Modelling and simulation of multi‐phase effects on X‐ray elasticity constants

Abstract

AbstractThis paper deals with the calculation of X‐ray Elasticity Constants (XEC) of phases embedded in multi‐phase polycrystals. A three scales (macroscopic, pseudo‐macroscopic, mesoscopic) model based on the classical self‐consistent formalism is developed in order to analyse multi‐phase effects on XEC values. Simulations are performed for cubic or hexagonal crystallographic structure phases embedded in several two‐phases materials. In fact, it is demonstrated that XEC vary with the macroscopic stiffness of the whole polycrystal. In consequence, the constants of one particular phase depend on the elastic behaviour and the volume fraction of all the phases constituting the material. Now, XEC play a leading role in pseudo‐macroscopic stresses determination by X‐Ray Diffraction (XRD) methods. In this work, a quantitative analysis of the multi‐phase effects on stresses determination by XRD methods was performed. Numerical results will be compared and discussed.