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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The effects of free surfaces on deformation twinning in HCP metals

Deformation twinning is a predominant mode of plastic deformation for hexagonal close packed metals, like Mg and Ti. The heterogenous microstructure and the local stresses associated with twinning play a key role in their mechanical response and fracture. Surface analyses, like electron microscopy, are frequently employed to spatially map microstructure and micromechanical fields in order to study twinning behavior. However, these measurements are inherently influenced by the vicinity of the free surface. In this work, an elasto-visco-plastic fast-Fourier-transform (EVP-FFT) polycrystal modeling approach is employed to investigate the effects of free surfaces on twin development before and after loading. We compare calculated micromechanical fields on free surfaces with those calculated inside the bulk and, in some cases, experimental surface measurements. The results indicate that the creation of free surfaces can promote twin propagation and growth and can influence twin morphology by causing a twin lamella to become larger, more blunted and irregular. The structure along the twin boundaries are also affected, due to the higher driving stresses that extend prismatic-basal and basal-prismatic facets. Furthermore, free surfaces invoke different slip activities in the twin and the surrounding parent crystal by enhancing basal, prismatic and pyramidal slip in some localized regions, while reducing slip in others. We demonstrate that the simulated free-surface effects lead to better qualitative and quantitative agreement with experimental measurements from scanning electron microscopy and digital image correlation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Maximum strength and dislocation patterning in multi–principal element alloys

Multi–principal element alloys (MPEAs) containing three or more components in high concentrations render a tunable chemical short-range order (SRO). Leveraging large-scale atomistic simulations, we probe the limit of Hall-Petch strengthening and deformation mechanisms in a model CrCoNi alloy and unravel chemical ordering effects. The presence of SRO appreciably increases the maximum strength and lowers the propensity for faulting and structure transformation, accompanied by intensification of planar slip and strain localization. Deformation grains exhibit notably different microstructures and dislocation patterns that prominently depend on their crystallographic orientation and the number of active slip planes. Grain of single-planar slip attains the highest volume fraction of deformation-induced structure transformation, and grain with double-slip planes develops the densest dislocation network. These results advancing the fundamental understanding of deformation mechanisms and dislocation patterning in MPEAs suggest a mechanistic strategy for tuning mechanical behavior through simultaneously tailoring grain texture and local chemical order.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A quantitative study of stress fields ahead of a slip band blocked by a grain boundary in unalloyed magnesium

Stress localization ahead of a slip band blocked by a grain boundary is measured for three different grain boundaries in unalloyed Mg using high-resolution electron backscatter diffraction (HR-EBSD). The results are compared with a theoretical dislocation pile-up model, from which slip system resistance and micro-Hall–Petch coefficients for different grain boundary types are deduced. The results indicate that grain boundary character plays a crucial role in determining micro-Hall–Petch coefficients, which can be used to strengthen classical crystal plasticity constitutive models to make predictions linked to the effect of grain boundary strengthening.

42 ENGINEERING↗
DOE OSTI2021

Variability of near-fault seismic risk to reinforced concrete buildings based on high-resolution physics-based ground motion simulations

Broadband physics-based simulated earthquake ground motions are utilized to characterize the regional-scale seismic risk to modern reinforced concrete (RC) structures. A highly dense dataset of ground motions covering a 100-km urn:x-wiley:00988847:media:eqe3413:eqe3413-math-0001 40-km domain was generated using kinematic fault rupture models with varying rupture characteristics to represent shallow crustal earthquakes and resolved up to frequencies of 5 Hz. Over 40,000 nonlinear response history simulations of short- and mid-rise RC special moment frame buildings were conducted using simulation models that are capable of representing nonlinear behavior and component deterioration effects. The spatial variability of structural risk within a single earthquake scenario and between different rupture scenarios is examined, and the regions of strongest directivity effects and highest structural demands are identified. The structural demands may vary by factor of up to 8.0 at very short distances from the fault, and the large dispersion in the demands decreases significantly beyond a distance of 15 km. The interstory drift and member rotation demands are substantially impacted by important features of the geological structure and the characteristics of the rupture scenarios, particularly the presence of localized high-slip regions. The frequency characteristics of the structures are found to play an important role in determining the effects of near-fault ground motions on the structural response and expected damage. The results of this study suggest that the simulated ground motions, particularly those generated using the hybrid rupture approach, may offer reasonable structural risk estimates for low-frequency structures and conservative estimates for high-frequency structures.

