Analysis of local microstructure after shear creep deformation of a fine-grained duplex γ-TiAl alloy

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Acta Materialia 58 (2010) 6431–6443 www.elsevier.com/locate/actamat

Analysis of local microstructure after shear creep deformation of a fine-grained duplex c-TiAl alloy D. Peter a,⇑, G.B. Viswanathan a,b, A. Dlouhy c, G. Eggeler a a

Institute for Materials, Ruhr University Bochum, Universita¨tsstraße 150, 44801 Bochum, Germany b Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, USA c Institute of Physics of Materials, Academy of Sciences of the Czech Republic, 61662 Brno, Zizkova 22, Czech Republic Received 10 June 2010; received in revised form 3 August 2010; accepted 5 August 2010

Abstract The present work characterizes the microstructure of a hot-extruded Ti–45Al–5Nb–0.2B–0.2C (at.%) alloy with a fine-grained duplex microstructure after shear creep deformation (temperature 1023 K; shear stress 175 MPa; shear deformation 20%). Diffraction contrast transmission electron microscopy (TEM) was performed to identify ordinary dislocations, superdislocations and twins. The microstructure observed in TEM is interpreted taking into account the contribution of the applied stress and coherency stresses to the overall local stress state. Two specific locations in the lamellar part of the microstructure were analyzed, where either twins or superdislocations provided c-component deformation in the L10 lattice of the c phase. Lamellar c grains can be in soft and hard orientations with respect to the resolved shear stress provided by the external load. The presence of twins can be rationalized by the superposition of the applied stress and local coherency stresses. The presence of superdislocations in hard c grains represents indirect evidence for additional contributions to the local stress state associated with stress redistribution during creep. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium aluminides; Shear creep deformation; Transmission electron microscopy; Dislocations; Twinning

1. Introduction TiAl-based intermetallic alloys are promising materials for high-temperature service in aerospace and automotive applications, owing to their low density in combination with good creep and high-temperature corrosion resistance. The latest generation of these alloys (TNB alloys) contains 5–10 at.% niobium (Nb) to improve strength and oxidation resistance further at elevated temperatures. Furthermore, micro-alloying with boron (B), the addition of carbon (C) and optimized processing routes (e.g., canned hot-extrusion) further improve creep resistance [1–5]. The creep behavior of c-TiAl alloys strongly depends on the alloy composition and the specific microstructure which forms ⇑ Corresponding author. Tel.: +49 0234 3228982; fax: +49 0234 3214235. E-mail address: [email protected] (D. Peter).

during the thermo-mechanical treatment [6–10]. Alloys with duplex microstructures, consisting of equiaxed c and lamellar a2/c colonies, have been considered for technical applications because they have good creep resistance in combination with improved room temperature ductility [6,11]. Different elementary processes contribute to creep strain accumulation at various temperatures and stresses. Creep in c-TiAl intermetallics is strongly affected by their tetragonal L10 crystal lattice. Ordinary dislocations (Burgers vector b = 1/2h1 1 0i{1 1 1}c), superdislocations (b = h1 0 1i or b = 1/2h1 1 2i) and mechanical twins (b = 1/ 6h1 1 2i{1 1 1}c) were reported to contribute to the timedependent accumulation of strain during creep [12–15]. For maintaining strain compatibility, shear along h1 1 0i alone is not sufficient. In addition, microscopic shear with a component in the c-direction of the L10 lattice (such as h0 1 1i and h1 1 2i) is necessary [16]. This c-component of the deformation can be provided by h0 1 1i and 1/2h1 1 2i

1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.08.005

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superdislocations and/or by 1/6h1 1 2i{1 1 1} twins [17]. The deformation of lamellar colonies has been reported to be highly anisotropic [18–20]. In poly-synthetically twinned crystals, higher yield strengths were observed for lamellar boundaries parallel or perpendicular to the direction of the applied stress than for inclined boundaries [21– 24]. In lamellar colonies, mutually rotated c lamellae coexist with a2 lamellae. The a2/c coherency is governed by the Blackburn orientation relationship (OR) ð0 0 0 1Þa2 ||{1 1 1}c and h1 1  2 0ia2 ||h1 1 0ic [25]. The crystallographic misfit associated with this c/c and c/a2 arrangement results in coherency stresses [26], and, depending on the specific orientations of lamellae, different deformation structures such as h1 1 0i ordinary dislocations, h0 1 1i superdislocations and 1/6h1 1 2i{1 1 1} twins have been observed [8,9,14,17]. The TiAl system has been extensively studied during the last two decades, and it has been shown that local dislocation configurations at lamellar interfaces can only be interpreted when coherency stresses are taken into account [27]. However, no effort was made to calculate local resolved shear stresses accounting for the presence of coherency stresses. The present study makes an attempt to rationalize local defect configurations on the basis of local stress states, which account for misfit at c/c and a2/ c boundaries. The results are discussed in the light of previous work published in the literature, and directions for further work are pointed out. 2. Material and experiments The c-TiAl alloy investigated in the present study was provided by Dr. W. Smarsly, MTU Aero Engines GmbH (Munich), and Dr. A. Otto, GfE Metalle und Materialien GmbH (Nuremberg). It is referred to as TNB-V5 and has the nominal composition Ti–45Al–5Nb–0.2B–0.2C (in at.%). The material was received as a hot-extruded cylindrical bar with a very fine duplex microstructure. A double shear creep sample was machined from the bar using spark erosion such that the shear direction was parallel to the extrusion direction. Shear creep testing was performed at a temperature of 1023 K (±1 K) and a shear stress of 175 MPa. The experiment was taken through to a shear strain of 20% (shear strain resolution 104). A description of the shear sample geometry and the shear test procedure is given elsewhere [28,29]. The as-received material was investigated using scanning electron microscopy (SEM). The SEM sample was electropolished at room temperature using a solution consisting of 600 ml methanol, 360 ml butyl glycol and 60 ml perchloric acid at 30 V for 24 s. SEM backscatter micrographs were taken using a LEO 1530 VP operating at 29.5 kV at a working distance of 4 mm. The creep test was terminated by cooling the specimen under load to preserve the defect structure for subsequent TEM analysis. Foils for TEM observations were prepared from thin discs taken perpendicular to the shear stress axis of the crept sample. The foils were prepared by twin-jet

