Modelling the Age-Hardening Precipitation by a Revised Langer and Schwartz Approach with Log-Normal Size Distribution

Abstract

A new numerical modelling approach integrating the Langer and Schwartz approach and log-normal particle size distribution has been developed to depict the precipitation kinetics of age-hardening precipitates in Al alloys. The modelling framework has been implemented to predict the precipitation behavior of the key secondary phases in 6xxx and 7xxx Al alloys subjected to artificial aging. The simulation results are in good agreement with the available experimental data in terms of precipitate number density, radius, and volume fraction. The initial shape parameter of the log-normal size distribution entering the modeling framework turns to play an important role in affecting the later-stage evolution of precipitation. It is revealed that the evolution of size distribution is not significant when a small shape parameter is adopted in the modelling, while an initial large shape parameter will cause substantial broadening of the particle size distribution during aging. Regardless of the magnitude of shape parameter, a broadening of the particle size distribution as predicted by the present model is in agreement with experimental observations. It is also shown that large shape parameter will accelerate the coarsening rate at later aging stage, which induces fast decreasing of number density and increased growth rate of mean/critical radius. A comparison to the Euler-like multi-class approach demonstrates that the integration of more realistic log-normal distribution and Langer and Schwartz model make the present modelling faster and equivalently accurate in precipitation prediction.

Thermodynamic modeling and computational predictions of NbC precipitation in Fe–Mn–Si-based shape memory alloys by the classical nucleation and growth theories

“…In addition to the experimental investigations, thermodynamic modeling is also feasible to explore the underlying precipitation mechanism. The precipitation predictions in some alloys by classical nucleation and growth theories have shown good agreement with experimental observations [28][29][30][31]. However, investigation of the precipitation behavior in Fe-Mn-Si-based shape memory alloys by thermodynamic modeling has not been reported.…”

“…The classical nucleation and growth theory was described for precipitation in detail in references [28][29][30][31][32]. Here we only present the main feature.…”

Modelling the Spatial Evolution of Excess Vacancies and its Influence on Age Hardening Behaviors in Multicomponent Aluminium Alloys

“…Over the last decades, plenty of models have been developed to simulate the age hardening precipitation kinetics in Al alloys during heat treatments [10,[55][56][57][58][59][60][61]. In most of the models, the influences of excess vacancies on precipitation kinetics are not taken into account.…”

A review on recent opportunities in MATLAB software based modelling for thermoelectric applications

“…[58] used TEG-leg to calculate the probabilities of failures in function between P-N-P-N-P-N connections; he used MATLAB algorithmic program formed from Weibull and lognormal distribution [10,28,34,71] for finding the stresses, tensile strength and compression phenomena in P-N-P-N-P-N TEG-leg connections.…”