Twin Variants Research Articles

Digital twins and their use in future power systems

The electric power sector is one of the later sectors in adopting digital twins and models in the loop for its operations. This article firstly reviews the history, the fundamental properties, and the variants of such digital twins and how they relate to the power system. Secondly, first applications of the digital twin concept in the power and energy business are explained. It is shown that the trans-disciplinarity, the different time scales, and the heterogeneity of the required models are the main challenges in this process and that co-simulation and co-modeling can help. This article will help power system professionals to enter the field of digital twins and to learn how they can be used in their business.

Study of Microstructural Morphology of Ti-6Al-4V Alloy by Crystallographic Analysis and Phase Field Simulation.

Formation of a habit plane during martensitic transformation is related to an invariant plane strain transformation, which involves dislocation glide and twins. In the current work, the Phenomenological Theory of Martensitic Transformation (PTMT) is employed to study the crystallographic features while the phase field simulation is used to study the microstructure evolution for martensitic transformation of Ti-6Al-4V alloy. Results show that mechanical constraints play a key role in the microstructure evolution. It is shown that a twinned structure with very small twinned variants is geometrically difficult to form due to the lattice parameters of Ti-6Al-4V alloy. It is concluded that the predicted habit plane from the PTMT is consistent with results of the micro-elastic theory. The formation of a triangular morphology is favored geometrically and elastically.

Tailoring the Texture and Mechanical Properties of Textured-AZ31 Mg Alloy Sheets by Twinning and Recrystallization

In this study, a method of corrugated width limit alignment processes (CWLA) was applied to pre-twin in hot-rolled Mg alloy sheets. The microstructure evolution and mechanical properties of the CWLA sheets were studied. The results demonstrated that the grain orientation was transformed from strong basal texture to RD-rotated texture after CWLA treatment and up to 22.2% of {10–12} tensile twin boundaries were produced in the microstructure. The 60 ± 5° < 10–10 > twin variant pairs were dominant in the twinned microstructure. Two kinds of dynamic recrystallization (DRX) mechanism, i.e., continuous DRX (CDRX) at low-temperature CWLA and the discontinuous DRX (DDRX) at high-temperature condition were observed. After post-annealing, the twin-induced static recrystallization (SRX) and abnormal grain growth were observed in the CWLA samples, and most twin boundaries were retained. After CAWL for 60 min at 300 °C and post annealing, an improvement on plasticity and strength were achieved with 55% increment for uniform elongation (UE) and 10% increment for ultimate tensile strength (UTS).

Deformation twinning and detwinning in extruded Mg-4Al: In-situ experiment and crystal plasticity simulation

Deformation twinning and detwinning in extruded Mg-4Al were investigated using in-situ SEM-DIC experiments and crystal plasticity finite element (CPFE) simulation. In this study, the in-situ SEM-DIC method was used to provide a unique set of data including twin/detwin characteristics and twin area fraction in addition to strain maps. A statistical analysis of the activation of twin variants and twin area fraction during both twinning and detwinning was conducted. A strong correlation was found between twin growth/shrinkage and the Schmid Factor (SF) for individual twin variants Higher twin SF during loading and unloading led to higher twin growth and shrinkage, respectively. However, after the applied compressive strain was removed, the pattern of the twin area fractions of the residual twin variants versus their nominal SFs did not follow the trend observed at the maximum compressive strain. Using a systematic methodology and an advanced twin/detwin model, the PRISMS-Plasticity CPFE simulation was calibrated using experimentally determined stress versus strain and twin area fraction versus strain information. A comprehensive evaluation of the CPFE model was conducted to determine its ability to capture the statistics of twin variants activation and twin area fraction. CPFE accurately captured the statistical aspects of both twinning and detwinning. It also predicted the first dominant twin variant for 47.5% of the grains and at least one of the two dominant twin variants for 80% of the grains at maximum compressive strain.

Polyphase crystal plasticity for high strain rate: Application to twinning and retwinning in tantalum

Upon increasing strain rate a switch operates in tantalum response from a plasticity dominated regime to a twinning dominated regime. This transition is investigated by means of a polyphase crystal plasticity model which combines a Phase Field-Reaction Pathway formalism and a dislocation-based crystal plasticity model. The proposed formalism for twinning considers an unbounded number of variants which permits the observation of twinning, detwinning and retwinning phenomena. The crystal plasticity model takes into account slip systems interactions and includes two glide regimes to deal with high strain rates. A model for dislocation inheritance during twinning is proposed. Simulations highlight a dual role of plasticity: strain hardening inside the matrix may, under certain conditions, hinder the formation of twin variants whereas plasticity inside the variants further relaxes the residual stress due to twins interaction and contributes to shape the variant.

