Microsegregation During Solidification
The DICTRA solidification simulation starts at a temperature above the liquidus of the system. This is the first peak temperature shown in Figure 4 and corresponds to the laser passing the tracked point the first time. At this time step, the whole DICTRA simulation domain is thus a homogenous liquid. When the laser passes the point during a second anti-parallel scan, the domain completely re-melts as the temperature reaches about 1700 K (second peak in Figure 4). During the third scan (third peak in Figure 4), further away from the point, the temperature is only increased to about 1050 K and the domain, which is fully solidified after the cooling down from the second scan, does not re-melt again. The distribution of alloying elements over the secondary arm spacing produced from these heating and cooling cycles is shown in Figure 5. Closest to the last solidified liquid (at x = − 150 nm and x = 150 nm in Figure 5), the microsegregation is the largest. The interdendritic regions are, in particular, observed to be enriched in Mo and Nb and depleted in Cr. Carbon also segregates towards the solidification front, whereas Fe segregates away from the solidification front. These solidification characteristics are in accordance with the experimental observations where energy dispersive spectroscopy (EDS) maps have shown enrichment of Nb and Mo as well as Cr depletion in interdendritic regions.[1,2]
The DICTRA simulation is an approximate representation of the AM process and several simplifications and assumptions are made such as assuming 1D planar solidification and local equilibrium at the interface. The latter assumption, in particular, is limiting when studying solidification at high cooling rates since deviations from local equilibrium due to finite interface kinetics and solute trapping are expected. By enforcing local equilibrium without accounting for trapping effects, the DICTRA simulation therefore overestimates the extent of segregation. In this aspect, phase-field solidification models that allow for both curved interfaces and solute trapping could be a way to go to produce estimations of microsegregation during AM, see, e.g., References 34,35,36,37. Uncertainties are also introduced by the applied time-temperature profile which is not as complex as could be expected for AM and by the estimation of the secondary arm spacing. However, in the following discussion, the calculated microsegregation shown in Figure 5 is assumed to be representative for an arbitrary location in the as-built IN625 microstructure.
Figure 6(a) shows the composition profiles as a function of distance in the vicinity of the interdendritic region. To investigate how the segregated as-built microstructure at these compositions may react upon heat treatment, the driving force, ΔG, for precipitates to nucleate from a γ matrix is calculated at 870 °C. Note that contributions from interfacial effects and kinetic obstacles are ignored. The results are shown in Figure 6(b) and include the phases of interest that showed the largest driving forces, i.e., MC, M23C6, M6C, σ, µ, laves, δ, and γ″. In the figures, − ΔG is plotted, and thus values greater than 0 indicate that nucleation from the γ matrix is thermodynamically favorable, whereas values less than 0 indicate non-favorable nucleation. In Figure 6(b), only values greater than 0 are shown. As the enrichment of Nb and Mo increases, when moving from the dendrite arm core towards the interdendritic region, the driving forces for all the phases increase. Hence, from a thermodynamic point of view, precipitation of all of the phases considered become more favorable in the segregated regions due to the increase in Mo and Nb composition. The driving forces for δ, γ″, and σ are particularly of comparable magnitude and, depending on process conditions, competitive precipitation of these phases is expected. The driving force for the laves phase becomes comparable to the δ and γ″ driving forces at the very center of the dendrite; i.e., according to the calculations, it is not thermodynamically favorable for laves to form unless the segregation is sufficiently severe.
