Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction

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Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction Premysl Beran a,n, Milan Heczko b, Tomas Kruml b, Tobias Panzner c, Steven van Petegem d a

Nuclear Physics Institute, ASCR, Rez, Czech Republic CEITEC, Institute of Physics of Materials, ASCR, Brno, Czech Republic SINQ, Paul Scherrer Institute, Villigen, Switzerland d Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland b c

a r t i c l e i n f o Article history: Received 18 November 2015 Received in revised form 4 April 2016 Accepted 3 May 2016 Keywords: A: Dislocations Twinning B: Polycrystalline material C: Neutron diffraction Electron microscopy

abstract A near-γ TiAl based alloy with 2 at% of Nb was investigated by means of collaborative research based on transmission electron microscopy and in-situ neutron diffraction techniques with the aim to study mechanical twinning and its role within the mechanisms governing fatigue response and material properties. In-situ neutron diffraction measurements were performed during low cycle fatigue straining at room temperature. Induced lattice strain related to the formation of deformation twins was detected and used to follow changes in the macroscopic material response caused by the twinning process during cycling. A microscopic insight was realised by using several transmission electron microscopy techniques to reveal in detail an internal deformation microstructure of the material at the beginning as well as at the end of the fatigue life. The study was focused on the first loading cycles where the material shows intense cyclic hardening. The effect of mechanical twinning on the material behaviour at several stages of the fatigue life is discussed for two different total strain amplitudes of 0.2% and 0.4%. & 2016 Elsevier Ltd. All rights reserved.

1. Introduction TiAl alloys are potential materials enabling further development of turbine engine designs for aeronautical applications or technical solutions in power generator systems. These alloys are essential due to their low density combined with exceptionally good high-temperature properties. On the other hand, there are some limitations such as room temperature brittleness and difficult machinability. Therefore, there is a serious need for investigation of inter-related effects of alloy composition, microstructure, deformation mechanisms and overall material response under load. During the last few years, considerable effort has been focused on the investigation of effects of alloying elements on the microstructure and phase composition of TiAl alloys, with the goal to enhance their mechanical and technological properties (Appel et al., 2011; Clemens and Mayer, 2013; Beran et al., 2014; Chlupová et al., 2014, 2016). Nb became one of the essential addition elements (Brookes, 2009; Appel et al., 2000). The third generation of these alloys contains high Nb addition,

n

Corresponding author. E-mail address: [email protected] (P. Beran).

http://dx.doi.org/10.1016/j.jmps.2016.05.004 0022-5096/& 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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typically 7–8 at%. However current applications use most often alloys with 2 at% of Nb (together with additional 2 at% of Cr). Several studies have shown that especially for this composition, beside dislocation glide and climb, mechanical twinning is an important deformation mechanism with a substantial positive effect on the fatigue behaviour. So far, several different approaches to investigate this phenomenon have been reported. An in-situ transmission electron microscopy (TEM) study of twin propagation in TiAl was done by Farenc et al. (1993) (Couret et al., 1994). They were also among first to mention that interactions between twins and ordinary dislocations should be considered in order to explain the mechanical properties. Later, Appel et al. (1999) presented the idea that twins would constitute a major source of hardening because the twin/matrix interface or twin intersection may serve as barriers for dislocation glide. On the other hand, Seo et al. (1997) and Morris and Lipe (1997); Morris and Leboeuf (1998) argued that twin interfaces hinder dislocation motion and, therefore, harden the γ-phase. This was further followed in a detailed study (Skrotzki, 2000) where Skrotzki suggested that coherent twin boundaries seems to represent only a minor obstacle to dislocation slip, since they can pass the interface by suitable dissociation processes. Recent investigations performed by Henaff and Gloanec (2005) (Gloanec et al., 2007) supported the hypothesis that room temperature hardening is related to the prevailing deformation mode governed by twinning which would at least delay the formation of the “vein-like” structure observed under conditions where the cyclic hardening is moderate. A similar idea, but from a different point of view, was presented by Kauffmann et al. (2000) and Marketz et al. (2002). They studied the role of twinning as a deformation mechanism during monotonic loading of near-γ TiAl by acoustic emission. Despite the progress that has been achieved during the last years in understanding the deformation mechanisms in γTiAl, thorough experimental investigations are still required, as noted for example in (Skrotzki, 2000). In this paper we study deformation twinning in γ-TiAl by in-situ neutron diffraction and detailed TEM investigations. Combination of these advanced characterisation techniques brings new insights into the material response during fatigue.

2. Experimental 2.1. Material The investigated material was titan-aluminide alloy Ti-48Al-2Nb-2Cr-0.82B (at%) with near gamma microstructure, received in the form of cast bars of about 57 mm in diameter and 200 mm in length from GfE Metalle und Materialien GmbH (Nürnberg, Germany). The average grain size was about 57 mm but grains with sizes up to 180 mm were also present in the structure. 2.2. In-situ neutron diffraction experiments Neutron diffraction experiments were performed at the engineering diffractometer POLDI located at the Swiss Neutron Spallation Source at the Paul Scherrer Institute (Stuhr et al., 2005). POLDI is a time-of-flight (ToF) neutron diffractometer with a wavelength range of 0.1–5 nm. A pulsed neutron beam is generated by a multi-slit chopper. For this work a chopper speed of 5000 rpm was employed. The diffracted neutron beam was detected by a 1D 3He wire chamber as a function of scattering angle and time of flight. The deformation experiments were performed with a 30 kN uniaxial deformation rig. The neutron beam was collimated on the sample by slits and a radial collimator. Cylindrical specimens with gauge volume diameter of 6 mm were used for all low cycle fatigue (LCF) experiments. The rig was mounted horizontally for measuring the longitudinal strains (with the scattering vector parallel to the loading direction) and vertically for the transverse strain (with

