Grouping Methods of Cluster Dynamics Model for Precipitation Kinetics

Kun Xu,Zhaoyang Wu,Hui Kong,Brian G Thomas,Haichuan Wang,Yueyue Wu

doi:10.3390/met10121685

Kun Xu, Zhaoyang Wu + Show 4 more

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https://doi.org/10.3390/met10121685

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Abstract

Due to its simplicity and efficiency, cluster dynamics modeling has been widely used to simulate microstructure evolution in materials, such as defect formation in metals. However, its computation cost becomes prohibitive when the clusters grow too large, so a particle-size-grouping method is often required. In this paper, three different size-grouping methods are compared with the exact solution of the ungrouped cluster dynamics model for Al3Sc precipitation in an Al-0.18 at.% Sc alloy. A new assumption of logarithmically-linear distribution of cluster number densities inside each size group is shown to be the most efficient way to match with all results of the ungrouped model. Finally, the calculated results are compared with the measured sizes and distributions of Al3Sc precipitates at different aging temperatures. The new size-grouping method is shown to have better accuracy for the chosen discretization and time-stepping method evaluated. This will enable significant computational savings, and the extension of time scales and cluster sizes to the ranges of realistic metallurgical systems, while preserving reasonable accuracy.

Highlights

The purpose of this paper is to develop and demonstrate a more accurate and efficient PSG Cluster dynamics (CD)
A new cluster dynamics model is presented for predicting precipitation formation, which is shown capable of reproducing many important metallurgical phenomena, such as matching the Gibbs–Thompson equation
The mean precipitate size calculated with the new PSG CD model matched reasonably well with the experimental measurements for different aging temperatures

Summary

Introduction

Cluster dynamics (CD) is a powerful tool to model microstructure evolution in materials, such as the nucleation, growth and coarsening of precipitates [1,2,3,4,5,6,7,8,9,10,11,12], point defects [13,14,15,16,17,18,19,20], bubbles [21,22,23], or inclusions [24,25,26]. The CD model has several unique advantages for describing precipitation kinetics, especially in irradiated materials or at an early stage of precipitation. It describes the entire evolution of every cluster as a single continuous and competing process, using the same set of equations and physically-based properties, so the different phenomena of incubation, nucleation, growth, and coarsening all arise naturally. Becker–Döring nucleation theory [27,28], which is very important for many kinetic models, such as modified Langer-Schwartz [29,30], Kampmann-Wagner Numerical [31,32], or Matcalc [33,34], is not needed in the CD model

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