Dislocation motion during high-temperature low-stress creep in Ru-free and Ru-containing single-crystal superalloys

Materials and Design 67 (2015) 543–551

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Dislocation motion during high-temperature low-stress creep in Ru-free and Ru-containing single-crystal superalloys X.G. Wang a, J.L. Liu a, T. Jin a,⇑, X.F. Sun a, Z.Q. Hu a, J.H. Do b, B.G. Choi b, I.S. Kim b, C.Y. Jo b a b

Superalloys Division, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China High Temperature Materials Research Group, Korea Institute of Materials Science, 797 Changwondaero, Changwon, Gyeongnam 641-831, Republic of Korea

a r t i c l e

i n f o

Article history: Received 1 August 2014 Accepted 1 November 2014 Available online 8 November 2014 Keywords: Ni-base single crystal superalloy Creep behavior Dislocation structure Transmission electron microscopy

a b s t r a c t Creep deformation of the two experimental single crystal superalloys at high-temperature low-stress (1140 °C/137 MPa) has been analyzed through transmission electron microscopy. Emphasis is placed on elucidating the dependence of dislocation motion on microstructural evolution. The detailed analysis demonstrated that the stacking fault energy of the c matrix significantly decreased with the addition of Ruthenium (Ru). The stacking faults presenting in the c matrix after heat treatment has been rarely reported previously. During the primary creep stage, the dislocations can easily cross-slip on the different {1 1 1} planes in the horizontal matrix and leave 60° dislocation loops on the (0 0 1) c/c0 interfacial plane. Furthermore, calculations demonstrated that it is difficult for the slipping dislocations to bow into the vertical c matrix channel. In the early stages of steady state creep, the interfacial dislocations reoriented slowly from the h1 1 0i slipping direction to the h1 0 0i well misfit stress relief direction. On the other hand, few dislocations shearing into the rafted c0 phase have been observed. In fact, during the middle stages of the steady state creep, although perfect dislocation networks have formed, some dislocations shearing into the c0 phase have also been observed. In addition, the a h0 1 0i type superdislocations (some with non-compact core) have also been observed in the two experimental alloys. At last, the Ru-containing alloy possesses more negative lattice misfit, denser c/c0 interfacial dislocation networks and higher microstructural stability, thus can maintain a minimum creep rate in the steady state stage and have a longer creep life. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Nickel-base single crystal superalloys have been widely used as important materials for turbine blades in modern aircraft because of their excellent mechanical properties at elevated temperatures [1–3]. These alloys have disordered solid solution gamma matrix (c, fcc structure) and strengthened by high volume fraction (about 65%) of the ordered gamma-prime precipitates (c0 , Ni3Al) with L12 structure. The matrix and the precipitates have a cube/cube orientation relationship. Due to a small difference in the lattice parameters between the two phases, a high misfit stress is present in the superalloys [2]. The misfit stress and the applied stress are of vital importance in driving the motion of dislocations during high-temperature low-stress creep [4]. During creep, the dislocation motion includes dislocation climb, cross-slip, reaction and pairwise shearing into the cubic or rafted c0 precipitates [2]. The dislocation movements have been investigated extensively under low-temperature highstress and high-temperature low-stress creep conditions [2,4–10]. ⇑ Corresponding author. Tel.: +86 24 2397 1757; fax: +86 24 2397 1758. E-mail address: [email protected] (T. Jin). http://dx.doi.org/10.1016/j.matdes.2014.11.002 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.

However, the creep tests in the previous works usually focused in the temperature range of 750–1100 °C [4–9]. In order to improve the net thermal efficiency further, higher temperature capabilities are required for the superalloys. For this purpose more refractory alloy elements, such as Re and Ru, have been added [11–18]. In fact, a few studies on the creep behavior at very high temperature (above 1100 °C) have been reported [10,19], and no reports on the microstructural evolution of dislocation movement were found elsewhere. Consequently, two experimental alloys with different Ru-containing (named 0Ru alloy and 3Ru alloy) have been prepared to reveal the microstructural evolution during creep at very high temperature (1140 °C). In addition, the correlations between the microstructural evolution and creep curves have been analyzed in detail. 2. Experimental procedures The nominal chemical compositions of the two experimental superalloys are listed in Table 1. Both alloys have similar chemical compositions except 3 wt.% Ru addition in the 3Ru alloy. The single crystal bars of the [0 0 1] orientation were cast by means of crystal

