Hexagonal Close-packed Metals Research Articles

Twin networks in hexagonal close-packed metals: morphology, connectivity, and incompatibilities

The mechanical response of hexagonal close-packed metals is mediated by the formation of three-dimensional twin domain networks. To assess the morphology of these networks and statistically characterize their fingerprint, a three-dimensional twin network in cryogenically compressed high-purity Ti was reconstructed using serial sectioning electron backscatter diffraction (EBSD). Adjoining intergranular twin pairs, high order twin intersections (e.g. triple junctions of twins), and twin network hubs with over 15 separate intergranular and intragranular contacts are found to be salient morphological features of these networks. Using kinematics, the interfacial incompatibilities arising from these twin contact at grain boundaries are studied. The analysis reveals that numerous misaligned paired twin configurations generate high incompatibilities, likely resulting from the contact between two initially distinct twin chains. These configurations generally induce higher incompatibilities than the ones of the individual twins, equivalent to introducing a dense wall of dislocations at twin-grain boundary facets with a dislocation spacing on the order of 1.3 nm or less. In contrast, the shear incompatibilities resulting from the formation of aligned twin pairs are generally reduced compared to non-transmitting twins. Further, twin triple junctions and branches – consisting of intergranular contact of three co-located twins – induce higher incompatibilities on average compared to adjoining twin pairs and represent sources of high shear localization in the domain network.

Strengthening of HCP metals with split basal texture through non-dislocation hardening mechanism

Work hardening mechanisms in metals have been extensively studied with a focus on the motion of dislocations and their inhibition, and these studies have provided in-depth knowledge of the relationship between dislocations and work hardening; however, other factors also influence the work hardening mechanism. When polycrystalline metals deform, the shape of the grain boundaries must match between neighboring grains, resulting in deformation constraint between the grains. Hexagonal close-packed (HCP) single crystals exhibit greater plastic anisotropy than those in body-centered cubic (BCC) and face-centered cubic (FCC) crystals, leading to stronger deformation constraint between grains in polycrystalline HCP metals. This study investigates the effects of deformation constraint between grains on macroscopic stress–strain curves by reproducing the deformation of HCP metals using crystal plasticity finite element analysis. The results indicate that in polycrystalline HCP metals, the non-dislocation effect, constraint between grains, also significantly affects work hardening.

Rules to identify and track the evolution dynamics of [formula omitted] twin variants in hexagonal close-packed metals

Twinning evolution laws derived based on physics are required to model plasticity and texture evolution resulting from the twinning in hexagonal close-packed structures. Atomistic simulations are employed to study the evolution of {101̄2} twins in Ti at 5 K temperature. The misorientation angle between the twinned region and parent matrix differs from the expected misorientation angle of 85.03∘. This closely aligns with the experimental findings. The deviation of twinning from {101̄2} twin plane makes it difficult to identify conjugate twins, leading to their coalescence. Both the c-vector and disorientation angle analyses are unable to track the variant type of the conjugate twins. The disorientation angle analysis can identify the conjugate twin variants but is unable to identify the variant type of the twin. The c-vector analysis can identify the conjugate twin variants as well as the variant type of the twin but is unable to track the variant type of the twin during its evolution. A set of rules are proposed to track the variant type of the twin during its evolution. These rules should help to understand the twin evolution dynamics in HCP metals and can be applied to study the twinning evolution dynamics at ambient conditions, even though they are designed for twinning evolution at 5 K temperature. The fundamental understanding of twin evolution dynamics should motivate the construction of the physics-based evolution laws for twinning.

[formula omitted] Twinning in hexagonal close-packed Re nanocrystals mediated by [formula omitted]|[formula omitted] interfacial facets

Twinning is an essential deformation mode of crystals which is attracting growing attention due to its potential in simultaneously improve the strength and ductility of metals. It is generally believed that twinning is mediated by shear and atomic shuffles on an invariant twinning plane. Here, by using in situ high resolution transmission electron microscopy, we report on an extension twinning mode in rhenium nanocrystals along the 〈101‾4‾〉 direction on the {202‾1} plane, which can be mediated by the formation of interfacial defects that fall between the parent prismatic plane and the twin pyramidal plane which are a pair of corresponding planes of the {202¯1} twinning mode. The incoherent twin boundary can partly evolve into the coherent twinning plane during detwinning. The findings provide direct evidences to the {202¯1} twin in hexagonal close-packed metals and corroborate the conjecture that twinning nucleation is essentially a transformation that conforms to and establishes the lattice correspondence which can be mediated by interfacial processes other than homogeneous shear on the twinning plane.