Twinning character and texture origination in the randomly-oriented AZ31B magnesium alloy during cold-rolling

Based on generalized Schmid factor (G-SF) calculation, the twinning character and texture development in the rolling plate of randomly-oriented AZ31B magnesium alloy were investigated in this work. The results showed that when the rolling reduction/nip angle is low, the twin type selection is independent of crystal orientation or G-SF due to the significant difference of critical resolved shear stress (CRSS) between extension twinning and contraction twinning. The twin variant selection does not intimately follow the Schmid criterion. In comparison, the extension twin variant selection departs more from the G-SF prediction than the contraction twin variant selection. The orientations of the matrix grains develop gradually tending to distribute around the normal direction (ND), which promote the activation of contraction twinning. The basal texture results only from the orientation development of the matrix grains, depending on the basal <a> slip and the pyramidal <c+a> slip, which was explained in terms of a crystal rotation by the dislocation interactions.

An alternative formation mechanism of {332}BCC twinning in metastable body-centered-cubic high entropy alloy

In this work, the origin of {332}BCC twinning was investigated in a body-centered-cubic (BCC) high entropy alloy (TiZrHf)87Ta13 (at.%). Detailed transmission electron microscopy analysis of the deformed microstructure revealed that a special ‘‘{351}’’<2¯11>α" type II twinning generates in the early deformation stage, and with further straining, the ‘‘{351}’’<2¯11>α" type II twin variant accommodates into a {351}α" type I twin variant. The resultant {351}α" type I twinning exhibits good lattice correspondence with the {332}BCC twinning and further propagates into the retained BCC grain with orientation relationship of {351}α”//(332)BCC, structuring into a {332}BCC twin-like configuration. Based on the experimental results and twinning analysis through evaluating twinning shear and atomic shuffle mechanism of this specific feature, our findings provide an alternative mechanism for the formation of {332}BCC twinning in which a special martensitic type II to type I twinning transformation mechanism took effect.

An experimental study of the mechanical behavior of rolled AZ31B magnesium alloy under combined axial-torsion loading

The mechanical behavior and microstructure at fracture of a rolled AZ31B magnesium alloy were experimentally investigated using tubular specimens subjected to combined axial-torsion loading with different ratios of the axial and shear stress components. The stress state influences the stress-strain responses. The equivalent stress-equivalent plastic strain curves under tension-torsion loading show a sigmoidal shape and the peak value of the equivalent strain hardening rate increases as the ratio of the axial stress to the shear stress increases. Under compression-torsion, the equivalent stress-equivalent plastic strain curves show a concave-down shape, and the equivalent strain hardening rate decreases at faster rates as the ratio of the axial stress to the shear stress increases. Among all the loading conditions investigated, pure tension and pure compression result in the highest strength, and torsion combined with a slight tension has the lowest strength. The trend of ductility is inversely proportional to the strength with respect to the influence of the combined axial-torsion loading. Detailed twinning structures reveal that extensive tension twins are induced under tension-torsion loading paths. Conversely, a combination of tension and compression twins is observed under compression-torsion loading due to the high Schmid factors of the compression twins resulted from the grains with favorable orientations. The significant effect of the stress state on the post-fracture texture is explained in terms of the twin variant favorability which is dominated by the crystal orientation relative to the orientation of the applied principal stresses. The experimental results are critical for the development and validation of constitutive models for magnesium alloys under multiaxial loading.

Characterizing Changes in Grain Growth, Mechanical Properties, and Transformation Properties in Differently Sintered and Annealed Binder-Jet 3D Printed 14M Ni–Mn–Ga Magnetic Shape Memory Alloys

Ni–Mn–Ga Heusler alloys are multifunctional materials that demonstrate macroscopic strain under an externally applied magnetic field through the motion of martensite twin boundaries within the microstructure. This study sought to comprehensively characterize the microstructural, mechanical, thermal, and magnetic properties near the solidus in binder-jet 3D printed 14M Ni50Mn30Ga20. Neutron diffraction data were analyzed to identify the martensite modulation and observe the grain size evolution in samples sintered at temperatures of 1080 °C and 1090 °C. Large clusters of high neutron-count pixels in samples sintered at 1090 °C were identified, suggesting Bragg diffraction of large grains (near doubling in size) compared to 1080 °C sintered samples. The grain size was confirmed through quantitative stereology of polished surfaces for differently sintered and heat-treated samples. Nanoindentation testing revealed a greater resistance to plasticity and a larger elastic modulus in 1090 °C sintered samples (relative density ~95%) compared to the samples sintered at 1080 °C (relative density ~80%). Martensitic transformation temperatures were lower for samples sintered at 1090 °C than 1080 °C, though a further heat treatment step could be added to tailor the transformation temperature. Microstructurally, twin variants ≤10 μm in width were observed and the presence of magnetic anisotropy was confirmed through magnetic force microscopy. This study indicates that a 10 °C sintering temperature difference can largely affect the microstructure and mechanical properties (including elastic modulus and hardness) while still allowing for the presence of magnetic twin variants in the resulting modulated martensite.

