Equiaxed growth of interacting Al–Cu dendrites in thin samples: a phase-field study at copper concentrations relevant for practical applications

Abstract

We perform three-dimensional phase-field simulations of equiaxed solidification in Al–Cu thin samples. Purely diffusive conditions are considered in order to describe systems where convection and gravity effects can be neglected. The use of a parallel adaptive finite element algorithm introduced recently [Gong et al., Comput. Mater. Sci. 147 (2018) p. 338-352] allows us to reach the domain of copper concentrations used in practical applications ($c \ge 3$ wt% Cu). We compare the present results with those of a previous study which was restricted to lower copper concentrations ($c \le 2$ wt% Cu) [Boukellal et al., Materialia 1 (2018) p. 62-69] due to the use of a finite difference code. In the fast dendritic growth regime, our results confirm that the dimensionless growth length $\Lambda $ is independent of the copper concentration and the average separation distance between the dendrite nuclei. The new data obtained at higher copper concentrations lead to a more accurate estimate of $\Lambda $. Physical arguments are developed to specify the meaning of $\Lambda $ and the grounds of the scaling law $\Lambda =\mathrm{cst}$. Comparisons with available experimental results of the literature give additional support to this scaling law.

Keywords

• Metals and alloys
• Solidification
• Solute diffusion
• Grain structure
• Phase-field
• Microgravity