各向异性功能梯度材料板Ⅰ型裂纹断裂力学研究

Fracture Analysis of Mode I Crack in Anisotropic Functionally Graded Materials

针对材料参数在厚度方向可按任意函数连续变化的梯度材料,给出了一个新的分层模型.恰当选取分析平面,使材料参数沿z轴方向按任意函数形式连续变化,利用该模型并借助复变函数方法,研究了各向异性功能梯度材料的Ⅰ型裂纹平面断裂问题.首次推出了材料参数沿梯度方向按任意函数连续变化的各向异性功能梯度材料板Ⅰ型裂纹尖端的应力场、位移场和梯度应力强度因子的理论计算公式.结果显示裂纹尖端应力场同样具有r反平方根的奇异性,因此可以运用广泛应用于均匀材料中的断裂力学方法来研究各向异性功能梯度材料问题.

A new multi-layered model was developed for the functionally graded materials with arbitrarily varying function parameter in the detection of thickness. By selecting the analyzed plane reasonably, the materialrs parameter could successively vary in term with arbitrarily function in the derection of z axis. By using this mode and the function of complex variable method,the crack of anisotropic functionally graded materials was studied. The stress and strain fields and graded stress intensity factor near crack tip were firstly introduced. It shows that the stess remains the singular behavior of the inverse square root of r near the crack tip. So those methods which had been applied in homogeneous materials widely can be used to resolve those problems of FGMs.