Influence of solid cohesion on viscous properties in Norton law for aluminum alloys during partial solidification

This study investigated the influence of the solid cohesion, f_sc, on the viscous properties (m-value and k-value in the Norton law) for aluminum alloys during partial solidification. In the previous study of Haaften (Mater. Sci. Eng. A, 336 (2002), 1–6), a constitutive model taking into account f_sc was proposed as ε˙ = k(T) (σ/f_sc(θ,T))^n(=1/m), where θ referred to the dihedral angle at the solid/liquid interface. However, even though it is well known that the m-value decreases with the decreasing temperature in the semi-solid state, the model defined the m-value as a constant to the temperature. Therefore, m = f(f_sc) and k = g(f_sc) during solidification were clarified in this study. The viscous properties were obtained by tensile tests during partial solidification for Al-5mass%Mg and Al-2mass%Cu alloys. As a result, it was found that the change in the m-value of 0 ≤ f_sc < f_sc|eut.st was expressed by the following linear rule-of-mixtures: m = m_solid(f_sc/f_sc|eut.st) + m_liquid(1–f_sc/f_sc|eut.st), where f_sc|eut.st is f_sc at the beginning of the eutectic solidification, while m_solid and m_liquid are the m-values just below the solidus temperature and at f_sc = 0, respectively. The increase in f_sc due to the eutectic solidification hardly affected the change in the m-value and such a value was equivalent to m_solid. On the contrary, the change in the k-values was found to obey the Arrhenius equation rather than be controlled by f_sc. It is suggested that regardless of the aluminum alloy composition, the viscous properties of partial solidification can be determined using the these relationships.