Hexagonal Close-packed Metals Research Articles

Constitutive Model for the Thermo-viscoplastic Behavior of Hexagonal Close-Packed Metals with Application to Ti–6Al–4V Alloy

In this paper, a new physically based constitutive model is developed for hexagonal close-packed metals, especially the Ti–6Al–4V alloy, subjected to high strain rate and different temperatures based on the microscopic mechanism of plastic deformation and the theory of thermally activated dislocation motion. A global analysis of constitutive parameters based on the Latin Hypercube Sampling method and the Spearman’s rank correlation method is adopted in order to improve the identification efficiency of parameters. Then, an optimal solution of constitutive parameters as a whole is obtained by using a global genetic algorithm composed of an improved niche genetic algorithm, a global peak determination strategy and the local accurate search techniques. It is concluded that the proposed constitutive modal can accurately describe the Ti–6Al–4V alloy’s dynamic behavior because the prediction results of the model are in good agreement with the experimental data.

Properties of Moving Discrete Breathers in Beryllium

Discrete breathers (DBs) have been described among pure metals with face-centered cubic (FCC) and body-centered cubic (BCC) lattice, but for hexagonal close-packed (HCP) metals, their properties are little studied. In this paper, the properties of standing and moving DBs in beryllium HCP metal are analyzed by the molecular dynamics method using the many-body interatomic potential. It is shown that the DB is localized in a close-packed atomic row in the basal plane, while oscillations with a large amplitude along the close-packed row are made by two or three atoms, moving in antiphase with the nearest neighbors. Dependences of the DB frequency on the amplitude, as well as the velocity of the DB on its amplitude and on parameter δ, which determines the phase difference of the oscillations of neighboring atoms, are obtained. The maximum velocity of the DB movement in beryllium reaches 4.35 km/s, which is 33.7% of the velocity of longitudinal sound waves. The obtained results supplement our concepts about the mechanisms of localization and energy transport in HCP metals.

An atomic displacive model for [formula omitted] twinning in hexagonal close packed metals with the emphasis on the role of partial stacking faults in formation of [formula omitted] twins

Anomalous basal type stacking faults (SFs) called partial SFs (PSFs) have been observed extensively within {101¯2} or extension twins for a variety of hexagonal close packed (HCP) metals. The formation of PSFs can generate a stacking sequence in which every other basal plane has been displaced by a 1/3101¯0 vector. Based on this special structural property of HCP metals, a new crystallographic model is developed for 101¯21¯011 twinning system. In contrast to homogenous lattice shearing process in classical twinning model, the new model describes that formation of PSFs can provide transient locations of atoms in such a way that a subsequent zonal-twinning mechanism including a set of relatively simple shear and shear-shuffle atomic displacements toward twinning direction is sufficient to accomplish 101¯21¯011 twinning. These shear and shear-shuffle atomic displacements are formally determined, and their analytical expressions are given in a generalized explicit form for a whole twinned domain of any HCP crystal with c/a ratio between 1.5 and 1.9. It will be shown that the macroscopic effect of spontaneous cooperative movements of atoms in the new mechanism is a simple shear, and the invariant plane strain condition of {101¯2} or twinning plane is preserved.

A Graph Theory-Based Automated Twin Recognition Technique for Electron Backscatter Diffraction Analysis

The present article introduces a new software, Microstructure Evaluation Tool for Interface Statistics (METIS), that performs high-throughput microstructure statistical analysis from electron backscatter diffraction maps. Emphasis is placed on the detection of twin domains in hexagonal close-packed metals. The numerical framework on which METIS is built leverages graph theory, group structures, and associated numerical algorithms to automatically detect twins and unravel both their intrinsic characteristics features and those pertaining to their interactions. The proposed graphical interface allows for the detection and correction of unlikely twin/parent associations rendering the approach applicable to highly deformed microstructures. Twin statistics and microstructural data are classified and saved in a relational database that can be interrogated via either GUI or SQL requests to reveal a wide spectrum of features of the microstructure. Illustration of the approach is performed in the case of zirconium.

