Segregation-Assisted Plasticity in Ni-Based Superalloys

The single-crystal prototype nickel-based superalloy MD2 of composition Ni-11.2Al-9.3Co-5.3Cr-2.6W-2Ta-1.65Ti-1.33Mo-0.2Si-0.03Hf (at. pct) is studied.[8] The material was solution treated at 1275 °C for 8 hours, followed by aging for 6 hours at 1080 °C and finally at 870 °C for 16 hours. The orientation of the bulk crystal was checked using backscattered electron diffraction (EBSD) analysis prior to extracting creep samples. Creep test pieces along the \(\langle 011 \rangle \) direction of gage volume \(16\,\,{\times }\,\,1.6\,\,{\times }\,\,1\,\)mm\(^3\) were manufactured using electrical discharge machining (EDM). Monotonic creep tensile tests were performed at 800 °C under an applied tensile load of \(650\,\)MPa, consistent with a region where a rich variety of complex deformation mechanism appears (SISFs, SESFs, microtwins, and APBs).[15‐18] Testing was conducted in an Instron electro-thermal mechanical testing (ETMT) machine with digital image correlation (DIC) as non-contact strain measurement. Three repetition tests were performed in order to validate the repeatability of the results.

Post-mortem examination prior to scanning transmission electron microscopy (STEM) analysis was carried out in order to identify the deformation regions after creep. The samples were prepared by grinding and polishing finished with colloidal silica. The examination plane was carefully selected for subsequent STEM foil extraction, with the foil plane normal oriented along the \(\langle 011\rangle \) axis perpendicular to the tensile direction of the specimen. The preliminary study was performed using a JEOL 6500F field emission gun scanning electron microscope (FEG-SEM) using an accelerating voltage of 10 kV and probe current of \(300\,\)pA. Backscattered electron images were acquired in order to reveal the deformed regions within the sample. An overview of the faulted deformed region studied later by STEM is shown in Figure 1(b).

STEM foils were extracted from these regions normal to \(\langle 011\rangle \) orientation using an FEI Helios NanoLab DualBeam 600 focused ion beam (FIB). This assures planar faults are viewed edge-on using high-angle annular dark field (HAADF) zone axis imaging as indicated in Figure 1(c). Samples were thinned at 5 kV and then further cleaned using a Fischione NanoMill. Energy-dispersive X-ray analysis (EDX) of the foils was performed on an image-corrected Titan3™ 60 to 300 kV with a Super-X detector utilizing the Bruker Esprit software. Integrated line scans were conducted and quantified through Cliff–Lorimer analysis[19] using experimental K\(_{\alpha }\) energies for Ni, Co, Al, Cr, and Ti. L\(_{\alpha }\) was used for the case of Mo. The Cu specimen holder signal was avoided by using the M\(_\alpha \) lines for Ta and W since the L\(_\alpha \) Ta and W peaks corresponded too closely to a Cu peak to be accurately considered. Deconvolution for the W and Ta M\(_\alpha \) peaks, as well as background subtraction, was used to reduce the influence of Bremsstrahlung. For EDS line scan analysis, to reduce the noise and smooth the data, small amounts of averaging were used. Using these setup, the noise can be reduced and no large effects on the variation of composition along the line scans were observed. Detrimental artifacts from foil thickness to the EDS spectrum like beam spreading or low EDS counts were mitigated by controlling the specimens thickness during the thinning process on the FIB. The FIB foil was thinned to around an estimated 20 to 50nm where both foil thickness effects are observed to be avoided. Higher atomic resolution STEM analysis was performed using a probe-corrected Titan3™ 60 to 300 kV.

Two different microtwins within \(\gamma '\) precipitates have been analyzed. HAADF-STEM images in the \(\langle 011\rangle \) zone axis of both microtwins are presented in Figure 2, left. The first microtwin is in an early stage of growth, with around 15 {111} planes thickness, while the second one is in a mature state extending over the whole field of view. The concentration profiles across the microtwins interfaces are shown in Figure 2, right from vertically integrated EDX line scans. They confirm the segregation of Cr—a well known \(\gamma \)-stabilizer—at the twin interfaces. For the case of the thin twin, the interfaces were also found to be slightly enriched with respect of Mo, although the background noise from the measurements makes this less clear. No conclusive fluctuations for Co are found. No relevant chemical changes associated with Ta, Nb, and W elements along faults were observed in any of the two twins.