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selection method in a directional solidification vacuum furnace under a high thermal gradient. The solution temperature of the two experimental alloys was determined by both the metallurgical analysis and the differential thermal analysis (DTA). Since the incipient melting temperature of the two experimental alloys is similar, both alloys were subjected to the same heat treatment. A two-step solution heat treatment and a two-step aging heat treatment were carried out on each alloy as follows: 1315 °C, 16 h + 1325 °C, 16 h + AC (air cooling) ? 1150 °C, 4 h + AC ? 870 °C, 24 h + AC. After heat treatment, the c0 precipitates regularly embedded in the c matrix. For the two alloys, the volume fraction of the c0 precipitates is approximately 70% and average size along the cube edge is approximately 0.3 lm. The standard deviation of average size of the 0Ru and 3Ru alloys is about 0.070 and 0.066 lm, respectively. In addition, the mean width of the c matrix is approximately 60 nm for the two experimental alloys. Cylindrical creep specimens, with a diameter of 5 mm and a gauge length of 25 mm, were machined from the post-heat treated single crystal bars. Creep rupture tests for both alloys were conducted at 1140 °C/137 MPa. The results of the experiment aiming at establishing the dependence of dislocation motion on the microstructural evolution are reported here. In order to clearly show this relationship further, the specimens have been interrupted after 2, 15 and 45 h creep tests for each experimental alloy, respectively. These interrupted specimens were cooled under load to maintain the deformation microstructures. Foils for transmission electron microscopy (TEM) were cut perpendicular to the longitudinal axis from the gage section of the post-creep specimens. For the rupture samples, the thin foils were cut about 5 mm away from the fracture surface. These foils were mechanically thinned down to a thickness of approximately 50 lm. After grinding, TEM foils were electrochemically thinned using a twin jet polisher in a solution of 5% acetic acid, 10% perchloric acid and 85% ethanol by volume. The optimum jet polishing conditions were determined to be at a temperature of 25 °C and a current of 30 mA. The resulting foils were examined in a JEM 2100 transmission electron microscope operating at 200 kV. 3. Results and discussion To study the evolution of microstructures and the process of dislocation motion, creep tests covering the temperature of 1140 °C/137 MPa were performed. In general the tests were not run to fracture, they were interrupted at primary stage, early steady state stages and middle steady state stages for the purpose of preserving the microstructure for microscopy. 3.1. Creep curves Representative creep curves at 1140 °C/137 MPa for the two experimental alloys are shown in Fig. 1. The inset shows the detail of 15 h initial creep. No incubation period and instantaneous plastic straining upon the application of the stress for the two experimental alloys have been observed. As a matter of fact, the two alloys are in a steady state creep region after 2 h test. The creep rupture life is approximately 93 and 113 h for the 0Ru alloy and the 3Ru alloy, respectively. It can be seen that the 3Ru alloy has a higher creep strain than the 0Ru alloy in the initial 13 h. However, after the initial 13 h the creep strain of the 0Ru alloy gradually higher than that of the 3Ru alloy until rupture. Table 1 Nominal chemical compositions (wt.%) of the experimental superalloys investigated. Alloy

Co

Al

Cr + Mo + W + Ta

Re

Ru

Ni

0Ru 3Ru

12 12

6 6

19.4 19.4

5.4 5.4

0 3

Bal. Bal.

Fig. 1. Creep curves for the 0Ru alloy and 3Ru alloy at 1140 °C/137 MPa. The inset shows the detail of 15 h initial creep.

3.2. Dislocation configurations in the interrupted and the ruptured creep specimens To study the effect of the dislocation motion on the creep process in single crystal superalloys, the microstructural evolution was monitored by observing the heat-treated, the interrupted and the ruptured creep specimens. 3.2.1. The heat treatment materials Fig. 2 shows micrographs of the c/c0 structure of the 0Ru alloy (Fig. 2a and b) and the 3Ru alloy (Fig. 2c and d) under the heat treated condition. Isolated misfit dislocations at the c/c0 interface are occasionally observed, as shown in Fig. 2a and c. The micrographs in Fig. 2a and c are representative of the typical structure over most regions in the heat treated materials. On the other hand, regions of ‘‘grown in’’ dislocations in Fig. 2b are also occasionally seen in the 0Ru alloy. These grown-in dislocations have the same Burgers vector and all lie in the matrix channel. It is interesting that the stacking faults in the c matrix of the 3Ru alloy are occasionally observed, as shown in Fig. 2d. The formation of the stacking faults during the heat treatment process is unusual, and is indicative of very low stacking fault energy. This phenomenon has been rarely reported previously. The driving force for the a/2 h1 0 1i perfect dislocations dissociating and extending must be related to the misfit stress. In previous study [20], Ru additions resulting in the lattice misfit more negative has been confirmed. Consequently, the misfit stress of the 3Ru alloy is higher than that of the 0Ru alloy. According to the above explanations, the stacking faults presenting in the c matrix is reasonable. For the two experimental alloys, the c0 phase is free from dislocations. 3.2.2. After 2 h of creep Fig. 3 shows the dislocation configuration of the 0Ru alloy interrupted after creep testing for 2 h at 1140 °C/137 MPa. Several kinds of typical slip dislocations with different characters have been observed as shown in Fig. 3a. These slipping dislocations are temporarily confined within the [0 0 1] c matrix channel. Dislocation ‘‘AB’’, as shown in the bottom right corner of Fig. 3a, is cross gliding  1Þ plane to the (1 1 1) plane in the c matrix channel. At from the ð1 1 ‘‘s’’, part of ‘‘AB’’ has bowed into the [0 1 0] vertical matrix channel. The stereoscopic configuration of dislocation ‘‘AB’’ is schematically illustrated in Fig. 3b. Geometrical considerations indicate that the segments of dislocation ‘‘AB’’ in the [0 0 1] c matrix having special  1 0 directions) can only be of 60° line directions (the [1 1 0] and ½1 dislocation [2,4,21]. Thus, the dislocation segments in the [0 1 0]

