118 7 Single Crystals of Superalloys amount of primary creep, 10 to 20%, is exhibited. The extent of the primary creep is found to vary with temperature and deviation of the orientation from the < 001 > direction. A long steady-state stage is typical. This constitutes a considerable proportion of the available rupture life of the material. The research group from the University of Cambridge and Rolls-Royce University Technology Center have been carried out investigations on the problem of deformation of the single-crystal superalloys in detail [37, 38, 41, 42] using the CMSX-4 superalloy (see the chemical composition in Table S1, Supplement 3). The obtained creep data for CMSX-4 superalloy are shown in Fig. 7.5 [41]. The orientations of the tested single crystals were found to lie within 10 ◦ of the < 001 > direction. The test results are plotted in two forms: strain versus time (A) and strain rate versus strain (B). At 1023K (750 ◦ C) the usual creep curve (with primary, steady-state and ter- tiary stages)is observed [Fig.7.5(a)].At1223K(950 ◦ C) the tertiary deformation begins almost at once [Fig. 7.5(b)]. One can see in the inset of Fig. 7.5(b) that, to a good approximation, the creep strain rate can be taken to be proportional to the accumulated creep strain. At higher temperature 1423K (1150 ◦ C) (and under a lower stress) a small amount of strain is accumulated but there exists a plateau where the creep strain is almost constant in time. Later the creep strain dramatically increases with rupture eventually occurring [the typical curve is Fig. 7.5(c)]. The dependence of the creep on the orientation of the CMSX-4 single crys- tals is shown in Fig. 7.6 [42]. The orientations of the specimens after the creep tests are plotted in the standard stereographic triangle in Fig. 7.7. Fig. 7.6 Creep curves from CMSX-4 superalloy single crystals tested at temperature 1023K and stress 750 MPa. The test temperature belongs to the lower temperature interval. Orientations of specimens are shown in Fig. 7.7. Reprinted from Ref. [42] with permission from Elsevier Science Ltd. 7.2 Deformation at Lower Temperatures 119 Fig. 7.7 The orientation of the CMSX-4superalloyspecimens within the stereographic triangle. The effect of misorientation on the behavior of specimens at lower temper- atures is very strong. The authors noted that the magnitude of the steady-state creep rate correlates with the maximum rate in the primary creep stage. The further from the < 001 > orientation the less the minimum creep rate (spe- cimens M, N, Fig. 7.6, 7.7). Primary creep at 1023K is due to a deformation on the {111} < 112 > slip system. After some deformation and a lattice rotation the strain is associated with at least two slip systems of type {111} < 112 >. The influence of stress on strain is of interest. When the stress is large enough to promote primary creep, then the creep strain evolution is relatively insensitive to its value (Fig. 7.8). The “threshold” stress for primary creep at 1023K appears to lie between 600 and 750 MPa. A physical mechanism of strain at a given temperature is supposed to be the cause of the observed creep behavior. This is confirmed by transmission electron microscopy. The γ/γ  structure of the cast single crystal may be considered as two inter- dependent systems. Therefore the properties of phases influence the genera- tion and motion of dislocations as do the phase boundaries. In the conditions under consideration the γ phase, being a soft constituent, is the source that generates deforming dislocations. The precipitates are permitted to deform only elastically, while the matrix can be deformed both elastically and plasti- cally. The slip in the γ phase occurs on octahedral planes, {111} < 110 >. The matrix dislocations have Burgers vectors of the type a/2 < 110 > in a plane of this type. The a/2 < 110 > dislocations spread through the γ channels between the dendrites of the cast structure. 120 7 Single Crystals of Superalloys Fig. 7.8 The creep curves from CMSX-4 superalloy single crystals tested at 1023K at various stress levels for specimens oriented within 10 ◦ of < 100 >. Reprinted from [42] with the permission from Elsevier Science Ltd. During the incubation period of creep the dislocations propagate from each dislocation grow-in source. The local density of grow-in dislocations was estimated to be about 10 11 m −2 in CMSX-3 superalloy tested at 1098K [43]. The deforming dislocations have most probably the same Burgers vectors for an orientation with the highest resolved shear stress. During creep deformation the ordered structure of the γ  phase requires that two dislocations in the γ phase must combine to be able to enter the γ  phase as a superdislocation (Fig. 6.18). The associated energy of the anti- phase boundary is a high barrier to the entry of dislocations, so the γ  phase remains largely undeformed