Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors

Piezoelectric semiconductors are materials which have the properties of both piezoelectrics and semiconductors. Many of these materials' properties are very sensitive to defects such as cracks. In this paper, we study cracks in two-dimensional n-type piezoelectric semiconductors by using the displacement discontinuity method. Based on the general solution and Fourier transform, the fundamental solutions for a line crack under uniformly distributed extended displacement discontinuities on the crack surface are derived, in which the extended displacement discontinuity denotes the displacement discontinuities along the x-axis and z-axis, electric potential discontinuity, electron density discontinuity, respectively. By using the obtained fundamental solutions, the extended displacement discontinuity boundary element method is developed to calculate the stress, electric displacement and electric current intensity factors at crack tip. Numerical calculations show how the mechanical, electrical and current loadings affect these intensity factors.