Inhomogeneous Deformation Research Articles

Micro-Scale Ice Shoveling Effect Induced by Magnetic-Responsive Microfins.

Icing is ubiquitous in nature and engineering applications, and imposes threats to road and air transportations, wind energy infrastructures, etc. However, current active de-icing solutions, especially the most popular one, i.e., heating, suffer from high energy consumption whilst passive methods are often ineffective at high-speed, long-term, or large-particle conditions. Herein, a promising strategy adopting magnetic-responsive microfins (MRS)featuring reversible deformations is developed for de-icing. A novel micro-scale ice shoveling effect induced by the localized destruction of the ice adhesion interface owing to the inhomogeneous deformation is demonstrated, and its dependence on the ice particle size and temperature is investigated. An analytical model is proposed to describe the mechanism of this effect, showing a linear relation between the position of the magnet and the induced force agreeing well with experiments, leading to a system straightforward to predict and control. Specifically, the de-icing capacity of the surface becomes prominent when small-scale ice particles merge to large ones, providing a promising solution for applications on aircraft, wind turbines, etc., as the first of its kind to remove large particles under high-speed conditions effectively.

Impact of Inhomogeneous Deformation of Shale Matrix on Gas Depletion Behavior at Field Scale: A Modified Triple-Porosity Model

Impact of Inhomogeneous Deformation of Shale Matrix on Gas Depletion Behavior at Field Scale: A Modified Triple-Porosity Model

Microstructure evolution after hot working and heat treatment in 6082 aluminum alloy manufactured by horizontal continuous casting

In this paper, 6082 aluminum alloy manufactured by horizontal continuous casting was subjected to high-temperature plastic deformation under 20–70 % deformation levels with following T6 heat treatment process. Microstructural and phase changes were investigated by light and scanning electron microscopy together with energy dispersive spectroscopy, while grain, grain boundary, dislocation and texture evolution was studied by electron-backscattered diffraction. The results are showing that continuous dynamic recrystallization processes are active during the hot working while influence of static recrystallization is significant only for highest deformation degrees. The abnormally coarse-grained microstructure does locally occur in the subsurface layer after the 70 % deformation and T6 heat treatment. Crystallographic texture components are gradually evolving from the various types (Goss, Brass, D) for the low deformations (up to 40 %) into fiber-type textures (α-fiber, γ-fiber or C2-fiber) for high deformations due to the inhomogeneity of plastic deformation. The formation of AlMnSi dispersoids, CSL-boundaries Σ25b and an increase in fraction of GND, MgSi and Fe-based intermetallic particles was observed during the phase transformation which promotes ongoing nucleation of recrystallization processes.

Nonlinear mechanical behaviour and visco-hyperelastic constitutive description of isotropic-genesis, polydomain liquid crystal elastomers at high strain rates

The mechanical behaviour of isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) at various strain rates is systematically investigated via experiments, theoretical analysis, and numerical modelling. Experiments encompassing SEM (scanning electron microscope), DSC (differential scanning calorimetry), TGA (thermogravimetric analyser), quasi-static and dynamic (SHPB – split Hopkinson pressure bar) mechanical tests, as well as drop-weight impact tests, are undertaken to identify the nonlinear, large-strain, rate-dependent relationship between compressive stress and deformation of the I-PLCEs studied. Subsequently, a three-dimensional compressible visco-hyperelastic constitutive model for the material is established based on the summation of Cauchy stress components. The as-used model yields good agreement with experimental data, particularly an excellent description of the mechanical responses at high strain rates of 103∼104 s−1. The fully-calibrated constitutive model is implemented in the commercial finite element code ABAQUS via a virtual user-defined material (VUMAT) subroutine. The inhomogeneous deformation processes of the I-PLCEs, corresponding to impact by a hemispherically-tipped drop weight, which induces complex stress states, are also well described. Finally, when evaluated by two dimensionless physical parameters, the I-PLCEs demonstrate a more pronounced strain rate sensitivity in terms of dynamic strength and impact toughness compared to other commonly used materials, highlighting their superior performance in dynamic loading scenarios. The present study is helpful for the design and development of impact-resistant LCE-based materials and structures.

