涂层中任意奇异点的弹性基本解研究

摘要

在涂层与基体分别为不同材料的涂层-基体体系中，涂层材料内存在一任意奇异点，运用格林函数法，推导得到这个问题的一般弹性基础解，运用几个退化模型证明基本解的正确性，并用三个简单的例子演示了此基本解的应用。一般任意奇异点可以是位错、点力、点距、点应变等，所以这个基本解是一系列不同奇异点弹性基本解的一般形式。这个广义的基本解可以作为格林函数法中的核函数用来求解其他更多更复杂的涂层基体问题，例如界面裂纹、TGO 残余应变、材料不匹配、夹杂及热膨胀问题、相变问题等。%A generic fundamental solution for an elastically dissimilar layer-substrate system with a generalized singularity embed-ded within the layer is derived in this study.The solutions can be used as Green’s functions for integral equation formulations of layer problems in layer-substrate systems.The application of the solutions is demonstrated with three simple examples.It should be noted that the term ‘singularity’will be used to refer to a broad class of fundamental solutions of elasticity.It may represent a dislocation,a concentrated force,a point moment,a point concentrated strain,or any other point nucleus of strain.The funda-mental solutions will be treated as kernel functions for the more rigorous formulation of integral equations for the layer-substrate problems,such as through-thickness or interfacial cracks,TGO problems,inclusions and thermal expansion problems,material mismatch problems,phase transformation,etc.