Abstract

The fracture behavior of a cracked functionally graded piezoelectric plane was investigated under in-plane mechanical and electrical loading. The electro-elastic properties of the plane exponentially varied along the y-axis. Employing the Fourier transform, stress analysis containing a Volterra edge dislocation in a functionally graded piezoelectric plane was carried out. These solutions were used to derive a system of Cauchy singular integral equations for analyzing the straight and curved cracks. Linear, arc, parabolic and sine wave-shaped cracks were evaluated. The integral equations were numerically solved using the Lobatto–Chebyshev integration formula for dislocation density functions on the crack face which were employed to calculate field intensity factors. The effects of the shaped crack, loading parameters, and non-homogeneity parameter on the stress and electric intensity factors were considered.

摘要

研究了面内机械和电载荷下裂纹功能梯度压电平面的断裂行为。平面的电弹性特性沿y呈指数变化-轴。采用傅里叶变换，对功能梯度压电平面中包含 Volterra 边缘位错的应力进行了分析。这些解用于推导柯西奇异积分方程组，用于分析直线和弯曲裂纹。评估了线性、弧形、抛物线和正弦波形裂纹。使用 Lobatto-Chebyshev 积分公式对裂纹面上位错密度函数的积分方程进行数值求解，用于计算场强度因子。考虑了成形裂纹、加载参数和非均匀性参数对应力和电场强度因子的影响。