三维二十面体准晶弹性半平面周期接触问题研究

Research on the Periodic Contact Problems of Three Dimensional Icosahedral Quasicrystal Elastic Half⁃Plane

借助平面弹性复变方法,研究了周期刚性压头作用下三维二十面体准晶弹性半平面的周期有限摩擦和周期粘结接触问题.从应力、位移分量的复变函数形式表达式出发,利用半平面Hilbert核积分公式、Plemelj公式,得到两类周期接触问题的解答.针对周期有限摩擦接触问题,得到了三类周期刚性压头(直水平、直倾斜和圆形基底)作用在准晶体半平面上接触应力的封闭解.针对半平面周期粘结接触问题,求得接触边界上作用周期尖劈形位移时接触应力的显式解答.当不考虑相位子场的作用时,文中求得的理论结果可退化到正交各向异性材料平面弹性周期接触问题的对应结果.数值算例说明准晶弹性常数对接触应力分布规律及大小的影响.本文结论可为分析准晶材料压痕实验结果及准晶材料性能提供一定理论依据.

Based on the plane elastic complex transformation method,the frictional and the adhesive periodic contact problems of a three-dimensional icosahedral quasicrystal elastic half-plane under the action of a periodic rigid indenter were studied.From the expressions of complex functions of stress and displacement components,two types of periodic contact problems were solved using the half-plane Hilbert kernel integral formula and Plemelj formula.For the periodic finite friction contact problem,the closed-form solutions of the contact stress of three different shapes of rigid indenters(flat,inclined and spherical base indenters)acting on the semi plane of a quasicrystal were obtained.For the problem of half plane periodic adhesive contact,the analytic expressions of contact stress were obtained in the case of the wedge-shaped periodic displacement on the contact boundary.Without considering the effect of phason field,the obtained results in the paper can degrade to the corresponding results of the periodic plane elastic contact problem of orthotropic materials.Numerical examples are used to illustrate the influence of quasicrystal elastic constants on the distribution and magnitude of contact stress.These conclusions can provide a theoretical basis for analyzing the indentation experiment results and properties of quasicrystal materials.