Selective Growth of Low Stored Energy Grains During δ Sub-solvus Annealing in the Inconel 718 Nickel-Based Superalloy
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The microstructure stability during δ sub-solvus annealing in Inconel 718 was investigated, focusing on the conditions that may lead to the development of very large grains (about 100 μm) in a recrystallized fine grained matrix (4 to 5 μm) despite the presence of second-phase particles. Microstructure evolution was analyzed by EBSD (grain size, intragranular misorientation) and SEM (δ phase particles). Results confirm that, in the absence of stored energy, the grain structure is controlled by the δ phase particles, as predicted by the Smith–Zener equation. If the initial microstructure is strained (ε < 0.1) before annealing, then low stored energy grains grow to a large extent, despite the Zener pinning forces exerted by the second-phase particles on the grain boundaries. Those selectively growing grains could be those of the initial microstructure that were the least deformed, or they could result from a nucleation process. The balance of three forces acting on boundary migration controls the growth process: if the sum of capillarity and stored energy driving forces exceeds the Zener pinning force, then selective grain growth occurs. Such phenomenon could be simulated, using a level set approach in a finite element context, by taking into account the three forces acting on boundary migration and by considering a realistic strain energy distribution (estimated from EBSD measurements).
KeywordsPhase Particle Boundary Migration Initial Microstructure Boundary Mobility Primary Recrystallization
The mechanical properties of Inconel 718, that is widely used for aircraft engine parts, are greatly influenced by the microstructure that has to be fine and homogenous to ensure the required performance is achieved in service conditions. For example, fatigue resistance is a critical attribute that is affected by the heterogeneity of the grain structure.[1, 2, 3] Hence, microstructure evolution during metal forming is of particular importance. The stability of the microstructure has to be under control during each stage of thermomechanical processing, notably during the annealing stages. All nickel-based superalloys contain secondary-phase particles that can be exploited to limit grain growth during annealing through the Smith–Zener pinning effect.[4,5] In the case of Inconel 718, the presence of δ phase particles (Ni3Nb) hinders grain growth during δ sub-solvus annealing. Nonetheless, during complex hot forging cycles, critical thermomechanical conditions can result in what has been referred to as abnormal grain growth during δ sub-solvus annealing stages. Despite the obvious industrial interest for understanding the origin of this phenomenon in order to avoid it, there are only very few studies addressing this problem in Inconel 718 alloy.[2,3,7] According to these studies, abnormal grain growth is not caused by local depletions of δ phase particles or by texture effects. On the contrary, the phenomenon seems to be initiated by small prior strains, but the underlying microstructural mechanisms were not investigated[2,3] or they were only partially observed in one experimental condition. It is worth mentioning that, since strain seems to be involved in the control of the phenomenon, the term abnormal grain growth is, strictly speaking, inappropriate. It was nevertheless used because the resulting possibly bimodal grain size distributions are very similar to those of abnormally grown microstructures.
The aim of this paper is to discuss the influence of different microstructural features (in particular δ phase particles and deformation stored energy) on the occurrence of that strain-induced selective grain growth during δ sub-solvus annealing in Inconel 718 superalloy.
2 Experimental Procedure
Chemical Composition of the Inconel 718 Piece (Weight Percent)
The fraction and morphology of δ phase particles were determined by image analysis using the UTHSCSA Image Tool software. At least five BSE (back-scattered electrons) images per sample (after polishing as described above, i.e., without etching) were analyzed, each image corresponding to an area of 100 × 150 μm. Grain size and intragranular misorientation were determined by analyzing EBSD datasets using the TSL OIM Analysis software. EBSD maps were acquired choosing an appropriate step size (0.2 to 1 μm) for each microstructure scale, each map containing about 1000 grains. The EBSD measurement angular resolution can be estimated to be about 0.5 deg under the configuration employed in the present study. For the detection of grains, a maximum misorientation angle of 5 deg was accepted between neighboring pixels belonging to the same grain and twin boundaries (defined by a misorientation of 60 deg along the axis 〈111〉 with a tolerance of 5 deg) were ignored. In all the reported results, the average grain size is calculated as the arithmetic mean (i.e., number-weighted average) of the diameters of circles having the same area as the measured grains.
Intragranular misorientation was estimated either by calculating the GOS (Grain Orientation Spread) or the GAM (Grain Average Misorientation) parameter provided by the OIM software. These parameters were chosen to provide relative information about the hardening state of individual grains, as the intragranular misorientations of grains can be related to the density of geometrically necessary dislocations (GNDs). The GOS is the average misorientation angle between each measured point (in a grain) and the average grain orientation. Thus, it does not depend on the step size and it takes into account long-range orientation gradients. The GAM is the average misorientation angle of all pairs of neighboring pixels in a grain. It depends on the step size as it is based on neighboring point-to-point misorientations: therefore, when using this parameter, the step size must be also specified (which is rarely the case in the literature).
