Studies on the fractal dimension of a fracture surface formed by slow stable crack propagation

Abstract

Fractal dimensions of different parts of a fracture surface formed by slow stable crack propagation, induced by the combined effect of hydrogen and static bending moment, were determined using the method of fracture profile analysis. The material used for this investigation was 30CrMnSiNi2A steel having the chemical composition (wt.%): 0.26% C, 1.02% Cr, 1.23% Mn, 1.08% Si, 1.56% Ni, 0.029% P and 0.007% S. The results showed that the fractal dimension increases with increasing transgranular fracture which increases as the crack propagates. This means that the increase of the fractal dimension responds to the increase of the energy needed to form the fracture surface, and in the authors' case the process of forming a fracture surface by slow stable crack propagation is one of increasing fractal dimension of the fracture surface; when the fractal dimension reaches a critical value, the crack propagation becomes unstable.

Fractal Surfaces

“…For noncrystalline materials such as glass, or single crystal materials such as silicon, there are no grain boundaries and the fracture can be considered as trans granular. Long, Suqin et al (1991) reported an increase in surface fractal dimension with increasing trans granular fracture and increasing energy required to form a crack. They also observe that in slow crack growth, the fractal dimension D increases until it reaches a critical value at which crack propagation becomes unstable.…”

“…Many authors worked with vertical elevation profiles through fracture surfaces (Chermant, Chennant et al 1987), although Long, Suqin et al (1991) have criticized the use of vertical sections to examine anisotropic fractal surfaces. Alexander (1990) misapplied the Richardson method to vertical elevation profiles and obtained log-log plots that are curved, taking the slope of the central portion as an estimate of the dimension.…”

Scaling of structural failure

“…This causes the portion of the fracture process zone near the surface to behave differently from that in the interior. IMandelbrot 1984;Brown, 1987;Mecholsky and Mackin 1988;Cahn, 1989;Chen and Runt, 1989;Hornbogen, 1989;Peng and Tian, 1990;Saouma et al, 1990;Bouchaud et al, 1990;Chelidze and Gueguen, 1990;Issa et al, 1992;Long et al, 1991;M%@y et al, 1992;Mosolov and Borodich, 1992;I3orodich, 1992;Lange et al, 1993;Xie, 1987Xie, , 1989Xie, , 1993Xie et al 1994Xie et al , 1996Saouma and Barton, 1.994;Feng et al, 1995;etc. 6. Time-dependent size effect caused by diffusion phenomena such as the transport of heat or the transport of moisture and chemical agents in porous solids (this is manifested e.g., in the effect of size on shrinkage and drying creep, due to size dependence of the drying half time (Baiant and Kim, 1991) and its effect on shrinkage cracking .…”

“…The answer has been negative. However, the fact that the surface roughness of cracks in many materials can be described, at least over a certain limited range, by fractal concepts, is not in doubt (e.g., Mandelbrot et al Brown, 1987;Mecholsky and Mackin 1988;Cahn, 1989;Chen and Runt, 1989;Hornbogen, 1989;Peng and Tian, 1990;Saouma et al, 1990;Bouchaud et al, 1990;Chelidze and Gueguen, 1990;Issa et al, 1992;Long et al, 1991;Mi%y et al, 1992;Mosolov and I3orodich, 1992;Borodich, 1992;Lange et al, 1993;Xie, 1987Xie, , 1989Xie, , 1993Xie et al 1!994, 1996;Saouma and Barton, 1994;Feng et al, 1995. ) In two dimensions, a fractal curve, which can be imagined to represent a crack, can be illustrated, for example, by the von Koch curves shown in Fig.…”

Fractial parameterization of the structure of filled polymers

“…Here, the greatest effect is achieved at relatively low values of Cp (up to ~0.10) with a subsequent asymptotic change of the function r According to the Mandelbrot rule [10], the fractal dimension of a set consisting of two independent fractal aggregates/)1 and P2 is equal to the sum of fractal dimensions of aggregates P1 and P2-In [40], it is assumed that the fractal dimension of the fracture surface is equal to the half-sum of fractal dimensions of the profiles of this surface in two orthogonal directions. Similarly, the fractal dimension of the structure of the filled polymer, d,, can be presented in the following form:…”