The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip

Abstract

Following a linear theory for soft ferromagnetic elastic solids, we consider the problem of determining the stress-intensity factors in an infinite strip of a soft ferromagnetic elastic material containing two coplanar Griffith cracks. We assume that the solid is a homogeneous and isotropic one and it is permeated by a uniform magnetostatic field normal to the cracks surfaces and that the cracks are opened by a constant internal pressure. By the use of Fourier transforms we reduce the problem to that of solving two simultaneous triple integral equations. These equations are reduced to a singular integral equation of the first kind. By expanding the solution into the form of the product of the series of Chebyshev polynomials of the first kind and their weight function, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. Numerical calculations are carried out and the influence of the magnetic fields on the stress-intensity factors is graphically shown in detail.