Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: A review

Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: A review

Journal Pre-proof Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: A review Wanshun Xia, Xinbao Zhao, Liang Yue,...

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Journal Pre-proof Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: A review Wanshun Xia, Xinbao Zhao, Liang Yue, Ze Zhang PII:

S0925-8388(19)34200-8

DOI:

https://doi.org/10.1016/j.jallcom.2019.152954

Reference:

JALCOM 152954

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Journal of Alloys and Compounds

Received Date: 17 May 2019 Revised Date:

6 October 2019

Accepted Date: 7 November 2019

Please cite this article as: W. Xia, X. Zhao, L. Yue, Z. Zhang, Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: A review, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.152954. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: A Review Wanshun Xiaa, Xinbao Zhaoa*, Liang Yuea, Ze Zhanga, b* a

Institute of Superalloys Science and Technology, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, Peoples R China. b

Zhejiang Univ, Ctr Electron Microscopy, Hangzhou 310027, Zhejiang, Peoples R China. *Corresponding author: [email protected]; [email protected]

Abstract Nickel-based single crystal superalloys (Ni-SXs) are of great interests in aircraft industry due to their excellent high temperature creep strength deriving from the rigid gamma/gamma prime (γ/γ′) microstructure and the single crystal nature. The creep properties of Ni-SXs depend strongly on the degradation rate of the original rigid γ/γ′ microstructure with the dislocation movements in the microstructure. Since the applied temperature and stress strongly affect the dislocation movements, the different creep mechanisms are displayed to Ni-SXs during low temperature (~750℃), mid-temperature (~950℃) and high temperature (~1100℃) creep. The creep deformation during low temperature creep is mainly caused by the shearing of γ′ phase by a limited number of dislocations, while high temperature creep mainly occurs to the accumulation of creep strains with the increased dislocation activities in γ phase. To enhance the creep properties of alloy, a variety of strategies of the microstructural optimization need to be considered. One is to increase the volume fraction of γ′ phase to enhance the precipitation strengthening effects. But excessive amounts of γ′ phase are disadvantageous to low temperature strength of alloy. The coarsening of γ′ phase and the rafting process strongly correlates to dislocation movements. It is of importance to discuss the specific mechanisms of coarsening and rafting as well as their influence to the creep properties of alloy. The lattice misfit between the γ and γ′ phase plays an important role in influencing the coarsening of γ′ phase and the creep properties of alloy. A proper lattice misfit helps to form the cubic γ′ phase which is advantageous to alloy. But a too large lattice misfit can promote the coarsening of γ′ phase that damages the structural stability of alloy at high temperatures. The increased additions of refractory elements in alloy promote the formation of topologically close-packed (TCP) phase. TCP phase facilitates the nucleation and propagation of micro-cracks around it that damages the creep properties of alloy. This review aims to summarize some aspects of microstructural evolution during creep of alloy with considering their effects to creep properties. To guide the design of Ni-SXs in future, some perspectives about the microstructural optimization are properly provided. Keywords: Nickel-based single crystal superalloys; microstructures; creep properties; dislocations; rafting; coarsening

1. Introduction The next generations of aircraft gas turbine engines need to operate at higher temperatures and stresses to improve their efficiency and reduce emissions. These operating conditions are beyond the capability of existing superalloys, raising the new requirements for advanced superalloys [1-4]. The fabrication of superalloy turbine blades is mainly based on the investment casting process [5]. The development of Ni-based superalloys has experienced three stages [6-9]. At the first stage, the casting equiaxed grain alloys were directly applied. But these alloys poorly performed at high temperatures since grain boundaries provide the sites for the nucleation and propagation of micro-cracks. At the second stage, the introduction of directional solidification technique helps to form the columnar grain alloys with the elimination of transverse grain boundaries to enhance the creep strength of alloy. The last stage denotes the fabrication of single crystal alloys. The completed elimination of high angle grain boundaries helps to greatly enhance the creep strength of alloy. The nickel-based single crystal superalloys (Ni-SXs) are extensively used in turbines, especially in turbine blades, according to their excellent durability under extremely complex and harsh service environments with centrifugal forces and thermal stresses behind the combustor [10-12]. The high temperatures and stresses acting on the turbine blades would result in the occurrence of creep deformation and reduce their service life [13-15]. Thus one major aim of designing new generations of Ni-SXs is to enhance their creep resistance at elevated temperatures [16-19]. It is widely accepted that the key element for guaranteeing high temperature strength of Ni-SXs is a high volume fraction of gamma prime phase (γ′ phase). The γ′ phase in nature is compound phase which has an ordered L12 structure in the form of cuboids. The gamma phase (γ phase) has a same FCC structure as Ni and forms the continuous solid solution in alloy as matrix to contain the γ′ precipitates. Because of the different lattice structure between the γ and γ′ phase, a single dislocation in γ phase is unable to move into the γ′ phase. To cut through the γ′ phase, dislocations in γ phase need to move in pairs with forming an anti-phase boundary (APB) between the two dislocations. However, a much larger energy is required to form the APB comparing to the gliding of dislocations in γ matrix. Therefore, dislocation movements are mainly restricted in the γ matrix and the γ′ phase provides alloy the main resistance to dislocations [20-23]. Below the yielding stress, the most common deformation mechanism in superalloys is creep which is time-dependent and inelastic. The creep deformation is very sensitive to the conditions of temperature and stress acting on alloy. Corresponding to applied stress and temperature, the displayed microstructures can be very different. At low temperatures, dislocation movements are not easily activated that the initiation and propagation of dislocations are restricted [24, 25]. As result, a limited number of dislocations are restrained in γ matrix and the γ/γ′ microstructure can keep stable under low external stresses. Only under a large enough stress, dislocations can cut into γ′ phase and cause obvious creep deformation [26, 27]. However, high temperature creep shows much different behaviors [28, 29]. At high temperatures, dislocations can quickly propagate along the γ matrix even under a low external stress, and the fast increased dislocations promote the formation of dislocation networks along the γ/γ′ interface. Dense dislocation networks conversely prohibit the glide of dislocations and restrict the creep deformation. Meanwhile, high temperatures help to decrease the activation energy of dislocation climbing. Thus, accompany by the formation of dislocation networks, dislocations can climb across the γ′ phase and annihilate with each other in γ channels. The propagation of dislocations represents to a hardening process to alloy, while

