A generalized and mathematically rigorous model is developed to treat the partially-debonded circular inhomogeneity problem in piezoelectric materials under antiplane shear and in plane electric field using the complex variable method. The principle of analytical continuation and the complex series expansion method were employed to reduce the formulations into Riemann Hilbert problems. This enabled the explicit determination of the complex potentials inside the inhomogeneity and the matrix. The resulting closed form expressions were then used to obtain the energy release rate for several interesting cases involving partial-debonding at the inhomogeneity-matrix interface.