RECOVERY STRESS GENERATION BY SHAPE MEMORY ALLOY POLYCRYSTALLINE ELEMENTS

Transcription

1 RECOVERY STRESS GENERATION BY SHAPE MEMORY ALLOY POLYCRYSTALLINE ELEMENTS P Šittner 1, V Novák 1, P Sedlák 2, M Landa 2, G N Dayananda 3 1 Institute of Physics, ASCR, Na Slovance 2, Prague 8, , Czech Republic 2 Institute of Thermomechanics, ASCR, Dolejškova 5, Prague 8, , Czech Republic 3 National Aerospace Laboratories, Bangalore 56-17, India ABSTRACT Understanding thermomechanical laws controlling the evolution of the recovery stresses with temperature changes in shape memory alloys is essential for successful development of SMA-polymer composites In this paper, the mechanism of the recovery stress generation by constrained NiTi wires in thermal cycles is discussed based on the results of in-situ neutron diffraction and ultrasonic experiments as well as micromechanics modelling of martensitic transformation in NiTi polycrystals 1INTRODUCTION Shape memory alloy /SMA/ wires embedded in a deformed shape in the elastic matrix of smart SMA-polymer composites tend to transform back to the parent austenite phase when heated above the austenite finish A f temperature Since their length is constrained by the adjacent composite matrix, the wires generate internal compressive stresses in it Understanding the thermomechanical laws controlling the evolution of these thermally activated recovery stresses is the key to the unique properties of smart SMA-polymer composite materials The recovery stress generation by SMA wires will be solely addressed in this paper The existing models of SMA-polymer composites [1,2] provide some insight into the mechanisms of the recovery stress generation For example, the phenomenological model [2] predicts how the magnitude of the recovery stress at given temperature depends on material parameters of the embedded SMA wires, polymer matrix and technological parameters as prestrain or volume fraction of SMA wires Nevertheless, reliability of the SMA models, which are always core parts of the SMA-composite models, is still questionable, namely due to their inability to treat properly the mechanics of the recovery stress generation by SMAs in polycrystalline form The mechanics of the recovery stress generation by SMA polycrystals is thus the key issue We are stressing the polycrystals since, in the case of SMA single crystals, it is relatively easy to understand the recovery stress generation based on the coupling between the stress and temperature driving the martensitic transformation given by Clausius Clapeyron equation 1 tr dσ S s = = tr (1) dt ε V S is the entropy change, ε tr is orientation dependent transformation strain associated with the martensitic transformation and V is the molar volume The equation describes very well the experimentally measured temperature dependencies of transformation stress in tensile tests on oriented SMA single crystals [3] When a single crystal specimen has been deformed so that it contains a nonzero volume fraction of the oriented martensite phase, its length is constrained while temperature is being increased, the specimen starts to generate stress with the rate given approximately by Eq 1 The stress varies linearly upon heating/cooling in such a way that the

2 system remains in thermoelastic equilibrium, the transformation strain due to oriented martensite phase exchanges for the elastic strain as the volume fraction of the martensite phase slightly decreases with increasing temperature This is the generally accepted simplified view on the mechanism of the recovery stress generation by SMA single crystals However, an assumption that Eq 1 holds equally well for the SMA polycrystals, which is commonly made in the SMA modeling literature [1,2], is not correct Considering that the constituent phases in SMAs have different elastic properties, are elastically anisotropic and the transformation strains and stresses are strongly orientation dependent, cooperative transformation of SMA polycrystals with mutually constrained component grains is by far more complicated The intergranular constraints affect the macroscopic constitutive σ ε Τ response of SMA polycrystals including recovery stress generation but is is not very clear how In addition, some alloys exhibit multiple martensitic transitions and elastic properties of constituent phases could be temperature dependent Because of