Crystal plasticity model

crystal plasticity model Based upon the kinematics of crystal deformation and dislocation interaction laws, dislocation generation and annihilation are modeled. The stress-strain relation in this model is written in terms of the this model by allowing for the evolution of dislocation density in the mantle, thus extending the model into the nano-crystalline regime. The relative spatial arrangement of the several pancake-shaped grains in a tensile sample is determined through in situ and ex Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method Dec 31, 2013 · In order to accurately predict necking and fracture phenomena, a crystal plasticity model is introduced in the finite element analysis of tensile tests. Now, all Rolex watches feature the sapphire crystal. It's part of the IMEX American Civil War Model Series. A bottom-up material modeling based on a nonlocal crystal plasticity model requires information of a large set of physical and phenomenological parameters. Keywords: crystal plasticity; grain boundary; size effects; slip transmission; strain gradient. 2nd World Congress on Integrated Computational Materials, May 2013, Salt Lake City, United States. Readers interested in DD simulation applica- Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. The crystal plasticity finite element model uses rate and size-dependent anisotropic elastoplasticity constitutive . This is a plastic collection of a 1/72 Union Infantry Set from the American Civil War. Acrylic plastic crystal model. Therefore, it is possible to model polycrystalline structures and to study the orientation of multiple slip dislocation structures with respect to the loading direction. These approaches, commonly referred to as crystal plasticity finite element models, are important both for basic microstructure-based mechanical predictions as well as for engineering design and performance simulations involving anisotropic media. Title: A new strain hardening model for rate-dependent crystal plasticity: Publication Type: Journal Article: Year of Publication: 2011: Authors: Brahme, A. The project involves the calibration and refinement of an inhouse crystal plasticity material model at different temperature and stress levels. A probabilistic crystal plasticity model for modeling grain shape effects based on slip geometry Shang Suna, Veera Sundararaghavanb,⇑ aDepartment of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Dr. Prof. This material implements the combined-constraints crystal plasticity model of Zamiri and Pourboghrat [1] for BCC crystals. . No. The general framework for the crystal plastic-ity formulation is taken to be the same for both the hcp and bcc phases, with the only difference introduced in the hardening laws. A significant advantage of this AE-CP model is that its high efficiency enables it to be effectively incorporated in polycrystalline crystal plasticity FE simula- Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. Imex # imx505. We analyze in detail stress regularization at a dislocation core given by the model, and show how the Burgers vector density can be Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. A crystal plasticity model of a formation of a deformation band structure J. P. The continuum model of a rate-independent, rigid-plastic crystal deformed by single slip is recalled in Section 2. Our atomistically-informed crystal plasticity model quantita-tively predicts the orientation dependent stress–strain behavior of BCC iron single crystals in a manner that is consistent with experimental results. For a given initial texture and material parameters of the model, the code computes the stress-strain response and orientation evolution of single In the present study, a physics-based method to develop the grain size-dependent crystal plasticity constitutive model on the core and mantle configuration for polycrystal materials is presented. The study contains a law A new dislocation-based crystal plasticity model is developed via the continuum description of the collective behavior of dislocations. ECCOMAS Congress 2016 Proceedings. of classes can be adjusted based on actual days available for classes. Rs 38,000/ Box. 5. The shear strain rate of slip system calculated via crystal plasticity was employed to determine model at the coarse scale (far region), where polycrystal aggregates are homogenized using the same crystal plasticity model. 8 Three-Dimensional Aspects of Oligocrystal Plasticity 130 Mar 09, 2012 · Validation of a Crystal Plasticity Model Using High Energy Diffraction Microscopy High energy diffraction microscopy is used to measure the crystallographic orientation and evolution of lattice strain in an Al Li alloy. It is based on a finding a mean-field approximation to the environment of each individual grain. Within the crystal plasticity framework, the theories for dislocation density evolution and DRX were introduced and modified. 