Periodic interfacial cracks in dissimilar piezoelectric materials under the influence of Maxwell stress

Abstract

This paper presents an analytical method to investigate the dissimilar piezoelectric materials containing periodic cracks in the presence of uniform electromechanical loads with consideration of the Maxwell stress. Using Stroh’s formalism and conformal mapping, electric and stress fields are obtained for the semi-permeable cracks with a constant dielectric parameter. An approximate method is developed to obtain the analytical solution to the crack opening displacement, and which is validated by the pre-existing solution and with numerical integral. Using the method developed in this paper, the results of the electric displacement field in cracks, the stress, and electric displacement intensity factors are obtained. The numerical results show uniform electric displacement field inside in cracks, and it is independent of the distribution or the size of cracks when under static uniform electromechanical loads. Additionally, it is found that the field intensity is roughly the same as that in the case of a single interfacial crack when the gap of periodic crack exceeds four times the crack length.