Modelling the magnetostriction of textured ferromagnetic materials with a cubic structure

A magneto-elastic model is presented to calculate the orientation dependence of the magnetostrictive strain, observed at saturated magnetisation in ferromagnetic materials with a cubic crystal structure and an arbitrary crystallographic texture. The formula of Becker and Doring is used to express the anisotropy of magnetostriction for a single crystal. In order to simulate the macroscopic average magnetostriction of a polycrystalline aggregate (with an arbitrary texture) the Reuss assumption of the elasticity theory was applied. According to this assumption the various orientations of the polycrystal can deform without constraints, producing local stain incompatibilities in the microstructure but observing total stress equilibrium. The macroscopic strain is calculated as the weighted average of the individual strains of all orientations composing the polycrystal. The weight factors are determined by the volume fractions of the corresponding orientations of the given texture, which can be measured by standard X-ray diffraction techniques. The model is applied to simulate the variation of magnetostriction (at saturation) with respect to the rolling direction for a standard grade of Goss-oriented electrical steel. A brief comparison with experimental data allows validating the basic model assumptions