固体之间接触面积的时间依赖性建模
Towards a modeling of the time dependence of contact area between solid bodies
摘要：
我提出了一个简单的模型，固体之间的接触面积的时间依赖性，假设一个完全不相关的表面形貌，或自仿射表面粗糙度。松弛效应的存在（我使用最近提出的模型）产生的时间增加的接触面积$A(t)$的渐近值，可以比标称接触面积小得多。对于一个不相关的表面形貌，$A(t)$的时间演变的数值被发现是很好地拟合的形式的表达式[ $A(\infty)-A(t)]\sim (t+t_0)^{-q}$，其中的指数$q$取决于正常负载$F_N$为$q\sim F_N^β$，与$β$接近0.5。特别地，当接触面积远低于标称面积I时，获得$A(t)/A(0) \sim 1+C\ln(t/t_0+1)$，即，根据实验观察，接触面积的对数时间增加。在这种情况下，低载荷的对数增长也可以通过分析获得。对于自仿射曲面的更现实的情况下，结果是定性相似的。
英文摘要：
I present a simple model of the time dependence of the contact area between solid bodies, assuming either a totally uncorrelated surface topography, or a self affine surface roughness. The existence of relaxation effects (that I incorporate using a recently proposed model) produces the time increase of the contact area $A(t)$ towards an asymptotic value that can be much smaller than the nominal contact area. For an uncorrelated surface topography, the time evolution of $A(t)$ is numerically found to be well fitted by expressions of the form [$A(\infty)-A(t)]\sim (t+t_0)^{-q}$, where the exponent $q$ depends on the normal load $F_N$ as $q\sim F_N^β$, with $β$ close to 0.5. In particular, when the contact area is much lower than the nominal area I obtain $A(t)/A(0) \sim 1+C\ln(t/t_0+1)$, i.e., a logarithmic time increase of the contact area, in accordance with experimental observations. The logarithmic increase for low loads is also obtained analytically in this case. For the more realistic case of self affine surfaces, the results are qualitatively similar.
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