Scaling of Crack Surfaces and Implications for Fracture Mechanics

Physical Review E, 2000

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L = 350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical "overlap cluster" length between pairs of such interfaces converges to a constant with L increasing.

Physical Review B, 1989

We studied numerically the fracture of three types of disordered media: a scalar, a centralforce, and a beam model. We discovered the following novel, universal laws: in an initial regime, force and displacement both scale as L with the system size L; the number of bonds that break scales during the whole process as L ', and the distribution of local forces is multifractal just before the system breaks, whereas it has constant-gap scaling when catastrophic breaking sets in.

Physical Review Letters, 2006

The self-affine properties of post-mortem fracture surfaces in silica glass and aluminum alloy were investigated through the 2D height-height correlation function. They are observed to exhibit anisotropy. The roughness, dynamic and growth exponents are determined and shown to be the same for the two materials, irrespective of the crack velocity. These exponents are conjectured to be universal.

1995

Abstract The morphology of fracture surfaces in complex metallic alloys is analysed. The simultaneous use of Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM) allows the measurement of the universal roughness exponent ζ┴= 0.78 over five decades of lengthscales (0.5 nm-0.5 mm). Furthermore, a small lengthscales regime (lnm-1 μm) is shown to be characterised by a roughness index ζ┴ QS≃ 0.5.

International Journal of Fracture, 1996

EPJ Web of Conferences, 2010

The present study is focused on the correlation of scaling properties of crack branching and brittle fragmentation with damage accumulation and a change in the fracture mechanism. The experimental results obtained from the glass fragmentation tests indicate that the size distribution of fragments has a fractal character and is described by a power law.

Frontiers in Physics, 2014

We analyze the intermittent dynamics of cracks in heterogeneous brittle materials and the roughness of the resulting fracture surfaces by investigating theoretically and numerically crack propagation in an elastic solid of spatially-distributed toughness. The crack motion splits up into discrete jumps, avalanches, displaying scale-free statistical features characterized by universal exponents. Conversely, the ranges of scales are non-universal and the mean avalanche size and duration depend on the loading microstructure and specimen parameters according to scaling laws which are uncovered. The crack surfaces are found to be logarithmically rough. Their selection by the fracture parameters is formulated in term of scaling laws on the structure functions measured on one-dimensional roughness profiles taken parallel and perpendicular to the direction of crack growth.

2006

We investigate the scaling properties of post-mortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular a roughness exponent ζ ≃ 0.75 in homogeneous glass and ζ ≃ 0.4 in glassy ceramics. The ranges of length-scales over which these two scalings are observed are shown to be below and above the size of process zone respectively. A model derived from Linear Elastic Fracture Mechanics (LEFM) in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect damage screening occurring for lengthscales below the size of the process zone. PACS numbers: 62.20.Mk, 46.50.+a, 68.35.Ct The morphology of fracture surfaces is a signature of the complex damage and fracture processes occurring at the microstructure scale that lead to the failure of a given heterogeneous material. Since the pioneering work of Mandelbrot [1], a large amount of studies have shown that crack surface roughening exhibits some universal scaling features: Fracture surfaces were found to be selfaffine over a wide range of length scales, characterized by a universal roughness exponent ζ ≈ 0.8, weakly dependent on the nature of the material and on the failure mode (see e.g.

Tectonophysics, 2001

An account on the role of higher order strain gradients in the mechanical behavior of elastic-perfectly brittle materials, such as rocks, is given that is based on a special grade-2 elasticity theory with surface energy as this was originated by Casal and Mindlin and further elaborated by the authors. The fundamental idea behind the theory is that the effect of the granular and polycrystalline nature of geomaterials (i.e. their microstructural features) on their macroscopic response may be modeled through the concept of volume cohesion forces, as well as surface forces rather than through intractable statistical mechanics concepts of the Boltzmann type. It is shown that the important phenomena of the localization of deformation in macroscopically homogeneous rocks under uniform tractions and of dependence of rock behavior on the specimen's dimensions, commonly known as size or scale effect, can be interpreted by using this ‘non-local’, higher order theory. These effects are demonstrated for the cases of the unidirectional tension test, and for the small circular hole under uniform internal pressure commonly known as the inflation test. The latter configuration can be taken as a first order approximation of the indentation test that is frequently used for the laboratory or in situ characterization of geomaterials. In addition, it is shown that the solution of the three basic crack deformation modes leads to cusping of the crack tips that is caused by the action of ‘cohesive’ double forces behind and very close to the tips, that tend to bring the two opposite crack lips in close contact, and further, it is demonstrated that the fracture toughness depends on the size of the crack, and thus it is not a fundamental property of the material. This latter outcome agrees with experimental results which indicate that materials with smaller cracks are more resistant to fracture than those with larger cracks.

Scripta Metallurgica, 1988

Several authors have recently discussed the use of fractals to describe fracture energies and their relationships to fracture surface geometries. A fractal is a self-similar geometric construction with non-integer dimensionality. Self-similarity means that the fractal appears the same under all magnifications. Dimensionalities are described below and more rigorously. Fracture energies (E) are quantified according to the scale of observation (L), e.g., J integrals on the macroscopic scale or interatomic potentials on the lattice scale. Surface geometries have been described by roughness parameters (R) or by the fracture surface dimensionality: D/sub s/ ..cap alpha..ln(R)ln(L). Another fractal dimensionality for fracture has been defined in terms of energy: D ..cap alpha..ln(E)ln(L). A frequently employed assumption is that D/sub s/ is the same for all scales, or that a plot of ln(R) versus ln(L) is linear. However, others have found that this is in general not true for fracture surfa...