Experiments concerning the morphology of fracture surfaces of various materials are reviewed. The observations are interpreted within the framework of models of lines moving in a random environment. This suggests that fracture of heterogeneous materials could be seen as a dynamic phase transition.

https://iopscience.iop.org/article/10.1088/0953-8984/9/21/002/pdf

Scaling properties of cracks

▪ Abstract Atomistic aspects of dynamic fracture in a variety of brittle crystalline, amorphous, nanophase, and nanocomposite materials are reviewed. Molecular dynamics (MD) simulations, ranging from a million to 1.5 billion atoms, are performed on massively parallel computers using highly efficient multiresolution algorithms. These simulations shed new light on (a) branching, deflection, and arrest of cracks; (b) growth of nanoscale pores ahead of the crack and how pores coalesce with the crack to cause fracture; and (c) the influence of these mechanisms on the morphology of fracture surfaces. Recent advances in novel multiscale simulation schemes combining quantum mechanical, molecular dynamics, and finite-element approaches and the use of these hybrid approaches in the study of crack propagation are also discussed.

ATOMISTIC ASPECTS OF CRACK PROPAGATION IN BRITTLE MATERIALS: Multimillion Atom Molecular Dynamics Simulations

The fractal characteristics of a series of fractured AISI 4340 steel specimens were studied experimentally by means of vertical sections through the fracture surface. Extensive fractal data have been generated for both the fracture surfaces and their profiles. Fractal plots for the irregular profile curves differ significantly from those of the infinitely subdivisible curves with “self-similarity” as postulated by Mandelbrot. Instead of a linear fractal curve and constant fractal dimension D , we find a reversed sigmoidal curve (RSC) and variable D . Because of the inadequacies of the linear Richardson fractal equation, we have developed an alternative procedure whereby constant slopes β and γ are obtained from the RSCs for both profiles and surfaces respectively. Since a fractal equation for surfaces apparently does not exist, we propose one that parallels the Richardson equation for profiles. Slopes from the RSCs are related to the new constant fractal dimensions D β and D γ in the modified fractal equations for profiles and fracture surfaces. Some insight into the physical nature of the fractal dimension is afforded by its close similarity to fracture roughness parameters that have simple physical meanings. It is believed that the results of the extensive study may have general validity for the irregular complex curves and surfaces of nature.

https://popups.ulg.ac.be/0351-580x/index.php?id=2985&file=1&pid=2965

Fractals in fractography

Non-linear and non-local transport processes in heterogeneous media: from long-range correlated percolation to fracture and materials breakdown

Fractal analysis of surface roughness by using spatial data (with discussion)

To examine the usefulness of the fractal concept in quantitative fractography, a series of classical fracture surfaces, namely transgranular cleavage, intergranular fracture, microvoid coalescence, quasicleavage and intergranular microvoid coalescence, are analyzed in terms of fractal geometry. Specifically, the five brittle and ductile fracture modes are studied, from three well characterized steels (a mild steel, a low-alloy steel and a 32 wt% Mn-steel) where the salient microstructural dimensions contributing to the final fracture morphology have been measured. Resulting plots of the mean angular deviation, and Richardson (fractal) plots of the lineal roughness, as a function of the measuring step size, are interpreted with the aid of computer-simulated fracture-surface profiles with known characteristics. It is found that the ranges of resolution, over which the fractal dimension is constant, correspond to the pertinent metallurgical dimensions on the fracture surface, and thus can be related to microstructural size-scales.

F.G. Haubensak

Papers

On the interpretation of the fractal character of fracture surfaces

Subcritical growth of microstructurally small cracks in silicon nitride ceramics