The isotropic shear modulus of multicomponent Fe-base solid solutions

Abstract

A critical analysis of the available experimental data for the effect of alloying elements on the isotropic shear modulus of bcc (body-centered cube) Fe– X ( X=Al, Be, C, Co, Cr, Ge, Ir, Mn, Ni, Pt, Re, Rh, Ru, Si and V) solid solutions is carried out. The total effect of a solute on the shear modulus is decomposed into two contributions: the electronic (or chemical) and the volumetric. A systematic trend of the electronic contribution is demonstrated as a function of electron-to-atom ( e/a) ratio and the ground-state electronic configuration of the solute atom. Based on the demonstrated trend, we predict the chemical contribution of the shear modulus of Cu, Mo, N, Nb, Ti and W in ferromagnetic α-Fe (bcc), and that of Ti and V in paramagnetic γ-Fe [face-centered cube (fcc)]. These along with the corresponding volumetric contributions enable us to predict the total effect of a solute on the shear modulus in α-Fe and γ-Fe. In the case of γ-Fe, we derive the chemical and volumetric contributions of Ni and Pt from the experimental shear modulus data of paramagnetic Fe–Ni and Fe–Pt alloys while those of C, Co, Cr, Mn, Mo, N and Si are derived from the shear modulus of paramagnetic Fe–Ni– X alloys. In the case of Al, Be, Cu, Ge, Ir, Nb, Re, Rh , Ru and W, the total effect on the shear modulus is calculated by assuming that the electronic contribution to the shear modulus in γ-Fe is the same as in α-Fe. To calculate the isotropic shear modulus of multicomponent bcc and fcc solid solutions, we propose linear superposition laws. The proposed relationships are validated using the experimental data of a large number of multicomponent alloys having austenitic, ferritic, and lath martensitic microstructures. It is demonstrated that for all three microstructures, in most cases the shear modulus can be predicted with an accuracy of ±3% in multicomponent solid solutions. It is also found that the high dislocation density in lath martensite accounts for a decrease in shear modulus by about 5% compared to the ferritic counterpart. We also demonstrate that the temperature dependence of shear modulus in multicomponent bcc and fcc solid solutions is similar to that of pure α- and γ-Fe, respectively, for up to about 800 K.