Precipitation During Post-treatments
Although the nucleation driving force is a useful quantity, when trying to elucidate how a microstructure may evolve, the kinetic aspects and interfacial energy contributions may play a decisive role. From the calculated equilibrium phase diagram in Figure 3(a), as well as from experimental observations, it is known that the δ-phase is an equilibrium phase at the industry-recommended stress-relieving temperature 870 °C for the nominal IN625 composition. However, the nucleation and its growth are too slow for it to reach a detectable volume fraction within the suggested heat treatment time (1 hour) in the case of wrought IN625 as shown by the experiments by Floreen et al. [9] and Suave et al.[10] To study the kinetics of the precipitation during heat treatment of AM IN625, and how it may alter locally throughout the as-built, highly segregated microstructure, TC-PRISMA simulations are performed for compositions at different locations along the dendrite arm spacing, i.e., at 30 nm, 20 nm, and 10 nm from the interdendrite region center, see Figure 6(a). The phases δ, γ″, σ, µ, and MC are included in the simulations. Although the laves phase has the same constituents as δ and thus could be an expected phase, it is not included in the simulations. The reason for this is that its driving force for nucleation is much smaller than the included phases at the selected composition as shown in Figure 6(b); i.e., even if laves would be included in the simulation, it would not form. Further, the laves phase is also not experimentally observed in the current work. For the simulations, the C content is kept the same in all simulations, i.e., at a mass fraction of 0.02 pct. Only isothermal precipitation kinetics are considered; i.e., heating and cooling are not included. Simulations are performed at several temperatures to enable the construction of TTT diagrams.
The results of the TC-PRISMA simulations at 800 °C and 870 °C in terms of volume fraction as a function of time are shown in Figures 7(a) and (b), respectively. For both temperatures and all compositions, the MC carbides precipitate first due to its high driving force for nucleation. The volume fraction of the phase is determined by the amount of C, and hence, it is the same for all simulations and reaches its maximal fraction value almost immediately (not visible in Figure 7(a) and (b). After precipitation of MC, γ″ precipitates followed by δ precipitation for all simulations. Evidence that the δ-precipitation in AM IN625 may be preceded by γ″ precipitation is reported in Reference 3 and the competition between γ″ and δ in the interdendritic regions is further discussed by Lass et al.[17] For the nominal composition (blue lines, Figure 7), the formation of the γ″-phase is more pronounced at lower temperature (Figure 7(a): dashed blue line) compared to higher temperature (Figure 7(b): dashed blue line) which is in accordance with experimental observations for wrought IN625.[9] The volume fraction of the precipitates also increases with decreasing temperature which is expected from the equilibrium calculations (Figure 3(a)).
When δ starts to form, the fraction of γ″ begins to decrease, and before the equilibrium fraction of δ is reached, the γ″ precipitates have completely dissolved. This can be explained by γ″ being metastable (in the IN625 system). As discussed in the previous section, the driving force for the γ″ and δ precipitates to nucleate from the γ matrix increases with increasing degree of segregation (mainly due to enrichment of Nb and Mo) which, consequently, contributes to earlier precipitation kinetics in segregated areas. For example, for the nominal composition at 800 °C, the δ-phase has reached a volume fraction of 1 pct after 13.5 hours, whereas for the composition 10 nm from the center of the interdendrite region, a volume fraction of 1 pct is reached after 8 minutes.
TC-PRISMA simulations are performed at several temperatures for the different segregated compositions and are presented in Figure 8(a) in terms of a TTT diagram. For each composition, the curves indicate the temperature-time combinations for which the δ-phase has grown to a volume fraction of 1 pct. From the TTT diagram, it can be concluded that the precipitation of the δ-phase, in addition to occurring at a shorter timescale, also is extended to higher temperatures with increasing segregation. While it takes thousands of hours for the δ-phase to form in the case of the nominal composition (blue solid curve in Figure 8(a)) at 870 °C, the δ-phase forms during early stages (seconds to minutes) up to over 1000 °C in the case of the 10 nm composition (purple curve in Figure 8(a)). Exact agreement with the experimental TTT curve is not expected due to the model assumptions and the use of the reduced composition. Yet the present calculations support the hypothesis that the accelerated precipitation kinetics observed in AM IN625 is due to local, extreme, compositional changes due to the microsegregation.
Since each calculated curve in the TTT diagram (Figure 8(a)) only represents one point in the microstructure, a single curve alone cannot describe the precipitation behavior in AM IN625. Instead, integrating over all the compositions would result in a volume phase fraction evolution more justifiably comparable to experimental observations. Performing TC-PRISMA calculations at all compositions in the segregation profile is, however, beyond the scope of this work and simulations are only performed at select compositions. Nevertheless, a simplified comparison is made by weighing the contribution of the different simulations to the overall volume fraction evolution differently depending on location. Here, it is assumed that the interdendritic regions represent about 20 pct of the microstructure and can be represented by the simulations for the composition at 10 nm from the interdendritic center, Figure 6(a). The remaining part of the microstructure is assumed to be represented by the simulation for the nominal composition. The resulting TTT curve is shown in Figure 8(b) and is comparable with the experimentally determined TTT diagram.
