Analytical modeling and analysis of fracture of functionally graded coatings

功能梯度涂层（FGCs）应用于不同领域，如核能、航空航天、工程等。它们受到不同的热载荷和机械载荷，并且必须抵抗高温，磨损和腐蚀性环境。然而，裂纹可能是由初始缺陷或在制造或使用过程中出现的微裂纹引起的。因此，研究FGC结构的断裂对更好地了解梯度涂层的抗断裂性能具有重要意义。该项目的主要目标是开发一个计算半分析模型，用于分析均匀基材上的FG热障涂层在热机械载荷下的断裂，并将塑性纳入模型中。FGC/均匀结构（半无限各向同性介质）的断裂问题将在热载荷和/或机械载荷的影响下进行研究（例如，热流，由冷却-加热引起的残余热应力，张力）。这些问题反映了在FGC结构开发过程中出现的最重要的情况。对于具有预先存在的裂缝系统（边缘裂缝、涂层与基体之间的界面裂缝或FGC内部裂缝）的FGC结构的问题，将一般通过积分方程和考虑裂缝处的塑性区域（在Dugdale模型的框架内）来表述。然后，在导出模型的基础上，详细研究了文献中实验得出的FGCs的典型裂纹模式。从热载荷和机械载荷下FGCs裂纹问题的适用性角度出发，对FGCs的热弹性特性进行建模。为了简化问题，将使用相关的函数形式，如指数或幂律函数来模拟FGCs的非齐次性质。在此半解析模型的基础上，将对FGC中不同的实际材料组合（陶瓷/陶瓷，陶瓷/金属）和材料性能变化进行FGC中断裂过程的模拟。该模拟将为选择合适的材料组合和FGCs的级配曲线提供知识，从而优化FGCs的抗断裂性能。

Functionally graded coatings (FGCs) are applied in thermal, wear and corrosion barriers which are used in different fields, such as, nuclear energy, aerospace, engineering, etc. They are subjected to different thermal and mechanical loading and have to resist high temperature, wear and aggressive environments. However, cracks can initiate from initial defects or micro-cracks appear during manufacturing or service. Therefore, the study of fracture of FGC structures is important for a better understanding of the fracture resistance of graded coatings. The primary objective of the project is to develop a computational semi-analytical model for the fracture analysis of FG thermal barrier coatings on a homogeneous substrate subjected to thermo-mechanical loading with plasticity incorporated in the model. The problem of fracture of FGC/homogeneous structures (semi-infinite isotropic medium) will be investigated under the influence of thermal and/or mechanical loads (e.g., a heat flux, residual thermal stresses caused by cooling-heating, tension). These problems reflect the most important cases which arise during the exploitation of FGC structures. The problem for FGC structures with pre-existing systems of cracks (edge cracks, interface cracks between the coating and substrate or internal cracks in the FGC) will be formulated in general by means of integral equations and with accounting for plastic zones (in the frame of the Dugdale model) at the cracks. Then, typical crack patterns for FGCs resulting from experiments available in the literature will be studied in detail on the basis of the derived model. The thermal and elastic properties of FGMs will be modeled from the point of view of its applicability to problems of cracks in FGCs under thermal and mechanical loadings. In order to simplify the problem relevant functional forms, such as, exponential or power law functions, will be used to simulate the non-homogeneous properties of FGCs. On the basis of this semi-analytical model the simulation of fracture processes in FGCs will be performed for different real material combinations (ceramic/ceramic, ceramic/metal) and material property variations in the FGC. This simulation will provide knowledge for choosing appropriate material combinations and the gradation profile of FGCs in order to optimize the fracture resistance of the FGCs.