Abstract
In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical -Al2Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate.
Highlights
The mathematical modelling of the growth and dissolution of precipitates in metals is of prime importance in the development of predictive tools dedicated to the optimization of heat treatments and material properties
Analytical models are preferred for the simulation of precipitate growth and dissolution in commercial software applications dedicated to precipitation kinetics
Some authors stated that the reverse-growth approximation is not the best method to calculate the dissolution rate of a precipitate, our results show that the agreement between our reversed-growth model and the DICTRA fully transient solution is excellent, and could only be improved if the analytical procedure accounted for the transient term in the mass conservation equation
Summary
The mathematical modelling of the growth and dissolution of precipitates in metals is of prime importance in the development of predictive tools dedicated to the optimization of heat treatments and material properties. Considering that the mixed-mode approach encompasses all previous diffusion-controlled models and gives the possibility to calculate more precisely interfacial compositions with better computational efficiency, we decided to find a solution for the dissolution of precipitates and to adapt the quasi-stationary mixed-mode solution to a finite system. This will give the possibility to use these solutions for the simulation of growth and dissolution of precipitates in a given volume. The mathematical treatment will be applied on a binary system, to focus the scope on the dissolution problem and on the time discretization procedure
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
