Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

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.

Multiphase modelling of the growth kinetics of precipitates in Al-Cu alloys during artificial aging

“…The mixed-mode model for the evolution of an ellipsoidal precipitate in a binary infinite matrix has already been reported in our previous contributions ( [16]: Growth model), and ( [18]: Dissolution model). During the mixed-mode regime, it is assumed that the precipitates evolve with a constant aspect ratio.…”

“…Similarly, the equations for the dissolution under the mixed-mode regime (reversed-growth approximation) are expressed as [18]:…”

“…Since non-isothermal precipitation is considered in this paper, the temperaturedependent parameters (c 1 eq , M and D) must be updated at each time step. Also, to transform the solution from a quasi-stationary case where c is constant, into a finite system where c changes gradually with time, the time discretization technique presented in our previous contribution [18] must be used to calculate the growth velocity ∂a 1 /∂t| c(t) at each time step. The size of the precipitates is then calculated with the following equation:…”

“…That model provided a quasi-stationary solution for a precipitate in an infinite binary matrix [16]. This approach was extended for the growth of multicomponent precipitates [17], and a time-discretization technique was introduced to upgrade the analysis capability of the model for finite systems, including the dissolution of the unstable phases [18]. Nevertheless, the application of all these contributions [16][17][18] was limited so far to the isothermal evolution of only one type of precipitate.…”

Phase-field study of elastic effects on precipitate evolution in (Al)0.05CrFeNi

“…On the other hand, the computational tools show their increasing impact in fostering the development of new alloys by predicting the microstructure evolution behavior before conducting experiments. The phase-field (PF) method has become one of the most commonly used computational modeling techniques for studying microstructural evolution in materials, e.g., grain growth [20,21], precipitate growth and dissolution [22,23] and intermetallic phase morphology evolution [24,25] interdiffusion [26,27], spinodal decomposition [26], solidifications [27,28], martensite transformation [29], fracture [30], and so on. However, difficulties in obtaining and describing the thermodynamic, kinetic, and elastic properties hindered the model's application on the phase transformation behaviors in HEAs due to the inherently complex composition dependence.…”