Simple model for carbonitride dissolution in microalloyed steels

Abstract

Based on local equilibrium at the moving phase boundary and diffusion control a simple but comprehensive model concerning the carbonitride dissolution kinetics has been constructed. This model describes the evolution of a single particle or a distribution of particles in a finite austenite matrix with annealing temperature or time. It is shown that at temperatures below the dissolution temperature of carbonitrides the particle size decreases rapidly in early stages and then slows down approaching the equilibrium state. When the temperature, however, exceeds the dissolution temperature of precipitates the particles will be completely dissolved. The time evolution curves of particle size and volume fraction drop quickly and level off at certain temperatures. In contrast, the volume fraction and mean radius of precipitates decrease slowly first at lower temperatures and then drop drastically at higher temperatures. Finally the present model has been validated by the experimental data in the literature.

Dissolution of interdendritic σ phase in cast Ni–Fe–Cr alloy

“…In addition, an interface reaction limited model was applied to predict the dissolution of the low melting points phases in Al alloys. 22 Moreover, Wang et al 23 proposed a model to describe the dissolution behaviour of a single particle or a distribution of particles in a finite austenite matrix. Recently, an empirical correlation between the kinetic parameter and the grain size has been used to quantify the dissolution behaviour of δ phase in superalloy GH4169.…”

“…It can be seen the s phase in specimens A1 dissolves more slowly than that in In order to quantitatively describe the dissolution behaviour, many kinetics models have been proposed in recent years. 14,[21][22][23][24] For example, on the basis of the classical numerical method, Vermolen et al 21 developed a semianalytical model for the dissolution of spherical particles in finite media. In addition, an interface reaction limited model was applied to predict the dissolution of the low melting points phases in Al alloys.…”

“…Recently, an empirical correlation between the kinetic parameter and the grain size has been used to quantify the dissolution behaviour of d phase in superalloy GH4169. 24 However, most of the above models [21][22][23] are in numerical form and inconvenient for direct application. Moreover, such models [21][22][23][24] have not considered the interactions of solute diffusion fields around adjacent dissolving particles, which should be taken into account for the multiparticle system just as the current case.…”

“…24 However, most of the above models [21][22][23] are in numerical form and inconvenient for direct application. Moreover, such models [21][22][23][24] have not considered the interactions of solute diffusion fields around adjacent dissolving particles, which should be taken into account for the multiparticle system just as the current case. Recently, we have developed a simple analytical model for dissolution kinetics in the multiparticle system, 14 and thus, it is employed in the current case.…”

Two-Stage Least Squares based Iterative Identification Algorithm for Box-Jenkins Model

“…Least-squares iteration identification method use all the data of the system in the process of every step iterative calculation, and extract information as much as possible from the data to improve the parameter estimation accuracy [12,13,14].For example, Ding et al presented least squares based iterative algorithms for Hammerstein nonlinear ARMAX systems [14], and for OE and OEMA systems [15] [19]. Also, a least squares based iterative algorithm is developed for BoxCJenkins systems, and the precision of parameter estimation is improved compared with recursive generalized extended least squares algorithm [20].…”