Changes in misorientations of $$ \{ 10\bar{1}1\} $$ { 10 1 ¯ 1 } twin boundaries in deformed magnesium alloy

Deformation twins usually play an important role in plastic deformation and undoubtedly influence the mechanical property of hexagonal close-packed (hcp) metals. Understanding the interfacial features of twinning boundaries and their evolution during the plastic deformation is crucial to hcp materials design, processing and application. In this work, the interfacial characteristics of $$ \{ 10\bar{1}1\} $$ contraction twin in deformed magnesium alloy are investigated by means of electron back-scatter diffraction, transmission electron microscope and high-resolution TEM. The results show that the misorientation angle across the boundaries of $$ \{ 10\bar{1}1\} $$ contraction twin can deviate from the theoretical value $$ \left( {56.2^\circ \left\langle {11\bar{2}0} \right\rangle } \right) $$ , resulting in that the $$ \{ 10\bar{1}1\} $$ twinning planes of the twin crystal and the matrix crystal do not coincide any longer. Multiple dislocation activities within the $$ \{ 10\bar{1}1\} $$ contraction twin and interfacial defects located on the $$ \{ 10\bar{1}1\} $$ twinning plane are also characterized. According to these experimental features, a possible mechanism responsible for such deviation phenomenon is proposed. In addition, the similar deviation phenomenon is also observed in the $$ \{ 10\bar{1}1\} $$ – $$ \{ 10\bar{1}2\} $$ double twin system.

Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study

A detailed statistical analysis is performed using Electron Back Scatter Diffraction (EBSD) to establish the effect of microstructure on twin nucleation and growth in deformed commercial purity hexagonal close packed (HCP) titanium. Rolled titanium samples are compressed along rolling, transverse and normal directions to establish statistical correlations for {10–12}, {11–21}, and {11–22} twins. A recently developed automated EBSD-twinning analysis software is employed for the statistical analysis. The analysis provides the following key findings: (I) grain size and strain dependence is different for twin nucleation and growth; (II) twinning statistics can be generalized for the HCP metals magnesium, zirconium and titanium; and (III) complex microstructure, where grain shape and size distribution is heterogeneous, requires multi-point statistical correlations.

Свойства движущихся дискретных бризеров в бериллии

AbstractDiscrete breathers (DBs) have been described among pure metals with face-centered cubic (FCC) and body-centered cubic (BCC) lattice, but for hexagonal close-packed (HCP) metals, their properties are little studied. In this paper, the properties of standing and moving DBs in beryllium HCP metal are analyzed by the molecular dynamics method using the many-body interatomic potential. It is shown that the DB is localized in a close-packed atomic row in the basal plane, while oscillations with a large amplitude along the close-packed row are made by two or three atoms, moving in antiphase with the nearest neighbors. Dependences of the DB frequency on the amplitude, as well as the velocity of the DB on its amplitude and on parameter δ, which determines the phase difference of the oscillations of neighboring atoms, are obtained. The maximum velocity of the DB movement in beryllium reaches 4.35 km/s, which is 33.7% of the velocity of longitudinal sound waves. The obtained results supplement our concepts about the mechanisms of localization and energy transport in HCP metals.

Proliferation of twinning in hexagonal close-packed metals: Application to magnesium

Plastic deformation of metallic alloys usually takes place through slip, but occasionally involves twinning. In particular, twinning is important in hexagonal close packed (HCP) materials where the easy slip systems are insufficient to accommodate arbitrary deformations. While deformation by slip mechanisms is reasonably well understood, comparatively less is known about deformation by twinning. Indeed, the identification of relevant twinning modes remains an art. In this paper, we develop a framework combining a fundamental kinematic definition of twins with large-scale atomistic calculations to predict twinning modes of crystalline materials. We apply this framework to magnesium where there are two accepted twin modes, tension and compression, but a number of anomalous observations. Remarkably, our framework shows that there is a very large number of twinning modes that are important in magnesium. Thus, in contrast to the traditional view that plastic deformation is kinematically partitioned between a few modes, our results suggest that deformation in HCP materials is the result of an energetic and kinetic competition between numerous possibilities. Consequently, our findings suggest that the commonly used models of deformation need to be extended in order to take into account a broader and richer variety of twin modes, which, in turn, opens up new avenues for improving the mechanical properties.

Twin-twin interactions and contraction twin formation in an extruded magnesium alloy subjected to an alteration of compressive direction

Twinning and detwinning represent major deformation mechanisms in hexagonal close-packed (hcp) metals. The aim of this study was to identify twin-twin interactions and contraction twin formation in an AZ31 magnesium alloy when the compressive direction was changed from the extrusion direction (ED) to the normal direction (ND) via electron backscatter diffraction (EBSD) and Schmid factor analysis. {101¯2} extension twins of multiple variants were observed after compressive deformation of 4.3% along ED. The detwinning of {101¯2} extension twins occurred along with the formation of {101¯1} and {101¯3} contraction twins, when the compressive direction was changed to ND. The extension twins in some grains almost fully vanished, making the grains back to a twin-free state. A new twin-twin interaction mechanism being different from double twinning (defined as twins within a twin) was identified, due to the impingement of {101¯1} contraction twins nucleated in the matrix grain on a pre-existing {101¯2} extension twin.