A new mechanism for nucleation of [formula omitted] twinning via interaction of [formula omitted] twin variants in hexagonal close-packed metals

Twin nucleation in high symmetry cubic structures is closely related to the activities of dissociated lattice dislocations. However, in low symmetry hexagonal close-packed (HCP) metals, the nucleation mechanisms for deformation twinning remain largely unclear. In this work, we conduct atomistic simulations and uncover a new mechanism for nucleation of {112¯2}〈112¯3¯〉 twinning which is an important mode in some HCP metals such as titanium and zirconium. Our simulations show that a coherent {112¯2} twin boundary can be formed as a result of twin-twin interaction between co-zone {112¯1} twin variants. During deformation, three co-zone {112¯1} twins form first and then interact. Two of the {112¯1} twin boundaries (TBs) merge into a coherent {112¯2} TB. This nucleation process does not involve any lattice dislocations or twinning dislocations. Lattice correspondence analyses indicate that such a nucleation process is feasible because all these {112¯1} and {112¯2} twins have the same (0001) K2 plane. The migration of {112¯2} TB is found to be mediated by the single-layer twinning dislocations.

Uncovering the Intrinsic High Fracture Toughness of Titanium via Lowered Oxygen Impurity Content.

Titanium (Ti) and its alloys are known to exhibit room-temperature fracture toughness below 130 MPa m1/2, only about one half of the best austenitic stainless steels. It is purported that this is not the best possible fracture resistance of Ti, but a result of oxygen impurities that sensitively retard the activities of plasticity carriers in this hexagonal close-packed metal. By a reduction of oxygen content from the 0.14wt% in commercial purity Ti to 0.02wt%, the mode-Ι fracture toughness of the low-oxygen Ti is measured to be as high as KJ Ic ≈ 255 MPa m1/2, corresponding to J-integral-based crack-initiation toughness of up to JIc ≈ 537kJ m-2. This extraordinary toughness, reported here for the first time for pure Ti, places Ti among the toughest known materials. The intrinsic high fracture resistance is attributed to the profuse plastic deformation in a significantly enlarged plastic zone, rendered by the pronounced deformation twinning ahead of the crack tip along with ample twin-stimulated 〈c+a〉 dislocation activities, in the absence of impeding oxygen. Controlling the content of a property-controlling impurity thus holds the promise to be a readily applicable strategy to reach for unprecedented damage tolerance in some other structural alloys.

Three-dimensional phase field modeling, orientation prediction and stress field analyses of twin-twin, twin-grain boundary reactions mediated by disclinations in hexagonal close-packed metals

Crystalline defects, such as dislocations, disclinations, twins and grain boundaries, play critical roles in determining the mechanical properties of metals and alloys. In particular, with multiple competitive deformation modes activated, the mechanical behaviors of hexagonal close-packed metals are strongly influenced by the interactions and reactions of various types of defects. Despite extensive studies on the elastic interactions of defects, a theoretical framework capturing crystallographic reactions, especially reaction products and associated local stress concentration, is still unavailable. Here we suggest a disclination-based method to quantify defect reactions. By using a combination of crystallographic calculations and phase field modeling/simulations, twin-twin and twin-grain boundary reactions in hexagonal close-packed metals have been quantitatively analyzed. It has been found that partial disclinations, accompanied with other defects (e.g., {112¯6} and {112¯2} high-index twins), can be generated by defect reactions as typical byproducts. The orientation change and stress fields caused by disclination formation have been systematically calculated, which offers a rigorous mathematical foundation to explore twin-twin, twin-grain boundary reactions. By quantitatively determining defect reactions and local stress fields, our work provides new insights into the deformation mechanism and microstructure-property relationship in metallic materials.