annihilation is the softening process. Both of them correlate to determine the overall creep rate of alloy. In these creep mechanisms, the most discussed one is high temperature and low stress creep which conforms to the practical conditions of Ni-SXs in blade application [30, 31]. At high temperatures, the γ/γ′ microstructure quickly degrades in a short period (within a few dozen hours) and forms the rafted structures. Rafting is advantageous to low stress creep because it greatly increases the climbing distance of dislocations. But under high stresses, rafted structures are unstable that dislocations can easily cut through them to greatly reduce the creep life. Thus it can be seen, creep deformation is closely related to the microstructures of Ni-SXs. The overall considerations of microstructural optimization on creep properties of Ni-SXs must include four main aspects: the volume fraction of γ′, the coarsening of γ′ phase [32-35], the lattice misfit of the γ/γ′ microstructure [36-40] and the formation of topologically close-packed (TCP) phase [41-44]. It is obvious that increasing additions of γ′ phase elements can increase the volume fraction of γ′ phase. The creep strength of alloy derives from the intrinsic γ/γ′ microstructure which consists of high volume fraction γ′ phase in the matrix. A high volume fraction of γ′ phase helps to restrict the dislocation movements in the γ/γ′ microstructure, thus enhancing the creep strength of alloy. Also, the thickness of γ channels is reduced with the increased γ′ volume fraction that further increases the resistance to dislocation movements. However, it is not the more γ′ phase, the best creep performance of alloy. The optimized volume fraction is experimentally confirmed to be in a range from 60% to 70% and excessive γ′ particles would adversely affect the creep properties. Besides, both the coarsening of γ′ phase and the lattice misfit are related to the movements and interactions of dislocations in the γ/γ′ microstructure which determine the creep properties of alloy. Coarsening of γ′ phase causes a gradual loss of interfacial coherency which can damage the creep resistance. However the phenomenon of directional coarsening called rafting is advantageous to the primary stage of high temperature and low stress creep [45-48]. The lattice misfit derives from the different partitioning behaviors of alloying additions in the two phases. Since the elements such as Al, Ti and Ta, which prefer to partition to the γ′ phase, have the larger atomic size than γ phase elements such as Co, Cr and Mo, the γ′ phase of Ni-SXs generally has a larger lattice parameter than γ phase giving rise to a positive lattice misfit at room temperatures. However, the positive lattice misfit of alloy would transform to negative one at high temperatures [49, 50]. This is because the much larger thermal expansion coefficients of γ phase. Although a lattice misfit exists between the two phases, the γ/γ′ interfaces stay stable at high temperature because the strong coherency stress derived from the nearly coherent interfaces helps to stabilize the microstructures. The lattice misfit between γ and γ′ phase was shown to determine the formation of dislocation networks and to affect the coarsening of γ′ precipitates [51]. Dense dislocation networks with small network spacing can restrain the dislocation motion to improve creep resistance of alloys [52]. But dense dislocations also promote the elemental diffusion across the γ/γ′ interfaces and thus enhancing the coarsening kinetics of γ′ phase [53]. The formation of TCP phase should be noticed since the creep life of alloys is greatly determined by the initiation and propagation of micro-cracks along TCP phase [54]. In most cases, the final failure of alloy resulted from the coalescence and prolongation of micro-cracks instead of the accumulated creep stain in the microstructures. As expected, the suppression of TCP phase can greatly increase the creep life of Ni-SXs.

2. Creep mechanisms in Ni-based single crystal superalloys 2.1 Compositions and microstructures in Ni-based single crystal superalloys To obtain required strengthening effects, generally over ten kinds of additions are included in Ni-SXs [2, 14, 55-57]. The common compositions include Ni, Cr, Co, Al, Mo, W, Ti, Ta, Re and Ru. According to different functions in alloys, these alloying elements are divided into two categories. Except for Ni as main additions in Ni-SXs, elements Co, Cr, Mo, W and Re are seen as the first class of alloying elements which form the solid solution together with Ni atoms. And the constructed solid solution (γ phase) has the same FCC crystal structure like pure Ni [58, 59]. Apart from being solid solution to provide basic structural and thermal stabilities, disordered γ phase also serves as continuous matrix to connect and contain other strengthening phases. The selections of γ phase elements are generally based on two purposes. The one is to use a certain amount refractory elements such as Cr, Mo, W and Re to increase the initial melting temperature and enhance the thermal stability of alloys [60, 61]. The second one is to enhance the structural stability. For example, additions of elements Co Re, and Ru, which have the HCP lattice structure, were shown to effectively reduce the stacking fault energy (SFE) that is advantageous to the creep properties. Since a great number of stacking faults formed during creep can restrain the dislocation movements to enhance the creep strength of alloys [62-66]. Elements Re and Ru are extensively applied in new generations of Ni-SX because of their great contributions to enhance the creep strength of alloy [67, 68]. Element Re is recently discovered to co-segregate with other γ phase elements at the γ/γ′ interfaces and to form the interfacial grooves with the intrusion of dislocations [69-71]. During creep, the interfacial segregation of Re can effectively decrease the inter-diffusion of elements across the γ/γ′ interface because of its low diffusion rate in Ni, thus stabilizing the interface and retarding the coarsening of γ′ precipitates [71]. Refractory elements such as Re, Cr, W and Mo are prone to segregate together to form TCP phase at high temperatures. It was suggested Ru strongly partitions to the γ phase, thus reducing the partitioning coefficients of refractory elements in γ phase [72, 73]. Therefore the nucleation and growth of TCP phase is suppressed and the high temperature stability of alloy is effectively enhanced. To enhance the volume fraction of γ′ phase, significant amounts of Al, Ti and Ta are included in alloys. Other than γ phase elements, which form the continuous solid solutions with Ni, the strong chemical degree of Ni-X bonds (X represents to Al, Ti or Ta) makes it advantageous to form Ni3X (Al, Ti and Ta) compounds named γ′ phase [74-77]. The γ′ phase has ordered L12 structure in the form of cuboids. In Ni-SXs, the γ′ precipitates embed in continuous γ matrix, while γ phase demonstrates as narrow channels between the γ′ precipitates with forming coherent interfaces with γ′ phase [71], as shown in figure 2.1a. Due to the highly ordered structure of γ′ phase, dislocations in γ matrix can hardly move into γ′ phase. Thus dislocation movements are mainly restricted in the matrix. To enhance the creep resistance and high temperature strength of Ni-SXs, generally high volume fractions of γ′ phases are applied in alloys [78]. Standard elemental distributions in Ni-SXs are exhibited in figure 2.1b.

Figure 2.1 Morphology of γ/γ′ microstructure and elemental distributions in Ni-SXs. Adapted from ref. [71].

2.2 Creep mechanisms in the gamma/gamma prime microstructure The creep properties are determined by the degradation rate of initial microstructures which is very sensitive to the external conditions of temperature and stress acting on alloy. Naturally, higher stress and temperature refer to the faster degradation rate and less creep life of alloy [79]. As shown in figure 2.2(a), within the same time, higher stresses can give rise to larger creep strain (ε). And figure 2.2(b) and 2.2(c) showed that higher stresses also increase the creep strain rates (ε). Meanwhile, at higher temperature, a same stress can create larger deformation. Interestingly, the stress-strain curves have shown distinct tendency under different external conditions which derived from different behaviors of dislocation motion and interactions. Since temperatures have the greatest influence on dislocation movements, the creep mechanisms of Ni-SXs are fundamentally divided to three types of behavior according to the external temperatures including low temperature creep around 750℃, mid-temperature creep around 950℃ and high temperature creep over 1100℃, as shown in figure 2.3, figure 2.4 and figure 2.5.

