Macrocrack–microcrack interaction problem in magnetoelectroelastic solids

Abstract

Aiming at investigating the macrocrack–microcrack interactions in magnetoelectroelastic solid, the elementary solutions for a semi-infinite macrocrack and a microcrack subjected to various loading conditions are derived first. Then by using the pseudo-traction–electric-displacement–magnetic-induction method that is motivated by the well-known pseudo-traction method [J. Mech. Phys. Solids 35 (1987) 601], the present interaction problem is reduced to a system of integral equations. After solving these equations numerically by using the Chebyshev numerical integration technique, the crack tip stress intensity factors (SIFs), the electric displacement intensity factor (EDIF), the magnetic induction intensity factor (MIIF) as well as the mechanical strain energy release rate (MSERR) are evaluated subsequently. The J-integral for magnetoelectroelastic medium is further deduced, and it is employed to examine the correctness of the calculation results derived. Finally, take both the stress intensity factors and the mechanical strain energy release rate as measures to investigate the influences of various loading conditions, the crack location and orientation as well as the number of microcracks on the macrocrack–microcrack interactions. It is found that both the electric and magnetic loadings have a significant influence on the fracture toughness of magnetoelectroelastic solid.