that, there is no guarantee that the σ=σ(t) recovery stress responses of the SMA polycrystals are linear and that correct value for the slope s is obtained from Eq 1 based upon experimentally obtained values of the entropy S and polycrystalline transformation stress ε tr Modeling the recovery stress generation by SMA wires based on the Clausius Clapeyron equation 1 implemented on the macrolevel into the phenomenological [2] or continuum based SMA models [1] is thus problematic and leads often to serious errors Micromechanics approach towards SMA polycrystal modeling [3,4], where Eq 1 is implemented on the microlevel of each single component grain, provides a better insight into the mechanics of the recovery stress generation as will be demonstrated in section 23, nevertheless, achieving reliable quantitative predictions is still a rather difficult task, since there is a lack of experimental evidence on what is exactly going on in the SMA polycrystal subjected to the recovery stress tests The purpose of this work is to discuss the mechanisms of the recovery stress generation by NiTi polycrystalline wires from experimental as well as micromechanics modeling point of view NiTi exhibits martensitic transformations between cubic B2 austenite, rhombohedral R- phase and monoclinic B19 martensite phase In the first part, recent new experimental results obtained by application of in-situ neutron diffraction and in-situ ultrasonic techniques towards the problem of thermomechanically driven martensitic transformations in NiTi will be briefly reviewed In the second part, results of micromechanics model simulation of the recovery stress generation due to the R B2 transformation taking place upon heating of the slightly prestrained NiTi wires in tension will be shown and confronted with the experimental observations 2 RESULTS & DISCUSSION In spite of the concerns raised above, the experiment shows that the recovery stress evolves even in the case of SMA polycrystals approximately linearly with temperature [2] Problems are, however, with predicting correctly the value of the rate of the stress generation upon heating from material parameters and its dependence on the prestrain, history etc In case of the practically most important NiTi wires, moreover, the elastic properties of the constituent phases do change markedly with temperature and multiple transformations exist This is a serious complication for modelling the recovery stresses in NiTi In order to learn more what is happening inside the NiTi wire subjected to the recovery stress tests, two kinds of in-situ studies were recently realized by the present authors in situ

3 neutron diffraction [5,6] and in-situ ultrasonic pulse-echo [7] tests While the former brings information on the evolution of the phase fractions and stresses in particularly oriented polycrystal grains and can be used to recognize the possibly interfering additional phase transition processes, the latter is sensitive mainly to the evolution of the elastic properties of the constituent phases The results of these novel experiments will be briefly discussed in sections 21 and 22 in order to provide experimental basis for the modelling ideas introduced in section 23 Details of the in-situ experimental techniques can be found in Refs [5-7] 21 In-situ neutron diffraction evidence on microstructure changes Similarly to X-ray powder diffraction structural studies, diffraction data can be obtained with neutron or synchrotron radiation The essential advantage of using the neutron over conventional X-rays in the in-situ diffraction experiments on SMAs is that the neutron radiation penetrates through the bulk and the obtained experimental information is averaged over the large gauge volume of the specimen exposed to stress-temperature loads inside the neutron diffractometer The neutron diffraction data are measured under applied stress in stopovers during thermal, mechanical and/or thermomechanical load cycles Individual Intensity [au] Stress, σ G a) f 12 5 d 4 3 e a c b Strain, ε G [%] c) T=373K T=33K T=295K Stress, σ G Intensity [au] 7 b) d b f e 2 a 15 c Temperature, T [K] 5 Cooling 4 3 R 2 1 d) 13, K 343K 323K 33K B19'-C ,3 1,4 1,5 1,6 1,7 1,8 1,9 2, 2,1 2,2 2,3 2,4 d-spacing [A] -1 B ,7 1,8 d-spacing [A] Figure 1: Results of in-situ neutron diffraction experiment on NiTi bar [6] - recovery stress test: macroscopic thermomechanical response in stress-strain(a) and strain-temperature (b) coordinates with denoted points in which the axial TOF diffraction patterns were recorded, c) comparison of the patterns recorded in axial geometry after unloading at room temperature (T=295K, point 8), after first constrained heating (T=373K, point 12), and after constrained cooling (T=33K, point 15), d) complex evolution of the shape of 111 A diffraction profile during constrained cooling (points 12-15) suggesting progress of the B2 R martensitic transformation