Symmetry and Structure of Cubic Semiconductor Surfaces.

A systematic stereographic approach to the description of surface symmetry and structure, applied previously to face-centered cubic, body-centered cubic, and hexagonal close-packed metals, is here extended to the surfaces of diamond-structure and zinc-blende-structure semiconductors. A variety of symmetry-structure combinations are categorized and the chiral properties of certain cases emphasized. A general condition for nonpolarity in the surfaces of zincblende materials is also noted.

Modeling the effect of neighboring grains on twin growth in HCP polycrystals

In this paper, we study the dependence of neighboring grain orientation on the local stress state around a deformation twin in a hexagonal close packed (HCP) crystal and its effects on the resistance against twin thickening. We use a recently developed, full-field elasto-visco-plastic formulation based on fast Fourier transforms that account for the twinning shear transformation imposed by the twin lamella. The study is applied to Mg, Zr and Ti, since these HCP metals tend to deform by activation of different types of slip modes. The analysis shows that the local stress along the twin boundary are strongly controlled by the relative orientation of the easiest deformation modes in the neighboring grain with respect to the twin lamella in the parent grain. A geometric expression that captures this parent-neighbor relationship is proposed and incorporated into a larger scale, mean-field visco-plastic self-consistent model to simulate the role of neighboring grain orientation on twin thickening. We demonstrate that the approach improves the prediction of twin area fraction distribution when compared with experimental observations.

A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method

Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.

Hard-sphere displacive model of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56°, a) contraction twins in magnesium.

Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation (56°, a). The classical shear theory of deformation twinning does not specify the atomic displacements and does not explain why contraction twinning is less frequent than extension twinning. The paper proposes a new displacive model in line with our previous work on martensitic transformations and extension twinning. A continuous angular distortion matrix that transforms the initial hexagonal close-packed (h.c.p.) crystal into a final h.c.p. crystal is determined such that the atoms move as hard spheres and reach the final positions expected by the orientation relationship. The calculations prove that the distortion is not a simple shear when it is considered in its continuity. The ({0{\overline 1}1}) plane is untilted and restored, but it is not fully invariant because some interatomic distances in this plane evolve during the distortion process; the unit volume also increases up to 5% before coming back to its initial value when the twinning distortion is complete. Then, the distortion takes the form of a simple shear on the ({0{\overline 1}1}) plane with a shear along the direction [{18,{\overline 5},{\overline 5}}] of amplitude 0.358. Experiments are proposed to validate or disprove the model.

Uniaxial stress-driven grain boundary migration in Hexagonal Close-packed (HCP) metals: Theory and MD simulations

Stress-driven grain boundary (GB) migration is an important plastic deformation mechanism in nanopolycrystalline metals. Recently, Liu et al. (2014) and Zong et al. (2015) have shown a new mechanism for GB migration in a Hexagonal Close-packed (HCP) bicrystal with 90° GB misorientation under uniaxial stress loading conditions, which is different from shear-coupled GB migration. In real polycrystals, GBs have random orientations. To investigate the effects of GB misorientation and loading directions, we propose a mechanics model for uniaxial stress-driven GB migration in which the GB misorientation varies from 0° to 90°. Two types of imposed uniaxial loadings with loading directions parallel and perpendicular to the GB are considered. The model prediction is compared with that by molecular dynamics (MD) simulations. The results reveal that the uniaxial stress-driven GB migration can only occur in some range of GB misorientation under both loading conditions. The critical strain to trigger the GB migration varies with GB misorientation in a non-monotonic way. The proposed model provides new insights into the GB migration in HCP metals.

Size dependent structural stability of Mo, Ru, Y and Sc nanoparticles

Abstracts The Gibbs free energy model was generalized to predict the phase stability of Mo, Ru, Y and Sc at all size range from nanometer to bulk size. The size-, shape- and temperature-dependent phase diagrams of Mo, Ru, Y and Sc were firstly computed to explain the corresponding experimental observations, including the latest one on Ru nanoparticles. Especially, we re-confirmed and summarized that there exists a general law for the stable phases of metal nanoparticles: for body-centered-cubic (BCC) metals (eg. Mo), there exists face-centered-cubic (FCC) phase at small size; for a kind of hexagonal-close-packed (HCP) metals (eg. Ru), they can transform into FCC at small size; for the other kind of HCP metals (eg. Sc or Y), they can change to BCC at high temperature (Y at 1754 K, and Sc at 1588 K) but to FCC at small size. This work establishes a map of the evolution of the structures from macro to nanoscale.