thinning, using the solution specified above at a temperature of 258 K while applying a voltage of 20.5 V for 5 min. TEM was conducted using a Philips CM20 microscope operating at 200 kV. 3. Experimental results 3.1. As-received material and creep deformation Hot-extrusion of the investigated c-TiAl alloy TNB-V5 at T > 1473 K results in a fine duplex microstructure with lamellar a2/c colonies and equiaxed c grains which are often subdivided by annealing twins. In addition, some a2 phase is present at the c grain boundaries. The microstructure of the as-received material is shown in the SEM backscatter electron micrograph in Fig. 1. The material exhibits an anisotropic microstructure with an alignment of lamellae parallel to the extrusion direction. The average grain area of the equiaxed c grains is 5 lm2. The lamellar colony areas were determined as 20 lm2 perpendicular and 40 lm2 parallel to the extrusion direction. The average lamellar spacing is 0.3 lm. The volume fraction of lamellar colonies varies between 25% and 35%. A detailed quantitative metallographic characterization of the as-received material is given elsewhere [30,31]. A plot of the logarithmic shear creep rate as a function of shear strain is shown in Fig. 2. The creep test was interrupted after a shear strain of 20%. The creep curve shows a primary creep regime where the shear creep rate steadily decreases, followed by a prolonged secondary creep regime with only a mild increase in creep rate. The moderate increase in creep rate shows that microstructural creep softening is not pronounced and allows for the conclusion that necking did not affect the creep experiment.

Fig. 1. SEM backscatter electron micrograph of the hot-extruded, asreceived Ti–45Al–5Nb–0.2B–0.2C. The initial material exhibits a duplex microstructure consisting of small equiaxed c grains and lamellar a2/c colonies. In addition, small amounts of a2 phase are present at c grain boundaries.

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the center (dark bands extending from left to right) are of h1 1 2i{1 1 1}-type. In Fig. 3, where ordinary dislocations and twins are present, no superdislocations are detected. In contrast, in grains without twins, contrast analysis suggests the presence of h0 1 1i superdislocations in addition to the 1/2h1 1 0i ordinary dislocations. This is shown in Fig. 4a, where the b = 1/2h1 1 0i ordinary dislocations and the b = h0 1 1i superdislocations are clearly visible at g(2 0 0). The ordinary dislocations are out of contrast for g(0 0 2) (Fig. 4b). The superdislocations remain visible and appear to be dissociated (as shown in the magnified rectangle in Fig. 4b). Fig. 2. Shear creep behavior at 750 °C and 175 MPa. The logarithmic shear creep rate is plotted as a function of shear strain. The creep test was interrupted after 68,900 s at a shear strain of 20%.

3.2. Defect structures after creep 3.2.1. Equiaxed c grains Conventional diffraction contrast TEM experiments indicate that most equiaxed c grains exhibit no dislocations. It is not difficult, however, to find grains which contain dislocations and twins. The TEM micrographs in Figs. 3 and 4 show typical deformation substructures as observed in those equiaxed c grains. Dislocations or twins or a combination of both are shown. For example, the TEM micrographs in Fig. 3 indicate that this particular c grain deforms by both twinning and dislocation plasticity. The dislocations, marked by black arrows in Fig. 3a, are ordinary dislocations with Burgers vector b = 1/2h1 1 0i. These dislocations are in contrast when imaged with g(2 0 0). They show no contrast at g(0 0 2), as shown in Fig. 3b. Fig. 3b also proves the absence of superdislocations with b = h0 1 1i. If they were present, they should be in contrast at g(0 0 2) in Fig. 3b. The twins close to

3.2.2. Lamellar colonies The deformation substructures from two specific c lamellae, labeled c1 and c2 in Fig. 5, are now considered. The lamellar interfaces in Fig. 5 are parallel to the incident electron beam. The interface plane was indexed as (1 1 1), and the specific beam direction depends on whether one considers c1 or c2. The OR between lamellae c1 and c2 is determined as [0 1 1]ð1 1 1Þc1 ||[1 1 0]ð1 1 1Þc2 . The crystal lattice of c2 is rotated counter-clockwise (CCW) by 120° around the [1 1 1] axis with respect to c1. The c-axes of the two lamellae are perpendicular to one another. Dislocations and twins are observed within c1. Thin deformation twins (labeled T in Fig. 5) cut across c1. The selected area diffraction (SAD) pattern taken at zone axis B½0  1 1c1 in Fig. 5 (SAD location marked with a little black circle) shows additional spots from these fine twins which are of [1 1 2](1 1 1) type. The two-beam contrast used for the TEM micrograph in Fig. 5 was adjusted for one lamella, and the resulting contrast condition for the other lamella was calculated using the OR (120° rotation around [1 1 1]). Both g vectors are indicated at the top of Fig. 5. For Fig. 5 (and all following TEM micrographs) the g for lamella c1 is given on the upper right of the micrograph,

Fig. 3. Dislocations and twins in an equiaxed c grain: (a) 1/2h1 1 0i ordinary dislocations and h1 1 2i(1 1 1) twins are observed at g(2 0 0) and (b) 1/2h1 1 0i ordinary dislocations are out of contrast at g(0 0 2).

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Fig. 4. Dislocation activity in another equiaxed c grain: (a) both 1/2h1 1 0i ordinary dislocations and h0 1 1i superdislocations are observed at g(2 0 0) and (b) only h0 1 1i superdislocations are observed when imaged with g(0 0 2). The weak beam micrograph (high mag insert in Fig. 4b) of the area marked by the white rectangle suggests that the superdislocations are dissociated.