Fig. 1. Tagged and coloured points show the positions on the hysteresis loop using the strain amplitude of 0.4% where neutron diffraction patterns were collected. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Fig. 2. On the left is 2D fit of registered POLDI diffraction data (intensity as a function of scattering angle and TOF) showing complex frame/reflection overlap features. On the right is a representative 1D correlated neutron diffraction pattern (red crosses). The black lines represent the fits and the green line the difference between data and fit. Reflections selected for further analysis are also noted. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the scattering perpendicular to the loading direction). The gauge volume for transverse and longitudinal strain measurements was 3.8
3.8
8 mm3 and 3.8
3.8
6 mm3 respectively. The macroscopically applied strain was measured with a MTS 632 extensometer with 8 mm gauge length. All experiments were performed at room temperature. The individual experiments consisted of cyclic loading with a predefined total strain amplitude and strain rate. At selected points on the cyclic deformation loops neutron diffraction patterns were accumulated. Due to the relative low neutron scattering power of both Al and Ti the needed measurement time for collecting one diffraction pattern with reasonable statistics was about 1 h. In general, two kinds of experiment were performed. The first one consisted of the measurement of diffraction patterns in the unloaded state, i.e. just after unloading from 7maximum total strain amplitude referred herein as ZFAT (Zero Force After Tension) and ZFAC (Zero Force After Compression). The main goal of these experiments was to follow the changes in the material response caused by twinning processes during the whole fatigue life. The specimens were generally fatigued until fracture unless otherwise specified. The second type of the experiment was focused mainly on the very first cycles (1– 5). In this case, in addition to the zero force measurements, the diffraction patterns were collected also at several points on the deformation loop when the material was loaded as depicted in Fig. 1. The diffraction spectra were reduced and analysed by the Mantid (Arnold et al., 2014) analysis software. Here each diffraction peak is fitted with a Gaussian function, yielding information on peak position, width and intensity. The multi-slit chopper allows that the sample is illuminated by neutrons with several wavelengths which increase an integral intensity coming from the sample. Data are registered like counts as a function of diffracted angle and time of flight (see Fig. 2 on the left). Each line on this 2D pattern corresponds to the diffraction footprint of one reflection and one chopper opening. Parallel lines in the plot correspond to the identical Bragg reflections but originate from different chopper slit. Lines with different slope correspond to the different Bragg reflections. For evaluation of this complex frame reflection overlap pattern a correlation method (Stuhr et al., 2005) was developed. This procedure transforms 2D pattern to 1D – intensity vs. diffraction vector Q or intensity vs. lattice spacing d (see Fig. 2 on the right). All diffraction patterns were evaluated in the following way. In a first step, correlated 1D pattern (intensity vs. d-spacing) was obtained from a raw data. On this correlated pattern appropriate reflections corresponding to γ-TiAl were identified and indexed. Afterwards, by using this structural information, a 2D fit of the raw data was performed so refined parameters (FWHM, intensity and position) were obtained for each identified reflection. 2.3. Transmission electron microscopy observations Internal deformation microstructure of the studied material was investigated by means of transmission electron microscopy (TEM). The spatial arrangement of the twins and dislocations in grains was determined using a technique of oriented foils. Thin plates were cut from the gauge length of the bulk specimens by electric-discharge machine at the angle of 45°, perpendicular and parallel to the loading axis. The samples were mechanically grinded to produce thin plates with a thickness of 0.1 mm, which were then punched out to produce discs with a diameter of 3 mm. These were marked to indicate the loading direction. The discs were then electrolytically polished using a double jet device TenuPol2. The electrolyte was composed of 85% of ethylalcohol, 8% of perchloric acid and 7% of butylalcohol. The polishing conditions were 40– 50 V, 200 mA and temperature of 40 °C to  55 °C. Thereafter, the samples were observed on a Philips CM12 TEM at 120 kV equipped with a double tilt holder. Highresolution TEM observations were conducted on a JEOL 2100 F TEM at 200 kV. The mark of the loading direction was aligned with respect to the holder axis in order to know the loading axis during observations. Microstructure arrangement of twins and dislocations was analysed using different diffraction vectors. The Burgers vectors and the types of dislocations were Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Table 1 An overview of the tested samples and their mechanical properties. Sample no.

E (GPa)

Y.S. at 0.2% (MPa)

U.T.S. (MPa)

Strain to fracture (%)

6 (tensile test)

213

289

381

2.05

εa (%) 0.2 0.2 0.4 0.4 0.4

N (cycles) 5 312* 2.5 7 32*

Comments Longitudinal Longitudinal, zero force measurement only, TEM Longitudinal, TEM Transverse Longitudinal, zero force measurement only, TEM

4 5 3 8 7

(LCF) (LCF) (LCF) (LCF) (LCF)

Longitudinal ¼ loading rig was mounted horizontally for measurement of longitudinal strains Transverse ¼loading rig was mounted vertically for measurement of transverse strains TEM ¼ sample was investigated by transmission electron microscopy Zero force measurement only¼neutron diffraction was measured only in the unloaded state as described in Section 2.2 * Loaded up to fracture.

determined by zero contrast conditions. Diffraction patterns and Kikuchi lines were used to determine the crystallographic orientation of the stress axis in individual grains. The Miller indices were permutated so that the tetragonal axis of the γ phase was always marked as [001]. This indexing scheme is fully in accordance with the approach introduced by Hug et al. (1986) for Miller indices for a tetragonal lattice.