In Figure 9, the evolution of the volume fraction of the δ-phase with time is shown for the simulations at 800 °C and 870 °C, in the case of the assumption described previously (contribution from the nominal and the 10 nm composition). The volume phase fractions determined experimentally, both by SEM and laboratory XRD,[5] and by USAXS/XRD, are also included. Some discrepancy in the two sets of experimental data is seen. Measuring phase fractions from SEM images leads to uncertainties, particularly at low δ fractions since it is difficult to separate between the δ-precipitates and the Mo-Nb-rich interdendritic regions using backscatter electron imaging or EDS. In addition, the δ-precipitates are thin, only about 30 nm to 50 nm thick, and resolving that thin of a precipitate to a level that provides highly accurate phase fractions is difficult. The USAX/XRD measurements are more quantitative since they directly measure phase fractions throughout the measured sample volume of approximately 1.2 × 0.8 × 0.03 mm3, and these measurements probed the same sample volume in situ during the isothermal anneals.
Nevertheless, comparison of the simulations with the experimental observations shows qualitative agreement. At 870 °C, both the simulations and experiments predict that the volume fraction is approaching a constant with increasing time. At 800 °C, both the simulations and experiments show the volume fraction increasing as function of time. The discrepancy between the experiments and simulations is in how fast the volume fraction of δ increases: the simulation predictions are much faster than what is observed. At 870 °C, the equilibrium volume fraction of δ is reached at approximately 1 hour; however, experimentally the volume fraction does not begin to plateau until 7 hours.
The simulations only assume contributions to the precipitation kinetics from compositions at two locations and do not average over all the compositions in the microstructure. In addition, the precipitation simulation using TC-PRISMA is based on a number of assumptions and approximations including uncertainties in the classical theory of nucleation, the choice of nucleation sites, interfacial energies, and in the thermodynamic and diffusion mobility databases. Small changes in input data and nucleation assumptions could alter the simulation outcome. Despite these shortcomings, the ability of the calculations to reproduce the experimental TTT curve, and qualitatively assess certain characteristics of the precipitation during post-processing, motivates exploring the possibility of using simulations to guide the selection of a stress-relieving treatment.
In Figure 10, the calculated phase fraction evolution is shown for the initial heat treatment (up to 2.5 hours) at 700 °C, 800 °C, and 870 °C. In comparison, the experimental results by Stoudt et al.[5] (800 °C and 870 °C) are shown as well as the USAXS/XRD results (700 °C, 800 °C, and 870 °C). According to the experimental work by Lass and Stoudt et al.,[3,5] the industry-recommended stress-relieving at 870 °C for an hour results in a volume fraction of about 2 pct δ-phase. If the stress-relieving temperature instead is lowered to 800 °C, they found that a volume fraction of less than 0.5 pct δ-phase forms during the first hour of heat treatment. Since IN625 reaches its optimal strength when as much alloying elements as possible are dissolved in the γ solid solution, a stress-relieving treatment that minimizes the δ-phase formation while removing residual stresses, and hence enables for efficient homogenization, should be aimed for. Thus, Lass et al.[3] recommended the stress-relieving temperature of 800 °C. The present simulations support this suggestion. Despite the discrepancy with regard to the measured phase fraction, the calculated phase fraction as a function of time in Figure 8 indicates that a stress-relieving at 870 °C for an hour would result in the formation of about four to five times as much δ compared to stress-relieving at 800 °C. For long-term treatment, however, heat treating at 800 °C will result in a larger δ-phase fraction. This is expected from the phase diagram for the IN625 nominal composition where the equilibrium phase fraction of δ increases with decreasing temperature (Figure 4). This is also in accordance with experimental findings for L-PBF IN625 (Figure 8).[5] Heat treating at 700 °C would result in even less δ formation. However, relieving the stresses at such a low temperature requires longer holding times, and hence, more time for δ to grow together with increased processing time and cost.