Double minimum creep of single crystal Ni-base superalloys

Double minimum creep of single crystal Ni-base superalloys

Acta Materialia 112 (2016) 242e260 Contents lists available at ScienceDirect Acta Materialia journal homepage: www.elsevier.com/locate/actamat Full...

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Acta Materialia 112 (2016) 242e260

Contents lists available at ScienceDirect

Acta Materialia journal homepage: www.elsevier.com/locate/actamat

Full length article

Double minimum creep of single crystal Ni-base superalloys X. Wu a, *, P. Wollgramm a, C. Somsen a, A. Dlouhy b, A. Kostka a, G. Eggeler a a b

€t Bochum, 44 780 Bochum, Germany Institut für Werkstoffe, Ruhr-Universita  zkova 22, 616 62 Brno, Czech Republic Institute of Physics of Materials, ASCR, Zi

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 February 2016 Received in revised form 31 March 2016 Accepted 5 April 2016 Available online 23 April 2016

Low temperature (750  C) and high stress (800 MPa) creep curves of single crystal superalloy ERBO/1 tensile specimens loaded in the 〈001〉 direction show two creep rate minima. Strain rates decrease towards a first sharp local creep rate minimum at 0.1% strain (reached after 30 min). Then deformation rates increase and reach an intermediate maximum at 1% (reached after 1.5 h). Subsequently, strain rates decrease towards a global minimum at 5% (260 h), before tertiary creep (not considered in the present work) leads to final rupture. We combine high resolution miniature creep testing with diffraction contrast transmission electron microscopy and identify elementary processes which govern this doubleminimum type of creep behavior. We provide new quantitative information on the evolution of microstructure during low temperature and high stress creep, focusing on g-channel dislocation activity and stacking fault shear of the g0 -phase. We discuss our results in the light of previous work published in the literature and highlight areas in need of further work. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Single crystal Ni-base superalloys Primary creep Transmission electron microscopy Dislocations Stacking faults

1. Introduction Single crystal Ni-base superalloys (SXs) are used for blades in advanced gas turbines for power plants and jet engines [1e5]. They operate in the creep range, where they have to withstand mechanical loads at temperatures above half of the melting point in Kelvin. During creep, strains gradually increase with time. Creep research focuses on explaining the shape of individual creep curves, which often show stages of decreasing, constant and increasing creep rates referred to as primary, secondary and tertiary creep [6e12]. However, under conditions of low temperature and high stress creep (LTHS-creep, here: 750  C, 800 MPa), SXs can show creep curves with peculiar shapes [13e22]. SXs operate at temperatures up to 1100  C. Therefore, in the present work, we refer to 750  C as a low temperature. Fig. 1 provides an example for LTHScreep. It shows data from five interrupted creep tests from the SX ERBO1/C [23,24]. We discuss the details of Fig. 1 later. Here it is important to highlight that when plotted as logarithmic of strain rate vs. strain or vs. logarithm of strain, the creep curves show two minima, separated by an intermediate maximum, Fig. 1b and c. This behavior which we refer to as double minimum creep (DM-creep) was first reported more than two decades ago [13e16]. While the

* Corresponding author. E-mail address: [email protected] (X. Wu). http://dx.doi.org/10.1016/j.actamat.2016.04.012 1359-6454/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

early decrease in creep rate towards the first minimum did not receive much attention, the subsequent increase of creep rate up to the intermediate creep rate maximum was reported in several studies [17e22]. Why creep rates evolve in this way is an open question. The scientific objective of the present work is to explain the elementary processes which govern DM-creep. 2. Material and experiments 2.1. Material and scanning electron microscopy The present work is part of the research program of the collaborative research center SFB/TR 103 [23]. We investigate a SX of type CMSX-4, referred to as ERBO/1C. All details concerning this designation, the alloy composition and the heat treatment of the material are given elsewhere [24]. Fig. 2 shows micrographs obtained using scanning electron microscopy (SEM) with secondary electron (SE) contrast. Fig. 2 shows the g/g0 -microstructure of the material before and after creep. SEM was performed using a FEI system of type Quanta 650 FEG, all details regarding the SEM procedure have been published elsewhere [25]. Fig. 2a shows a {100} cross section prior to creep. The g0 -cubes (ordered L12 phase) have average cube edge lengths of 0.4 mm (present work and [24]). Their volume fraction is between 70 and 80%. The average gchannel (fcc crystal structure) width is 65 nm (present work and [24]). Fig. 2b shows a SEM micrograph taken from a {111} cross

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contains only a low dislocation density in the g-channels and no planar faults in the g0 -phase [25,28]. 2.2. Miniature creep testing

Fig. 1. Creep curves from interrupted tests of ERBO/1C (750  C, 800 MPa). (a) Strain ε as a function of time t. (b) Logarithm of creep rate as a function of strain. (c) Logarithm of creep rate as a function of logarithmic strain.

section prior to creep. Due to the spatial arrangement of the g0 cubes these can have triangular (small arrow pointing up) and hexagonal (small arrow pointing down) g0 -shapes on the metallographic cross section (see schematic sketches in Refs. [26,27]). Fig. 2c and d shows {100} and {111} cross sections after 5% (260 h) creep at 750  C and 800 MPa. From Fig. 2c and d it is clear that there is no significant rafting. Previous transmission electron microscopy (TEM) studies have shown that the initial material prior to creep

Miniature creep specimens have two advantages as compared to standard size specimens. First, a larger number of creep specimens can be obtained from a limited amount of material. Second, it is easy to obtain precisely oriented specimens. 〈001〉 miniature tensile creep specimens were prepared combining the Laue method with electro discharge machining. Miniature creep testing was performed using a creep machine from Denison Mayes, equipped with a vertically movable three zone furnace. The heating zones were monitored by three thermocouples and controlled by Eurotherm controllers. The miniature creep specimens (gauge length: 9 mm) were positioned in the temperature constant zone of the furnace (at 750  C: > 100 mm). In addition to the three thermocouples which control the three heating zones, two measurement thermocouples were fixed to the upper and lower ends of the gauge lengths. The precision of the temperature measurement at 750  C is ±1.5  C. The miniature specimens are mounted in special grips consisting of an ODS alloy PM 3030, reinforced by ceramic Al2O3 insets. Displacements were measured using ceramic rod in tube extensometry and strain sensors positioned outside of the furnace. In the present work, the specimens were heated to the test temperature of 750  C under a preload close to 20 MPa in 2 h. The small preload is required to keep the load line aligned. The load, corresponding to a stress of 800 MPa, was then applied within only a few seconds. The immediate elastic reaction of the specimen/grip assembly was not considered as creep strain. With respect to the scientific objectives of the present work it is important to highlight that the specimen was heated up to test temperature as fast as possible, that the preload was much smaller than the test load and that the full test load was applied within only a few seconds. Further details of miniature tensile creep testing have been published elsewhere [29e34]. Miniature creep tests were interrupted after strain intervals ranging from 0.1 to 5%. Fig. 1a presents corresponding creep data in a strain ε vs. time t plot. Fig. 1b shows how the creep rate evolves with strain in a log-linear plot of strain rate vs. strain. Fig. 1a and b prove that our material shows a reproducible creep behavior. This also holds for very small strains, as can be seen from the logarithm of strain rate vs. logarithm of strain plot in Fig. 1c. The first dashed vertical line in Fig. 1c corresponds to a plastic strain of 0.01%. For our specimen geometry (gauge length: 9 mm) this corresponds to a displacement of about 1 mm. This type of displacement can be resolved by electronic/mechanic data collection systems. It is, however, close to the resolution limit of creep testing. The scatter of the five creep curves shown in Fig. 1c between 0.01 and 0.1% strain is small and decreases with increasing strain. The results presented in Fig. 1c clearly show that there is a decrease of creep rate between 0.01 and 0.1%, where the first creep rate minimum is observed (marked by the second vertical dashed line in Fig. 1c). It takes about 30 min to reach this first creep rate minimum. The creep rate then increases towards an intermediate maximum at about 1% (third vertical dashed line in Fig. 1c), before it decreases towards a global minimum close to 5% strain. In Fig. 1c we identify three regimes referred to as I, II and III. In regime I creep rates sharply decrease towards a first minimum. In regime II, the creep rate increases from the first sharp minimum towards an intermediate maximum. Then, in regime III, creep rates decrease from the intermediate maximum towards the second broad global minimum. A full 750  C and 800 MPa 〈100〉 tensile creep curve for the material of the present study which shows the evolution of creep rate after the second minimum towards final rupture is shown in Ref. [34]. Tertiary creep