Asymmetry evolutions in microstructure and strain hardening behavior between tension and compression for AZ31 magnesium alloy

This work investigated the asymmetry evolutions in the microstructure and the plastic deformation behavior between the entire tension and compression for AZ31 magnesium alloy by combining the experiment and visco-plastic self-consistent (VPSC) model. Large yield stress asymmetry between the tension and the compression existed at the onset of plastic deformation, but such stress asymmetry slightly increased first and then gradually decreased to 1.01 with the increase of logarithmic plastic strain. This kind of asymmetry variation was ascribed to the microstructure evolution asymmetry. Compared to the tension deformation, tension twin boundaries migrated more easily in the compression deformation owing to the appropriate crystal orientation, producing more obvious fraction variation of tension twin boundary and the intersection of different tension twin variants. The VPSC model clarified the texture evolution asymmetry between the tension and the compression by the contribution of each deformation mechanism to the macroscopic strain, revealing that prismatic slip activation in the tension triggered the development of ⟨101‾0⟩//LD (LD: loading direction) type texture while abundant tension twinning in the compression laid the foundation of ⟨0002⟩//LD type texture. Additionally, owing to the deformation mechanism transformation from basal slip to prismatic slip in tension deformation, the attenuation degree in the strain hardening rate was gradually weakened, while in compression deformation, the participation of elastic deformation contributed to the increasing stage of strain hardening rate after the exhaustion of tension twinning. In addition, the geometrical orientation factor and deformation mechanism factor together contributed to the decline of flow stress asymmetry.

Unveiling the mechanical response and accommodation mechanism of pre-rolled AZ31 magnesium alloy under high-speed impact loading

Split Hopkinson pressure bar (SHPB) tests were conducted on pre-rolled AZ31 magnesium alloy at 150–350 ℃ with strain rates of 2150s -1 , 3430s -1 and 4160s -1 . The mechanical response, microstructural evolution and accommodation mechanism of the pre-rolled AZ31 magnesium alloy under high-speed impact loading were investigated. The twin and shear band are prevailing at low temperature, and the coexistence of twins and recrystallized grains is the dominant microstructure at medium temperature, while at high temperature, dynamic recrystallization (DRX) is almost complete. The increment of temperature reduces the critical condition difference between twinning and DRX, and the recrystallized temperature decreases with increasing strain rate. The mechanical response is related to the competition among the shear band strengthen, the twin strengthen and the fine grain strengthen and determined by the prevailing grain structure. The fine grain strengthen could compensate soften caused by the temperature increase and the reduction of twin and shear band. During high-speed deformation, different twin variants, introduced by pre-rolling, induce different deformation mechanism to accommodate plastic deformation and are in favor for non-basal slip. At low temperature, the high-speed deformation is achieved by twinning, dislocation slip and the following deformation shear band at different deformation stages. At high temperature, the high-speed deformation is realized by twinning and dislocation slip of early deformation stage, transition shear band of medium deformation stage and DRX of final deformation stage.

Deformation twins stimulated by {11[formula omitted]2} twinning in adjacent grain in titanium

Deformation twins are likely nucleated at and impeded by grain boundaries (GBs), developing shear transformation bands. Knowing the accommodated deformation in adjacent grains to the twinning shear is essential for understanding mechanical properties and the evolution of microstructure and texture of polycrystalline aggregates. Based on EBSD analysis, we characterize and statistically group accommodated deformation modes in the neighbor to {112¯2} compression twins (CTWs) in titanium with respect to the misorientation axis/angle. Two types of CTWs are preferably activated in adjacent grains with low misorientation angles, two types of extension twins (ETWs) are favorably activated in adjacent grains with high misorientation angles, and some of {112¯2} CTWs terminate at GBs with high misorientation angles. We discuss the preference of accommodated deformation modes and the selection of twin variants based on the SDGA criterion which couples the displacement gradient accommodation (DGA) and stress driven accommodation (SDA) criteria. Although misorientation angle of GBs is widely used to predict the preferred deformation modes, we demonstrate that misorientation axis that was often ignored, must be considered in determining the preferred deformation modes especially for large misorientation angles. Finally, we predict the misorientation angle/axis pairs with respect to the activity of four twinning modes and two slip systems as the best accommodation mechanism in adjacent grains. The results are useful for the implementation of intergranular deformation mechanisms in multiscale modeling and the design of HCP materials with specific GB characteristics.