½1 0  1 ! 1=2  ½1 0  1 þ APB þ 1=6  ½1  1  2 þ SF þ 1=6  ½2 1  1

ð1Þ

It must be pointed out that a twofold decomposition of superdislocations was detected, but it is not intended in the present work to contribute to the discussion of this phenomenon, which has received considerable attention in the literature, e.g., Refs. [32,33]. The dislocation labeled 2 in Fig. 6a also represents a dissociated superdislocation. The closely spaced superpartials can be clearly distinguished in Fig. 6a, b and e when imaged with g(1 1 1), g(0 0 2) and g(2 0 2). The image contrast suggests that superdislocation 2 has a Burgers vector b = h1 0 1i. The corresponding dissociation reaction is ½1 0 1 ! 1=2  ½1 0 1 þ APB þ 1=2  ½1 0 1 Fig. 5. Bright field TEM micrograph showing defects in the lamellar region of the crept specimen. Thin twins (labeled T) are cutting across lamella c1. The insert shows the SAD pattern taken from the encircled region at zone axis B[0 1 1] with extra spots from these twins.

while the corresponding g for lamella c2 appears on the upper left. Lamellae c1 and c2 contain dislocations which were analyzed using the g  b criterion, given in Figs. 6 and 7. The results of the g  b analysis are summarized in Table 1. Five dislocation configurations (numbered 1–5) are in good contrast in lamella c2 (Fig. 6a). Dislocation configurations 1 and 2 are highlighted by white rectangular frames in Fig. 6b and e. Corresponding higher magnification micrographs of these two superdislocations are shown in Fig. 7a–c. The dislocation labeled 1 in Fig. 6a represents a twofold superdislocation associated with the following dissociation reaction:

ð2Þ

The 1/2h1 0 1i superpartials of superdislocation 2 are not further dissociated. The dislocations labeled 3 and 4 are out of contrast with g(0 0 2). They are in contrast for g(1 1 1), g(1 1 1), g(2 0 0), g(2 0 2) and g(2 0 2). It can therefore be concluded that their Burgers vector is b = 1/2h1 1 0i. Dislocation 5 in Fig. 6a shows three invisibilities at g(1 1 1), g(2 0 2) and g(0 2 0). Its Burgers vector is therefore b = h1 0 1i. The dislocations marked U in Fig. 6c are in contrast at g(2 0 0), g(1 1 1), g(0 2 0) and g(2 2 0). They are out of contrast at g(1 1 1), g(2 2 0) and g(0 0 2). This proves that they are ordinary dislocations with Burgers vectors of type b = 1/2h1 1 0i. When imaged with g(0 0 2), no other dislocations were observed. This shows that lamella c1 is free of h1 0 1i superdislocations. 3.3. Resolved shear stresses The experimental results presented in the previous subsections suggest that specific defect structures are observed

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Fig. 6. TEM bright field micrographs taken at different g vectors: (a) five dislocations (numbered 1–5) are observed in lamella c2, (b) superdislocation configurations 1 and 2 are in contrast in lamella c2 (white frame: location of superdislocations), (c) dislocations are in contrast in lamellae c1 and c2. Ordinary dislocations are highlighted by “U” in lamella c1, (d) twins in lamella c1 and ordinary and superdislocations in c2 are in contrast, (e) twins in lamella c1 and ordinary and superdislocations in c2 are in contrast (white frame: location of superdislocations), and (f) ordinary dislocations are in contrast in lamella c2 and out of contrast in lamella c1.

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Fig. 7. TEM g/3g weak beam micrographs taken at different g (indicated on micrographs). (a)–(c) Superdislocation configuration in lamella c2 (frames indicate the corresponding locations in Fig. 6b and e). (d) No twins and dislocations are in contrast in lamella c1 at g(2 2 0).

Table 1 Analysis of dislocations in lamellae c1 and c2 from Fig. 6. Lamella

Dislocation

g1

g2

g3

g4

g5

g6

g7

c1



111

200

1 1 1

020

2 2 0

220

002

c1

U

0

1

1

1

2

0

0

c2

–

111

002

1 1 1

200

2 0 2

202

020

c2 c2 c2 c2 c2 c2 c2 c2

1 1 1 1 2 3 4 5

0 0 1/3 1/3 1 1 1 1

2 1 2/3 1/3 1 0 0 1

2 1 1/3 2/3 0 1 1 0

2 1 1/3 2/3 1 1 1 1

4 2 1 1 0 1 1 0

0 0 1/3 1/3 2 1 1 2

0 0 1/3 1/3 0 1 1 0

in individual lamellae. It seems reasonable to assume that these defect structures depend on local orientations and on local stress states. Three factors affect deformation

Resulting b 1=2  ½1 1 0 ½1 0 1 1=2  ½1 0 1 1=6  ½1 1 2 1=6  ½2 1 1 [1 0 1] 1/2  [1 1 0] 1/2  [1 1 0] [1 0 1]

events and contribute to the driving forces that are required for dislocation and twin activity in lamellar microstructures. These are: (i) the resolved shear stresses related to

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the external load and the local crystallography, (ii) coherency stresses in the lamellar structure due to c/c and c/a2 epitaxy [26,34], and (iii) internal stresses (including compatibility stresses) associated with defect structures that form during deformation [35–37]. The present calculations consider the first two contributions. They do not account for stress redistributions during creep. The calculation focuses on local normalized resolved shear stresses ri;j xy /sc, where ri;j xy is the resolved shear stress on the ith microscopic slip or twinning system in the jth lamella. This resolved shear stress results from a superposition of the external shear stress sc applied in the double shear creep experiment and the local coherency stresses. The micro-mechanical calculations were performed for the two specific orientations of lamellae c1 and c2, and the corresponding ratios rxy/sc (Schmid factors) are plotted in Figs. 8 and 9. The details of the numerical procedure are given in Appendix A. In Figs. 8 and 9, the resolved shear stresses are normalized by sc and are plotted as a function of angle u, which describes the orientation of the external shear plane. A zero-rotation reference shear plane (u = 0) was selected, which contains the shear direction d and a

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perpendicular vector tZR situated in the crystallographic plane (0 0 1) of the lamella c1 (for details, see Appendix A). The calculations were performed for twins and superdislocations; ordinary dislocations were not considered. First, the focus is on twinning and the four twinning systems given in Table 2 are considered. The twinning system DT4 (DT for deformation twinning) is activated in lamella c1 (Figs. 5 and 6). Fig. 8 shows a plot of normalized resolved twinning shear stresses as a function of u. Only the positive range of normalized resolved shear stresses is considered, because twinning only operates in the positive sense of the crystallographic direction and cannot be activated by negative driving forces (e.g., Ref. [15]). The results shown in Fig. 8a were obtained for fully relaxed coherency stresses (rcs = 0; see Appendix A), and, consequently, the normalized resolved shear stresses only depend on the external loading. The angular range is limited to u-values where the twinning mode DT4 (which was observed in the present TEM experiments) is favored, because the associated normalized resolved shear stresses are highest (region depicted by horizontal double arrow in Fig. 8a, between 0.3p and

Fig. 8. Normalized resolved shear stresses for four deformation twinning systems (DT1–DT4) as a function of the shear plane angle u. The gray horizontal region (marked CRSS-DT) indicates the critical normalized resolved shear stresses for twinning. Normalized resolved shear stresses result from: (a) the external load alone (in the absence of coherency stresses) and (b) the superposition of stresses associated with external load and coherency stresses.