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Fig. 2. SEM micrographs of the g/g0 microstructure of ERBO/1C before and after creep (750  C, 800 MPa, 5%). (a) Initial state, {100} section. (b) Initial state, {111} section. (c) After creep, {100} section. (d) After creep, {111} cross section.

is not considered in the present study. 2.3. Transmission electron microscopy (TEM) In order to prepare TEM foils, thin slices were prepared using an Accutom 5 cutting disk from Struers. The slices were ground to a thickness of 90 mm, using emery paper of 4000 mesh size. Subsequently, electron transparent thin foils were prepared by double jet electrochemical thinning in a TenuPol-5. Optimum thinning conditions were obtained using an electrolyte consisting of 70 vol.% methanol, 20 vol.% glycerin and 10 vol.% perchloric acid at 20  C. Different flow rates (of the order 20) and voltages (of the order of 10 V) were applied. TEM investigations were performed using a €t Bochum) and a Tecnai Supertwin F20 G2 (at the Ruhr-Universita Jeol TEM of type JEM-2100F (at the IPM Brno) both operating at 200 kV. Conventional diffraction contrast TEM techniques were employed to identify dislocations and associated planar faults in the g0 phase. All details on specimen preparation, on imaging procedures and on schematic 3D views have been reported elsewhere [25e28]. A scanning transmission (STEM) stereo method helps to obtain information on the spatial arrangement of defects in the microstructure [35]. Fig. 3 shows a (100) cross section after 0.1% creep. From the region highlighted by the white rectangle, we simply use projected area fractions to estimate the volume fractions of the g0 - and g-phase as fg0 ¼ 73% and fg ¼ 27%, respectively. This is in good agreement with the value of 72% obtained for the g0 volume

fraction of the same material with complementary methods [24]. There are two vertical and two horizontal reference lines in Fig. 3a, which were used to measure the distributions of g-channel widths (average: 65 nm) and g0 -cube edge lengths (average: 442 nm) by means of a line intersection method. The resulting size distributions are presented in Fig. 3b and c. Elementary deformation processes are investigated using (111) TEM foils. The TEM micrographs presented in Fig. 4 were obtained after 2% of creep strain. Fig. 4a represents a schematic Kikuchi map which identifies eight tilt positions close to a [111] zone. The corresponding eight TEM micrographs are shown in Fig. 4b to i. With the exception of Fig. 4c (centered dark field mode) the images were taken in bright field contrast. The individual contrast conditions are given in the upper right corners of Fig. 4b to i. In Fig. 4b, a central arrow pointing up marks a planar fault which extends through the central g0 particle. This planar fault is effectively invisible in Fig. 4e and i. Such effective visibility/invisibility results provide information on the nature of the planar fault [20,36e42]. The inset in Fig. 4c shows that a fine dark fringe (next to the prominent white fringe) limits the planar fault. Additional information from stereo TEM (not shown) allows to conclude that this fine dark line represents the intersection of the planar fault with the upper surface of the TEM foil. As was pointed out by Williams and Carter [40], the interpretation of stacking fault contrast and especially of the contrast of the terminating fringes is delicate and requires proper attention. Table 1 summarizes the g-vectors from Fig. 4 together with the

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Fig. 3. Montage of TEM micrographs taken after 0.1% creep deformation (750  C, 800 MPa). TEM foil perpendicular to [001] and to the direction of the applied stress. (a) TEM montage with horizontal and vertical reference lines. (b) Histogram showing g channel widths distributions. (c) Distribution of g0 cube edge lengths.

corresponding visibilities (þ) and invisibilities () of the central planar fault. The results presented in Fig. 4 and Table 1 allow to conclude that the fault has a displacement vector which is in the plane of ð111Þ and of type 〈121〉. In order to evaluate the densities of dislocations and planar faults, we use montages of TEM micrographs which were taken for g-vectors of type {111} [20,36,39e42]. Fig. 5 illustrates details of our measurement procedures. Fig. 5a shows a montage of TEM micrographs after 2% creep. It consists of 9 individual images which were

taken at a magnification of 8700 (g-vector: (1 1 1), foil thickness tF: 373 nm). Foil thicknesses were measured using the Kossel fringe technique [40,43]. The projected area am of the montage in Fig. 5a is 33.7 mm2, it contains 112 g0 -particles. Fig. 5a shows that there are locations in the g-channels where the dislocation density is high (arrow 1) while there are others, where the dislocation density is significantly lower (arrow 2). Two fields, F1 and F2, are highlighted by white dashed rectangles. These two regions are shown at higher magnifications in Fig. 5b (F1) and c (F2). In Fig. 5b, the (111) TEM foil

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Fig. 4. TEM micrographs taken after 2% creep strain (750  C, 800 MPa) under different two beam conditions. (a) Kikuchi map indicating tilt positions and g-vectors. (b, d to i) Bright field images. (c) Centered dark field image.

Table 1 g vectors and effective visibilities/invisibilities of the planar fault in the TEM images shown in Fig. 4. (þ: visible; : invisible). g

ð1 1 1Þ

ð1 1 1Þ

ð2 2 0Þ

ð2 0 2Þ

ð0 0 2Þ

ð0 2 2Þ

ð1 1 1Þ

ð1 1 1Þ

SF

þ

þ

þ



þ

þ

þ



intersects the central g0 particle (marked with white arrow 1) close to one of its corners. Arrow 2 points to the leading segment of a dislocation in a horizontal g channel. Note that when preparing a (111) TEM foil after [001] tensile testing one cannot easily recognize the orientations of horizontal and vertical channels (with reference to the [001] loading axis). We therefore indicate the direction of horizontal channels where necessary. Thickness fringes due to the presence of inclined g/g0 -interfaces are marked with a small arrow 3. For the scientific objective of the present work it is important to quantify the appearance of planar faults. It is possible to determine a projected area fraction of all planar faults. For this purpose we count the numbers nPF of all planar faults and add up all their

projected areas aPF in the projected area of the TEM foil am. This yields a projected area fraction APF as given in Equation (1):

