Numerical Simulation of Copper Precipitation during Aging in Deformed Fe-Cu Alloys

Abstract

A numerical model was developed to simulate the competing precipitation of Cu particles on dislocations and in the matrix in Fe-Cu alloys. The nucleation and growth rates and the remaining Cu concentration in the matrix were calculated successively at a large number of fine discrete time steps. In the absence of dislocations the results for precipitation in the matrix that was assumed to occur homogeneously were in essential agreement with those of Langer-Schwartz (L-S) model and Lifshitz-Slyozov-Wagner (LSW) coarsening theory. The heterogeneous precipitation on dislocations was incorporated taking into account the development of solute-depleted zone around dislocations. The coarsening behavior of particles on dislocations and in the matrix deviated substantially from those of previous theories probably due to the interaction of diffusion fields between heterogeneous and homogeneous precipitation zones. In other words, coarsening can occur at the expense of smaller particles nucleated in the matrix at later stages. The bcc to fcc transformation of Cu particles that occurs during growth was likely to accelerate the coarsening of Cu particles. The simulation results agreed well with experiment in respect of the particle number and mean particle radius, but the model yielded a considerably narrower particle size distribution than experiment reported in the literature.

The Role of Excess Vacancies on Precipitation Kinetics in an Al-Mg-Sc Alloy

“…Figure 8 shows the comparison between measured and calculated precipitate size distributions. The model captures the size distribution reasonably well, though it does tend to underpredict the width of the distribution, a feature that has been previously reported for KWN models, [12] and slightly underpredicts the mean precipitate size for aging at 300°C. Importantly, the model is able to capture the size distributions obtained under isothermal aging conditions, as well as those obtained for samples that were up-quenched from 300°C to 425°C.…”

Simulation of Nucleation of Proeutectoid Ferrite at Austenite Grain Boundaries during Continuous Cooling

“…The so-called N model is widely used for simulating precipitation in aluminum [15][16][17][18] and iron alloys [19,20] that takes place at small supersaturations. In the experiment by Offerman et al, it seems that the supersaturation remained relatively low at nucleation stages because of the slow cooling rate.…”

“…Whereas the stationary interface approximation [24] is often used in the N model, [16,20] the growth rate of ferrite is calculated from the equation of spherical growth given by…”

Computer-Aided Design of Manufacturing Chain Based on Closed Die Forging for Hardly Deformable Cu-Based Alloys

“…[25,26] The interaction between dislocations and precipitates was based on the assumption that the dislocation core energy over the precipitate radius is spent for the nucleation. Thus, the activation energy, DG, for the formation of the critical nucleus of radius, r c , is the sum of the chemical free energy À 4 3 pr 3 DG V À Á , the interfacial free energy 4pr 2 c À Á , and the dislocation core energy À0:4lb 2 r À Á .…”