Origin And Interpretation Of Psi-Splitting And Out Of Plane Shear Stress When Using Diffraction Techniques

Psi-splitting is a phenomenon often observed in interplanar d-spacing vs. sin²ψ plots during the analysis of residual stress measurement data when employing the X-ray diffraction (XRD) method. Deviations from the expected linear relationship between interplanar d-spacing and sin²ψ are typically caused by the presence of out-of-plane shear stresses or inhomogeneous stress distributions within the measured phase of the material. In such cases, the d-spacing values measured at different ψ tilt angles deviate from the anticipated linear trend, resulting in a characteristic splitting of the d-spacing vs. sin²ψ plot data, where the shape of the data in the plot takes the form of an ellipse. When this occurs, the stress state in the material cannot be accurately described by a simple biaxial stress model, necessitating a more comprehensive analysis to account for the triaxial nature of the stress field and to accurately calculate the components of the stress tensor. Most critically, the presence of non-zero out-of-plane shear stresses directly affects the accuracy of the normal and shear stress tensor components being determined in the plane of the measurement. Psi-splitting typically occurs in inhomogeneous and multiphase materials subjected to cold working processes such as machining, shot peening, or other surface treatments. This paper aims to explain the origin and mechanism of Psi-splitting, detailing how it occurs and how it should be interpreted in single and multiphase materials. It also seeks to bridge the gap between materials scientists and mechanical engineers. It is important to note that this phenomenon does not alter the biaxial macroscopic stress state of the material, and that the boundary conditions at the surface remain valid because the overall effect is balanced at the macroscopic level if all constituent phases present in the material are considered