APF ¼

nPF X

, aPF;i

am

(1)

i¼1

This projected area fraction does not give fair credit to the inclined faults, which only provide small contributions to APF while their role may well be as important as that of the faults which are parallel to {111} plane of the TEM-foil (their measured projected area fraction may underestimate their importance). On the other hand, as the TEM foil represents a thin slice which probes the SX microstructure. Parallel faults have a higher probability of not being

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Fig. 5. TEM images taken after 2% strain. g: ð1 1 1Þ. (a) Montage of nine TEM-micrographs. (b) Field F1 from Fig. 5a at a higher magnification. (c) Reference grid for determination of dislocation densities from field F2 of Fig. 5a. (d) Illustration of counting procedure.

part of the TEM foil volume (their smaller number may suggest that they are less important). As a reasonable compromise we consider a qualitative intensity parameter IPF which is based on both inputs, the projected area fraction APF of all faults (which overestimates the importance of the faults which lie in the plane of the TEM foil) and the total number of planar faults nPF (which underlines the importance of inclined faults). Both input parameters must be normalized with respect to the thickness tF of the TEM foil. In order to account for the intensity of planar fault cutting, we use an expression of type

IPF ¼ ðnPF $APF Þ=tF

(2)

Fig. 5c shows field F2 from Fig. 5a at a higher magnification. Fig. 5c contains a system of thin horizontal and vertical reference lines, which were used to determine average dislocation densities following Ham's method [44,45]. The total length of all horizontal P P (H) and vertical (V) lines in the evaluation grid is lH and lV , respectively. Our counting procedure is illustrated at a higher magnification in Fig. 5d for the rectangular region highlighted by the dashed white rectangle in Fig. 5c. The white dots in Fig. 5d represent counts of intersections of the reference lines with dislocations. In a first step, we count the total number of intersections between dislocations and horizontal and vertical reference lines (without differentiating between dislocations in the g and g0 phase: P P nHALL and nVALL , respectively). This yields the average

dislocation density in the g/g0 -microstructure

X

rg=g0 ¼ ð1=tF Þ$

nHALL

.X

lH þ

X

nVALL

.X

lV



(3)

In order to determine average dislocation densities we evaluate areas between 5 and 15 mm2 from the six montages listed in Table 2. In average, 10 horizontal and 10 vertical reference lines were used per image. Keeping track of the dislocation counts in the g and g0 phase regions, one can differentiate between the dislocation densities in the two phases. We consider the volume fractions fg and fg᾽ and obtain the dislocation density in the g-phase as

rg ¼ ð1=tF Þ$

X

nHg

.X

fg $lH þ

X

nVg

.X

fg $lV



(4)

Table 2 Overview of experimental details characterizing the TEM experiments performed in the present work. g vector

am/mm2

Number of g0 particles

335

1 1 1

32.1

111

0.2

160

1 1 1

33.2

122

0.4

260

1 1 1

29.4

117

1.0

295

1 1 1

24.2

102

2.0

373

1 1 1

33.7

112

5.0

238

1 1 1

29.3

104

Strain/%

tF/nm

0.1

248

X. Wu et al. / Acta Materialia 112 (2016) 242e260

The same approach allows to calculate the dislocation density

rg0 in the g0 -phase. The dislocation density is a microstructural parameter which shows high local scatter (see locations highlighted by arrows 1 and 2 in Fig. 5a). In the present work we quantify this scatter by determining the two highest/lowest measured dislocation densities and use them as upper/lower limits of error bars. Table 2 shows an overview of experimental details which characterize our TEM experiments. Given the fact that in 〈001〉 tensile testing eight microscopic crystallographic slip systems experience the same resolved shear stress, each g-vector shows a similar part of the overall dislocation density. Table 2 lists the amount of pre-deformation, the foil thickness tF, the g-vector, the projected area of the evaluated TEM montage am and the number of g0 -particles contained in the area of observation. 3. Results 3.1. Creep behavior Fig. 1 shows data from five creep experiments which fall into a narrow scatterband. Fig. 1a shows the creep data plotted as strain ε vs. time t. In Fig. 1b the logarithm of creep rate log ε_ is plotted as a function of strain. Fig. 1c presents the logarithmic creep rate as a function of the logarithm of strain. In Fig. 1c the creep rates recorded at very low strains are better resolved. As can be seen in Fig. 1b and c, there is an initial sharp decrease of creep rate. A first minimum is reached after a short strain interval in a short time (0.1%, 30 min). Then there is an increase of creep rate towards an intermediate local maximum at strains of the order of 1% (reached after 1.5 h). Subsequently, creep rates steadily decrease towards a broad second minimum which is observed at strains of the order of 5% after 260 h of creep exposure. Note that the strain time plot shown in Fig. 1a does not allow to appreciate the DM-type of creep behavior. Instead, one may well obtain the impression, that there is a primary creep regime which extends up to strains of the order of 5%. Previous researchers have come to that conclusion [4,20e22,37,38]. However, Fig. 1b and c clearly show, that the deformation rates measured in the LTHS regime cannot simply be attributed to traditional primary, secondary and tertiary creep regimes. Our creep data presented in Fig. 1b and c shows that there is a short early period of decreasing creep rates. The effect is reproducible and occurs in all creep experiments performed in the present study. Stages II (increasing creep rate towards intermediate maximum) and III (decrease of creep rate towards second broad minimum) were also experimentally reproduced, Fig. 1b and c. 3.2. Dislocation analysis Fig. 6 shows four STEM micrographs which were taken after 1% creep deformation as part of a tilt series. Nine dislocations (1e9) and two planar faults (10 and 11) are highlighted in Fig. 6. Fig. 6a to c shows bright field images, while Fig. 6d represents a STEM HAADF image in the same tilt position as Fig. 6b. Dislocation 1 is in full contrast in Fig. 6a and c, while it is out of contrast in Fig. 6b. The dislocations 3, 4, 5 and 7 are visible in Fig. 6b, while they are invisible in Fig. 6c. In Fig. 6c the two faults 10 and 11 are oriented edge on and provide no contrast. Fig. 6d was taken to identify the character of the two faults, details are shown at higher magnification (insets). The g-vector of type ð11 1Þ in Fig. 6d points away from the bright outer fringe of stacking fault 10. Therefore, this fault represents a superlattice intrinsic stacking fault (SISF). The fault 11 exhibits opposite contrast (note that there is a very fine thin dark line next to the prominent white line). Fault 11 thus represents a superlattice

