To describe the thermomechanical behaviour of the semi-solid state during alloy solidification, specific viscoplastic constitutive laws are derived for the coherent and noncoherent regime of the mush. For the coherent semi-solid regime an original viscoplastic flow potential is derived, which includes micro-structural parameters. This potential takes also isotropic hardening, pressure dependence of yielding and the strength difference in tension and compression into account. For the non-coherent mushy state of suspensions under shear loading, a simplified viscoplastic potential is adopted by neglecting pressure effects on the solid dendrites. Continuity at mechanical coherency is imposed and allows the reduction of the model parameters of the non-coherent regime. The developed constitutive laws are implemented in Abaqus via a user-defined CREEP routine. Simulations of uniaxial tension, compression or pure shear experiments allow identifying the model parameters of an A356 aluminium alloy.
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