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压电半导体中I型偏心裂纹的瞬态响应

TRANSIENT RESPONSES OF AN ECCENTRIC MODE-I CRACK IN A PIEZOELECTRIC SEMICONDUCTOR STRIP

  • 摘要: 压电半导体特有的力-电-载流子多场耦合特性使其在传感、换能以及晶体管等领域展现出广阔的应用前景. 然而, 在复杂的多场服役环境下, 其脆性特征容易导致材料内部产生裂纹, 从而引起器件功能退化甚至断裂失效. 鉴于此, 本文针对压电半导体中I型偏心裂纹的瞬态断裂问题进行了研究. 首先, 采用 Laplace 变换和Fourier 变换, 将混合边值问题转化为Laplace转换域内的第一类Cauchy奇异积分方程, 然后利用Gauss-Chebyshev雪夫配点法求解该方程, 获得Laplace转换域内的断裂参数, 通过数值反演得到时间域中的动态广义场强度因子和能量释放率. 数值结果表明: 压电半导体材料的导电性对断裂特性的影响取决于外加载荷类型: 在纯机械载荷下, 导电性增强会促进裂纹扩展; 而在纯电载荷作用下, 导电性增强会抑制裂纹扩展. 增加层厚度可有效降低断裂参数值, 提高材料安全性; 裂纹越接近边界, 断裂参数越大. 动态断裂参数达到峰值的时间与材料性能、层厚度及裂纹位置密切相关.

     

    Abstract: Due to the inherent mechanical-electro-carrier multi-field coupling characteristic, piezoelectric semiconductors (PSCs) exhibit significant potential for application in sensors, transducers and transistor devices. However, their intrinsic brittleness may lead to crack propagation under complex multi-field operating conditions, which can degrade functionality or cause catastrophic failure. This study investigates the transient fracture behavior of a PSC strip containing an eccentric Mode-I crack. By applying Laplace and Fourier transforms, the mixed boundary-value problem is converted into a standard Cauchy singular integral equation of the first kind in the Laplace transform domain. Then this integral equation is solved by Gauss-Chebyshev collocation method to obtain the fracture parameters in the Laplace domain. Through numerical inversion, the dynamic generalized field intensity factors and energy release rate in the time domain are obtained. The numerical results indicate that the influence of conductivity is strongly dependent on the type of applied loading. Under purely mechanical loading, higher conductivity may accelerate crack growth, whereas under purely electrical loading, it produces a marked decrease in fracture parameters. Increasing the layer thickness effectively reduces the fracture parameters and thus enhances the reliability, while cracks located closer to the boundary exhibit larger fracture parameters. Moreover, the time at which the dynamic fracture parameters reach their peak values is governed by the material properties, crack location and layer thickness.

     

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