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At least 361 records · Page 20

A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Finally, further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.

42 ENGINEERING↗

On the implementation of dislocation reactions in continuum dislocation dynamics modeling of mesoscale plasticity

The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport equations for dislocations concurrently with crystal mechanics equations, with the latter being cast in the form of an eigenstrain problem. Incorporating dislocation reactions in the dislocation transport equations is essential for making such continuum dislocation dynamics predictive. A formulation is proposed to incorporate dislocation reactions in the transport equations of the vector density-based continuum dislocation dynamics. This formulation aims to rigorously enforce dislocation line continuity using the concept of virtual dislocations that close all dislocation loops involved in cross slip, annihilation, and glissile and sessile junction reactions. The addition of virtual dislocations enables us to accurately enforce the divergence free condition upon the numerical solution of the dislocation transport equations for all slip systems individually. A set of tests were performed to illustrate the accuracy of the formulation and the solution of the transport equations within the vector density-based continuum dislocation dynamics. Comparing the results from these tests with an earlier approach in which the divergence free constraint was enforced on the total dislocation density tensor or the sum of two densities when only cross slip is considered shows that the new approach yields highly accurate results. Bulk simulations were performed for a face centered cubic crystal based on the new formulation and the results were compared with discrete dislocation dynamics predictions of the same. The microstructural features obtained from continuum dislocation dynamics were also analyzed with reference to relevant experimental observations.

36 MATERIALS SCIENCE↗

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↗

Analysis of plastic deformation in silicon web crystals

Numerical calculation of 111-plane 110-line slip activity in silicon web crystals generated by thermal stresses is in good agreement with etch pit patterns and X-ray topographic data. The data suggest that stress redistribution effects are small and that a model, similar to that proposed by Penning (1958) and Jordan (1981) but modified to account for dislocation annihilation and egress, can be used to describe plastic flow effects during silicon web growth.

Spitznagel, J. A.↗

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials

This work examines the frame-invariance (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as informed, directed graphs, where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed, directed graph yield significantly more accurate rotation prediction than the other tested approaches.

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Investigation of crossed-twin structure formation in magnesium and magnesium alloys

In this work, the effect of alloying addition on the propensity for twin-twin interactions to transform into crossed-twin structures in magnesium alloys is investigated. A full-field elasto-viscoplastic fast Fourier transform (EVP-FFT) framework combined with a discrete twin model and dislocation density-based hardening law for slip strengths is used to calculate the micromechanical fields in the crystalline matrix around the interacting twins. AZ31 and MgLi alloys are selected along with pure Mg to study the influence of plastic anisotropy in connection with alloying elements. These alloys were selected since their plastic anisotropy measure, which is defined as the ratio between the critical resolved shear stress for pyramidal $\langle$c +a$\rangle$ and basal $\langle$a$\rangle$ slip modes, spanned a wide range. To quantify the role of twin thicknesses, we probe a range of impinging twin thicknesses while fixing the recipient twin thickness. The analysis reveals that: (i) the local driving stress for crossed twin structure formation generated from the interaction of the two twins is lower in a low plastically anisotropic material, like a MgLi alloy, than a high plastically anisotropic material like pure Mg and (ii) the critical impinging twin thickness needed to form the crossed twin structure in pure Mg, AZ31 and MgLi alloys is ~0.5, ~0.75 and ~1.5 times the recipient twin thickness. We propose a relationship between the tendency for crossed twin structure formation and the experimentally observed higher ductility in MgLi alloys compared to pure Mg. Finally, one key implication of the findings is that crossed- twin structure formation can be hindered and the ductility of magnesium alloy thereby improved by properly choosing alloying elements that lower the slip strength for pyramidal $\langle$c + a$\rangle$ slip.

36 MATERIALS SCIENCE↗

Uniaxial stress increases layer stacking disorder in calcium silicate hydrates with low calcium content

The long-term stress response of concrete is controlled by the intergrain and intragrain interactions of calcium-silicate-hydrates (C-S-H), nanocrystalline forms of tobermorites. To investigate both types of interactions, we examined the deviatoric stress response of 11 Å tobermorite powder with X-ray diffraction, finding that its layer stacking (i.e., sliding) disorder significantly increases. A similar experiment was performed on nanocrystalline C-S-H powders before and after applying a 360 MPa uniaxial stress. Layer stacking disorder (in the form of intragrain deformation) increases when there is low water content and when the basal spacing is large. We also find that grains with a smaller thickness-to-diameter aspect ratio are first to develop preferred orientation (in the form of intergrain sliding), facilitated by gel water. Furthermore, these findings show that intragrain deformations in C-S-H can occur at relatively low stresses and provide insights into the creep mechanism of C-S-H.