Fig. 9. Normalized resolved shear stresses for one mechanical twinning system (DT4 in lamella c1 and DT3 in lamella c2) and eight superdislocation systems as a function of the shear plane angle u. All results were obtained for superimposed coherency stresses of the same intensity as in Fig. 8b. Two threshold domains are indicated. The lower gray threshold regime (CRSS-DT) indicates critical stresses for twinning. The upper gray threshold regime (CRSS-SD) shows critical stresses that are expected to activate superdislocations: (a) lamella c1 and (b) lamella c2.

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Table 2 Deformation twinning systems. System

DT1

Plane Direction

(1 1 1) ½1 1  2

DT2 ð1 1 1Þ  ½1 1 2

DT3 ð1 1 1Þ  ½1 1 2

DT4 ð1 1 1Þ  ½1 1 2

0.75p). As Fig. 8a shows, the resolved shear stresses in the considered angular range fall below the narrow horizontal gray threshold range (marked CRSS-DT), which indicates the normalized critical resolved shear stresses expected for twinning [17,38–41]. Fig. 8a shows that, in the absence of coherency stresses and stress redistributions due to creep, external loading on its own cannot activate mechanical twinning in lamella c1. Fig. 8b differs from Fig. 8a in that the coherency stresses now contribute to the local stress state (rcs = 0.5, see Appendix A). Fig. 8b shows that the normalized resolved shear stresses for twinning can be strongly affected by superimposed coherency stresses. Note that the two twinning modes DT3 and DT4 are promoted by coherency stresses, while the twinning modes DT1 and DT2 are not affected. This result can be readily understood: The coherency stress state P0;1 1 1 (see Appendix A) is dom11 inated by its component P 0;1 , and thus has the character xx of a tensile stress in the direction of [1 1 0]I [26]. Consequently, the stress P0;1 1 1 provides no contribution to systems DT1 and DT2 because their twin plane normals are perpendicular to the [1 1 0]I direction. It is important to highlight that mechanical twinning, which cannot operate under the external stress alone, is activated when coherency stresses are superimposed. The angular ranges where the twinning mode DT4 has the highest normalized resolved shear stresses are similar in Fig. 8a and b. They do not fully coincide because Fig. 8b deals only with situations where twinning mode DT4 can be activated, i.e., where the resulting normalized resolved shear stresses are higher than the required critical resolved shear stresses (gray CRSS-DT range in Fig. 8b). This proves that realistic estimates for coherency stresses rationalize the presence of the twinning system DT4 in lamella c1 (marked with a T on the TEM micrograph in Fig. 5). The u-range identified in Fig. 8b is now considered. In this angular range, the normalized resolved shear stresses that drive the eight families of superdislocations (compiled in Table 3) are compared with the results for the twin systems subjected to the highest shear stress in lamellae c1 and c2. These twinning systems are DT4 and DT3, respectively. Fig. 9 shows the results for the angular range of interest in the presence of coherency stresses which are large enough to promote twinning system DT4 in lamella c1. In Fig. 9,

a narrow horizontal gray threshold range (marked CRSSSD) indicates estimated critical resolved shear stresses associated with superdislocation slip [40,41]. The results shown in Fig. 9a suggest that normalized resolved shear stresses are high enough to activate twinning of system DT4 in lamella c1. Even though the normalized resolved shear stresses of the superdislocation (SD) systems SD8 and SD2 are of the same magnitude, they cannot contribute to the deformation, since they fall below the critical CRSS-SD range. The results shown in Fig. 9b suggest that the resolved shear stresses in lamella c2 are generally not high enough to activate either twinning or superdislocation shear. There is only a limited chance for the highly loaded twinning system DT3 being activated in a narrow angular range between 0.65p and 0.8p. 4. Discussion In the experimental part of the present work, 1/2h1 1 0i ordinary dislocations that do not provide c-component displacements in the L10 lattice were identified. This type of displacement is required, however, to fulfill the von Mises criterion for strain compatibility [16]. h0 1 1i superdislocations can account for this type of c-component deformation [42–44]. The presence of h0 1 1i superdislocations is documented in both equiaxed and lamellar c grains after shear creep deformation. Another way of achieving c-component slip is by twinning [15,45]. Mechanical twinning also allows for creep strain accumulation in the c-direction. Deformation twins are also observed after shear creep deformation in equiaxed and lamellar c grains. These findings are not fully in line with a scenario proposed by Goo [46], who suggested that ordinary dislocations on their own are sufficient to fulfill the von Mises criterion for overall strain compatibility when all three orientation variants occur in the lamellar microstructure. This view cannot rationalize the local deformation structures observed in c lamellae where all three fundamental deformation modes are activated and compatibility stresses play an important role. Another important factor that may influence the local stresses in the microstructure and thus affect deformation modes is related to the texture in the hot-extruded bar [31]. This effect is due to a preferential orientation of c lamellae and has been discussed extensively in the literature, e.g., Refs. [20,47,48]. Further work is required to analyze this contribution quantitatively. Different researchers working on different titanium aluminides come to different conclusions concerning the

Table 3 Superdislocation slip systems. System

SD1

Plane Direction

(1 1 1) ½1 0 1

SD2 ð1 1 1Þ ½1 0 1

SD3 (1 1 1) ½0 1  1

SD4 ð1 1 1Þ ½0 1 1

SD5  ð1 1 1Þ

SD6 ð1 1 1Þ

SD7  ð1 1 1Þ

SD8 ð1 1 1Þ

[0 1 1]