3. Results 3.1. Mechanical properties Table 1 displays an overview of the tested samples. One sample (No. 6) was tensile loaded up to facture in order to determine the mechanical properties, as listed in Table 1. This measurement was done on the same deformation rig as for all other samples but without collection of neutron diffraction pattern. Note that compared to the lamellar γ-TiAl tested by Gloanec et al. (2007) the near γ-TiAl investigated in this study exhibits a slightly higher Young's modulus and a lower yield strength. Five cyclic experiments were performed with two strain amplitudes and various number of loops. Most of the samples were measured in longitudinal arrangement where stress–strain loops for individual reflections have the same shape as mechanical ones. For the strain amplitude of 0.4% also the transversal orientation was applied (sample no. 8). Evaluated lattice strains at zero force for both orientations (longitudinal/transversal) were found to be the same within the error bars.

Fig. 3. Comparison of cyclic hardening curves for two different total strain amplitudes in linear-log scale plot. To emphasise significant change in hardening rate at the beginning of cycling, cyclic hardening curves are shown separately for each strain amplitude in linear-linear scale plots on the right.

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Fig. 3 shows cyclic hardening curves at room temperature during cyclic loading. Here the stress amplitude sa is plotted as a function of the number of cycles N for two different total strain amplitudes. In cycling with a strain amplitude of 0.2%, during the first two cycles, the material exhibits a significant hardening with a cyclic hardening rate of 6 73 MPa/cycle. This initial period, in which the total stress amplitude increases approximately by 7%, is followed by a slight saturation for the next 13 cycles and then by an additional secondary hardening, however with a substantially lower cyclic hardening rate of 8672
10  3 MPa/cycle, for the rest of the fatigue life. In the case of cycling with total strain amplitude of 0.4% a few considerable differences were found. First, no tendency for saturation of the stress amplitude was observed. The initial hardening period could be characterised by a hardening rate of 1374 MPa/cycle, which leads to an increase of the stress amplitude by 11% during the first 4 cycles. This stage is followed immediately by an additional secondary hardening with a hardening rate of 1.2870.04 MPa/cycle, which is almost 15
higher compared to the similar stage of the cycling with the lower strain amplitude of 0.2%. For these tests the strain rate was 4.6
10  5 s  1. For running a higher number of cycles between measurements of neutron diffraction, a higher strain rate of 32
10  5 s  1 was used. No effect of the strain rate on the hardening/softening behaviour of the material has been observed, which is in a good agreement with the observations made by Gloanec et al. (2007). However, it is important to note that a small shift (drop-downs) of measured data noticeable in the case of the hardening curve of 0.4% strain amplitude was caused by issues with the experimental setup. Since the shift was not higher that 2.5%, the influence of the effect was considered as negligible for the purposes of this study. 3.2. Neutron diffraction 3.2.1. Theoretical considerations All reflections on the neutron diffraction patterns were identified and indexed as ones belonging to the γ-TiAl phase, what supports the assumption that the samples are near γ-TiAl. γ-TiAl phase have an ordered tetragonal structure with the space group P4/mmm (123) and c/a ratio of 1.013(4). Deformation twins in γ-TiAl are observed but only four twin directions of 112̅ ⎤⎦-type preserve the ordered structure (Mecking et al., 1996). According to the approach used by Skrotzki (2000) a relative length change was calculated for selected directions (represented by reflections in the diffraction patterns) caused by twinning. As a powder diffraction is not ̅ , 111̅ , 111 ̅ , an average conable to distinguish a contribution from individual planes, such as, for example (111) , 111 tribution of individual twinning systems to the change of the length of selected planes needs to be calculated. As the sample is considered as a fully random powder the individual contributions are averaged with the same weight factor. Based on the calculation of the length change of individual directions in combination with the diffraction data (reflections with high intensity and without overlap) three representative reflections were selected for further investigation and comparison. They represent elongation (110), shortening (112) and mostly neutral behaviour (312) caused by twinning when averaged over all possible twinning systems. The relative change of length of a crystal direction υ0 can be calculated as λ = (υ′0 M υ0 )−1/2 Skrotzki (2000) where M is deformation matrix. Deformation matrixes for all four twinning systems in γ-TiAl are listed in Table 2 and were calculated based on assumption noted by Skrotzki (2000).

(

A total strain caused by twinning along the direction

(

υ0 can be calculated as δ0= λ −

)(

1 υ0

)(

)

). Calculated values of the total

strain δ0 for the selected reflections and the individual twinning system are listed in Table 3 together with average values over all twinning systems. In general, all planes parallel to the c axis are shortened and along a and b axis are elongated. The total twinning strain δ0 correspond to the change of length when 100% of the sample is twinned. If only a partial twinning is applied then a sample strain can be calculated as a fraction of this total strain δ0

δ=f ·δ 0

(1)

where f is the twin fraction. Based on these theoretical calculations all the experiments performed on the POLDI instrument were evaluated. TEM analysis of the virgin state (as prepared) of the material revealed that none or only a few twins are present in the majority of grains. Therefore it was supposed that the most of the deformation twins have been formed during the fatigue tests. This means that a position of the reflection at the virgin state was used as d0-hkl for a lattice strain evaluation using following formula Table 2 Calculated deformation matrixes for four twinning systems available in γ-TiAl. Twinning system

