由于涂层优异的隔热、耐磨、抗腐蚀等性能，涂层/基底体系在航空航天、汽车和船舶等领域具有广泛应用。例如，热障涂层应用于航空发动机涡轮叶片，可有效降低高温合金基底的温度，从而保护叶片并提高发动机的热效率。

由于涂层/基底体系在实际应用中不可避免地会承受机械载荷，因此涂层除了发挥隔热等重要功能，还会表现出对体系的强化效应。前人研究发现这种强化效应非常显著，且涉及到多种复杂的微观机制，但对强化效应的宏观行为的关注相对较少，譬如，涂层的区域大小、涂层模量等涂层性质和界面性质如何影响这种强化效应。而在强化之后，涂层开裂以及界面层裂等失效行为可能导致强化效应和隔热等功能的丧失。因此，研究涂层/基底体系的强化及失效机制具有重要的现实意义。本论文通过理论建模和结合内聚力模型的有限元模拟，系统地研究了涂层/基底体系的强化及失效行为。主要研究工作及取得的成果如下：

(1) 基于梁理论和界面应力假设，建立了三点弯曲载荷下反映涂层强化效应的理论模型。从理论上给出了体系刚度的显式表达式，揭示了涂层参数和界面参数对界面应力、体系刚度的影响规律。研究表明随着基底上涂层的粘结长度增加，体系的刚度会逐渐增加直至趋于饱和，而界面应力在涂层端部的奇异性减弱。随着涂层厚度、涂层模量的增加和界面刚度的减小，对应刚度饱和的临界涂层粘结长度单调增加。因此，涂层取到临界粘结长度是最为高效且经济的，但涂层端部的应力奇异性应当慎重处理。

(2) 作为对涂层/基底失效行为模拟的理论铺垫，首先根据串联模型，从理论上推导了引入内聚力模型后系统的总体力学响应。对于单一材料介质内部引入内聚力单元，为保证内聚力单元的引入不影响材料的力学性质，提出了有限厚度内聚力单元刚度的选取准则。而对双材料界面，如涂层/基底体系界面，通过引入内聚力单元，揭示了宏观尺度下体系依赖于厚度的断裂特征：随着体系厚度如涂层厚度的增加，体系的断裂越趋于灾变。这一结论与文献中微观尺度下的分子动力学模拟结果一致。

 (3) 通过结合内聚力模型的有限元方法，模拟了三点弯曲载荷下的涂层/基底体系在不同失效模式下的失效行为，讨论了涂层厚度、涂层和界面的强度及断裂韧性的影响规律。当界面结合非常强时，体系的失效模式主要为涂层开裂，因此仅在涂层内部引入横向内聚力单元，内聚力单元的刚度是根据本文提出的选取准则而确定的。研究发现随着涂层强度的增加，横向裂纹长度先增大后减小；随着涂层断裂韧性的增加，横向裂纹长度单调减小。当界面结合很弱时，体系的失效模式主要为界面层裂，因此仅在涂层和基底的界面引入内聚力单元。结果表明：随着界面强度的增加，界面层裂先变容易后变难；随着界面断裂韧性的增加，界面层裂越来越难。对于一般情形下的混合失效模式，体系的主导失效模式与涂层厚度密切相关：随着涂层厚度的增加，主导的失效模式从涂层开裂过渡到界面层裂，模拟结果与实验结果相符。由无量纲裂纹长度定义的损伤和无量纲位移之间遵循幂次损伤失效模型，损伤率在灾变点附近具有0.5次方奇异性，且界面层裂主导的厚涂层体系较涂层开裂主导的薄涂层体系损伤更快。研究还发现随着界面强度的增加，厚涂层体系损伤更慢，这一结论可以用来解释为何具有更高界面强度的纳米陶瓷涂层体系的损伤更慢。

Coating/substrate systems have been widely used in aerospace, automobile and ship industry due to the coating’s excellent properties of thermal insulation, wear resistance, corrosion resistance and so on. For example, thermal barrier coatings (TBCs) are used in turbine blades of aircraft engines to reduce the temperature of superalloy substrate, which can protect turbine blades and improve thermal efficiency of engines.