4 reflections of the constituent austenite and martensite phases are analyzed for integral intensities and positions reflecting the phase fractions and lattice strains in phases, respectively [5,6] The evolution of such obtained quantities with macroscopic stress, strain and temperature is of the main interest [6] and this information can be interpreted in terms of micromechanics of NiTi polycrystal transformation with the help of the micromechanical modelling [8] Results of the in-situ time of flight /TOF/ diffraction experiment focused on the generation of recovery stress are shown in figure 1 The NiTi thick wire specimen (d s =5mm, l s =5mm, R s =22 o C, M s =-1 o C) was deformed at room temperature in tension and unloaded (stages a,b) Subsequently, it was thermally cycled (heating-cooling-heating) while the strain ε G =35% was held constant (c,d,e) The specimen was finally unloaded at T=348K (f) Neutron diffraction patterns were recorded in denoted stress-strain-temperature points The essential macroscopic stress-temperature response (Fig 1b) upon constrained thermal cycling shows a typical V-shaped curve characteristic for the recovery stress cycles [9] The rate of the stress change with temperature is s=~6 MPa/K (stages d,e) This is a rather common value observed experimentally on NiTi polycrystals in tension Instead of discussing systematically the diffraction results (see [6] for this), let us only point out here those details important for comprehending the mechanism of the recovery stress generation by the NiTi polycrystal The evolution of the diffraction patterns during first heating-cooling cycle (Fig 1c) suggests that a massive B19 B2 transformation takes place upon the first constrained heating (stage c), but corresponding reverse process does not occur upon subsequent cooling (stage d) Compare the diffraction patterns recorded at T=295K (point 8) and at T=33K following the constrained cooling (point 15) Volume fraction of the martensite phase is much smaller in the latter case as evidenced by sharp decrease of the integral intensity of martensite reflections (compare eg -13 M and 22 M reflections) Some martensite reflections do not exists at T=33K at all (- 12 M and 2 M ) This suggests that, in spite of equal strain and similar temperatures and stresses, very different martensite variant microstructures exist in the specimen This clearly explains why the stress-temperature response during the first heating branch (stage c, s=~75 MPa/K), always significantly differs from that observed upon the second heating (stage e, s=~6mpa/k) [9] It is thus evident that the σ Τ response upon the first heating branch is not representative for cyclic recovery stress generation exploited in SMA composites The very small change of the volume fraction of the martensite phase observed upon thermal cycling (stages d,e) is clearly evidenced by the negligible variation of martensite peak intensities This is fully consistent with the above discussed scenario of the recovery stress generation, in which the stress and temperature vary in such a way that the alloy stays in thermoelastic equlibrium Since the crystallographic transformation strains are large particularly for B2-B19 transformation, only very small change of the martensite volume fraction is sufficient for compensation of the small elastic strains The constrained thermal cycle thus represents a partial hysteretic cycle [2] The hysteresis width of the σ=σ(τ) response (1K) (Fig 1b) is consequently much smaller compared to the hysteresis width of the complete cycle (6K) observed in stress free thermal loading of the same specimen It is, however, surprising to see that the small volume fraction of the martensite phase in the point 15 (at T=33K and σ=2mpa) is sufficient to accommodate the constrained macroscopic strains as large as 36% (elastic strains are smaller than 5%) Another striking observation is that the austenite 111 A reflection does not shift on the d-scale when the stress varies during the thermal loading as much as would be expected for the elastic strains corresponding to the 4MPa stress change (Fig 1d) Instead of shifting, the observed profile

