A new criterion for the appearance of hot tears in metallic alloys is proposed. Based upon a mass balance performed over the liquid and solid phases, it accounts for the tensile deformation of the solid skeleton perpendicular to the growing dendrites and for the induced interdendritic liquid feeding. This model introduces a critical deformation rate ( p,max ) beyond which cavitation, i.e., nucleation ⅐ ε of a first void, occurs. As should be expected, this critical value is an increasing function of the thermal gradient and permeability and a decreasing function of the viscosity. The shrinkage contribution, which is also included in the model, is shown to be of the same order of magnitude as that associated with the tensile deformation of the solid skeleton. A hot-cracking sensitivity (HCS) index is then defined as . When applied to a variable-concentration aluminum-copper alloy, this HCS ⅐Ϫ1 ε p,max criterion can reproduce the typical ''⌳ curves'' previously deduced by Clyne and Davies on a phenomenological basis. The calculated values are in fairly good agreement with those obtained experimentally by Spittle and Cushway for a non-grain-refined alloy. A comparison of this criterion to hot cracks observed in ring-mold solidification tests indicates cavitation depression of a few kilo Pascal and tensile stresses in the coherent mushy zone of a few mega Pascal. These values are discussed in terms of those obtained by other means (coherency measurement, microporosity observation, and simulation). Even though this HCS criterion is based only upon the appearance of a first void and not on its propagation, it sets up for the first time a physically sound basis for the study of hot-crack formation.

The rheological behavior of a solidifying alloy is modeled by considering the deforming material as a viscoplastic porous medium saturated with liquid. Since the solid grains in the mush do not form a fully cohesive skeleton, an internal variable that represents the partial cohesion of this porous material is introduced. The model parameters are identified using shear and compressive stress states under isothermal conditions on an Al-Cu model alloy. The model is partially validated with nonisothermal conditions and we complete this study with tensile conditions. Such conditions, when applied on the mush, may lead to severe defects in many casting processes. The model has been implemented into a commercial finite-element code to simulate a tensile test. Comparison with experimental data shows that the model is able to reproduce the main features of a solidifying alloy under tension, although fracture is not directly addressed here. We show that two critical solid fractions must be introduced in the model to account for the rheology: the coherency solid fraction at which the mush acquires significant strength and the coalescence solid fraction at which solid grains start to form solid bridges.

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The deformation-induced macrosegregation in continuous casting of steel has been simulated using a finite-volume scheme. For that purpose, a two-dimensional heat-flow computation was first performed in a Eulerian reference frame attached to the mold, assuming a unique solidification path, i.e., a unique relationship between temperature and enthalpy. This gave the stationary enthalpy field in the longitudinal section of the slab. On the other hand, bulging of the slab between two rolls was calculated in the same section, assuming plane-strain deformation and using the ABAQUS code. The Lagrangian reference frame was attached to the slab, and the rolls were moved at the surface until a stationary, bulging deformation profile was reached. The bulging of the surface was then used as an input condition for the calculation of the velocity and pressure fields in the interdendritic liquid. Using a fairly simple hypothesis for the deformation of the solid skeleton, the mass conservation and Darcy equations were solved in a Eulerian reference frame. This calculation was performed in an iterative loop, within which the solute conservation equation was also solved. At convergence and using the enthalpy field, this calculation allowed to obtain the temperature, the volume fraction of solid, and the average concentration fields, in addition to the fluid velocity and pressure. It is shown that the positive centerline segregation of carbon in the slab is well reproduced with this model. The effects of shrinkage and soft reduction were also investigated.

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.