Two-Phase Modeling of Hot Tearing in Aluminum Alloys: Applications of a Semicoupled Method
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TRODUCTION
HOT tearing is a severe defect that occurs in solidification processes. Tears form in the mushy zone due to the interplay between two main mechanisms: deformation of the partially coherent solid and lack of interdendritic liquid feeding.[1–4] This phenomenon has been studied for several decades, from both theoretical and experimental standpoints. Classical hot tearing tests, which consist of inducing strains in a mushy alloy,[5,6] have been reviewed in Reference 1. From the modeling point of view, continuum-scale approaches have been developed, in order to predict the occurrence of hot tears at least semiquantitatively.[7,8] In order to obtain a quantitative numerical tool for the prediction of hot tearing, several important contributions have been reported. First, a description of the mechanical behavior of mushy alloys is necessary. In this area, a major contribution for aluminum alloys has been proposed recently by Ludwig et al.[9] This work has provided crucial information for the relevant prediction of the amount of strain and the magnitude of the strain rate experienced by the material in the mushy state. Second, the problem of feeding the mushy zone by the intergranular liquid has been addressed in the porosity
V. MATHIER, Software Developer, is with Calcom-ESI SA, Parc Scientifique, CH-1015, Lausanne, Switzerland. M. RAPPAZ, Professor, Computational Materials Laboratory, Institute of Materials Science, School of Engineering, is with the Ecole Polytechnique Fe´de´rale de Lausanne, CH-1015 Lausanne, Switzerland. Contact e-mail: vincent. [email protected] S. VERNE`DE and P. JARRY, Inge´nieurs expert de recherche´, are with the Alcan CRV, FR-38341 Voreppe, France. Manuscript submitted July 22, 2008. Article published online February 5, 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A
model of Pequet et al.,[10] using a refined mesh locally. Third, the probability of finding a hot tear in a casting can be assessed by defining a suitable hot tearing criterion. Various criteria have been proposed in the literature and are reviewed in Reference 1. These criteria can be based on a critical quantity such as the stress,[11] the strain,[12] or the strain rate.[4] Lately, a granular approach, in which the mushy zone is considered as a population of discrete solid grains surrounded by the liquid phase, has been explored.[13,14] Such models bring complementary information to the standard mixture approach used in continuum-scale modeling. However, they cover length scales that are too small for them to be applicable for the entire process scale. In order to model hot tearing using a two-phase average approach, it is necessary to solve three problems: energy conservation, momentum conservation, and liquid flow in the mushy zone (possibly coupled with the nucleation and growth of microporosity). Moreover, they must be addressed at the scale of the entire process. A method for doing this was proposed recently by M’Hamdi et al.;[8] the resulting software is known as TearSim (SINTEF Materials Technology, Oslo, Norway).
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