5 shape changes upon constrained cooling in a complex way it splits into two overlapping reflections The splitting of the austenite reflections suggests that transformation to the oriented R-phase [6] takes place upon cooling Three separate peaks can be clearly identified within the pattern observed after first constrained cooling (point 15, T=33K, σ=2mpa) A, 3 R and 13 R The 421 R peak is missing since the R-phase is preferentially oriented for tension It thus comes out that, surprisingly, the B2 R transformation massively proceeds upon constrained cooling (Fig 1c,d) and affects the variation of the stress The R-phase thus likely plays significant role in the mechanism of the recovery stress generation in NiTi, namely in case of the small prestrains (<3%) This shall be taken into account in modelling the recovery stresses 22 In-situ ultrasonic evidence on the elastic property changes Since the transformation strain accompanying the phase fraction change during the recovery stress generation is compensated by the elastic deformation, the second crucial issue for the recovery stress generation is the temperature stability of the elastic properties of the phases involved It seems to be well recognized that the elastic properties of the B2 austenite phase in NiTi do vary significantly with temperature [1] upon cooling close above the phase transition and that the elastic properties of the austenite and martensite phases are different This issue has been scarcely addressed in the SMA literature It was proposed [11] that the temperature dependence of transformation stress becomes nonlinear when the elastic properties of the parent and product phases are different The elastic properties of NiTi wires can be conveniently evaluated by measuring the speed C L and attenuation of longitudinal ultrasonic wave by pulse-echo technique, since the Young s modulus of the wire can be considered proportional to the square of the C L for wire shape Figure 2 shows how the C L varies upon stress free cooling of the thick NiTi wire used in the diffraction experiment (Fig 1) The wire undergoes the B2 R B19 phase transition characterized by the superimposed DSC cooling curve There is a deep decrease of the C L accompanying the B2 R transformation, but upon further cooling below R f, at Wavespeed C L [1 3 m/s] 3,8 3,76 3,72 3,68 3,64 3,6 3,56 3,52 3,48 3,44 3,4 3,36 3, Temperature [ o C] temperatures where the R-phase structure undergoes further continuous distortion [12], the C L steeply increases back Such a pronounced variation of the elastic properties is typical only for the B2 R transformation and does not happen during the subsequent R B19 transformation B19' R M f M s R f R s B2 C L DSC Figure 2: Variation of the wave speed of longitudinal ultrasonic wave C L measured by pulse-echo method [7] on a thick NiTi wire upon cooling The undergoing phase transformations are characterized by the superimposed DSC curve suggesting B2 R transition taking place at T=2 o C and R B19 at T=-25 o C Heat Flow [au]

6 Figure 3 shows results of in-situ ultrasonic and electric resistance measurements carried out during tensile loading of NiTi 25 mm thin and 2 mm long wire (R s =18 o C, M s =- o C) at two different temperatures T=22 o C and T=37 o C While the R-phase is stress induced at stresses ~15MPa in the former case, it appears only at stresses ~45MPa in the latter case It is very interesting to see the dramatic difference between the two tests registered by all three in-situ evaluated characteristics, in particular, the pronounced nonmonotonous variation of the wave speed C L and the increase of the electric resistance ρ measured in the apparently elastic range at T=22 o C The behavior of the C L is analogous to that recorded during the thermally induced B2 R transition (Fig 2) The stress induced B2 R transformation occurs first (C L decreases) followed by further continuous distortion of the R-phase structure (C L increases) due to the still increasing stress Electric resistance ρ, on the other hand, increases with increasing stress (strain) for both