Pergamon International Journal of Plasticity, Vol. 10, No. 6, pp. 663-693, 1994 Copyright © 1994 Elsevier ScienceLtd Printed in the USA. All rights reserved 0749-6419/94 $6.00 + .00 0749-6419(94)00022-0 THEORETICAL AND EXPERIMENTAL STUDY OF THE ISOTHERMAL MECHANICAL BEHAVIOUR OF ALLOYS IN THE SEMI-SOLID STATE T.G. NGUYEN, D. FAVIER, and M. SUERY Institut National Polytechnique de Grenoble Abstract-An isothermal constitutive model for semi-solid alloys based on the concepts of mechanics of continuous media and the theory of mixtures is presented. The model is applica- ble to semi-solid states obtained either by solidification from liquid state or partial remelting from solid state in which each of the solid and the liquid phases is contiguous. During defor- mation their behaviours are coupled: the densification of the solid matrix considered as a porous viscoplastic medium saturated with a liquid drives the fluid flow behaviour, and the resulting pressure distribution in the liquid affects in turn the stresses and the densification of the solid. The identification procedure of the model uses two types of mechanical tests: uniaxial compres- sion and drained die pressing (filtration) carried out with A356 alloy. The identification results are then validated using drained triaxial compression. !. INTRODUCTION Semi-solid metal forming processes are now becoming of industrial interest for the pro- duction of metal components and metal matrix composites. However, the material behaviour in the semi-solid range is not sufficiently known although it controls the whole process through forces and geometry evolutions (LEvAmLA_~T [1990]). A research effort is conducted currently not only to produce experimental data but also to model theo- retically the rheological behaviour of alloys in the semi-solid state. The behaviour of metal slurries is complex, with history-dependent, non-steady-state (thixotropic) constitutive behaviour dominating in certain processing regimes and steady- state (pseudoplastic) behaviour dominating in other regimes. The pseudoplastic behav- iour is generally expressed by a power law dependence of the apparent viscosity on the shear rate (LAx.V_A~rA~ & FLE~IN~S [1980]). This dependence leads to a stress-strain rate relation of Norton-Hoff type that is often used to describe the hot deformation of alloys in the solid state. For steady-state flows of metallic slurries, the rate sensitivity is in the range 0.2-0.7 (LEvAIU.ANT [1990]) depending on the liquid volume fraction. The tem- perature dependence is generally expressed in terms of thermal activation through a material parameter that depends itself on the volume fractions of the phases. Compar- atively, the modelling of the thixotropic effects is not developed, although it is of major interest for practical purpose (LEvi~mLAa, rT [1990]). A new approach has been proposed by BROW~ [1989] for systems of suspensions considering a parameter taking into account the degree of agglomeration in the slurry. The parameter evolution equation is consti- tuted of two components, the first one representing the increase of the degree of agglom- eration of the globules and the second one representing the disruption of the clusters due mainly to the shear action. This model has been first fitted on shear rate ramp down 663