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

Yoshihiro Nagata*, Ryosuke Takai, Toshimitsu Okane, Muhammad Khairi Faiz, Makoto Yoshida

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This study investigated the influence of the solid cohesion, fsc, 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 fsc was proposed as ε˙ = k(T) (σ/fsc(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(fsc) and k = g(fsc) 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 ≤ fsc < fsc| was expressed by the following linear rule-of-mixtures: m = msolid(fsc/fsc| + mliquid(1–fsc/fsc|, where fsc| is fsc at the beginning of the eutectic solidification, while msolid and mliquid are the m-values just below the solidus temperature and at fsc = 0, respectively. The increase in fsc due to the eutectic solidification hardly affected the change in the m-value and such a value was equivalent to msolid. On the contrary, the change in the k-values was found to obey the Arrhenius equation rather than be controlled by fsc. It is suggested that regardless of the aluminum alloy composition, the viscous properties of partial solidification can be determined using the these relationships.

Original languageEnglish
Article number142339
JournalMaterials Science and Engineering: A
Publication statusPublished - 2022 Jan 14


  • Aluminum alloy
  • Constitutive behavior
  • Direct chill casting
  • Mechanical properties
  • Semi–solid
  • Solidification cracking

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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