基于偶应力理论涂层半平面的二维滑动摩擦接触分析

Two-dimensional sliding friction contact analysis of a coated half-plane with coupled stress

本文基于偶应力理论,研究了平面应变状态下刚性压头与均匀涂层半平面之间的二维滑动摩擦接触问题.该理论通过引入材料特征长度来描述微结构材料的尺寸效应.采用傅里叶积分变换方法将此尺寸依赖的接触问题转化为第二类Cauchy奇异积分方程.然后,通过数值求解该类方程来确定涂层表面法向应力和面内应力的分布.详细讨论了尺度参数、剪切模量比和摩擦系数对表面法向接触应力和面内应力的影响.结果表明基于偶应力理论得到的接触应力明显偏离基于经典弹性理论预测的结果,而且表现出对材料特征长度的强烈依赖性.

Based on the couple stress theory, we study the two-dimensional sliding friction contact between a rigid punch and a homogeneous coated half plane. This theory describes the size effect of microstructure materials by introducing characteristic material length. Using the Fourier integral transform method, the size-dependent contact problem is reduced into a Cauchy singular integral equation of the second kind. Then, it is numerically solved to determine the distribution of the normal contact stress and in-plane stress on the contact surface. The effect of the length scale parameter, the ratio of the shear modulus and the friction coefficient on the normal contact stress and in-plane stress are discussed in detail. The results indicate that the contact stress considering the couple stress departs significantly from the prediction of the classical elastic theory, and shows a strong dependence on the characteristic material length.