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At least 217 records · Page 12

Distorted dislocation cores and asymmetric glide resistances in titanium

The determination of Critical Resolved Shear Stress (CRSS) in titanium for basal, prismatic, and pyramidal slip-planes without empirical constants is presented by combining Density Functional Theory (DFT) and anisotropic elasticity. A new mechanism leading to tension-compression (T-C) asymmetry in the CRSS levels has been revealed for the first time. The conditions for this asymmetry are established, involving a complex interplay between the dislocation core-structure and core-advance behavior. The three conditions for T-C asymmetry that need to be simultaneously satisfied can be summarized as: (1) a medium stacking fault width, d, (3 < d/b F < 10, where b F is the magnitude of the Burgers vector of the full dislocation), (2) an asymmetric core-structure of the extended dislocation (ξ 1 ≠ ξ 2 , where ξ 1 and ξ 2 are the core-widths of the first and second partials, respectively), and (3) intermittent motion of the partials (Δd/b F ≠ 0, where Δd is the magnitude of fluctuation in stacking fault width during intermittent motion). Pyramidal-slip in titanium satisfies all three conditions, resulting in significant T-C asymmetry. The CRSS theory considers a Wigner-Seitz (W-S) cell based domain area assigned to each lattice site for the calculations of core-energies accurately capturing the slip-plane lattice. The W-S based approach is essential due to the lower symmetry of the HCP crystal circumventing potential errors associated with the one-dimensional atomic-row approximation. Dislocation core structures are obtained for all the slip-systems in titanium showing significant distortion of the disregistry profile governing the core-advance behavior. The CRSS values predicted from the theory show agreement with the experimental CRSS levels reported in the literature.

Dislocation core↗

Atomistic Investigation of Plastic Deformation and Dislocation Motion in Uranium Mononitride

Uranium mononitride (UN) is a promising advanced nuclear fuel due to its high thermal conductivity and high fissile density. However, many aspects of its mechanical behavior, particularly at reactor-relevant conditions, remain unclear. In this study, molecular dynamics (MD) simulations were employed to investigate the deformation behavior and dislocation motion in UN. We found that the Kocevski potential predicts the principal slip system as $\frac{1}{2}$ $\langle110\rangle${110}, aligning with experimental data. On the other hand, the Tseplyaev potential predicts slip to primarily occur on $\frac{1}{2}$ $\langle110\rangle${111}. MD simulations of stress–strain behavior were used to estimate the nanoindentation hardness, revealing that the Kocevski potential accurately predicts hardness even though it fails to model dynamic plasticity. Complete dislocation mobility functions have been fitted for the edge and screw dislocations in both the thermally activated and phonon-drag regimes. The 300 K linear mobility of the edge dislocation using the Tseplyaev potential was found to be 817 Pa -1 ·s -1 , whereas that of the screw dislocation using the Kocevski potential was found to be 4546 Pa -1 ·s -1 . At intermediate stresses, we observed that the subsonic steady-state motion of the edge dislocation in UN is intermittently interrupted by velocity jumps, reaching the average sound velocity. Finally, the threshold Schmid stress is calculated as 179–197 MPa, which gives an upper-limit estimate of the uniaxial yield stress of polycrystalline UN of 548–603 MPa. These findings, including the fitted dislocation mobility function, provide essential input for future plasticity and dislocation dynamics models of nuclear fuels.

36 MATERIALS SCIENCE↗

Dislocation line tension model to improve understanding of the effects of hydrogen on the deformation of structural materials

