Mechanical twinning in Ni-based single crystal superalloys during multiaxial creep at 1050 °C

Mechanical twinning in Ni-based single crystal superalloys during multiaxial creep at 1050 °C

Author’s Accepted Manuscript Mechanical Twinning in Ni-based Single Crystal Superalloys during Multiaxial Creep at 1050°C Jean-Briac le Graverend, Flo...

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Author’s Accepted Manuscript Mechanical Twinning in Ni-based Single Crystal Superalloys during Multiaxial Creep at 1050°C Jean-Briac le Graverend, Florence PettinariSturmel, Jonathan Cormier, Muriel Hantcherli, Patrick Villechaise, Joël Douin www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(18)30305-8 https://doi.org/10.1016/j.msea.2018.02.086 MSA36173

To appear in: Materials Science & Engineering A Received date: 23 December 2017 Revised date: 20 February 2018 Accepted date: 22 February 2018 Cite this article as: Jean-Briac le Graverend, Florence Pettinari-Sturmel, Jonathan Cormier, Muriel Hantcherli, Patrick Villechaise and Joël Douin, Mechanical Twinning in Ni-based Single Crystal Superalloys during Multiaxial Creep at 1 0 5 0 ° C , Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.02.086 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Mechanical Twinning in Ni-based Single Crystal Superalloys during Multiaxial Creep at 1050°C

Jean-Briac le Graverenda*,Florence Pettinari-Sturmelb, Jonathan Cormierc*, Muriel Hantcherlib, Patrick Villechaisec, Joël Douinb

a

Texas A&M University, Departments of Aerospace Engineering and Materials Science & Engineering, TAMU 3141, College Station, TX 77843, USA b

CEMES CNRS University of Toulouse, INSA, 29 Rue Jeanne Marvig, 31055 Toulouse, Cedex 4, France

c

Institut Pprime, CNRS-ENSMA-Université de Poitiers, UPR CNRS 3346, Département Physique et Mécanique des Matériaux, ISAE-ENSMA-Téléport 2, 1 avenue Clément Ader, BP 40109, 86961 FUTUROSCOPE CHASSENEUIL cedex, France

[email protected] [email protected]

*

Corresponding author. Tel.: +1 (979)-845-1703; fax: +1 (979)-845-6051 Corresponding author. Tel.: +33 (0)5-49-49-80-97; fax: +33 (0)5-49-49-82-38

*

Abstract: Multiaxial high-temperature creep tests have been performed at 1050°C on a first-generation Ni-based single-crystal superalloy through the use of asymmetric notched specimens. Mechanical twins have been observed by EBSD and TEM analyses. A finite element simulation in a crystal plasticity framework has also been carried out to better understand the

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presence of mechanical twins at stress concentrators depending on stress triaxiality, plastic strain rate, and damage level.

Keywords: Nickel base single crystal superalloy; Mechanical twinning; Deformation mechanism; Creep; High temperature

1. Introduction The development and exploitation of gas-turbine blades casted from Ni-based superalloys in single crystal form has been one of the most successful industrial and commercial ventures relating to advanced structural materials over the last twenty years. These limiting components are used in the hot sections of gas-turbine engines and are, therefore, subjected to high-temperature creep deformation in addition to multiaxial loading due to both their intricate geometry and their advanced design, such as internal cooling channels, aimed to increase the exhaust-gas temperature during service operations. Therefore, in addition to the stress, temperature, and microstructure gradients developing because of the complex thermomechanical environment [1, 2], cooling channels acting as stress concentrators require a better understanding of the mechanical behavior and damage under multiaxial conditions. Despite this harsh environment, Ni-based single-crystal superalloys offer a high temperature creep resistance for a wide range of temperature/stress regimes [3, 4]. It is attributed to the precipitation of a high volume fraction (close to 70 %) of the long-range ordered L12 ’ phase which appears as cubes coherently embedded in a face-centered cubic (fcc) solid solution γ matrix [5]. Depending on the alloy’s chemistry, the temperature, and the strain rate, the active deformation mode can change significantly under creep conditions [6, 7]. However, the plastic deformation of the strengthening γ’ phase is often considered as a damaging process