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Fig. 2. Two-beam TEM bright field images of the 0Ru alloy (a) and (b) and the 3Ru alloy (c) and (d) in the as-heat treated condition. All images were taken close to the [0 0 1] directions.

Fig. 3. Two-beam TEM bright field images show dislocation configurations of the 0Ru alloy interrupted after creep testing for 2 h at 1140 °C/137 MPa. (a) The cross-slip dislocations are spreading through the horizontal matrix channel. (b) and (c) Schematic illustrations to show the stereoscopic configuration of the dislocations ‘‘AB’’ and ‘‘MN’’ in (a), respectively. (d) Most of the matrix regions are still free from dislocations. Beam = [0 0 1].

vertical matrix channel interface can be either of 60° (‘‘rs’’ segment) or screw (‘‘st’’ segment) character. Another noteworthy observation is the cross slipping dislocation loop ‘‘MN’’ in the middle of Fig. 3a. The stereoscopic configuration of dislocation loop ‘‘MN’’ has been schematically illustrated in Fig. 3c. Dislocation loop ‘‘MN’’ is completely arrested in the [0 0 1] matrix channel. Near the area marked ‘‘o’’, ‘‘p’’ and ‘‘q’’ dislocation loop ‘‘MN’’ appears to have taken a 90° change in direction during the process of spreading in the matrix channel. These three right angles appearing in the dislocation loop ‘‘MN’’ resulted from the cross gliding of the leading screw dislocation segment (as

 1Þ plane to the (1 1 1) plane. shown in Fig. 3c, near N) from the ð1 1 In this case, the dipole segments (60° in character, e.g., ‘‘op-o0 p0 ’’ and ‘‘pq-p0 q0 ’’ as shown in Fig. 3c) are left at the c/c0 interfaces during the leading screw dislocation cross gliding from ‘‘M’’ to ‘‘N’’. Long ‘‘straight’’ dislocations in the vicinity of ‘‘E’’ are contained in the [0 0 1] matrix channel spanning across a quantity of c0 precipitates, as shown in Fig. 3a. Further analysis demonstrates that these dislocations are of 60° mixed character. The line direction of these dislocations is mainly along the h1 1 0i direction as a result of the dislocation loops spreading through the c matrix channel on the {1 1 1} slip plane. Although, the line direction of these dislocations

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is not the well-defined misfit orientation (the [1 0 0] and [0 1 0] directions) [10], the misfit stress on the (0 0 1) interface is at least partially relieved during primary creep. A significant difference has been obtained through comparing the expanding process of the dislocations in the vicinity of ‘‘E’’, dislocation loop ‘‘MN’’ and single dislocation ‘‘AB’’. They are all of 60° dislocation character. However, only dislocation ‘‘AB’’ bowing into the vertical channel has been observed. The widths of the c matrix are of vital importance for 60° and screw dislocations expanding in the horizontal channel and bowing into vertical channel [21–23]. The critical resolved shear stress (CRSS) for dipole expansion is a function of the channel width [22]. As the width of matrix channel increases the CRSS which is necessary for the dislocations creating dipoles of 60° or screw segments at the c/c0 interfaces decreases [21–23]. For SRR99, (the width of the c matrix is about 50 nm) the dipoles with 60° interfacial segments cannot bow into the vertical channel [22]. Whereas, for alloy SC16 (the width of the c matrix is about 180 nm), the dipoles can easily bow into the vertical channel [23]. As mentioned above, the mean width of the c matrix is approximately 60 nm for the two experimental alloys. Therefore, it is difficult for the dislocations (60° and screw) to bow into the vertical channel. The case, as shown in Fig. 3b, is only occasionally observed. Detailed calculations have been conducted in the Section 3.3. In some areas, the interrupted samples after 2 h creep resembled the heat treated samples, no dislocation has been observed as shown in Fig. 3d. Fig. 4 shows the microstructures of the 3Ru alloy interrupted after 2 h creep at 1140 °C/137 MPa. The dislocations as pointed out by arrows in Fig. 4a are the same as those in Fig. 3a with 60° character. These dislocations cannot bow into the vertical channel either. In Fig. 4, two different characters compared with Fig. 3 have been observed. (1) Two sets of dislocations with different Burgers vectors, in the vicinity of ‘‘F’’ in Fig. 4a, present in the [0 0 1] matrix channel, leading to reactions between the different dislocations. (2) A number of dislocations presenting in the vertical c matrix channel have been observed, as shown in Fig. 4b. These dislocations originate from the operating of the slipping systems in the vertical channel. These observations are consistent with the changing of the strain rate at the primary creep stage of the 3Ru alloy as shown in Fig. 1. The relationships of the dislocation motion depending on the creep curves have been discussed in detail in Section 3.3. Here, it is not surprising that the stacking faults still present in the c matrix. Because 2 h creep is considered to be too short for the atoms to diffuse and rearrange, even though the creep temperature is very high. Again referring to Fig. 1, according to the creep curves 2 h interrupted creep testing belongs to the primary creep. Although a quantity of dislocations in the c matrix have been observed, most of the matrix channels are still free from dislocations.

