Quantitative analysis of a fracture surface by atomic force microscopy

Abstract

The fracture surface of a Ti 3 Al-based alloy is studied using both an atomic force microscope and a standard scanning electron microscope. Results are shown to be quantitatively comparable. Two fracture regimes are observed. It is shown in particular that the roughness index characterizing the small lengthscales regime is equal to 0.5. Furthermore, the large lengthscales fractal domain is found to spread over nearly six decades of lengthscales.

Fracture through cavitation in a metallic glass

“…≈ 0.55) was observed on metallic fracture surfaces [8][9][10] at small length scales/low crack velocities. It was shown that the crossover length separating this regime from the ζ 0.75 regime at higher length scales was inversely proportional to the average crack velocity V .…”

“…Bonamy et al [12] have shown that the set of exponents {ζ 0.75, β 0.6} define a universality class corresponding to length scales smaller than the process zone size, where non linear elastic processes take place. Above this process zone size, another university class is observed [12,20,21] characterized by a set of exponents {ζ 0.4, β 0.5} that can be understood theoretically within the Linear Elastic Fracture Mechanics framework.A third regime arises at very small length scales, characterized by a roughness index close to ζ ≈ 0.5, observed in a metallic alloy and in a soda-lime silicate glass [8][9][10] along a direction perpendicular to the direction of crack propagation. This regime was suggested [22] to be…”

“…A third regime arises at very small length scales, characterized by a roughness index close to ζ ≈ 0.5, observed in a metallic alloy and in a soda-lime silicate glass [8][9][10] along a direction perpendicular to the direction of crack propagation. This regime was suggested [22] to be (a) E-mail: elisabeth.bouchaud@cea.fr characteristic of small damage cavities, i.e.…”

“…The fracture surfaces of various materials have shown surprising scaling properties (see for example [2][3][4] for reviews) over a wide range of length scales. Fracture profiles of materials as different as metallic alloys [5][6][7][8][9][10], silicate glasses [11,12], quasi-crystals [13], rocks [14], mortar [15], sea ice [16], and wood [17,18] have shown to be self-affine, with a roughness exponent ζ ≈ 3/4 in spite of huge differences in the fracture mechanisms. It was therefore suggested [5,19] that ζ might have a universal value, i.e., independent of the fracture mode and of the material.…”

Continuum Field Description of Crack Propagation

“…The phenomenology of the crack propagation is wellestablished by recent experimental studies [3][4][5][6][7][8][9]: once a flux of energy to the crack tip passes the critical value, the crack becomes unstable, it begins to branch and emits sound. Although this rich phenomenology is consistent with the continuum theory, it fails to describe it because the way the macroscopic object breaks depends crucially on the details of cohesion on the microscopic scale [10].…”