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[8, 9]. Two regimes of temperature can be considered and come along with their specific deformation mechanisms: low/intermediate (T < 900°C) and high-temperature regimes (T ∈ [900,1150]°C). Independently of the creep condition, creep deformation always occurs first in the γ phase by extremely planar slip of either strongly or weakly paired 1/2110 dislocations which can dissociate for shearing the ’ phase, creating then superlattice intrinsic and extrinsic stacking faults (SISF and SESF) [10-12]. Contrary to lower temperatures at which the γ’ morphology remains almost stable, γ’ rafting plays a prominent role on the deformation mechanism and rupture life at high temperatures [13-15]. For instance, it was reported that rafting modifies the yield stress in tension for temperatures between 930 and 1040°C because the shearing of the γ’ phase is the principal strain mechanism and is favored by wider γ channels [16]. For sufficiently high stress levels, plasticity may not be restricted only to the γ phase anymore. In fact, the γ’ particles are likely to be sheared by dislocation ribbons of overall Burgers vector 112 dissociated into 1/2110 superlattice partial dislocations separated by intrinsic and extrinsic stacking faults [17, 18], a process which leads to the primary creep stage. However, this strain mechanism only occurs for matrix having low stacking fault energy, which is true for alloys containing rhenium or ruthenium [19] and is not the case for the investigated first-generation MC2 superalloy. In addition to 110 superdislocations, 100 ones may also shear the γ’ phase in the high-temperature regime (T≥ 1000°C) by suppressing 110 dislocations observed at the γ/γ’ interfaces and destabilizing the /’ interfacial dislocation network [2026]. Mechanical twinning is typically a deformation mode that is important at low temperatures and high strain rates [27] and is particularly observed seldom in face-centered cubic (fcc) alloys. In fact, only a few studies reported such a deformation mechanism during creep and almost only in the low/intermediate temperature regime (mainly at 800-850°C and

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up to 950°C) for stresses above 500 MPa [28-33], except for Liu et al. [34] who reported mechanical twinning at 1010°C/248 MPa, and mainly for 110-oriented specimens. In addition, mechanical twins have been observed more often in compression [35-40] than in tension [36-39] in 001-orientated specimens. According to Kakehi [41], it is indeed easier to form twins when a compressive stress is applied along the 001 direction since directional twinning preferentially shears in compression on the ( 111 ) plane in the [ 112 ] direction. Finally, mechanical twinning was found to be one of the main deformation mechanisms operating during out-of-phase thermo-mechanical loading, i.e., compressive load at elevated temperature and tensile load at low temperature [42-52], which is consistent with the experimental results obtained in creep. The observation of mechanical twinning acting as a creep deformation mechanism in Nibased superalloys is, therefore, puzzling and is worthy of an in-depth investigation. It is especially relevant in the very high-temperature creep regime (T ≥ 1000°C) and under multiaxial conditions in order to better understand the strain mechanisms that operate close to stress concentrators as, e.g., cooling holes and profile/shrouds junctions in turbine blades. To the best knowledge of the authors, this is the first time that mechanical twinning is reported in a Ni-based single crystal superalloy at such a very high temperature (1050°C) during creep loading.

2. Experimental procedure 2.1 Material

Experiments were performed on the first-generation Ni-based single-crystal superalloy MC2. Its nominal composition is given in Table 1. Experiments were carried out on specimens which had received the MC2 standard heat treatment (3h/1300°C/air-quenched (AQ) + 6h/1080°C/AQ + 20h/870°C/AQ) leading to a 0.4 µm average γ’ precipitate size and to a 4

70%-average precipitate volume fraction (a typical as-received microstructure is shown in Fig. 1) [53-55]. The testing specimens had a gage length of 14 mm with a prismatic section 4 mm wide and 1.2 mm thick and were oriented close to a 001 crystallographic orientation (deviation less than 5°). All samples were machined from MC2 rods from the same heat master and were heat treated simultaneously (solution+aging treatments).

