The gradual transformation of a mushy zone during alloy solidification, from a continuous liquid film network to a fully coherent solid, has been simulated using a granular model. Based on a Voronoi tessellation of a random set of nucleation centers, solidification within each polyhedron is computed considering back-diffusion and coalescence. In the network of connected liquid films, a pressure drop calculation is performed assuming a Poiseuille flow in each channel, Kirchhoff's conservation of flow at nodal points and flow Losses compensating solidification shrinkage (KPL model). In addition to intergranular liquid pressure maps, the model shows the progressive formation of grains clusters, the localisation of the flow at very high solid fraction, and thus natural transitions of the mushy zone.

A simple model for the solidification of globular grains in metallic alloys is presented. Based on the Voronoi diagram of the nuclei centers, it accounts for the curvature of the grains near triple junctions. The predictions of this model are close to those of more refined approaches such as the phase field method, but with a computation cost decreased by several orders of magnitude. Therefore, this model is ideally suited for granular simulations linking the behavior of individual grains to macroscopic properties of the material. arXiv:0711.4122v1 [cond-mat.mtrl-sci]

While studies of solidification microstructures have focused mainly on the tips of the dendrites, the last stage solidification is equally important from the point of view of defect formation (porosity, hot tearing), mechanical strength build-up and precipitation of phases. In particular, the transition from continuous liquid films to a coherent solid in low concentration alloys is of crucial importance for hot tearing formation, and more generally speaking for liquid feeding ability and coherency development. Based on a fairly recent theoretical model of coalescence which will be recalled briefly, new results obtained for a population of equiaxed grains will be presented. A granular-type model based on a Voronoi tessellation has been used for the description of the gradual disappearance of liquid films and the clustering of equiaxed grains. This percolation-type approach has been used then to calculate the pressure drop in the mushy zone on the assumptions of a Poiseuille flow in between the grains and a Kirchhoff model for the connectivity of the liquid films including the Losses associated with solidification shrinkage (i.e, PKL model). Comparison with a standard average pressure drop calculation based on Carman-Kozeny's relationship will be presented.-1 -

We present a two-dimensional granular model for the mechanical behavior of an ensemble of globular grains during solidification. The grain structure is produced by a Voronoi tessellation based on an array of predefined nuclei. We consider the fluid flow caused by grain movement and solidification shrinkage in the network of channels that is formed by the faces of the grains in the tessellation. We develop the governing equations for the flow rate and pressure drop across each channel when the grains are allowed to move, and we then assemble the equations into a global expression that conserves mass and force in the system. We show that the formulation is consistent with dissipative formulations of non-equilibrium thermodynamics. Several example problems are presented to illustrate the effect of tensile strains and the availability of liquid to feed the deforming microstructure. For solid fractions below g s ¼ 0:97, we find that the fluid is able to feed the deformation at low strain, even if external feeding is not permitted. For solid fractions above g s ¼ 0:97, clusters of grains with ''dry" boundaries form and fluid flow becomes highly localized.

We show that a length scale ξ can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above ξ, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below ξ, long-range spatial correlation lead to a multi-fractal behavior of the surface, reminiscent of turbulent flows. Our results support a unifying conjecture for the geometry of fracture surfaces: for scales > ξ the surface is the trace left by an elastic line propagating in a random medium, while for scales < ξ the highly correlated patterns on the surface result from the merging of interacting damage cavities.After thirty years of research, it is now well established that fracture surfaces exhibit robust universal fractal statistical properties, first reported in [1] and recently reviewed in [2]. Yet, identifying the physical mechanisms that lead to such fractal structures is still an open problem [3]. The most commonly used approach to characterize the roughness of fractal cracks is to study the scaling of the off-plane height variation δh of the fracture surface with the observation scale δr. The variance of this distribution shows a scaling law δh 2 ∼ δr 2ζ where ζ is the so-called roughness exponent. For purely brittle failure, the roughness exponent is reported to be ζ ≈ 0.45 [5,6] whereas for materials that undergo damage during failure, ζ ≈ 0.75 [7,8]. It has been conjectured that these exponents are the signature of the fracture mechanism above and below the size of the process zone [4]. However, standard methods for extracting roughness exponents are not able to elicit the differences between the fracture mechanisms in the two regimes.Here we propose a different approach for characterizing crack roughness statistics by focusing on the local slopes of the fracture surfaces and their spatial correlations. This allows us to identify unambiguously two scaling regimes: above some length scale ξ, the slope amplitudes are uncorrelated and the fracture surface displays a mono-affine Gaussian behavior with a roughness exponent of ζ ≈ 0.45. Below ξ, long-range spatial correlations do appear and lead to a multi-fractal behavior of the surface. Our findings show that the presence of two distinct regimes of roughness first reported in Refs. [9, 10] is a generic feature of fracture surfaces and is reminiscient of the brittle mode of failure that takes place at large scale and of the damage mechanisms present in the tip vicinity. In addition, it reveals the subtle organization of crack roughness at small length scales δx < ξ, reminiscent of the phenomenology of turbulent flows [11]. In particular, we relate quantitatively the multi-fractal spectrum measured at these length scales with the spatial correlations of the local slopes, and show that the largest slopes organize into a network of lines or "steep cliffs" that exhibit universal statistics. This new approach to Top: h, height of the measured fracture surface. Bottom: ω transformation providing the field of local slopes computed at a scale ...