Decarbonization efforts highlight hydrogen as an attractive alternative to fossil fuels, but its tendency to embrittle structural metals demands careful consideration when designing hydrogen infrastructure. Moreover, the mechanisms by which hydrogen degrades these materials are still being elucidated. The current work develops new computational tools to quantify the different contributions of hydrogen to the energy barrier of cross-slip, a key deformation mechanism. Novel features are implemented to a line tension model, which include the use of non-singular dislocation interactions, character-dependent dislocation energies and simulations of the constriction configurations. A new molecular dynamics technique is developed to calculate the interaction energy between the partials of a dissociated dislocation via fixing the centers of mass of the regions below and above the Shockley partials and performing time-averaged calculations. Hydrogen is found to impact the stacking fault width of dislocations in different ways depending on their characters: it decreases for dislocations with a character θ > 30°, remains unchanged for θ = 30° and increases for θ < 30°. The latter regime is a newly identified mechanism by which hydrogen inhibits cross-slip. Moreover, formation of nano-hydrides is predicted to occur around screw dislocations for high hydrogen concentrations, a phenomenon previously identified only in dislocations with an edge component. If nano-hydrides develop, their influence extending the equilibrium stacking fault width and increasing both the constriction and cross-slip energy barriers dominate over all other hydrogen contributions. The theory and tools developed will pave the way towards a comprehensive understanding of hydrogen-dislocation interactions in structural metals.

08 HYDROGEN↗

Shallow Aseismic Slip in the Delaware Basin Determined by Sentinel-1 InSAR

The Delaware Basin, Texas is currently a hot-spot of induced seismicity and ground deformation due to fluid extraction and injection associated with horizontal drilling techniques; however, the driving mechanism behind the seismicity and deformation remains under debate. Here, using vertical and east-west horizontal surface deformation measurements derived from Sentinel-1 interferometric synthetic aperture radar (InSAR), we show that the subsurface responds differently to oil and gas activity in the northern and southeastern portions of the basin. In the north, where there is little seismicity, deformation patterns display long-wavelengths and equidimensional patterns. In contrast, the southeast region hosts most of the seismicity and displays spatial deformation patterns with narrow linear features that strike parallel to the maximum principal horizontal stress and to trends in seismicity, suggesting movement along normal faults. We model a linear deformation feature using edge dislocations and show that the InSAR observations can be reproduced by slip on normal faults contained within the Delaware Mountain Group (DMG), the formation that hosts local wastewater injection and the majority of earthquakes. Our model consists of three parallel, high-angle normal faults, with two dipping toward one another in a graben structure. Slip magnitudes reach up to 25 cm and are spatially correlated with injection wells. Measured seismicity can only explain ~2% of the fault motion predicted by our fault model, suggesting that slip leading to the deformation is predominantly aseismic. We conclude that seismic and aseismic fault motion in the southeastern Delaware Basin is likely driven by wastewater injection near critically-stressed normal faults within the DMG.

58 GEOSCIENCES↗

Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates

Here, this paper presents a novel formulation and its robust numerical implementation of strain-gradient (SG) crystal plasticity within a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. The resulting non-local SG-LS-EVPFFT formulation is used to model and understand the process of kink band formation during layer-parallel compression of nano-metallic laminates (NMLs). NMLs are layered composites with nanoscale thicknesses, thus requiring consideration of the interaction between dislocations and interfaces within the micromechanical model. The length-scale parameter of the SG model is calibrated by simulating a double pile-up and comparing predictions to analytical solution. This required new expressions for the defect energy, resulting in more accurate double pile-up predictions. The calibrated SG-LS-EVPFFT model is then used to simulate layer-parallel compression of copper-niobium NML. Formation of kink bands is predicted, and the model is used to rationalize the microscopic mechanisms enabling the formation process. It is found that accumulation of dislocations at interfaces leads to activation of layer-parallel slip, which in turn leads to kink band formation.