Table 1: Composition of the MC2 nickel base single crystal superalloy (in wt.%). Ni Cr Co balance 8.0 5.0

Mo W Al Ti Ta 2.0 7.8 5.0 1.5 6.1

Fig. 1: Microstructure of the MC2 single crystal superalloy after the standard heat treatments (as defined in section 2.1).

2.2

Creep experiment

A specimen was designed to generate a non-uniform and multiaxial complex mechanical field by the presence of two asymmetrical notches machined with a radius of 0.9 mm (see Fig. 2). Thus, the γ/γ’ microstructure should evolve according to the local mechanical field generated during the two isothermal conditions investigated, namely 1050°C/F=506 N/σnominal=138 MPa and 1050°C/F=477 N/σnominal=130 MPa. Only the σnominal=138 MPa test was led up to failure and the second one was interrupted in the apparent tertiary creep stage. The creep tests were performed using a test bench equipped with a radiant furnace that is automatically switched off once the specimen is broken to avoid any subsequent microstructure evolution that could occur by maintaining the specimen at high temperature after failure, such as annealing twins. The temperature was controlled using a S-type thermocouple spot-welded in the notched areas of the specimens with a 2°C accuracy [56, 57]. During testing, the overall displacement of the specimens was recorded by a laser extensometer measuring the distance between two flags

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located at the specimens heads (Fig. 3). In addition, the creep set-up allowed the specimen to have transversal displacement and lattice rotation, as it can be seen in Fig.4 where the edges of the specimen are not aligned because of what happened at the center of the specimen. The specimen’s macroscopic loading axis is oriented along the [001] crystallographic orientation and [100] and [010] directions are parallel to the width and thickness of the specimens.

Fig. 2: Schematic illustration of the asymmetric-notched creep specimen used for doing the creep experiments with its dimensions and orientations. Fig. 3: Elongations of the bi-notched specimen presented in Fig. 2 at 1050°C under a constant force of F=506 N (red curve), namely a nominal stress of 138 MPa, and a constant force of F=477 N (blue curve), namely a nominal stress of 130 MPa.

2.3 Microstructure analysis The microstructure analyses were carried out using a JEOL 7000F field emission gun scanning electron microscope operating at 25 kV. The samples were cut parallel to the [001] crystallographic direction and then polished mechanically up to a mirror finish. γ’ precipitates were revealed by a selective dissolution of the γ’ phase using a solution made of 66% HCl, 34% HNO3 at room temperature. Deformation mechanism observations were further conducted at different places of the tested specimens, e.g, Fig. 4. TEM observations were done using a JEOL 2010 transmission electron microscope operating at 200 kV. Thin foils of 10 m x 5 m x 100 nm were extracted by cross-sectioned FIB and normal foils from the gage length of the tested specimens at different locations by means of an electric discharge technique. The thickness of the samples was reduced to below 70 μm by mechanical grinding. The electron transparent foils for TEM were then prepared by twinjet polisher using a solution made by 5% perchloric acid, 35% glycerol in methanol. The polishing conditions were −20 °C and 30 V. EBSD analyses were also carried out using a JEOL 6100 SEM coupled with an OIM post-processing

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software. To achieve a good diffraction quality of the specimens, mechanical polishing up to a mirror finished followed by a chemico-mechanical polishing using a silica-suspension (OPS type) for 1 hour followed by a 1 hour cleaning using distilled water were employed. A particular attention was made to remove the least possible material while polishing.

Fig. 4: Locations of the microstructural observations along with the observation technique used for each of them.