Atomistic investigation on the anisotropic elastic and plastic responses of nanotwinned metals

Introducing nanotwins into materials is one of the important strengthening methods to achieve the synergistic improvement of strength and ductility. The anisotropic mechanical behaviors of nanotwinned materials have been widely studied by experimental and computational methods. The dominant deformation mechanisms about dislocation slippages can be effectively switched among three modes, and controlled by twin spacing and the angle between twin boundaries (TBs) orientation and loading direction. Particularly, most of previous researches mainly focused on the deformation mechanisms during the plastic flow stage and researchers paid little attention on the anisotropic characteristics of TBs at the elastic stage which are also essential to manufacture the high-performance materials. Therefore, this study is aiming to systematically investigate the anisotropic effect of TBs both at the elastic and plastic stages within the single crystalline or polycrystalline systems by molecular dynamics (MD) simulations. It is revealed that, when the loading direction is parallel to twin planes, the introduction of TBs in single crystalline models will significantly affect the characteristics of atomic bond rotation and elongation dominated elastic deformation, which can alter the Poisson’s ratio of materials, generate elastic-softening behavior and inhomogeneous elastic deformation. At the plastic flow stage, the deformation mechanism transforms from trans-twin dislocation slippage into the coexistence of Hard Mode I and threading dislocation slippage (Hard Mode II) when the loading direction changes from parallel to perpendicular direction with respect to TBs. Moreover, the dislocation segments at the conjunction of trans-twin dislocation play a momentous role in enhancing material strength. The results for polycrystalline models are consistent with that of single crystalline ones. These findings are expected to be beneficial for the development of high-performance nanostructured materials for structural and functional applications by strain engineering and defect regulation.

MUsculo-Skeleton-Aware (MUSA) deep learning for anatomically guided head-and-neck CT deformable registration

Deep-learning-based deformable image registration (DL-DIR) has demonstrated improved accuracy compared to time-consuming non-DL methods across various anatomical sites. However, DL-DIR is still challenging in heterogeneous tissue regions with large deformation. In fact, several state-of-the-art DL-DIR methods fail to capture the large, anatomically plausible deformation when tested on head-and-neck computed tomography (CT) images. These results allude to the possibility that such complex head-and-neck deformation may be beyond the capacity of a single network structure or a homogeneous smoothness regularization. To address the challenge of combined multi-scale musculoskeletal motion and soft tissue deformation in the head-and-neck region, we propose a MUsculo-Skeleton-Aware (MUSA) framework to anatomically guide DL-DIR by leveraging the explicit multiresolution strategy and the inhomogeneous deformation constraints between the bony structures and soft tissue. The proposed method decomposes the complex deformation into a bulk posture change and residual fine deformation. It can accommodate both inter- and intra- subject registration. Our results show that the MUSA framework can consistently improve registration accuracy and, more importantly, the plausibility of deformation for various network architectures. The code will be publicly available at https://github.com/HengjieLiu/DIR-MUSA.

Combined extension and torsion of hydrogels with chemo-mechanical coupling: Revealing positive poynting effect

In this paper, combined extension and torsion of hydrogel subject to a chemo-mechanical coupled loading is described in the framework of continuum mechanics, where the free energy density consists of the elastic, mixing and chemical contributions. A simplified, closed-form and exactly analytical solution to the mechanical response is obtained, which accounts for the coupling effect of external loading, chemical potential and microstructural parameters, such as crosslinking degree, Flory-Huggins parameter, etc. In particular, the effect of free swelling and microscopic diffusion on deformation of the hydrogel at equilibrium state is discussed, reaching some fundamental conclusions. Negative axial forces are captured, revealing the typical positive Poynting effect where the cylinder tends to elongate on twisting, and an inhomogeneous deformation, induced by torsion, along the radial direction is demonstrated. Furthermore, the dynamic competition between external loading and solvent environment is revealed and investigated, where the direct connection between internal micro-physical parameters and macroscopic deformation is demonstrated. The theoretical results presented in this paper may provide predictions and guidance for the mechanical analysis and design of hydrogel cylinder subject to extension and torsion in a solvent.