Figure 2.2 Series of creep curves in a Ni-SX according to different applied stresses and temperatures. Adapted from ref. [79]. (a) Stress vs. time creep curves recorded for 560, 600 and 640 MPa at 1123 K; (b) Creep rate vs. strain curves in a log–linear-plot for stresses of 560, 600 and 640 MPa at 1123 K; (c) High temperature and low stress regime: stress dependence at 1323 K.

At low temperatures, particularly in the vicinity of 750℃, the dislocations are restrained in the γ matrix and the dislocation motion is inactive referring to the stable γ/γ′ microstructure under low stresses. As applied stress increasing, the creep deformation occurs according to the movements and interactions of dislocations [80, 81]. As shown in figure 2.3a, prominent creep deformation occurs only to a relatively high stress, suggesting a threshold stress for low temperature creep [82].

Provided that the threshold stress for particle cutting events is exceeded, a considerable amount of primary creep occurs [83, 84]. Dislocations sweep across the γ/γ′ microstructure with forming the APBs and eventually shear the γ′ precipitates, as shown in figure 2.3b [85, 86]. The shearing of γ′ phase is seen as the sign of primary creep under high stresses [87]. In this condition, external stress provides the main driving force of creep deformation and the creep strain rate first increases and then decreases with the accumulation of creep strains. Before primary creep, there is a short incubation period of dislocations that dislocations propagate in regions where are initially free of dislocations [88]. For the substantial creep deformation, dislocations percolate along the γ/γ′ microstructure through the cross-slip behavior. In the cross-slip process, dislocations first multiply from dislocation sources and the glide of dislocations then occurs preferentially in γ channels normal to applied stress. In such incubation period, the dislocation density quickly increases with the increasing creep strain, showing the increased strain rate. Following the dense dislocations in γ channels will adversely restrain the dislocation motion. Thus it was shown the decreasing tendency of strain rate after the short period of incubation [20]. Consequently, the primary creep leads to a secondary creep with showing the approximately invariant creep strain rate. The creep strain rate in the secondary creep is relatively low that minor creep deformation accumulated in this stage [83]. Finally, as the creep strain reaching to a threshold, the creep strain rate increases again until the final rapture of alloy.

Figure 2.3 Low temperature and high stress creep of a Ni-SX. Adapted from ref. [82]. (a) Creep curves as strain vs. time under different applied stresses; (b) Shearing events occur in the γ′ precipitates denoting the onset of primary creep during low temperature and high stress creep.

By comparing the low temperature (750℃) creep, lower stresses can produce the prominent creep deformation at relatively high temperature (950℃). As shown in figure 2.3a, 5% creep strains are accumulated for over 500h during 750℃ and 650MPa creep. But for mid-temperature (950℃) creep in figure 2.4, 320MPa stress can produce the 5% creep strains in less than 200h. Similarly, the increased applied stress can facilitate the creep of alloy at mid-temperatures with showing a fast increase of strain rate. For low temperature creep, prominent creep deformation results from the dislocation shearing of γ′ precipitates under high stresses. But the creep mechanism during mid-temperature creep is very different. On the one hand, at the relatively high level of temperature around 950℃, the activation energy for dislocation gliding is apparently

decreased that more dislocation movements occurred in the matrix [89]. On the other hand, most of the dislocation movements are restrained in the matrix because of the lower applied stress during mid-temperature creep. And dislocations are unable to travel into the γ′ precipitates unless the creep strain reaches a very high degree. The increased dislocation activities account for a part of the softening effects to enhance the strain rate [82]. Also at these elevated temperatures, a gradual coarsening of the γ′ precipitates is responsible for the softening of alloy. Similarly, with the increased density of dislocations, the dislocation movements are adversely restrained referring to a hardening effect [82]. The mid-temperature creep of alloy generally shows a continuous softening process as the tertiary creep. The strain softening behavior is associated with a proportionality of the creep strain rate and the accumulated creep strain without showing a steady-state regime. [90, 91]. Until final rupture, the creep strain rate increases monotonically with creep strain in tertiary creep, as shown in figure 2.4.

Figure 2.4 Creep curves as strain vs. time during 950℃ ℃ creep of a Ni-SX with different applied stress. Adapted from ref. [82].

Figure 2.5 Creep curves of High temperature and low stress and creep. Adapted from ref. [84].

Figure 2.6 Evolution of dislocation networks of a Ni-SX during the high temperature and low stress creep (1293K and 160MPa).Adapted from Ref. [92].

Finally, at high temperatures (over 1100℃), the creep deformation is related to the formation of rafted structures which was seen as the directional coarsening behavior of γ′ precipitates [46]. Since the exposing temperatures are very high, in most cases there are no obvious incubation periods in such conditions, as shown in figure 2.5a [93, 94]. Under low stresses, the dislocation movements are restricted in the matrix and dislocations travel across the γ′ precipitates through the climbing and gliding process. The increased activities of dislocation in the matrix also give rise to the formation of complex dislocation networks, as shown in figure 2.6a. The formation of dislocation networks can relax the misfit stress. With the formation of rafted structures, the length of γ channels for dislocation climbing is greatly increased. Thus the creep rate can decrease to a very low value [95]. On the basis of dislocation climb, dislocations of opposite sign in different glide planes can approach each other to react and annihilate. This is a dynamic recovery process which counteracts strain hardening associated with the increase of dislocation density during plastic deformation [96]. Simulation works have shown the interfacial dislocation motion and the dynamic recovery are greatly affected by interfacial dislocation interactions and lattice misfits [97, 98]. As reaching the dynamic equilibrium between creation of new dislocations (strain hardening) and annihilation of dislocations (recovery), the strain rate reaches to a very low value (figure 2.5b) and keeps nearly invariant denoting the secondary creep. And the creep in this stage accounts for the most proportion in the entire creep life. In this situation, the formed dislocation networks gradually become denser with the movements of dislocations, as shown in figure 2.6b. Once a critical level of creep strain is reached, high local stress and interaction of interfacial dislocations may result in a great amount of shearing events in γ′ precipitates [99-101]. Ultimate failure is highly localized and the creep cracks are always initiated in regions where stresses are most concentrated [84]. Also, high stresses in the fracture zone are sufficient to cause reorientation of the rafts, due to the changed triaxiality of the stress state in the vicinity of the fracture surface [94]. As a result, the creep strength deteriorates quickly with showing a fast increase of train rate, as shown in figure 2.5a.

