Long Distance Roughness of Fracture Surfaces in Heterogeneous Materials

Abstract

The long distance roughness of fatigue fracture surfaces of a nickel-based superalloy is reported for two samples of different grain size. Statistical analysis over a wide range of length scales, from a few nanometers to a few millimeters, using scanning electron microscopy and atomic force microscopy allows to obtain accurately the self-affine correlation length. Long distance fracture profiles of 14,000 points were obtained and digitized from overlapping electron micrographs at a resolution of 0.22 micrometers/point. We have also analyzed the long distance roughness of the mirror zone on a soda-lime glass using atomic force microscopy. In the case of the nickel superalloy, correlation lengths are found to correspond well to the grain size. This result gives information about the mechanism of crack propagation in heterogeneous materials and shows that the correlation length of fracture surfaces is of the order of the largest microstructural heterogeneity.

Failure of heterogeneous materials: A dynamic phase transition?

“…53) was claimed to be the size of the largest heterogeneities both for fracture of 3D samples of partially demixed glass [96] and for interfacial fracture in PMMA [55]. Although this is not what was found in steel [94], this interpretation is compatible with experiments on other metallic alloys [67,69] for which, as already mentioned, the upper bound of this regime was found to be of the order of the metallurgical grains. In principle, it is also compatible with the results obtained on mortar fracture surfaces, for which the crossover length was found to be ∼1 mm [93].…”

“…Let us note that in this case, 5nm is the AFM resolution, while 0.5 mm is very close to the grain size. Fracture profiles of an aluminum alloy [69] plated with nickel and observed with SEM were also shown to be characterized by a roughness index ζ ≃ 0.77 for length scales between 5nm and 0.1 mm (see Fig. 29).…”

Scaling properties of fracture surfaces on glass strengthened by ionic exchange

“…6a and b, which corresponds to the non-treated and treated specimens, respectively. In both cases the roughness exponent has values consistent with the claimed universal value z $0.8 [5][6][7][8][9]. This implies that the ionic exchange treatment does not modify the exponent characterizing the self-affine regime.…”

“…It is now accepted that fracture surfaces are selfaffine objects, that is to say, they are anisotropic fractals whose self-affine character can be quantified by one roughness exponent z. Different workers [5][6][7][8] conclude that this exponent reflects a somehow ''universal'' behavior and the existence of a characteristic regime with z $0.8 is accepted for rapid crack propagation conditions. Now a question immediately arises: If the roughness exponent has a universal value, what is the role of microstructure in determining the self-affine behavior?…”

“…Now a question immediately arises: If the roughness exponent has a universal value, what is the role of microstructure in determining the self-affine behavior? In 1998 Hinojosa et al [7] demonstrated that the correlation length j is directly related to the largest heterogeneities in crystalline metals. This correlation length is the upper limit of the self-affine regime.…”