Graded nanostructured (GNS) materials has attracted widespread attention in the recent years. The gradually changed microstructures and mechanical properties from the surface to the interior layer in graded nanostructured materials can improve the mechanical properties of the surface. The motivation of this research was to explore the effect of size effect, adhesion and gradient on the mechanical properties in contact between GNS coating and spherical indenter. The multi-layer couple-stress elastic structures is used to simulate the GNS coating with arbitrarily varying material properties. Based on the Maugis-Dugdale theory, the axisymmeric adhesive contact problem for multi-layer couple-stress elastic coated substrate system indented by spherical punch is converted to singular integral equations. Numerically calculation are conducted to obtain the influence of the characteristic material length, adhesion parameter and gradient index on the indentation, surface stress, surface displacement, total attraction force. The present results should be helpful for the understanding of the micro contact mechanics of GNS coating.

近年来，梯度纳米结构（GNS）材料引起了广泛关注。渐变纳米结构材料从表面到内层逐渐改变的微观结构和力学性能可以提高表面的力学性能。本研究的目的是探索尺寸效应、附着力和梯度对 GNS 涂层与球形压头接触机械性能的影响。多层耦合应力弹性结构用于模拟具有任意变化材料特性的 GNS 涂层。基于Maugis-Dugdale理论，将球面冲头压痕的多层偶应力弹性涂层基体系统的轴对称胶粘接触问题转化为奇异积分方程。数值计算得到特征材料长度、粘附参数和梯度指数对压痕、表面应力、表面位移、总吸引力的影响。目前的结果应该有助于理解 GNS 涂层的微接触力学。