分布载荷作用下多铁性圆柱复合材料的断裂分析

Fracture Analysis of Multiferroic Cylindrical Composites under Distributed Loads

针对多铁性圆柱复合材料因其外表面上存在不同类型的轴向分布载荷而出现的界面裂纹问题,建立了断裂力学分析模型。首先利用分离变量法和无穷级数法推导出该模型的Cauchy奇异积分方程组,然后利用Lobatto-Chebyshev配点法离散该方程组为代数方程组,进而得到裂纹尖端应力强度因子(Stress Intensity Factor,SIF)的数值解。通过对数值结果的分析得到:在不同类型的分布载荷作用下,压电层厚度以及分布载荷大小是影响裂纹尖端SIF的主要因素。该研究结果可为此类复合材料在实际工程应用中的防断裂优化设计提供理论参考。

The fracture mechanics analysis model is established for the problem of interfacial fracture with different types of axial distributed loads on the outer surface of multiferroic cylindrical composites. The Cauchy-type singular integral equations of the fracture model are derived by the methods of variable separation and infinite series,which are further dispersed into algebraic equation group by the Labatto-Chebyshev point collection. Numerical solution of the Stress Intensity Factor（ SIF） is finally obtained at the crack tip. The numerical results show that the thickness of the PE layer and the size of the distributed loadings are the main factors affecting the SIF at the crack tips under the different types of distributed loads. The obtained results can provide theoretical references for the anti-fracture optimal design of such composite materials in practical engineering applications.