DELTA PHASE IN SUPER-ALLOY INCONEL 718: ITS CHARACTERIZATION, PRECIPITATION AND DISSOLUTION KINETICS
Metastable δ phase in super-alloy Inconel 718 is examined by means of characterization, precipitation and dissolution. Recent time-temperature-transformation diagram as well as the liquidous/solidus temperatures of the precipitations are provided. Equilibrium state of the δ phase from the literature along with the morphological scanning electron microscopy images are included. A model from the literature which is developed for predicting the transformation curve of δ phase is provided including the matching data from the experiments. Findings and key points of the studies for δ phase in Inconel 718 are given in the summary section latterly.
In the last decade, the attention the Ni-based super-alloys attracted has grown incredibly . Among them, owing to the contribution of their superior properties specifically high temperature (up to 700oC) oxidation resistance, today Inconel 718 are the most widely used Ni-based super-alloy in aerospace industry . During the operation conditions, as a result of extensive heat and pressure cycles that are applying to the alloy structure, the microstructural characteristics of Inconel 718 may undergo some transformations and noticeably lower the lifetime of the alloy. In this literature review occurrence of δ phase is examined closer in terms of its characterization, precipitation and dissolution into the matrix.
Characterization of the equilibrium state of δ phase
The typical chemical composition of Inconel 718 is given in Table 1.
Characterization of the equilibrium state of δ phase by disregarding impurity elements and atoms trapped in γ“ precipitates can be simply given as :
The rate constant, K, is given by :
is the activity of
. With the assumption of ideal behavior, the equilibrium conditions are given by :
is the free enthalpy of the formation of δ phase from solid solution. The above equation is used to determine the content of δ phase in regard to the temperature along with δ solvus for any chemical composition .
Precipitation of δ phase
The order of precipitation throughout the isothermal heating initiate with small precipitates at grain boundaries. Then proceeds as the growth of grouping small precipitates typically near the grain boundaries. Finally, at higher volumes, the phase gathers along the grains . Besides grain boundaries, Mahadevan et al.  similarly observed δ precipitates along coherent/incoherent parts of twin boundaries. This twin boundary mechanism is attributed to the ‘borders of twinned and un-twinned parts’ in the matrix be acting as nucleation sink. This area reported to be along
planes, which is correspondingly the habit plane of the δ phase as it was deliberated by Sundararaman et al. .
Time-Temperature-Transformation (TTT) diagrams are useful tools to determine various phases precipitating in the alloy during cooling. The very first example of the TTT curves for Inconel 718 case was generated by Eiselstein in 1965  holding MC, M6C, Laves, Ni3Cb and γ` phase transformations. Advancements in technology and variations in composition of Inconel 718 reformed the TTT curves of Inconel 718 . One example TTT diagram for Inconel 718 can be seen in Figure 1.
The major precipitates in Inconel 718 are metastable body-centered-tetragonal (BCT) coherent γ“ phase and face-centered-cubic (FCC) coherent γ` phase which both are the main strengthening phases precipitating in the austenitic matrix . Their characteristic temperatures determined by DTA experiments among different manufacturing types of Inconel 718 are given in Table 2 below.
In equilibrium conditions the metastable γ“ phase turns into stable orthorhombic Ni3Nb based incoherent δ phase [1, 10, 11]. Transformation of δ from γ“ occurs initially at grain boundaries by cellular reaction. δ phase mainly precipitates heterogeneously due to the different structure regarding FCC matrix . The solvus of the δ phase varies between 990 oC and 1020 oC depending on the Nb composition [5, 11]. At temperatures below solvus, δ phase precipitates through γ“ precipitation whereas at higher temperatures directly from the austenitic matrix [12, 13]. Such transformation may interfere with the alloy properties due to formation kinetics of δ phase. It has been shown that [14, 15] δ phase may develop in the alloy with round shape (see Figure 3) during processing or in service. In the literature, there are numerous studies that take the strengthening effect of γ“ and γ` phases along with toughening effect of δ phase on microstructure and mechanical properties of Inconel 718 parts. Although γ“ precipitation strengthens the alloy, δ phase has significance on stabilization of the grain size [4, 11] as well as improving the high temperature stress value of the super-alloy 718 . Besides, due to its morphology, δ phase does not further increase the alloy’s strength. In fact, it causes it to decrease by depleting γ“ . Essentially, taking control over the δ phase specifically at grain boundaries is believed to be the key point in parts with better mechanical properties . Thus, controlling δ precipitation makes it possible to control microstructural properties to meet the industrial demands for Inconel 718.