3. Microstructural evolution during creep in Ni-based single crystal superalloys 3.1 The influence of volume fraction of gamma prime phase The γ′ precipitate is hard to penetrate by dislocations during creep deformation. Thus, to enhance the creep strength of alloy, the volume fraction of γ′ phase is increased with the reduction of γ phase. Many fine γ′ particles form the optimized structures embedded in γ matrix. At a moderate level of temperature and stress, the dislocations movements are restricted to the thin γ channels. Because of the impenetrability of the γ′ precipitates, dislocations move through the γ matrix by forced Orowan bowing, and this accounts for a major component of the creep resistance [78]. Surely, a high volume fraction of γ′ precipitates is important to enhance the creep resistance. However, the creep performance does not increase monotonically with the increase of γ′ phase. The volume fraction of γ′ precipitates needs to be control in an appropriate range, generally 60%-70% for single crystal superalloys. In the discussions of the influence of γ′ volume fraction on creep rupture life of Ni-SXs TMS-75 and TMS-82, both of them exhibited an first increase and then decrease tendency with showing a peak value of rupture life for about 70% γ′ phase, as shown in figure 3.1 [102]. Several reasons account for this phenomenon. Firstly, continued creep leads to a build-up of nodal network of dislocations in the γ channels which provides a site for the proliferation of dislocations with a period of steady state creep in achieving a quasi-stationary structure in time [103]. To suppose the γ′ fraction is very high, for example, up to 90%, and the volume fraction of γ phase is greatly reduced to form exceedingly thin channels. Consequently, the steady state period is shorten with the fast deterioration of creep resistance [103]. Secondly, evidence has shown that the minimum creep rate in γ/γ′ microstructure is lower than that of pure γ′ phase alloy under the same applied stress [104]. Thus, it can be said that the high temperature strength of Ni-SXs mainly derives from the γ/γ′ interfaces instead of the γ′ precipitates. Excessive γ′ precipitates give rise to the decrease of gross area of the γ/γ′ interfaces with the reduction of interfacial coherency, thus the overall creep resistance is reduced [102].

Figure 3.1 Relationships between volume fraction of γ′ phase and creep rupture life of Ni-SXs. Adapted from ref. [102].

3.2 Coarsening mechanism of gamma prime phase The mean size of γ′ precipitates in the typical γ/γ′ microstructure greatly determines the main microstructural parameters such as the lattice misfit, the matrix channel width and the volume fraction of γ′ phase; thus determines the dislocation motion, the elemental segregation and the stress distribution in the γ/γ′ microstructure and the consequent creep properties of alloy. It was suggested that alloys with larger γ′ particles performed better creep performance during low temperature creep, while smaller γ′ size showed a slight advantage at high temperatures [34, 105, 106]. The different size dependence derives from the distinction in creep modes at different temperatures. As stated above, during the low temperature creep, the creep deformation is mainly caused by the dislocation shearing of γ′ precipitates under high stress. Thus lager γ′ precipitates make dislocations harder to pass through, thus enhancing the creep resistance. But at high temperatures, the creep deformation depends on the dislocation motion in the γ channels. Smaller γ′ precipitates result in thinner γ channels which help to limit the movements of dislocations and improve the creep resistance. Generally, long time exposure to high temperature and/or strain stress can cause undesired coarsening of γ′ precipitates [107-110]. Coarsening of γ′ phase causes a gradual loss of interfacial coherency to damage the creep resistance of alloys [111-114]. At high temperatures, larger γ′ precipitates tend to grow at the expense of smaller ones to decrease the total interfacial free energy. In this situation, coarsening is dominated by the reduction in free energy achievable by minimizing the system's interfacial energy [115, 116]. As shown in figure 3.2, the area fraction and mean size of γ′ precipitates are strongly affected by duration time and ageing temperature of alloy. Larger temperature results in smaller area fraction but larger mean size of γ′ precipitates, suggesting coarsening of larger γ′ phase is at the expense of smaller ones [117]. Thus some extended researches were shown to use these relationships to control the morphology of γ′ precipitates as well as their volume fraction and distribution. For example, higher cooling rate may result in more regular γ′ precipitates with showing more uniform distribution in the matrix and higher volume fraction [118-120]. Another cyclic ageing research exhibited the mean size and volume fraction of primary γ′ phase were able to remain closely constant after multiple thermal cycles, while secondary γ′ phase showed periodic behaviors according to the consecutive heating and cooling process [39]. These provided us new insights in the choice of thermal-treatment of alloy.

Figure 3.2 Coarsening of γ′ precipitates. Adapted from ref. [117]. (a) Influence of duration time and ageing temperature on area fraction of γ′ precipitates; (e) Influence of duration time and ageing temperature on mean size of γ′ precipitates.

Figure 3.3 Interfacial width and its influence on coarsening rate and W diffusivity of alloys. Adapted from ref. [121]. HAADF-STEM images of the three alloys: (a) Co-7Al-7W aged at 765℃ for 200 h, (b) Co-10Al-5W-2Ta aged at 900℃ for 100 h, (c) Co-7Al-7AW-20Ni aged at 790℃ for 200 h; (d) Coarsening rate constants normalized by the absolute coarsening temperatures and the γ/γ′ lattice misfit, δ, plotted against the mean structural interface gradient widths; (e) Coarsening rate constants K normalized by the absolute annealing temperatures and W diffusivity.

According to classical Lifshitz-Slyozov-Wagner (LSW) theory, for ordered γ′ phase within the γ matrix, the growth rate of precipitates is conventionally assumed to be controlled by the diffusion kinetics in γ matrix [32]. Classical LSW theory assumed that the γ/γ′ interface is atomically sharp and the volume fraction of precipitates is small that γ′ particles grow independently [122, 123]. These assumptions are proved not accurate today, since the growth of a γ′ particle is an interactive process with other particles around it. And the γ/γ′ interfaces are not sharp as hypothetical and always have a diffusive width of a few atomic layers [124, 125]. The diffusive width across the interface is considerably to be determined by the partitioning behavior of elements near to the interface, thus the rate of coarsening is decided by the combined process of the elemental diffusion and partitioning in γ matrix [126, 127]. Strong relationships are exhibited between coarsening rate and interactions of solutes which are codetermined by both electronic structure and chemical bonding [128]. In addition, the compositional gradient across the γ/γ′ interface is a main factor which determines the diffusion and partitioning of additions [129]. The γ′ precipitates with wider γ/γ′ interface have the higher compositional gradient referring to greater coarsening kinetics and faster coarsening rate [121, 130]. Comparing the interfacial gradients in figure 3.3a-c, in a Co-7Al-7W ternary system, both Al and W are required to form the L12 structure, thus the stoichiometry of the γ′ phase is the strictest in the ternary alloy giving the sharpest interfacial gradients. Alloying with Ta and Ni can reduce the dependence on W allowing broader interfaces

(figure 3.3b-c). As result, the coarsening rate of γ′ particles in the ternary alloy is slowest, because of the narrowest interface and the lowest interface gradient (figure 3.3d-e) [121]. However, the temporal evolution of the normalized interfacial width would decrease with the increased ageing time because of the elemental homogenization across interface during extended heating [131]. Furthermore, coarsening has been analyzed as a purely elastic phenomenon where the particle shape evolves toward a best compromise between surface energy and elastic strain energy [132-134]. For γ/γ′ microstructure with large lattice misfit, the large strain energy can cause morphological instability and the strong elastic constrain between γ′ precipitates can cause γ′ particles to split into smaller cuboids showing a reversal coarsening behavior [135, 136]. The elastic interaction between γ′ particles formed by the split reduces the total energy of the system [137, 138]. In addition, even in a system with small lattice misfit, elastic strain energy resulted from local compositional variations can greatly influence the precipitate morphology [37, 139]. As shown in figure 3.4, in a near-zero misfit alloy, the secondary γ′ precipitates showed the abnormal behavior of cyclic coarsening and reversal coarsening because of localized elemental segregations [140, 141]. With the combined consideration of the surface energy and elastic strain energy, it is instructive to build the regular system of coarsening for guiding the microstructural designing of alloy [142-144].

