Equiaxed growth of interacting Al–Cu dendrites in thin samples: a phase-field study at copper concentrations relevant for practical applications - Gong, Tong Zhao; Boukellal, Ahmed Kaci; Chen, Yun; Debierre, Jean-Marc (Comptes Rendus. Mécanique, 2023)
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 $Λ $ 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 $Λ $. Physical arguments are developed to specify the meaning of $Λ $ and the grounds of the scaling law $Λ =cst$. Comparisons with available experimental results of the literature give additional support to this scaling law.