Since coating/substrate systems are always subjected to mechanical loads inevitably in practical applications, coatings not only play a role in important functions like thermal insulation, but also strengthen the system. It has been found that the strengthening effects are actually remarkable, which involves various complex micro mechanisms. However, little concern is paid on the macro strengthening behaviors, for example, influences of coating properties including the coating bonding area and the coating modulus as well as the interface properties on strengthening effects. Furthermore, the failure behaviors involving coating cracking and interface delamination after the strengthening may lead to the loss of strengthening effects and other functions such as thermal insulation. Therefore, it is of great practical significance to investigate the strengthening and failure mechanisms of coating/substrate systems. In this thesis, by means of theoretical modelling and finite element simulations using cohesive zone model, strengthening and failure mechanisms of coating/substrate systems were studied systematically. The main work and results could be stated as follows:

(1) Based on the beam theory and some assumptions about interfacial stresses, a theoretical model to reflect the strengthening effects for systems under three-point bending was developed. The explicit expression of the system stiffness was given. Influences of coating properties and interface properties on the system stiffness and interfacial stresses were revealed. It is found that with the increase of coating bonding length, the system stiffness increases and tends to saturation eventually, while singularities of interfacial stresses at the coating end become weaker. The critical coating bonding length corresponding to the saturation of system stiffness increases monotonously with the increase of coating thickness and coating modulus, as well as the decrease of interfacial stiffness. Thus, it is most efficient and economical to take the critical bonding length as the coating length, but the singularities of interfacial stresses at the coating end should be taken into consideration carefully.

(2) The overall mechanical responses of systems with cohesive zone model were derived theoretically from a series model at first, which serves as a theoretical basis for modelling of failure behaviors of coating/substrate systems. When cohesive elements are introduced into single-material media, in order to ensure that the introduction of cohesive elements should not affect the original mechanical properties, a selection criterion of stiffness of finite-thickness cohesive elements was proposed. As for bi-material systems, for example, coating/substrate systems, the thickness-dependent fracture characteristic on the macroscopic scale was revealed by introducing cohesive elements to the interface: as the system thickness such as coating thickness increases, the fracture of the system tends to be closer to the catastrophic failure. This is in accordance with literature results of molecular dynamics simulations on the microscopic scale.

(3) Through finite element method (FEM) using cohesive element model, the failure behaviors of coating/substrate system under three-point bending in different failure modes were modelled, and influences of coating thickness, the strength and fracture toughness of coatings and interface were discussed. For systems with very strong interface, the failure mode is mainly coating cracking. Thus, only transverse cohesive elements were inserted into the coating, and values of cohesive stiffness were chosen according to selection criterion proposed in this thesis. The results indicate that with the increase of coating strength, transverse crack length increases firstly and then decreases. And with the increase of coating fracture toughness, transverse crack length decreases monotonously. For systems with very weak interface, the failure mode is mainly interface delamination. Thus, only cohesive elements were inserted to the interface of coating and substrate. The results imply that with the increase of interfacial strength, interface delamination is easier at first and then becomes harder, while the increase of interfacial fracture toughness always makes the delamination harder to occur. Generally, for systems in mixed failure mode, the dominated failure mode is closely related to coating thickness: with the increase of coating thickness, the dominated failure mode transitions from coating cracking to interface delamination, which is consistent with experimental results. The damage defined by dimensionless crack length with dimensionless loading displacement obeys the power-law damage and failure model, and the damage rate shows the singularity of 0.5 near the catastrophic failure point. The damage of thick coating systems whose failure are dominated by interface delamination is faster than thin coating systems whose failure are dominated by coating cracking. It can be found that with the increase of interfacial strength, the damage of thick coating systems is slower, which can be used to account for the slower damage of nanostructured ceramic coatings with higher interfacial strength.