during the majority of the specimen rupture life under low and moderate stresses. In CMSX-4 superalloy tested at 1023K the ribbons of net Burgers vector a/6 < 112 > are the most striking feature of the structure of crept speci- mens. The term “ribbon” is used to describe the observed configuration of overall Burgers vector a<112 > separated by superlattice stacking faults and anti-phase boundary faults [38]. The authors note that large numbers of a/2 < 110 > dislocations are present in the structure of tested specimens. The dislocations expand in the γ channels when creep deformation proceeds. The two dislocations a/6 < 112 > are separated as the partials pass through the γ phase. Where the ribbon of two partial dislocations passes the γ  phase they are constricted by the anti-phase boundary energy. As the primary creep deformation proceeds, the creep rate drops since secondary slip systems become activated. The lattice rotation which occurs is considered to be a superposition of the deformation associated with two or more {111} < 112 > slip systems. 7.2 Deformation at Lower Temperatures 121 The authors [38] describe the physical mechanism of the primary creep of the < 001 > oriented single crystals as follows. “The first step”: two dislocations, both slipping in the γ phase on the (111) plane, combine to produce the leading half of the a<112 > ribbon: a/2[10 ¯ 1] + a/2[01 ¯ 1] → a/2[11 ¯ 2] “The second step” consists in the dissociation: a/2[11 ¯ 2] → a/3[11 ¯ 2] + a/6[11 ¯ 2] The leading a/3[11 ¯ 2] dislocation is able to penetrate into the γ  -particle, shearing it to leave a superlattice intrinsic stacking fault bounded by the a/6[11 ¯ 2] partial which remains at the γ/γ  boundary. The trailing dislocation cannot enter the γ  phase without forming an anti-phase boundary. Entry would increase the energy on the deforming plane. In order to form the full a[11 ¯ 2] dislocation, which is able to pass through the γ  phase and to restore the unfaulted structure, presumably two further dislocations of the same Burgers vectors are necessary: a/2[10 ¯ 1] + a/2[01 ¯ 1] + a/2[10 ¯ 1] + a/2[01 ¯ 1] → → a/3[11 ¯ 2] + a/6[11 ¯ 2] + a/3[11 ¯ 2] + a/6[11 ¯ 2] In Fig. 7.9 one can see the early stages of the ribbon nucleation that have been proposed by Rae et al. [38]. Two dislocation loops of Burgers vectors a/2[10 ¯ 1] and a/2[01 ¯ 1] have moved in the γ phase on the same (111) plane [see the right lower corner of scheme (b)]. They have combined to form a leading a/3[11 ¯ 2] dislocation. This slips through γ  particles leaving a small circle of the superlattice intrinsic stacking fault surrounded by the trailing a/6[11 ¯ 2] dislocation lying at the γ/γ  boundary. To complete the ribbons two further dislocations of the same Burgers vector would be needed to thread their way into the narrowchannel of the γ phase. Oncenucleated the dislocation ribbons move until they are halted by interaction with other dislocations. The ribbon velocity has been estimated to be of the order of 1.2 nm s −1 . This corresponds to a ribbon crossing one γ  particle every 340 s. The primary creep is related to a rise in the population of a/2 < 110 > dislocations. A primary creep strain of the order of 5% can be achieved by the movement of ribbons. Dislocations accumulating at the γ/γ  interfaces provided effective pinning for the mobile dislocation ribbons and play a role 122 7 Single Crystals of Superalloys Fig. 7.9 The first stage of the nucleation of a dislocation ribbon. The CMSX-4 single-crystal superalloy tested at 1023K. (a) Electron micrograph. (b) Diagram identifying the dislocations in (a). The area of the superlattice intrinsic stacking fault (SISF) is shaded. Reprinted from [38] with permission from Elsevier Science Ltd. in terminating the primary creep. Thus, the primary creep at lower tempera- tures starts with the propagation of a/2 < 110 > dislocations through the γ channels. The sources of these dislocations supposedly are grow-in disloca- tions that are located between the dendrites. A primary creep can also occur when a population of a/2 < 112 > dislocations has become established and if the shear stress is sufficiently high. The addition of rhenium and ruthenium and the ageing heat treatment have an important effect on the properties of a new generation of single- crystal superalloys. Experiments have revealed that as the alloys have become more creep resistant, the propensity for primary creep has increased. Two different types of creep behavior have been observed at 1033K under a stress of 840MPa with the superalloys denoted as MC544, CMSX-10M and MC544 (Fig. 7.10) [34]. The first is characterized by a high amount of primary creep (3–10%). As a result the rupture life is reduced. The primary creep stage is preceded by an incubation period and is followed by a distinct secondary creep stage. The minimum creep rate increases with the primary