The dependence of stress and strain rate on the deformation behavior of a Ni‐based single crystal superalloy at 1050°C

Ni‐based single crystal (SX) superalloys are important high‐temperature materials used for manufacturing turbine blades in aero‐engines. During service under combinational impacts of temperature and stress, the SX superalloy may reach its life due to plastic deformation, which normally accompanies time‐dependent microstructural degradation. To reveal this dynamically mechanical response, tensile tests at 1050°C are carried out to record stress‐strain curves at five stain rates as well as creep curves at four applied stresses. Deformed microstructures and defects have been analyzed to understand mechanical behaviors and the underlying mechanism by using advanced scanning electron and scanning transmission electron microscopes. Results show that the deformation mode of the alloy strongly depends on the strain rates/applied stresses under mechanical loading. The dislocation density inside the γ phase is extremely low at all tests, indicating that the γ phase is relatively weak and ready to flow at this temperature even at a very fast strain rate. The deformation behavior of the γ′ phase is much complicated. At fast strain rates or high applied stresses, the dislocation density in the γ′ phase is very high, contributing to high‐stress requirements to deform the material. At slow strain rates or low applied stresses, rafting microstructures develop and the deformation mode becomes directional coarsening/diffusion‐dominated. Our results demonstrate a comprehensive understanding of the deformation mechanism of Ni‐based SX superalloys, which may provide lifetime prediction of the mechanical failure, as well as the database for superalloy applications in mechanical systems.


| INTRODUCTION
Ni-based single crystal (SX) superalloys are currently the most important material, which can be selected to manufacture turbine blades for aero-engines, due to their superior overall performance, including excellent high-temperature mechanical properties and good oxidation resistance. 1,2 Composition and microstructure are the two key factors determining the performance of such alloy. 1,[3][4][5][6][7] Ni-based SX alloy generally consists of two coherent phases. [8][9][10][11] One is the face-centered cubic (FCC) γ matrix phase, the other is the cubic γ′ strengthening phase with ordered L1 2 structure whose ideal size is about 300-500 nm. The γ′ precipitates are homogeneously distributed in the continuous γ matrix, with γ/γ′ interface along {001} planes after proper fabrication and heat treatment processing. The typical morphology of the two phases keeps changing when the alloy is under service conditions. [12][13][14][15] For example, γ′ rafting, secondary γ′ precipitation, formation of interfacial dislocation network, and so forth, would occur when Ni-based SX alloys are exposed to high temperature, stress, and prolonged time, which eventually lead to material failure. [16][17][18][19] Therefore, revealing deformation mechanism of an SX superalloy by understanding the relationship between microstructural evaluation and mechanical behavior under stress/ temperature combination is the key research topic for SX superalloys.
Moreover, at elevated temperature, microstructure degradation and material failure are time-related dynamic processes, and understanding how stress/temperature/time in combination affects the material degradation/failure is essential for part design, life prediction, and processing optimization of the alloy.
Ding et al. 20 have systemically studied tensile properties of a second-generation SX alloy at 10 −3 s −1 strain rate and revealed mechanical responses and deformation mechanisms of the two phases at different temperatures from room temperature (RT) to 1100°C. Clearly, the geometry of both γ/γ′ phases varies throughout the entire deformation process, especially at high temperatures. For example, at a temperature of 1100°C, the strength of the γ matrix is very low and ready to flow under mechanical loading. Although a raft-like microstructure is observed at a normal strain rate (10 −3 s −1 ), but the mechanism seems to be different from that caused by the creep experiment. In a common tensile strain rate of 10 −3 s −1 , the γ′ cubes are clearly elongated along the tensile direction (this is easy to imagine). The raft-like microstructure is caused mainly by Poisson's effects where the γ phase in vertical channels is squeezed into horizontal channels making γ′ precipitates joining together. In traditional creep testing, however, initial γ′ cuboidal phases transform into plates or lamellar, which is also referred to as directional coarsening. 21,22 For typical second-generation SX superalloys with negative lattice mismatch, so-called Type N (normal) rafting microstructures form where the cuboids coarsen preferentially transverse to the direction of the external tensile stress. For example, for a [001] orientated SX, if tensile loading is also along [001] direction, γ′ cuboidal particle will directionally coarsen in the (001) plane normal to the tensile direction; moreover, the thickness of the γ′ plates becomes shorter than the edge length of the γ′ cube. It is believed that the rafting microstructure during creep tests is caused by the directional diffusion of alloying elements. 23,24 The microstructure and mechanism comparison between normal tensile and traditional creep tests suggest that the deformation rate plays an important role in the mechanical behavior of SX Ni-based superalloys at elevated temperatures because diffusion is a timedependent process. A comprehensive understanding of the ratedependent mechanism, especially the dependence of stress and strain rate on the deformation behavior of the alloy, can provide lifetime prediction and the database for mechanical systems design for superalloy applications. Therefore, we design tensile tests at five strain rates and four applied stresses to obtain strain-rate-sensitive stressstrain curves and stress-dependent creep curves to reveal the ratedependent mechanical behavior of a Ni-based SX superalloy at 1050°C. By using advanced scanning electron microscopy (SEM) and transmission electron microscopy (TEM), the microstructures and their evolution under the combinational effect of stress and strain rate are investigated to explore the rate-dependent deformation mechanism of Ni-based SX superalloys.

