A semi-analytical model is developed for the two-dimensional fretting contact of layered materials with vertical cracks near surfaces to investigate the effects of layers and cracks on the contact behaviors. The layer is assumed as an infinitely extended inclusion with unknown equivalent eigenstrain values based on Eshelby's equivalent inclusion method. The mixed-mode I and II cracks are assumed to have opened faces and closed tips, each of which is simulated by a distribution of climb and glide dislocations with unknown density values according to the discrete dislocation technique. The unknowns are sequentially determined in two separate subroutines based on the conjugate gradient method. The eigen-displacement and crack-induced displacement are introduced into the contact model with the loading history considered. The stress intensity factors are determined based on the solutions of the dislocation densities, assuming the plots of the crack-induced displacement are in parabolic shapes at the tips. It is concluded that the contact loading produces a tendency to close crack faces but in different patterns in the substrate and layer. Mode II stress intensity factors depend on crack locations and layer stiffness. Stress concentrations at the layer/substrate interface and crack tips that may lead to material failures are investigated. The conclusions provide insights into fretting fracture in layered materials.

针对层状材料在表面附近有垂直裂纹的二维微动接触，建立了一个半解析模型，以研究层和裂纹对接触行为的影响。根据Eshelby的等效包含方法，该层被假定为具有未知等效特征应变值的无限扩展包含。假定混合模式的I型和II型裂纹具有张开的面和闭合的尖端，根据离散位错技术，每个裂纹都是通过具有未知密度值的爬升和滑移位错的分布来模拟的。未知数是基于共轭梯度法在两个单独的子例程中顺序确定的。考虑位移历史，将特征位移和裂纹诱发位移引入接触模型。应力强度因子是根据位错密度的解确定的，假设裂纹诱发位移的曲线图在尖端处为抛物线形状。可以得出结论，接触载荷会导致闭合裂纹面的趋势，但在基板和层中的裂纹模式不同。模式II应力强度因子取决于裂纹位置和层刚度。研究了可能导致材料失效的层/基体界面和裂纹尖端处的应力集中。结论为层状材料的微动断裂提供了见识。可以得出结论，接触载荷会导致闭合裂纹面的趋势，但在基板和层中的裂纹模式不同。模式II应力强度因子取决于裂纹位置和层刚度。研究了可能导致材料失效的层/基体界面和裂纹尖端处的应力集中。结论为层状材料的微动断裂提供了见识。可以得出结论，接触载荷会导致闭合裂纹面的趋势，但在基材和层中会以不同的方式出现。模式II应力强度因子取决于裂纹位置和层刚度。研究了可能导致材料失效的层/基体界面和裂纹尖端处的应力集中。结论为层状材料的微动断裂提供了见识。