creep strain. The tertiary stage is short. If the primary stage is limited (0.25 %, MC534 superalloy) then a continued steady state creep leads to relatively long rupture life of the specimen. The increase in the size of the γ  particles promotes glide of a/2 < 110 > dislocations within the γ matrix and leads to a decrease in the primary creep amplitude. However, the excessive increase in the size of the γ  particles 7.2 Deformation at Lower Temperatures 123 Fig. 7.10 The results of tests on various single-crystal superalloys at 1033K and stress 840MPa. Nominal chemical compositions are listed in Table S1. (a) Entire creep curves, (b) enlarged view of the primary creep stage. Reprinted from Ref. [34] with permission from Elsevier Science Ltd. facilitates the deformation by Orowan bypassing and reduction of the rupture life. The various structure factors are likely to affect the physical mechanism of strain of the investigated superalloys. There exists a competition between the Orowan mechanism of bowing of the dislocations between the γ  particles and the cutting of particles by partial dislocations. The difficulty for matrix dislocations in moving between γ  precipitates by {111} < 110 > slip results in the short incubation period. It is energetically more favorable for γ disloca- tions to dissociate to produce a/3 < 112 > partial dislocations, which will cut the γ  particles than to by-pass them by the Orowan bowing. The a/2 < 110 > matrix dislocation dissociates creating two partial dislocations (Table 7.1). An a/3 < 112 > partial shears the precipitate by leaving a superlattice stacking fault which stays at the γ/γ  interface. 124 7 Single Crystals of Superalloys 7.3 Deformation of Single-crystal Superalloys at Higher Temperatures and Lower Stress Increase in temperature up to 1223K results in a change in the shape of the curves. The tertiary stage follows the short steady-state stage (Fig. 7.11, specimens I G, H and J). The tertiary creep rate depends more upon the applied stressthanon the misorientation(Fig. 7.12).It is of interestto compare the shape of curves in Figs. 7.12 and 7.8. The effect of misorientation from the < 001 > direction on creep strain is relatively weak at this temperature. According to the data obtained in [42] the mode of lattice deformation of CMSX-4 superalloy changes from {111} < 112 > at 1023K to {111} < 110 > at 1223K. The authors suggest that the occurrence of {111} < 112 > and {111} < 110 > strain should be modelled as two separate curves which are associated with the hardening and the softening, respectively. All dislocations were found to have Burgers vectors consistent with the type a/2 < 110 >. The authors observed neither any dislocations in the γ  phase nor partials separated by the anti-phase boundary. The activity of the {111} < 110 > slip dominates at higher temperatures where the γ matrix is relatively weak for the tension tests close to the < 100 > orientation. The strain occurs on planes with greater Schmid factors. More- over, slip is confined witin the matrix channels. Mayr et al. [44] studied the dislocation structure of CMSX-6 single crys- tals at 1298K. The strain rate was studied under a pure shear stress. It is the shear testing that allows a direct loading of a specific macroscopic crys- Fig. 7.11 Creep curves from the CMSX-4 superalloy single crystals tested at 1223K under stress 185MPa. Orientation of specimens is shown in Fig. 7.7. Reprinted from [42] with permission from Elsevier Science Ltd. 7.3 Deformation at Higher Temperatures 125 Fig. 7.12 Creep curves from CMSX-4 superalloy single crystals tested at temperature 1223K under various stress for specimens oriented within 10 ◦ of the < 100 > direction. Reprinted from Ref. [42] with permission from Elsevier Science Ltd. talline slip system. Two macroscopic shear systems, namely the octahedral {111} < 110 > and the cubic {100} < 010 >, were analyzed. The effect of the crystal orientation on the shear strain rate is presented in Fig. 7.13. The obtained curves exhibit initially a decreasing primary creep rate, followed by a creep rate minimum and then a slow increase in the shear rate after the minimum. An incubation period for creep is not observed. The primary creep begins with a relatively high strain rate in both systems. Initially the macroscopic shear system {111} < 110 > deforms by a factor Fig. 7.13 The shear strain rate as a function of shear strain in the CMSX6 superalloy. B, The slip system {111} < 110 >; C, the slip system {100} < 010 >. Temperature 1298K, stress 85MPa. Experimental data from Ref. [44]. 