3. Results SEM and TEM observations were first carried out on the failed specimen and away from the crack (see Fig. 5). One can notice that the microstructural state, namely rafts perpendicular to the load axis (Fig. 5 (a)) and cuboidal ’ particles close to the notches (Fig. 5 (b)), is the same than the one in [58]. This microstructural gradient is due to the differences in the magnitude of the local state of stresses that generate different accumulated plastic strain values that are known to drive the kinetics of microstructure evolution [59-61]. In addition, it also appears that the occurrence of a[110] edge dislocations within the ’ rafts is greater close to the crack (compare Fig. 5(d) with Fig. 5(c) and (e)), viz. where the plastic strain is maximum.

Fig. 5: (a) and (b), and (c), (d), and (e) are respectively SEM (blue rectangles) and TEM (green rectangles) observations of the specimen after failure at the locations 1, 2, 3, 4, and 5, as specified in Fig. 4.

Furthermore, an EBSD analysis coupled with SEM observations revealed that the orientations of the ’ rafts matched the local crystallographic orientations (see Fig. 6), as already pointed out by le Graverend et al. [58] and observed by Touratier et al. [62]. Therefore, lattice rotation does not only modify the local mechanical behavior and trigger the

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activation of new slip systems, it also controls the progressive tilting of the /’ interfaces. In addition to the EBSD analysis, TEM (Fig. 7 (a) and (b)) and higher magnification SEM (Fig. 7(c) and (d)) observations were performed in the same area than in Fig. 6, viz. close to the crack path. Wide and long slip bands corresponding to intense plastic activity were observed.

Fig. 6: SEM observations close to the crack at the bottom notch. A rotation of the ’ rafts is highlighted by the red-dotted lines added to the micrographs and related to the lattice rotation that occurred, as highlighted by the EBSD measurement. The color code used in the EBSD map is coded along the macroscopic loading direction (horizontal in the present figure). Fig. 7: TEM ((a) and (b) or green rectangles) and SEM ((c) and (d) or blue rectangles) observations on the failed specimen, respectively in area , and in areas  and , close to the crack and pointing out large slip bands with intense plastic activity.

The area  in Fig. 7 was analyzed in more details via an EBSD analysis (see Fig. 8). Along the path  (see Fig. 8(a)), large bands observed in Fig. 7 have a 60° misorientation with the rest of the lattice (see Fig. 8(b)) which corresponds to micro-twins. In addition, one can also observe a recrystallized area close to the mechanical twins (see Fig. 8(a)). It is shown at the very beginning of the mechanical twinning process in the interrupted experiment that no recrystallization is detected. Thus, the recrystallization is due to the large strain and the high temperature level that trigger dynamic recrystallization, as already observed by Moverare et al. [39] for single crystal superalloys. Indeed, dislocation pile-ups are preferred sites for dynamic recrystallization, since local dislocation gradients are high enough to force the lattice to minimize its free energy by re-orienting itself and forming a new crystal [63]. Mechanical twins have also been observed by TEM (see Fig. 9). Indeed, the pole figures that have been added to Fig. 9(b) clearly show a 60° misorientation between the rafted and the plastic band areas which corresponds to micro-twins.

Fig. 8: EBSD observation of the large bands observed in Fig. 7/area . The profile  in (a) shows that these bands have a 60° misorientation (see (b)) which corresponds to micro-twins. 8

Fig. 9: TEM observations at 100 μm from the crack on the failed specimen. (a) is the general view of the area highlighted in the SEM observation by a blue rectangle. (b) and (c) are magnifications of zones in (a). It has been added pole figures to (b).

