Stress-dependent deformation behaviour in bulk nanocrystalline titanium–nickel alloys

Introduction

In nanocrystalline (NC) materials, especially the grain size below a critical value d_c ∼ 10–20 nm, the nucleation and motion of dislocations become more difficult, and thus the materials usually have high strength together with disappointingly low ductility, which significantly undercuts their structural applications. The strength and ductility of polycrystalline materials composed of many crystallites (grains) are determined by their deformation mechanism. To enhance the disappointing ductility many studies have focused on their plastic deformation mechanisms.^1–8 Molecular dynamics (MD) simulations predict,^2–4 below the critical grain size grain boundary (GB)-mediated plasticity, e.g., GB sliding and grain rotation govern plastic deformation of NC materials. This has been confirmed by in situ straining transmission electron microscope (TEM) observations of NC thin films.^5,6 Recently, however, some in situ straining TEM studies of NC films demonstrate that dislocations are highly active in nano-scale grains (d < ∼10 nm).^9–11 These inconsistent investigations raise a question: what deformation mechanisms are most likely to be active for a given NC solid with d < d_c? To reveal these deformation mechanisms, the microstructure evolution during the deformation process of a bulk NC material with extremely small grains below 20 nm should be studied in detail. However, it is difficult to prepare a bulk NC material with extremely small grains below 20 nm and further study the structural evolution under high stress and strain. Here we prepared a bulk NC titanium–nickel (TiNi) alloy with extremely small grains below 20 nm by applying a stress-driven phase transition from austenite (B2 phase) to martensite (B19′ phase) at room temperature. ¹² And we make an experimental observation on the deformation process under increasing stress and strain up to failure in the bulk NC TiNi. An unexpected deformation behaviour is revealed, i.e., a sequential variation of the deformation mechanism from GB sliding and grain rotation to grain growth and dislocation activity with the increase of the deformation stress. This study provides new insights into plastic deformation mechanisms of NC materials.

Experimental methods

Bulk NC TiNi precursors with a thickness of ∼0.4 mm were prepared by electroplastic rolling coarse-grained Ti_49.3Ni_50.7 strips and subsequent thermal annealing (450°C for 1 h in vacuum).^12,13 The electroplastic rolling was performed at room temperature with a current density of 84 A mm⁻², pulse frequency of 10³ Hz, pulse duration of 8 × 10⁻⁵ s and a true strain e = 1.7. To get a NC TiNi alloy with small grains below 20 nm and further study its deformation process under increasing stress and strain, room-temperature tensile deformation to failure of the bulk TiNi precursors was carried out. The NC TiNi with extremely small grains was obtained by applying a stress-driven phase transition from austenite (B2 phase) to martensite (B19′ phase) of the above precursors. To investigate the deformation behaviour of the NC TiNi under a high stress, the microstructure evolution of the area near the fracture surface was observed. To determine the exact sampling positions with different stress, the spatial distributions of the effective stress in the bulk NC TiNi alloy deformed to failure were computed by finite element analysis (FEA) using a commercial finite element modelling package (LS-DYNA). This calculation was carried out according to the method reported in Ref. 14. Three-dimensional cell SOULD164D consisting of eight nodes was implemented for three-dimensional structure solid element. The property parameters of the simulated materials, e.g., the elastic model, Poisson's ratio and density, were taken from the experimental values. Then the three-dimensional geometry in units of metre magnified from the real experiment specimen for the simulated model was meshed by hexagonal shell elements. The enlargement of the geometry to metre scale aims at yielding a low tension speed for the simulations to approach the real experimental condition. The simulations were performed by employing an elasto-plastic constitutive law using a von Mises yield criterion based on the experimentally measured stress–strain curve of the real specimen. Fixing the left of the model by imposing boundary conditions, the tensile load with a uniform displacement speed of 1.5 mm s⁻¹ was exerted on the right of the model. After adjusting the parameters in the LS-DYNA software, the non-linear calculations can provide the whole stress and strain distributions at any moment during the deformation and fracture processes. Intercepting the moments of crack appearance and propagation, an obviously stress concentration occurs ahead of the tip of fracture crack, yielding high stress gradients with the distance from the fracture face.

