of eigenstrain interpolation parameters assembled vector of measured stress changes linear system relating to W, T, D width, thickness, and depth of welded sample B size of the region of interest ξ non-dimensional measure within the chunk geometry