COUPLED MAGNETOELASTIC THEORY OF MAGNETIC AND MAGNETOSTRICTIVE HYSTERESIS

A physical model is developed for the coupling between magnetic and ma gnetostrictive hysteresis and for the effect of mechanical stress on b oth types of hysteresis. The Jiles-Atherton-Sablik model for magnetome chanical hysteresis is reviewed and interpreted. In that model, under applied stress, the magnetization is coupled to magnetostriction throu gh the derivative of the magnetostriction with respect to magnetizatio n (dlambda/dM). The magnetostriction is also a function of the magneti zation even in the absence of stress. An expression for the magnetostr iction is derived from minimization of the internal energy with respec t to strains, which is necessary for mechanical equilibrium. In the ca se where stress sigma and field H are coaxial and where the material i s assumed to be isotropic, the resulting strain consists of a mechanic al strain sigma/Y, where Y is Young's modulus, and a magnetostrain whi ch goes to zero at saturation (DELTAE effect). From the magnetostrain, the magnetostriction is obtained, using the convention that magnetost riction is zero in the unmagnetized state. By taking into account fluc tuations 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 ma gnetostriction exhibits a nonzero value at the lowest value of its hys teresis loop, although in the unmagnetized state, the magnetostriction is zero. Various numerical cases are evaluated, and the modeling is c ompared to previous measurements in polycrystalline iron and steel and in terfenol and Ni-Zn ferrites.