Collinear crack problems in a soft ferromagnetic solid

Abstract

The 2D problems of a soft ferromagnetic solid with collinear cracks are studied based on the complex variable method. First, the general solutions for potential functions of magnetic fields and stress fields are derived by using magnetically permeable, impermeable and conducting crack models, respectively. Then, for special cases of one and two cracks, more explicit solutions are given for potential functions and intensity factors of total stresses. Finally, numerical results are presented to discuss the effects of applied magnetic loading on fracture behavior of the ferromagnetic solid. It is found that the total stresses always have the classical singularity of the r^{ - 1/2} type at the crack tips for the considered three crack models, and the applied magnetic loading may either enhance or retard crack growth depending on the adopted crack models.