Critical volume fraction of multiple cracks for fracture in piezoelectric media

This paper concerns an infinite piezoelectric solid containing multiple pen ny-shaped cracks subjected to a set of uniform electromechanical loads. Bas ed 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 finit e concentration through the use of electroelastic Eshelby tensors. By using this theory, the averaging electroelastic field and the effective electroe lastic moduli of the piezoelectric cracked body are expressed explicitly. F urthermore, an interaction energy density function is introduced to take th e 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 vol ume fraction is a function of the geometrical dimension of the crack length , electromechanical loading, acid the piezoelectric properties of the surro unding matrix.