Nanoindentation-induced deformation twinning in MAX phase Ti2AlN

Plastic deformation mechanisms have been investigated in the MAX phase Ti2AlN. Nanoindentation has been used to induce plastic deformation in a single grain, and a Transmission Electron Microscopy (TEM) lamella has been extracted in cross section through the indent by using Focused Ion Beam (FIB) technique. By combining TEM observations and automated crystal orientation mapping (ACOM), highly misoriented domains (HMD) have been revealed below a nanoindentation imprint. Thanks to a careful analysis of the relative crystal orientations between these HMD, {112¯2} and {112¯1} deformation twins have been identified for the first time in a MAX phase. Complex structures, involving secondary twinning or different {112¯2} twin variants have also been characterized.

{10–12} twinning relationship in Mg-Gd-Y(-Sn)-Zr alloys under uniaxial compression at room temperature

After homogenization treatment, uniaxial experiments at room temperature with strain rate of 1 s−1 are carried out on Mg-Gd-Y(-Sn)-Zr alloys, and the maximum strain is controlled to 8%. Plenty of {10–12} tensile twins appear in the deformed microstructure of Mg-Gd-Y-Zr and Mg-Gd-Y-Sn-Zr alloys. The addition of Sn significantly improves the nucleation ability of twins and effectively reduces the lamellar thickness. In Mg-Gd-Y-Zr alloy, the twins are mostly coarse parallel, while in Mg-Gd-Y-Sn-Zr alloy, they are mostly thin cross. A great quantity of closed regions and twin boundaries introduced by high-density thin cross twins are the main reasons for the high flow stress of Mg-Gd-Y-Sn-Zr alloy. In addition, the analysis of twin variant selection behavior, twin interaction and dislocation transmutation reaction in this paper is conducive to consummate the theory of room temperature deformation of magnesium alloys.

Between microscopic and mesoscopic descriptions of twin–twin interaction

Abstract On a microscopic scale, deformation twinning is carried by the motion of twinning disconnections. A disconnection is an interfacial line defect characterized by a Burgers vector, a line vector, and a step vector. The Burgers vector (dislocation component of the disconnection) carries the deformation while the step vector (ledge component) carries the transformation from one twin variant to the other. On a mesoscopic scale, the deformation produced by twinning is a simple shear. A moving disclination dipole provides a mesoscopic model accounting for the twinning shear. Twin – twin interaction processes including the intersection of twins, the formation of structured twins, and the nucleation of cracks, may feature very complex mechanisms when analyzed on a microscopic scale. It turns out, however, that these mechanisms are controlled by the properties of large disconnection groups containing up to 10 000 disconnections and more. These properties are sufficiently well approximated in the disclination dipole model. The disclination model for twin – twin interaction predicts orientation and volume fractions of secondary twins. The model also predicts the nucleation of cracks and crack growth. The disclination model was used to analyze the ductile-to-brittle transition of austenitic steel deformed at low temperature. The mesoscopic disclination model for twinning is successful because it accounts for the properties and mechanisms of disconnection groups.

In-situ high-energy X-ray diffraction and crystal plasticity modeling to predict the evolution of texture, twinning, lattice strains and strength during loading and reloading of beryllium

Deformation behavior of beryllium during compressive loading and cross-reloading is studied using in-situ high energy synchrotron X-ray diffraction microscopy and crystal plasticity modeling. The evolution of texture, twinning, elastic lattice strains, and flow stress are measured and compared with the predictions of an advanced elastic-plastic self-consistent (EPSC) crystal plasticity model. The model is initialized with the experimentally measured texture and residual stress produced by a simulation of cooling and calibrated to establish a set of model parameters using a portion of the measured data. The rest of the measured data is used for validation of the model. It is shown that the model is sufficiently flexible to reproduce the particularities pertaining to the complex strain-path-change and strain rate sensitive deformation of the material including the evolution of texture, twinning, lattice strains, transients in the stress-strain response, and anisotropic hardening with great accuracy using a single set of model parameters. From the comparison of the experimental data and predictions, we infer that the shifts in active deformation mechanisms between the slip systems from soft to hard and vice versa as well as between twinning to de-twinning are primarily responsible for drastic changes in the flow stress from one path to another. In particular, deformation twins form during compressive in-plane loading followed either by de-twinning during compressive cross-reloading in the through-thickness direction or by forming additional twin variants with some de-twinning of the existing variants during a compressive cross-reloading in another in-plane direction. The shifts in active deformation mechanisms are a consequence of changes in texture relative to the compression direction mediated with the deformation history and strain rate dependent dislocation density evolution governing hardening. The secondary effects improving the predictions come from accounting for residual stress, slip system-level backstress, and latent hardening.

