Regular Article

An analytical model for the magnetostriction strain of ferromagnetic materials subjected to multiaxial stress

GeePs − Group of Electrical Engineering − Paris, UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Université Paris-Saclay, Sorbonne Université, 3 rue Joliot-Curie, Plateau de Moulon, 91192 Gif-sur-Yvette Cedex, France

^* e-mail: laurent.daniel@centralesupelec.fr

Received: 2 February 2018
Received in final form: 23 May 2018
Accepted: 26 June 2018
Published online: 6 November 2018

Abstract

Magnetostriction is the magnetisation-induced strain in ferromagnetic materials. It highly depends on mechanical stress. Stress state in electromagnetic devices is usually multiaxial and its effect on magnetostrictive properties is not easily predicted. In this paper, an original three-parameter analytical model for the stress-dependent magnetostriction strain of ferromagnetic materials is proposed. It is based on a simplified energetic description of magneto-elastic behaviour. It follows a similar method previously adopted for the description of the effect of stress on the magnetic permeability of magnetic materials. It is applied for the first time to the magnetostriction behaviour and results in a simple formula to express the effect of multiaxial magneto-mechanical loadings on the magnetostriction strain. The approach also naturally includes the description of the so-called ΔE effect. The analytical formula is derived in the paper. It shows very satisfying agreement with experimental results on iron–cobalt alloy and pure iron specimen.