Nevertheless, the cores of both twins recover the nominal concentration of the \(\gamma '\)-precipitate confining the segregation to just the twin interfaces. Barba et al.[14] and Smith et al.[2] have proposed a model to rationalize this phenomenon. In their models there is a local shift of chemistry from \(\gamma ' \rightarrow \gamma \) at the microtwin interfaces. This is needed to lower the energy of the high-energy faults formed at the twin boundaries as a result of the Shockley partial shearing, whereas the core of the twin recovers the perfect lattice structure.

A HAADF-STEM image of a region containing five different planar faults is shown in Figure 3(a). These correspond to two CESFs/SESFs on a first {111} slip plane and two CESFs/SESFs and a CISF/SISF on a complementary {111} slip system. The faults can be either complex faults (CESF and CISF) or regular faults (SESF and SISF) as the present analysis cannot distinguish between them. The planar faults cut each other presenting interesting interactions and blocking the growth of some of them. Some of the interaction spots and fault ending points present a higher intensity in the HAADF-STEM image which might be related with a higher concentration of heavier elements. This observation is consistent with the previous work in ME3 alloy by Smith et al.[24] The rationalization of these higher density regions associated with the fault growth is discussed in the following section.

The EDX maps of the faults region are presented in Figure 3(a). These maps highlight the segregation of Cr and Co along the planar faults. Enhanced Cr fluctuations at the faults are observed to a higher degree than Co in these maps. Conversely, Al and Ni maps show a slight depletion of these elements along the stacking faults. The compositional changes for each fault have been quantified and they are shown as compositional profiles in Figure 3(b). They have been integrated parallel to the plane of each fault as indicated in Figure 3(a). For the case of the CISF/SISF, the results confirm the segregation of Cr and Mo. Co segregation is much less pronounced. Slight depletion of Ni and Al from the fault lines is observed. These data confirm the qualitative results of the elemental maps presented before. For the case of the CESFs/SESFs, Co is segregated to a slightly higher intensity for fault (2) CESF/SESF than in the CISF/SISF. For fault (3) CESF/SESF, the Co segregation is almost negligible. For both CESF/SESF faults, Cr segregation levels are similar than for the CISF/SISF case. Non-conclusive data were found for Mo segregation in the case of the CESFs/SESFs. No relevant chemical changes associated with Ta, Nb, and W elements along faults were observed.

Finally, an array of planar faults containing an APB within a \(\gamma '\)-precipitate has been studied. A HAADF-STEM image of the dislocation/fault array is shown in Figure 4(a). Several dislocations can be observed coinciding, after atomic resolution fault analysis, with the higher intensity locations observed in the image. These locations have been reported before to be associated with clouds of higher atomic number elements.[25]

Analysis of this array of dislocations indicates that there has been interaction of the primary (horizontal) {111} slip system with the conjugate {111} slip system. It has been found that a series of \(a/2\langle 110\rangle \) dislocations from the conjugate system are incorporated in the dislocation array of the primary slip plane. This is apparent since Burgers circuits around the individual dislocations configurations produce closure failures containing a component pointing out of the primary glide plane, see Figure 4(b). In fact, this is consistent with the presence of conjugate \(a/2\langle 110 \rangle \) dislocations content within the array.

The details of these interactions, and the steps leading to this configuration, are difficult to deduce from this post-deformation analysis; however, the most remarkable feature is between dislocations D1 and D2 shown in Figure 4(a). A higher-magnification atomic resolution STEM micrograph of the region around dislocation D2 is shown in Figure 4(b). To the left of this dislocation, there is a stacking fault that could be either an SISF or CISF. To the right of dislocation D2, there is a region that apparently has perfect crystal stacking (i.e., no structural fault is present). However, closer inspection demonstrates that the higher intensity planes (corresponding to the higher atomic number, Ni-rich sublattice in the \(\gamma '\)-structure) are actually offset by a \(a/2\langle 110\rangle \) displacement in the vicinity of the \(\{111\}\) plane that would project the stacking fault located to the left of D2. Note that the contrast from this superlattice fringe intensity is not uniform, and is only clearly observed in certain regions of the image. This lack of uniformity in contrast may be due to several factors, including the presence of surface contamination in these electropolished TEM foils, as well as local compositional fluctuations that may lead to a decrease in superlattice contrast. It is noted that a similar patchiness to the superlattice contrast is found in all regions investigated, as indicated, for example, in Figure 2(a).

