4.1. Temperature Dependence of Slip System in the Superalloys
The true strain-true stress curves for the samples undergoing quasi-static compressive tests at various deformation temperature are shown in
Figure 1a. A curved shape conforming to a classic elastic-plastic constitutive relationship can be observed, which shows a linear elastic relationship and a clear yield behavior on the two sides of the yield point. The corresponding yield stress at different temperatures is given in
Figure 1b, from which it can be concluded that the Ni-base superalloy continually hardens with the increase in temperature until approximately 850 °C, and then softens when the temperature exceeds 1000 °C.
The temperature dependence of deformation mechanisms in SX Ni-base alloys has been investigated through experiments [
28,
35,
36]. Plastic deformation at ambient temperature occurs in face-centered cubic (FCC) metals mainly through the activated slip system consisting of <110> and {111}. When temperature increases to 800 °C, slip-line analysis in a deformed SX superalloy has revealed that the mode of slip deformation changes from α/2 <110> {111} to α/2 <110> {001} [
1]. Reference [
37] indicates that the slip modes activated at different temperature can be divided into three types for DD3 superalloy: (1) <110> {111} below 600 °C; (2) <110> {111} and <110> {001} in the range of 600 °C~850 °C; (3) <110> {111}, <110> {001} and <112> {111} above 850 °C. These three slip modes, octahedral (Oct1) <110> {111}, hexahedral (Cub) <110> {100} and dodecahedral (Oct2) <112> {111} have 12, six and 12 individual slip systems, respectively [
38]. At 980 °C, three types of slip modes (<110> {111}, <110> {100}, <112> {111}) are assumed to be activated in DD6 Ni-base superalloy according to Reference [
38]. The slip mode activated at different temperatures for DD6 superalloy is presented in
Table 4, and corresponding schematic illustration of activated slip systems are shown in
Figure 2.
The variations of activated slip systems are explained by the variation of dislocation Peierls–Nabarro stress on crystal planes at different temperature [
39]. The crystal plane with minimum Peierls-Nabarro stress at high temperature is different from that at low temperature. Another opinion is that the slip on the sub close-packed lattice plane of FCC crystal (001) is controlled by the cross slip of screw dislocation, which is essentially a process of thermal activation. Hence, the slip of the sub close-packed lattice plane tends to occur at high temperature. Various dislocation movement mechanisms were proposed to describe the deformation behavior of superalloy, such as antiphase boundary (APB) shearing, stacking fault (SF) shearing and Orowan bypassing [
29,
40,
41].
The calculated (Cal) and experimental (Exp) stress-strain curves for CMSX-4 superalloy and DD6 superalloy deformed at RT are shown in
Figure 3a. The parameters of CMSX-4 superalloy are from Reference [
24], and those of DD6 superalloy are calibrated from quasi-static compressive test. The parameters used for CPFEM calculation are presented in
Table 5. The simulated results of RT-deformation agree well with the experimental results of Reference [
24] and the present compression experiments, as shown in
Figure 3a. The hardening parameters are assumed to be identical for different slip systems at elevated temperature owing to the similar underlying characteristic dislocation reactions [
42,
43]. The CPFEM calculation with one, two and three slip modes activated were tested at 980 °C as shown in
Figure 3b. This indicates that the slip modes which are assumed to be activated can significantly influence calculation results. Actually, for the samples compressed along [001] orientation, the Schmid factors of all slip systems of <110> {001} slip mode
, hence this slip mode is not activated in present test condition. This explains why the simulated strain-stress curves with one and two slip modes activated overlap with each other.
4.2. Microstructural Evolution
The microstructural evolutions of S-RT (specimens deformed at RT) in different stages of SSHT under OM are shown in
Figure 4. Some newly formed RX grains are marked by the yellow line. With the increase in annealing temperature and holding time, the elemental microsegregation between DAs and IDRs gradually decreases, as well as the area of IDRs and γ/γ’ eutectics, leading to a progressively homogeneous SX matrix. In an as-cast deformed sample (
Figure 4a), dendritic morphology can be easily identified from the OM micrograph owing to the different solidification sequence of DAs and IDRs and elemental microsegregation. Almost no RX grain forms in the first (1290 °C,
Figure 4b) and second (1300 °C,
Figure 4c) stages of SSHT. In the third stage, irregular RX grains rapidly grow until the whole matrix is occupied (
Figure 4d,e). The eutectics dissolved during heat treatment and the holes formed near them (
Figure 4f). In OM micrograph these holes seem like black spots (
Figure 4e,f).
The microstructural evolutions of S-980 (specimens deformed at 980 °C) are shown in
Figure 5. As shown in
Figure 5a, many RX nuclei appear in the initial period (10 min) of the first stage of SSHT process, which is quite different from the observation of S-RT. This indicates that setting different critical temperatures for RX nucleating according to deformation temperature is reasonable. The RX grains show dendritic morphology over a long period of SSHT (
Figure 5b,c). With the increase of annealing temperature and holding time, the number of RX grains significantly decreases, and the grains gradually evolve to an irregular morphology (
Figure 5e).