58 GEOSCIENCES↗
DOE OSTI2021

A stochastic solver based on the residence time algorithm for crystal plasticity models

Abstract The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

42 ENGINEERING↗
DOE OSTI2021

Nonlinear Interface Reduction for Time-Domain Analysis of Hurty/Craig-Bampton Superelements with Frictional Contact

Virtual prototyping in engineering design relies today on modern numerical models of contacting structures with accurate resolution of interface mechanics, which strongly affect the system-level stiffness and energy dissipation due to frictional losses. High-fidelity modeling within the localized interfaces is required to resolve local quantities of interest that may drive design decisions. The high-resolution finite element meshes necessary to resolve inter-component stresses tend to be computationally expensive, particularly when the analyst is interested in response time histories. The Hurty/Craig-Bampton (HCB) transformation is a widely used method in structural dynamics for reducing the interior portion of a finite element model while having the ability to retain all nonlinear contact degrees of freedom (DOF) in physical coordinates. These models may still require many DOF to adequately resolve the kinematics of the interface, leading to inadequate reduction and computational savings. This study proposes a novel interface reduction method to overcome these challenges by means of system-level characteristic constraint (SCC) modes and properly orthogonal interface modal derivatives (POIMDs) for transient dynamic analyses. Both SCC modes and POIMDs are computed using the reduced HCB mass and stiffness matrices, which can be directly computed from many commercial finite element analysis software. Comparison of time history responses to an impulse-type load in a mechanical beam assembly indicate that the interface-reduced model correlates well with the HCB truth model. Localized features like slip and contact area are well-represented in the time domain when the beam assembly is loaded with a broadband excitation. The proposed method also yields reduced-order models with greater critical timestep lengths for explicit integration schemes.

42 ENGINEERING↗
DOE OSTI2022

Resonant interaction between phonons and PbTe/PbSe (001) misfit dislocation networks

Here this work aims at a quantitative and mechanistic understanding of the dynamic process of the phonon-dislocation interaction in PbTe/PbSe (001) heterostructures using the Concurrent Atomistic-Continuum (CAC) method as the simulation tool. The misfit dislocation network and the atomic-scale dislocation core structure obtained in the simulations are found to agree reasonably well with the experimental observations of the PbTe/PbSe (001) interface. Through visualizing the dynamic interaction between phonons and dislocations, as well as quantifying the dislocation vibration amplitude, the phonon energy transmission, and the thermal resistance of the misfit interfaces, this work has illustrated and quantified two mechanisms for phonon-dislocation interaction: (1) phonon scattering by the strain field of dislocations, and (2) phonon scattering by dislocations that vibrate via the local modes of a dislocation network; the latter, leads to resonant phonon-dislocation interaction, which is manifested as local maxima of out-of-phase vibration of the atoms on the two sides of the slip plane, leading to local minima of the energy transmission in the heterostructure that contains one interface. The local vibrational modes are found to be excited only by shear stress induced by transverse phonons. Among various resonant modes, the one with the lowest frequency has the strongest effect. This work has also demonstrated the collective motion of dislocations under ultrafast phonon pulses. In addition, the dynamic properties of the misfit dislocation network localized within one interface are found to be significantly altered by the presence of misfit dislocations at other interfaces, thus further confirming the cooperative dynamic nature of the motion of dislocations and phonons.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Can Glacial Sea‐Level Drop‐Induced Gas Hydrate Dissociation Cause Submarine Landslides?

Abstract We conducted two‐dimensional numerical simulations to investigate the mechanisms underlying the strong spatiotemporal correlation observed between submarine landslides and gas hydrate dissociation due to glacial sea‐level drops. Our results suggest that potential plastic deformation or slip could occur at localized and small scales in the shallow‐water portion of the gas hydrate stability zone (GHSZ). This shallow‐water portion of the GHSZ typically lies within the area enclosed by three points: the BGHSZ–seafloor intersection, the seafloor at ∼600 m below sea level (mbsl), and the base of the GHSZ (BGHSZ) at ∼1,050 mbsl in low‐latitude regions. The deep BGHSZ (>1,050 mbsl) could not slip; therefore, the entire BGHSZ was not a complete slip surface. Glacial hydrate dissociation alone is unlikely to cause large‐scale submarine landslides. Observed deep‐water (much greater than 600 mbsl) turbidites containing geochemical evidence of glacial hydrate dissociation potentially formed from erosion or detachment in the GHSZ pinch‐out zone.