Automated analysis framework of strain partitioning and deformation mechanisms via multimodal fusion and computer vision

Simultaneously investigating strain partitioning and the underlying deformation mechanisms for both the grain interior and the grain boundary (GB) is essential for understanding the complex plastic deformation of hexagonal close-packed metals. To this end, an automated analysis framework based on high-resolution digital image correlation (HRDIC) and electron backscatter diffraction (EBSD) data fusion and computer vision, integrating nanoscale resolution and a large field of view, is proposed. This framework consists of: (1) HRDIC-EBSD data fusion; (2) Segmenting the strain field into individual grains each with a core and a mantle; (3) Data clustering of the Matrix and slip bands (SBs) for each grain; (4) Full slip system (SS) identification and SS assignment to the SBs. The capabilities of this framework were demonstrated on Mg-10Y during compression. The strain field data, which was segmented into different clusters, including grain mantle, grain core, Matrix, and SBs, was analyzed statistically and quantitatively. The pixel-based slip activity, which considers the SB morphology, was obtained from a statistical perspective. Inter-granular accommodating mechanisms, including GB strain, slip transfer, and GB sliding, were quantitatively analyzed. Overall, this analysis framework, which can be applied to other materials, can automatically and statistically evaluate both nanoscale strain fields and underlying intra- and inter-granular deformation mechanisms grain-by-grain. This work provides valuable experimental insights into plastic deformation and accommodation mechanisms for polycrystals.

Interactions between basal dislocation and [formula omitted] twin boundary in HCP metal: A molecular dynamics study

For hexagonal close-packed (HCP) metals having a c/a<3, basal <a> slip is the most common slip system, and {112̅2} twinning is one of the primary plastic deformation modes when compressive stress is applied along the c-axis. In this work, molecular dynamics simulations have been applied to reveal the interaction mechanism between different basal <a> dislocations and {112̅2} twin boundaries (TBs) in Mg, Zr and α-Ti. When the 000113[112̅0] dislocation interacts with the {112̅2} TB, it is transmuted into a 112̅2-{112̅1} double twin (DT). With increasing shear stress, the growth of the 112̅2-{112̅1} DT is impeded by the other side of the {112̅2} TB, it transmutes into (0001)13<101̅0> dislocations and twin dislocations (TDs). Furthermore, the {112̅1} TB is capable of transforming into a {112̅2} TB and a new co-zone {112̅1} TB, which then forms a twin-twin junction (TTJ) to release stress concentration. When the 000113[21̅1̅0] dislocation interacts with {112̅2} TBs, it transmuted into a I2 SFs in the twin and a TD with one-layer height on the {112̅2} TB. But the 000113[1̅21̅0] dislocation would be impeded by the {112̅2} TB and couldn’t be transmuted further.

Microstructural and Textural Evolution in Hexagonal Close-Packed Metals: The Case of Zirconium, Magnesium, and Titanium

Microstructural and Textural Evolution in Hexagonal Close-Packed Metals: The Case of Zirconium, Magnesium, and Titanium

Atomic scale investigation of the phase transformation path from HCP to FCC in high-purity hafnium during torsion deformation

Although the hexagonal close-packed (HCP) to face centered cubic (FCC) martensitic phase transformation has been frequently observed and discussed in many HCP metals and alloys, the detailed phase transformation path has been disputed. Here, we studied the potential phase transformation path from HCP to FCC phase in high-purity hafnium (Hf) under torsional deformation condition. Results indicated that the HCP to FCC phase transformation was not accomplished directly by the glide of a/3[11¯00] Shockley partial dislocations on every other {0001} planes, but progressively transitions to the FCC lattice through multiple intermediate states. The complete phase transformation process can be further refined as: HCP → body-centered tetragonal (BCT)-like structure → 12R long-period stacking-ordered (LPSO) structure → FCC, and each step was accommodated by basal stacking faults. This work is instructive on the phase transformation from HCP to FCC not only in Hf but also in other HCP metals.

Predicting surface-energy anisotropy of metals with geometric properties of surfaces and atoms

Surface-energy anisotropy of metals is crucial for the stability and structure, however, its determining factors and structure-property relationship are still elusive. Herein, we identify three key factors for predicting surface-energy anisotropy of pure metals and alloys: the surface-atom density, coordination numbers and atomic radius. We find that the coupling rules of surface geometric determinants, which determining surface-energy anisotropy of face-centred-cubic (FCC), hexagonal-close-packed (HCP) and body-centred-cubic (BCC) metals, are essentially controlled by the crystal structures instead of chemical bonds, alloying or electronic structures. Furthermore, BCC metals exhibit material-dependent surface-energy anisotropy depending on the atomic radius, unlike FCC and HCP metals. The underlying mechanism can be understood from the bonding properties in the framework of the tight-binding model. Our scheme provides not only a new physical picture of surface stability but also a useful tool for material design.