Figure 3.4 Cyclic coarsening of secondary γ′ particles exhibited in a near-zero misfit alloy. Adapted from ref. [140]. (a) SEM images illustrating the temporal cyclic evolution of precipitate size after different ageing times; (b-c) Analysis of SEM images to determine (b) mean radius and (c) mean sphericity of secondary γ′ precipitates. Dashed green lines indicate annealing times where splitting has just occurred.

3.3 Rafting mechanism of gamma prime phase Because of the high volume fraction of γ′ precipitates, Ni-SXs particularly exhibit the tendency of forming rafted structures when they are stressed at high temperatures [46]. Rafting is a two-stage process. At the early stage, a tensile stress would lead to a tiny shrinking of γ′ precipitates along

the stress axis and the total number of particles decreases according to the usual process of Ostwald ripening [30, 31]. Thus, the thickness of γ′ particles slightly decreases in the transverse direction, while the γ channels parallel to the γ′ particles thicken a bit. At the later stage, adjacent γ′ particles meet and fuse together, and then produce extended rafted structures, as shown in figure 3.5 [145]. The formation of rafts consumes the γ′ particles that partly decrease the volume fraction of γ′ phase to relieve the lattice misfit. And the load is transferred from the creeping γ matrix to the γ′ precipitates [145]. Rafting is seen as the process of directional coarsening of γ′ precipitates which has been analyzed as a purely elastic phenomenon. But rafting always evolves in the presence of dislocations in γ channels, thus it is more accurate to consider the rafting as the elastic–plastic behavior [95, 146]. Without considering the contribution of plasticity to rafting, the formation of same rafted microstructure requires much longer time [147, 148]. With the change of γ/γ′ microstructure, behavior of rafting once in the “elastic” regime could transform to one in “plastic” regime with exhibiting a threshold strain ( Ф ) in distinguishing the two kinds of behavior [149]. The magnitude of Ф confers a reduction in γ/γ′ interfacial coherency and a relaxation of interfacial misfit stress. Thus, for strains smaller than Ф , rafting occurs very slowly [150]. In the process of rafting, minor grooves and ledges (typical size: <100 nm) formed at the γ/γ′ interfaces. It was found the evolution of rafts is always associated with the formation of minor ledges at the interface which is more pronounced in γ channels with higher dislocation densities [146]. It was qualitatively interpreted these ledges as evidence for a direct link between dislocation plasticity and rafting [151-153]. Parsa et al. [154] suggested that grooves and ledges are formed by local dissolution events which are triggered by dislocations at γ/γ′ interface, as shown in figure 3.6a-b. The localized stress field of dislocations can affect the local chemical potential across the γ/γ′ interface and can drive diffusional fluxes to form grooves. Evidence was given by the three-dimensional atom probe tomography (3D-APT) analysis which confirmed there is no local enrichment of alloy elements in the groove regions (figure 3.6c-d). Therefore, the formation of grooves was suggested to be the purely plastic behavior caused by dislocation motion, and plasticity must play part in rafting.

Figure 3.5 Establishment of rafted structures. Adapted from ref. [145]. (a) In early stage, γ′ particles shrink along the tensile stress with dissolution of the little ones; (b) In later stage, γ′ particles meet and fuse together to form rafted structures.

Figure 3.6 Analysis of grooves at γ/γ′ interfaces confirming the plasticity. Adapted from ref. [154]. (a) Anaglyph of three groove/dislocation pairs at a γ′ cube corner showing the dislocations at γ/γ′ interfaces; (b) Schematic illustration of a dislocation close to a γ/γ′ interface; (c) Multiple beam micrograph with all 13 dislocation segments in contrast; (d) EDX maps of elemental distribution near grooves at γ/γ′ interfaces.

Figure 3.7 Directional sensitivity of rafting. Adapted from ref. [155]. γ′ rafting morphology for a 100 h interrupted creep test (b)–(h) as a function of the stress triaxiality after stress redistribution showing in (a).

Since the applied stress provides main driving force of forming rafted structures, the rafting rate should be liner to stress [156]. In many alloys, under the combined influence of tensile stress and temperature, the γ′ cuboids transform into flat shapes perpendicular to the stress axis (N-type rafts), while compressive stress promotes the formation of needles or platelets parallel to the axis (P-type rafts) [157]. But some other alloys exhibited the reversed behavior that tensile stress forms P-type

rafts and compressive stress forms N-type rafts [158]. Clearly the morphology of rafts is highly sensitive to the sign and orientation of stress. By analyzing the morphology evolution during rafting according to the change of stress triaxiality, a recent research provided some instructions of the rafting mechanisms [155]. In figure 3.7, the morphology and orientation of rafts is highly sensitive to the sign and magnitude of the stress triaxiality. P-type rafts are exhibited in the value of stress triaxiality from -0.33 to -0.6, while standard N-type rafts are observed for stress triaxiality values near to 0.33. Corresponding to the area of nearly zero stress triaxiality, an abrupt change from N-type to P-type (figure 3.7e) is observed over a limited spatial extent. Furthermore, the driving force of rafting is proportional to the lattice misfit of γ/γ′ microstructure, even to a small degree. In practice, alloy with a negative misfit tends to form N-type rafts and positive misfit promotes the formation of P-type rafts under tensile stresses [159], while compressive stresses form the reversed rafted structures [160]. These behaviors greatly agree with the movements of dislocations in γ matrix [20]. For example, negative misfit and tensile stress promote the glide of dislocations in channels normal to the stress axis tending to move the interfaces parallel to stress axis outward and form the N- type rafts.

Figure 3.8 HAADF-STEM images of crept microstructures of a Ni-SX. Adapted from ref. [79]. (a) After 5% creep deformation at 1323 K and 160 MPa tensile stress; (b) After 5% creep deformation at 1123 K and 160 MPa tensile stress.