The same type of analysis than in Fig. 6 and Fig. 8 was performed on a specimen interrupted at the onset of the apparent tertiary creep stage (see Fig. 10) with the same outcomes: a large lattice rotation occurs between the two notches where the plastic strain is maximum and where the multiaxial state of stresses develops (see profiles  and  in Fig. 10). Also, first evidences of micro-twinning are observed very close to where the plastic deformation is localized (see profiles  and  in Fig. 10), as observed in Fig. 8 and Fig. 9 for the failed specimen. It can also be pointed out that the observed twin is very close to where one of the two cracks initiates, but not too close to the surface which is consistent with previous observations [30, 39, 47, 52]. This highlights the necessity to have a stress concentrator, at least at a mesoscopic scale (crack in the present case), to trigger deformation twinning.

Fig. 10: EBSD observations on an interrupted specimen subjected to 1050°C/σnominal=130 MPa. The two notches show large lattice rotation along the [001]-[111] edge of the stereographic triangle and validated by the plotting of the misorientation profiles  and . In addition, two extra profiles, viz.  and , have been plotted for characterizing a local and isolated misorientation equal to 60°.

4. Discussion It has already been established that mechanical twinning is the principal deformation mechanism during tensile creep tests at low/intermediate temperatures and low applied stresses (~250 MPa) in polycrystalline superalloys [64], e.g., René 104 [65] and René 88DT [66]. The observation of mechanical twinning in Ni-based single crystal superalloy is more seldom because it mainly requires a small number of active slip systems, and, hence, a

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crystallographic orientation that is favorable to single slip (e.g. <112> or slightly misoriented <011> crystals). Thus, twinning generally occurs when slip systems are restricted or when an event increases the critical resolved shear stress (CRSS) so that the stress level required to trigger a mechanical twin is less than for a slip [67]. Because of the lattice rotation toward the [111] crystallographic orientation (see Fig. 10), i.e., along the [001]-[111] boundary of the standard stereographic triangle, the observed twins cannot entirely be due to an increase in the CRSS, i.e., an increase in the shear stress required to shear the γ’ precipitates, since it decreases from [001] to [111], as shown by Osterle et al. [68] based on the relationship proposed by Miner et al. [69]. It is worth pointing out that the twins observed in the present study for an originally 001-oriented specimen solicited in the same direction have been for a local crystallographic orientation of [111], which has been commonly reported for fcc structures [70-72]. When the crystallographic orientation changes from [001] to [111], the number of active slip systems evolves from 8 octahedral slip systems with a Schmid factor of

√ for perfectly [001]-oriented smooth specimens to 6 octahedral

slip systems with a Schmid factor of

√ for perfectly [111]-oriented smooth specimens.

Cubic slip systems are not considered, even if they are observed at the macro-scale, since they are just the macroscopic manifestation of successive cross-slip between {111} slip planes [7375] or collinear annihilation between dislocations with the same Burgers vector gliding in different slip planes [76]. It is, therefore, consistent with the fact that mechanical twins are formed when it is not possible to accommodate the deformation anymore due to a lack of active slip systems, as already reported in nickel-enriched 304 austenitic steel for which twinning was not observed in [001] and [101] grains [77]. In fact, even if the material seems to verify the Taylor’s criterion of 5 independent slip systems to accommodate any arbitrary deformation [78], the criterion was designed for homogeneous, generalized ductility of polycrystalline aggregates at low temperatures and is rate-independent [78, 79]. Thus,

