The main objective of this paper is to study the singular nature of the crack-tip stress andelectric displacement field in a functionally gradient piezoelectric medium having material coefficients with adiscontinuous derivative.The problem is considered for the simplest possible loading and geometry,namely,the anti-plane shear stress and electric displacement in-plane of two bonded half spaces in which the crack isparallel to the interface.It is shown that the square-root singularity of the crack-tip stress field and electricdisplacement field is unaffected by the discontinuity in the derivative of the material coefficients.The prob-lem is solved for the case of a finite crack and extensive results are given for the stress intensity factors,elec-tric displacement intensity factors,and the energy release rate.
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