1080/14786435. Crystal Plasticity Model Crystal plasticity models have constitutive equations (similar to Chaboche model) for each slip system to determine inelastic shear strain rate on each of them as a function of critically resolved shear stress (Han et al. Aug 09, 2012 · We present a crystal plasticity model that incorporates cross-slip of screw dislocations explicitly based on dislocation densities. Besides the discussion of the constitutive laws, kinematics, homogenization schemes, and To overcome the limitations of crystal plasticity models based on a rate insensitive idealization of crystalline slip, Asaro and Needleman (1985) developed a simple rate-dependent crystal plasticity model, which uniquely predicts constitutive response for arbitrary deformation histories. pdf (799,5Kb) Comparteix: Veure estadístiques d'ús. It is implemented for solid elements and for explicit analysis only. The phase-field crystal model in an amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. Jun. The method is based on the assumption that any resistance to dislocation nucleation and motion in a material manifests as an increase in yield elastic-plastic, finite strain, crystal plasticity formulation, follow-ing 11,13,17–19 . Versatile material models are helpful in the design process of superalloys. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method Feb 26, 2018 · A phase-field model of a crystalline material is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model of polycrystalline metals and alloys, which A crystal plasticity model for metal matrix composites considering thermal mismatch stress induced dislocations and twins Sci Rep . 2021 Aug 6;11(1):16053. -10. , K Dec 01, 2020 · * To use the word crystal for the top glass, or lens, of a watch is a bit confusing. The single crystal PHCPM development process involves: (i) construction of statistically-equivalent representative volume elements, (ii) image-based modeling with dislocation-density crystal plasticity model, (iii) identification of representative aggregated microstructural parameters, (iv) selection of PHCPM framework and (v) self-consistent A new crystal plasticity model was proposed for synchronously responding dynamic recrystallization (DRX) and thermomechanical behavior of wrought two-phase titanium alloys. The simulated results show that the changes of the reference value of slip γ0 and the reference strain rate a Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method A coarse-grained phase-field crystal model of plastic motion Marco Salvalaglio a, b , ∗, Luiza Angheluta c, Zhi-Feng Huang d, Axel Voigt a, e, Ken R. 9. Furthermore, the modeling of deformation twinning in polycrystalline microstructures is incorporated in Section 5. By data collapsing the event energy Aoshima 1/32 Scale Vellfire (White Pearl Crystal Shine) - Plastic Model Buiding Set # 56301 Aoshima's "Raku Pura" series of snap-fit kits continues with this luxury minivan, the Vellfire. 2. Union Artillery Civil War Figure Set. 09. A stochastic model is used to nucleate twins at grain boundaries, and Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. A new crystal plasticity constitutive model for simulating precipitation-hardenable aluminum alloys. We prove that the rank-1 convex envelope of the condensed energy density is obtained by infinite-order laminates, and express it explicitly via the 2 F 1 hypergeometric function. microtwins in the grain-scale crystal plasticity model and probes its effect on tension–compression asymmetry in the creep response of single-crystal Ni-based superalloys. The predicted temperature and Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. and Pourboghrat, F. VII European Congress on Computational Methods in Applied Sciences and Engineering, 5. A crystal plasticity finite element method (CPFEM) model has been developed to investigate the effects of BW hardening model parameters on nano-indentation deformation behaviour and texture evolution. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method sity based crystal plasticity finite element model of polycrystals with grain boundary effect . 