A Study of Crack Propagation Paths in Functionally Graded Material Plates

本课题主要包括两个部分：[1]含裂纹功能梯度材料板在热载荷作用下的热应力强度因子研究;[2]热载荷作用下功能梯度材料板裂纹扩展路径的有限元研究;[1]热载荷作用下功能梯度材料本构方程研究。(1)本文提出了一种层合复合材料模型来研究具有任意成分剖面的功能梯度材料在热载荷作用下的行为。(2)本文提出的复合材料层合板模型可以处理多裂纹问题。(3)含共线裂纹的功能梯度材料在热载荷作用下，共线裂纹内边缘处的应力强度因子大于外边缘处的应力强度因子，且应力强度因子随裂纹间距的减小而增大。(1)可以编制一个有限元网格自动生成程序。(2)对于单裂纹扩展模拟，直或弯曲的裂纹得到的热冲击和成分分布的几个条件。有些裂纹弯曲得很厉害，并沿平行于表面的方向扩展。这样的裂纹导致表面的分层。其他裂纹在板的中间被阻止。(3)由于双裂纹扩展是复合热裂纹的基本形式之一，因此讨论了双裂纹间的相互作用。当裂纹距离较近时，裂纹沿曲线生长，且相互远离。对于从长距离彼此靠近的剥落裂纹，随着裂纹尖端靠近，裂纹在垂直于表面的方向上弯曲。然后裂纹在板的中间被阻止。

This research project consists of two parts : [1] Study of thermal stress intensity factors in the functionally graded material plates (FGPs) with cracks under thermal load, [2] A study of crack propagation paths in FGPs under thermal load by Finite Element Methods (FEM).PART [1] : Study of constitutional equations of the functionally graded materials (FGMs) under thermal loading.(1) We proposed a laminated composite model to study FGMs with arbitrary compositional profile subjected to thermal loading.(2) Multiple crack problems could be treated by the proposed a laminated composite model.(3) When FGPs with collinear crack are subjected thermal loading, stress intensity factor at an inner edge of collinear crack is larger than one at outer edge and increases with decreasing the distance of each crack.PART [2] : A study of crack propagation paths in FGPs under thermal load by Finite Element Methods (FEM).(1) We could develop a program with automatically production of mesh of FEM.(2) For the single crack growth simulation, the straight or curved cracks are obtained for several conditions of the thermal shock and the compositional profiles. Some cracks curve sharply and grow in the direction parallel to the surface. Such cracks cause delamination of the surface. The other cracks are arrested in the middle of the plate.(3) As two crack growths is one of the basic forms of the multiple thermal cracking, the interaction between the two cracks are discussed. The cracks grow in curve and away from each other, when the cracks exist in short distance. For spalling cracks that come close to each other from a long distance, the cracks curve in the direction normal to the surface as the crack tips come closer. Then the cracks are arrested in the middle of the plate.