(111)/⎡⎣112̅ ⎤⎦

( 1̅ 11̅ )/⎡⎣ 1̅ 12̅ ̅ ⎤⎦

(111̅ )/⎡⎣112̅ ̅ ⎤⎦

̅ )/⎡⎣ 112 ̅ ̅ ⎤⎦ ( 111

M

⎛ 5 −1 2⎞ 1⎜ ⎟ −1 5 2⎟ 6⎜ ⎝ 2 2 11⎠

⎛ 5 − 1 2⎞ 1⎜ ⎟ − 1 5 2⎟ 6⎜ ⎝ 2 2 3⎠

⎛5 1 2 ⎞ 1⎜ ⎟ 1 5 − 2⎟ 6⎜ ⎝ 2 − 2 11 ⎠

1⎜ 6⎜

⎛ 5 1 − 2⎞ ⎟ 1 5 2 ⎟ ⎝− 2 2 11 ⎠

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Table 3 Total strain δ0 calculated for the selected crystallographic planes and the individual twinning system. Bottom lines report average total strain δavg over all twinning systems and a word representation. Total strain δ0 for reflections (%) Twinning system (111)/⎡⎣112̅ ⎤⎦

100 9.54

001  26.14

110 15.89

112  11.12

312  4.37

( 1̅ 11̅ )/⎡⎣ 1̅ 12̅ ̅ ⎤⎦ (111̅ )/⎡⎣112̅ ̅ ⎤⎦ ̅ )/⎡⎣ 112 ̅ ̅ ⎤⎦ ( 111

9.54

 26.14

15.89

0

6.01

9.54

 26.14

0

 8.09

 3.98

9.54

 26.14

0

 8.09

0

δavg (%)

9.54 Elongation

 26.14 Shortening

7.95 Elongation

 6.83 Shortening

 0.59 Small shortening

εhkl=

dhkl −d0 − hkl d0 − hkl

(2)

where dhkl is the interplanar distance (position of the reflection) at a given state and d0-hkl is the interplanar distance without twins – virgin state. When εhkl is positive, the hkl planes are in tension and when εhkl is negative the hkl planes are in compression. 3.2.2. Evolution of residual lattice strain The calculated lattice strain after unload from both tension and compression at zero force for three selected reflections as a function of the number of cycles for the test with 0.4% strain amplitude is shown in Fig. 4. It is evident that the residual strain on the planes {312} is negligible as it is predicted from Table 3. The {112} planes are in the tension (εhkl 40) which corresponds to an elongation along the [112] direction. This is the exact opposite of what is noted in the Table 3. An explanation of this seeming discrepancy is illustrated in Fig. 5. Due to the twinning the d112 shortened as predicted. But when the applied stress is released the sample tries to accommodate the original shape due to the effect of neighbouring grains. Shortened {112} planes are therefore in tension to fulfil it. The same explanation is consistent also with the planes {110} which are in compression after twinning. The twinning process elongates d110 but when the applied stress is released this enlarged planes need to fit the origin grain shape so they will turn into compression. The lattice strain after unload for both 112 and 110 reflections changes with the number of cycles very rapidly and reaches a certain saturation level after 2–3 cycles (see Fig. 4). It is interesting to note that the saturation level is lower for the unloading from compression (ZFAC) than for the unloading from tension (ZFAT). This can be related to the lower activity of the twinning during compression what is in a good agreement with findings of Skrotzki (2000) and Sun et al. (1993). They showed that for certain grain orientations, twinning cannot take place under compression while for other orientations it is forbidden under tension. In γ-TiAl tetragonal crystal with randomly oriented grains, formation of twins under tension is more probable than in compression. From the values of the lattice strain after unload a fraction of the created twins can be estimated using Eq. (1) for the individual reflections. The twin fraction estimated for the strain amplitude εa ¼0.4% is about 0.5% for the unloading after tension and 0.4% for the unloading after compression. It can be understood either by assuming

Fig. 4. Calculated lattice strains after unload for selected reflections in LCF experiments with a strain amplitude of 0.4%. ZFCT – zero force after tension. ZFAC – zero force after compression.

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Fig. 5. Illustration of the influence of (111)/⎡⎣112̅ ⎤⎦ twinning on the behaviour of interplanar distances in a grain during loading. After applying stress the twins are formed which causes elongation of the grain along the [110] direction and shortening along the [001] direction. After stress release the (110) and (001) planes will be compressed and elongated, respectively due to the constraints of the neighbouring grains.

Fig. 6. A comparison of the lattice strain after unload of the selected reflections for the two applied strain amplitudes.

that the detwinning process during compression removes about 20% of the volume of twins formed during tension halfcycle or considering twinning in compression. Quite possibly both processes are operating. Fig. 6 compares the evolution of lattice strain after unload for the 112 and 110 grain family for two different strain amplitudes. An evident correlation between the magnitude of the lattice strain and strain amplitude could be observed, where higher strain amplitude leads to larger residual lattice strains. Note that the tension/compression asymmetry found in Fig. 4 is also present for the tests with 0.2% strain amplitude. Here the twin fraction is about 0.3% after tension and 0.2% after compression again calculated from both 112 and 110 reflections. 3.2.3. Evolution of lattice strain during 1 loop Fig. 7 displays the evolution of the lattice strain as a function of applied strain during cycling with maximal strain amplitude of 0.4%. In the first half-cycle, the curves have a usual convex shape. In further cycling, concave features near maximum or minimum of the loop are clearly seen on the loop shape for both 110 and 112 reflections. This means that there is a slowdown of lattice strain increase before maximum applied strain. Such behaviour of shape of stress–strain hysteresis loops is typical for the materials with intense twinning – detwinning activities, as e.g. hcp crystals (Horynova et al., 2013; Matsuzuki and Horibe, 2009). At certain stress level, twinning (or detwinning) process is activated, which causes straining of the sample without substantial increase of mechanical stress (mechanical hysteresis loop) and consequently also lattice strain (Fig. 7). On the other hand, the concave features are very little visible on the loop of reflection 312, which is explained by very small change of lattice strain due to the twinning. This observation underlines the above-mentioned conclusions. Similar behaviour was found also for samples with strain amplitude of 0.2% but there were not as profound as for ε Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Fig. 7. Evolution of the lattice strain during whole fatigue experiment with strain amplitude of 0.4% measured in axial direction for the selected reflections. The first and the second one half cycles are plotted with close and open symbols, respectively, to underline evolution with cycling. A direct comparison of the lattice strain of the reflection (112) in tension for different applied strain amplitude is shown in the bottom right plot.