Thermal-mechanical-chemical coupled model and three-dimensional damage evaluation based on computed tomography for high-energy laser-ablated CFRP

High-energy laser is widely used for machining carbon fiber reinforced polymer (CFRP) composites because of their high precision and fine quality. However, the mechanism by which CFRPs are damaged by high-energy laser in processing is unclear. In this article, the coupled mechanism of laser-ablated CFRPs is investigated experimentally and theoretically. The three-dimensional morphology of laser-damaged CFRPs is captured by computed tomography (CT), which quantitatively characterizes the degree of pyrolytic charring and internal delamination. Accordingly, a thermal-mechanical-chemical coupled model is established considering the matrix pyrolysis, pyrolysis gases flow, sublimation of the charring layer and mechanical failure. The progressive loss of solid media and the inhomogeneous deformation of CFRPs are incorporated into the traditional ablation kinetic model, making it possible to describe the damage to CFRPs caused by both chemical reactions and thermal stress. The predicted damage morphology is consistent with the experimental results, revealing the generation of internal defects due to the synergistic effects of interlaminar tensile stress and matrix pyrolysis. Additionally, the effects of charring layer sublimation, laser power and process time on damage responses are analyzed, and the real-time evolution of damage degree is investigated.

Interfacial inhomogeneous plastic deformation during rotary friction welding of dissimilar AA2219-SS321 joint combination with AA6061 interlayer

This research investigates the inherent radial non-uniformity within the rotary friction welding process, particularly concerning microstructure attributes like grain size, grain boundaries, misorientation angles, and interlayer presence along the radial axis. SS321-AA2219 rotary friction welding was carried out with and without an AA6061 interlayer. The numerical thermal model suggests increase in temperatures from the center to the periphery, due to non-uniform heat generation. Also, dissimilar material across the interface resulted in an asymmetric temperature profile along axial direction. Plastic deformation on the Aluminum side suggests dynamic recrystallization and grain refinement, whereas pronounced low-angle grain boundary (LAGB) formation near the SS side interface validates dynamic recovery. A radial non-uniformity in microstructure is observed, with metrics such as average grain size, LAGB fraction, and misorientation showing an increase from the center towards the periphery. The insertion of an interlayer alters process dynamics, manifesting in reduced temperatures and heightened forces, resulting in a more consolidated joint by enhancing the strength by 31 %. Interdiffusion of elements across the interface formed Fe-Al intermetallic compounds (IMC) confirmed with X ray diffraction. Fractography analysis elucidates the presence of rubbing marks and facet surfaces in interlayer-less joints, while joints with interlayer display sticking and dimples.

Inhomogeneous deformation in the radial direction of the cold radial forged 30SiMn2MoVA steel tube

In this paper, the inhomogeneous deformation in the radial direction of the cold radial forged 30SiMn2MoVA steel tube was studied by finite element method, analyzing the microstructure and mechanical tests. The simulated result shows that the inhomogeneous deformation mainly distributed from the inner layer to the middle layer. In this region, the equivalent plastic strain rapidly decreases. The change from the middle to the outer is not significant. The distribution of microstructure and the results of mechanical properties also follow this pattern. The inner layer has the most refined grain size and the highest dislocation density. The strongest {110}<110> texture component has also been formed in the inner layer. The strength value of the inner layer is the highest, and the elongation is the lowest. There is not much difference in these indicators between the middle and outer regions. By calculating the strengthening contributions of solid solutions, dislocation density, and grain boundaries to yield strength, it was found that dislocation density is the main contributor. The calculated yield strength value is consistent with the experimental value.

Insight into elongation and strength enhancement of heat-treated LPBF Ni-based superalloy 718 using in-situ SEM-EBSD

This study presents a detailed investigation into the deformation behaviour and the factors affecting the strength and ductility of laser powder bed fusion (LPBF) Ni-based superalloy 718 (Inconel 718) in both as-printed and heat-treated conditions using in-situ SEM + EBSD. The results show that following post-deposition high homogenization temperatures, the columnar grain structure of the as-printed Inconel 718 alloy successfully transformed to a nearly uniform grain size and the subsequent aging processes facilitated the precipitation of strengthening phases (γ′, γ''). The specimen subjected to heat treatment (HT1) exhibited higher strength but lower ductility, while the as-printed specimen shows higher tensile elongation due to high initial dislocation density. In contrast, the heat-treated (HT2) specimen presented a more optimal combination of strength and ductility. The underlying mechanism for the enhanced tensile properties in the HT2 specimen was nearly homogeneous deformation trend across the grains and ultrafine precipitation of hardening phases. In addition, the twin boundaries were stable in the early deformation stages and maintained their orientation. Multiple slip systems were activated at the high-deformation stage, resulting in a high proportion of geometric necessary dislocations. Further, the interaction of deformation-induced dislocation with twin boundaries transformed them into general boundaries such as high and low-angle grain boundaries, ultimately increasing ductility. On contrary, in the HT1 specimen, the deformation inhomogeneity in grains enabled the strain localization at grain boundaries, which ultimately caused the early formation of cracks.

