[论文解读] Adhesive rough contacts near complete contact

M. Ciavarella|arXiv (Cornell University)|Apr 30, 2015

Adhesion, Friction, and Surface Interactions参考文献 9被引用 5

一句话总结

本文提出了一种新型的近全接触粘附粗糙接触模型，将孤立缝隙视为受压裂纹，利用Bueckner原理与全接触应力场的抛物线近似。结果表明，当分形维数 D < 2.5 时（这在自然表面中很常见），粘附性仍能强烈维持；而当 D > 2.5 时，粘附性才被抑制，该结果挑战了经典峰体理论，并通过缝隙尺度力学机制解决了粘附悖论。

ABSTRACT

Recently, there has been some debate over the effect of adhesion on the contact of rough surfaces. Classical asperity theories predict, in agreement with experimental observations, that adhesion is always destroyed by roughness except if the amplitude of the same is extremely small, and the materials are particularly soft. This happens for all fractal dimensions. However, these theories are limited due to the geometrical simplification, which may be particularly strong in conditions near full contact. We introduce therefore a simple model for adhesion, which aims at being rigorous near full contact, where we postulate there are only small isolated gaps between the two bodies. The gaps can be considered as "pressurized cracks" by using Ken Johnson's idea of searching a corrective solution to the full contact solution. The solution is an extension of the adhesive-less solution proposed recently by Xu, Jackson, and Marghitu (XJM model) (2014). This process seems to confirm recent theories using the JKR theory, namely that the effect of adhesion depends critically on the fractal dimension. For D&lt;2.5, the case which includes the vast majority of natural surfaces, there is an expected strong effect of adhesion. Only for large fractal dimensions, D&gt;2.5, seems for large enough magnifications that a full fractal roughness completely destroys adhesion. These results are partly paradoxical since strong adhesion is not observed in nature except in special cases. A possible way out of the paradox may be that the conclusion is relevant for the near full contact regime, where the strong role of flaws at the interfaces, and of gaps full of contaminant, trapped air or liquid in pressure, needs to be further explored. If conditions near full contact are not achieved on loading, probably the conclusions of classical asperity theories may be confirmed.

研究动机与目标

• 为了解决尽管存在强范德华力，尤其在粗糙表面上却未观察到强粘附的悖论。
• 在经典峰体理论因几何简化而失效的近全接触区域，建立一个严谨的粘附模型。
• 研究分形维数 D 如何决定粗糙弹性接触中粘附性的持久性。
• 将 XJM 无粘附接触模型扩展，通过受压裂纹力学与应力强度因子平衡引入粘附性。
• 调和经典峰体理论与近期理论（如 Pastewka 和 Robbins）在粗糙表面粘附性问题上的分歧。

提出的方法

• 将界面建模为粗糙表面之间的一组孤立小缝隙，假设处于近全接触状态。
• 应用 Bueckner 原理，将缝隙中的应力场视为全接触解所产生的拉应力作用下的受压裂纹。
• 使用泰勒展开将缝隙附近的全接触应力场近似为抛物线，从而实现解析处理。
• 在裂纹边缘保持恒定的应力强度因子，以确定稳定缝隙闭合，从而导出缝隙半径与施加压力之间的线性关系（带截距）。
• 引入一个与尺度相关的压力 p₀，其包含粘附能，并替代非接触区域方程中的平均压力。
• 推导无量纲接触定律，并证明其在无粘附极限下退化为 Persson 理论，从而验证该方法的有效性。

实验结果

研究问题

• RQ1 当系统处于近全接触状态而非孤立峰体接触时，粘附性在粗糙弹性接触中如何表现？
• RQ2 分形维数 D 在决定粗糙表面上粘附性是否被保留或破坏方面起什么作用？
• RQ3 能否通过将缝隙建模为近全接触状态下的受压裂纹，来解决粘附悖论（即强范德华力未导致宏观粘附）？
• RQ4 脱附压力如何依赖于表面粗糙度和分形参数，特别是在高放大倍数极限下？
• RQ5 所提出的模型是否调和了经典峰体理论与近期无参数理论（如 Pastewka 和 Robbins，2014）的预测？

主要发现

• 对于分形维数 D < 2.5 的情况（包括大多数自然表面），由于与尺度相关的压力 p₀ 随 D 减小而无界增长，粘附性被强烈维持。
• 当 D > 2.5 时，粘附性在高放大倍数下被抑制，表明仅高分形维数的表面才会因粗糙度而失去粘附性。
• 脱附压力（p̄_pulloff）与 −p₀ ∼ −m₆¹ᐟ¹⁰ ∼ −ζ^(3−H)/⁵ 成比例，表明随着放大倍数增加，脱附变得更困难，这与经典峰体模型相反。
• 该模型预测，当 D < 2.5 时，可在有限施加压力下实现全接触，这是由于 p₀ 发散所致，意味着在特定条件下可自发接触。
• 推导出的接触定律在无粘附极限下与 Persson 理论高度吻合，验证了该方法在近全接触条件下的有效性。
• 该模型解释了壁虎仿生系统中粘附性的持久存在，不仅源于材料柔软性，更源于分层粗糙度与缝隙尺度力学的协同作用。