Guided by the FEA-calculated spatial distribution of the effective stress field that is yielded by the tension fracture process, the TEM specimen within ∼500 µm from the fracture face, which shows the maximum stress and the stress variations with the distance from fracture face, was prepared. This TEM specimen was cut from the fractured sample, grinded on waterproof abrasive paper to <10 µm in thickness and mounted onto a Mo ring brace. Then the specimen was thinned by GATAN 691 precision ion polishing system with the specimen off-centre rotation and ion beam modulation mode, producing a large ellipse hole near the fracture face with the observed thin areas approximately along the direction of 45° angle from the tensile axis (see Fig. 1). To avoid the temperature increase during the ion polishing processes, a low ion beam energy of 3.5 keV and a low polishing angle of ∼3° were used. To achieve significant stress variations with the distance from fracture surface, the locations C, D, E and J on a same sample were characterised by TEM. And the exact locations were determined by measuring the distance from the point to the fracture surface along the direction of 45° angle by magnification of the TEM (see Fig. 1). A post-mortem TEM and a high-resolution TEM (HRTEM) observations were performed on a JEM-2010 and a JEM-200CX, respectively. Dark-field (DF) TEM images were taken under identical conditions using the (020) diffraction patterns of B19′ phase. The imaged microstructures from TEM observations on regions of ∼28 µm² were analysed using a Digital-Micrograph software to yield grain size by a circle equivalent diameter.

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Schematic diagram of the preparation of TEM specimen. The top and bottom ion beam polishes the specimen in turn not simultaneously. During the working time each ion beam stops the polishing when the Mo ring rotates to the position where the fracture face nearly parallel to its path to obtain an ellipse hole with the thin areas approximately along the direction of 45° angle from the tensile axis

The microstructures of the samples before and after room-temperature tension to break were studied by employing an X-ray diffractometer (XRD) with a Cu Kα radiation combined with the TEM analysis. The average size of the bulk NC TiNi from XRD observations was calculated from the broadening of corresponding diffraction peaks, after accounting for the instrumental broadening, by employing the Williamson–Hall method. ¹⁵ The critical grain size d_c ∼ 15 nm of B19′-TiNi was calculated by the conventional method described in Refs 16–18.

The nanohardness of the fractured NC TiNi was measured at different positions on a same sample by employing a Hystron TriboIndenter at room temperature. Beginning at fracture face, four horizontal routes kept away from each other along the tensile axis were selected to investigate hardness variations with the distance apart from the fracture face.

Results and discussion

As-prepared bulk NC TiNi precursor consists of roughly equiaxed grains with an average size of ∼45 nm (see Fig. 2a and b). The very strong (110) B2 peak in XRD patterns (Fig. 2c) shows that a large fraction of the material is the B2 phase, which is consistent with electron diffraction (ED) studies (the inset in Fig. 2a). It was then deformed in tension up to failure at room temperature. XRD and post-mortem TEM studies of the sample within 1 mm from fracture surface (inset in Fig. 2d) demonstrate that the B2 phase transforms into the B19′ phase (Fig. 2d) with a considerably strong (020) crystalline texture.

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Microstructure of as-prepared bulk NC TiNi alloys. a The bright-field TEM image and ED patterns (inset). b The statistical distribution of grain size from TEM images. XRD patterns of the as-prepared sample c before and d after room-temperature tension to break (within 1 mm from fracture face) show a deformation-induced transition from B2 to B19′ phase

To observe a whole deformation process with increasing stress and strain of the bulk NC TiNi, the spatial variations in the stress states were deliberately introduced into the sample by the actual tensile failure process. The spatial stress field ahead of the tip of fracture crack calculated by FEA (see Fig. 3a) shows that stress increases with decreasing the distance to the crack tip along the tensile axis. To achieve significant stress variations with the distance from fracture surface, a specifically designed TEM sample at location B indicated in Fig. 3a was prepared with observed thin areas approximately along the direction of 45° angle from the tensile axis (Fig. 3b). The microstructures at locations C, D, E and J indicated in Fig. 3b were characterised in detail, where stress is expected to increase continuously.