Investigation of Debye temperature and temperature-dependent EXAFS cumulants of Zn, Zr, α-Ti, Ru and Hf metals

In this work, the anharmonic Einstein model is developed to determine the Debye temperature and investigate the temperature effects on the extended x-ray absorption fine structure (EXAFS) cumulants of hexagonal close-packed (hcp) metals. We have derived the analytical expressions of the anharmonic effective potential, the effective force constant, the Debye temperature and the first four EXAFS cumulants as a function of axial ratio e = c/a. Numerical calculations have been conducted for hcp Zn, Zr, α-Ti, Ru and Hf metals up to temperature 800 K. Our findings indicate that the anharmonicity of thermal lattice vibrations significantly influences the EXAFS cumulants, particularly at high temperatures. Ru atoms have the strongest coupling force causing a phenomenon that Ru lattice shows a smaller thermal disorder, and Zn has a greater thermal disorder. Additionally, we highlight the significant contributions of thermal disorder to the mean-square relative displacement at high temperatures due to thermal lattice vibrations. Moreover, our Debye temperatures derived from the developed model align reasonably well with those reported in previous studies.

Macroscopic low-friction via twinning assisted lattice reconstruction in magnesium

One-fourth of the global energy losses are spent to overcome friction, making it particularly important to reduce and minimize friction between contacting materials. Hexagonal close-packed (HCP) metals are an important class of structural materials. It has not been possible to reduce their friction, primarily because of friction-induced dislocation slip and twinning. Here, we find particularly low friction when sliding perpendicular to the a-axis on the basal plane in HCP Mg single crystals. This is in contrast to the common belief that friction is small along the preferred dislocation slip direction (a-axis). This macroscopic low-friction stems from twinning assisted lattice reconstruction sharing a common rotation axis, confirmed by atomistic simulations and strain energy analysis. While sliding along the a-axis and other directions, 〈c + a〉 dislocation activity accounts for high frictional resistance. By unambiguously decoupling the contributions of dislocation slip and twinning, this discovery reveals potential opportunities in mitigating the energy dissipation at tribological interfaces of HCP metals, e.g. through crystallographic texture design.

Pressure and non-ideal axial ratio effects on thermodynamic properties of hexagonal close-packed Mg and Zn metals

ABSTRACT The Debye model has been developed to study the pressure dependence of the extended X-ray absorption fine structure Debye–Waller factor, the Debye frequency and temperature of hexagonal close-packed (hP2) metals. The effects of the non-ideal axial ratio c/a of hP2 structure on these thermodynamic quantities at high pressures have also been considered. Additionally, based on the combination of the Debye model and the Lindemann melting law, we derive the analytic expression of melting temperature of hP2 metals as a function of pressure. Numerical calculations have been implemented for Mg and Zn metals up to 20 and 50 GPa, respectively. We have shown that Debye frequency and temperature, as well as melting temperature of these two metals increase robustly with pressure and non-ideal axial ratio plays important role in these thermodynamic quantities. The remarkable consistency observed between our calculations and various experimental results validates the reliability of the currently presented melting curve. Meanwhile, at high pressure non-ideal axial ratio gives a small contribution to pressure-dependent Debye–Waller factor of Mg (up to 20 GPa) and Zn (beyond 20 GPa), and can be safely neglected in the suggested pressure range.

Achieving strength-ductility synergy in zirconium via ultra-dense twin-twin networks

Hierarchical nano-twinned structures have been proven to be an effective way in breaking the strength-ductility dilemma in face-centered cubic metals. However, it is challenging to introduce high-density of twinned structures in hexagonal-close packed (HCP) metals because deformation twinning are limited in fine-grained structures. Here, we propose an approach to introduce ultra-dense twin-twin networks in high purity HCP Zr with ultra-large grain size (>200 µm) via cryogenic biaxial-rolling. Tensile tests show that the yield strength and the elongation of the densely twinned Zr are increased by 76.5 % and 28.6 % compared with its coarse-grained counterparts, and reaches 360 MPa and 13.5 %, respectively. The strength of twinned Zr is enhanced by the synergy effect of grain refinement (from 241 µm to 1.2 µm) and the obstruction of dislocations by high-density intersecting twin boundaries (TBs). The ductility and strain-hardening ability are improved by the activation of massive prismatic 〈a〉 and pyramidal 〈c + a〉 dislocations. The three-dimensional TB networks are effective 〈c + a〉 dislocation sources which enhance the plasticity along 〈c〉 direction. Our work provides a new strategy to design ultra-dense twinned structures and sheds light on the twinning-induced plasticity in HCP metals.

