功能梯度材料的裂纹分析及有限元计算

摘要

非均匀介质力学的早期研究最先始于密度及力学性质随深度变化的弹性波问题.此后,非均匀介质力学的研究便云集了广泛的研究者.本文,分析和计算了功能梯度材料的裂纹尖端场及应力强度因子.比较了均匀材料与非均匀材料裂纹尖端场,指出:材料梯度不影响裂纹尖端的奇异性阶次和角分布函数,但影响应力强度因子(SIF)值.作为断裂力学的重要参数,应力强度因子是材料梯度,外载荷及构件几何形状的函数.文中,假设材料的弹性摸量按具有不同系数的指数变化,使用有限元方法获得了裂纹尖端位移,然后使用外推法得到了功能梯度材料张开型断裂的应力强度因子.%The earliest research on mechanics of non - homogenous medium is about the elastic wave (the density and mechanical properties vary along the depth). Since that time, the mechanics research of non - homogeneous medium has been the focus of worldwide researchers. In this paper, both the crack -tip field of graded materials and the stress intensity factor are analyzed and calculated. And the crack -tip field between homogeneous and non -homogeneous materials is compared. It boils down to that the material gradients do not affect the order of singularity and the angular functions of the crack tip fields,but do affect the stress intensity factor. As the important factor of fracture mechanics, the SIF is function of material gradients, external loading and geometry. Commonly, the solution of SIF is calculated through displacement method and stress method. In this paper, the Young's modulus is assumed as exponential variable, with different coefficient, the displacement of crack - tip is obtained first using FEM, and then the SIF of FGM opening mode fracture at the crack - tip is obtained using the extrapolating method.