36 MATERIALS SCIENCE↗

3D interface size effects on slip transfer in Ti/Nb nanolaminates

Two-phase nanolaminates are well-renowned for achieving extraordinarily high strengths but at the sacrifice of reduced toughness and strain to failure. Recently ”thick” interfaces, or so called 3D interfaces, in Cu/Nb nanolaminates were experimentally shown to improve both of these mechanical properties. Here, in this work, we study the effect of 3D interfaces in the hexagonal close packed (HCP)/body centered cubic (BCC) Ti/Nb nanolaminate system. Nanoindentation hardness testing suggests increased strength with the introduction of a 3D Ti–Nb interface and a positive size effect with increases in 3D interface thickness from 5 nm to 20 nm. To understand this effect from a single dislocation perspective, we present a phase-field dislocation dynamics (PFDD) model for multi-phase HCP/BCC systems. We employ the model to simulate stress-driven transfer of single dislocations across 3D Ti/Nb interfaces of various thicknesses. Our results show that the critical stress for slip transfer increases with the thickness of the interface. This positive size effect is stronger for transfer from basal or prismatic dislocations in the Ti layer to 110$\langle$111$\rangle$ dislocations in the Nb layer than the reverse. For this Ti/Nb system, a critical thickness of 2 nm is identified at which the asymmetry in slip transfer is minimized. This work showcases 3D interfaces as a beneficial microstructure modification to strengthen as well as reduce anisotropy in nanocrystalline materials containing HCP phases.

Dislocations↗

Effects of Internal and External Hydrogen on Inconel 718

Internal hydrogen embrittlement (IHE) and hydrogen environment embrittlement (HEE) tensile and bend crack growth tests were performed on Inconel 718. For the IHE tests, the specimens were precharged to approximately 90 ppm hydrogen by exposure to 34.5 MPa H2 at 650 C. The HEE tests were performed in 34.5 MPa H2. Parameters evaluated were test temperature, strain rate for smooth and notch specimen geometries. The strain rate effect was very significant at ambient temperature for both IHE and HEE and decreased with increasing temperatures. For IHE, the strain rate effect was neglible at 260'C, and for HEE the strain rate effect was neglible at 400 C. At low temperatures, IHE was more severe than HEE, and at high temperatures HEE was more severe than IHE with a cross over temperature about 350 C. At 350 C, the equilibrium hydrogen concentration in Inconel 718 is about 50% lower than the hydrogen content of the precharged IHE specimens. Dislocation hydrogen sweeping of surface absorbed hydrogen was the likely transport mechanism for increasing the hydrogen concentration in the HEE tests sufficiently to produce the same degree of embrittlement as that of the more highly hydrogen charged IHE specimens. The main IHE fracture characteristic was formation of large, brittle flat facets, which decreased with increasing test temperature. The IHE fracture matrix surrounding the large facets ranged between brittle fine faceted to microvoid ductility depending upon strain rate, specimen geometry as well as temperature. The HEE fractures were characteristically fine featured, transgranular and brittle with a significant portion forming a "saw tooth" crystallographic pattern. Both IHE and HEE fractures were predominantly along the {1 1 1) slip and twin boundaries. With respect to embrittlement mechanism, it was postulated that dislocation hydrogen sweeping and hydrogen enhanced localized plasticity were active in HEE and IHE for concentrating hydrogen along (1 1 1) slip and twin planes. Final brittle failure occurred by hydrogen induced planer decohesion.

Walter, R. J.↗

Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)

The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.

36 MATERIALS SCIENCE↗

Dislocation interactions in olivine control postseismic creep of the upper mantle

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, commonly induce a period of transient creep, which is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at temperatures ≤600 °C, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25 °C or 1150–1250 °C both preserve stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 μm. The similar stress distributions formed at these different temperatures indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle.

58 GEOSCIENCES↗

Modeling of the surface static displacements and fault plane slip for the 1979 Imperial Valley earthquake

Three-dimensional finite element modeling techniques are used to synthesize geodetic and seismological results for 1979 Imperial Valley earthquake. The strategy pursued consists of two principal steps. In the first step, the seismologically-derived coseismic fault slip is taken as a function of position in the fault plane and is applied directly to the three-dimensional dislocation model. In the second step, a physical model of stresses and constitutive parameters is perturbed so as to reproduce the observed fault slip. Hence, the principal features of the coseismic slip pattern are explained by a stress-driven fault model in which: (1) a spatially unresolved asperity is found equivalent to a stress drop of 18 MPa averaged over an area of 15 sq km, and (2) driving stress is essentially absent on the fault segment overlapping the 1940 earthquake rupture zone.