3 Microstructure Evolution During δ Sub-solvus Annealing
3.1 Initial Microstructure
3.2 Stability of the Initial Microstructure and Smith–Zener Pinning
Summary of Microstructural Properties of Samples (Measured in the Whole Region Defined by 2.7 mm < radius < 3 mm) Before and After Annealing: The Equivalent Circular Radius of δ Phase Particles is Around 0.25 μm in All Samples
ε = 0
ε = 0.05
ε = 0.1
ε = 0.3
Average δ phase fraction (pct)
Average grain diameter (µm)
Average grain diameter (µm)
3.3 Influence of Hardening on Microstructure Stability
As it will be discussed in Section IV, such heterogeneous microstructure is very likely due to the discontinuous growth of few grains, a phenomenon that can be referred to as selective grain growth, and is comparable to abnormal grain growth with regard to the resulting bimodal grain size distribution. It could also be referred to as a static recrystallization phenomenon, with regards to the stored energy being the main driving force.
3.4 Selective Grain Growth Evolution
4 Factors Contributing to the Selective Grain Growth Process
It is well known from literature that abnormal grain growth (also called secondary recrystallization) may be initiated during annealing of microstructures when normal grain growth is inhibited (e.g., by the presence of particles) and/or certain grains enjoy some growing advantage over their neighbors. For example, few bigger grains due to broad initial grain size distributions, higher mobility boundaries due to texture, or lower energy boundaries can give rise to the phenomenon. Moreover, several studies[14, 15, 16] have reported that also small prior strains (ε < 0.1) can produce abnormal grain growth during annealing both in single-phase materials and in alloys containing second-phase particles. In fact, it remains questionable if in this case the phenomenon can still be considered a case of abnormal grain growth (driven by capillarity).
Now, since in the case under study strain stored energy appears to be the main parameter controlling the selective grain growth, the phenomenon should probably be better treated as a primary recrystallization process (driven by stored energy). However, it is not possible to exclude that also the classical factors producing abnormal grain growth may contribute as well.
Hence, the most probable factors for abnormal grain growth which could occur in the sample deformed up to ε = 0.1 are investigated in the following sections.
4.1 Grain size Advantage
4.2 Grain Boundary Mobility or Energy Advantage
The presence of lower energy grain boundaries (usually verifying a specific crystallographic misorientation relationship) may also lead to abnormal grain growth. If some boundaries exhibit a lower energy compared to general random boundaries, they promote the growth of grains having these low energy boundaries, which often correspond also to special grain boundary planes. Once again, such phenomenon is supposed to occur only in strongly textured materials, otherwise the “special” misorientation is lost once the first neighboring grains are consumed. However, it is worth noting that even in non-textured materials, the presence of “complexions” (which are particular configurations of the atomic structure of the interface at grain boundaries) may also lower the energy of few grain boundaries, producing abnormal grain growth. The analysis of the crystallographic misorientation of grain boundaries between overgrown and fine grains in sample ε = 0.1 did not provide any evidence for the influence of crystallographic effects on abnormal grain growth in this case. More precisely, the abnormal/normal grain boundaries are mostly random high-angle boundaries.
4.3 Stored Energy Advantage
As detailed previously, the phenomenon under study is very unlikely to be due to one of the cases of abnormal grain growth described so far. However, the effect of low strains seems to play an important role in this case. Supposing that the GOS parameter can describe semi-quantitatively the energy stored in grains, then Figure 7 shows that strain stored energy is distributed heterogeneously in the microstructure of the sample strained to ε = 0.1 before annealing. In addition, it reveals that after annealing few low energy grains grew selectively despite Smith–Zener pinning at the expense of higher energy grains pinned by particles (Figures 9, 10 and 12). The plausibility of this scenario can be quantitatively assessed by estimating the three driving and pinning forces which govern grain boundary migration: the capillarity force, the force resulting from a stored energy difference across a grain boundary and the Smith–Zener pinning force.
4.3.1 Estimation of the competing forces
It is noted that such a formula probably underestimates the real pinning pressure.
As already pointed out, strain-induced selective grain growth supposedly involves the growth of few lower energy grains at the expense of higher energy grains pinned by particles. Such lower energy grains are possibly either already present in the initial microstructure or they form by nucleation.
In the following, only the contribution of GNDs to strain energy is taken into account (i.e., s = 1 in Eq. ). Hence, strain stored energy estimations are indeed lower with respect to real values.