Fig. 8. Characteristic internal microstructure observed in the sample no. 7 loaded with εa ¼0.4% to fracture. Fraction area of the deformation twins is given for each micrograph.

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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a ¼0.4% because a twinning activity is lower for this amplitude as was described above. This slowdown of strain increase is visible on the points on the deformation loop (samples with εa ¼0.2%) which are higher that 70.12% of applied strain. It indicates that twins starts to form within the grains when applied stress is higher than a certain critical value, which is estimated to 230 MPa. It is interesting to note that no significant changes of the peak broadening were observed. This means therefore that no significant changes in an inter-granular stress can be addressed so that only a very small stress for the twinning activation is needed.

3.3. Transmission electron microscopy The deformation induced microstructure was investigated by TEM on three samples – after 2.5 cycles with a strain amplitude of 0.4% (sample no. 3), and after rupture with strain amplitudes of 0.2% (no. 5) and 0.4% (no. 7) (see Table 1). Three different types of TEM foils were produced for each studied sample as mentioned in Section 2.3. Tens of grains were investigated on the each foil and particular grains were then selected for a detailed analysis in terms of crystallography. The fractional area of deformation twins in each grain was determined by following procedure: first the number of twins in each grain Nt and the area of the grain Ag are determined. Then the fraction area of deformation twins is calculated as (Nt  ta)/Ag where ta is the average thickness of twins (discussed further at the end of Section 3.4). It is known that the number of twins within an individual grain depends on how favourably it is oriented for twinning (Farenc et al., 1993). Again, it is important to note that twinning is unidirectional (Sun et al., 1993) and every grain behaves differently under tension and compression depending on mutual orientation of uniaxial load and tetragonal crystal. A main effort has been focused on the analysis of the specimen loaded with 0.4% strain amplitude. Based on the detailed observation of the microstructure the grains can be divided into two groups:

3.3.1. Type I Grains, in which the twinning was a prevailing deformation mode, are classified as Type I grains. Characteristic is a relatively low dislocation density with distinguishable individual dislocations. No tangles, spatial dislocation structures and slip localisation were observed. Two or three different deformation twin systems were usually activated in these grains. The fraction area of the deformation twins was mostly between 2.35% and 2.60% at the end of fatigue life (see Fig. 8).

3.3.2. Type II In the case of Type II grains, when compared to the Type I, the most distinctive differences are 1) much higher dislocation density and 2) lower fraction area of the deformation twins, which was mostly between 0.33% and 1.40% (see Fig. 8). It was clearly observed that in these grains there is a correlation between the amount of deformation twins and the dislocation structure within the grain. The higher the fraction area of deformation twins was, the more heterogeneous the distribution of dislocations was in terms of alternating areas with high and low dislocation density.

Fig. 9. TEM bright field micrograph showing part of investigated grain (Type I) was taken at following conditions: foil plane (6¯ 11 8), loading axis [6¯ 11 8] , ¯ ¯ ⎤⎦ . Loading conditions: εa ¼ 0.4%, N ¼ 2.5 cycle. beam direction B = ⎡⎣1¯ 4 3⎤⎦ , diffraction vector g = ⎡⎣111

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Fig. 10. Detail of annealing twin/parent crystal boundary, which acts as a deformation twin nucleation site. Micrograph was taken at two different diffraction conditions.

3.4. Detailed analysis of a representative Type I grain A typical example of the deformation microstructure of a Type I grain after 2.5 cycles of loading at 0.4% strain amplitude is shown in an overview in Fig. 9. It is obvious that twinning is the prevailing deformation mechanism in this grain. Two ̅ ̅ ] and the secondary system (111) [112̅ ], which deformation twinning systems activated: the primary system (11̅ 1) [112 correspond to Schmid factors (SF) 0.317 and 0.152, respectively. The amount of primary twins is noticeably higher compared to secondary system. The right side of the grain contains an annealing twin, which was formed by an activation of the (111̅ ) [112] twinning system. A diffraction condition in which the primary dislocation slip system was observable was found by tilting of the sample in the double-tilt holder (see details in Fig. 10). Both screw segments of ordinary dislocations with Burgers vector 1 [11̅ 0] and 1 [110] were clearly visible in diffraction condition g¼[200]. The SF of the activated primary 2 2 dislocation slip system (111) [11̅ 0] was the highest and equal to 0.408.

Fig. 11. Nucleation site for deformation twinning at the boundary of annealing twin and parent crystal. Shockley partial dislocations with Burgers vector 1 ̅ ̅ ] rotate on a (11̅ 1) twinning plane around an ordinary pole dislocation and generates homogeneous twin by the propagation from the nucleation site [112 6 ̅ ̅ ] is marked in the image as well as trace of twinning plane (11̅ 1). (marked by symbol A) into the parent crystal. Projection of vector [112

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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̅ ]. (b) Detail of twin/parent crystal Fig. 12. (a) High resolution TEM micrograph of deformation twin. Beam direction B¼[110], diffraction vector g¼[ 111 boundary. (c) IFFT filtered image showing details of the (1̅ 11) twin plane. Important directions are highlighted in the crystal.

