功能梯度材料涂层平面运动裂纹分析

Moving Crack Analysis in a Functionally Graded Coating under Plane Deformation

研究粘结于均匀材料基底上功能梯度材料涂层平面运动裂纹问题,假设功能梯度材料剪切模量和密度为坐标的指数函数,而泊松比为常数。采用Fourier变换和传递矩阵法将该混合边值问题转化为一对奇异积分方程,通过数值求解奇异积分方程组获得功能梯度材料涂层平面运动裂纹的应力强度因子。考察了结构几何尺寸、裂纹运动速度以及材料梯度参数对运动裂纹的应力强度因子的影响,发现材料梯度参数、结构几何尺寸、裂纹长度以及运动速度均对功能梯度材料动态断裂行为有显著影响。

A finite crack with constant length propagating in a functionally graded coating with spatially varying elastic properties bonded to homogeneous material under in-plane loading was studied. By utilizing Fourier transformation technique, the mixed boundary problem was reduced to a system of singular intergral equations. The stress intensity factors were obtained by solving the singular intergral equations. Moreover, the influences of geometric parameters, the graded parameter, the crack length and speed on the stress intensity factors were investigated. The numerical results show that the graded parameters, the thicknesses of functionally graded strip and the homogeneous material substrate, the crack size and speed have significant effects on the dynamic fracture behavior.