3.2.3. After 15 h of creep Fig. 5 shows the microstructures of the 0Ru alloy (Fig. 5a and b) and the 3Ru alloy (Fig. 5c and d) interrupted after 15 h creep tests at 1140 °C/137 MPa. According to the creep curves, as shown in Fig. 1, 15 h creep interrupted testing belongs to the early stages of steady state creep. Directional coarsening (rafting) takes place for the two experimental alloys under current creep test condition. In this work, due to the presence of the negative misfit stress field, N-type directional coarsening is considered to take place [24]. The activities of these dislocations are confined within the rafted c matrix structures effectively and lead to a steady state creep [25]. The c/c0 interfaces are now not as sharply defined along the (1 0 0) and (0 1 0) planes as those were the case in the 2 h interrupted specimens. Consequently, the relatively perfect dislocation networks are not lying on the (1 0 0) and (0 1 0) planes but approximately on {1 1 1} planes [2,24]. However, the dislocation networks of the horizontal channel are still approximately on the (0 0 1) plane [4,10,26]. More details of the c/c0 interfacial networks of the 0Ru and the 3Ru alloy are given in Fig. 5a and c, respectively. Comparing the dislocation networks, it can be found that the dislocation networks of the 3Ru alloy are more regular than those of the 0Ru alloy. For the 3Ru alloy (near the area marked ‘‘B’’ in Fig. 5c), the dislocations are still on the way to change their direction from the h1 1 0i to h1 0 0i direction. However, in most of the areas of the interfacial networks, the dislocation lines mainly orientated the [1 0 0] and [0 1 0] directions, as shown in Fig. 5a and c marked ‘‘A’’. Some dislocations in the c0 precipitates are occasionally observed which are not associated with the three dimensional networks, as shown in Fig. 5b. The line direction of these dislocations (projected on the (0 0 1) plane) is mainly orientated the [1 0 0] direction. These dislocation segments are very short, which manifests that they are in a steeply inclined state. Since the electron beam is along the [0 0 1] direction, the line direction of these dislocations might be along the h1 0 1i direction. Further analysis demonstrates that these superdislocations are a h1 0 1i type. The formation and shearing process of this type dislocation have been shown in details in Ref. [10]. A lower magnification view of the microstructure of the rafted c and c0 phases is shown in Fig. 5d. Few dislocations shearing into the c0 phase have been observed. Furthermore, no traces of the stacking faults in the c matrix of the 3Ru alloy have been observed again. The reason of the plane defects disappearing must be related to the rafting process. The dependence of the dislocation shearing process on the creep deformation has been discussed in Section 3.3. 3.2.4. After 45 h of creep Fig. 6 shows the dislocation configurations of the 0Ru alloy (Fig. 6a and b) and the 3Ru alloy (Fig. 6c and d) interrupted after 45 h creep tests at 1140 °C/137 MPa. Once again referring to

Fig. 4. Two-beam TEM bright field images show microstructures of the 3Ru alloy interrupted after creep testing for 2 h at 1140 °C/137 MPa. (a) General morphology of dislocations in the matrix and some matrix regions are still free from dislocations. (b) Dislocations from widely spaced sources begin to interpenetrate and react. Beam = [0 0 1].

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Fig. 5. TEM images of interrupted specimens of the 0Ru alloy (a) and (b) and the 3Ru alloy (c) and (d) after creep testing at 1140 °C/137 MPa for 15 h. (a) and (c) Bright field conditions; (c) and (d) Two-beam bright-field conditions. Beam = [0 0 1].

Fig. 6. TEM micrographs of interrupted creep specimens of the 0Ru alloy (a) and (b) and the 3Ru alloy (c) and (d) after creep testing at 1140 °C/137 MPa for 45 h. (a) and (c) Bright field conditions; (c) and (d) Two-beam bright-field conditions. Beam = [0 0 1].