Origin of thermal deformation induced crystallization and microstructure formation in additive manufactured FCC, BCC, HCP metals and its alloys

The additive manufacturing (AM) technology has received the widespread attention in the industrial application because of its unique ability to achieve the complex shape and ideal performance. Unfortunately, the impact of the material natural characteristics, such as the crystal structure and alloying, on the microstructure formation at the nanoscale has never been revealed in AM metals. Here, we use large-scale molecular-dynamics simulations to study the rapid thermal deformation processes of additively-manufactured face-centered-cubic (FCC), body-centered-cubic (BCC), hexagonal close-packed (HCP) metals and their alloys (FCC Cu, CuAl0.1, BCC Fe, FeAl0.1, and HCP Mg, MgAl0.1) in the molten pool, in an attempt to elucidate the intrinsic physical mechanisms controlling the crystal nucleation and growth under the complex thermal stress. The results show that the arcuate solid-liquid interface migrates towards the liquid phase until the complete crystallization, in good agreement with the experimental observation. The solidification rate follows a unified slow-to-fast law in the three types of metals, due to the competition between the compressive thermal stress and fast atomic motion. It is noteworthy that the critical radius of the crystal nucleus in the FCC and BCC metals is smaller than that in the HCP metal. The FCC metal exhibits the weak nucleation ability and growth rate, and yet the HCP metal shows the fast growth rate and stable columnar crystal nucleation. Especially, due to the dual regulation of the steep thermal gradient and solute redistribution on the growth driving force, the alloying increases the constitutive supercooling of the solidification front and inhibits the growth of columnar crystals. This trend is particularly prominent in FCC alloys, which is manifested by the obvious amorphous phase and discrete nucleation point in the upper part of the melt pool. The nucleation barrier free energy descends in order of FCC, BCC, and HCP pure metals, but the alloying would increase this energy in the corresponding alloys. The current work gives an insight into the atomic mechanism of the nucleation and growth in AM FCC, BCC, and HCP metals.

A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

On the co-nucleation of adjoining twin pairs at grain boundaries in hexagonal close-packed materials

This work addresses the formation of adjoining twin pairs (ATPs) at grain boundaries (GBs) in hexagonal close-packed (hcp) metals from the perspective of the co-nucleation (CN) of pairs of deformation twins. A continuum defect mechanics model is proposed to investigate the energetic feasibility of the CN of ATPs resulting from the dissociation of GB dislocations. Application of the model to a set of GBs in Mg reveals that CN is largely preferred over the nucleation of a single twin variant for low misorientation angle GBs, which is consistent with previous experimental analyses. The CN events are subsequently analyzed considering the GB character, and the twin system alignment (m′) and Schmid factors to obtain better insights into the conditions governing the formation of ATPs via CN. The likelihood of CN even at low m′ values reveals that CN events could be responsible for the formation of ATP pairs in these scenarios.

Dynamic deformation behavior and constitutive model of a Zr–W alloy

In this paper, a Zr–5W alloy was fabricated via casting. In order to obtain the mechanical properties of the material, quasi-static compression tests at room temperature and split Hopkinson pressure bar tests at various temperatures were carried out. The x-ray diffraction result showed that the main components of the alloy were αZr and W2Zr, where αZr is the matrix and W2Zr is the reinforcement. The metallographic characterization results showed that there were two main forms of W2Zr in the material, namely, large particle boundary and small diffuse submicrometer precipitates. The reinforcements of both distributions have the effect of increasing the strength of the material, but the small submicrometer W2Zr precipitates would cause microcrack nucleation during the late plastic deformation stage, resulting in damage softening. In order to make theoretical calculations of the mechanical properties of materials, the Johnson–Cook (JC) constitutive model and Zerilli–Armstrong (ZAM) constitutive model of the material were obtained. It was found that the JC constitutive model had poor consistency in describing material properties. Although the consistency of the ZAM constitutive model was higher than that of the JC constitutive model, it still had obvious shortcomings. Combined with the deformation mechanism of the alloy, a modified constitutive relation was established by adding damage softening terms based on the hexagonal close-packed metal constitutive model inferred by the kinetics of heat-activated dislocations. The relative error results of all working conditions show that the correlation consistency of the improved constitutive model in this paper is significantly better than that of JC constitutive and ZAM constitutive.