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a The contours of effective stress at a moment in tensile facture processes showing high stress gradients ahead of fracture crack tip. b A schematic of the specifically designed TEM sample with observed thin areas approximately along the direction of 45° angle from tensile axis. Microstructures in regions C, D, E and J were characterised and shown in c, d, e and j, respectively, and the inset shows the ED patterns of corresponding region. f The higher magnification DF TEM image of the feature indicated by the arrow in e. h ED patterns of nanocrystals in e. g HRTEM and DF TEM (the inset) images of an agglomeration with discernible notches (indicated by the arrows) in region E. Two subgrains (10–15 nm) with a small misorientation ∼9° are directly identified in the agglomeration. i Statistical distributions of grain size in regions C, D and E

Combining quantitative microstructural analysis at the locations C, D, E and J with a continuum description of stress gradient reveals a stress-dependent deformation behaviour in the bulk NC TiNi. At location C (Fig. 3c), grain size has a wide distribution with a statistical average value of ∼20 nm, and some large roughly equiaxed grains (indicated by the arrows, 40–70 nm) consist of small subgrains. The subgrains are shown by both the contrast change within the grains and the ED arcs spreading up to ∼15° (the inset in Fig. 3c). With increasing stress at location D (Fig. 3d), the grain size is apparently small with an average value of ∼14 nm below the critical size d_c ∼ 15 nm of B19′ phase, and its distribution becomes narrow without the large grains observed at location C. This implies that stress induces the splitting of the large grains consisting of small subgrains and yields much small grains below critical size, as verified by more continuous ED rings in region D (the inset in Fig. 3d). Similar TEM observations on the stress-induced splitting of grain agglomerations have also been reported in NC Ni films.^19,20 With further increasing stress at location E (Fig. 3e), many large grains appear, which are much bigger than those at location D. The higher magnification TEM image (Fig. 3f) shows that the larger grain has an irregularly elongated shape with many discernible notches, indicating that it is not a single large grain. HRTEM observations reveal that the large agglomeration in a strong diffraction condition consists of some small subgrains (10–15 nm) with misorientations below 9° (see Fig. 3g). In addition, the ED patterns with diffraction arcs spreading up to ∼9° (Fig. 3h) also demonstrate the small-angle misorientation nature among subgrains in the large agglomerations. Furthermore, the statistical number of grains with size below 15 nm decreases significantly accompanying with an increase of grain number in the size range of 20–60 nm (Fig. 3i), as compared with that in region D. A direct comparison of microstructures at locations E and D indicates that the grains smaller than 15 nm at location E experienced stress-driven GB sliding and rotation processes, e.g., through rotating into a similar orientation with neighbouring grains to yield the observed grain agglomerations with elongated shape. This result, considering the critical size d_c ∼ 15 nm of B19′ phase, is consistent with previous MD simulations and TEM studies of NC thin films,^2–6 in which GB-mediated processes govern plastic deformation of grains below critical size. It is well known that a new nucleation process refers to a phase transition process. No nucleation process takes place at location E, which is due to the existence of only pure B19′ phase (see Fig. 2d).

Under further increased stress at location J (Fig. 3j), many nanocrystals have a lath shape and a large size. HRTEM observations reveal that most of the lath nanocrystals (35–45 nm in length and 12–16 nm in width) have only a single grain (see Fig. 4a), yielding a circle equivalent diameter of 23–30 nm much larger than the average grain size in region D (∼14 nm). This demonstrates obvious grain growth at high stress. Due to mechanically driven grain rotation having been experimentally confirmed at low stress at location E, this extraordinary grain growth at high stress may be reasonably interpreted as a stress-driven grain rotation process combined with GB migration. Such a stress-driven GB migration process has been experimentally observed in the NC metals^14,21 and theoretically described. ²² This explanation is supported by the findings that a few lath nanocrystals, with a size comparable to that of the nanocrystal in Fig. 4a, consist of two subgrains with a small misorientation of ∼6° (Fig. 4b). The migration of the low-angle GB between the subgrains under stress, which has been well described by the collective movement of the individual dislocations in low-angle GBs,^14,22 will eventually yield the observed lath nanocrystals with a single large grain. Moreover, a gradual decrease of the misorientation between two subgrains (e.g., from 9° to 2°) (see Fig. 4c), accompanying with the appearance of lattice distortion regions (marked with white circles) around the subgrain boundary, is observed in a large grain. This may be taken as a direct evidence for grain rotation and GB migration in grain growth processes. It is suggested that GB migration will make the lattice undergo an irreversible shear within the volume traversed by the GB, ¹⁴ yielding lattice distortions.