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criterion cannot be fulfilled since the experiments were performed on a single crystal at 1050°C – temperature for which only the glide and climb deformation mechanisms operate – for which the plastic strain rate is locally very fast close the notches. In addition, the  channels become wider during the creep test, namely γ’ rafting, due to an increased amount of plastic strain [58, 80, 81], which lowers the CRSS [82]. Indeed, as shown by Vattre et al. [82] who did dislocation dynamics simulations with different γ-channel widths, the CRSS decreases when the γ channels become wider. The authors found that it exists a strong gliding correlation between pairs of dislocations in the channels. This correlation facilitates the formation of superdislocations and the subsequent process of precipitate cutting. The latter phenomenon is assisted by the dislocations bowing out in the channels. As a result of this mechanism, the CRSS measured in their simulations are strongly dependent on the width of the channels, as also shown by Tinga et al. [83] and Fedelich et al. [84]. This size effect in the process of bowing-assisted cutting was also obtained by Nembach [85] on a different alloy. Therefore, mechanical twinning mainly occurs because the slip systems are restricted, but also because the CRSS is altered by cubic cross-slip and a constriction stress acting on the partial dislocations [86]. Thus, the classic deformation mechanisms that accommodate the plastic deformation are no longer sufficient to accommodate the locally-fast creep rate. Furthermore, Benyoucef et al. [87] and Pessah-Simonetti et al. [88] showed that a low stacking fault energy, as in the MC2 alloy, promotes the splitting of superdislocations in two super Shockley, i.e. 1/3112 dislocations (1/6112 dislocations have also been shown to induce twinning in the ’ structure [89]), separated by a superlattice intrinsic or extrinsic stacking fault (SISF or SESF, depending on the sense of dislocation motion) ribbon instead of the classical dissociation in two superpartials bordering an APB. The accumulation of such stacking faults by successive shear in neighboring slip planes leads to a situation where

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energy minimization favors the formation of new faults alongside existing ones, resulting in the nucleation of thin twins in the ’ phase [64, 90]. A similar result has been obtained by Unocic et al. [91] who found that matrix dislocation decorrelation, viz. 1/2112 dissociating into super Shockley, seems to be a key precursor to micro-twinning. Thus, the combination of localized deformations ahead of crack tip and the thermal assistance drive the formation and propagation of twins, and result in twins localized near fractured surface [31, 92]. Twins have already been preferentially observed to form near crack tips when cracks have reached a certain size [30, 39, 47, 52] which is consistent with what was observed in Fig. 10 where the twin is on the crack path but not too close to the surface, i.e., the notch. The incubation time should be enough so that a sufficient density of dislocations can act as nucleation sites for the twins [37, 41]. Furthermore, the strain level should be sufficient so that the {111}112 viscous slips associated with the deformation twins can extensively occur [40, 93]. Therefore, the microstructure was first saturated with dislocations and, because the recovery rate was not fast enough to bear the deformation, twins was formed in the meanwhile. It is, however, worth noticing that this process seems to be a diffusion-assisted phase transformation, viz. not athermal, even if their formation is very fast [32]. In order to better understand the role played by the multiaxial loading applied, a finite element (FE) simulation for the creep test at 1050°C/F=506 N/σnominal=138 MPa has been performed using the crystal plasticity framework coupled with a damage model developed by le Graverend et al. [58, 94]. The model is based on a partitioning of the macroscopic strain into an elastic and a viscoplastic part and a finite strain theoretical setting, as in [95-98]. The relationships defining the elasticity are written at the macroscale, whereas the viscoplastic constitutive equations are written at the microscale, viz. at the slip system level.  s is the viscoplastic shear strain rate on a given slip system s in which the effective resolved shear stress  effs is obtained by the tensorial product between the macroscopic effective stress tensor

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σs

eff

, calculated using σ and the fourth-order anisotropic damage variable D evolving from 0,