1038/s41598-021-95439-z. 7 Evolutionof Dislocation Density in a Crystal Plasticity Model 129 9. Crystal plasticity constitutive relations Feb 19, 2019 · This paper develops a single-crystal plasticity model with Johnson–Cook-type hardening laws to examine the strain rate and temperature sensitivities of magnesium (Mg). Crystal Plasticity model in coded the subroutine UMAT describes the deformation of single crystals and polycrystals assuming crystallographic slip as the main deformation mode. Best Glue for Plastic Model Kits – Buying Guide and Reviews for 2021 Almost all plastic model kits require you to glue the parts of the kit together. This model considers the inelastic mechanism of kinematic hardening which is captured using the Back stress. Keywords: precipitation, coherency loss, crystal plasticity, zirconium hydride (Some figures may appear in colour only in the online journal) 1. Dieses Archiv kann nicht den Volltext zur Verfügung stellen. the framework of continuum crystal plasticity. Add To Cart. 271-276. In this study, a new crystal plasticity phase-field model is developed by coupling the phase-field microelasticity theory and the crystal plasticity theory. 75 $10. A tensile specimen is modeled by many grains that have their own crystalline orientation. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method Sep 16, 2021 · Crystal Visco-Plasticity (CVP) theory integrates this phenomenon to describe the effects of plasticity more accurately. [1] Zamiri, A. Mostra el registre d'ítem complet. The developed model has been validated by comparison with experimental observations. 11Oe0. Kratochvíl & M. 2016, Crete Island, Greece. 2015. [5]. But, one way or another, the word crystal — or glass — is used to determine the part that transparently protects the dial and hands. Toth University of Lorraine, France The dislocation-based crystal plasticity model considering higher-order stress has been constructed and a finite element (FE) analysis is conducted for both a single crystal and polycrystal with a long-period stacking ordered (LPSO) phase on the basis of the obtained model. To describe the overall softening behavior under cyclic loading, a slip system-level dislocation density-related damage model is proposed and implemented in the finite element analysis with Voronoi The crystal plasticity model accounts for microstructural features such as hardening due to statistically stored dislocation and geometrically necessary dislocation densities. By 1991, the Rolex Perpetual was the last watch to possess a acrylic crystal. We first conduct the simulation of uniaxial tensile loading of a single crystal and confirm the developed model can describe the elastic and plastic deformation behaviors depending on The model is implemented in a crystal plasticity finite element solver, describing all the slip systems. Whatever material it’s made of. Plastic Model. In the model, dislocations are naturally created, without any ad hoc creation rules, by applying a shearing force to the perfectly periodic ground state. Kružík (2015) A crystal plasticity model of a formation of a deformation band structure, Philosophical Magazine, 95:32, 3621-3639, DOI: 10. 02Ale0. Subgrain scale model for the c–c0 microstructural RVE The material studied is a two-phase, binary Ni model can be easily generalized to incorporate any glide systems and coupled to phase-field models in order to study the effect of coherency loss on microstructure evolution. Grading: Exams/Tutorials: Midterm, Final, group discussions of journal articles/relevant topics. A dislocation density based crystal plasticity finite element model (CPFEM) is developed for aluminum in which dislocation densities evolve on all octahedral slip systems. Issue 9 - June 2015 - Physically Justified Models for Crystal Plasticity Developed with Dislocation Dynamics Simulations AL09-022 crystal plasticity. The twinning-induced lattice reorientation is implemented by taking the initial grain after reorientation as a “new” grain with an updated Crystal Plasticity Model With Back Stress Evolution. El Feb 10, 2018 · The presented model is an extension of the conventional crystal plasticity model. crystal models. Wei Huang Louisiana State University and Agricultural & Mechanical College Follow this and additional works at crystal plasticity flow rule. The model accounts for microstructural morphology through accurate phase vol-ume fractions, and orientation distributions that are statis-tically equivalent to those observed in orientation imaging May 28, 2021 · The constitutive model is implemented into a thermo-mechanical Crystal Plasticity (CP) Finite Element Method (FEM) formulation to study the bulk material properties of QP1180 steel. The collective behavior of dislocations enters this framework trough hardening coefficients and through the inner structure of the lamellae and the energy of their boundaries. An element elimination and reactivation method is proposed to model the melting and solidification and to reinitialise state variables, such as the plastic deformation, in the reactivated elements. Jul 08, 2009 · We consider a geometrically nonlinear model for crystal plasticity in two dimensions, with two active slip systems and rigid elasticity. The paper concludes this development with a summary in Section 6. Aug 06, 2021 · In this paper, we propose a physics-based crystal plasticity model that has the capability of dealing with thermal mismatch stress induced dislocations and twins (denoted as TMDT model). The model parameters are calibrated from experiments conducted at a range of strain-rates. R. Crystal is a totally different material from plastic. Rs 2,500/ each. Kružík To cite this article: J. $12. Two different microstructures, emanating from different processing conditions are considered. