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 defonn without constraints, producing local strain 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. IntroductionBecause of tougher environmental constraints, the noise reduction in transformer cores has become increasingly important. It is generally accepted that the main source of noise is magnetostriction, which is known to be caused during the magnetisation process by the movement of 90° magnetic domain walls and the rotation of the magnetisation vector out of the easy directions. Therefore, it is obvious that when a ferromagnetic body is magnetised to saturation, the resulting magnetostriction will be dependent on the distribution of magnetic domains in the initial state.In the literature two coefficients are used to describe the resulting magnetostriction at a saturating magnetic field. The total strain, measured from an arbitrary demagnetised state to technical saturation, is called the saturation magnetostriction, and is denoted by (~)s. The tenn magnetostriction coefficient will be employed to designate the strain measured from the ideal demagnetised state (i.e. one in which no preferred orientation of domains exists) to technical saturation. Failure to recognise the difference between these two quantities has led to considerable confusion in the literature.The magnetostriction coefficient for a single crystal is a well-known property for ferromagnetic cubic materials. In 1939 Becker and Doring [1] have derived the following relation, describing the magnetostriction coefficient for single crystals with a cubic symmetry:"