磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性，且表面电势和磁势是常数。微动接触依赖载荷的加载历史，所以首先求解单独的法向加载问题，然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区，其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换，磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组，然后数值离散为线性代数方程组，利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。

Two-dimensional fretting contact analysis of magneto-electro-elastic materials under a rigid conducting cylindrical punch

Magneto-electro-elastic composite materials (MEEMs), comprised of piezomagnetic and piezoelectric phases, possess superior mechanical performance and intrinsic electro-magnetic-mechanical coupling effects. MEEMs have been widely used in various hi-tech smart structures and devices, such as, micro power generators, transducers and actuators. In practical engineering applications, due to the intrinsic brittleness of MEEMs, the smart devices and structures made of MEEMs will easily suffer from surface contact damage when subjected to the highly concentrated local contact loads and friction forces. In addition, these structures are often served in the vibration environment. Therefore, fretting contact damage and fatigue failure inevitably occur in these smart devices. In this paper, the two-dimensional fretting contact between an MEEM half-plane and a rigid conducting cylindrical punch are investigated to improve the resistance to fretting contact damage and electromagnetic failures. The punch is assumed to be a perfect electro-magnetic conductor with constant electric potential and constant magnetic potential within the contact region. Since the fretting contact problem is loading history dependent, the two bodies are brought into contact first by a monotonically increasing normal load, and then by a cyclic tangential load, which is less than that necessary to cause complete sliding. It is assumed that the whole contact region contains an inner stick region and two outer slip regions where Coulomb’s friction law is applied. By using the Fourier integral transform technique, the problem is reduced to a set of coupled Cauchy singular integral equations. An iterative method is used to determine the unknown stick/slip region, normal contact pressure, electric charge, magnetic induction and tangential traction. The effects of the friction coefficient, total electric charge, total magnetic induction and conductivity of the punch on the surface electromechanical fields are discussed for different loading phases. It is found that the peak value of tangential traction for the insulating punch is larger than that of the conducting punch, but the size of the stick region is smaller than that of the conducting punch. The maximum values of the in-plane tensile stress, the in-plane electric displacement and the in-plane magnetic induction occur at the edges of the contact region during the tangential loading phase, which implies a possible site of the contact damage and fretting crack initiation.