Quantitative Phase-field Simulation of Dendritic Equiaxed Growth and Comparison with in Situ Observation on Al – 4 wt.% Cu Alloy by Means of Synchrotron X-ray Radiography

Abstract

Dendritic equiaxed growth from the melt by continuous cooling-down is investigated by quantitative 2D phase-field simulations. The results are compared with detailed data from solidification experiments on Al-4 wt.% Cu alloy with in situ X-ray monitoring. In a first step, the simulation of an isolated equiaxed alloy dendrite growing freely in <100>-direction in the melt is performed. Then, the impingement between two grains is considered by simulating two dendritic crystals growing towards each other in <100>-direction. From the phase-field simulations, the time evolution of the equiaxed crystals is characterized by measuring the lengths and tip velocities of the primary dendrite arms in free growth and in the presence of neighbor interaction, which enables the analysis of growth dynamics. In a second part, the results of the phase-field simulations are compared to data extracted from an experiment on Al -4 wt.% Cu alloys carried out at the European Synchrotron Radiation Facility (ESRF), with in situ and real-time characterization by means of X-ray radiography, and to analytical relationship for dendrite tip growth. The limitations of 2D-phase-field simulations to fully describe the dynamic formation and interaction of dendritic equiaxed grains are briefly discussed.

A quantitative phase-field model combining with front-tracking method for polycrystalline solidification of alloys

“…This result thus approves the assumption of the model that the influence of the grain boundary energy on the growth dynamics of dendrites can be neglected before fully solidified. This phenomenon is in agreement with the in situ and real time observed experiments during solidification of Al-Cu alloys by continuously cooling down [34,35]. In these experimental observations, besides the sedimentation of some grains leading to their closer touching with other grains, direct contacts between grains could not take place commonly at the early stage of solidification.…”

“…The ended liquid phase transformation fraction matches the fraction determined by the equilibrium phase-diagram using the lever rule. The significant advantage of high computing efficiency of the model makes it feasible for quantitative simulations of many dendrites growing from melt simultaneously in a large scale comparable to experimental observations by in situ and real-time synchrotron radiography [34,35]. When the phase-field formulations in present model are replaced with the schemes for fast solidification with the modeling of non-equilibrium effects [41], as well as taking account of crystal orientation angle gradients [11], the proposed model and fronttracking method can be extended to rapid solidification processes and to concentrated alloy systems [42].…”

“…It can be seen that almost each crystal is isolated from other grains by solute. The previous experimental characterizations and phase-field simulations have revealed that the grains undergo free and soft impingement growth regimes [34,35]. Nevertheless, the two regimes where the grain boundary energy can be neglected are the crucial processes for understanding polycrystalline growth dynamics.…”

“…Fig. 1 shows the equiaxed dendritic crystals recorded in situ by means of synchrotron X-ray radiography during continuously cooling the melt of Al-4 wt.% Cu alloy [34]. It can be seen that almost each crystal is isolated from other grains by solute.…”

“…The image of equiaxed dendritic crystals recorded in situ by means of synchrotron X-ray radiography during continuous cooling the melt of Al-4 wt.% Cu alloy[34]. The cooling-down rate is 0.5 K/min.…”