复合材料的裂纹动力学问题的模型

A Crack Dynamics Problem Model of Composite Materials

复合材料产生裂纹后,其纤维处形成“桥连”,这是一个不可避免的现象。由于桥连问题很复杂,在数学方法的处理上有很大困难,至今人们研究的大多是桥连的静力学问题,而对其动力学问题研究得很少。只有建立复合材料的桥连动力学模型,才能更好地研究复合材料的断裂动力学问题。为了便于分析复合材料的问题,将桥连处用载荷代替,当裂纹高速扩展时,其纤维也连续地断裂。通过复变函数论的方法,将所讨论的问题转化为Riemann-Hilbert问题。利用建立的动态模型和自相似方法,得到了正交异性体中扩展裂纹受运动的集中力Px/t及均布载荷作用下位移、应力和动态应力强度因子的解析解,并通过迭加原理,最终求得了该模型的解。

A composite material appears crack, its fibrous position forms bridge, and this is an inevitable phenomenon. Problem on bridge is complex, there is much diffculty to treat with them in mathematical methods. Up to now a bridging fiber crack has been studied on its statics and studies on its dynamics problem are few. If dynamics model of bridging fiber is built, the dynamics problem of composite materials is solved very convenient. In order to analyze the problems of composite materials easily, the bridging fiber section is substituted by loads, when a crack extends its fiber continues to break. By the theory of complex functions, the problems can be transformed into Riemann-Hilbert problems. Utilizing the built dynamic models and the self-similar methods, the analytical study on the displacements, stresses and dynamic stress intensity factors of crack propagation under a concentrated force Px/t as well as uniform loads is firstly attained in orthotropic body and it is utilized to obtatin the concrete solution of the model by the ways of superposition.