[0 1 1]

[1 0 1]

[1 0 1]

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importance of twinning, ranging from not very important [49] to contributing as much as 30% to the overall creep strain [39,50]. It has also been suggested that superdislocations alone can provide all the c-component displacements required for strain compatibility when their activation is easier than twinning [16]. The present study provides clear microscopic evidence for the simultaneous presence of twins and superdislocations. It appears to be easier to activate twins than superdislocations. But the higher resolved shear stresses required to promote superdislocation activity may well build up during creep, as stresses redistribute from soft to hard regions. Further work is required to clarify this point. Superdislocation glide and twinning are associated with planar faults. As a consequence, the energies of these planar faults are critically important for respective critical resolved shear stresses [40,41]. Thus, superlattice intrinsic stacking fault (SISF) energies are important for 1/2h1 1 2i superdislocations and 1/6h1 1 2i twins. Furthermore, both antiphase boundary (APB) and SISF energies govern the behavior of h0 1 1i superdislocations. APB energies have been shown to be higher than SISF energies in TiAl alloys [40,41]. More extensive twinning has been reported at higher temperatures [8,51], suggesting that, under creep conditions, twinning is absolutely necessary to shoulder c-component shear. This shows that mechanical twinning is not merely a low-temperature/high-stress process. Lower SISF energy is expected to promote twinning. Nb-containing alloys were reported to show a higher intensity of twinning [3,52,53], and it was suggested that this is a result of Nb lowering the SISF energy in TiAl. Whether this applies in the creep regime is not clear. In the present work, an effort was made to rationalize the presence of twins and superdislocations in a specific local lamellar region of a TEM foil. All parameters describing crystallography, loading and lattice coherency were taken into account. The presence of twins and superdislocations has received attention from experimental and theoretical material scientists [8,17–24,35–37], and attempts were made to estimate local coherency stresses near lamellar boundaries by analyzing dislocation shapes based on the line tension model [27]. However, to the best of the authors’ knowledge, this study represents the first effort to integrate coherency and applied stresses into resolved shear stress calculations to rationalize local defect structures. The results show that only half of the original coherency stress is sufficient to promote twinning in favorably oriented lamellae, where twinning could not have been activated as a result of the applied stress alone. Note that the partially relaxed stress state considered in the present study (rcs = 0.5, see Appendix A) results in a contribution to the slip and twinning shear stresses (of 170 MPa; see Fig. 8), which is not far from the value of 130 MPa obtained experimentally previously [27]. Even when coherency stresses partly relax, they may still be large enough to provide essential contributions to the activation of twin-

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ning. The presence of the twins marked with T in Fig. 5 can be explained on this basis. It should be highlighted that while the observation was made after 20% of shear creep deformation, the twins shown in Fig. 5 may well have formed early in the deformation process. Further work is required to clarify this point. In contrast, the presence of the superdislocations shown in Fig. 6 cannot be rationalized by superimposing the applied stress and local coherency stresses. The results shown in Fig. 9 suggest that lamella c2 is in a hard orientation where resolved shear stresses available for twinning and superdislocation glide were initially low. It is well known that stresses in hard regions of this type increase at the expense of local stresses in soft regions of favorably oriented crystallites [54]. It therefore seems reasonable to assume that the presence of superdislocations in lamella c2 represents indirect evidence for stress redistribution during high-temperature plasticity of TiAl-based alloys. Further work integrating micro-mechanical calculations addressing local stress redistribution and the evolution of coherency stresses during creep is required to confirm this assumption. It may be argued that it is tedious to obtain the results summarized in the present work, that the findings are not comprehensive and that the results leave many questions open. But it is this type of combined microstructural and micro-mechanical analysis which is needed to interpret local microstructures in the light of previous seminal contributions [18–20,35–37]. More work is required to progress the field of high-temperature plasticity of titanium aluminides. 5. Summary and conclusions The present work characterizes the microstructure of a hot-extruded Ti-45Al–5Nb–0.2B–0.2C (at.%) alloy with a fine-grained duplex microstructure after shear creep deformation (temperature 1023 K; shear stress 175 MPa; shear strain 20%). From the results obtained in the present study, the following conclusions can be drawn: (1) Ordinary dislocations, superdislocations and twins can be observed using diffraction contrast TEM. Both twins and superdislocations can provide the c-component displacements in L10 lattice that are required to satisfy the von Mises criterion for overall strain compatibility. (2) A procedure is suggested which allows for the calculation of resolved shear stresses for ordinary dislocations, twins and superdislocations while taking crystal orientations, shear loading and coherency stresses into consideration. (3) The presence of twins can be fully rationalized by the superposition of the applied stress and local coherency stresses, even when assuming that initial coherency stresses relax by a factor of two during heat treatment or creep.

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(4) To explain the presence of superdislocations, it is not enough to consider the external shear load and coherency stresses. The presence of superdislocations in hard c grains represents indirect evidence for additional contributions to the overall local stress state associated with stress redistribution during creep.