when material is undamaged, to 1, at failure, and the orientation tensor m s , calculated knowing the normal to the slip system plane n s and the slip direction in this plane l s . A nonlinear kinematic x s and an isotropic r s hardening on the system s are also used. The fourthorder anisotropic damage variable D [99-103] is formulated with a density of damage (scalar D) that depends on the hardening variables known to bring to light microstructure evolutions [104-106], verifies the second law of thermodynamics, i.e. D  0 , and is based on the Rabotnov-Kachanov’s formalism [107, 108]. The model only uses octahedral slip systems and lattice rotation is not considered. The crystal plasticity and the damage models were calibrated at 1050°C on the alloy investigated in this study, viz. the MC2 alloy, using creep; strain-controlled mechanical cycling; stress relaxation; and tensile tests. Therefore, the parameters used in the flow rule, the kinematic and isotropic hardenings, the kinetics of rafting, and the damage density function are all specific to the considered alloy. The mesh (17,228 linear tetragonal elements, i.e. C3D4, having an approximate size of 0.08 mm close to the notches) and the boundary conditions are highlighted in Fig. 11. The simulation predicted a failure after 17.8h compared to the experimental failure at 17.9h (see Fig. 12). The numerical results are qualitatively consistent with the experimental result (see Fig. 10), namely the crack initiated at the notches where the accumulated plastic strain (see Fig. 12(a)) and the damage level (see Fig .12(b)) were maximum. The  channels are wider (see Fig. 12(c)) where the von Mises stress (see Fig. 12(d)) and the accumulated plastic strain (see Fig. 12(a)) are greater, as already shown in [58]. In addition, the channels are oriented to match the local lattice rotation. It is, therefore, easier for the crack to propagate along the /’ interface, as already observed in [109, 110]: ’ rafts act as a barrier to crack propagation when they are perpendicular to the crack. The simulation

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also points out that the crack may have initiated for a stress triaxiality factor around 0.5 (see Fig. 12(e)) which is close to the value for which a metal transitioned from shear fracture to fracture by void nucleation [111]. A triaxiality factor of 0.5 corresponds to a decreased strain to failure compared to the one dimensional case [112], namely 80% of the rupture strain in 1D. Therefore, the local amount of active slip systems is reduced which fosters the formation of pile-ups in the area and, then, of slip bands leading to twins [113]. These phenomena are also greatly helped because of the very high local plastic strain rate where the crack initiates. Fig. 12(f) shows the evolution of the plastic strain rate at the Gauss point developing the highest damage value (see Fig. 12(b)), viz. where the crack is likely to initiate. It can be observed that the plastic strain rate reaches almost 0.08 s-1 which is very fast, namely 3 orders of magnitude higher than the plastic strain rates reached during uniaxial creep deformations at 1050°C on [001]-oriented specimens (between 10-5 s-1 and 10-9 s-1) and for which no mechanical twins have been observed after failure [114-117]. Furthermore, the sensitivity of the viscoplastic flow to the applied stress has a transition at ~ 10-3 s-1 due to changes in the deformation mechanisms, viz. from by-passing to shearing the γ’ precipitates, which also explained the formation of mechanical twins for a local plastic strain rate of 0.08 s1

. Thus, not enough time is provided to the usual deformation mechanisms to accommodate

the deformation leading then to slip band and twin formations. Even if the proposed crystal plasticity model does not take into account explicitly micro-twinning as a deformation mechanisms, it clearly highlights that micro-twinning is triggered at locations where large creep strain and creep strain rates are encountered, with a large stress triaxiality factor.

Fig. 11: Boundary conditions and mesh (17,228 linear tetrahedral elements of type C3D4 corresponding to 4,014 nodes) used for the FEM simulation. Fig. 12: FEM simulation results for the creep test at 1050 °C/F=506 N/σnominal=138 MPa. Distributions of (a) the accumulated plastic strain, (b) the damage level, (c) the  channels width (nm), (d) the von Mises stress (MPa), and (e) the stress triaxiality factor, viz. 1/ 3  11   22   33 /  eq . (f) is plastic strain rate field in s-1.

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Conclusion Mechanical twinning has been observed in a Ni-based single crystal superalloy during creep tests at a temperature as high as 1050°C. It has been reported that the multiaxial loading on originally 001-oriented specimens was a necessary condition to observe twins since multiaxiality fosters lattice rotations toward the [111] orientation. This last possesses less active slip systems than [001] and [011] which ease strain localizations, pile-ups, slip bands, and finally twins. The triaxiality factor that has been investigated also assisted the observation of twins by even more promoting strain localizations which can be generated either by cracks or pores. Finally, a fast plastic strain rate that makes difficult to accommodate the deformation is a necessary condition for observing mechanical twins at such very high temperature (T=1050°C).

