This paper presents a fracture analysis of ultra-thin coating/substrate structures with interface cracks. For this purpose, an advanced boundary element method (BEM) is adopted. To correctly describe the oscillatory displacement and stress fields near the interfacial crack-tip, a new set of novel special crack-tip elements are implemented. The complex interfacial stress intensity factors (SIFs) can be directly and accurately computed at the collocation points extremely close to the crack-tip by using the proposed computational strategy based on the novel special crack-tip elements. Furthermore, the troublesome nearly-singular boundary integrals, which are crucial in the application of the BEM for both crack-like and ultra-thin structural problems, are calculated accurately by using a nonlinear coordinate transformation method. It is shown that the advanced BEM based on the novel special crack-tip elements and appropriate technique for evaluating nearly-singular boundary integrals provides an accurate and robust numerical tool for interfacial crack analysis of ultra-thin coating structures. Accurate and reliable BEM results with only a small number of boundary elements can be obtained for a relative coating-to-substrate thickness as small as 10^-9, which is important for modeling ultra-thin coating structures as used in smart materials and micro/nano-electro-mechanical systems (MEMS/NEMS). Several representative numerical examples will be presented and discussed to reveal the effects of the key geometrical and material parameters, the crack configuration and the loading conditions on the interfacial fracture parameters such as energy release rate and complex SIFs

本文介绍了具有界面裂纹的超薄涂层/基体结构的断裂分析。为此，采用了高级边界元方法（BEM）。为了正确描述界面裂纹尖端附近的振荡位移和应力场，实现了一组新的新型特殊裂纹尖端元素。通过使用基于新型特殊裂纹尖端元素的拟议计算策略，可以在极其接近裂纹尖端的配置点上直接且精确地计算出复杂的界面应力强度因子。此外，使用非线性坐标变换方法可以准确地计算出麻烦的近奇异边界积分，这对于在BEM应用中解决裂纹状和超薄结构问题都是至关重要的。结果表明，基于新型特殊裂纹尖端元素的先进边界元分析方法和用于评估近奇异边界积分的适当技术为超薄涂层结构的界面裂纹分析提供了准确而可靠的数值工具。对于相对于涂层到基材的最小厚度为10的情况，仅需少量边界元素即可获得准确而可靠的BEM结果^-9，对于在智能材料和微/纳米机电系统（MEMS / NEMS）中使用的超薄涂层结构建模很重要。将给出并讨论几个代表性的数值示例，以揭示关键的几何和材料参数，裂纹配置和加载条件对界面断裂参数（例如能量释放率和复杂SIF）的影响