| Materials
The nominal composition of the selected Ni-based SX superalloy in this study is 4.2 Cr-8.8 Co-2.2 Mo-9.0 Ta-2.3 Re-0.5 Nb-5.1 Al-0.1 Hf-Ni (all in wt%). The fabrication processes of the SX superalloy are the same as those previously reported. 20,25 Briefly, the SX superalloy is grown by using the Bridgman method, and homogeneous γ/γ′ two-phase microstructure is obtained after solid solution treatment (1290°C/1 h + 1300°C/2 h + 1315°C/2 h + 1325°C/ 4 h + 1330°C/4 h/air cooling [AC]) and subsequent two-step aging treatment (1120°C/4 h/AC + 870°C/24 h/AC). Figure 1 shows the typical homogeneous γ/γ′ two-phase microstructure in the SX superalloy. Cubic γ′ precipitates, with a size of about 400 nm, and distributes in the continuous γ matrix channel ( Figure 1A). An annular dark-field scanning TEM (ADF-STEM) image ( Figure 1B Table 1. It is obvious that the higher the strain rate, the higher the strength. To visualize the strength versus strain rate relationships, data in Table 1 are plotted in Figure 2B. Clearly in log-log plot, straight lines can be used to well represent the power law relation between flow stress (σ) and strain rate (ε) at a certain strain level, 27 which is:

| Microstructure characterization
where C 1 is a constant and m 1 is the strain rate sensitivity, which is the slope of the green, red, and blue dash lines in Figure 2B.  Figure 3B), whose deformation process to reach~20% strain takes about 20 s, is similar to that deformed at 10 −1 s −1 , except that the corners of the square prisms become rounder. When the strain rate further decreases to 10 −3 s −1 , tensile testing takes about 200 s, as shown in Figure 3C. The degree of spheroidization becomes more severe in the corners of γ′ precipitates, in the meanwhile, vertical γ channels seem to be narrower, and horizontal γ channels seem to be wider than those deformed at much higher strain rates ( Figures 3A,B). In addition, some precipitates start to coalesce from the corner to form bands, as indicated by red arrows in Figure 3C, leaving vertical lath-shaped γ phase between γ′ bands. Note that many γ′ precipitates are still not connected. When the strain rate is further decreased to 10 −4 s −1 (tensile process takes 35 min), as shown in Figure 3D, γ′ precipitates coalesce from the corners and form rafting-like microstructure, and the majority of residual γ phases in the rafted γ′ band are lenticle-like (indicated by blue arrows in Figure 3D) or spherical shapes (indicated by white arrows in Figure 3D). When tensile time prolongs to~200 min at a strain rate of 2 × 10 −5 s −1 , microstructure ( Figure 3E) is similar to that deformed at 10 −4 s −1 , but the rafted γ′ bands seem to be more continuous, and the residual γ phases in γ′ are all spherical, indicating that γ′ precipitates almost coalesce together to form continuous bands.
The effects of temperature (thermal coarsening) and stress (deformation) on the microstructure are quantified as size variations of both phases at high temperatures with and without stress. Microstructure in the grip area of tensile tested specimens, as shown in Figure S1, see Supporting Information, represents locations where the changes of phases are solely due to thermal effects. The microstructure in the gauge section (e.g., Figures 3A,B) represents the locations where changes are due to both thermal and stress effects. Therefore, we measure the lengths of both phases along the tensile direction in both grip and gauge sections and the result is shown in Figure 3F. The upper part of Figure 3F is the percent of length changes of both γ and γ′ phases compared to the initial phase sizes (e.g., Figure 1) in the grip section (without deformation, Figure S1, see Supporting Information), reflecting thermal coarsening effects. The bottom part of Figure 3F is the percent changes of phase sizes between gauge and grip area (e.g.,  (1)). The slopes of green, red, and blue dash lines are 0.105, 0.093, and 0.101, which respectively correspond to the strain sensitivity coefficient (m 1 ) at three different strain levels  Figure 3F, it is found that both γ and γ′ phases at the gauge section are longer than those at the grip area, indicating partly tensile force effects.
Length changes of γ phase are all higher than 46%, indicating that plastic strains accumulated in γ matrix are more significant than that accumulated in γ′ phase, as the total plastic strain of the alloy is less than 20%. Another reason for the big length changes of γ channels normal to tensile direction is that the materials in vertical γ channels are squeezed to the horizontal channels due to Poisson's effect, both suggesting that the γ phase is much weaker than γ′ phase at this temperature. In addition, with decreased strain rate and prolonged deformation time, the size variation of γ channels perpendicular to tensile direction monotonically increases from 46% (strain rate 10 −1 s −1 ) to 107% (strain rate 2 × 10 −5 s −1 ), demonstrating that deformation of γ becomes increasingly severe with decreased strain rate. In contrast, the size variation of γ′ precipitates decreases with decreased strain rate.
For example, it is 27.9% at strain rate of 10 −1 s −1 , and decreases to 11% for strain rate of 10 −4 s −1 and 13.6% for strain rate of 2 × 10 −5 s −1 . This may be caused by directional coarsening/diffusion, which compensates for the stress-induced elongation, similar to the rafting in creep test, which will be presented in the following sections.  Figure 4C and summarized in Figure 4D. ε min is an important reference index for design purposes, and is related to the applied stress (σ app ) by the relationship: [27][28][29]