Effect of precipitation phase on the flow behavior of a nickel-based superalloy during compressive deformation

Nickel-based superalloys have become indispensable in micro-forming processes owing to their outstanding mechanical properties. The size effect significantly impacts the formability of components at the mesoscopic scale, resulting in compression deformation behaviors distinct from those observed at the macroscopic scale. The classical Hall-Petch formula can hardly express this phenomenon precisely. This study conducted compression tests of a nickel-based superalloy at the mesoscopic scale, exploring the role of the feature size (specifically, the ratio of sample diameter to grain size, D/d) and the precipitation phase on the plastic deformation behavior. The results show that increasing feature size of samples as well as particle size and volume fraction of γ′ and γʺ phases enhance the flow stress of the superalloy. When the feature size exceeds 8.6, the flow stress decreases with decreasing feature size. However, when the feature size is below 8.6, the flow stress increases with decreasing feature size. A model is proposed to comprehensively explain the size effect and the precipitation phase on compressive flow stress. The surfaces of samples experience inhomogeneous deformation during compressive deformation. The trend towards inhomogeneous deformation has become more pronounced as feature size decreases. Furthermore, the increase in particle size and volume fracture of γ′ and γʺ phases limits the inhomogeneous deformation of the sample surface.

Tailoring macrostructure and texture in bobbin-tool friction stir weld via manipulation of deformation behaviour of plasticised metal during welding enabled by modifying tool profile

Bobbin-tool friction stir welding is a variant of friction stir welding with high process flexibility that has garnered considerable attention from the community. The reliability of the weld is sensitive to the macrostructure and texture of the stir zone, which must be carefully tailored. The macrostructure of the stir zone is governed by the refill behaviour of the plasticised metal associated with the bobbin-tool; refill occurs preferentially near the upper and lower shoulders, creating a triangular gap at the mid-thickness level that is subsequently closed by the confluence of the layered refilling plasticised metal from the upper and lower levels. Volumetric defects easily develop in this triangular confluence region because the symmetrical confluence of the layered refilling metal has the inherent characteristic of limited intermixing. The visual appearance of the triangular region, featuring limited voiding, was improved by tapering the stirring probe. This modification reduced the volume of displaced metal, leaving a smaller gap to be refilled during welding. Concurrently, the symmetrical confluence pattern was altered to an asymmetrical pattern, which enhanced the intermixing of the layered refilling metal from the upper and lower levels and promoted gap closure. For defect-free welds, macroscopic deformation inhomogeneity under tensile loading was observed due to the presence of a strong basal texture in the stir zone. The texture was scattered by disrupting the regular shear deformation pattern in the stir zone, which was achieved by modifying the tool profile. The activation capability of both basal slip and extension twinning among various local regions across the stir zone was substantially reduced through texture tailoring, resulting in more homogeneous tensile deformation. Consequently, elongation was enhanced by 66 %. This study highlights an easy-to-perform and generic strategy that can improve the quality of bobbin-tool friction stir welds.

On the effect of deformation conditions on the metal flow behavior during upsetting process using finite element simulation DEFORM 3D software

AbstractThe study reports on the metal flow behaviour during upsetting or forging using the finite element method. Forging simulation studied the metal flow behaviour of a laboratory-sized specimen and a cylindrical engine connecting rod specimen of AISI 52100 high-chromium steel specified in the software database. The focus was to study the effect of deformation conditions (temperature and die velocity) on metal flow behaviour during forging. The simulation results showed heterogeneous metal flow behaviour during forging. Hence, this indicates that effective flow stress and flow strain, particle flow velocity, effective strain rate, damage and temperature distribution exhibited inhomogeneous deformation behaviour. As the temperature increased, the forging load decreased, thus a decrease in deformation resistance. The simulation of the engine connecting rod further confirmed inhomogeneous deformation during forging. Damage coefficient results show that the crack pin end had a higher damage probability during forging. This study clearly showed that finite element simulation can predict metal flow behaviour during the forging of AISI 52100 steel. The study output provides a basis for analysing and optimising most industrial metal forming processes using a numerical simulation approach. Hence, this method is effective in predicting flow behaviour.