extrinsic stacking fault (SESF). The spatial orientation of dislocations and faults was characterized using HAADF STEM stereo microscopy [35]. One stereo image of faults 10 and 11 is provided as supporting material on the journal's web page (for 3D impression use coloured glasses as indicated). Stereo microscopy shows that the faults 10 and 11 are parallel to one common crystallographic plane ð11 1Þ. Our stereo assessment suggests that dislocation 5 (in the g channel between faults 10 and 11) and channel dislocation 3 (at the upper g/g- interface) are located in the same ð11 1Þ plane as the two faults. A partial dislocation 6 borders the fault 11 (at the lower g/g-interface of the g-channel between the two faults). In Table 3, the visibility/invisibility results of Fig. 6a to c are listed (highlighted in light grey). Table 3 also contains all other effective visibility/invisibility results of the tilt series. There were cases where the projections of dislocations overlapped and where it was not possible to properly analyze their contrast. These cases are marked with a “?” in Table 3. Table 3 summarizes the resulting Burgers vectors of dislocations and the planar fault displacement vectors. The effective visibility/invisibility criterion g$b ¼ 0 applied to perfect a/2 〈110〉 g channel dislocations only yields the types of their Burgers vectors. In Table 3, all Burgers vector types of these dislocations are listed together with a pre-factor of a/2, even though no large-angle convergent-beam electron diffraction (LACBED) experiments were performed to fully characterize the Burgers vector magnitude [46]. On the other hand, the effective visibilities/invisibilities may result in a more complete characterization of the partial dislocations which border the stacking fault ribbons [36]. For small deviations from the Bragg reflection positions (w < 0.3, for definition of w see Ref. [36]) applied in our tilting experiments, it is expected that partial dislocations are effectively invisible for g$b ¼ ±1/3. However, they show contrast for resulting scalar products of ±2/3 and ± 4/3 [36]. This allows to conclude that the dislocation 6 in Fig. 6 has a Burgers vector ± a/6 [211]. (Note that the last row of Table 3 presents 2b/a and 3R/a values, so the Burgers vector of dislocation 6 is ± a/6 [211].) 3.3. Dislocations and planar faults In this section we document the evolution of microstructures in regions which contain a representative number of g0 particles. Fig. 7 shows a montage of TEM micrographs which was obtained after 0.2% creep strain (experimental details: row 2 of Table 2). The microstructure in Fig. 7 characterizes the transition from stage I (early decrease of creep rate) to stage II (intermediate increase of creep rate) of DM-creep. The dashed reference line in the center of Fig. 7a indicates the direction of horizontal g-channels (with reference to [001] tensile testing). These channels show a high dislocation density. Two arrows point to leading dislocation segments. These appear to be blocked by irregularly positioned g0 particles, which interrupt their free paths. In the SEM-micrographs shown in Fig. 2a and b, two dashed lines mark open g-channels which are terminated by irregularly positioned g0 -particles. Arrow 2 in Fig. 7a marks a location which shows that the applied stress was high enough to drive a leading screw segment through a vertical channel (vertical with respect to the [001] tensile loading axis). This is rarely observed in the early stages of creep. In their wake, the leading dislocation segments deposit dislocation dipoles at the g/g0 -interfaces as schematically illustrated in Fig. 1 of [26]. Fig. 7a suggests that dislocations do not all emerge from one common remote source. Instead, it appears as if dislocations can also emanate from local sources. A dislocation substructure, with a higher density of dislocations in horizontal channels, is typical for the early stages of LTHS-creep. The arrows 3, 4 and 5 mark planar faults, which have just started to form in g0 particles. Note that

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Fig. 6. Four STEM micrographs which were taken as part of a tilt series to determine Burgers vectors b of dislocations and displacement vectors R of planar faults after creep at 750  C and 800 MPa to 1%. (a), (b) and (c) Bright field images. (d) HAADF image. (a) g: ð200Þ. (b) g: ð111Þ. (c) g: ð11 1Þ. (d) g: ð111Þ.

Table 3 Results from TEM tilt experiments after 1% creep strain. g-vectors: g (1e11), defects: d (1e9: dislocations, 10 and 11: planar faults). Fields highlighted in grey: Fig. 6a to c. g and d

1

2

3

4

5

6

7

8

9

10

1: ð200Þ

þ

þ

þ

þ

e

þ (±2/3)

þ

þ

e

þ

11 þ

2: ð1 1 1Þ

e

þ

þ

þ

þ

e (±1/3)

þ

þ

þ

þ

þ e

3: ð1 1 1Þ

þ

e

e

e

e

e (0)

e

res

e

e

4: ð022Þ

þ

res/do

þ

þ

þ

e (0)

þ

þ

þ

e

e

5: ð1 1 1Þ

þ

e

e

e

þ

 (±1/3)

e

e

þ

þ

þ

6: ð1 3 1Þ

e

þ/do

þ

þ

þ

 (0)

þ

þ

þ

e

e

7:ð220Þ

þ

þ

þ

þ

þ

 (±1/3)

þ

þ

þ

þ

þ þ

8: ð3 1 1Þ

þ

þ

þ

þ

res

þ (±2/3)

þ

þ

res

þ

9: ð1 1 3Þ

þ

þ/do

þ

þ

þ

 (0)

þ

þ

þ

e

e

10:ð002Þ

þ

?

þ

þ

?

?

þ

?

þ

þ

þ

11: ð202 Þ 2b/a and 3R/a

þ

e

e

e

þ

 (±1/3)

e

res

þ

þ

þ

± ½101

± ½1 0 1

± ½1 0 1

± ½1 0 1

± ½011

±1=3 ½21 1

± ½1 0 1

± ½1 0 1

± ½011

± ½112

± ½112

res: residual contrast, do: double contrast, ?: no determination possible, b: Burgers vector, R: planar fault displacement vector.

there are many dislocations, while only a few planar faults can be detected. Fig. 7b documents the two-beam condition which was established for the images of the montage. Fig. 7c shows the corresponding Kikuchi line diffraction pattern, which documents the

tilt position of the TEM foil (beam direction close to the [121] direction). Fig. 8 (stage II of DM-creep) and 9 (end of stage III of DM-creep) present TEM montages for the material states after 0.4 and 5%

250

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Fig. 7. TEM results after 0.2% strain (750  C, 800 MPa). (a) Montage. (b) Two beam contrast. (c) Tilt position.

creep. Both montages show dislocations in the g-channels and planar faults in the g0 -particles. As compared to Fig. 7a (0.2%), Fig. 8 shows significantly higher densities of dislocations in the g-channels and of planar faults in the g0 -particles. The horizontal channels clearly show higher dislocation densities. As compared to Fig. 7a (0.2% strain), the dislocation density in the other two channels has increased. As expected for high symmetry [001] loading, planar faults are detected in the g0 -phase on all {111} planes (three planar faults on different {111} planes marked by arrows 1 to 3. The fourth {111} plane is perpendicular to the g-vector of the image, the corresponding planar faults are oriented edge on and are therefore out of contrast. Arrow 1 highlights a fault which lies in the {111} plane

of the TEM foil. Fig. 8 shows that only few dislocations have entered the g0 -phase. One dislocation in the region in the upper part of the micrograph which is highlighted by a white circle appears to interact with a planar fault. Fig. 9 shows the microstructure after 5%, at the end of stage III of DM-creep. For this material state, good contrast conditions were obtained using the STEM HAADF image mode [35], where dislocations and planar faults show a bright contrast. The microstructures after 0.4 and 5% strain show clear differences. After 5%, the dislocation densities in all three types of channels are now similar. Planar faults are present, however it appears that their density has decreased. In contrast, the density of dislocations in the g0 -phase has clearly increased. More frequent

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Fig. 8. Montage of TEM micrographs obtained for a material state which was deformed to 0.4% strain (750  C, 800 MPa). Bright field image, two beam contrast: g ¼ ð1 1 1Þ.