| The applied stress effects
where C 2 is a constant and m 2 is a stress exponent. All data can be represented by a Norton law (the red dash line in Figure 4D) with a stress exponent m 2 = 8.6 and Equation (2)  measured using the same method as described in Figure 3F after creep tests. Figure 5E is the percentage length changes of both γ and γ′ phases compared to the initial phase sizes in the grip section (without deformation, Figure S2, see Supporting Information), reflecting thermal coarsening effects, the same as Figure 3F, upper part. Figure 5F shows the phase length changes of γ and γ′ phases between the gauge section and the grip area, which is also similar to that observed in Figure 3F  Note that in all four applied stresses, the γ phase is almost dislocation-free after creep tests ( Figure 3F). The γ′ phase behaves very differently as strain rates change. When the strain rate is high and deformation is fast (e.g., at 10 −1 s −1 , deformation takes only~3 s), there are large amounts of dislocations existing in γ′ precipitates ( Figure 6A). When strain rate decreases to 10 −3 s −1 , dislocation density in γ′ ( Figure 6B) is much lower than that in γ′ tensile deformed at 10 −1 s −1 . When deformed at 10 −4 s −1 , γ′ precipitates are almost dislocation-free, and dislocations are observed mainly on the γ/γ′ interface ( Figure 6C). At this strain rate, γ′ precipitates seem to be rafting in SEM image ( Figure 3D), but they are still separated by interfacial dislocation network in TEM ( Figure 6C). With strain rate further decreased to 2 × 10 −5 s −1 , as shown in Figure 6D, the γ′ actually are rafted with almost no dislocation inside the entire γ′ bands, but containing little spherical residual γ phase, which is consistent with SEM observation ( Figure 3E). The high dislocation density in the γ′ phase at a high strain rate suggests that those dislocations do not have time to escape from the γ′ phase, contributing to the high-stress requirement to deform the material. Meanwhile, the γ phase is relativity weaker and ready to flow, thus the γ phase in the vertical channels is squeezed into the horizontal channels, which is consistent with previous studies. 20 When strain rates decrease and the deformation processes prolong, time becomes enough to allow dislocation escape and deposit into the interfaces, and the strength decreases. Moreover, directional diffusion/coarsening become more dominated, which can be clearly observed in the crept specimens. with prolonged time at high temperature, γ′ forming elements may redissolve back to γ phase from the horizontal interface, which is normal to tensile direction, leading to a phenomenon that the γ′ at the tensile direction becomes even short (opposed to otherwise elongation along the tensile direction). Clearly, at low applied stress or low strain rate, the deforming mode mainly is a creep, which is controlled by elemental diffusion and redissolution, resulting in directionally coarsening (rafting) microstructure. 14,16,30 Collectively, the effects of stress rate and applied stress on deformation behavior and mechanism of the SX superalloy at 1050°C are summarized in Figure 8. Strain rate versus strength or creep rate versus applied stress curves all follow classic power law relationships described in Equations (1) and (2)  prompts the element's directional diffusing from vertical channels to horizontal channels. The latter case is more pronounced at a low strain rate or low creep stress because the deformation time is prolonged.
The deformation behavior of the γ′ phase is much complicated. At high strain rates or high applied stresses, the dislocation density in the γ′ phase is very high, indicating a high-stress requirement to deform the material. In this case, plastic deformation stretches the γ′ phase along the tensile direction, and we call this stage "stress-dominated." At low strain rates or low applied stresses, rafting microstructures develop and the deformation mode becomes directional coarsening/ The deformation mode of the alloy strongly depends on the strain rates/applied stresses under mechanical loading; the γ phase is relatively weak and ready to flow at 1050°C even at very fast deformation mode. The deformation behavior of the γ′ phase is much complicated as a function of strain/stresses. At high strain rates or high applied stresses, the dislocation density in the γ′ phase is very high, which contributes to the high-stress requirement to deform the material where deformation mode is stress/ dislocation-dominated. At low strain rates or low applied stresses, plastic deformation results in rafting microstructures due to directional coarsening where the deformation mode becomes diffusion-dominated.