processes No such behavior is observed upon deformation at T=37 o C when R-phase is possibly involved only marginally at stresses higher than 45MPa Upon deformation at still higher temperatures, the C L remains practically constant when the stress induced B2 B19 transformation proceeds in the plateau range suggesting that the difference between elastic properties of austenite and stress induced martensite is in fact very small in contrast to generally accepted view [11] It is thus clear that the elastic properties of the NiTi wire vary mainly during the B2 R transition and change in the reverse direction when the rhombohedral distortion of the R-phase structure proceeds with changing temperature or stress The electric resistance, on the other hand, varies about equally during both transformations, even if scales very differently with the strain 7 6 T=22 o C R->B19',98,96 5,94 4,92 3,9 2,88,86 B19'->B2,84,82,,5,1,15,2,25,3 7,16 6,14 5,12 4,1 3,8 2,6,4,2,,5,1,15,2,25,3 7 6 E=75GPa 3,4 5 3, B2 B2->R R=> 3, 2,8 2,6 2,4,,5,1,15,2,25,3 Strain R-> B2 R<= El resistivity [ohm x µm] Wavespeed C L [1 3 m/s] Attenuation [1- -3 db/m] 7 6,98 T=37 o C,96 5,94 4,92 3 B19'->R,9 2 R->B2,88,86,84,82,,5,1,15,2,25,3 7,16 6 E=75GPa,14 5,12 4,1 3,8 2,6,4,2,,5,1,15,2,25, ,4 5 3, B2 B2->R(B19') 3, 2,8 2,6 2,4,,5,1,15,2,25,3 Strain B2+R->B19' Figure 3: Variation of the electrical resistance, wave speed C L and attenuation of longitudinal ultrasonic wave measured in-situ during tensile deformation of 25 mm NiTi wire (R s =18 o C) at room temperature T=22 o C and ambient temperature T=37 o C B2 R<= El resistivity [ohm x µm] Wavespeed C L [1 3 m/s] Attenuation [1-3 db/m]

7 Taking advantage of that knowledge, the electric resistivity and ultrasonic techniques were employed to detect the R-phase related phenomena occurring in recovery stress tests on NiTi wires in which both temperature and stress change simultaneously Selected result is shown in figure 4 The wire was heated to T=95 o C (stage a), deformed at this temperature up to prestrain ε=85% (b), the wire was subsequently cooled(c)-heated(d)-cooled(e) while the prestrain ε=85% was kept constant (Fig 4a,b) Finally, the wire was finally unloaded at T=22 o C (f) Clearly, as the temperature approaches the temperature T=4 o C upon cooling (Figs 4c,d), the stress starts to decrease and the electric resistance, wave speed C L and attenuation drastically change, which suggests the start and progress of the B2 R transformation Similarly, the limited recovery stress generation upon heating is clearly related to the termination of the R B2 transformation due to expiration of the R-phase There are thus two very important differences between recovery stress generation due to the R B2 and B19 B2 transformations The rate of the stress variation with temperature is much steeper (~2 MPa/K) in case of the R B2 and there is a natural limit of the stress increase ( σ=~3mpa) related with the fast expiration of the R-phase due to small associated transformation strains (ε tr =~6%) The stress-temperature curve from figure 4 is redrawn within the stress-temperature diagram in figure 5 to support the claim that the stress does indeed vary along the B2-R transformation line With increasing magnitude of the prestrain in recovery stress tests, when more B19 martensite phase has been induced (as eg in the test shown in Fig 1), the macroscopic stress variation approaches the B2-B19 transformation line with much smaller slope (~6 MPa/K) The macroscopically measured stress-temperature response of the NiTi wire during constrained thermal loading is thus mostly due to mixture of both R B2 and B19 B2 transformations ie the macroscopic dσ/dt rate lies somewhere between 6 MPa/K (B19 B2) and 2MPa/K (R B2) and much depends on the value of the prestrain and Temperature [ o C] a) b) a b c d e Time [au] f,1,8,6,4,2, Strain Attenuation [1- -3 db/m] R<->B2 B ,16 d),14,12,1,8,6,4, e d c Temperature T [C] c),9,85,8 3,6 3,4 3,2 3, 2,8 2,6 2,4 Resistivity [ohm x µm] Wavespeed C L [1 3 m/s] Figure 4: Variation of the temperature (a), stress and strain (b), stress and electric resistance (c), wave speed C L and attenuation of longitudinal ultrasonic wave (d) measured in-situ during recovery stress test on 25 mm NiTi wire (cooling-heating-cooling at tensile prestrain 85%, see text for details)