Acknowledgements The authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) through Project EG 101/ 20-1 and by the Interdisciplinary Centre of Advanced Materials Modelling (ICAMS) through the Advanced Study Group Input Data and Validation. A. Dlouhy acknowledges financial support from the Czech Science Foundation under Contract No. 106/07/0762. Appendix A Normalized resolved shear stresses acting on h1 0 1i{1 1 1} slip systems and on h1 1 2i{1 1 1} twinning systems were calculated in the present study. In the firstorder approximation, the microscopic stresses ri;j xy result from a superposition of coherency stresses P in the lamellar microstructure [26] and external loading L represented by a {x y z} shear plane and the [2 5 2] shear direction in lamella c1. Indices of slip and/or twinning systems always relate to a specific coordinate system of individual lamellae. Hazzledine [26] analyzed the coherency stresses in TiAl/ Ti3Al lamellar microstructures. The coherency stresses P result from crystallographic incompatibility at c/a2 and c/c interfaces. c/c lamellae (slightly tetragonal L10 lattice) adjacent to the common (1 1 1) interface plane are mutually rotated CCW with respect to a common [1 1 1] axis. Rotation angles increase in 60° steps from 0° to 360°, and the corresponding lamellae are referred to as c0, c60, c120, c180, c240 and c300. Three orthonormal {[1 0 0], [0 1 0], [0 0 1]} coordinate systems O, I and II (generally different from each other) are considered. The first coordinate system O is associated with the crystal lattice of lamella c0. This lamella plays a specific role in all the calculations, since the normalized vectors [1 1 0]O, [1 1 2]O and [1 1 1]O of system O compose a basis (the 1 1 1-basis) in which all coherency stress tensors are first represented. The second coordinate system (system I) is associated with lamella c1, and the third coordinate system (system II) with lamella c2. Lamellae c1 and c2 belong to the set {c0, c60, c120, c180, c240, c300}. Based on the experimental results reported in Section 3.2.2, lamella c2 (coordinate system II) is rotated 120° CCW with respect to the common axis [1 1 1]I||[1 1 1]II with respect to coordinate system I (lamella c1). There are three distinct pairs of lamellae with mutual CCW rotations of 120°, pair c0–c120, pair c60–c180 and pair c120–c240. Each of these three pairs thus can represent the pair of lamellae c1 and c2 studied in the present TEM experiments.

Hazzledine’s [26] solution suggests that distinctly different coherency stresses exist in lamellae of a2 phase and in c lamellae (c0, c60 and c120), while lamellae of twin-oriented c variants such as c0–c180, c60–c240 or c120–c300 exhibit identical coherency stress states. Here, general analytic solutions are presented for non-zero P components in lamellae a2 and in c lamellae c0, c60 and c120, which then also apply for the twin-oriented variants c180, c240 and c300, respectively. The solution for individual variants is obtained using the indices j = a2, 0, 60 and 120 for the lamellae a2, c0, c60 and c120:   M j hMðDxx þ Dyy Þi  ðDjxx þ Djyy Þ P jxx ¼ hMi 2   hlðDxx  Dyy Þi j j  ðDxx  Dyy Þ þ lj ðA:1Þ hli   M j hMðDxx þ Dyy Þi  ðDjxx þ Djyy Þ P jyy ¼ hMi 2   hlðDxx  Dyy Þi  ðDjxx  Djyy Þ  lj ðA:2Þ hli   hlDxy i j j  Dxy P xy ¼ 2lj ðA:3Þ hli In Eqs. (A.1)–(A.3), lj are shear moduli, Mj biaxial moduli M j ¼ 2lj ð1 þ mj Þ=ð1  mj Þ, mj Poisson ratios, Dj represent the transformation strains, and hQi is a volume average of a quantity Q. Volume averages are calculated as P hQi ¼ j ðfj Qj Þ, where fj are volume fractions of the corresponding lamellae, and Qj is the value of Q in the jth lamella. Thus, for example, the volume average hlðDxx  Dyy Þi is X hlðDxx  Dyy Þi ¼ fj lj ðDjxx  Djyy Þ ðA:4Þ j

The (stress-free) transformation strains Dj characterize (1 1 1)-plane strain distortions of the c0 crystallographic cell and transform the c0 cell into either the a ro2 cell or ap ffiffiffi tated c p variant. In the 1 1 1-basis ½1 1 0= 2; ffiffiffi pffiffiffi ½1  1 2= 6; ½1 1 1= 3gO , the strains Dj can be represented as (see also Ref. [26]) 0 1 pffiffiffi 1 1= 3 0   p ffiffi ffi 1 c B C ðA:5Þ  1 @ 1= 3 D60 ¼ 1 0A 2 a 0 0 0 0 1 pffiffiffi 1 1= 3 0  1 c B pffiffiffi C ðA:6Þ D120 ¼  1 @ 1= 3 1 0A 2 a 0 0 0 and Da2 ¼



0 1 pffiffiffi a B 1 2 @0 aa2 0

0

1

pffiffi 2=3 2a=aa2 ðc=a1Þ pffiffi 1 2a=aa2

0

0

1

0C A

ðA:7Þ

0

In Eqs. (A.5)–(A.7), a and c are lattice constants of the c phase and aa2 is the a-lattice constant of the hexagonal a2 phase. It is noted in passing that, as a consequence of the

D. Peter et al. / Acta Materialia 58 (2010) 6431–6443

adopted (1 1 1)-plane strain approximation, all the out-ofplane components of the transformation strains are zero and, in particular, D0 ¼ D180  0. The transformation strains (Eqs. (A.5)–(A.7)) and, therefore, also the coherency stresses (Eqs. (A.1)–(A.3)) are sensitive functions of the lattice parameters. A literature survey of lattice parameters was performed focusing on alloy compositions similar to the one investigated in the present study and also on the temperature regime relevant to the present double shear creep experiments. This survey yielded lattice parameters that are summarized in Table A.1. Table A.1 also presents elastic constants and additional microstructural characteristics required in the calculations. It must be mentioned that the calculations assume that the three types of c lamellae occur in equal volume fractions. The stress components P jxx , P jyy and P jxy given in Eqs. (A.1)–(A.3) form tensors Pj;1 1 1 which express the coherency stress states pffiffiin ffi the jth lamella pffiffiffi with respect pffiffiffi to the 1 1 1-basis  ½1 1 0= 2; ½1  1 2= 6; ½1 1 1= 3 O . However, the superposition of coherency and loading stresses requires that all contributions are expressed in one coordinate basis. The superposition is most easily achieved in coordinate basis I of lamella c1. Therefore, the stress states Pj;1 1 1 are transformed to coordinate system O (lamella c0) 1

j;1 1 1 Pj;O ¼ T O  ðT O 111  P 1 1 1Þ

ðA:8Þ TO 111

is given by where the transformation matrix 0 pffiffiffi pffiffiffi pffiffiffi 1 1= 2 1= 6 1= 3 pffiffiffi pffiffiffi pffiffiffi C B O T 1 1 1 ¼ @ 1= 2 1= 6 1= 3 A pffiffiffi pffiffiffi 0 2= 6 1= 3

ðA:9Þ

If lamella c1 was not identical to lamella c0, a second transformation would be needed to represent the coherency stress tensors in coordinate system I: 1

