Critical volume fraction of multiple cracks for fracture in piezoelectric media

This paper concerns an infinite piezoelectric solid containing multiple penny-shaped cracks subjected to a set of uniform electromechanical loads. Based on the eigenstrain formulation, the crack is treated as an inclusion by taking the electroelastic moduli of the inclusion as zero. The Mori-Tanaka theory is employed to account for the effects of crack interaction at finite concentration through the use of electroelastic Eshelby tensors. By using this theory, the averaging electroelastic field and the effective electroelastic moduli of the piezoelectric cracked body are expressed explicitly. Furthermore, an interaction energy density function is introduced to take the interaction between electromechanical loads and cracks into account. With this interaction energy density function, the critical volume fraction of multiple cracks for fracture is obtained for a simple tension, a pure shear, and a normal electric displacement, separately.The resulting critical volume fraction is a function of the geometrical dimension of the crack length, electromechanical loading, acid the piezoelectric properties of the surrounding matrix.