Slade, M. A.↗

Fatigue and creep-fatigue deformation of several nickel-base superalloys at 650 C

Transmission electron microscopy has been used to study the bulk deformation characteristics of seven nickel-base superalloys tested in fatigue and creep-fatigue at 650 C. The alloys were Waspalloy, HIP Astroloy, H plus F Astroloy, H plus F Rene 95, IN 100, MERL 76, and NASA IIB-7. The amount of bulk deformation observed in all the alloys was low. In tests with inelastic strain amplitudes less than about 0.003, only some grains exhibited yielding and the majority of those had the 110 line near the tensile axis. Deformation occurred on octahedral systems for all of the alloys except MERL 76 which also showed abundant primary cube slip. Creep-fatigue cycling occasionally produced extended faults between partial dislocations, but otherwise deformation was much the same as for fatigue cycling.

Miner, R. V.↗

Spatial description of dislocation nucleation in the shock response of single-crystal aluminum

Nonequilibrium molecular dynamics simulations of shock loaded single-crystal Al in the $\langle$100$\rangle$, $\langle$110$\rangle$, $\langle$111$\rangle$, and $\langle$123$\rangle$ orientations are conducted to study elastic and plastic shockwave formation and details associated with dislocation activity. A computer vision-based approach is implemented to capture the presence of dislocations and describe their spatial characteristics in the zone of nucleation behind the propagating shockwave. The methodology developed relies on the sequences of images extracted during shock loading that show dislocation activity within a cross section of the sample. Results reveal that the spacing between activated slip systems is orientation dependent and exhibits a modest reduction for the $\langle$100$\rangle$ and $\langle$111$\rangle$ orientations as shock pressure increases. Comparisons are made to existing theoretical models. Such relationships between shock pressure and dislocation activity, extracted from molecular dynamics simulations, can be used to inform higher length scale simulations or modeling of dislocation-based plasticity during shock.

36 MATERIALS SCIENCE↗

Ductile-brittle transition of thoriated chromium.

Unalloyed chromium and chromium containing approximately 3 wt % ThO2 were prepared from powder produced by a chemical vapor deposition process. When rolled to sheet and tested in tension, it was found that the thoriated material had a lower ductile-to-brittle transition temperature (DBTT) than unalloyed chromium. This ductilizing was evident both in the as-rolled condition and after the materials had been annealed for 1 hour at 1200 C. The improved ductility in thoriated chromium may be associated with several possible mechanisms: (1) particles may disperse slip, such that critical stress or strain concentrations for crack nucleation are more difficult to achieve; (2) particles may act as dislocation sources, thus providing mobile dislocations in this normally source-poor material, in a manner similar to prestraining; and (3) particles in grain boundaries may help to transmit slip across the boundaries, thus relieving stress concentrations and inhibiting crack nucleation.

Wilcox, B. A.↗

High purith low defect FZ silicon

The most common intrinsic defects in dislocation-free float zone (FZ) silicon crystals are the A- and B-type swirl defects. The mechanisms of their formation and annihilation have been extensively studied. Another type of defect in dislocation-free FZ crystals is referred to as a D-type defect. Concentrations of these defects can be minimized by optimizing the growth conditions, and the residual swirls can be reduced by the post-growth extrinsic gettering process. Czochralski (Cz) silicon wafers are known to exhibit higher resistance to slip and warpage due to thermal stress than do FZ wafers. The Cz crystals containing dislocations are more resistant to dislocation movement than dislocated FZ crystals because of the locking of dislocations by oxygen atoms present in the Cz crystals. Recently a transverse magnetic field was applied during the FZ growth of extrinsic silicon. Resultant flow patterns, as revealed by striation etching and spreading resistance in Ga-doped silicon crystals, indicate strong effects of the transverse magnetic field on the circulation within the melt. At fields of 5500 gauss, the fluid flow in the melt volume is so altered as to affect the morphology of the growing crystal.