Comparison of Driving Forces and Pinning Force in the Sample Strained Up to ε = 0.1 for the Growth of Existing Grains
Now, Figure 15 illustrates that the fraction of boundaries separating two crystals with a GAM/x difference of at least 0.4 deg/0.8 μm in sample ε = 0.1 is about 30 pct; by comparison, in the sample deformed up to ε = 0.05 the fraction is only about 15 pct. These results confirm that small stored energy differences, which can initiate the growth of some grains that exceed the Smith–Zener limit, are indeed present in the microstructure before annealing. Moreover, the probability to initiate the growth of a grain increases with strain, as the fraction of boundaries separating two crystals with a given GAM/x difference increases as well. It was indeed observed that the number fraction of overgrowing grains is raising (and accordingly their size is decreasing) when the prior strain increases.
In conclusion, the estimation of the three driving forces governing grain boundary migration confirms that their orders of magnitude are compatible with the selective growth of low energy grains against the Smith–Zener pinning pressure, including if those low energy grains are small ones arising from a nucleation process. Thus, these grains may have two different origins: either they were recrystallization nuclei or they were already present in the microstructure before annealing.
It is nevertheless worth mentioning that the dependence of the fraction of concerned grains on strain is fully compatible with the nucleation process: the higher the strain, the higher the nucleation density, and the smaller the resulting grain size. The incubation time pointed out in Section III–D is also in favor of such a mechanism. Yet, further dedicated experiments are required to definitely demonstrate that static nucleation occurs in Inconel 718 after such low straining. But whatever their origin, the reason why the low energy grains can overgrow is their low dislocation density (or stored energy).
5 Numerical Simulation of Strain-Induced Abnormal Grain Growth
Experimental analyses provided the evidence that small prior strains produce selective grain growth overcoming the Smith–Zener pinning pressure during annealing. Intragranular misorientation (GOS, GAM) data suggest that low strains induce critical strain stored energy distributions: as a consequence, few lower energy grains grow at the expense of higher energy grains pinned by particles. In this section, numerical modeling is exploited to test if the strain energy distributions estimated from EBSD measurements in sample ε = 0.1 can initiate the abnormal growth of lower energy grains (assuming that nucleation does not take place, but low energy grains arising from a nucleation process would behave the same).
5.1 Estimation of Strain Energy Distribution
5.2 Numerical Model
The numerical model used in this work allows one to simulate microstructure evolution, taking into account Smith–Zener pinning, capillarity and stored energy driven grain growth in a single framework. It is based on a level set description of interfaces in the context of a finite element formulation coupled with an anisotropic meshing and remeshing strategy. This approach was already used to simulate both 2D and 3D primary recrystallization and grain growth in the presence of second-phase particles.
It is worth noting that the extrapolation of the mobility value at δ sub-solvus temperatures from δ super-solvus data does not take into account the fact that in the δ super-solvus domain, all niobium atoms are in solid solution, while in the δ sub-solvus domain a fraction of niobium atoms are present in δ phase particles. Indeed, in the δ sub-solvus domain, less niobium atoms are in solid solution, which may affect the mobility value that was extrapolated from δ super-solvus data.
5.3 Simulation Results
Overall, these numerical results seem to support the proposed mechanism, which involves the growth of lower energy grains in a pinned microstructure and the sensitivity of the phenomenon to the initial stored energy distribution.
The critical microstructural parameter governing the stability during δ sub-solvus annealing in Inconel 718 is the deformation stored energy distribution with respect to the δ phase particles distribution.
In the absence of deformation stored energy, a fine microstructure (5 μm) remains stable during annealing provided that the fraction of δ phase particles is higher than 1 pct (average particle size of 0.2 to 0.3 μm). This is fully consistent with the classical particle pinning model of Smith–Zener.
If strain is applied before annealing, then the microstructure becomes unstable and the final stable grain structure is governed by the level of applied strain. If the strain is higher than 0.1, then an homogeneous but coarser microstructure (3 to 4 times compared to the initial grain size) is formed. In the critical range 0.05 < ε < 0.1, selective grain growth leads to an heterogeneous microstructure formed by overgrown grains (ten times larger compared to the initial grain size) and fine pinned grains. This phenomenon is best interpreted as a case of strain-induced selective grain growth in a pinned microstructure leading to the possible formation of bimodal grain size distributions. Since stored energy provides the driving force for the phenomenon, it should also be regarded as a primary recrystallization phenomenon. The origin of those overgrowing grains can be either a nucleation process, or the presence of very few deformed grains in the microstructure before annealing. The dependence of the number fraction of those grains on strain is in favor of the nucleation hypothesis, but the latter could not be definitely demonstrated here. Whatever their origin, the reason for which these grains can overgrow is their energy advantage which allows them to overcome the Smith–Zener pinning pressure.
The validity of the proposed mechanism is furthermore corroborated by the numerical simulation of the phenomenon taking into account in a single framework a strain energy distribution estimated from EBSD data, capillarity, and particle pinning.
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