The samples deformed at different temperature show different RX behavior during the SSHT procedure. Cox [
44] and Panwisawas [
16] drew the conclusion that RX grains tend to occur in the samples deformed at elevated temperatures, while Li [
34] found the highest RX propensity occurs in the samples deformed at 980 °C for DD6 superalloy. From TEM observation it is inferred that a large amount of stacking faults induced at 980 °C could facilitate RX through thermal twinning nucleation [
34]. This could be an important factor in the improvement of RX propensity. Besides, the strengthening effect of γ’ phases increases the superalloy strength at elevated temperature, and the γ’ phases play a role of second phase particles which can lead to an increase of dislocation density in the deformed matrix by several orders of magnitude as dislocations pass around the particles. Hence the equivalent strain induced at elevated temperatures can produce a higher dislocation density and stored energy compared to RT, which conforms with the TEM observation of Cox’s [
44] and Li’s [
34] studies. The simulation results present the same tendency, that the calculated stored energy of S-RT and S-980 are 1.56 × 10
6 J/m
3 and 2.75 × 10
6 J/m
3, respectively. With the increase of alloy strength and the number of slip systems at elevated temperatures, the dislocation density and corresponding energy stored in the deformed samples increases as well.
The simulated RX morphologies of S-RT and S-980 are shown in
Figure 6 and
Figure 7, respectively. As the critical nucleation temperature for S-RT reaches as high as 1310 °C, no RX grains appear in the first (1290 °C) and second (1300 °C) stage of SSHT process (
Figure 6a). In the third stage (1315 °C), the γ’ phases have completely dissolved into the matrix, and the whole region has become homogeneous. Hence, the RX can nucleate and grow homogeneously (
Figure 6b,c), which is quite different from S-980. For S-980, RX initially nucleates in DAs and grows individually with a dendritic morphology (
Figure 7a). Migration of RX grain from DAs to IDRs gradually proceeds until they contact each other (
Figure 7c), and then the grains continuously coarsen and compete until the end of SSHT.
4.3. Dependence of Inhomogeneous Microstructure on RX Behavior
A higher magnification of some regions in
Figure 5b is shown in
Figure 8. For S-980, most of the RX grains arise from the DAs and grow individually (
Figure 8a). The migrations of RX grain boundaries stop outside the eutectic particles (
Figure 8b). According to previous research [
45,
46,
47,
48], RX is very sensitive to secondary phase particles or microstructural inhomogeneity, while undissolved γ’ phase and incoherent eutectic particles act exactly as these kinds of barriers to retard the migration of RX grain boundaries owing to various pinning mechanisms.
The microstructure of S-980-1, S-980-2 and S-980-3 are hard to distinguish in the OM micrographs; hence EBSD technology is employed to test these specimens. The IPF maps of S-980-1, S-980-2 and S-980-3 are shown in
Figure 9a, c and d, and the KAM map of S-980-1 is shown in
Figure 9b. The microstructure evolution in IPF maps strongly indicate that RX firstly nucleates and grows in DAs, while most IDRs still maintain SX state (
Figure 9a,c). The local misorientation in recrystallized areas (DAs) tends to be close to zero, while that of unrecrystallized IDRs is higher, revealing that the deformation matrix still exists in IDRs (
Figure 9b). With the increase of annealing temperature and holding time, the recrystallized areas were gradually enlarged and migrated from DAs to IDRs until they overgrew the whole deformed matrix (
Figure 9d). As the secondary phase particles, the eutectics are hard to dissolve even after SSHT, and they still exist in the recrystallized areas (red spots in
Figure 9d) when the RX process completes.
The DD6 Ni-base superalloy consists of ten elements, and they can exacerbate the microstructural and chemical heterogeneities. The elements enriched in DAs are Co, W and Re, while those enriched in IDRs are Al, Cr, Mo, Ta and Nb [
26]. As the main precipitated strengthening phases, γ’ phase plays a role in deformation mechanism of Ni-base superalloys. Dislocations can accumulate around the cubic-shaped γ’ phase. In addition, the migration of RX grain boundaries is a process controlled by solute redistribution and diffusion; hence, the solution behavior of the extant phases significantly influences the RX behavior. The elemental compositions in γ, γ’ phases, DAs, IDRs and γ/γ’ eutectics are different, and hence the RX behavior depends on regions.
Based on the chemical compositions quantitatively detected by EPMA (
Table 6), which are reported in our previous study [
26], the solution behavior of γ’ phases in DAs, IDRs and eutectics is calculated by the commercial thermodynamic calculating software JMatPro. As shown in
Figure 10, the full solution temperatures of DAs, IDRs and γ/γ’ eutectics are 1284 °C, 1330 °C and 1364 °C, respectively. This means that the region will become homogeneous when it reaches this temperature. Although the calculation is conducted based on the database measured from experiment, this value may not absolutely conform with the solidification reality, but the tendency still has important reference meaning. The full solution temperatures of the γ’ phase in different regions follow the order of Das < nominal composition < IDRs <γ/γ’ eutectics, which conforms with the solution behavior of γ’ phase reported in Reference [
49]. Because the critical RX nucleating temperature of S-RT are higher, the influence of solution sequence on RX behavior cannot be observed in them. However, for S-980, the γ’ phases mostly dissolved into a γ matrix in the first stage (1290 °C) of SSHT, while the γ’ phases in IDRs only dissolved by 50% according to the thermodynamic calculation. Hence, each dendritic arm became an individual homogeneous region. Once RX nucleation occurred, they could rapidly grow in such regions. With the increase of annealing temperature and holding time, the γ’ phases in IDRs gradually dissolved, and the RX grain boundaries migrated from DAs to IDRs. However, the dissolution temperature of γ’ phases in eutectics is the highest and the dissolution rate is very slow; hence, these regions are most difficult for RX grain to occupy, and the SX eutectics can still be observed in
Figure 9d (red spots).