It has been already well documented that potential nucleation sites for the twinning in single-phase alloys are grain boundaries, dislocations, free surfaces and crack tips. In polycrystalline alloys, grain boundaries are the most potent sites (Yoo, 1998). Farenc et al. (1993) (Couret et al., 1994) showed that deformation twins are nucleated within the grain interior by a polar source mechanism due to a partial dislocation turning around a perfect dislocation. The so-called pole mechanism proposed by Cottrell and Bilby (1951) for twin nucleation in BCC crystals assumes that a pole dislocation exists with a Burgers vector (b) perpendicular to the twinning plane. A partial dislocation on the twinning plane rotates around the pole, produces twinning in successive layers and generates a homogeneous twin (Mecking et al., 1996). It is evident that nucleation site for deformation twinning in studied grain is formed by the boundary between the parent crystal and the annealing twin (see Fig. 9). This is well documented by observation that some of the twins, both in parent crystal and annealing twin, initiated at this boundary but have not propagated yet through the whole grain (see black arrows in Fig. 9). Detail from the area of annealing twin boundary marked by letter A is showed in Fig. 11 along with a schematic drawing of the pole mechanism. Dislocations of the primary slip system are in condition of invisibility g.b¼0. On the contrary activated secondary slip system (1̅ 11) [110] with SF¼0.231 is very well resolved. In (Couret et al., 1994) it was proposed that specifically for γ-TiAl the splitting of a 60° ordinary dislocation into a sessile Frank dislocation and a Shockley dislocation may lead to the nucleation of the initial partial dislocation under an appropriate applied stress. This initial partial dislocation then forms a polar source. In case of the investigated grain in Fig. 11, deformation twins of primary system are ̅ ̅ ] gliding on (11̅ 1) planes. generated by Shockley partial dislocations 1 [112 6

¯ ¯ ) , loading axis Fig. 13. (a) TEM bright field micrograph showing part of the investigated grain (Type II) was taken at the following conditions: foil plane (811 ̅ ̅ ], diffraction vector g¼[111̅ ]. Loading conditions: εa ¼ 0.4%, N ¼2.5. (b) Detail of internal deformation substructure. Screw [1¯ 29 15], beam direction B¼[523 ̅ )[112 ̅ ̅ ] and ̅ ] are visible along with two deformation twinning systems (111 segments of the ordinary dislocations from primary slip system (111)[110 (111)[112̅ ]. The measured dislocation density is ρ¼ (6.8 70.7)
1012 m  2.

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Fig. 14. (a) Detail of a twin intersection (marked by letter B in Fig. 13) visualised in three diffraction conditions to emphasise deformation microstructure arrangement and interaction of ordinary dislocations from the primary slip system with primary deformation twins. (b) Magnified area between two twin intersections shows the interaction of screw segments and tangles of primary system dislocations with the primary twinning system. A few isolated edge ̅ ) [011̅ ] are highlighted by arrows. Micrograph was taken in diffraction condition g3 ¼ [111̅ ]. segments of superdislocations of slip system (111

The fraction area of the twins in examined grain was calculated to approximately 1.02%. For that purpose the average thickness of deformation twins was determined by means of high resolution TEM on selected grains with a proper orientation with respect to the beam direction. Fig. 12 shows an example of a HR-TEM micrograph of a deformation twin of the system (1̅ 11) [1̅ 12̅ ]. The (1̅ 11) twinning planes that form the boundaries between parent and twinned crystal are clearly visible, which allows a reliable determination of the twin thickness. This procedure was followed for various twins, leading to an averaged value of 32 nm. In the inset in Fig. 12b, a twin/parent crystal boundary is shown in high magnification. Here the electron beam direction was parallel with the [110] direction. An Inverse Fast Fourier Transformation and mask was applied to the HR-TEM image, resulting in a filtered image (Fig. 12c) that shows the details of the (1̅ 11) twin plane. Important directions are highlighted in the crystal.

Fig. 15. TEM micrograph showing the internal deformation substructure of a Type II grain at the end of fatigue life for two diffraction conditions: g1 ¼[200], ̅ ], foil plane (376 ̅ ]. Loading conditions: εa ¼0.4%, Nf ¼ 32 cycles. ̅ ], beam direction B2 ¼[ 154 ̅ ), loading axis [376 beam direction B1 ¼ [054], g2 ¼ [ 1̅ 11