Beaubois et al.  studied precipitation kinetics of delta phase of Inconel 718 by attempting to quantify the nucleation and growth kinetics of the δ phase of Inconel 718. With the assumption of δ precipitates which are large enough to be spotted by the detection instrument as well as small enough to characterize the initiation of the precipitation, they suggested an expression for
, time needed to reach the above-defined value. For δ phase the value of
is given by :
where, the units for
is hours and for
is Celsius. The curve corresponding the equation above can be seen in Figure 2.
Figure 2. Diagram showing relationship between time and aging temperature for initial precipitation of δ phase: line corresponds to the Equation (4) .
The dissolution kinetics of δ phase
The dissolution kinetics of δ phase in Inconel 718 is investigated by Cai et al. . Change in the amount of δ phase in Inconel 718 can be seen in Figure 4. It is clear from Figure 4 that δ phase amount decreases with increasing holding time at all three given temperatures. It is worth noting that δ phase does not fully dissolve into the matrix at 980 oC rather follows no relationship following some certain holding time.
The dissolution of δ phase is a Nb atom controlled diffusion process , which advances as short and long range diffusion process . In shorter-range diffusional process, atoms migrate from one side of the phase boundary alongside δ phase to the other side alongside the austenitic matrix . The driving force regarding the flux of atom
across the phase boundary is given by :
where, M is the migration rate. In longer-range diffusional process, the flux is dominated by the cubic diffusion coefficient and concentration gradient among the phase boundary and the austenitic matrix and is given by :
are frequency factor and activation energy, respectively. The migration rate of diffusional process atoms migrate from one side of the phase boundary alongside δ phase to the other side alongside the austenitic matrix relies on the accommodation probability which can also be defined as carrying factor . The δ phase and austenitic matrix boundary is reported to be incoherent which approximates the carrying factor to unity. The slowest step is going to act as dominating process which in this case would be the longer-range diffusion process .
SUMMARY AND CONCLUSIONS
δ phase in super-alloy Inconel 718 is discussed through characterization, precipitation and dissolution. Equilibrium state of the δ phase from the literature accompanied by the morphological scanning electron microscopy images are investigated. A model which is developed for predicting the transformation of δ phase from the literature is examined. Following conclusions regarding the δ phase may be drawn considering the literature survey done:
- The major precipitates in Inconel 718 are metastable BCT coherent γ“ phase and FCC coherent γ` phase
- Both the γ“ and γ` phases are the main strengthening phases precipitating in the austenitic matrix.
- In equilibrium, the γ“ phase dissolves into orthorhombic Ni3Nb based incoherent δ phase.
- At temperatures below solvus, δ phase precipitates through γ“ precipitation whereas at higher temperatures directly from the austenitic matrix.
- Transformation of δ from γ“ arises initially at grain boundaries by cellular reaction.
- δ phase mainly precipitates heterogeneously in the FCC matrix.
- The solvus of the δ phase varies depending on the Nb composition.
- δ phase has proven to be stabilizing the grain size of the alloy.
- Precipitation of the δ phase throughout isothermal annealing begins with forming of small precipitates at grain boundaries.
- Precipitation of δ phase as well as the nose of the C-curve can be predicted.
- Dissolution of δ phase again relies on the Nb content in the alloy.
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2H.Y. Zhang, S.H. Zhang, M. Cheng, and Z.X. Li, “Deformation characteristics of δ phase in the delta-processed Inconel 718 alloy”. Materials Characterization. 61  49-53 (2010).
3N.B. Dahotre, M.H. McCay, T.D. McCay, C.R. Hubbard, W.D. Porter, and O.B. Cavin, “Effect of grain structure on phase transformation events in the inconel 718”. Scripta Metallurgica et Materialia. 28  1359-1364 (1993).
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7M. Sundararaman, P. Mukhopadhyay, and S. Banerjee, “Precipitation of the δ-Ni3Nb phase in two nickel base superalloys”. Metallurgical Transactions A. 19  453-465 (1988).
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16D. Cai, W. Zhang, P. Nie, W. Liu, and M. Yao, “Dissolution kinetics of δ phase and its influence on the notch sensitivity of Inconel 718”. Materials Characterization. 58  220-225 (2007).
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