Acknowledgments The authors are particularly grateful to SAFRAN Helicopters Engines for providing the material. Dr Zéline Hervier (Materials Department at SAFRAN Helicopters Engines) is gratefully acknowledged for her continuous interest in this work. Florent Mauget is acknowledged for his help to prepare the specimens during the interruptions.

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γ’ γ

Fig. 1: Microstructure of the MC2 single crystal superalloy after the standard heat treatments (as defined in section 2.1).

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[100] [010]

[001]

Thickness = 1.2 mm

Fig. 2: Schematic illustration of the asymmetric-notched creep specimen used for doing the creep experiments with its dimensions and orientations.

Fig. 3: Elongations of the bi-notched specimen presented in Fig. 2 at 1050°C under a constant force of F=506 N (red curve), namely a nominal stress of 138 MPa, and a constant force of F=477 N (blue curve), namely a nominal stress of 130 MPa.

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F 3

5

29.07° 2

4 1 6

SEM observations

TEM

SEM

and

TEM

Fig. 4: Locations of the microstructural observations along with the observation technique used for each of them.

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(c)

σ [100] [001] (e)

(b) edge dislocations Fig. 5: (a) and (b), and (c), (d), and (e) are respectively SEM (blue rectangles) and TEM (green rectangles) observations of the specimen after failure at the locations 1, 2, 3, 4, and 5, as specified in Fig 4.

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σ 2 mm

2 mm

Fig. 6: SEM observations close to the crack at the bottom notch. A rotation of the ’ rafts is highlighted by the red-dotted lines added to the micrographs and related to the lattice rotation that occurred, as highlighted by the EBSD measurement. The color code used in the EBSD map is coded along the macroscopic loading direction (horizontal in the present figure).

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(a)

(b)

(c)

(d)

Fig. 7: TEM ((a) and (b) or green rectangles) and SEM ((c) and (d) or blue rectangles) observations on the failed specimen, respectively in area , and in areas  and , close to the crack and pointing out large slip bands with intense plastic activity. 28

Recrystallization (a)



(b)



1 μm

 5 μm IPF TD axis = σ axis Fig. 8: EBSD observation of the large bands observed in Fig. 7/area . The profile  in (a) shows that these bands have a 60° misorientation (see (b)) which corresponds to micro-twins

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Rafted area

Plastic

band

Fig. 9: TEM observations at 100 μm from the crack on the failed specimen. (a) is the general view of the area highlighted in the SEM observation by a blue rectangle. (b) and (c) are magnifications of zones in (a). It has been added pole figures to (b).

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Lattice rotation



1 mm





35.5°





25.9 



Fig. 10: EBSD observations on an interrupted specimen subjected to 1050°C/σnominal=130 MPa. The two notches show large lattice rotation along the [001]-[111] edge of the stereographic triangle and validated by the plotting of the misorientation profiles  and . In addition, two extra profiles, viz.  and , have been plotted for characterizing a local and isolated misorientation equal to 60°.

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F

Negative pressure on the top

y z

x

Uy and Ux = 0 on the bottom as well as one node with Uz = 0.

Fig. 11: Boundary conditions and mesh (17,228 linear tetrahedral elements of type C3D4 corresponding to 4,014 nodes) used for the FEM simulation.

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Damage Width of the  channels (nm)

Plastic strain (a)

(c)

(b)

Stress triaxiality factor (d)

(e)

von Mises stress (MPa) Plastic strain rate (s-1)

(f)

Fig. 12: FEM simulation results for the creep test at 1050 °C/F=506 N/σnominal=138 MPa. Distributions of (a) the accumulated plastic strain, (b) the damage level, (c) the  channels width (nm), (d) the von Mises stress (MPa), and (e) the stress triaxiality factor, viz. 1/ 3  11   22   33 /  eq . (f) is plastic strain rate field in s-1.

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