Pj;I ¼ T IO  Pj;O  ðT IO Þ

ðA:10Þ

The transformation matrix T IO would then describe an appropriate transformation between systems O and I, 120 e.g., T 60 O or T O for situations in which lamella c1 corresponds to c60 or c120, respectively. The other important contribution to local stress states in the lamellar microstructure is due to the external doubleshear loading. The results of a careful FEM analysis showed that a substantial part of the deforming zone in a double-shear specimen is subjected to a homogeneous shear stress state [28]. Therefore, in the calculations, it is

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assumed that the loading stress L results from homogeneous shear associated with a shear plane with a unit normal n (the external shear loading plane) and a shear direction d in the macroscopic coordinate system of the specimen. Since the TEM foils were cut perpendicular to direction d, this direction d can be directly related to the by TEM foil normal, which, in lamella c1, is represented pffiffiffiffiffi the normalized crystallographic direction [2 5 2]I/ 33. However, it is experimentally difficult to fix the direction n in the plane of the TEM foil. Therefore, all possible orientations of the external shear loading plane (shear plane normal n) are considered by permitting its rotation around the shear direction d by an arbitrary angle u. Thus, for u in the range 0–2p, all possible shear loading systems are taken into account which share the common shear direction d. In the rotated loading systems {n, d, t} (see Fig. A.1) the loading contribution to the stress state can be represented by a tensor 0 1 0 sc 0 B C Lr ¼ @ sc 0 0 A ðA:11Þ 0 0 0 This stress state is first transformed to a reference (zero rotation) loading system with the coordinate basis {nZR, d, tZR}I, where unit directions tZR and nZR are defined as tZR ¼ d  ½0 0 1=kd  ½0 0 1k and nZR ¼ d  tZR . Note that u equals zero for the reference loading system (see Fig. A.1). The loading stress state after the transformation to the reference (zero rotation) loading system is thus given by  ZR 1 r LZR ¼ T ZR ðA:12Þ r  L  Tr where T ZR r represents the transformation matrix from the rotated to the reference loading system 0 1 cos u 0 sin u B C 0 1 0 A ðA:13Þ T ZR r ¼ @  sin u

0

cos u

In a second step, the tensor LZR is transformed to coordinate system I of lamella c1  1 LI ¼ T IZR  LZR  T IZR ðA:14Þ where the transformation matrix 0 1 nZR;1 d 1 tZR;1 B C T IZR ¼ @ nZR;2 d 2 tZR;2 A nZR;3 d 3 tZR;3

ðA:15Þ

Table A.1 Input parameters for calculations of resolved shear stresses. Quantity Value Reference a b

1073 K. 1373 K.

lc/la2 (GPa/GPa) 70.4/57.0 [26]

mc/ma2 0.236/0.295 [26]

f0 = f60 = f120 0.27 [55]

fa2 0.19 [55]

a (nm) a

0.4044 [56]

c (nm) a

0.4078 [56]

aa2 (nm) 0.5793b [56]

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D. Peter et al. / Acta Materialia 58 (2010) 6431–6443

shear stresses in lamella c2. However, one additional transformation is required before the stress state can be defined with regard to the microscopic system of lamella c2:  1 120;I r120;II ¼ T II  T II ðA:18Þ I r I Eq. (A.18) describes the transformation of the combined stress state r120;I (j = 120) from coordinate system I into coordinate system II of lamella c2, using the transformation matrix 0 1 0 1 0 B C 0 1A ðA:19Þ T II I ¼ @0 1 Fig. A.1. Rotation of the shear loading system {n, d, t} by an angle u with respect to the reference system {nZR, d, tZR}.

and nZR,i, di and tZR,i are coordinates of the vectors nZR, d and tZR in the basis I of lamella c1. Here, particular interest is in the driving forces for local deformation processes in lamellae c1 and c2. The calculations of driving forces assume symmetry of the microstructure, where all the three distinct c variants c0, c60 and c120 have equal volume fractions (see Table A.1). As a result of this simplification, the three pairs of c variants that are mutually rotated by 120°, c0–c120, c60–c180 and c120–c240, (and thus can represent lamellae c1 and c2) are all equivalent in terms of stress distributions. Consequently, the adopted symmetry permits the calculations to be limited to only one specific pair of c variants, e.g., the pair c0– c120, and in what follows, the lamellae index j represents only this c pair (j = 0, 120). Since, as a result of the transformations described by Eqs. (A.8), (A.10), (A.12), and (A.14), both contributing stress states Pj;I and LI are represented in the same coordinate system I of lamella c1. The two stresses can now be superimposed to approximate a real stress distribution in the loaded lamellar microstructure rj;I ¼ LI þ rcs  Pj;I

ðA:16Þ

The factor rcs in Eq. (A.16) accounts for an expected relaxation of coherency stresses due to interfacial dislocation networks [34] and can acquire values in the range 0–1. The stress state rj;I for j = 0 can now be transformed directly into microscopic slip and twinning systems (sorted by the index i) of lamella c1 ri;0 ¼ T iI  r0;I  ðT iI Þ1

ðA:17Þ

T iI in Eq. (A.17) are transformation matrices between coordinate system I of lamella c1 and coordinate frames {ei,1, ei,2, ei,1  ei,2} of the microscopic systems. Note that the unit vectors ei,1 and ei,2 represent the ith slip (twinning) plane normal (“1”) and the slip (twinning) direction i;0 (“2”). Consequently, components ri;0 reprexy of tensors r sent required resolved shear stresses in lamella c1. The same procedure is also applicable for the analysis of resolved