36 MATERIALS SCIENCE↗

Inverse design of hypoeutectoid pearlite steel microstructures using a deep learning and genetic algorithm optimization framework

Goal-oriented microstructure design in metallic materials is a challenging task due to complex structure-property relationships. Traditional experimental and computational approaches are time-intensive and economically inefficient, limiting their applicability for large-scale design space exploration. Here, in this work, we propose an end-to-end framework that integrates deep learning models with genetic optimization to design microstructures with targeted mechanical properties. Deep learning models enable accurate forward design, while their integration with genetic optimization enables efficient inverse design within a few hours, compared to days or weeks using conventional finite element simulations. The framework combines experimental characterization and finite element modeling to analyze the influence of microstructural features on the mechanical behavior of hypoeutectoid steels. Data from both experiments and simulations are used to train the deep learning models. To demonstrate its effectiveness, we apply the framework to 0.63% carbon steel with proeutectoid ferrite and pearlite phases, commonly used in industrial applications. In this study, 2D microstructures were used for modeling, selected primarily for computational efficiency and to establish proof of concept. The framework successfully optimizes microstructures for targeted yield strength, ultimate strength, and stress concentration factors while significantly reducing computational time. Beyond hypoeutectoid steels, this scalable framework can be extended to other material systems and integrated with additive manufacturing, offering an efficient approach for accelerating microstructure design for specific engineering applications.

ConvLSTM↗

Analytic model of the remobilization of pinned glide dislocations: Including dislocation drag from phonon wind

Here, we discuss the effect of a non-constant dislocation drag coefficient on the very high strain rate regime within an analytic model describing mobile-immobile dislocation intersections applicable to fcc polycrystals. Based on previous work on dislocation drag, we estimate its temperature and pressure dependence and its effects on stress–strain rate relations. In the high temperature regime, we show that drag can remain the dominating effect even down to intermediate strain rates. We also discuss the consequences of having a limiting dislocation velocity, a feature which is typically predicted by analytic models of dislocation drag, but which is somewhat under debate because a number of MD simulations predict supersonic dislocations.

42 ENGINEERING↗

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗

Elucidating texture and grain morphology contributions to the micromechanical response of additively manufactured Inconel 625

Microstructural variation of additively manufactured (AM) metal components in comparison to wrought counterparts makes certification for critical applications a challenge. Microscale simulations leveraging modern computational tools may be used to supplement testing of AM microstructures, thus accelerating certification by reducing the number of experiments needed. However, as micromechanical response is closely tied to critical properties like fatigue-life and fracture, utilization of these simulations with macroscale experimental data alone is insufficient. One means to attain microscale experimental data is in situ diffraction data collected from synchrotron X-ray sources. In this work, such data were collected during in situ compression of AM Inconel 625 superalloy. Interpretation of experimental results was assisted by massive (8M element) complementary micromechanical simulations performed on sets of virtual microstructures generated using cellular automata. Together, micromechanical data from diffraction experiments and simulations were used to probe the effects of textured “track” microstructures generated during laser powder bed fusion and directional strength-to-stiffness on micromechanical response. Though fiber-averaged directional strength-to-stiffness ratios were expected to dominate given the high elastic anisotropy of the material, the combination of small variations in texture and specific grain configurations unique to AM microstructures lead to significant variability in micromechanical response after yield. The findings emphasize the importance of high-fidelity microstructural representation that captures key texture components and AM-specific morphology for property prediction of AM metals.

36 MATERIALS SCIENCE↗

Twinning pathways enabled by precipitates in $\mathrm{AZ91}$

While precipitates have been shown to substantially strengthen magnesium alloys by blocking the glide of dislocations inside the grain, the interactions between these precipitates and deformation twins, which commonly occur in these alloys, are much less understood. Here, in this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) model is used to study the interactions between plate-shaped basal precipitates and propagating $10\bar{1}2$ tensile twins in AZ91 Mg alloy. The results suggest that while precipitates may impede the propagation and thickening of twins, they can also cause stress localizations that can promote the formation of multiple new twins of the same or different crystallographic variants. We show that the location of the twin-precipitate interaction site, whether precipitate-central or precipitate-edge impingement, and the thickness of the precipitate can influence the propensity for twins to expand around the precipitate or nucleate a new twin on the other side of it. Depending on the twin-precipitate impingement site, we propose multiple twinning pathways that can help explain how twins can proliferate in the magnesium alloys in the presence of precipitates.

36 MATERIALS SCIENCE↗

Calibration of RAFM Micromechanical Model for Creep Using Bayesian Optimization for Functional Output

A Bayesian optimization procedure is presented for calibrating a multimechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on Fe(8–9)%Cr are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600°C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework (Huang et al., 2021, “Bayesian optimization of functional output in inverse problems,” Optim. Eng., 22, pp. 2553–2574). Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. In conclusion, validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel.

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