126 7 Single Crystals of Superalloys of five faster than the system {100} < 010 >. This difference between creep rates increases during deformation. At the minimum creep rate the system {111} < 110 > is deformed by a factor of ten faster than the crystalline system {100} < 010 >. Recall that the repetition factor is 48 for the former slip system and 18 for the other. Furthermore, the {111} type slip plane is the most close-packed plane in the face-centered crystalline lattice. The distance between the nearest parallel {111} planes is maximal in the fcc lattice. Thus, this is an expected result. During the primary creep a considerable part of the dislocations on the {111} < 110 > slip system is associated with long dislocation segments. Their Burgers vector was found to be of the type a/2[0 ¯ 11]. After a minimum shear rate the dislocation segments enter the γ  interface. A common microstructural feature of both macroscopic crystalline shear systems in the above quoted study is that cutting of γ  particles is not observed during primary creep but does occur after the shear rate minimum. This is also typicalforther superalloys inthe higher temperature, lowerstress regime. Macroscopic shear loading of the CMSX-6 superalloy results in slip in sev- eral microscopic systems of type {111} < 110 > and {100} < 100 >. Slip on {111} < 110 > systems is clearly favored in the case of the (111)[01 ¯ 1] macroscopic system compared with the (001)[100]. In Table 7.3 are listed ratios of the resolved to the applied shear stresses calculated for all microscopic slip systems. The shear creep deformation is revealed to be always associated with the multiple slip. The single slip (which sometimes is intuitively associated with the pure shear deformation) is never observed. Thus, matrix channel deformation always precedes the cutting of the γ  particles. The γ/γ  -interface represents an obstacle to the motion of channel Tab. 7.3 Ratios of resolved to applied shear stresses in the 12 crystallographic {111} < 110 > slip systems for the two macros- copic crystallographic shear systems (111)[01 ¯ 1] and (001)[100]. Reprinted from Ref. [44] with permission from Elsevier Science Ltd. Macroscopic Number of microscopic Ratio of resolved to system slip systems applied stress (111)[01 ¯ 1] 1 1.00 2 0.67 4 0.50 1 0.33 4 0.17 (001)[100] 8 0.41 4 0.00 7.3 Deformation at Higher Temperatures 127 dislocations. In order to start pairwise cutting a second channel dislocation segment must approach the first segment against the repulsive forces, which the two segments of equal sign exert on each other (see Fig. 6.18). This re- sults in a critical interface stress for cutting. It is important that cutting of γ  particles can only start when the resolved shear stress, which acts on two interface dislocation segments, exceeds the critical interface stress. The dominant mechanism of strain is likely to be a function of the applied loading condition. Crystal twin formation occurs in superalloy CMSX-4 un- der unaxial load [45]. The twinning was observed during the compression, demonstrating a mode distinction from results of the tensile tests. The dislocation-free γ  particles are resistant to shearing by dislocations in the temperature range 1073 to 1123K under compressing stresses of 550MPa or lower. This was observed by Pollock and Argon [43] for the CMSX-3 su- peralloy single crystals. The incubation period lasts for 4h at 1073K, while at 1123K it is reduced to about 10 min. During the incubation stage the grown-in dislocations serve as sources, and deforming dislocations spread from these areas throughout areas that were previously dislocation free. Dur- ing the primary creep the material continues to be filled by dislocations. All creep deformation is accomplished by movement of the dislocations on {111} planes through matrix channels. The movement of dislocations through ma- trix channels seems to be a general tendency. It is related to high levels of misfit stresses present in the matrix due to coherent precipitates. When the steady-state creep is reached the matrix is completely filled with dislocations. The multiple slip systems are activated during the steady-state stage. There are very few dislocations left which are not associated with the three-dimen- sional network. We have discussed the formation of the dislocation sub-boundaries in the matrix in Section 6.1, see Figs. 6.4 and 6.7. It turns out that this phenomenon is intrinsic to single crystals of superalloys as well as to polycrystals. However, in the former case, dislocations fill the narrow channels between dendrites. The structure of cast single crystals is more heterogeneous than that of poly- crystals. The spacing of dislocations in the network of stressed specimens was found to be in the range 50–120nm. Dislocations of the network lie in the {111} planes. The networks that consist of a/2 < 110 > slipping dislocations are a common characteristic of the steady-state stage creep. Dislocations of this type have been observed in many electron microscopy studies. During the later stages of steady-state creep the γ  particles are sometimes sheared. In the tertiary stage creep strain is accumulated in the matrix and shearing increase steadily. The particles become coarse at the same time. Srinivasan et al. [46] investigated the dislocation cutting of the γ  particles in the single-crystal superalloy CMSX-4. Shear creep curves were obtained at [...]