Fig. 1, according to the creep curves, 45 h creep interrupted testing is in the middle of the steady state creep of the two experimental alloys. The dislocation networks of the 0Ru alloy are not perfect and some of them are still on the way of evolution (in the vicinity of ‘‘A’’ and ‘‘C’’), as shown in Fig. 6a. However, perfect dislocation networks in the 3Ru alloy have been established, as shown in Fig. 6c. It can be clearly seen that the dislocation networks of the 3Ru alloy are denser and more regular than those of the 0Ru alloy. The denser dislocation network is of vital importance for maintaining a low minimum creep rate [27]. The interfacial networks in Fig. 6a might lie on the {1 1 1} plane, whereas the networks in Fig. 6c might lie on the (0 0 1) plane [26]. This statement can be supported by the detailed examination of the dislocation networks.

According to the difference of contrast and dislocation configuration in Fig. 6a, the dislocation networks can be divided into three parts, as marked ‘‘A’’, ‘‘B’’ and ‘‘C’’. These three parts of networks might be located at different {1 1 1} slip planes [24]. However, no difference of the dislocation contrast and configuration in Fig. 6c has been observed. Furthermore, their line directions are precisely orientated to the [1 0 0] and [0 1 0] directions and remain in a good rectangle shape. Thus, it can be confirmed that the c/c0 interfacial dislocation networks in Fig. 6c lie on the (0 0 1) plane. Here, it should be noted that the images of Fig. 6a and c are taken under the same operating conditions. Two beam bright-field images of the dislocations in the c0 precipitates of the 0Ru alloy and the 3Ru alloy are shown in Fig. 6b

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and d, respectively. In fact, they are all a h0 1 1i or a h1 0 1i type superdislocations. Further analysis demonstrates that dislocations ‘‘H’’ in Fig. 6b and ‘‘N’’ in Fig. 6d are of the a h0 1 1i type, and dislocations ‘‘E’’, ‘‘F’’, ‘‘K’’ and ‘‘L’’ in Fig. 6b are of the a h1 0 1i type (under the operation vector of ~ g ¼ 020, the contrast of dislocations ‘‘E’’, ‘‘F’’, ‘‘K’’ and ‘‘L’’ is weak). It is interesting to note that most of these dislocation lines (projected on the (0 0 1) plane) either parallel or perpendicular to the ~ g ¼ 020 operation vector. 3.2.5. After creep rupture Fig. 7 shows the morphologies of c/c0 interfacial dislocation networks and dislocations in the c0 precipitate after creep rupture in the 0Ru alloy (Fig.7a and b) and the 3Ru alloy (Fig. 7c and d). It can be clearly seen that the dislocation networks in the 3Ru alloy (Fig. 7c) are denser than those of the 0Ru alloy (Fig. 7a). The dense dislocation networks can prevent the dislocations shearing into the c0 phase effectively [4,27]. A number of dislocations shearing into the rafted c0 phase have been observed, as shown in Fig. 7b and d. These shearing events are more common as creep strain accumulated in the deformed c matrix in the tertiary stage. Comparing the rupture microstructure of Fig. 7b and d, the number of dislocations in the 0Ru alloy is more than that in the 3Ru alloy. Dislocations ‘‘A’’ and ‘‘D’’ in Fig. 7b and ‘‘N’’, ‘‘R’’, ‘‘S’’ and ‘‘T’’ in Fig. 7d are considered to be of the same type. Dislocations ‘‘B’’, ‘‘C’’ and ‘‘M’’ in Fig. 7b are considered to be of the same type. The configuration of the dislocations is same as that in Fig. 6b and d. The processes of these dislocations shearing into the rafted c0 phase have a great contribution to the rapid failure of the two experimental alloys. In fact, these superdislocations are usually with a compact core. Here, another type superdislocation of a h0 1 0i with several segments has also been observed, as shown in Fig. 8. Dislocation ‘‘AB’’ consists of three segments with the directions of [1 1 0], [010] and  0; Dislocation ‘‘CD’’ also consists of three segments along the ½1 1 [1 0 0] and [1 1 0] directions. All the segments of the dislocations ‘‘AB’’ and ‘‘CD’’ are located in the (0 0 1) plane. The formation of this type superdislocation is by two a/2 h0 1 1i dislocations with different Burgers vectors combining together and the equation is as the following [10,28,29]:

