Three-dimensional mesoscopic modeling of equiaxed dendritic solidification of a binary alloy

Abstract

The mesoscopic envelope model is a recent multiscale model that is intended to bridge the gap between purely microscopic and macroscopic approaches for the study of dendritic solidification. It consists of the description of a dendritic grain by an envelope that links the active dendrite branches. The envelope growth is deduced from an analytical microscopic model of the dendrite tip growth kinetics matched to the numerical solution of the mesoscopic solute concentration field in the vicinity of the envelope. The branched dendritic structure inside the envelope is described in a volume-averaged sense by phase fractions and averaged solute concentrations. We present a careful quantitative analysis of the influence of numerical and model parameters on the accuracy of the model predictions. We further perform a validation study through comparisons of 3D simulations to experimental scaling laws giving the shape and the internal solid fraction of freely growing binary alloy dendrites and to analytical solutions for the primary dendrite tip speed. We provide generally valid guidelines for the calibration of the mesoscopic model, enabling reliable control of the accuracy of model predictions over a wide range of undercoolings. The model is applied to simulate strong solutal interactions in large ensembles of equiaxed grains. The potential for mesoscopic simulations to provide refined modeling of microstructures in volume-averaged macroscopic models via scale bridging is demonstrated.

Multiscale dendritic needle network model of alloy solidification with fluid flow

“…Because of these limitations, several scale-bridging approaches have been proposed to simulate dendritic growth at scales larger than those accessible to phase-field. These models include continuum volumeaveraged approaches [14,15,[37][38][39], models based on dynamics of average dendritic grain envelopes [40,41], and approaches coupling cellular automata with finite elements [42,43], finite differences [44], or Lattice Boltzmann methods [45]. Granular models, with approximate grain shapes based on Voronoi space tessellation, have also been used to study the occurrence of solidification defects resulting from the coupling between grain growth and fluid flow, such as porosities and hot cracking [46,47].…”

Phase-field numerical simulation of three-dimensional competitive growth of dendrites in a binary alloy

“…However, few studies have been carried out on the competitive growth among dendrites. Souhar and De Felice et al [32] simulated the mutual influence and competition of multiple 3-D dendrites simultaneously growing in a binary alloy by employing a mesoscopic model for solidification. Compared with PFM, mesoscopic models can readily simulate the mutual influence and competitive growth of 3-D dendrites due to the simplicity of calculation.…”

Micro‐macro modelling of steel solidification: A continuum mechanical, bi‐phasic, two‐scale model including thermal driven phase transition

“…e.g. Steinbach [2], Souhar et al [3], Alves et al [4] and Takaki et al [5]. The large mechanical deformation description requires finite kinematics, where the overall deformation gradient is decomposed multiplicatively into several intermediate stress-free configurations.…”