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Journal Articles IOP Conference Series: Materials Science and Engineering Year : 2020

Comparing mesoscopic models for dendritic growth

Damien Tourret
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Laszlo Sturz
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Alexandre Viardin
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Miha Založnik


We present a quantitative benchmark of multiscale models for dendritic growth simulations. We focus on approaches based on phase-field, dendritic needle network, and grain envelope dynamics. As a first step, we focus on isothermal growth of an equiaxed grain in a supersaturated liquid in three dimensions. A quantitative phase-field formulation for solidification of a dilute binary alloy is used as the reference benchmark. We study the effect of numerical and modeling parameters in both needle-based and envelope-based approaches, in terms of their capacity to quantitatively reproduce phase-field reference results. In light of this benchmark, we discuss the capabilities and limitations of each approach in quantitatively and efficiently predicting transient and steady states of dendritic growth. We identify parameters that yield a good compromise between accuracy and computational efficiency in both needle-based and envelope-based models. We expect that these results will guide further developments and utilization of these models, and ultimately pave the way to a quantitative bridging of the dendrite tip scale with that of entire experiments and solidification processes. 1. Introduction In metallic alloys obtained by solidification processing, dendritic microstructures are common [1]. From a fundamental standpoint, dendritic growth theory and modeling stands as a challenge to combine phenomena across a wide range of scales, from microscopic capillarity at dendritic tips to macroscopic transport of heat and solute in the melt [2,3]. Due to this multiscale aspect, numerous approaches have emerged over the years that aim at bridging length scales in solidification modeling [4-6]. Each of these approaches operates within a different range of scales, which makes them valuable tools from a technological innovation perspective, since a key hurdle on the way to effective ICME (Integrated Computational Materials Engineering) implementations relies upon our ability to couple models at different length scales [7,8]. Yet, most modeling approaches to dendritic growth have thus far been developed separately, with little effort to compare them and to discuss their capabilities and limitations on a quantitative basis. In this article, we focus on models of solidification that operate from the microscopic to an intermediate, or mesoscopic, scale between that of the microscopic solid-liquid interface pattern and that of the macroscopic solidification process. At this intermediate scale, interactions between grains occur that determine microstructural features such as grain size, shape, morphology, and crystal texture. Mesoscopic models are more recent than their microscopic and macroscopic counterparts, such that a rigorous quantitative assessment of their relative advantages and limitations remains to be performed. We also focus on moderate solute supersaturation, Ω ≤ 0.25, which is a common regime for most processes that do not involve rapid solidification.
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hal-02978745 , version 1 (23-12-2020)





Damien Tourret, Laszlo Sturz, Alexandre Viardin, Miha Založnik. Comparing mesoscopic models for dendritic growth. IOP Conference Series: Materials Science and Engineering, 2020, 861, pp.012002. ⟨10.1088/1757-899X/861/1/012002⟩. ⟨hal-02978745⟩
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