8 history Since different transformations are differently involved at different stress levels and elastic properties are vary significantly with temperature in the R-phase, it is clear why the σ Τ response does not have to be necessarily linear as suspected These experimental results suggest that understanding and consideration of the R-phase related processes is essential for successful modelling of the recovery stress generation in NiTi wires 23 Micromechanics modelling of the recovery stress generation When deriving a micromechanics model of SMA, equation 1 is always in some form introduced on the microlevel of single oriented grains It represents the essential thermodynamical relationship between stress and temperature required to induce the martensitic transformation Since the value of the transformation strain ε tr (Eq 1) is strongly orientation dependent, the slope s and consequently stresses in individual grains are also very sensitive to the orientation of the grain with respect to the load axis The stresses and strains in grains are, however, mutually constrained across grain boundaries and their interactions are taken into account in modeling while making the scale transition to the macrolevel Macroscopic σ G ε G Τ response of the polycrystal is obtained as a complex average over the responses of multiple interacting grains In the particular case of the recovery stress test (constrained heating), the instantaneous value of the predicted slope s=dσ G /dt is dependent, in addition to the basic material parameters as transformation temperatures M s, A f, entropy change S, transformation strain ε tr, also on polycrystal texture, prestrain, history etc and cannot be expressed simply by Eq NiTi 25mm FWM wire B19'Martensite R-phase T=22 o C T=37 o C ε ~6% ε ~6% B2 austenite Temperature T [ o C] Figure 5: Experimentally determined stress-temperature diagram of NiTi 25mm wire (, B2-B19, 7 B2-R,! R-B19 ) The vertical dashed lines denote the σ Τ path of the tensile experiments (Fig3) Complete σ-t response measured in the recovery stress test (Fig 4) is superimposed An earlier developed micromechanics model [3,4,8] has also been used to simulate recovery stress tests on NiTi wire Let us focus here on a simulated result for a special test, in which the stress is generated by the R B2 transformation upon constrained heating (stage 3 in Fig 6) The model was originally developed to interpret the results of in-situ neutron diffraction experiments and yields not only the σ G ε G Τ macroscopic responses in the recovery stress test (Figs 6a,b), but also the responses of the families of equally oriented grains (Figs 6c,d) tracked down in diffraction experiments [6] Interesting theoretical information on the partitioning of the load and phase fraction between variously oriented grains during the constrained recovery is obtained Notice for example, that each <hkl> family of grains exhibits different σ hkl AM -T response (Fig 6c) The <111> oriented grains, providing largest tensile strains due to B2-R transformation (ε tr =12%, inset in Fig 6d), are surprisingly predicted to develop maximal stresses upon heating (Fig 6c) and keep transforming until the highest temperature (Fig 6d)

9 It should be emphasized that the response of NiTi wires that is solely due to R B2 transition is extremely convenient for applications in smart SMA-polymer composites [1,2] Main advantages are : i) the predicted rate of the recovery stress generation due to the R B2 transformation is very large (s = 2MPa/K), and ii) the magnitude of the maximum reached recovery stress is naturally limited ( σ G = ~ 3MPa) due to the small transformation strains ε tr and resulting fast expiration of the R-phase upon heating, and iii) the σ G =σ G (Τ) response was found experimentally to be very stable and practically does not change with thermomechanical cycling An essential advantage of the micromechanics model [4] is that simultaneous activity of all three possible transitions R B2, R B19 and B2 B19 in NiTi is allowed An important conclusion that comes from simulations of the recovery stress tests on NiTi wires showing the R-phase transformation reported elsewhere [13] is that the σ Τ responses are somehow affected by the B2 R transition mainly for the small but also for the large prestrains (>3%) This is in agreement with the neutron diffraction evidence presented in sections 21 (Fig 1) The predicted R-phase activity at lower