interactions between dislocations and planar faults are observed (three locations marked by white circles). After 5% creep deformation the dislocation density in all g-channels is high and the dislocation density distribution appears to be uniform. In Fig. 10 we show how dislocation densities evolve as a function of strain. Fig. 10a shows the evolution of the overall dislocation density rg=g0. Fig. 10b and c differentiate between the evolution of dislocation densities in the g-channels (rg ) and in the g-phase (rg0 ). As the TEM montage in Fig. 9 suggests and as can be seen from the quantitative data in Fig. 10c, the dislocation density in the g-particles increases in the later stages of creep. Fig. 11 shows the evolution of the total density of all planar faults with strain. In Fig. 11a we plot the number density of planar faults per area of the corresponding montage nPF/am as a function of strain. Fig. 11b shows how the projected area fraction APF evolves during creep. Finally, in Fig. 11c, we plot the planar fault density intensity parameter IPF as defined in Equation (2) as function of strain. Fig. 11 suggests that the formation of a small number of planar faults starts early. Then there appears to be an optimum condition for the formation of planar faults in the g0 -phase at accumulated strains between 0.4 and 1%. With further increasing strain, the contribution of cutting processes which create planar faults decreases. 3.4. Local observations The objective of the present work is to identify elementary deformation processes which rationalize the macroscopic DMcreep behavior. Therefore, in Figs. 12 and 13, some relevant details are presented at higher magnifications. Fig. 12 compiles four characteristic dislocation TEM images. Fig. 12a shows one dislocation which glides in a (111) plane along a horizontal channel

(direction indicated by black dashed line). It seems as if the dislocation makes attempts to enter non-horizontal channels (the dislocation line bulges out) but does not succeed. The tips of leading dislocation segments can be approximated by semicircles, with radii which range from 27 (segment 1 marked by white arrow pointing to the upper left) to 55 nm (segment 2 marked by arrow pointing to the lower right). In Fig. 12b there is a central irregularly placed g0 particle marked with a full white circle. There are two g-channel segments which are parallel to the black dashed line, indicating the orientation of horizontal channels. Fig. 12b shows, that the central g0 particle impedes continuous dislocation glide between the upper and the lower g-channel segments. The positions where dislocations from both channels hit the irregularly placed g0 particle are marked by white arrows. Fig. 12b also shows, that at 0.2%, dislocations occasionally succeed to circumvent blocking particles by expanding into non-horizontal channels. It should be highlighted that at 0.2% strain, the majority of g0 particles are free of dislocations. As documented in Fig. 12c, after 1% creep strain, dislocations enter the g0 -phase (two highlighted by white arrows). When the accumulated creep strain reaches 5%, we observe two relevant microstructural features, Fig. 12d. First, we find similar high dislocation densities in all g-channels. Second, all g0 -particles contain dislocations and stacking faults. For clarity, in Fig. 12d the six sided shape of a g0 -particle in the (111) TEM foil is marked by a white dashed line. Inside this particle we find dislocations (one marked with an arrow pointing to the lower left) and a planar fault (marked with an arrow pointing to the upper left). Fig. 13 shows four TEM images which document relevant details associated with planar faults in g0 -particles. Fig. 13a represents a centered dark field image which was taken to establish the nature

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Fig. 9. Montage of STEM HAADF images obtained for a material state which was deformed to after 5% strain (750  C, 800 MPa). g: ð1 1 1 Þ.

of the planar fault [39,40]. The image was taken after 0.2% of creep strain. A planar fault in the center of the image shows a dark/bright fringe contrast. Since the g-vectorð1 1 1Þ points away from the outer bright fringe, this planar fault represents a SISF. In fact, in Fig. 13a, two SISFs spread out from the g/g0 -interfaces of the central g-channel into the two g0 -particles on its left and right. The TEM image in Fig. 13b was taken after 1% creep deformation. It shows two planar faults (highlighted by white arrows) which extend in the (111) plane of the TEM foil. The two faults can be distinguished from the surrounding microstructure by their darker contrast. The two images shown in Fig. 13a and b suggest that planar faults are not isolated. Instead, they are associated with dislocations in the gchannels. The TEM micrograph in Fig. 13c, taken after 2% creep strain, suggests that there is a direct link between the g-channel dislocation in the lower right part of the image (highlighted by an arrow) and a planar fault. High resolution TEM allows to resolve atomistic details of planar faults. One example is shown in Fig. 13d. In this high-resolution TEM micrograph, the fault extends on að1 1 1Þ plane and is oriented edge on. 4. Discussion 4.1. Decrease of creep rate in stage I of DM-creep The decrease of creep rate towards an early minimum in stage I of DM-creep was previously documented [13e16]. Two types of dislocation processes can explain this phenomenon. First, there can be contributions from in-grown misfit dislocations in the vertical channels. To discuss this effect, we introduce a model system with only two slip systems, Fig. 14a. An external tensile stress (two large vertical arrows) drives dislocations into the directions defined by

the small arrows (representing resolved shear stresses [47,48]). The plus and minus signs close to the dislocation in the lower right schematically indicate the presence of compressive and tensile stress states [47,48]. Fig. 14b to d shows a 2D array of four g0 -particles and a central g-channel crossing. The two slip systems introduced in Fig. 14a can operate in the g-phase of this model system. In Fig. 14b, there is no external stress. However, internal stresses associated with the g/g0 -misfit (negative in most SX, i.e. the lattice constant of the g0 -phase is smaller than the lattice constant of the g-phase [3e5]) attract channel dislocations towards the particles. Two long arrows illustrate misfit stresses in Fig. 14b. The arrows with tips pointing outwards/inwards indicate that misfit stresses are of a tensile/compressive nature. It is well known that misfit stresses can be as high as 500 MPa [26,49]. The formation of misfit dislocations represents an accommodation process, which results in a decrease of the intensity of the overall stress state (or of elastic strain energy) [26]. Fig. 14b schematically illustrates, that the compressive/tensile regions around the dislocations are directed towards the regions with tensile/ compressive stress states in the g/g0 -microstructure. The presence of in-grown misfit dislocations [49e51] prior to creep can partly account for stage I of DM-creep. As schematically illustrated in Fig. 14c and d, the high applied stresses pull misfit dislocations (from vertical channels) away from the g/g0 -interfaces. After a short glide period they annihilate in the channel centers, Fig. 14c and d. This represents one contribution to the decrease in creep rate in stage I of DM-creep. As was already outlined by Leverant and Kear [37], the density of in-grown dislocations is a crucial factor in this scenario. Our TEM results presented in Figs. 3, 7a and 12b suggest that a second mechanism contributes to the decrease of creep rate in stage I of DM creep. This process consists of immediate glide of

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Fig. 10. Dependence of dislocation densities on creep strain. (a) Overall dislocation density rg=g0 . (b) Dislocation density in g channels rg . (c) Dislocation density in g0 particles rg0 .

pre-existing dislocations through continuous parts of the channel network when the load is applied. These fast glide processes come to an abrupt stop when leading dislocation segments hit irregularly located g0 -particles. Micromechanical models which do not address the presence of in-grown dislocations and which assume high symmetry g/g0 -microstructures cannot capture this run and stop mechanism [19,52,53]. In the high temperature and low stress creep no early intermediate minimum is observed [e.g. 25, 28, 33, 34], €hler forces are not high enough to pull in-grown because Peach-Ko

Fig. 11. Evolution of planar defects with creep strain. (a) Number density of planar faults per area nPF/am. (b) Projected area fractions APF. (c) Intensity parameter IPF.

misfit dislocations away from g/g0 -interfaces. Moreover, at elevated temperatures, climb processes help dislocations to overcome constraints imposed by crystallographic slip and by microstructural irregularities.

