An internal crack subjected to a thermal flow in magnetoelectroelastic solids : exact fundamental solution

The analysis of intensity factors for cracks under thermal, mechanical, electrical and magnetic boundary conditions has become a very important topic in fracture mechanics. In this paper, an exact and complete fundamental solution is derived for the problem of a penny-shaped crack in magneto-electro-thermo-elastic material under prescribed thermal flux on the crack faces. The problem is analyzed within the framework of the theory of linear magneto-electro-thermo-elasticity. Electro-magneto-thermo-elasticity includes the effective elastic, piezoelectric, piezomagnetic, dielectric permittivity, magnetic permeability and electromagnetic coupling moduli, as well as the effective thermal expansion coefficients and the associated pyroelectric and pyromagnetic constants. The coupling features of transversely isotropic magneto-electro-thermo-elastic solids are governed by a system of partial differential equations with respect to the elastic displacements, the electric potential and the magnetic potential and temperature field. The heat conduction equation and equilibrium equations for an infinite magneto-electro-thermo-elastic media are solved by means of Hankel integral transform. The intensity factors of thermal stress, electric displacement and magnetic induction are derived explicitly for impermeable and permeable cracks. Due to its explicitness, the solution is remarkable and should be of great interest in the magneto-electro-thermo-elastic material analysis and design.