Accompanied by the establishment of rafted structures, the applied stress must strain the samples to slowly transform the microstructures. The APT results in γ channels have shown no obvious change during creep [161]. This suggested that rafting is actually a diffusional process of dislocations operating on local scales of the γ′ precipitates without disturbing the compositional homogeneities [162]. Under stresses, dislocations move into the highly stressed γ matrix and the rafts are formed through the coalescence of the γ′ particles in the plane of the initially less stressed γ channels. The specific coalescence process of γ′ particles is related to a long time hypothesis of elemental transporting through a ‘pipe diffusion’ process with dislocation movements [163]. It is assumed that the presence of very dense dislocations in the γ matrix can greatly promote the transportation of solutes that leads to a local inhomogeneity of alloying elements [151]. The giant diffusivity of elements along the dislocation core has been observed to laterally confirm the mechanism of pipe diffusion [164]. Under external stresses, dislocations strongly concentrate at the γ/γ′ interfaces, while the interior of the elongated γ phase is empty (Figure 3.8a). Knitting

reactions in the γ/γ′ network must therefore occur to allow the dislocations to move and the enhanced inhomogeneity near to the γ′ precipitates consequently promotes the dissolution of γ′ precipitates and ultimately results in the directional coarsening. A recent research of Kontis et al. [53] provided the near atomic scale evidence to verify the segregation of solutes to dislocations within deformed γ/γ′ microstructure. The APT analysis confirmed the segregation of Cr and Co at dislocation cores at the interface, thus strongly supported the assumption of ‘pipe diffusion’. The mass transport of Cr and Co assisted by the pipe diffusion locally increased the solubility of Ni in γ phase resulting in the partial dissolution of γ′ precipitates and rafting under creep conditions, as shown in figure 3.9.

Figure 3.9 Mass transport of Cr and Co assisted by the pipe diffusion. Adapted from ref. [53]. (a-b) cECCI micrograph showing a high dislocation density in the fully rafted γ/γ′ microstructure; (c) APT reconstruction from a rafted γ′ precipitate, showing a γ/γ′ interface, dislocations within a γ′ precipitate and tertiary γ′ particles in the γ matrix; (d) Detail of the atom probe reconstruction from (c); (e) 1D concentration profile perpendicular to the dislocation denoted by the red arrow within the γ′ particle in (d).

The creep process is essentially determined by dislocation movements occurred in relevant γ/γ′ microstructure, thus the formation of rafted structures must affect the dislocation movements and the resulted creep properties. The common patterns show that the rafted structures are resistant to creep at high temperatures, while the low temperature creep is accelerated with the formation of rafted structures [46, 165]. At high temperatures, dislocation activities are intense that dislocations can easily travel across the γ′ particles. In low stress regime, creep deformation in alloys occurs mainly by deformation of the γ phase and climb of dislocations along the γ/γ′ interfaces [166]. The formation of rafted structures greatly extends the length of channels where dislocations need to climb, thus enhancing the creep resistance of γ/γ′ microstructure [156, 167]. At relatively low temperatures, the dislocation activities are weak. The creep deformation begins at higher levels of external stress in which the dislocations are able to cut through the γ′ particles. Figure 3.8b shows that there is a high density of dislocations in the γ channels and dislocation networks are not as regular as those in low stress regime (Figure 3.8a). One can also observe more γ′ cutting events as compared to the high temperature and low stress creep [79]. Evidence has shown that rafting

facilitates the plastic shearing of γ′ phase and the shearing stress ultimately allows large amounts of dislocations to pass through the γ′ precipitates with enhancing the creep rate [168, 169]. In addition, since the plastic deformation is promoted with the formation of rafted structures, the plasticity of alloy would also be damaged [170].

3.4 Adjusting the lattice misfit of gamma/gamma prime microstructure The high temperature strength of Ni-SXs depends on the interfacial coherency. The degree of coherency is generally described by the lattice misfit, δ, defined according to δ = 2 × [(aγ′-aγ)/( aγ′ +aγ)]. The parameters aγ′ and aγ, which represent to the lattice constants of the γ′ phase and γ phase, strongly depend on the types and mole fractions of added solutes. Thus, the lattice misfit can be either positive or negative in sign according to the lattice constants of γ′ and γ phase. The γ′ phase represents to a Ni-Al-X structure that some atomic sites are replaced by alloying element X in a Ni-Al binary system. Thus, the replacement of Ni increases the lattice parameter, while the substitution of Al decreases the lattice parameter. This is because most of the alloying elements have a smaller atomic size to Al, except for Ta and Ti. But the lattice parameter of γ phase significantly differs to that of γ′ phase. This is because the addition of other elements into Ni lattice always increases the lattice parameter according to the smaller atomic size of Ni. Figure 3.10a gives the relation between rate of solid solution hardening, dσ/dc and that of lattice parameter change in ternary Ni3Al with addition of transition metal as well as B-subgroup elements [171]. And the relation between the rate of solution hardening per one atomic per cent of solute, dσ/dc, and a combined parameter appropriate for the elastic interaction involving screw dislocations, εs, is provided in figure 3.10b [172]. We can found the lattice parameters of the γ and γ′ phase are strongly influenced by alloying additions giving rise to the strengthening effects of the two phases. Since the γ′ phase elements have the larger atomic size and the lattice parameters of γ′ phase are generally larger than those of γ phase, the lattice misfits always have the positive value at the room temperature. But at high temperatures, the lattice misfits are usually negative due to different thermal expansion coefficients of the two phases [49, 50]. Moreover, the lattice parameter of the γ phase shows the greater sensitivity to solute additions according to its disordered lattice structure [173].

Figure 3.10 Effects of alloying additions on the lattice parameter in tertiary Ni3Al and Ni and the solution hardening effects on with the addition of strengthening elements. Adapted from ref. [171] and ref. [172]. (a)

Relation between rate of solid solution hardening, dσ/dc and that of lattice parameter change in ternary Ni3Al with addition of transition metal as well as B-subgroup elements; (b) Relation between the rate of solution hardening per one atomic per cent of solute, dσ/dc, and a combined parameter appropriate for the elastic interaction involving screw dislocations, εs.

Figure 3.11 Effects of lattice misfit on shape of γ′ phase. Adapted from ref. [174].