 ! ah0 1 0i a=2h0 1 1i þ a=2h011i

ð1Þ

It is considered that the mobility of this superdislocation is very low since the Burgers vector a h0 1 0i is not at the typical fcc {1 1 1} slip plane. In fact, some superdialocations with a non-compact core have also been observed, such as the dislocation ‘‘E’’ in Fig. 8a and the segment ‘‘2’’ of the dislocation ‘‘CD’’ in Fig. 8b. This superdislocation (or segment) consists of two superpartials of equal Burgers vector of the a/2 h1 1 0i type which move on {1 0 0} plane with a combination of glide and climb [14,28,29]. It is believed that the low creep rate in the steady state stage during high temperature low stress creep is correlates with the moving of these superdislocations [29]. 3.3. Correlation between the microstructural evolution and creep curve The dislocation configurations of creep at different stages have been stated in the above sections. To give a comprehensive illustration, the microstructural evolution of the two experimental superalloys during the primary stage and the early of steady state stages together with creep curves are shown in Fig. 9a, the middle steady state stages and after rupture are shown in Fig. 9b. During the early stages of primary creep (within 1 h), the creep rate of the two experimental alloys is similar and this phenomenon has been observed in many other superalloys [4,8]. The dislocation smoothly spreading in the dislocation-free c matrix channel is considered to be the major deformation mechanism. However, during the later primary stage (about 2 h), the creep rate of the 3Ru alloy is a little higher than that of the 0Ru alloy, as shown in Figs. 1 and 9a. This phenomenon might be correlated with the change in partition coefficient of other elements between c and c0 phases with the addition of Ru. As the most important strengthening element, more Re strongly partition from the c matrix to the c0 precipitates with Ru additions [20]. Consequently, the strength of the c matrix of the 3Ru alloy might be lower than that of the 0Ru alloy. In other words, under nearly the same creep conditions, more dislocations in the matrix of the 3Ru alloy have been activated. This statement is supported by the observation in Fig. 4b.

Fig. 7. TEM microstructures of the 0Ru alloy (a) and (b) and the 3Ru alloy (c) and (d) after creep rupture at 1140 °C/137 MPa. (a) and (c) Bright-field conditions; (c) and (d) Two-beam bright-field conditions. Beam = [0 0 1].

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Fig. 8. Two-beam TEM bright-field images of dislocations in the c0 phase with several segments in different orientations after creep rupture at 1140 °C/137 MPa. (a) The 0Ru alloy; (b) The 3Ru alloy. Beam = [0 0 1].

be neglected), b = 0.254 nm and h = 60 nm. This gives an Orowan resistance of 133 MPa. The misfit stress distributions in the c matrix are shown in Fig. 10b. Due to the negative misfit, there are two compressive misfit stresses (r1 and r2) and a tensile misfit stress (r3) in the horizontal c matrix, as shown by the small cuboid marked ‘‘1’’ in Fig. 10b. In the vertical matrix channel, there are also two compressive misfit stresses (r4 and r6) and a tensile misfit stress (r5), as marked ‘‘3’’ in Fig. 10b. However, at intersection of the horizontal and vertical matrix channel, the c matrix in a stress state of a compressive misfit stresses (r0 1) and two tensile misfit stresses (r0 2 and r0 3), as marked ‘‘2’’ in Fig. 10b. In order to calculate the misfit stress, the lattice misfits in the horizontal and vertical c/c0 interfaces of the two alloys were determined by X-ray diffraction method. A three peaks fitting model has been used to determine the two sub-peaks for the c matrix and one peak for c0 precipitates ({0 0 4} reflection), and the detailed measurement can be seen in Ref. [20]. The results of the lattice misfits are as follows: for 0Ru alloy, d\ = 0.07%, dk = 0.20%; For 3Ru alloy, d\ = 0.11%, dk = 0.35% (d\ is vertical c/c0 interface misfit and dk is horizontal c/c0 interface misfit). According to Ref. [30,31], the misfit stress can be given as follows:

rc ¼ f

4lð1 þ mÞ ð1  2tÞe 3ð1  mÞ

ð3Þ

where rc is the misfit stress of the c matrix, f is the volume fraction of the c0 precipitates, m = 0.35 is the Poission’s ratio, e⁄ is the total strain and it contains two parts:

e ¼ ethermal þ ecmech

ð4Þ

ethermal ¼ Da  DT

ð5Þ

ecmech Fig. 9. Combination of creep curves with microstructural evolution during the primary stage and the early steady state stages (a) and the middle steady state stages and after rupture (b) of the two experimental superalloys.

In fact, during the primary creep stage or before the remarkable rafting take place, if a dislocation bows from one matrix channel into another, the driving force must be high enough to overcome the local Orowan resistance. An illustration of the calculation of Orowan resistance is shown in Fig. 10a. Dislocation ‘‘AB’’ is gliding on the (1 1 1) plane (as marked ‘‘rkt’’). The Orowan resistance (sor) can be simply calculated as follows [2]:

sor ¼

rffiffiffi 2 lb 3 h

ð2Þ

 0 1 is the Burgers vector b ¼ 1=2½1 where l is the shear modulus, ~ and h is the width of the c matrix channel. For the two alloys, l = 38.5 GPa (the effect of Ru additions on the shear module can