0

0

Now, in close analogy to Eq. (A.17), the stress state in the microscopic system of lamella c2 can be calculated as  1 ðA:20Þ ri;120 ¼ T iII  r120;II  T iII Eq. (A.20) allows for the derivation of the driving forces of the ith dislocation slip or mechanical twinning system in the c2 lamellae. References [1] Paul JDH, Appel F, Wagner R. Acta Mater 1998;46:1075. [2] Appel F, Lorenz U, Paul JDH, Oehring M. In: Kim YW, Dimiduk DM, Loretto MH, editors. Gamma titanium aluminides 1999. Warrendale (PA): TMS; 1999. p. 381. [3] Zhang WJ, Appel F. Mater Sci Eng 2002;A329–331:649. [4] Appel F, Oehring M, Wagner R. Intermetallics 2000;8:1283. [5] Nickel H, Zheng N, Elschner A, Quadakkers W. Microchim Acta 1995;119:23. [6] Beddoes J, Wallace W, Zhao L. Int Mater Rev 1995;40:197. [7] Zhang WJ, Deevi SC. Mater Sci Eng 2003;A362:280. [8] Appel F, Wagner R. Mater Sci Eng 1998;R22:187. [9] Worth BD, Jones JW, Allison JE. In: Kim YW, Wagner R, Yamaguchi M, editors. Gamma titanium aluminides. Warrendale (PA): TMS; 1995. p. 931. [10] Kim YW. JOM 1989;41:24. [11] Kim YW. JOM 1994;46:30. [12] Morris MA. Philos Mag 1993;A68:259. [13] Morris MA, Leboeuf M. Intermetallics 1997;5:339. [14] Morris MA, Lipe T. Intermetallics 1997;5:329. [15] Skrotzki B. Acta Mater 2000;48:851. [16] Mecking H, Hartig C, Kocks UF. Acta Mater 1996;44:1309. [17] Jin Z, Bieler TR. Philos Mag 1995;A71:925. [18] Fujiwara T, Nakamura A, Hosomi M, Nishitani SR, Shirai Y, Yamaguchi M. Philos Mag 1990;A61:591. [19] Inui H, Nakamura A, Oh MH, Yamaguchi M. Philos Mag 1992;A66:557. [20] Kishida K, Inui H, Yamaguchi M. Philos Mag 1998;A78:1. [21] Kim HY, Wegmann G, Maruyama K. Mater Sci Eng 2002;A329– 331:795. [22] Wegmann G, Yamamoto R, Maruyama K, Inui H, Yamaguchi M. In: Kim YW, Dimiduk DM, Loretto MH, editors. Gamma titanium aluminides 1999. Warrendale (PA): TMS; 1999. p. 717. [23] Paidar V. Interface Sci 2002;10:43. [24] Nomura M, Kim MC, Vitek V, Pope DP. In: Kim YW, Dimiduk DM, Loretto MH, editors. Gamma titanium aluminides 1999. Warrendale (PA): TMS; 1999. p. 67. [25] Blackburn MJ. In: Jaffee RI, Promisel NE, editors. Technology and application of titanium. Oxford: Pergamon; 1970. p. 633. [26] Hazzledine PM. Intermetallics 1998;6:673.

D. Peter et al. / Acta Materialia 58 (2010) 6431–6443 [27] Appel F, Christoph U. Intermetallics 1999;7:1173. [28] Peter G, Probst-Hein M, Kolbe M, Neuking K, Eggeler G. Mat-wiss u Werkstofftech 1997;28:457. [29] Mayr C, Eggeler G, Webster GA, Peter G. Mater Sci Eng 1995;A199:121. [30] Peter D, Pfetzing J, Wagner MFX, Somsen C, Pesˇicˇka J, Skrotzki B, et al. Prakt Metallogr 2008;45:210. [31] Peter D, Pfetzing J, Wagner MFX, Eggeler G. Mater Sci Eng 2009;A510–511:368. [32] Court SA, Vasudevan VK, Fraser HL. Philos Mag 1990;A61:141. [33] Veyssie`re P, Douin J. In: Westbrook JH, Fleischer RL, editors. Intermetallic compounds, vol. 1. Chichester: John Wiley; 1995. p. 3. [34] Kad BK, Hazzledine PM. Philos Mag Lett 1992;66:133. [35] Schlo¨gel SM, Fischer FD. Philos Mag 1997;75:621. [36] Paidar V, Imamura D, Inui H, Yamaguchi M. Acta Mater 2001;49:1009. [37] Paidar V, Yamaguchi M. Mater Sci Eng 2007;A462:460. [38] Farenc S, Coujou A, Couret A. Philos Mag 1993;A67:127. [39] Dlouhy´ A, Kucharˇova´ K, Brˇezina J. Mater Sci Eng 2001;A319– 321:820. [40] Yuan Y, Liu HW, Zhao XN, Meng XK, Liu ZG, Boll T, et al. Phys Lett 2006;A358:231. [41] Zhang WJ, Appel F. Mater Sci Eng 2002;A334:59. [42] Rudolf T, Skrotzki B, Eggeler G. Mater Sci Eng 2001;A319–321:815.

[43] [44] [45] [46] [47]

[48] [49] [50] [51] [52] [53] [54] [55] [56]

6443

Orlova´ A, Kucharova´ K, Dlouhy´ A. Z Metallkd 2004;95:1011. Viguier B, Hemker KJ. Philos Mag 1996;A73:575. ¨ nal M, Eggeler G. Scripta Mater 1998;39:1023. Skrotzki B, U Goo E. Scripta Mater 1998;38:1711. Thomas M, Naka S. In: Kim YW, Dimiduk DM, Loretto MH, editors. Gamma titanium aluminides 1999. Warrendale (PA): TMS; 1999. p. 633. Muto S, Yamanaka T, Johnson DR, Inui H, Yamaguchi M. Mater Sci Eng 2002;A329–331:424. Lu M, Hemker KJ. Acta Mater 1997;45:3573. Orlova´ A, Kucharova´ K, Dlouhy´ A. Mater Sci Eng 2008;A483– 484:109. Singh SR, Howe JM. Philos Mag Lett 1992;65:233. Appel F. In: Ankem S, Pande CS, editors. Advances in twinning. Warrendale (PA): TMS; 1999. p. 171. Zhang WJ, Liu ZC, Chen GL, Kim YW. Mater Sci Eng 1999;A271:416. Nix WD, Ilschner B. In: Haasen P, Gerold V, Kostorz G, editors. Strength of metals and alloys, vol. 3. Exeter: Wheaton; 1980. p. 1503. Peter D, Wagner MFX, Eggeler G. Prakt Metallogr Sonderbd 2008;40:317. Novoselova T, Malinov S, Sha W, Zhecheva A. Mater Sci Eng 2004;A371:103.