The salient point is that this region to the right of D2 appears to have the structural attributes of an APB. Compositionally, it is also distinct from the perfect \(\gamma '\) regions as shown in the analysis of this region shown in the EDX maps of Figure 4(c). The elemental maps of the faults for Cr, Co, and Al are presented here. The maps show that segregation of Cr is strongly localized to the APB and more limited for the case of the CISF or SISF; the same phenomenon is observed for Co. Additionally, severe depletion of Al is observed for both, the APB and the CISF or SISF. Integrated concentration profiles of the detailed region have also been computed for quantitative analysis and are presented in Figure 4(d). The quantitative results confirm the strong segregation of Co and Cr to the APB. No segregation of Ta, Nb, and W elements were observed in any of the faults.

Summarizing, the quantitative results for the segregation of \(\gamma \)-stabilizers (Co, Cr, and Mo) to the different types of planar faults are given in Table I. The compositional values at the faults have been calculated from the integrated average between the mid-points of the concentration peaks. These results are averaged, if possible, from all analyzed cases for each kind of fault. The repeatability of the segregation pattern for all the different planar faults is substantial proof that the deformation kinetics of all shearing mechanisms is affected by the long-range diffusion required for extensive elemental segregation. This process is defined here as segregation-assisted shearing, and it is further analyzed in the next section.

In this section, focus is put on the diffusion mechanisms controlling the lengthening of the faults. Figure 5(a) shows the STEM image of the growing tip of a CESF/SESF fault. EDX elemental maps of the same region are presented in Figure 5(b). The dislocation core is surrounded by an enriched atmosphere of Cr and Co. The wake of the solute atmosphere leaves behind a segregated trail of solute. In contrast, both regions show a pronounced depletion of Al. The chemical compositions of the solute atmosphere and the \(\gamma '\)-precipitate are presented in Figure 5(c) for comparison. They have been obtained by integration of the maps values. These results show that the local elemental composition shifts from \(\gamma '\) \(\rightarrow \gamma \) equilibrium chemistry.

This shift is further confirmed by the extended study presented in Figure 6 for all the type of faults presented here. In this figure, the ratios of \(\gamma '\)- and \(\gamma \)-stabilizers with respect to the \(\gamma '\)-phase values for the different faults are shown. These ratios are calculated asFor all the faults, a loss of \(\gamma '\)-stabilizers and conversely, an increase of \(\gamma \)-stabilizers is observed. Similar results have been reported by Smith et al.[17] for the case of SESFs on the disk-type alloy ME3. The same phenomenon is generalized in this work for CISFs/SISFs and APBs.

The results presented in Figure 5 indicate the presence of at least two diffusion processes taking place simultaneously during dislocation shearing:Additionally, a third diffusion mechanism might be operative simultaneously for the case of CESFs/SESFs and microtwins. This mechanism implies the short-range atomic reshuffling of the Ni and Al lattice sites at the fault line leading to the perfect SESF-twin structure.[13,28]

Two different diffusion scales can be identified among the different diffusion mechanisms. For the latter case of the atomic reshuffling and the solute-atmosphere motion, the diffusion scale relative to the dislocation motion can be considered as short-range atomic movement. Nonetheless, the extended segregation events observed require long-range diffusion which, at the same time, implies much slower time scales. It is well known that when several mechanisms are coupled simultaneously, the slowest one is limiting the advance of the rest.[29] Therefore, in the light of this, it seems reasonable to assume that as a first approximation, the lengthening of the different faults under these conditions (800 °C and 650 MPa) is governed by the segregation of \(\gamma \)-stabilizers to the fault. This is further supported by the work of Smith et al.[30] where a comparative study of the lengthening rates for the different diffusion processes taking place is presented. This picture of the plastic deformation proposed here is probably applicable across a range of medium-high temperatures and high stresses. These ideas are further developed and incorporated into a mathematical model to estimate the diffusion kinetics of the different faults in the following section.

