Rheological behavior of Al-Cu alloys during solidification constitutive modeling, experimental identification, and numer
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I. INTRODUCTION
DURING solidification of metallic alloys, a continuous transition from liquid to solid state takes place. In the first stage of solidification, solid dendrites are completely free to move in the liquid matrix and the alloy can be considered, from a rheological point of view, as a suspension. As solidification progresses, solid fraction increases and interactions between dendrites begin to occur extensively. At this stage, the solid-liquid mixture is defined as a coherent mush (or “mushy zone”) and develops shear strength due mostly to dendrite entanglement.[1,2,3] The solid skeleton deforms essentially by rearrangement of dendrites at this stage and shear strength is of the order of tens of kPa.[2,3] For higher solid fractions, dendrites become highly interlocked and deformation of the mush must proceed both by rearrangement and deformation of the dendrites. The resulting shear strength is of the order of 0.1 to 1 MPa and the mush also starts to develop tensile strength, although such strength is still very low.[2,3] The solid fraction at which the mush develops such significant shear strength has been termed the “maximum packing solid fraction,” gspk, by Dahle and StJohn.[2] At this point, the mush also exhibits some tensile strength that must be related to the establishment of mechanical coherence. Thus, arguably, we prefer to define this point as the coherency solid fraction (gcoh s ). At this stage, OLIVIER LUDWIG, formerly with the GPM2 Laboratory, UMR 5010, Institut National Polytechnique de Grenoble, is Postdoctoral Fellow, Computational Materials Laboratory, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland. JEAN-MARIE DREZET, Senior Scientist, is with the Computational Materials Laboratory, Ecole Polytechnique Fédérale de Lausanne. CHRISTOPHE L. MARTIN, CNRS Research Associate, and MICHEL SUÉRY, CNRS Research Director, are with the GPM2 Laboratory, UMR 5010, Institut National Polytechnique de Grenoble, BP46 36402 St Martin d’Hères, Cedex, France. Contact e-mail: [email protected] Manuscript submitted July 21, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS A
liquid fraction is still large enough to allow liquid feeding to accommodate local dilatation of the solid skeleton that constitutes the mush. Toward the very end of solidification, solid dendrites start to coalesce and solid permeability drops dramatically. Thus, the thin liquid films that remain in the mush at the end of solidification cannot accommodate tensile strains but still account for its fragile behavior. Any tensile strain at this stage is potentially dangerous for the integrity of the solidifying material. In particular, aluminum alloy processing technologies such as DC casting, laser welding, mold casting, or strip-casting involve thermally induced deformations arising from the contraction that occurs during casting (both solidification shrinkage and thermal contraction of the solid skeleton). These thermal strains can lead to the formation of casting defects such as macrosegregations (if liqui
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