Residual Stress in Heterogeneous – Two-Phase Materials

Abstract Most materials can be considered heterogeneous, consisting of multiple phases. A simple example is steel, which contains ferrite and cementite (or carbides in general). Depending on the alloying elements, these phases can sometimes combine to form new compounds or structures within the steel. The amount of cementite can be significant, resulting in a multi-phase material. When performing residual stress measurements using x-ray diffraction (XRD), all phases can be analyzed separately. These stresses can be macroscopic (bulk stresses) or microscopic (inter-phase stresses), depending on the loading conditions and processing history. Within the sampled (or diffracted) volume, the stress components can be triaxial, including all normal and shear stress components. Scientists have developed models based on Eshelby’s equivalent inclusion method to calculate these microscopic stresses between phases. These considerations have, to some extent, been ignored by both industry and academia. In this paper, we show that triaxial stress components can be measured via XRD and calculated using Eshelby-based models. The average stress across all phases corresponds to the macroscopic stress, and the boundary conditions at the surface remain valid.