In this section, the model presented by Barba et al.[14] for segregation-assisted growth of microtwins is extended for the case of CISFs/SISFs, CESFs/SESFs, and APBs. The mathematical model is summarized in Appendix A. As reported in the previous section, up to three different diffusional processes can be acting simultaneously at the tip of the growing faults. Here, the bulk diffusion process supporting the segregation (assumed to be the time-limiting process) is modeled in order to compute the fault lengthening rates. This is done by solving the diffusion fields around the faults (see Appendix A) faithfully with the concentration data for each type of fault obtained by the EDX analysis and presented in Table I. A schematic illustration of the lengthening problem is presented in Figure 8(a). The lengthening rate of the faults \(v_{{\text {f}}}\) is then computed from the mass conservation law at the growing interfacewhere \(v_{{\text {f}}}\) is the fault growth rate, \(\frac{\partial c}{\partial x}\biggr |_{{\text {interface}}} \) is the concentration gradient at the growing interface, \(D_{{\text {eff}}}=\frac{D_{{\text {Cr}}}\, c_{{\text {Cr}}} + D_{{\text {Co}}} \, c_{{\text {Co}}}}{c_{{\text {Cr}}}+c_{{\text {Co}}}}\) is the effective diffusivity of Cr and Co in the \(\gamma '\) parent phase, and \(c_{{\text {f}}}\) and \(c_{{\text {p}}}\) are the effective Co+Cr concentrations (\(c=c_{\text {Cr}}+c_{\text {Co}}\)) at the fault and in the parent phase next to the fault tip, respectively. No conclusive results were obtained for molybdenum segregation and therefore, it is not included in this problem. It is important to notice that the APB case is slightly different from the other kind of faults as they do not extend along the whole precipitate but instead a fault of finite extension moves with the segregation line. Then the mathematical problem presented here differs slightly from the real case but in any case, the values obtained here for APBs velocities represent a lower bound. For more details of the mathematical model, the reader is referred to the work of Barba et al.[14]

The segregation-assisted dislocation shearing presented here might be crucial for understanding one of the still daunting aspects of the superalloys: the sudden drop of yield-strength properties at high temperatures (\(T\approx\,\, > 800\,\,^\circ \)C). This concept is illustrated in Figure 9 where the diffusivities of Cr and Co are computed against the yield stress along the \(\langle 001 \rangle \) orientation of the commercial superalloy CMSX-4. This superalloy has a similar composition and mechanical behavior to MD2. During plastic deformation at low temperatures (\(T<700\,\,^\circ \)C), the diffusion processes are still limited and the dislocations need to enter into the \(\gamma '\)-precipitates without the assistance of segregation. This creates ‘full-energy’ faults within the \(\gamma '\)-precipitates which strengthen considerably the alloy. This regime is where the wide variety of standard plasticity theories for superalloys are applicable.[11,34] As the temperature increases, the diffusion processes gradually start to become more and more important during plastic deformation. The dislocation shearing within the \(\gamma '\)-precipitates is now assisted by local changes in the chemistry and reordering processes, and the classical strengthening mechanism for Ni-based superalloys (the high-energy faults shearing) vanishes. This provokes a reduction of the stress required to shear the \(\gamma '\)-precipitates and, as a consequence, a sudden drop of the plastic strength of the alloy, as observed in Figure 9. At really high temperatures (\(T>900\,\,^\circ \)C), the dislocation climbing of \(\gamma '\)-precipitates and the rafting processes becomes the dominating plastic mechanisms degrading even more the mechanical strength of the alloy.[35‐37]

As a result, the strong effect of the local chemical changes on the creep and plastic strength must be included in future models. One of the first experimental attempts to accomplish with this purpose has been presented by Smith et al.[2] proposing the addition of certain elements (Ti, Ta, and Nb) to block the effect of the \(\gamma \)-stabilizers and eventually strengthening the alloy. In order to push forward the temperature capabilities of these alloys, these segregation processes need to be fully integrated in multi-physics continuum models which potentially will allow to capture the dependence of the strength of the alloy on its chemical composition.