Octahedral Tilting and Modulation Structure in Perovskite‐Related Compound La1/3NbO3

The crystal structure of the A‐site‐deficient perovskite La1/3NbO3 is investigated using X‐ray powder diffraction, transmission electron microscopy (TEM), and computational methods. The NbO6 octahedral tilting is observed and confirmed to be in an a − b 0 c 0 manner in Glazer's notation. An incommensurate modulation structure in La1/3NbO3 is observed. Using scanning TEM (STEM) analyses and Monte Carlo simulations, the modulated structure is shown to originate from a striped arrangement of La and vacancies. The satellite reflections arising from the modulation structure are observed as a diffuse scatter in the electron diffraction patterns. By analyses with STEM and molecular dynamics calculations, it is concluded that the origin of diffuse scattering is the existence of nanoscale twin variants with different crystal orientations. The Nb ions in NbO6 octahedra represent an off‐center shift like a pseudo‐Jahn–Teller distortion. The shift of Nb ions is found to be cooperative with the concentration modulation of La ions.

Effects of cerium addition on the microstructure, mechanical properties and strain hardening behavior of TWIP steel Fe-18Mn-0.6C

The effects of cerium (Ce) on the microstructure, mechanical properties and strain hardening behavior of Fe-18Mn-0.6C twin-induced plasticity (TWIP) steel were investigated by electron backscatter diffraction, X-ray diffraction and transmission electron microscopy. Compared with the addition of Al, the addition of Ce significantly reduced the stacking fault energy of TWIP steel, which promotes the formation of deformation and annealing twins. The dynamic strain aging behavior of TWIP steel was inhibited by Al and Ce atoms during plastic deformation. The optimal mechanical properties were obtained when 0.015 wt% of Ce was added, resulting in a tensile strength of 1023 MPa; and an elongation was 92%. The interaction of twin variants in the Ce-containing alloys exhibited an X shape, which was significantly different from the T shape in the non-Ce containing alloy. This is mainly attributed to the fact that Ce promotes dislocations near grain boundaries, where for the nucleation of deformation twins at grain boundaries is favored. Compared with the T-shaped twin variants, the dynamic Hall-Petch effect caused by the X-shaped staggered twin variants was stronger, which improved the strain hardening ability of TWIP steel. • The addition of Ce can improve the stacking fault probability and increase the fraction of twin in TWIP steel. • The initial strain can be reduced during the strain hardening equilibrium stage after the addition of Ce. • Compared with T-shape, the interaction of twin variants in TWIP steel modified by Ce tends to X-shape. • The dislocation entanglement near grain boundaries is easily induced by the addition of Ce in TWIP steel.

Selection Behavior of {10-12} Tensile Twin Variants and its Contribution During Plastic Processing of Magnesium Alloy

Selection Behavior of {10-12} Tensile Twin Variants and its Contribution During Plastic Processing of Magnesium Alloy

Grain size and specimen thickness effects on twinning behaviors in high strain rate deformation of ultra-thin pure titanium sheet

Identifying grain size and specimen thickness effects on the twinning characteristics and texture evolution of ultra-thin pure titanium sheet is essential for its extensive applications in many industries. In this research, ultra-thin pure titanium sheet with different grain sizes and thicknesses were deformed to different strains by electromagnetic-assisted bulging. Then the deformation twins were analyzed on a grain-by-grain basis to determine both the volume fraction of twins and the Schmid factor of twin variants in each grain. Results indicate that twin density of ultra-thin pure titanium sheet decreases when sample thickness decreases from 205 μm to 45 μm. Moreover, deformation twinning can be promoted when grain size increases from 7.5 μm to 27.4 μm but also can be restricted to a certain extent when grain size increases to 38.2 μm. In addition, grain size plays an evidently positive effect on multiple twin variants activation so as to affect the misorientation distributions. Furthermore, the frequency of twin variants with lower Schmid factor decreases with the increase of grains size from 7.5 μm to 38.2 μm. This is well explained by the strain accommodation criterion. By affecting the deformation mechanism of ultra-thin pure titanium sheet, size effects also play significant roles in the texture evolution.