58 GEOSCIENCES↗
DOE OSTI2022

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto-Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

We present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2-D planar rate-and-state fault with off-fault visco-plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co-evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off-fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off-fault bulk even at higher angles of maximum compression. In conclusion, this produces damage patterns that deviate from the traditional off-fault fan-like distribution observed in dynamic rupture simulations and emphasizes the significance of long-term deformation in interpreting observations.

58 GEOSCIENCES↗
DOE OSTI2023

Tailoring planar slip to achieve pure metal-like ductility in body-centred-cubic multi-principal element alloys

Uniform tensile ductility (UTD) is crucial for the forming/machining capabilities of structural materials. Normally, planar-slip induced narrow deformation bands localize the plastic strains and hence hamper UTD, particularly in body-centred-cubic (bcc) multi-principal element high-entropy alloys (HEAs), which generally exhibit early necking (UTD < 5%). Here we demonstrate a strategy to tailor the planar-slip bands in a Ti-Zr-V-Nb-Al bcc HEA, achieving a 25% UTD together with nearly 50% elongation-to-failure (approaching a ductile elemental metal), while offering gigapascal yield strength. The HEA composition is designed not only to enhance the B2-like local chemical order (LCO), seeding sites to disperse planar slip, but also to generate excess lattice distortion upon deformation-induced LCO destruction, which promotes elastic strains and dislocation debris to cause dynamic hardening. Further, this encourages second-generation planar-slip bands to branch out from first-generation bands, effectively spreading the plastic flow to permeate the sample volume. Moreover, the profuse bands frequently intersect to sustain adequate work-hardening rate (WHR) to large strains. Our strategy showcases the tuning of plastic flow dynamics that turns an otherwise-undesirable deformation mode to our advantage, enabling an unusual synergy of yield strength and UTD for bcc HEAs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The effect of microstructure on the relationship between grain boundary sliding and slip transmission in high purity aluminum

The relationship between grain boundary sliding (GBS) and slip transmission is investigated experimentally at grain boundaries in 99.99% aluminum with a through-thickness, coarse grained microstructure deformed in tension at 190 °C. Using scanning electron microscope enabled digital image correlation (SEM-DIC) and electron backscatter diffraction (EBSD), high resolution strain fields and microstructural information were measured to examine the influence of microstructural neighborhoods on interactions between GBS and slip transmission and strain localization. Several distinct cases are presented that highlight important microstructural factors that govern deformation near grain boundaries. The findings include (1) direct transmission and GBS were anti-compatible and facilitated by opposing boundary types (low misorientation and high energy grain boundaries respectively); (2) increased GBS activity was correlated with decreased indirect transmission behavior; (3) GBS accommodation at triple junctions was enabled by intragranular plasticity; and (4) the local intragranular plastic strain discontinuity between grains determined the magnitude of GBS gradients. Finally, this work provides insight into the nature of these mechanisms and can be used to identify strain transfer criteria that can lead to improved GBS-sensitive crystal plasticity models.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Analysis of Microseismicity and Reactivated Fault Size to Assess the Potential for Felt Events by CO 2 Injection in the Illinois Basin

The results of monitoring of carbon dioxide (CO 2 ) injection at the Illinois Basin—Decatur Project (IBDP) and the companion Illinois Industrial Carbon Capture and Sequestration Sources (IL-ICCS) project—have shown that reservoir response to fluid pressure changes can vary significantly at different injection locations within the same reservoir. Predrill reservoir characterization is important to identify potentially seismogenic faults. However, interpretations of newly reprocessed 3D seismic reflection data illustrate the challenges related to their identification in a region dominated by faulting with small vertical offsets. Faults interpreted in the 3D seismic volume range from ~300 to 1200 m wide and are in the same size range as faults that could have been the source of historical events up to Mw 2.7 in central Illinois. The array of monitoring sensors that was installed for the IBDP continues to collect data, as injection operates in IL-ICCS, the second injection well. CO 2 injection rates for the IL-ICCS well are on average 1.7 times the rates injected in the IBDP well, but a significantly reduced rate of induced seismicity is observed. This article presents results of passive seismic monitoring for the duration of the project to date, integrating active and passive seismic data to develop a new interpretation of the subsurface structure at the Decatur site that explicitly identifies pathways for fluid flow into the basement leading to induced seismicity, and provides a geological explanation for the sharp reduction of induced seismicity during injection at higher rates into the second well. The use of seismic moment to estimate the length of seismogenic slip planes in the local subsurface suggests that faults large enough to produce felt seismicity are unlikely to be present at or near the Decatur site.