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A typical HRTEM image of the lath nanocrystal consisting of a a single large grain and b two subgrains with a small misorientation (GB is delineated by white dashed line). c The higher magnification HRTEM image of a grown grain showing a gradual decrease of the misorientation between two subgrains, e.g., from 9° to 2°. Lattice distortion regions (marked with white circles) appear around the subgrain boundary (GB). d The inverse Fourier-filtered image from inside the white box in a showing the trapped lattice dislocations (white Τ) within the grain with more clarity.

Besides the grain growth observed at location J, within the single large grains dislocations become active, which is directly captured by HRTEM observations (Fig. 4d). However, only a small amount of dislocations can be observed, which is due to that many dislocations have disappeared at GBs. Furthermore, the ED patterns with very strong diffraction spots (the inset in Fig. 3j) show that these nanocrystals possess a crystal texture, which is consistent with XRD measurements (see Fig. 2d). The texture originates from grain growth. When the sizes of grain are large enough, the dislocation accumulation is possible. This is indicative of dislocation activity in the deformation processes, ²¹ demonstrating a dislocation-mediated plasticity at high stress.

We want to point out that the FEA only can give a qualitative description of the stress variety. The exact value of the effective stress from location C to J cannot be given from this calculation. The deformation process especially the dislocation activity process can only be observed under a high press produced near the fracture surface. This is the reason why we choose the actual tensile failure process instead of the multiple tensile test and in situ tensile test to capture the mechanism.

To corroborate the change in deformation mechanism, the nanohardness variety of the fractured NC TiNi in the field with decreasing the distance to fracture face was studied (see Fig. 5). With decreasing the distance to fracture face, the sample shows a hardening first due to the decrease of grain size (Fig. 3c and d) and then a softening that may originate from the GB-mediated deformation. Following the softening an unexpected hardening occurs (the highlight). Thus, this unexpected hardening demonstrates the strength increased with the increasing stress, indicating a transition in deformation mechanisms from the GB-mediated plasticity at low stresses to dislocation-mediated plasticity at high stresses. One point should be mentioned that only pure B19′ phase exists at locations C, D, E and J (see Fig. 2d). Therefore, the measured nanohardness was not affected by phase composition.

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Hardness variations in the fractured NC TiNi. The line on experimental data is drawn for guiding the eye. The nanohardness value for each location of interest is determined through averaging the values of 5–10 measured points with the same distance along the tensile axis to the fracture face, yielding an error bar

It is well known that dislocation activity is popular in large grains, leading to an enhanced strain hardening and then an increased ductility.^23,24 Our findings that the mechanically driven grain growth and dislocation-mediated plasticity occur at high stresses may yield high ductility in NC materials. Moreover, the new findings of stress-dependent deformation mechanism in TiNi alloys provide an insight into the deformation process in the shape memory effect which is governed by either the deformation of martensite or the stress-induced transformation.

Conclusions

In conclusion, the present study on the bulk NC TiNi with extremely small grain sizes demonstrates a stress-dependent deformation behaviour. At low stresses, the plastic deformation of the bulk material is governed by GB sliding and grain rotation processes, while at high stresses, the mechanically driven grain growth combined with dislocation activity dominates deformation processes. The present study provides new insights into deformation mechanisms at small grain sizes, and has a direct implication for designing NC materials with high intrinsic ductility through employing mechanically driven grain growth and dislocation activity.