Fracture and damage at a microstructural scale

Abstract

E xamining surfaces of broken samples is invaluable in metallurgy for understanding relationships between microstructures, crack paths, damage, and toughness. Experiments in the past two decades have established this link firmly on a quantitative basis. Although a good material design based on these observations is far from being straightforward, experiments have been able to discriminate between theoretical models of crack propagation through complex microstructures. In this sense, experiments are very useful for models and numerical simulations. As we will see later on, experimental results compare well with molecular-dynamics simulations, even though the latter involve dynamic fracture while the former consider quasi-static crack growth.These quantitative observations can indeed separate morphological parameters of fracture surfaces such as the microstructure's dependence on parameters that are independent of material properties. In fact, fracture surfaces are selfaffine (anisotropic scale-invariant objects whose roughness exponents are invariant and whose characteristic length scales are linked to their microstructure). The conjecture that the roughness exponents are universal has spurred great interest among statistical physicists because they are familiar with problems of disordered media. A very special roughnessBenoît Mandelbrot and his colleagues first showed that steel's fracture surfaces are selfaffine; so, the typical height difference defined, for example, from the fluctuations of the height z is a power law of the distance r measured within the horizontal plane for the points at which the heights are measured. 1 This defines the surface-roughness index ζ, which lies between 0 and 1: (h(r) ∝ r ζ )The smaller the value of ζ, the rougher the surface, because this relationship is only valid when r is smaller than the so-called correlation length ξ, which is precisely the upper limit of the domain where scaling is valid (see Figure 1).Measuring ζ requires cutting the fracture surface so that this cut either contains the z-axis or is perpendicular to it. The first case involves 1D profiles that are generally perpendicular to the direction of crack propagation. In the second case, the surface heights are eroded, and the analysis involves contours that are the intersection of the surface of interest with the cutting plane. The second method, first used by Mandelbrot and his colleagues, is called the slitisland method. 1 COMPUTING IN SCIENCE & ENGINEERING FRACTURE AND DAMAGE AT A MICROSTRUCTURAL SCALEStudying fracture surfaces of materials has been very useful in discriminating between different theoretical models. In the future, models and simulations should be able to help design suitable microstructures for tough materials.

Nano-ductile crack propagation in glasses under stress corrosion: spatiotemporal evolution of damage in the vicinity of the crack tip

“…In both types of materials, the crack progresses through the nucleation, growth and coalescence of damage cavities. These latter should thus be printed in the post-mortem fracture surface (Bouchaud and Paun, 1999). Consequently, their size should set the range of the different self-affine regimes observed on the fracture surface, leading to crossover lengths of a few tens nanometers in glass and a few hundreds micrometers in metallic alloys, in good agreement to what was reported in Daguier et al (1997).…”

Failure of heterogeneous materials: A dynamic phase transition?

“…As already discussed in the past [42,34,7,119], as long range elastic interactions are screened out by damage, one gets into a different universality class, whatever the nature of damage. Universality should persist.…”

Random and correlated roughening in slow fracture by damage nucleation

“…A crucial aspect of this model is the existence of a typical length scale ξ c ahead of the crack tip where damage nucleation can take place [7]. A physical picture that might support such a scenario (though definitely not a unique one) is that a small plastic zone of linear dimension ξ c forms around the crack tip and the relevant damage units involved in the process are plastic voids.…”