With the change of lattice misfit, the γ/γ′ microstructure experiences the significant variation to especially influence the phase stability. This is because the driving force for the coarsening of the γ′ phase at high temperatures originates from the interfacial energy which is partly decided to the coherency stress induced by the lattice misfit [51]. Reduced misfit implies the decrease of coherency strains and the decrease of coarsening kinetics. If the lattice misfit is not too large, the γ/γ′ interface remains the coherency with low interfacial energy to stabilize the interface. In an early research of Ricks and co-authors [30], the correlations between the morphology and size of γ′ phase and the γ/γ′ lattice misfit were identified in a number of Ni-SXs. Interestingly, the procedure of spherical γ′ particles growing to cubical morphology is influenced by the degree of lattice misfit. For alloy with low lattice misfit, the misfit strains growing out of the low interfacial energy are not sufficient to influence the particle shape quickly, thus there is a period of time for spherical γ′ particles growing larger before turning into cubical form. In addition, coarsening of γ′ particles promotes the loss of interfacial coherency with an increase in the magnitude of degree of misfit. As lattice misfit increased, the interfacial energy is enhanced which leads to the cubical change of γ′ precipitates. Besides, the increased interfacial energy helps to minimize the enhanced elastic strain energy associated with the large lattice distortion [175]. It can be concluded that the morphology change of γ′ phase is affected by the degree of lattice misfit of alloy and the coarsening of γ′ precipitates is somewhat decided. The cuboidal shape of the particles minimizes the strain energy because the elastic moduli of both phases have minima along <100> directions [95]. To reduce the strain energy and enhance the phase stability, the shape of γ′ phase needs to be strictly in a cuboidal form. However, further increase of misfit can give rise to irregular coarsening of γ′ particles that leads to a reversed spherical transformation with the decrease of creep strength [174, 176]. As shown in figure 3.11, with the increase of lattice misfit, the nearly spherical

morphology of γ′ phase gradually changes to cubic. But the γ′ phase suffers to the undesired coarsening with the continuously increased lattice misfit, thus leading to the change of γ′ morphology away from cube again. This phenomenon also exhibited in many other commercial superalloys [177-179]. It is clear that the morphology of γ′ phase during high temperature deformation is changed with the variation of the lattice misfit which depends on the partitioning behavior of alloying elements. Meantime the creep strength of alloys is greatly decided by the morphology of γ′ precipitates. Thus it is quite natural to expect that adjustments of lattice misfit to refine the γ′ particles can serve as an effective way of enhancing the creep strength. In an early assumption, a large lattice misfit can produce large random stress in the matrix that helps to impede the movements of dislocations. Therefore, alloys with larger lattice misfits can perform better in creep resistance [52]. Under a high temperature and low stress condition, it was found that alloys with higher negative misfits (TMS-138, -0.33%) exhibited the cross-slip behavior of dislocations with forming the complete dislocation network, while dislocations moved in alloys (TMS-75+Ru, -0.16%) with lower misfits through the climbing and gliding process and the resultant γ/γ′ interfacial dislocation networks are incomplete, as shown in figure 3.12. The creep curves showed that the creep life and the minimum creep rate are remarkably different between the two alloys that the alloy with higher lattice misfit exhibited much superior creep performance because of the different dislocation motion under varied lattice misfit conditions [180]. In fact, the rupture life of some superalloys has been shown consistent decrease if the γ/γ′ misfits are increased to a relatively high level. To enhance the lattice misfit, alloying elements are increasingly added which promotes the precipitation of undesirable intermetallic phase in the γ matrix and reduces the creep resistance [181]. In another consideration, too large misfit will decrease the shape parameter ratio of γ′ phase which means the shape deformation of γ′ phase. As results, the creep resistance and creep life are reduced. As shown in figure 3.13, with the enhanced additions of Mo, the lattice misfit gradually increased giving rise to the firstly increased and then decreased creep life. This curve greatly meets to the relationship between misfits and shape of γ′ phase in alloy (figure 3.11).

Figure 3.12 Combination of creep curves with microstructural evolution during the steady creep stage.

Adapted from ref. [180].

Figure 3.13 Creep lives of a Ni-SX as a function of molybdenum content. Adapted from ref. [181].

3.5 Detriments of the formation of topologically close-packed phase As discussed above, a limit exists in the process to enhance the high temperature strength through increasing the addition of refractory materials, such as Cr, Re, Mo and W. Excessive additions of these elements in alloys accelerate the precipitation of TCP phase which is enriched in these refractory elements [182-185]. In nature, the formation of TCP phase is caused by element diffusion. Take Re as an example, as one of the slowest diffusion elements in Ni, the addition of Re can reduce the diffusion coefficient and enhance the segregation ratio of other elements in the γ/γ′ microstructure [186]. In this manner, the element segregation promotes the formation of TCP phase enriched of Re in a needle-shape during long-term exposure to high-temperatures and/or stresses. Many researches have conducted on the microstructural developments of TCP phase according to varied external conditions. Generally, the formation of TCP phase is greatly influenced by the operating conditions including temperature [187, 188], applied pressure [189] and time of duration [190]. As shown in figure 3.14a-d, after 900h of exposure at 950℃, long needle-shaped TCP phase appeared to extend across the γ/γ′ interfaces, while it was no clear change in the microstructure after 500h of exposure at 950℃. With further increase of exposure time, more TCP phase needles were randomly formed, and long TCP phase needles also appeared to break up into shorter and thicker rod-like shapes. Furthermore, the γ channels adjacent to the TCP phases appeared to be “dissolved” and the initial regular across-networks consisting of γ matrix and γ′ cubes were broken. Figure 3.14e-h gives the pictures of the same alloys aging at a higher temperature of 1100℃. Higher exposure temperature can reduce the nucleation rate but increase the growth rate of TCP phases, finally promote the precipitation [188]. After 500h exposure, short and coarse rod-shaped TCP phase particles were exhibited, implying a shorter incubation time of precipitation of TCP phase. As the exposure time increased, the TCP phase particles became larger and thicker in a lath-like form. In another research, the relationship of the formation of TCP phase and applied stress was discussed [189]. Interestingly, the applied stress greatly changed the amount of TCP phase, but weakly influenced their morphology, as shown in figure 3.15a-c. In addition, the change in amount of TCP phase was decided by the type of applied stress. Under tension, the amount of TCP phase decreased first with an increase in applied stress

until about 50 MPa and then started to increase greatly. Under compression, it showed adverse results that the amount firstly increased to the peak of 50 MPa and then decreased. The relation curve is exhibited in figure 3.15e. In this experiment, it should be noted that applied stresses were shown to decrease the amount of µ phase regardless of tensile or compressive stress if the applied tensile reaches a relative high level (figure 3.15d).

Figure 3.14 Relationships between morphology of TCP phase and ageing temperatures and duration times. Adapted from ref. [190].

Figure 3.15 Effects of applied stress on the amounts of TCP precipitates. Adapted from ref. [189]. (a-d) Evolution of TCP phase in alloy CMSX-4 at 1050 °C under different applied stresses; (e) Stress dependence of the amounts of TCP phase.

