This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. AbstractA three-dimensional (3-D) granular model which simulates fluid flow within solidifying alloys with a globular microstructure, such as that found in grain refined Al alloys, is presented. The model geometry within a representative volume element (RVE) consists of a set of prismatic triangular elements representing the intergranular liquid channels. The pressure field within the liquid channels is calculated using a finite elements (FEs) method assuming a Poiseuille flow within each channel and flow conservation at triple lines. The fluid flow is induced by solidification shrinkage and openings at grain boundaries due to deformation of the coherent solid. The granular model predictions are validated against bulk data calculated with averaging techniques. The results show that a fluid flow simulation of globular semi-solid materials is able to reproduce both a map of the 3-D intergranular pressure and the localization of feeding within the mushy zone. A new hot cracking sensitivity coefficient is then proposed. Based on a mass balance performed over a solidifying isothermal volume element, this coefficient accounts for tensile deformation of the semi-solid domain and for the induced intergranular liquid feeding. The fluid flow model is then used to calculate the pressure drop in the mushy zone during the direct chill casting of aluminum alloy billets. The predicted pressure demonstrates that deep in the mushy zone where the permeability is low the local pressure can be significantly lower than the pressure predicted by averaging techniques.

A three-dimensional (3-D) coupled hydromechanical granular model has been developed and validated to directly predict, for the first time, hot tear formation and stress-strain behavior in metallic alloys during solidification. This granular model consists of four separate 3-D modules: (i) the solidification module is used to generate the solid-liquid geometry at a given solid fraction; (ii) the fluid flow module (FFM) is used to calculate the solidification shrinkage and deformation-induced pressure drop within the intergranular liquid; (iii) the semi-solid deformation module (SDM) simulates the rheological behavior of the granular structure; and (iv) the failure module (FM) simulates crack initiation and propagation. Since solid deformation, intergranular flow and crack initiation are deeply linked together, the FFM, SDM and FM are coupled processes. This has been achieved through the development of a new three-phase interactive technique that couples the interaction between intergranular liquid, solid grains and growing voids. The results show that the pressure drop, and consequently hot tear formation, depends also on the compressibility of the mushy zone skeleton, in addition to the well-known contributors (lack of liquid feeding and semi-solid deformation).

The mechanical behavior of partially solidified Al-Cu alloys is investigated to assess the influence of mushy zone deformation on hot tearing. For this purpose, the results of a semi-solid tensile test conducted in situ using X-ray microtomography are compared with the predictions of a coupled hydromechanical granular model in order to both validate the predictions of the model and explain the experimental observations. It is shown that hot tears initiate in the widest liquid channels connected to the free (oxidized) surfaces as long as there is contact between the intergranular liquid and the ambient air. The necking behavior is associated with the deformation-induced liquid pressure drop. Overall, the stresses predicted by the granular model under tensile and shear deformations agree well with the experimental data. Thus, the granular model achieves an important step in predicting hot tearing formation.

As a necessary step toward the quantitative prediction of hot tearing defects, a three-dimensional stress-strain simulation based on a combined finite element (FE)/discrete element method (DEM) has been developed that is capable of predicting the mechanical behavior of semisolid metallic alloys during solidification. The solidification model used for generating the initial solid-liquid structure is based on a Voronoi tessellation of randomly distributed nucleation centers and a solute diffusion model for each element of this tessellation. At a given fraction of solid, the deformation is then simulated with the solid grains being modeled using an elastoviscoplastic constitutive law, whereas the remaining liquid layers at grain boundaries are approximated by flexible connectors, each consisting of a spring element and a damper element acting in parallel. The model predictions have been validated against Al-Cu alloy experimental data from the literature. The results show that a combined FE/DEM approach is able to express the overall mechanical behavior of semisolid alloys at the macroscale based on the morphology of the grain structure. For the first time, the localization of strain in the intergranular regions is taken into account. Thus, this approach constitutes an indispensible step towards the development of a comprehensive model of hot tearing.

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