Characterizations of microstructure and crystallographic orientation in a near-α titanium alloy billet

Previous studies have found that the α+β and near-α titanium alloys often contain large regions, referred as macrozones, with sharp local texture that differs from one region to the next. In this work the characterizations of microstructure and crystallographic orientation heterogeneities were studied by optical microscopy and electron backscattered diffraction techniques in a billet of a near-α titanium alloy Ti60. It was found that a heterogeneous microstructure, both in orientation distribution and morphology, comprising remnants of α lamellae along the axis direction and equiaxed α grain was found in the longitudinal section of the billet. In the billet, a weak <11–20>//AD fiber texture component was found, and this texture component was related to the special deformation mode for the billet and recrystallization texture in hexagonal close-packed metals. The deformation was mainly supported by prismatic <a> slip in the α phase during forging according to in-grain misorientation axis analysis, while many subgrains/grains with low-angle boundaries were found within an apparent α grain under EBSD observation.

Shock compression and release of a-axis magnesium single crystals: Anisotropy and time dependent inelastic response

To gain insight into inelastic deformation mechanisms for shocked hexagonal close-packed (hcp) metals, particularly the role of crystal anisotropy, magnesium (Mg) single crystals were subjected to shock compression and release along the a-axis to 3.0 and 4.8 GPa elastic impact stresses. Wave profiles measured at several thicknesses, using laser interferometry, show a sharply peaked elastic wave followed by the plastic wave. Additionally, a smooth and featureless release wave is observed following peak compression. When compared with wave profiles measured previously for c-axis Mg [Winey et al., J. Appl. Phys. 117, 105903 (2015)], the elastic wave amplitudes for a-axis Mg are lower for the same propagation distance, and less attenuation of elastic wave amplitude is observed for a given peak stress. The featureless release wave for a-axis Mg is in marked contrast to the structured features observed for c-axis unloading. Numerical simulations, using a time-dependent anisotropic modeling framework, showed that the wave profiles calculated using prismatic slip or (101¯2) twinning, individually, do not match the measured compression profiles for a-axis Mg. However, a combination of slip and twinning provides a good overall match to the measured compression profiles. In contrast to compression, prismatic slip alone provides a reasonable match to the measured release wave profiles; (101¯2) twinning due to its uni-directionality is not activated during release. The experimental results and wave profile simulations for a-axis Mg presented here are quite different from the previously published c-axis results, demonstrating the important role of crystal anisotropy in the time-dependent inelastic deformation of Mg single crystals under shock compression and release.

Dislocation-dynamics-based dynamic constitutive model of magnesium alloy

Since the dynamic plastic deformation of magnesium alloy, a hexagonal close-packed metal, consists of dislocation slipping and twinning, it is assumed that the dynamic plastic deformation of magnesium alloy is controlled by the mechanism with lower resistance, i.e., dislocation slipping or twinning. So, the evolution law of dynamic plastic deformation of the alloy can be determined by that of the resistance of dislocation slipping or twinning. After the evolution equations of the deformation resistances are deduced, the dynamic constitutive model of magnesium alloy is developed in this work. The proposed model is further verified by describing the dynamic tensile and compressive deformation of AZ\(_{31}\)B magnesium alloy obtained by the split Hopkinson pressure bar device. It is observed that the simulations agree well with the experimental results.

Effect of Lattice Rotation on Hardening Behavior of HCP Metals

Strain hardening behavior is known to strongly affect the formability of metallic sheets. The effect of lattice rotation on the hardening behavior of hexagonal close-packed (HCP) metals is numerically investigated using a homogenization-based crystal plasticity model to represent the polycrystalline behavior. The effect of lattice rotation on strain hardening behavior evaluated using different initial textures, and the geometrical hardening effect of HCP metals is investigated. In addition, the critical resolved shear stress of each slip system is varied and is shown to affects the strain hardening in HCP metals. In this study, we further discuss the possibility to improve the formability of HCP metals.

Ab initio reappraisal of the dislocation-associated stacking faults in hcp titanium: a new dissociation mechanism

The slip is a secondary slip system in hexagonal close-packed metals which is often activated when they undergo a c-axis deformation. The behaviour of the screw dislocation remains unclear. Via ab initio calculations with an all atom all direction relaxation method, we find a stable 0.57 stacking fault on plane () and a stable nanotwinned 0.215 stacking fault on plane () in -Ti. Based on these results, we propose a screw dislocation dissociation mechanism which allows a split to three partials. This suggests a more complex screw dislocation-related cross-slip mechanism.