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Fig. 12. TEM micrographs of dislocation events. (a) Dislocation expanding along g-channel in (111) plane of TEM foil e 0.2% strain. (b) Irregularly located g0 -particles impedes dislocation motion e 0.2% strain. (c) g0 -phase cutting by dislocations e 1% strain. (d) High dislocation densities in all g-channels after 5% strain. Central g0 -particle contains planar faults and dislocations.

4.2. Time spent at the first local minimum The time spent close at the first local minimum shown in Fig. 1b and c, which separates stages I and II of DM-creep, is of the order of 30 min. It should be kept in mind that this time spent at the first creep rate minimum does not represent an incubation period, where no strain accumulates. Other research have observed incubation periods [37,49]. Leverant and Kear [37] associated such incubation periods with the time required to produce new dislocations. After introducing a high dislocation density by applying shock waves, Leverant and Kear [37] no longer observed such incubation periods. Pollock and Argon [49] suggested that during such incubation periods dislocations emanate from ingrown nests of dislocations (see Fig. 8 of [49]). Our montage of TEM micrographs presented in Fig. 7 suggests that the increase of dislocation density can also be associated with the activity of local sources. The time spent at the first minimum suggests that diffusion processes are involved. Based on our TEM observations in Figs. 3, 7a and 12b, it seems reasonable to assume, that interface dislocations can climb in vertical g-channels along g/ g0 -interfaces to reach the next horizontal g-channels where they can resume glide and act as dislocation sources. In order to assess this hypothesis, we consider a dislocation climb process, which takes 30 min (1800 s) and involves diffusion over a typical g0 particle distance (e.g. 0.2  106 m). Using the well-known equation

x2 ¼ 4$D$t

(5)

where x is the diffusion distance, D is an appropriate diffusion coefficient and t is the diffusion time. This yields a diffusion coefficient D of 0.6  1017 m2/s, which is reasonably close to the values of diffusion coefficients reported for relevant d-shell elements in Ni [5,54]. We do not expect that this calculated diffusion coefficient fully matches literature Ni-data [5,54]. But our rough estimate shows that the time spend at the first local minimum may well be related to short range diffusion processes which govern dislocation climb. In the present study we take advantage of the (111) TEM foils which show dislocations which glide in the plane of the TEM foil. The TEM micrograph in Fig. 12a shows one typical situation, which allows to estimate local stresses opposing the expansion of one dislocation loop with different local curvatures highlighted by white arrows in position 1 (r ¼ 27 nm) and position 2 (r ¼ 55 nm). It is straightforward to calculate local Orowan stresses associated with these two local curvatures. Taking a shear modulus of 100 GPa and a Burgers vector of 0.254 nm allows us to calculate local Orowan stresses of 376 (position 1) and 185 MPa (position 2). These stresses resist loop expansion. The resolved shear stresses which promote dislocation glide must be calculated considering the superposition of the external stress (326 MPa) and different shear stress components associated with horizontal (position 1) and

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Fig. 13. TEM micrographs of planar faults. (a) Centered dark field image. Example for stacking fault analysis e 0.2% strain. (b) Two planar faults marked by white arrows spread out in the (111) plane of the TEM foil e 1% strain. (c) Microstructural evidence for planar faults in g0 -particles originating from g-channel dislocations e 2% strain. (d) High resolution TEM image showing a planar fault in the g0 -phase e 1% strain.

vertical (position 2) g-channels (20 and 200 MPa, respectively). The result of this first order approximation shows that the resolved shear stress which acts in horizontal channels is 346 MPa, while only 126 MPa act in vertical channels. This is why in Fig. 12a, the loop cannot expand in the two highlighted locations.

4.3. Increase of creep rate in stage II of DM-creep, dislocations and planar faults In stage II of DM-creep, the creep rate increases up to an intermediate maximum. This early increase of creep rate has been reported in several studies [13e19,22]. It is clear from Fig. 2, that this increase of creep rate is not associated with rafting, the directional coarsening of the g0 cubes [e.g. 3e5, 12]. Our results presented in Figs. 10 and 11 clearly suggest that the increase of creep rate in stage II of DM-creep is associated with an increase of both, g-channel dislocation density and the density of planar faults in g0 -particles, Figs. 10b and 11 a to c. The formation of planar faults as a result of the cutting of ordered phases by dislocations has received considerable attention throughout the last five decades [17,18,20-22,37,38,41,42,55-79]. This particularly holds for the shearing of g0 -particles in Ni-base SX. The topic has been covered in text books and overview articles [e.g. 4, 5, 12]. There are different types of planar defects, including anti phase boundaries (APBs), superlattice intrinsic and extrinsic stacking faults (SISFs and SESFs) and complex stacking faults (CSFs). Several authors have proposed that a$½112 dislocation ribbons (decomposed into two a=2$½112 ribbons) are involved in the shearing of the g0 -phase [4,12,18,22,59]. Each of the two a=2$½112 ribbons can form by a reaction of two ordinary g-channel

dislocations:

h i h i a=2$½101 þ a=2$ 011 ¼ a=2$ 112

(6)

This part of the total planar fault can further decompose

h i h i h i a=2$ 112 ¼ a=3$ 112 þ a=6$ 112

(7)

and it has been suggested, that a leading a=3$½112 dislocation enters the g0 -phase creating a SISF while the trailing a=6$½112 dislocation remains at the interface (Fig. 3a of [22]). The second part of the overall a$½112 fault also represents a dislocation ribbon

h i h i h i a=2$ 112 ¼ a=6$ 112 þ a=3$ 112

(8)

When available driving forces are high enough, the leading partial a=6$½112 of this second fault can push the a=6$½112 interface dislocation of the first fault into the g0 -particle, such that a SISF/APB/SESF-ribbon forms (Fig. 3b of [22], Fig. 12 of [59], Fig. 8 of [60]). Once this four-dislocation-assembly has moved through the g0 -phase, the order of the L12-phase is re-established. Alternatively it has been proposed that a=2$½101 dislocations cut into the g0 phase [67] and create an APB, as was first reported by Gleiter and Hornbogen [56e58]. Then, in a second step, the a=2$½101 dislocation dissociates, which creates an SISF between a leading a=3$½211 and a trailing a=6$½1 2 1 dislocation segment (Fig. 12 of [67]).

h i a=2$½101 ¼ a=3$½211 þ a=6$ 12 1

(9)

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Fig. 14. Misfit dislocation model. (a) Dislocations in two slip systems. (b) 2D projection of g/g0 model system with misfit dislocations. (c) Reaction of misfit dislocations to applied load. (d) Annihilation of misfit dislocation in vertical channels.