... concentration of chromium has decreased over the last decades Superalloys of the first and second generation contained up to 10–20 wt.% chromium Superalloys of the third and fourth generations have a lower chromium content 2–3% (CMSX-10, CMSX-10M, TMS-75, TMS-138, Rene N6) • Addition of rhenium and ruthenium are under investigation for superalloys which must withstand high stresses at temperatures from... 4 .9 × 10−7 s−1 This agrees satisfactorily with the experimentally observed value of the secondary creep rate This result implies that the cutting of the γ phase may indeed be a possible rate-controlling step in the high- temperature and low-stress creep of single crystals 7.4 On the Composition of Superalloys Some data about the influence of alloying elements on the strength of nickelbased superalloys...128 7 Single Crystals of Superalloys 1 293 K under shear stress 80MPa for the macroscopic crystal shear system (111)[01¯ The dislocation density of the produced single crystals is low The 1] γ channels are filled with dislocations in the early stage of high- temperature deformation of the GMSX-4 superalloy γ particles are free from dislocations The increase in dislocation... influence of high temperature and centrifugal stresses the cubic particles are transformed into flat shapes, which are called rafts At 1423K, for example, the evolution of the γ/γ structure from cuboidal to a plate-like structure takes place at a very early stage of the creep strain The driving force for rafting has been shown to be proportional to the applied stress, to the γ/γ -misfit and to the... motion due to cutting of γ particles Reprinted from Ref [46] with permission from Elsevier Science Ltd 7.4 On the Composition of Superalloys γ/γ system makes it easy for dislocations to enter the γ channel, and as a result the tertiary stage of creep begins The transmission microscopy investigations show that two partial γ channel dislocations with different Burgers vectors combine and form an a[010]... Rene N6 and others) The reason for the positive influence of the Re and Ru additions has not been studied sufficiently It is possible that these elements make the lattice γ/γ misfit more negative (see below) • The volume fraction of the γ phase in contemporary superalloys is greater than 50% The maximum rupture life of single crystals is found with a γ fraction as high as 60 to 75% 7.5 Rafting At temperatures... limited number of elements The rate of solution hardening per at.% of solute, dσ/dc, was measured at 77K The coefficient dσ/dc in MPa (at.%)−1 is equal to 6.5 for titanium, 15.0 for molybdenum, 43.0 for tantalum and 24.8 for tungsten [34] It is appropriate to mention briefly the current trends in the development of superalloy compositions (see Table S1) 1 29 130 7 Single Crystals of Superalloys • The... that the direction of rafting depends upon the direction of loading and on the sign of the lattice misfit The rafted structure seems to resist creep strain under low stresses only It appears that rafting accelerates the creep more often than not A scheme illustrating the rafting process is shown in Fig 7.15 [48] Deformation is different in the horizontal and vertical channels The misfit strain is usually... obvious that the climb of dislocation edge components is necessary in order for this process to occur The cutting of γ particles decreases the dislocation density in the γ channels The minimum creep rate corresponds to this mechanism Later the morphological instability of the Fig 7.14 Annihilation of dislocations in a cast superalloy single crystal (a) Motion of dislocation of opposite signs in the... concentration of titanium has decreased Some contemporary superalloys do not contain any titanium (EI867, Rene N5, Rene N6, MC534, TMS75, TMS-138) Titanium increases the energy of the anti-phase boundary of the γ phase, which makes the cutting of particles by dislocations more difficult However, titanium atoms are bigger than aluminum atoms Therefore they induce an increase in the γ parameter and cause . mechanism of strain of the investigated superalloys. There exists a competition between the Orowan mechanism of bowing of the dislocations between the γ  particles and the cutting of particles by partial. the high- temperature and low-stress creep of single crystals. 7.4 On the Composition of Superalloys Some data about the influence of alloying elements on the strength of nickel- based superalloys. 118 7 Single Crystals of Superalloys amount of primary creep, 10 to 20%, is exhibited. The extent of the primary creep is found to vary with temperature and deviation of the orientation from the