轴向剪切条件下功能梯度圆柱形复合材料的界面开裂问题研究

Study on the Interfacial Fracture in a Functionally Graded Cylindrical Composite Material under Axial Shear

针对外覆功能梯度涂层的圆柱形复合材料在轴向剪切作用下的界面开裂问题,建立了断裂力学分析的理论模型。运用分离变量和无穷级数法,推导了奇异积分方程;利用Lobatto-Chebyshev配点法将其离散为代数方程组,最后得到了应力强度因子的数值解。对数值结果的讨论表明:在涂层外表面固定的条件下,可以通过降低涂层厚度和设计内侧软而外侧硬的涂层2种途径来有效地减小界面的断裂驱动力。研究结果可为工程中该类复合材料的防断裂优化设计提供理论参考。

Theoretical model is established for the problem of interfacial fracture in a composite material consisting of a central cylinder and an outer functionally graded coating under the action of axial shear. The techniques of variable separation and infinite series are employed to derive the singular integral equa-tion,which is further discretized into algebraic equations (AEs)by the Lobatto-Chebyshev collocation. Numerical results of the stress intensity factor are finally obtained from the AEs and parametric studies are then performed to reveal the fracture behavior of the interface.It is indicated that when the outer surface of the coating is stiffly fixed,there are two ways to reduce the fracture driving force.One is to decrease the thickness of the coating and the other is to design a coating whose inner side is softer than its outer side.The conclusions of the present work can provide theoretical references to the fracture-proof optimal design of such kind of composite material in engineering.