  1  2t d ¼ 2f 1þt

ð6Þ

where ethermal is the thermal strain, emech is the mechanical strain, Da is the difference in thermal expansion coefficients between the c and c0 phases and about 3  106 °C1 [30] (results show Ru additions almost has no effect on thermal expansion coefficients from room temperature to 1140 °C), DT is the change of the temperature. Consequently, the misfit stress can be obtained and the results of the calculation are as follows: for the 0Ru alloy, r1 0Ru = 147 MPa and r6 0Ru = 56 MPa; For the 3Ru alloy, r1 3Ru = 251.5 MPa and r6 3Ru = 84 MPa. Here, for simplicity, r1 = r2 = r5, r4 = r6 are adopted. It should be noted that any interface dislocations that might reduce the misfit between the two phases at the initial stage are neglected. In fact, the stress r4 does not have a component on the  1 dislocation. The calculation of the resolved shear stress a=2½0 1  1 dislocation on the (1 1 1) plane of the (srss) of the slipping a=2½0 1 vertical channel is as follows [4]:

srss ¼ ðr  r6 þ r5 Þ  cos54:74  cos45

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Fig. 10. (a) Schematic illustration of dislocation ‘‘AB’’ bowing into the vertical c matrix channel on the slip plane ‘‘rkt’’ (i.e., (1 1 1) plane). (b) Stress state of the c matrix channel during creep for superalloys with a negative misfit (see text for details).

where r is the applied stress, 54.74° is the angle between the direction of the three normal stresses and the normal direction of the (1 1 1) plane, and 45° is the angle between the direction of the three  1 slip direction. For the 0Ru alloy, srss normal stresses and the ½0 1 0Ru = 93 MPa, and for the 3Ru alloy, srss 3Ru = 124 MPa. It can be seen that the resolved shear stress of the two experimental alloys is lower than the Orowan resistance. Consequently, it is difficult for the slipping dislocations to bow into the vertical channel. As stated above, the average width of the c matrix channel is approximately 60 nm, but the width of some matrix channels can reach 100 nm. Under this condition, the Orowan resistance is only about 80 MPa, thus the dislocation bowing events can be occasionally observed (as dislocation ‘‘AB’’ in Fig. 3). Here, it should be noted that the resolved shear stress at the intersection of the horizontal and vertical matrix channel is higher than that in the vertical channel. The resolved shear stress at location ‘‘2’’, as shown in Fig. 10b, significantly increases, because the stress along the [0 0 1] direction changes from compressive to tensile. This statement is consistent with the observation of many dislocations can easily slipping through the intersections, as shown in Figs. 2a, 3a and 9a. The creep rate significantly decreased after 5 h continuous creep of the two experimental alloys, as shown in Figs. 1 and 9a. Formation of the interfacial dislocation networks originate from the local reactions of the slipping dislocations on the stressed octahedral systems [26]. It is generally accepted that this microstructural deformation mechanism has a direct relationship with the decreasing of the creep rate. On the other hand, the misfit energy and dislocation line energy are considerably reduced accompanying the formation process of the interfacial dislocation networks [2,4,10,21]. The driving force of dislocation slipping decreases significantly due to the effective relief by the h1 0 0i orientated dislocations. During the early stages of the steady state creep (about 15 h), the interfacial dislocation networks are somewhat irregular, with spacings and arrangements varying from place to place, as shown in Figs. 5a, c and 9a. This phenomenon is due to the fact that the formation of the interfacial networks is derived from the dislocation reactions as they bowed into the c matrix channel at different stress state. The creep rate, as shown in Figs. 1 and 9a, is at a very low level. It can be interpreted from the following aspects: (i) As mentioned above, the driving force for dislocation slipping is significantly decreased; (ii) The dislocations in the c matrix channel are expected to offer some resistance to each other in terms of a dislocation resistance, which originate from the self-stress field; (iii) As a result of rafting having taken place, it is difficult for dislocation to climb or bow into the vertical channel; The motion of dislocation is confined in the ‘‘elongated’’ c matrix channel. At the early stages of the steady state creep (about 15 h), the creep strain of the 0Ru alloy is a little higher than that of the 3Ru alloy. It might