Unveiling the mechanisms behind texture formation and its impact on the torsional performance of cold-drawn pearlitic steel wires

High carbon pearlitic steel wires are widely used in the industry, such as for producing tyre cords and steel cables due to its excellent mechanical properties. Cold drawing is a crucial step in steel wire production. Due to the loading state during the cold drawing process, pearlitic wires tend to exhibit a <110> fiber texture. The non-uniform texture distribution on the cross-section of steel wires has been observed experimentally. The mechanisms yielding this non-uniformly distributed texture are carefully investigated in this study using a multi-scale computational approach. Firstly, a macroscale finite element model is established to simulate the deformation behaviour of pearlitic steel wires during cold drawing, with the aim of thoroughly investigating the inhomogeneous elastic-plastic deformation behaviours. Secondly, the macro mechanical responses are incorporated into the mesoscale representative volume element model as boundary conditions to comprehensively study the effect of inhomogeneous deformation characteristics on texture formation. The results present a significant advancement by revealing that the non-uniform texture distribution in a steel wire can primarily be attributed to the multiaxial stress state on the cross-section. Notably, at the center of the steel wire, the maximum principal stress aligns with the drawing axis, resulting in a dominant <110> fiber texture. Conversely, at the subsurface, the maximum principal stress progressively shifts towards the circumferential direction, yielding an evolving texture characterized by a {110}<110> circumferential texture. Furthermore, the research uncovers a crucial finding that it is the {110}<110> circumferential texture that significantly weakens the torsion ability of the wires. This is due to the limited activation of slip systems, marking a key advancement in understanding the mechanical properties of steel wires.

Inhomogeneous deformation in melt-pool structure of Al-Fe-Cu alloy manufactured by laser powder bed fusion

Abstract The laser powder bed fusion (L-PBF) processed Al–2.5Fe–2Cu (mass%) alloy exhibited a high tensile strength above 340 MPa and pronounced directional dependence. The sample exhibited a characteristic inhomogeneous microstructure (in melt-pool structure) arising from the local melting and rapid solidification in the L-PBF process. The coarsened cellular structure localized along the melt pool boundary resulted in the local soft regions affected by the melt pool structure. The local vulnerability contributed to the direction dependence of the tensile ductility of the specimen.

The Role of Deformation and Microstructure Evolution on Texture Formation of a TA15 Alloy Subjected to Plane Strain Compression.

In this study, the texture formation mechanism of a TA15 titanium alloy under different plane strain compression conditions was investigated by analyzing the slipping, dynamic recrystallization (DRX) and phase transformation behaviors. The results indicated that the basal texture component basically appears under all conditions, since the dominant basal slip makes the C-axis of the α grain rotate to the normal direction (ND, i.e., compression direction), but it has a different degree of deflection. With an increase in deformation amount, temperature or strain rate, {0001} poles first approach the ND and then deviate from it. Such deviation is mainly caused by a change in slip behaviors and phase transformation. At a smaller deformation amount and higher strain rate, inhomogeneous deformation easily causes a basal slip preferentially arising from the grain with a soft orientation, resulting in a weak basal texture component. A greater deformation amount can increase the principal strain ratio, thereby promoting other slip systems to be activated, and a lower temperature can increase the critical shear stress of the basal slip, further causing a dispersive orientation under these conditions. At a higher temperature and a lower strain rate, apparent phase transformation will induce the occurrence of lamellar α whose orientation obeys the Burgers orientation of the β phase, thereby disturbing and weakening the deformation texture. As for DRX, continuous-type (CDRX) is most common under most conditions, whereas CDRX grains have a similar orientation to deformed grains, so DRX has little effect on overall texture. Moreover, the microhardness of samples is basically inversely proportional to the grain size, and it can be significantly improved as lamellar α occurs. In addition, deformed samples with a weaker texture present a higher microhardness due to the smaller Schmidt factors of the activated prism slip at ambient loading.

