[3]
Results and Discussion In this section, the present simulation method is utilized to simulate experimental data of number density N, mean radius r and phase fraction f from ref. [1] as well as to determine the 10% and 90% precipitation lines for the Fe-1.4 wt.% Cu alloy as investigated in ref. [7]. A series of simulated plots is presented, incorporating the previously discussed effects (i)-(v). All plots are compared to the reported experimental data. The precipitation of Cu in a Fe-1.4 at.% Cu alloy at 500°C was investigated by Goodman [1], providing us with important data-triplets of N, r and f. The simulation is carried out as an isothermal treatment at 500°C. Figure 2 shows the results, which are split into (a)-(c) for easier interpretation. The simulation is run until a constant phase fraction is reached. With the correct evolution of all three Cu precipitation parameters from early stages to coarsening, this methodology is applied to the calculation of the ttp-plot for Cu-precipitation from ferrite. To generate the ttp-plots, the relative phase fractions of the cumulative curve are evaluated from isothermal kinetic simulations carried out with MatCalc in 25K steps between 400°C and 700°C. Figure 3 shows the ttp-plots for the different simulation steps, starting with the simulation for ortho-equilibrium nuclei (Fig. 3 (a)). Stepwise, the impact of the variable nucleus composition (Fig. 3 (b)) together with the effects of precipitate size and atomic mixing across the interface (Fig. 3 (c)) and, finally, coalescence (Fig. 3 (d)) are taken into account. This is discussed in more detail subsequently. In the evaluation of the times for 10% and 90% ttp-lines, the maximum precipitated phase fraction of each considered temperature was used as reference. Figure 2. Results of the kinetic simulation for Fe-1.4 wt.% Cu alloy investigated by Goodman [1]. (a)-(c) show the phase fraction f, mean radius r and number density N of the three considered populations bcc, 9R and fcc. All effects (i) to (v) were considered. In Fig. 3 (a), the precipitate fractions are evaluated numerically using the assumption of a maximum chemical nucleation driving force, which corresponds to the assumption of ortho-equilibrium composition for the precipitate nucleus [22,23]. No further assumptions are made and the evaluation routines in MatCalc are utilized as developed originally in refs. [9,10,11] and without any undetermined fitting parameter. The agreement of simulation and experiment in this case is poor. The precipitation start times are orders of magnitude too late and the maximum precipitation temperature is evaluated too low by values of more than 100K. Figure 3 (a)-(d). Calculated ttp-plots for 10% and 90% Cu-precipitation compared with the experimental data referred in [1] triangles and [7] circles, with (a) ortho-equilibrium nucleus composition, (b) minimum G* nucleus composition and precipitate size effect, (c) entropic effect of mixing at interface and (d) coalescence and, therefore, all different effects (i)-(v). In Fig. 3 (b), the simulation is adapted such as to take into account the compositional variations of the Cu nuclei as well as the precipitate size effect. Even though precipitation start times occur an order of magnitude earlier, the process is still too slow, and the evaluated temperatures are also still off by about 100K. In Fig. 3 (c), the entropic effect of mixing at the interface is considered. Compared to the prior results, the precipitation start times are considerably shorter and in good qualitative and quantitative agreement with experimental evidence. Especially, the 10% line closely matches the experimental data. Fig. 3 (d) finally incorporates all effects, comparable to the detailed simulation results of Fig. 2. With all mechanisms, excellent agreement between simulation and experiment in the entire temperature range can be achieved. Moreover, not only the phase fraction lines shown in Fig. 3 (d) are simulated correctly, but all three precipitation parameters, phase fraction, mean radius as well as number density, are consistently reproduced. The main difference between plot (c) and (d) is the correct treatment of growth and coarsening of bcc-precipitates due to the consideration of particle coalescence.
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[4]
Summary An advanced simulation approach is developed for the numerical simulation of Cu-precipitation in ferritic steel, taking into account the major mechanisms affecting the precipitation kinetics in Cu-alloyed ferritic steels. These are the varying nucleus composition, the transformation sequence from coherent bcc-Cu to incoherent fcc-Cu, the interfacial energy size correction due to the curvature of small particles and the temperature-dependent reduction of the interfacial energy of the coherent bcc Cu precipitates due to diffuse interfaces as well as the coalescence and high cluster mobility of Cu-particles. With these model ingredients, the experimental ttp-data for Fe-1.4wt.% Cu is reproduced consistently and in a predictive manner. Acknowledgement Financial support by the Austrian Federal Government (in particular from Bundesministerium für Verkehr, Innovation und Technologie and Bundesministerium für Wirtschaft, Familie und Jugend) represented by Österreichische Forschungsförderungsgesellschaft mbH and the Styrian and the Tyrolean Provincial Government, represented by Steirische Wirtschaftsförderungsgesellschaft mbH and Standortagentur Tirol, within the framework of the COMET Funding Programme is gratefully acknowledged. References
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