be correlated with the process of some dislocations occasionally shearing into the rafted c0 phase in the 0Ru alloy, as shown in Fig. 5b. However, few dislocations shearing into the rafted c0 phase in the 3Ru alloy have been observed. Additionally, another factor should not be neglected: as stated above more Re partition from the c to c0 phase with the addition of Ru, thus the strength of the c0 phase of the 3Ru alloy is higher than that of the 0Ru alloy, especially at the elevated temperature. During the middle of the steady state of creep, as shown in Figs. 6 and 9b, the c/c0 interfacial dislocation networks are well developed in the 3Ru alloy. These interfacial dislocation networks can effectively prevent the slipping dislocations in the c matrix from shearing into the c0 phase. However, for the 0Ru alloy, the interfacial dislocation networks are not perfect, as seen in the area of ‘‘A’’, and ‘‘C’’ in Fig. 6a. In the vicinity of ‘‘C’’, the dislocations of square and hexagon arrangements can be clearly seen. These dislocations are still on the way to adjust their line directions from the h1 1 0i direction to the h1 0 0i direction. Consequently, the number of dislocations in the c0 phase of the 0Ru alloy is more than that of the 3Ru alloy. This observation is consistent with the changing tendency of creep rate, as shown in Figs. 1 and 9b. During the later stages of the steady state creep (as revealed by the microstructures after rupture), some dislocations with different Burgers vectors in the c0 phase are observed. The APB coupled pair of a/2 h1 0 1i type dislocations (with the same Burgers vector) cutting into the rafted c0 phase is considered to be an important deformation mechanisms at this stage of creep [10]. Another deformation mechanism at the steady state stage which cannot be ignored is that two a/2 h0 1 1i dislocations with different Burgers vectors combine together and form a a h0 1 0i type superdislocation at the c/c0 interface and then shear into the c0 phase. It is generally believed that the shearing events have a great contribution to the rupture process. Here, an inevitable problem is the precipitation of the topologically close-packed (TCP) phase during the creep process. The solid solution strengthening elements, such as Re, Mo and Cr, are depleted from the c matrix when the precipitation of TCP phase occurs within the system. The c matrix near the TCP phase disappeared and these TCP precipitates are surrounded by the rafted c0 phase. The coarsening of the rafted structure in the vicinity of TCP phase is accelerated by the precipitation process. On the one hand, the precipitation of TCP phase will result in the inhomogeneous deformation taking place. On the other hand, it is difficult for the dislocations to cut into the brittle TCP phase, so these precipitates can serve as sites of microcrack initiation. Consequently, the precipitation of TCP phase is detrimental to mechanical properties. Preventing the precipitation of TCP phase and maintaining a stable rafted microstructure are critical in controlling the creep resistance of single crystal superalloys at elevated temperature. It has been reported that Ru suppresses

X.G. Wang et al. / Materials and Design 67 (2015) 543–551

the formation of TCP phase and maintains the microstructure stability [15,17,25]. This effect is one of the reasons why the 3Ru alloy has a relatively longer creep life. 4. Conclusions The dependence of the microstructural evolution on the dislocation motion of the 0Ru and 3Ru alloys during creep tests (at 1140 °C/137 MPa) of different stages has been investigated. The following conclusions can be drawn from this work: 1. The stacking faults in the c matrix of the 3Ru alloy after heat treatment have been occasionally observed. This indicates that the 3Ru alloy has very low stacking fault energy, whereas the misfit stress between the c and c0 phases is higher. 2. In the primary creep stage, the movement of dislocations is confined in the c matrix channel. For the two experimental alloys, the dislocations can easily cross-slip at different {1 1 1} planes in the horizontal matrix and leave the 60° dislocation loops on the (0 0 1) plane. Calculations demonstrate that it is difficult for the slipping dislocations to bow into the vertical c matrix channel. Some dislocations in the vertical matrix of the 3Ru alloy have been observed. 3. During the early stages of steady state creep, the interfacial dislocation networks have formed in both of the two experimental alloys. The networks of the 3Ru alloy are more regular than those of the 0Ru alloy. Few dislocations shearing into the rafted c0 phase have been observed. In the middle of the steady state stages, although perfect dislocation networks have formed, some dislocations shearing into the c0 phase have been observed. The a h0 1 0i superdislocation has also been observed in the two experimental alloys. 4. The 3Ru alloy possesses more negative lattice misfit, denser c/c0 interfacial dislocation networks and higher microstructure stability, thus it can maintain a minimum creep rate in the steady state stage.

Acknowledgements The financial support provided by the National Basic Research Program (973 Program) of China under Grant No. 2010CB631200 (2010CB631206) and the National Natural Science Foundation of China (NSFC) under Grant Nos. 50931004, 51331005, 51101153, 11332010 and U1037601 for carrying out the present research work are gratefully acknowledged. The authors are grateful to S. Guan, Z.W. Shi and W.Y. Guo (Institute of Metal Research) for the useful discussions. References [1] Reed RC. Superalloys: fundaments and applications. New York: Cambridge University Press; 2006. [2] Pollock TM, Argon AS. Creep resistance of CMSX-3 nickel base superalloy single crystals. Acta Metall Mater 1992;40:1–30. [3] Huda Z, Edi P. Materials selection in design of structures and engines of supersonic aircrafts: a review. Mater Des 2013;46:552–60. [4] Zhang JX, Harada H, Koizumi Y, Kobayashi T. The effect of lattice misfit on the dislocation motion in superalloys during high-temperature low-stress creep. Acta Mater 2005;53:4623–33. [5] Tian SG, Su Y, Qian BJ, Yu XF, Liang FS, Li AA. Creep behavior of a single crystal nickel-based superalloy containing 4.2% Re. Mater Des 2012;37:236–42.

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