Inhomogeneous deformation behavior and recrystallization mechanism of Mg-Gd-Y-Zn-Zr alloy containing only intragranular lamellar LPSO phase

Inhomogeneous plastic deformation and recrystallization behavior of Mg-Gd-Y-Zn-Zr alloy containing only intragranular lamellar long-period stacking ordered (LPSO) phase were investigated by isothermal compression experiments at the temperatures of 350–450 °C, and the strain rates of 0.001 ∼ 10 s−1. Results showed that Mg-Gd-Y-Zn-Zr alloys with varying degrees of bimodal structures were obtained after compression. The lamellar LPSO phase directions in residual coarse grains were aligned in the radial direction (RD). Dynamic recrystallization (DRX) grains induced at grain boundaries, kinked bands, and lamellar shearing regions during compression synergistically promoted coarse grain refinement. Moreover, the condition of high temperature and medium strain rate (450 °C-0.1 s−1) contributed to the uniform extension of "mantle layers" of fine DRX grains. In contrast, the condition of medium temperature and high strain rate (400 °C-10 s−1) could accelerate the deflection of CD-directed (compression direction) LPSO lamellae and the formation of local high-energy regions, facilitating the generation of recrystallization band. In addition, a high strain rate (400 °C-10 s−1) is more conducive to the formation of a heavily bimodal structure than a high temperature (450 °C-0.1 s−1). Only a larger spacing of LPSO lamellae (∼1.4 μm) could meet the spatial requirements of recrystallization. Further analysis revealed that the continuous dynamic recrystallization (CDRX) mechanism characterized by the expansion of "mantle layers" and nucleation along kinked boundaries and lamellar shearing regions was the primary grain refinement mechanism. The discontinuous dynamic recrystallization (DDRX) mechanism only exhibited a limited role due to the inhibition of the highly dense lamellar LPSO phase on grain boundaries bulging. After compression, the orientation of residual coarse grains gradually deviated toward the CD. While the recrystallization with limited proportion and random orientation cannot significantly weaken the basal texture.

Orientation dependence of nickel-based single crystal superalloys in VHCF regime

Aimed at research the deformation orientation in VHCF regime under different temperatures, fatigue behavior of [111]-oriented DD6 single crystal superalloy at 1000 °C and 760 °C was studied. Using the stress range criterion, the [111] orientation shows higher fatigue resistance. This difference decreases with lower stress ranges and almost vanishes near 109 cycles. In contrast, the [111] orientation has lower fatigue resistance than the [001] orientation by using the total strain range criterion. Dislocations are restricted from shearing the γ’ phase due to the lower octahedral resolved shear stress in the [111]-oriented, decreasing the deformation in γ’ phase. Combined with distinctive cross-slip behavior, this further increased the deformation along the γ-channel, significantly enhancing deformation inhomogeneity between the γ’ phase and γ-channels. At elevated temperatures, thermally activated dislocation climb and higher climb stress factor lead to a greater reduction in fatigue performance for [111] orientation at lower stress level.

Cryogenic mechanical behavior and FCC → HCP phase transformation mechanism in a Si-added CrCoNi medium-entropy alloy under quasi-static and dynamic tension

The CrCoNiSi0.3 MEA exhibits excellent cryogenic mechanical properties upon both quasi-static and dynamic tension. Under quasi-static tension at cryogenic temperature, the engineering yield and ultimate tensile strengths (UTS) reach 980 MPa and 1800 MPa, respectively, with notable ductility (62 %). The product of UTS and total elongation (TE) is 111.6 GPa %, surpassing most cryogenic high strength-ductility alloys. The significant mechanical strength enhancement is attributed to the denser deformation twins (DTs), multiple twinning, and extensive face-centered-cubic to hexagonal-close-packed (HCP) phase transitions, resulting in a high work hardening capacity. Upon dynamic tension at cryogenic temperature, the strength and strain hardening are further improved, which originates from the thickening DTs and HCP sequence and localized plastic deformation. The effects of temperature and strain rate on phase transition are studied. It is proposed that there is a competing relationship between high strain rate and increased stacking fault energy (SFE) due to temperature rise. The coupling effect of cryogenic temperature and high strain rate inhibits phase transition due to the deformation inhomogeneity in CrCoNiSi0.3 MEA. The findings make a valuable contribution to understand the influence of temperature and strain rate on the mechanism of FCC-to-HCP phase transition.