Geochemistry & Geophysics↗
DOE OSTI2021

Identifying geological structures through microseismic cluster and burst analyses complementing active seismic interpretation

At the Decatur carbon capture and storage site (IL, USA) CO 2 has been injected from 2011–2014 and from 2017 to present near the base of the Lower Mt. Simon Sandstone saline reservoir, resulting in microseismicity. Microseismicity is mainly located in the basement and distributed in distinct spatial clusters. The lack of significant impedance contrasts within the basement makes the interpretation of active-source seismic reflection data challenging, however, recent reprocessing allowed to resolve faults above and at the top of the basement. These faults generally do not coincide with the location of microseismic events and their continuation to the general depth of the seismic events cannot be assumed. This paper shows how the interpretation of the microseismicity can complement structural interpretations of active-source seismic reflection data. In particular, we analyze clusters and bursts (abrupt increases) of microseismicity, identify unresolved, smaller-scale weaknesses and extract statistical parameters. These parameters allow comparisons with the interpreted faults, and with fracture sets intercepted by boreholes. During injection at the Decatur site, the injection pressure was kept far below fracture pressure, nevertheless, seismic events were induced and spread far beyond the expected extent of the CO 2 plume. We argue that local stress transfers related to the CO 2 injection reactivated pre-existing fractures within the critically stressed basement. Finally, we conducted a slip tendency analysis for faults interpreted from active seismic, selected cluster, bursts and nodal planes from focal mechanisms to determine if the interpreted structures are optimally oriented with respect to the stress regime. Our results suggest that the orientation of fractures close to the injection well, generally shows slight deviations from the optimal orientation for slip. This might indicate either slight local deviations of the maximum horizontal stress azimuth from the average direction used in the analysis, or the lack of optimally oriented fractures at this location.

58 GEOSCIENCES↗
DOE OSTI2022

Schmid factor crack propagation and tracking crystallographic texture markers of microstructural condition in direct energy deposition additive manufacturing of Ti-6Al-4V

Metallic additive manufacturing (AM) provides a customizable and tailorable manufacturing process for new engineering designs and technologies. The greatest challenge currently facing metallic AM is maintaining control of microstructural evolution during solidification and any solid state phase transformations during the build process. Ti-6Al-4V has been extensively surveyed in this regard, with the potential solid state and solidification microstructures explored at length. In this study, we evaluate the applicability of previously determined crystallo- graphic markers of microstructural condition observed in electron beam melting powder bed fusion (PBF-EB) builds of Ti-6Al-4V in a directed energy deposition (DED) build process. The aim of this effort is to elucidate whether or not these specific crystallographic textures are useful tools for indicating microstructural conditions in AM variants beyond PBF-EB. Parent β-Ti grain size was determined to be directly related to α-Ti textures in the DED build process, and the solid state microstructural condition could be inferred from the intensity of specific α-Ti orientations. Qualitative trends on the as-solidified β-Ti grain size were also determined to be related to the presence of a fiber texture, and proposed as a marker for as-solidified grain size in any cubic metal melted by AM. Analysis of the DED Ti-6Al-4V build also demonstrated a near complete fracture of the build volume, suspected to originate from accumulated thermal stresses in the solid state. Crack propagation was found to only appreciably occur in regions of slow cooling with large α +β colonies. Schmid factors for the basal and prismatic α-Ti systems explained the observed crack pathway, including slower bifurcation in colonies with lower Schmid factors of both slip systems. Colony morphologies and localized equiaxed β-Ti solidification were also found to originate from build pauses during production and uneven heating of the build edges during deposition. Tailoring of DED Ti-6Al-4V microstructures with the insight gained here is proposed, along with cautionary insight on preventing unplanned build pauses to maintain an informed and controlled thermal environment for microstructural control.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A VOI Web Application for Distinct Geothermal Domains: Statistical Evaluation of Different Data Types within the Great Basin

The Great Basin region contains different domains that have different structural and hydrothermal flow patterns. Depending on the characteristics of these patterns, certain data types may be more successful at detecting hidden geothermal resources. In this paper, we quantitatively evaluate if certain data types are more successful in certain domains. Given different aquifer, strain and structural conditions, we explore which data types statistically reveal positively labeled geothermal sites. We utilize value of information (VOI) metrics to help quantify the reliability of data types to discriminate against "positive" and "negative" labeled geothermal sites. We also evaluate how kernel density estimation can help generalize the statistics that inform VOI, which is necessary given the limited data in geothermal exploration. Except for the Carbonate Aquifer, the highest ranking of the Vimperfect is the Local Structural Setting. Next, the slip and dilation tendency is first for Carbonate Aquifer and second for Central Nevada Seismic Belt and Western Great Basin. For the Carbonate Aquifer, heat flow is has the lowest Vimperfect value compared to the other three domains, which is consistent with the understanding of how heat flow measurements are masked by regional groundwater flow.