It is clear that high quantities of TCP phases adversely affect creep strength of superalloys. The acceptable content of TCP phases is generally less than 1 vol%. For example, with increasing TCP phase contents up to 0.85 vol%, the single crystal alloy MC2 showed a reduction in minimum creep rates at 1010 ℃, but faster creep rates were observed with a higher TCP phase content of 1.05 vol% [191]. The precipitation of TCP phase reduces the high temperature strength of alloys in two main aspects. Firstly, by comparing the hardness of TCP phase to γ and γ′ phase, the nanoindenting AFM test showed that TCP phase is much harder than both the γ and γ′ phase. But the work hardening behavior of TCP phase is less pronounced [192]. Also, the formation of TCP phase inevitably consumes the strengthening elements and destroys the original regular

cross-networks in the vicinity [193]. And the precipitation of TCP phase also causes the discontinuities of the regular γ′ rafted structure, which provide paths for mobile dislocations to circumvent the interfacial barriers [194, 195]. As results, the strength deriving from the γ/γ′ microstructure is damaged and especially the retarding effect of the γ′ phase on dislocation movements is reduced. Once a TCP particle has formed and dissolved the elements locally, it is then surrounded by γ′ precipitates and the TCP elements are required to diffuse through the γ′ phase to the TCP particle. As can be seen, the TCP particles act as sites for the nucleation of pores, which presumably arise as a consequence of condensation of vacancies [54]. Secondly, large misfit exists between the TCP phase and γ phase that generates high localized stress at the interfaces. At high temperature, stress concentrates on the vicinity of TCP phase which makes it easier for the nucleation of micro-cracks near TCP phases [196]. In addition, TCP phase can act as obstacles against dislocation movements in a slip system. Dislocations pile up at the TCP phase boundaries that cause the strong stress concentration, and then the micro-cracks generate and propagate along the TCP phase according to the movement of dislocations [42, 197], as shown in figure 3.16. In service, the critical damages in alloy are mainly resulted from the severe nucleation and propagation of micro-cracks, and final rupture happened when the damages accumulated to certain amounts.

Figure 3.16 Initiation and propagation of micro-cracks along the TCP phase. Adapted from ref. [42].

4. Conclusion and perspective Ni-SXs derive high creep strength from their single crystal nature and intrinsic microstructures formed between disordered γ matrix and highly ordered γ′ phase, which are basically decided by the composition of alloy. In the process of creep, the original γ/γ′ microstructure would suffer to continuous evolution according to a series of external conditions such as temperatures, stresses and exposed atmosphere. And the evolution of γ/γ′ microstructure consequently determines the dislocation motion and the resulted creep mechanisms. For these considerations, this review firstly summarizes some characteristics of creep deformation in Ni-SXs according to external conditions. To sum up, dislocation motion naturally derives from the process of atomic diffusion which is greatly decided by temperatures. The movements and interactions of dislocations are restricted at low temperatures, thus obvious creep can only be discovered when high stresses facilitate a large amount of dislocations to cut through γ′ phase and degrade the γ/γ′ microstructure. However, high temperatures promote dislocation diffusion in γ matrix that dislocations can move across γ′ phase

in the gliding and climbing process even under low stresses. Meanwhile, fast increase of the dislocation density in γ matrix can give rise to formation of dense dislocation networks which also influence subsequent dislocation motion. It should be noted that the rigid γ/γ′ microstructure always faces to irreversible degradation under external conditions. Typically γ′ phase undergoes the directional coarsening behavior known as rafting process under stresses and high temperatures. The formation of rafted structures is very sensitive to external stresses and internal lattice misfits. For negatively mismatched Ni-SXs, tensile stresses promote N-type rafts which arrange in directions approximately normal to stress axis while compressive stresses give rise to P-type rafts which are parallel to stress axis. And positively mismatched Ni-SXs normally exhibited contrary behaviors. Since γ′ particles are fused and connected together in rafting process, γ phase elements are inevitably ejected from the γ channels between γ′ particles to channels paralleled to rafts. Consequently, the volume fraction of γ′ phase is decreased and the γ channels are widened along the stress direction. Therefore the rafted structures are less restricted to dislocation motion and dislocations can easily cut through rafts under high stresses. However rafting is advantageous to high temperature and low stress creep where dislocation motion is restrained in γ channels. Since dislocations can hardly move into γ′ phase in this situation, the gliding and climbing process of dislocations determines the main creep life of alloys. The formation of rafted structures greatly extends the length of channels where dislocations need to climb, and then enhances the creep resistance of γ/γ′ microstructure. These provide us some insights that creep properties are greatly decided by formation and evolution of microstructures of alloy in creep process and it will be valuable to enhance creep properties by optimizing the microstructures. To establish the relationships between creep properties and microstructures, four main aspects should be synthetically discussed including the volume fraction of γ′ phase, the coarsening of γ′ phase, the lattice misfit and the formation of TCP phase. At first, the creep strength of Ni-SXs derives from intrinsic γ/γ′ microstructure instead of separated γ′ or γ phase. Large amounts of γ′ phase help to restrict dislocation motion, while γ matrix provides alloys strength to restrain the plastic deformation. Therefore optimized volume fraction of Ni-SX is generally in a range from 60% to 70%. Secondly, coarsening of γ′ phase is inevitably when alloys are exposed to high temperatures and/or stresses. With coarsening of γ′ phase, the initial rigid γ/γ′ microstructure is significantly degraded and the resulting creep strength is reduced. In addition, lattice misfit between γ and γ′ phase should be particularly considered since the coherency stress derived from the mismatched γ/γ′ interface plays a part in deciding the size and morphology of γ′ precipitates. A proper lattice misfit helps to form the regular cubic γ′ phase which is proved to be advantageous to the creep properties of alloy. However large lattice misfit can produce large mismatch stress at γ/γ′ interface that promotes the coarsening of γ′ phase. The reduction of structural stabilities would finally damage the creep properties of alloys. For these reasons, future works need to establish accurate relationships between coarsening kinetics and lattice misfit, as well as related predicted models of degradation. At last, large amount of TCP phase is harmful to the creep properties of Ni-SXs. This is because the formation of TCP phase greatly consumes the refractory elements around it and results in the degradation of γ/γ′ microstructure. Meanwhile, the difference of elastic energy between TCP phase and its surroundings makes internal stresses easily concentrated. Large internal stresses around TCP phase would promote the initiation and propagation of micro-cracks, then giving rise to the failure of alloys. The formation of TCP phase is primarily related to compositions of Ni-SXs. Because large amounts of refractory elements such as Re, W, Mo and Cr

are easily segregated to form TCP phase. Also subsequent thermal process of alloys is significant, since optimized thermal process can reduce the segregation of alloying elements. Increased elemental homogeneity in alloys can help to reduce the nucleation probability of TCP phase, thus increasing the microstructural stability and the overall creep properties of alloys.

Acknowledgements This work was jointly supported by the Fundamental Research Funds for the Central Universities (2019QNA4012), the Innovation Fund of the Zhejiang Kechuang New Materials Research Institute (ZKN-18-Z01).

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1. The creep properties of Nickel-based superalloys are greatly decided by the microstructural evolution during creep. 2. Different external conditions determine the different creep mechanisms according the intrinsic interactions between dislocation motion and microstructures. 3. The coarsening of γ′ phase which is closely related to creep properties needs to be emphasized, especially the rafting process under high temperature and low stress creep deformation. 4. Lattice misfit is the key factor to be discussed in superalloy design, since it is related to the formation of dislocation networks and coarsening of γ′ phase. 5. The formation of TCP phase which is detrimental to creep properties need to be strictly restricted in superalloy design.

Declaration of interest statement

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.