A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation

Abstract

The sin²⁡ψ method is the general method for analyzing X-ray diffraction stress measurements. This method relies on the estimation of a parameter known as 12S2hkl, which is generally considered as a material constant. However, various studies have shown that this parameter can be affected by plastic deformation leading to proportional uncertainties in the estimation of stresses. In this paper, in situ X-ray diffraction measurements are performed during a tensile test with unloads on a low-carbon high-strength steel. The calibrated 12S2hkl parameter varies from 3.5×10−6 MPa−1 to 5.5 ×10−6 Mpa−1, depending on the surface condition and on the plastic strain state, leading to a maximum error on the stress level of 40% compared to reference handbook values. The results also show that plastic strain is responsible for 6 to 14% of the variation, depending on the initial surface sample condition. A method is then proposed to correct this variation based on the fit of the 12S2hkl evolution with respect to the peak diffraction width, the latter being an indication of the plasticity state. It is shown that the proposed methodology improves the applied stress increment prediction, although the absolute stress value still depends on pseudo-macrostresses that also vary with plastic strain.