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. Such models can play a significan Software and Hardware Technology for Multiscale, Multiphysics Crystal Plasticity Models (1) [38] Based on the above it will take 38 hours i. Computation is very inhomogeneous: A large effort is expended everywhere, but only a small portion of the computational domain is doing anything interesting. Slip, twinning and their interactions are deemed the dominant plastic mechanisms. And each of the grains is discretized by many elements. In addition, once the elasto-plastic transition is over, the evolution of stress in the grains is controlled by plastic relaxation (slip activity). , Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method (typically 10-3) by comparison to the plastic component (typically >10-1). Material points are considered as aggregates of grains, subdivided into several ctitious grain fractions: a single crystal vol- This thesis develops an experimentally calibrated computational model based on crystal plasticity for the analysis of α-Ti-7Al polycrystalline alloys. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method Self-Consistent Model Following slides contain information about a more sophisticated model for crystal plasticity, called the self-consistent model. 6 Application of a Grain Boundary Constitutive Model to Simple Shear Tests of AluminumBicrystals with Different Misorientation 124 9. 3 Conclusions 123 9. A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1012} tensile twins. years, but a general crystal plasticity material model is still missing. Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. Elder f, Jorge Viñals g a Institute of Scientic Computing, Technische Universität Dresden, Dresden 01062, Germany Jun 28, 2010 · The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal model. Introduction crystal plasticity (AE-CP) FEM model is developed for the grain-scale, accounting for characteristic parameters of the sub-grain scale c c0 morphology. 1090638 Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. pp. A coarse-grained phase-field crystal model of plastic motion Research output : Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review Overview Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. Crystal graphic slip is taken in to account by the incorporation of 12 Octahedral slip systems. , Ann Arbor, MI 48109, USA Feb 28, 2006 · A finite element model, incorporating rate dependent elastocrystal plasticity, is developed for analyzing evolving variables in material microstructure. Because of the many material parameters, it is inherently difficult to determine the nonlocal crystal plasticity parameters. ” Materials Theory, 1(1):6, 2017 The boundary-value-problem simulated is for a three-dimensional polycrystal. The residence plane of screw dislocations is determined based on a probability function defined by activation energy and activation volume of cross-slip. See the above reference for additional details regarding the model. The proposed model includes the effect of mechanics-based quantities, such as stress triaxiality, initial porosity, crystal orientation, void growth and coalescence, on the deformation and failure of a single crystalline material. Cita com: hdl:2117/182870. ~ 25 classes. 2 Size Dependence of the Nonlocal Model 120 9. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method A phase-field model of a crystalline material is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. May 29, 2019 · “Diffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations. The crystal plasticity parameters are characterized by a combination of microtesting, orientation imaging microscopy, computational simulations, and minimization process involving Genetic In the present study, a viscoplastic self-consistent crystal plasticity model (VPSC-RGBV), whichaccounts for various microstructural features, including the accumulation and annihilation ofdislocations due to slip activity and latent hardening originated from interactions betweengliding dislocations on different slip planes, is described. �hal-01694522� May 04, 2016 · A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. A strain gradient dependent crystal plasticity approach is used to model the constitutive be-haviour of polycrystal FCC