Fractal geometry of contacting patches in rough elastic contacts
Fractal geometry of contacting patches in rough elastic contacts
复制标题
粗糙弹性接触中接触斑块的分形几何
DOI：
10.1016/j.jmps.2022.104797
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发表时间：
2022
影响因子：
5.3
通讯作者：
Robbins, Mark O.
中科院分区：
文献类型：
--
作者：
Monti, Joseph M.;Pastewka, Lars;Robbins, Mark O.
许多自然形成和加工的表面在很大范围的长度范围内都是粗糙的。表面粗糙度减小了固体之间的接触面积，对取决于界面几何形状和直接接触量的现象产生了影响，包括摩擦和粘合。在这项工作中，我们使用大规模的非粘附性、弹性固体的边界元模拟来研究具有自仿射表面粗糙度的固体之间形成的七十年的贴片区域中接触片平均压力和几何形状的尺寸依赖关系。直径小于交叉长度量级、最小粗糙度波长的接触贴片一般结构紧凑，几何形状简单，承受的压力由赫兹理论很好地描述。大于交叉尺度的接触贴片中的贴片压力对数上升，然后在有限值饱和。此外，在我们的模拟过程中形成的最大接触贴片被分支并填充了非接触区域或气泡，这减少了贴片面积并增加了贴片周长。结果表明，最大斑块的平均接触直径趋于饱和，表明斑块的接触面积与总的斑块周长成正比。我们量化了气泡对斑块面积和周长的影响，作为赫斯特指数的函数，并将我们的发现与可比轴承面积模型的计算结果进行了对比。在我们的大规模计算中，平均斑块压力随斑块大小的缓慢演变解释了通常的观测结果，即全球平均接触压力取决于粗糙度结构、接触面积，甚至取决于系统大小。
Many naturally formed and processed surfaces are rough over a broad range of length scales. Surface roughness reduces the area of contact between solids, with ramifications for phenomena that depend on the geometry of the interface and the amount of direct contact, including friction and adhesion. In this work, we employ large-scale boundary-element simulations for nonadhesive, elastic solids to study the size dependence of contact patch mean pressure and geometry for patches formed between solids with self-affine fractal surface roughness across seven decades in patch area. Contact patches with diameters smaller than a crossover length scale of order the minimum wavelength of roughness are generally compact with simple geometries and bear pressures well described by Hertz theory. The patch pressure in contact patches larger than the crossover scale rises logarithmically before saturating at a finite value. Furthermore, the largest contact patches formed during our simulations are ramified and populated with regions out of contact, or bubbles, which reduce patch area and increase patch perimeter. As a result, we show that the mean contact diameter of the largest patches saturates, indicating that the patch contact area is proportional to the total patch perimeter. We quantify the effects of bubbles on patch area and perimeters as a function of Hurst exponent and contrast our findings with results of comparable bearing-area model calculations. The slow evolution of the mean patch pressure with patch size in our large-scale calculations explains the common observation that the global mean contact pressure depends on the structure of the roughness, the contact area, and even on system size.
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