COUPLED MAGNETOELASTIC THEORY OF MAGNETIC AND MAGNETOSTRICTIVE HYSTERESIS

A physical model is developed for the coupling between magnetic and magnetostrictive hysteresis and for the effect of mechanical stress on both types of hysteresis. The Jiles-Atherton-Sablik model for magnetomechanical hysteresis is reviewed and interpreted. In that model, under applied stress, the magnetization is coupled to magnetostriction through the derivative of the magnetostriction with respect to magnetization (dlambda/dM). The magnetostriction is also a function of the magnetization even in the absence of stress. An expression for the magnetostriction is derived from minimization of the internal energy with respect to strains, which is necessary for mechanical equilibrium. In the case where stress sigma and field H are coaxial and where the material is assumed to be isotropic, the resulting strain consists of a mechanical strain sigma/Y, where Y is Young's modulus, and a magnetostrain which goes to zero at saturation (DELTAE effect). From the magnetostrain, the magnetostriction is obtained, using the convention that magnetostriction is zero in the unmagnetized state. By taking into account fluctuations in the magnetic energy due to hysteresis, one finds that the magnetostriction initially moves to higher values as the magnitude of the flux density B decreases from its extremum value in lambda versus B plots. Also, in a quasi-dc variation of the external field H, the magnetostriction exhibits a nonzero value at the lowest value of its hysteresis loop, although in the unmagnetized state, the magnetostriction is zero. Various numerical cases are evaluated, and the modeling is compared to previous measurements in polycrystalline iron and steel and in terfenol and Ni-Zn ferrites.