metals under large plastic deformation. Somjeet BiswasIIT Kharagpur, India& Prof. The parts come molded in multiple colors, including the pearly white of the car body, so no paint is required to finish this miniature beauty. A full description of this computer code has been presented in numerous studies [7][21] and was recently described in some detail in [8]. CVP constitutive models can capture the orientation, temperature, and rate dependence of these materials under a variety of conditions. doi: 10. Compared with conventional crystal plasticity models, a microforce balance equation is involved that combines the equation of dislocations motion and Orowan's law. If Rolex has to replace a sapphire crystal, they require a complete watch service because of the high probability of crystal shrapnel landing inside the movement, potentially causing major damage. Feb 10, 2018 · This work presents a porous crystal plasticity model which incorporates the necessary mechanisms of deformation and failure in single crystalline porous materials. Jun 10, 2016 · Ilyas, Muhammad Umer und Kabir, Mohammad Rizviul (2016) A TEMPERATURE SENSITIVE CRYSTAL PLASTICITY MODEL FOR THE PREDICTION OF HIGH TEMPERATURE MECHANICAL BEHAVIOUR OF MULTI-PHASE TIAL ALLOY. Wish List. 1. 015Fe (wt %) or Tie7Al. We also determine the Sep 19, 2021 · Ilyas, Muhammad Umer und Kabir, Mohammad Rizviul (2016) A Temperature Sensitive Crystal Plasticity Model For The Prediction Of High Temperature Mechanical Behaviour Of Multi-Phase TiAl Alloy. Optimization most often leads to more “Crystal plasticity” is a computationally intensive way of computing the behavior of materials undergoing large permanent deformations. Nov 02, 2020 · To predict this coupling effect between crystal plasticity and deformation twinning, we introduce a mathematical model and the corresponding monolithic and operator splitting solvers that couple the crystal plasticity material model with a phase field twining model such that the twinning nucleation and propagation can be captured via an The temperature profile and grain structure from thermal-fluid flow and grain growth simulations are implemented into the crystal plasticity model. The initial material microstructure is characterized using Electron Backscatter Diffraction (EBSD) and Scanning Electron Microscope (SEM) data. While the grain interiors were modeled using a limited form of crystal plasticity, the grain boundary influence regions were modeled using an isotropic plasticity model with a Jun 11, 2019 · A crystal plasticity model is developed to predict the fatigue crack nucleation of polycrystalline materials, in which the accumulated dislocation dipoles are considered to be the origin of damage. This provides the basis for the popular code VPSC made Jul 01, 2018 · A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1 ¯ 012} tensile twins. Manufacturer of a wide range of products which include crystal models, Acrylic plastic crystal model, Geomorphology Models, structural geology models, Microscopic Thin Section and Working Fault Model. The only exceptions are the snap-fit kits and even those can be glued to achieve a much better overall look. ISBN 978-618-82844-0-1. , 2001). 1/72 Scale. e. Model prediction qualitatively agrees with experimental observations and results of discrete dislocation dynamics simulations. While the method combines the best aspects of both hierarchical and concurrent methods, it is still computationally expensive to model polycrystalline aggregates at every coarse-scale material point. COMPLAS2013-75_Crystal plasticity model. This means that the size and evolution of the single crystal yield surface controls the stress in the grain. Laszlo S. Title: A new crystal plasticity constitutive model for simulating Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method Crystal Plasticity Based Fe Model for Understanding Microstructural Effects on Creep and Dwell Fatigue in Ti-6242 Author: Gayathri Venkataramani Dhyanjyoti Deka and Somnath Ghosh Journal: Journal of Engineering Materials and Technology Issue Date: 2006 Page: 356-365 Nov 05, 2019 · The rate dependent crystal visco-plastic model consists of a flow rule and internal state variables. model for Ti-6242, incorporating a rate-dependent aniso-tropic crystal plasticity constitutive model has been devel-oped by the authors in Ref. The part II develops an image based crystal plasticity FE model for the single-phase Ti alloy Tie7. We first obtain the elastic stress from the phase-field crystal free energy under weak distortion and show that it obeys the stress-strain relation of linear elasticity. These dislocations diffuse, interact and annihilate with one another, forming avalanche events. crystal plasticity model

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