Bayesian analysis↗
DOE OSTI2022

Study of the interplay between lower-order and higher-order energetic strain-gradient effects in polycrystal plasticity

in this report strain-gradient (SG) plasticity refers to a class of non-local theories in which gradients of plastic slip determine the storage of geometrically necessary dislocations, introducing a length-scale dependence in the mechanical behavior of crystalline materials, which is otherwise lacking in local theories. In this work, we incorporate lower-order (LO) and higher-order energetic (HOE) strain-gradient effects into a crystal plasticity fast Fourier transform (FFT)-based formulation to investigate the interplay of the length scale that each strain-gradient term introduces at the microscale, and the mechanical properties that result at the macroscale. For an applicable range of length scales, we consider two systems: a 1-D two-phase face centered cubic (FCC) laminate and a 3-D FCC polycrystal, and two uniaxial deformation modes: monotonic tension and cyclic tension–compression. We show that increases in the individual LO and HOE length scales increase the hardening rate and strength of the material, respectively. When combined, the strong LO hardening is less pronounced than the effect alone due to the lowering of the gradients due to the HOE microstress. We demonstrate that the LO and HOE hardening manifest as “isotropic” (yield surface expansion) and “kinematic” (yield surface shift) effects, respectively, consistent with their theoretical origins. We show that in cyclic loading, the Bauschinger effect emerges in both local and non-local calculations and link its origins and severity to the behavior in the strain field, slip-system rates, and the HOE microforce.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Several theoretical studies have reported that the geometry and structure of grain boundaries in polycrystalline materials could impose a significant effect on the Hall-Petch slope. However, experimental observations are primarily limited by the ability of the techniques to accurately quantify the grain boundary strength and validate these theoretical models. Using high-resolution electron backscatter diffraction (HR-EBSD), the local stress tensor ahead of a slip band blocked by a grain boundary was quantified and coupled with a continuum dislocation pile-up model to assess the barrier strength of specific grain boundaries to specific slip systems, referred to as micro-Hall-Petch coefficient. For basal slip system in a deformed Mg-4Al alloy, the micro-Hall-Petch coefficient ($k^{basal}_{μ}$) varied significantly, from 0.054 to 0.184 MPa - m 1/2 for nine different grain boundaries. These results were correlated with geometric descriptors of the respective grain boundaries, with three-dimensional GB profile additionally measured via focused ion beam milling. It was found that the angle between the two slip plane traces on the grain boundary plane was the most sensitive parameter affecting $k^{basal}_{μ}$, followed by the angle between the slip directions. A functional form for calculation of $k^{basal}_{μ}$ depending on these two angles is proposed to augment crystal plasticity constitutive models with slip resistance dependent on some measure of the grain size. The method allows a new pathway to calibrate grain size strengthening parameters in crystal plasticity models, allowing further computational investigations of the interrelationship between texture, grain morphology, and the Hall Petch effect.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A crystal plasticity model with an atomistically informed description of grain boundary sliding for improved predictions of deformation fields

Crystal plasticity (CP) is a powerful meso-scale technique for deformation modeling in polycrystalline materials. Crystal plasticity models typically do not include an explicit description of grain boundary (GB) sliding, which could lead to inaccurate predictions of strain distributions, especially in the vicinity of GBs. In the present study, a CP model is developed that includes GB sliding as an additional deformation mechanism and models the interaction between slip and GB sliding. Atomistic simulations are used to formulate the constitutive model for GB sliding and its interaction with incident slip. The deformation fields and structure of the GBs are obtained directly from experimental characterization and are faithfully reproduced as bicrystal systems for molecular dynamics simulations. The GBs are modeled as random-type (non-coincidence, asymmetrical) boundaries as observed from experimental data. The underlying atomistic-scale mechanism for pure sliding of random GBs was found to be analogous to fluid-flow. The interaction between incident slip and a sliding GB caused local increases in stress concentration, which further led to a momentary increase in the local sliding rate. The displacement profiles at the sliding GBs computed from the CP model with sliding accommodation are 38% more accurate than the baseline CP model as quantified by the mean squared error between the simulations and experiment. Here these results help improve the sophistication and accuracy of deformation modeling by including physics-based descriptions for GB sliding and its interaction with slip, eventually leading to more reliable predictions of micromechanical quantities.

36 MATERIALS SCIENCE↗