Electric and magnetic polarization saturations for a thermally loaded penny-shaped crack in a magneto-electro-thermo-elastic medium

This paper is devoted to investigating the thermal-induced electric and magnetic polarization saturations (PS) at the tip of a penny-shaped crack embedded in an infinite space of magneto-electro-thermo-elastic medium. In view of the symmetry with respect to the cracked plane, this crack problem is formulated by a mixed boundary value problem. By virtue of the solution to the Abel type integral equation, the governing equations corresponding to the present problem are analytically solved and the generalized crack surface displacement and field intensity factors are obtained in closed-forms. Applying the hypothesis of the electric and magnetic PS model to the analytical results, the sizes of the electric and magnetic yielding zones are determined. Numerical calculations are carried out to reveal the influences of the thermal load and the electric and magnetic yielding strengths on the results, and to show the distributions of the electric and magnetic potentials on the crack surfaces. It is found that the sizes of electric and magnetic yielding zones are mainly dependent on the electric and magnetic yielding strengths, respectively. Since the multi-ferroic media are widely used in various complex thermal environments, the present work could serve as a reference for the designs of various magneto-electric composite structures.