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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3.5. Detailed analysis of a representative Type II grain Fig. 13a shows the major part of a Type II grain that was investigated in detail. Analysis of deformation substructures revealed that both dislocation slip and deformation twinning are present. In contrast with the examined grain presented in Section 3.4 a significantly higher dislocation density was observed (see detailed micrograph in Fig. 13b). Dislocations are also spread more homogeneously within the grain volume. The primary activated dislocation slip system (111) [11̅ 0] has the highest SF with a value 0.494. The analysis of the Burgers vectors using different extinction conditions indicates that mainly the screw segments of the ordinary dislocations 1 [11̅ 0] are observable. 2 Two deformation twinning systems are activated in this grain. The primary (11̅ 1)[1̅ 12̅ ] system with higher SF¼ 0.200 prevails over secondary (111) [112̅ ] system with SF¼ 0.020. The fraction area of twins in this grain was calculated to be 0.52%. Several twin intersections that are present were studied in detail and TEM bright field micrographs in three different diffraction conditions were compared (see Fig. 14a). Only dislocations of the secondary slip systems are partially visible for ̅ ̅ ] twin system. A magnified picture of the deg2 ¼[020] and it is obvious that they interact with the primary (11̅ 1) [112 formation twin in diffraction condition g3 ¼[111̅ ] in Fig. 14b shows dislocation tangles gathered at the twin boundary. Moreover, interactions between screw segments of ordinary 1 [11̅ 0] dislocations of the primary slip system and primary 2 ̅ )[011̅ ] slip system with lower deformation twins are apparent. A few isolated edge segments of superdislocations of the (111 SF¼0.241 are visible in the location of cross twinning marked by letter B in Fig. 13b. Using the knowledge of the twin orientation in the crystal and tilting for different diffraction conditions, the foil thickness in area in Fig. 13b was determined to (488750) nm. Subsequently dislocation density was calculated in the selected area of examined grain to ρ ¼(6.870.7)
1012 m  2. The internal deformation substructure of Type II grain (with a fraction area of twins equal to 0.66%) studied at the end of the fatigue life is shown in two diffraction conditions in Fig. 15. Both deformation modes, dislocation slip and twinning, were activated. It is obvious that the plasticity of this grain was governed mainly by slip of ordinary dislocations from the primary (111) [11̅ 0] slip system with the highest SF of 0.434. It could be seen that the screw segments and high density tangles (called as “vein-like” structure in (Henaff and Gloanec, 2005), but we prefer “high density of dislocation tangles”) of 1 [11̅ 0] 2 dislocations are completely invisible in diffraction condition g2 ¼[1̅ 1̅ 1] and only a few ordinary 1 [110] dislocations from the 2 secondary slip systems can be observed. Also a few edge segments of superdislocations from slip system (111) [1̅ 01] with the second highest SF 0.391 were identified. ̅ ̅ ] deformation twins with the highest SF¼0.221 and secondary A detailed study revealed that both primary (11̅ 1)[112 (111) [112̅ ] deformation twins with SF¼0.201 influence the arrangement of ordinary dislocations from the primary slip system. For instance, it could be seen, that two (11̅ 1) deformation twins (see white arrows in Fig. 15) form a relatively narrow band of approx. 0.3 mm thick area of parent crystal with a different arrangement of the dislocation substructure when compared to other parts of the grain. It is clear that there is a significantly lower dislocation density and no dislocation tangles in between the two twins. Low dislocation density areas of rectangular shape are also observed between the primary (111) deformation twins. It suggests that the deformation twins have significant influence on dislocation arrangement within the grain. 3.6. Analysis of a sample cycled with 0.2% strain amplitude The deformation microstructure of a sample cycled with a total strain amplitude of 0.2% up to fracture (Nf ¼312, sample no. 5) was investigated. Fig. 16 shows an overview picture of two typical deformation substructures. For these loading conditions, the fraction area of deformation twins was mostly between 0% (such as in Fig. 16a) and 0.20%. No grains with higher area fraction of twins were observed. A detailed analysis of the grain visualised in Fig. 16b was performed to reveal more details about the dislocation structure and deformation twins.

Fig. 16. Micrographs of two typical and representative deformation substructures observed in the material tested at loading conditions: εa ¼0.2%, Nf ¼ 312 ̅ ], beam direction B ¼[459 ̅ ], foil plane and cycle. (a) A grain with no deformation twins. (b) A grain with 0.20% fraction area of deformation twins. g¼[111 loading axis [3¯ 15 11] .

Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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Three dislocation families were recognised along with two deformation twin systems. Most of the observed dislocations were edge segments of ordinary dislocations from the primary (111) [11̅ 0] slip system with the highest SF¼0.476. Since pileup structures and arrangements are formed by these dislocations, it could be stated that dislocation slip presents the governing deformation mode during cyclic loading. Edge segments of superdislocations from the (111) [011̅ ] slip system with SF¼0.106 were observed as well as few screw segments of (1̅ 11) [101] superdislocations with SF¼ 0.267. It should be noticed that some of the superdislocations could have been present in the crystal in the as-received state. Few primary (111) [112̅ ] deformation twins are present along with one annealing twin of the additional (111̅ ) [112] system. Estimation of dislocation density within the studied grain was determined to be approximately ρ E(3 71)
1012 m  2. That is notably lower than in the case of material loaded at εa ¼0.4%. Moreover, no spatial structures and dislocation tangles were observed.