The SISF eventually consumes all of the APB area and only the SISF remains. It seems reasonable to assume that a second a=2$½110 dislocation can follow (splitting up in a similar way) and can restore the order of the lattice. The fact that we find both SISFs and SESFs in Figs. 4, 6 and 13 can be interpreted in the light of both scenarios briefly outlined above, the one proposed in Refs. [22,59] (〈112〉 cutting) and the other suggested by Ref. [67] (〈101〉 cutting). The results presented in Fig. 6 and Table 3 are relevant in this context. Fig. 6 shows a region of a g/g0 -microstructure after 1% strain, which represents a material state close to the intermediate creep rate maximum. According to the results reported in Fig. 11, there are optimum conditions for the formation of planar faults. The results presented in Fig. 6 and Table 3 show that different types of a/2 〈101〉 dislocations are present at the g/g0 -interfaces. In contrast, a/2 〈112〉 type of dislocations are not observed. The invisibilities of faults 10 and 11 reported in Table 3 do not allow to differentiate between the three types of 〈112〉 fault vectors in plane ð11 1Þ, namely ½1 21, ½112 and ½211. The fault vectors ½112 proposed at the bottom of Table 3 can be directly related to the Burgers vectors of dislocations 3 and 5, which can react and form an a=2$½112 dislocation as required in a scenario outlined by Equations (6) and (7). These fault vectors support the scenario proposed by Rae and Reed [22]. If the actual fault vectors were of type ½211,

they would support the mechanism suggest by Decamps et al. [67], where the cutting event is triggered by the penetration of an a/2$ 〈101〉 dislocation from g-channel into the g0 -particles. Further work is required to collect additional data, which allow to differentiate between the two cutting mechanisms, which do have SISFs in common. g0 -phase cutting can also result in the formation of SESFs [67]. A combination of SISF/SESF-cutting events has also been reported [69], and it has been claimed that CSFs can form, which can promote the formation of deformation twins [69]. The evidence gained in the present work supports cutting scenarios where SISFs and SESFs play a role. Which types of dislocations manage to enter the g0 -phase and which types of planar faults form depends on the possibility of appropriate dislocation reactions to occur prior to cutting. It also depends on the magnitude of APB-, SISF-, SESF- and CSF-energies. The dislocation reactions which can trigger cutting events depend on line energies, on local resolved shear stresses and on local dislocation densities [47,48]. Each individual cutting event depends on the local stress state, which is influenced by the external stress, the misfit stress and the stress fields of other dislocations [26,27]. Many of the relevant parameters which govern the formation of faults have been discussed in the literature, a recent publication has

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associated differences in g0 -phase cutting events in Co- and Ni-base SX with differences in APB- and SISF-energies [42]. It has been reported that the formation of planar faults can trigger local displacive transformations in the g0 -phase [75]. It has also been reported that atomic re-ordering and segregation of alloy elements can alter planar faults [77e80], this implies that planar fault energies can change during high temperature exposure. Moreover, it has been shown that there is a strong dependence of fault energies on local fault chemistry [76]. A coupling between cutting events and short range diffusion must therefore also be considered [77,79]. 4.4. On the composite character of Ni-base SX The experimental results presented in Figs. 10 and 11 suggest, that acceleration of creep rate in stage II of DM-creep is related to the increase of the overall density of dislocations. This corresponds to a classical alloy-type of primary creep scenario [81], where solid drag forces limit the rate of dislocation glide and creep rates increase as the density of mobile dislocations increases. This broad view does not reflect important details of microstructural evolution which were observed in the present work. Thus, a state-of-the-art discussion of high temperature plasticity in cast Ni-base SX must also account for differences in local alloy composition between prior dendritic and interdendritic regions [24]. This does, however, not affect the chemical compositions of the g0 particles and g channels in these two regions. Instead, this chemical difference is accommodated by slightly lower g0 volume fractions in the dendritic regions [24]. Macroscopically, our cast SX represents a composite material, where stresses are transferred from softer dendritic to stronger interdendritic regions, as schematically illustrated in the central part of Fig. 15. This stress transfer may also contribute to the decrease of creep rate in the early stages of creep. After stress redistribution, the average stress in the interdendritic regions is

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slightly higher. However, g-channel widths and g0 -cube edge lengths show wide distributions, Fig. 3b and c. Therefore, local stress states vary considerably in both regions of the cast microstructure and one can observe similar dislocation processes in both regions. More importantly, SXs also exhibit composite character on the microscale. As is clear from Figs. 7a and 12b, g-channels deform first and g0 -particles, which represent the harder phase, follow. Classical composite materials, like fiber reinforced Al-alloy metal matrix composites (MMCs) [82,83] combine a soft matrix with a hard strengthening phase. It has been discussed in the literature [4,12,84], that the creep rates from g- and g0 -phases are both faster than the creep rates of SXs. This raised the question why combining two soft materials yield a stronger composite. This is related to the fact, that a bulk Ni3Al material contains in-grown dislocations, while the g0 -particles, which form during the multiple step heat treatment of SXs, are dislocation free, Fig. 3a. The difficulty to inject dislocations from the cubic face centered g-channels into the ordered and defect free L12 g0 -particles is the key for understanding the good creep resistance of SXs [4,5,12]. There are analogies between threshold events in conventional MMCs and in the g/g0 micro composite. Fiber breakage in the Dlouhy model [82,83] for short fiber reinforced Al-MMCs does not start immediately. Instead, stress transfer from the matrix to the fibers is required, until a critical stress is reached. In case of a g/g0 microstructure, cutting does not start immediately, Figs. 10c and 11c. Stress transfer from plastically deformed g-channels to the dislocation free g0 -particles must precede g0 -phase cutting. Eventually, at higher strains, the two phases which deform in parallel must accumulate similar amounts of plastic strain. For the case of a Co-based SX, subjected to a total creep strain of 0.6%, Titus et al. [75] estimated the contribution of stacking fault shear to the overall strain as 22%. In view of a composite scenario this value

Fig. 15. Composite character of SX Ni-base superalloys on two length scales. Center: Small differences between prior dendritic and interdendritic regions. Left and right: Micro composites with slightly higher (left: ID) and slightly lower (right: D) g0 -volume fractions.

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The closing of the Rae window [20e22] coincides with the beginning of stage III of DM-creep. In this context it is interesting to compare the TEM micrographs presented in Fig. 8 (0.4% strain, before the intermediate maximum) and 9 (5% strain, at the global minimum). In the (111) TEM montage shown in Fig. 8, a dashed line marks the orientation of the g-channels, which are referred to as horizontal channels during [001] tensile creep loading. Fig. 8 shows that the dislocation density in the horizontal channels is high, while other channels show significantly lower dislocation densities. The local stress states in these other channels keep dislocations out. The montage of TEM micrographs in Fig. 9 shows that all g-channels are filled with dislocations. Dislocations cannot simply enter all channels by glide, Fig. 12a. We therefore conclude that g0 -phase stacking fault shear represents an alternative mechanism which accounts for the increase of dislocation densities in channels with unfavorable local stress states. As empty channels (receiving channels) fill up with dislocations by stacking fault shear (initiated by dislocations from sources in horizontal channels), back stresses build up and it becomes more and more difficult to inject more dislocations into the receiving channels (either by dislocation glide or by stacking fault shear). Therefore, the decrease of creep rate in stage III of DM-creep can be qualitatively rationalized by a combination of elementary processes. First, the closure of the Rae window is one factor. It depends on interactions between source channel dislocations (dislocation stress fields, lack of space for reactions) and on the formation of low energy networks, which stabilize interface dislocation segments. Second, back stresses build up in the receiving channels. Finally, it seems reasonable to assume that the inherent resistance of the g0 -phase to stacking fault shear increases. This may be related to chemical changes on the nanoscale [e.g. 78e80] and also to the increase of the density of dislocations in the g0 -phase, Figs. 9 and 10c.

