Closed-form solution for a mode-III crack at the mid-plane of a piezoelectric layer (Q1348232)

This paper presents a closed-form solution for a through mode-III crack situated at the mid-plane of a piezoelectric layer. Within the framework of linear piezoelectricity, a cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. By using the Fourier integral transform technique, the problem is reduced to two simultaneous dual integral equations. Then, these equations reduce to weakly singular integral equations with logarithmic kernel, which can be solved analytically. Generally, two cases are considered, namely an impermeable crack, being an extreme case of a hole full of vacuum, and a permeable crack, i.e. a crack filled with an electrolyte solution and acting as a conductor. For both cases explicit expressions for electroelastic field, the field intensity factors and the energy release rate are given for a crack of finite length. As a limiting case, analytical results for a semi-infinite crack embedded in a piezoelectric layer are derived in a straightforward manner.