In this paper, we study a penny-shaped crack model with electrically and thermally semi-permeable boundary conditions in a three-dimensional transversely isotropic piezoelectric semiconductor. An extended displacement discontinuity boundary element method together with an iterative process is proposed to analyze the penny-shaped crack model. The extended displacement discontinuities across crack face, electric displacement and heat flux along an inner crack cavity, as well as extended stress intensity factors near crack front are obtained via the proposed method. The effects on extended intensity factors near crack front are discussed, including boundary conditions across crack face, applied loads and initial electron concentration. It is shown that boundary conditions across crack face significantly affect extended stress intensity factors near crack front. This implies that a larger initial electron concentration can lead to electrical failure.

在本文中，我们研究了三维横向各向同性压电半导体中具有电和热半渗透边界条件的便士形裂纹模型。提出了一种扩展位移不连续边界元方法和迭代过程来分析便士形裂纹模型。通过该方法获得了裂纹面的扩展位移不连续性、沿内部裂纹腔的电位移和热通量，以及裂纹前沿附近的扩展应力强度因子。讨论了对裂纹前沿附近扩展强度因子的影响，包括裂纹面的边界条件、施加的载荷和初始电子浓度。结果表明，裂纹面的边界条件显着影响裂纹前沿附近的扩展应力强度因子。这意味着较大的初始电子浓度会导致电气故障。