4. Discussion 4.1. Neutron diffraction measurements Despite the fact that twinning is a direction sensitive phenomenon, in-situ neutron powder diffraction could reveal some interesting averaged macroscopic features of twinning during a low cycle fatigue experiment. The average contribution of individual twin systems to the induced lattice strain of selected planes was identified and followed during cyclic loading. Twinning causes a shortening of {110} and elongation of {001} inter-planar distances as was described previously in (Skrotzki, 2000). The effect of twinning on lattice strain along the [312] direction is negligible due to the effect of averaging over several twin systems. This considerably helped to create average model for macroscopic description of observed phenomena by diffraction methods. The volume fraction of twins was calculated from the evolution of the lattice strain of the selected reflections. It increases very rapidly with the number of cycles and reaches a certain saturation level after 3–5 cycles. Then the fraction of twins after unloading in tensile or compression half cycle is almost constant. Lattice strain at this saturation level increases when total strain amplitude is higher. This indicates that more twins are produced for εa ¼0.4% when compared to εa ¼0.2%. It is obvious that residual strain caused by twins present after tensile half cycle is different from that after compression half cycle. In particular, after compression it is lower, what is in a good agreement with the fact that the twinning behaves differently under tension and under compression in case of tetragonal crystals (Sun et al., 1993). Skrotzki (2000) presented qualitative representation of the active twinning systems with respect to the orientation of the uniaxial load within the extended unit stereographic triangle for the tetragonal crystal system. It shows that for 34% of all possible grain orientations, there is no deformation twinning in compression. Interestingly there are only 11% of such orientations where the twinning is forbidden on all four twinning systems in tension. The twin fraction created during cycling was calculated by using the adopted equation presented by Skrotzki (2000) from the saturation value of the lattice strain. The average twin fraction formed after tension was found to be 0.5% and 0.3% for strain amplitudes of 0.4% and 0.2%, respectively. The volume twin fraction detected after compression was about 0.1% lower for both strain amplitudes what again corresponds well to statements presented in (Skrotzki, 2000; Sun et al., 1993). These findings are also in quite a good accordance with TEM observations when the overall average is taken into consideration. The shape of hysteresis loops (Fig. 7) in cycling with strain amplitude higher than 0.12% contains convex parts before maximum or minimum of the loop (see comments there). This behaviour is attributed, in agreement with the literature, to twinning – detwinning process. Moreover, this explication was supported also by the fact that the convex feature is very much reduced on the evolution of lattice strain of {312} planes during cycling. It was shown that lattice strain of {312} planes is very little affected by twinning due to averaging processes, so no effect caused by twinning could be detected on the loop shape. It is also interesting to note that this study is, up to our knowledge, the first time that macroscopic powder diffraction technique was used for studying a direction sensitive phenomenon as twinning in TiAl alloys. 4.2. Transmission electron microscopy The evolution of the microstructure during cycling has been studied in detail by TEM. Dozens of grains of samples cycled with a total strain amplitude of εa ¼0.4% for 2.5 cycles were investigated and compared to the as received material as well as to samples cycled to the end of their fatigue life. This investigation clearly revealed that the amount of deformation twins has risen significantly during the initial period for both Type I and Type II grains. On contrary, the comparison with the material state at fracture showed that increase of amount of deformation twins during further cycling (from 2.5 cycles to fracture) is negligible. These observations are fully in accordance with neutron diffraction measurements and support hypothesis (Henaff and Gloanec, 2005; Gloanec et al., 2007) that initial hardening period is caused mainly due to the intensive deformation twinning during the first three to four cycles. Generally, together with deformation twinning, also evolution of dislocation arrangement has to be accounted for when looking at cyclic response of material. It was observed that the more deformation twins are formed in grain during initial period of cycling, the less developed dislocation arrangement and the lower dislocation density is found. The dislocation structure in Type I grains, i.e. grains with high fraction of twins, does not change considerably during additional cycling. On Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i

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the contrary, in the case of Type II grains, the dislocation density (primary ordinary dislocations) rises significantly and the dislocation substructure rearranges between first cycles and the end of fatigue life. Despite the fact that ratio between Type I and Type II grains is not known precisely, our observations indicate that number of Type II grains prevails. Both neutron diffraction and TEM has shown that there are only few new deformation twins formed during additional cycling. Therefore the dislocation slip becomes governing deformation mode within the period from the third/fourth cycle to the fracture of the sample. The evidence of mutual relation of twins and dislocation structure was studied. The interaction of ordinary dislocations from the primary slip system with deformation twins was noticed in several cases. The major finding is that the arrangement of deformation twins could lead to presence of areas where the movement of dislocations from primary slip system is limited. Numerous dislocation free areas of different sizes were observed. These signs were spotted mainly in Type II grains after 2.5 cycles of loading and were even more distinctive at the end of fatigue life. In regard to material response, further continuous secondary hardening is strongly connected with the increase of dislocation density and changes in dislocation arrangements. However, as these processes are influenced by the presence of deformation twins within grains itself, the formation of deformation twins during initial period of cycling has an indirect, but significant effect on material behaviour characteristic by secondary hardening within the rest of the fatigue life. Both neutron diffraction data and TEM observations of material tested at total strain amplitude 0.2% indicate that amount of deformation twins created during cyclic loading is substantially lower in comparison with higher amplitude. Initial hardening period as well as following mild secondary hardening is caused by successive increase of dislocation density and rearrangements of dislocation structure within the fatigue life.

5. Conclusions A complementary study of deformation twinning and its relation to the fatigue behaviour of the near-γ TiAl based alloy with 2 at% of Nb at room temperature using neutron diffraction and transmission electron microscopy led to the following conclusions:

 Induced lattice strain after unload related to the formation of deformation twins was detected by neutron diffraction. This allows following changes in the material response caused by twinning process during the fatigue life.

 A majority of the deformation twins are formed in the early stage of the fatigue life within the first 3–5 cycles. A fatigue response of the material in this period is characterised by significant hardening.

 The amount of the deformation twins strongly depends on the strain amplitude. From the neutron diffraction experiments we can derive an average twin volume fraction of about 0.5% and 0.3% for εa ¼0.4% and for εa ¼0.2%, respectively.  The number of the twins present in the grains differs depending on how favourably is each grain oriented for twinning. The deformation twins have substantial influence on dislocations movement and arrangement.

 The number of the twins created after tension is slightly bigger than after compression.  According to the deformation microstructure, the observed grains were divided into two groups. Type I – grains oriented favourably for twinning with high twin fraction; Type II – grains with high dislocation density and low fraction of twins.

 Continuous secondary hardening in case of high strain amplitude is caused mainly by an increase in dislocation density and rearrangement of the dislocation structure. Dislocation arrangement is however influenced by presence of deformation twins formed during the initial period of cycling.

Acknowledgements Support of the project of the Czech Science Foundation 107/11/0704 is acknowledged. The research was partially conducted in CEITEC research infrastructure supported by the project CZ.1.05/1.1.00/02.0068 financed from European Regional Development Fund.

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Please cite this article as: Beran, P., et al., Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction. J. Mech. Phys. Solids (2016), http://dx.doi.org/10.1016/j.jmps.2016.05.004i