incubation periods at the beginning of creep. SX researchers were often not too much worried about the early stages of [001] LTHS tensile creep. They took an engineering view and assessed the dependence of primary creep on stress, crystallographic orientation and on microstructural details like g0 -volume fraction [18,22,37,85e87] based on strain time curves like shown in Fig. 1a. Without further analysis, the results presented in Fig. 1a may well lead to the conclusion, that there is an extended period of classical primary creep, which accounts for a strain interval of 3% (methods of how to determine this strain interval have been proposed in the literature [17,37]). There is no doubt that this strain interval is important from a technological point of view. However, this type of analysis neglects subtle features, like the decrease of creep rate towards the first local minimum and the presence of an intermediate maximum. Performing a step wise loading procedure (as documented in British Standard UDC 629.7 and used in Refs. [18,22]) may make it difficult to observe the first local creep rate minimum shown in Fig. 1b and c. In this context it is important to highlight, that creep testing is always associated with a heating period (it takes some time before the system reaches the targeted test temperature) under a small preload (which is required to keep the load line aligned). In high temperature technology, this period is typically much shorter than the duration of a creep test. Test standards require that heating and loading occur in a reproducible manner. In view of the small effects which are in the focus of the present work, the details of this loading period may well be important. In the present work, specimens were heated up to test temperature as fast as possible, pre-loads were much smaller than the test loads and the full test load was applied fast, within only a few seconds. Some of the previous studies which were published in the literature completely lack this type of information. Further work is required to investigate the effect of different types of preloading on the early stages of low temperature and high stress creep. Classical definitions of primary, secondary and tertiary creep [6e12] are not helpful in describing stage I of DM-creep. The results obtained in the present work do not allow to directly relate the start of primary creep to the onset of stacking fault shear [22], because gchannel dislocation plasticity always precedes g0 -cutting. In view of the results obtained in the present work, the opening and closure of the Rae-window rationalizes stage II of DM-creep and represents an inverse or abnormal type of primary creep [88,89]. This inverse primary creep is later followed by an extended period of normal primary creep caused by dynamic strain hardening. The presence of incubation periods of creep during LTHS creep has been repeatedly reported, e.g. for Mar-M200 tested at 690 MPa and 760  C [37] and for CMSX-3 tested at 552 MPa at 800  C [49]. During these incubation periods [37,49] no strain accumulated during a few hours, before creep started. It is difficult to comment on these results [37,49], without a precise description of the creep test procedures (loading, heating). In none of the five experiments performed in the present study such incubation periods were observed. Creep always started directly after the specimens were loaded. It is difficult to understand why no microscopic strain is measured when dislocations spread into previous dislocation free areas [49]. The durations of the incubation periods reported in Refs. [37,49] are of the same of order of magnitude as the time required to reach the beginning of stage II of DM-creep in the present work. Given the importance of creep for all SX applications, further efforts are required to clarify this point.

4.6. On the term primary creep and on incubation periods

5. Summary and conclusions

The results obtained in the present work raise two questions, one related to the term primary creep and another related to

In the present work we use a miniature tensile creep test procedure with precisely oriented [001] tensile specimens (±1 ) to

seems low. The left and right parts of Fig. 15 represent simplified micromechanical analogons for the g/g0 -microstructures in interdendritic and dendritic regions. In the spring dashpot analogon in the upper left of Fig. 15, the extension of the g-dashpot is larger than that of the g0 -dashpot. This captures the essence of the microstructural information contained in Figs. 7a and 12b. The difference in plastic strains is balanced by the difference in elastic deformations of the two phases (springs in the schematic scheme of Fig. 15). This results in a stress transfer from the g-phase to the g0 -phase. This is why stage I of DM-creep is important. It represents experimental evidence for stress transfer from the g-channels to the g0 -particles. As has been elegantly described by Rae et al. [20e22], a window of opportunity opens at the beginning of stage II. As g-channel dislocation densities increase, the number of dislocation reactions which provide 〈112〉 segments for g0 -particle cutting increases. The dislocation density at the beginning of stage II is low enough to allow dislocation reactions to occur. At a strain of 0.4%, the Rae window [20e22] is wide open, Figs. 8 and 11. It closes as channel dislocation densities become so high, that the movement of ribbons is suppressed [22]. This view is fully based on elementary processes in the g-channels, which provide dislocations for cutting. It allows in principle to interpret our quantitative results presented in Fig. 11, where fault densities first increase (Rae-window opens) and then decrease (Rae-window closes). 4.5. Decrease of creep rate towards the global creep rate minimum

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study low temperature (750  C) and high stress (800 MPa) creep (LTHS-creep) of the Ni-base single crystal superalloy ERBO1. Five creep tests were interrupted after strains between 0.1% and 5% and microstructures were investigated using diffraction contrast transmission electron microscopy. From the results obtained in the present work the following conclusions can be drawn: (1) Low temperature and high stress creep starts as soon as the load is applied. No incubation periods of creep were observed. This is not in line with results frequently reported in the literature and further work is required to clarify this point. (2) In LTHS-creep, there is a first sharp decrease of creep rate towards a first local minimum (stage I). Then the creep rate increases and reaches an intermediate creep rate maximum (stage II). It finally decreases towards a global minimum, which is reached after 5% strain (stage III), before creep rates decrease towards final rupture (not investigated in present work). (3) It is difficult to address this unusual type of creep behavior in terms of classical primary, secondary and tertiary creep periods. The present engineering definition of LTHS primary creep encompasses stages I, II and the early parts of stage III of DM-creep. (4) Three elementary processes can contribute to the sharp decrease of creep rate during stage I of DM-creep. First, an exhaustion mechanism, where the high external stresses which govern LTHS creep, pull misfit dislocations away from g/g0 -interfaces. Second, a run and stop mechanism, where favorably oriented dislocation segments start to glide along open g-channels before they hit irregularly positioned g0 particles. Stress transfer from interdendritic (higher g0 volume fraction) to dendritic regions (lower g0 volume fractions) may also contribute. (5) Dislocation plasticity in g-channels always precedes stacking fault shear of g0 -particles. The g/g0 -microstructure represents a composite where stresses are transferred from the gchannels to the g0 -particles. When a critical stress is reached, stacking fault shear starts. (6) Stage II of DM-creep is characterized by an increase of overall dislocation density in the g-channels and an increase of the density of planar faults in the g0 -particles. It is best described by the opening and closing of the Rae-window, as described in the literature [20e22]. (7) The decrease of creep rate in stage III of DM-creep is governed by several elementary processes. There is normal strain hardening in the g-phase. The dislocation density in gchannels is so high that they can no longer integrate new dislocations which arrive by either hampered channel glide or by delayed stacking fault shear. Stacking fault shear itself can become more difficult, because dislocations strain harden the g0 -phase. Moreover, the stabilization of interface dislocation networks and atomic re-ordering processes may slow down stacking fault shear.

Acknowledgement All authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) through projects A1 and A2 of the collaborative research center SFB/TR 103 on superalloy single crystals. X. Wu acknowledges funding by the International Max Planck Research School SurMat. AD acknowledges funding by the Czech Science Foundation under contract no. 14-22834S.

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