Kimura, H.↗

Molecular models for creep in oriented polyethylene fibers

Highly oriented and crystalline polyetheylene (PE) fibers have a large failure stress under rapid tensile loading but exhibit significant creep at much smaller stresses that limits applications. A possible mechanism is slip of chains due to stress-enhanced, thermally activated nucleation of dislocations at chain ends in crystalline regions. Molecular dynamics simulations are used to parameterize a Frenkel–Kontorova model that provides analytic expressions for the limiting stress and activation energy for dislocation nucleation as a function of stress. Results from four commonly used hydrocarbon potentials are compared to show that the qualitative behavior is robust and estimate quantitative uncertainties. In all cases, the results can be described by an Eyring model with values of the zero-stress activation energy Ea0≈1.5 eV and activation volume V* ≈ 45 Å3 that are consistent with the experimental results for increasingly crystalline materials. The limiting yield stress is ∼8 GPa. These results suggest that activated dislocation nucleation at chain ends is an important mechanism for creep in highly oriented PE fibers.

O’Connor, Thomas C. (ORCID:0000000293930295)↗

Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary–dislocation interactions

A new phase field dislocation dynamics (PFDD) formulation for homogeneous and heterogeneous materials is presented, which couples micromechanical solvers and the time-dependent Ginzburg–Landau equation. The strain fields are obtained from the micromechanical solver by solving the Lippmann–Schwinger equation and then used to define energy terms to model the evolution of the dislocations. Grain boundary (GB)–dislocation interactions are studied using the coupled PFDD formulation and by describing GBs as inclusions. GB energy and stiffness tensors are computed from molecular statics simulations, and a newly proposed lattice energy term that is dependent on the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle ⟨110⟩ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our PFDD formulation and molecular dynamics simulations of grain boundary–dislocation interactions.

36 MATERIALS SCIENCE↗

Low-temperature solid-state phase transformations in 2H silicon carbide

Single crystals of 2H SiC were observed to undergo phase transformations at temperatures as low as 400 C. Some 2H crystals transformed to a structure with one-dimensional disorder along the crystal c axis. Others transformed to a faulted cubic/6H structure. The transformation is time and temperature dependent and is greatly enhanced by dislocations. Observations indicate that the transformation takes place by means of a slip process perpendicular to the c axis. Cubic SiC crystals were observed to undergo a solid state transformation above 1400 C.

Will, H. A.↗

Twin nucleation and growth in hexagonal close-packed metals: The role of slip-mediated plasticity on twin embryo formation and evolution

Twinning is a key deformation mechanism in hexagonal close-packed (hcp) metals, which are typified by a lack of easily activated slip systems that can accommodate a general state of loading. Pragmatically, the nucleation and evolution of twin domains occurs concomitantly with slip, such that the eventual twin network is conditioned by both external and internal stresses resulting, among others, from the evolution of dislocations. However our understanding of the interplay between dislocations, and twin nucleation and stability remains limited. This work focuses on elucidating the influence of dislocation-mediated plasticity on the formation, growth, and stability of twin embryos. First, a new mesoscale spectral crystal plasticity-twinning framework is developed and used to quantify the change in the free energy landscape following the nucleation {$10\bar{1}2$} of twins in Mg. Representative twin morphologies are modeled under conditions of limited and profuse slip activity, which are emulative of small- and bulk-scale samples, respectively. Then, the driving traction profiles around twin embryos are investigated via a sharp interface approach to obtain insights into how concurrent slip-mediated plasticity can influence the growth/stabilization of nanometric twins. The driving traction profiles are further utilized to determine the stability of twin embryos post loading. The initial dislocation density in the samples, and within the different domains (i.e., twin vs. parent), is seen to have a significant effect on the twin nucleation stress. Namely, the activation of high levels of concomitant plasticity in the parent grain is seen to significantly drive the formation of nanometric twin nuclei at stresses as low as 250 MPa. Further, the sharp interface analysis reveals that profuse plasticity in the parent grain simultaneously alters the forward and back stresses, such that the magnitude/polarity of the driving tractions become increasingly favorable for nanometric twin growth when slip is active. Finally, prior plasticity in the parent grain is seen to result in favorable driving tractions for nanometric twin growth, even at applied stresses as low as ~ 100 MPa. In conclusion, these results are in stark contrast to a case without any dislocations, wherein applied stresses as high as ~ 500 MPa are necessary to grow the twin domains.

36 MATERIALS SCIENCE↗