表面应力对平压头摩擦接触问题的影响

Effect of surface stress on frictional contact problem of flat indenter

基于Gurtin-Murdoch表面理论,采用Fourier积分变换法,讨论了具有表面效应的刚性平压头与弹性半平面摩擦接触问题,得到问题的奇异积分方程.再利用Gauss-Chebyshev求积公式,得到受表面应力和摩擦影响的弹性半平面应力和位移的数值解.结果表明,当压头尺寸下降到纳米量级时,表面应力效应显著,可消除压力和应力在接触边缘处的奇异性,并减小表面位移且使得位移梯度在边缘处连续.此外,在考虑表面应力情形下,摩擦的影响几乎可以忽略.

Based on the surface theory of Gurtin and Murdoch and employing the Fourier integral transform method,the problem of frictional contact of rigid flat indenter with elastic semi-plane was discussed in the case that they both have surface effect and a singular integral equations of the problem was obtained.Using further the Gauss-Chebyshev quadrature formula,the numerical solutions of stress and displacement on elastic semi-plane affected by surface stress and friction were achieved.The result showed that when the size of the indenter is reduced to the nanoscale,the effect of surface stress would be remarkable,being able to eliminate the singularities of pressure and stress at the contact fringe.And it would also reduce the surface displacement,making the displacement gradient at the fringe continuous.In addition,in the case of considering the influence of the surface stress,the effect of friction could almost be ignored.