CEA, IRAMIS, SPCSI, Grp. Complex Systems & Fracture, F-91191 Gif Sur Yvette, France.
Phys Rev Lett. 2010 Jan 15;104(2):025502. doi: 10.1103/PhysRevLett.104.025502. Epub 2010 Jan 11.
The roughness of fracture surfaces exhibits self-affinity for a wide variety of materials and loading conditions. The universality and the range of scales over which this regime extends are still debated. The topography of these surfaces is however often investigated with a finite contact probe. In this case, we show that the correlation function of the roughness can only be measured down to a length scale Deltax{c} which depends on the probe size R, the Hurst exponent zeta of the surface and its topothesy l, and exhibits spurious behavior at smaller scales. First, we derive the dependence of Deltax{c} on these parameters from a simple scaling argument. Then, we verify this dependence numerically. Finally, we establish the relevance of this analysis from AFM measurements on an experimental glass fracture surface and provide a metrological procedure for roughness measurements.
断裂表面的粗糙度对于各种材料和加载条件表现出自相似性。这种状态的普遍性和扩展的尺度范围仍存在争议。然而，这些表面的形貌通常使用有限接触探针进行研究。在这种情况下，我们表明，粗糙度的相关函数只能测量到依赖于探针尺寸 R、表面的 Hurst 指数 ζ 和拓扑长度 l 的长度尺度 Deltax{c}，并且在较小的尺度上表现出虚假行为。首先，我们从一个简单的标度分析中推导出 Deltax{c}对这些参数的依赖关系。然后，我们通过数值验证了这种依赖性。最后，我们通过对实验玻璃断裂表面的 AFM 测量验证了这种分析的相关性，并提供了一种粗糙度测量的计量程序。
