Mechanical and magnetic hardening of ferromagnetic bodies: Influence of residual stresses and applications to nondestructive testing

Abstract

Abstract A thermodynamical theory of the elastoplasticity of ferromagnetic materials is presented in which both phenomena of plasticity with hardening and magnetic hysteresis are coupled in the manner of magnetostriction. The coercive magnetic field depends on the level of magnetic loading as well as on the state of stresses. In order to simulate the magnetic hysteresis curve, one needs the equation of the first magnetization curve while magnetic hardening, like mechanical hardening, is taken into account through an internal variable which can later be interpreted as the cumulated residual magnetization. The derivative curve of the hysteresis loops provides butterfly loops of which the main parameters markedly depend on the state of stresses. This reminds one of the signal recorded with a view to measuring residual stresses via the Barkhausen effect in magnetizable solids, and this approach may be one step toward a phenomenological interpretation of such recordings. Numerical simulations are given.