temperature and stresses in recovery stress tests on NiTi wires also rationalizes the experimentally observed and earlier curious [9] nonlinearity of the σ G =σ G (Τ) response, electric resistance behavior ρ=ρ(τ) and increase of the rate dσ G /dt with decreasing prestrain 25 a) 25 b) Stress, σ G Stress σ G s=2 MPa/K Component stress, σ hkl AM,,2,4,6,8 1, 1,2 Strain, ε G [%] c) Temperature [K] 1,,8,6,4,2, Temperature, T[K] 1 11 R phase tension Stress, σ G Figure 6: Simulation of the constrained recovery of NiTi wire upon heating after tension due to R B2 transformation by micromechanical model [4]: a) stress-strain response - loading in R-phase state (stage 1) and unloading (stage 2) is followed by heating (stage 3) under constant strain 32%, b) stress-temperature response in stages 1-3 Evolution of the c) average component stress and d) R-phase volume fraction in grains oriented with <hkl> crystal directions parallel to the load axis The inset in (d) shows orientation dependence of transformation strains of the B2 R transformation in tension R-phase volume fraction, ξ R hkl d)

10 3 CONCLUSIONS Mechanism of the recovery stress generation by constrained NiTi wires in thermal cycles has been discussed based on the results of in-situ neutron diffraction and ultrasonic experiments and micromechanics modelling of martensitic transformation in NiTi polycrystals It is claimed that, in addition to the cubic to monoclinic (B2 B19 ) transformation, the R- phase transformation (B2 R) is frequently involved in the recovery stress generation by commercial NiTi wires and optional activity of this transformation is responsible for large variation of the experimentally observed rates of recovery stress generation dσ/dt In cases when solely B2 R phase transformation is behind the recovery stress generation (wire showing R-phase transformation, small prestrain <1%), the NiTi wire exhibits σ Τ responses that are extremely convenient for applications in smart SMA-polymer composites ACKNOWLEDGEMENTS The neutron diffraction work of P Lukas and his coworkers in NPI Rez as well as supports of the Grant Agency of the ASCR (contract No A14817) and Grant Agency of the Czech Republic (contract 22/4/216) are sincerely acknowledged References: 1 Lu ZK, Weng GJ, A Two-level micromechanical theory for shape memory alloy reinforced composite, Int J Plasticity, 16 (2), Šittner P, Michaud V and Schrooten J, Modelling and Material Design of SMA Polymer Composites, Mater Trans JIM, 43 (22), Šittner P, Novák V, Anisotropy of martensitic transformations in modeling of shape memory alloy polycrystals, Int J Plasticity, 16, (2) Novák V, Šittner P, A network micromechanics model of thermomechanical behaviors of SMA polycrystals, Scripta Materialia, 5 (23), Šittner P, Lukáš P, Neov D, Daymond MR, Novák V, Swallowe GM, Stress induced martensitic transformation in CuAlZnMn polycrystal investigated by two in situ neutron diffraction techniques, Mat Sci Eng A 324/1-2, (22), Šittner P, Lukáš P, Novák V, Daymond MR, Swallowe GM, In-situ neutron diffraction studies of martensitic transformations in NiTi polycrystals under tension and compression stress, Mat Sci Eng A, (24), in print 7 Landa M, Novak V, Sedlak P, Sittner P Ultrasonic characterisation of Cu-Al-Ni single crystals lattice stability in the vicinity of the phase transition, Ultrasonics 42 (24), Novák V, Šittner P, Micromechanics modelling of NiTi polycrystalline aggregates transforming under tension and compression stress, Mat Sci Eng A, (24) in print 9 Šittner P, Vokoun D, Dayananda G N and Stalmans R, Recovery stress generation in shape memory Ti5Ni45Cu5 thin wires, Mat Sci Eng A, 286/3 (2), Ren X, Miura N, Zhang J, Otsuka K, 21, Tanaka K, Koiwa M, Suzuki T, Chumlyakov YuI, Asai M, Understanding the martensitic transformations in TiNi-based alloys by elastic constants measurement, Mat Sci Eng A, 312, Huang WM On the effects of different Young's moduli in phase transformation start stress vs temperature relationship of shape memory alloys, Scripta Materialia, 5 (24) Miyazaki S, Kimura, S, Otsuka K, Shape memory effect and pseudoelasticity associated with R- phase transition in Ti55at%Ni single crystals, Philosophical Magazine A, 57 (1988) Novak V, Sittner P, Micromechanical model simulation of thermomechanical behaviors of NiTi polycrystals undergoing B2-R-B19 transformation, SMST 4 Baden-Baden, (24), in preparation