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Mgd Marc Geers - One of the best experts on this subject based on the ideXlab platform.
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Reduced Crystal Plasticity for materials with constrained slip activity
Mechanics of Materials, 2016Co-Authors: F Francesco Maresca, V Varvara Kouznetsova, Mgd Marc GeersAbstract:In a number of materials, Plasticity occurs along preferential directions or slip systems, while other directions barely contribute to deformation. This can occur due to the specific Crystalline nature of the materials (e.g. in polymers) or due to the morphology of the Crystalline material itself, like in metal laminates. In the latter case, when the layers are very thin, the surrounding material acts as a constraint and only preferential slip directions are activated. This observation suggests the reduction of the underlying full Crystal Plasticity model within those regions to a more computationally efficient model which still retains the main deformation mechanism, i.e. Plasticity occuring along a few slip systems only. In this paper we propose such a reduced Crystal Plasticity model in a finite deformation setting. In the limit of either no active slip system or five linearly independent slip systems, the model reduces to isotropic Plasticity and standard Crystal Plasticity, respectively. The model is validated on a specific case, i.e. lath martensite microstructures consisting of alternating Crystalline layers of martensite and austenite. The characteristic material behaviour (i.e. stress-strain response and slip activity on the most active slip systems) is correctly reproduced by the reduced model at a significantly lower computational cost compared to a fully resolved Crystal Plasticity model.
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Coupled glide-climb diffusion-enhanced Crystal Plasticity
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Mgd Marc Geers, Maeva Cottura, Benoît Appolaire, Esteban P. Busso, Samuel Forest, A VillaniAbstract:This paper presents a fully coupled glide-climb Crystal Plasticity model, whereby climb is controlled by the diffusion of vacancies. An extended strain gradient Crystal Plasticity model is therefore proposed, which incorporates the climbing of dislocations in the governing transport equations. A global–local approach is adopted to separate the scales and assess the influence of local diffusion on the global Plasticity problem. The kinematics of the Crystal Plasticity model is enriched by incorporating the climb kinematics in the Crystallographic split of the plastic strain rate tensor. The potential of the fully coupled theory is illustrated by means of two single slip examples that illustrate the interaction between glide and climb in either bypassing a precipitate or destroying a dislocation pile-up.
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Energetic dislocation interactions and thermodynamical aspects of strain gradient Crystal Plasticity theories
Journal of the Mechanics and Physics of Solids, 2009Co-Authors: I Isa Ertürk, Van Jaw Hans Dommelen, Mgd Marc GeersAbstract:Abstract This paper focuses on the unification of two frequently used and apparently different strain gradient Crystal Plasticity frameworks: (i) the physically motivated strain gradient Crystal Plasticity models proposed by Evers et al. [2004a. Non-local Crystal Plasticity model with intrinsic SSD and GND effects. Journal of the Mechanics and Physics of Solids 52, 2379–2401; 2004b. Scale dependent Crystal Plasticity framework with dislocation density and grain boundary effects. International Journal of Solids and Structures 41, 5209–5230] and Bayley et al. [2006. A comparison of dislocation induced back stress formulations in strain gradient Crystal Plasticity. International Journal of Solids and Structure 43, 7268–7286; 2007. A three dimensional dislocation field Crystal Plasticity approach applied to miniaturized structures. Philosophical Magazine 87, 1361–1378] (here referred to as Evers–Bayley type models), where a physical back stress plays the most important role and which are further extended here to deal with truly large deformations, and (ii) the thermodynamically consistent strain gradient Crystal Plasticity model of Gurtin (2002–2008) (here referred to as the Gurtin type model), where the energetic part of a higher order micro-stress is derived from a non-standard free energy function. The energetic micro-stress vectors for the Gurtin type models are extracted from the definition of the back stresses of the improved Evers–Bayley type models. The possible defect energy forms that yield the derived physically based micro-stresses are discussed. The duality of both type of formulations is shown further by a comparison of the micro-boundary conditions. As a result, this paper provides a direct physical interpretation of the different terms present in Gurtin's model.
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non local Crystal Plasticity model with intrinsic ssd and gnd effects
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: L Laurens P Evers, Wam Marcel Brekelmans, Mgd Marc GeersAbstract:A strain gradient-dependent Crystal Plasticity approach is presented to model the constitutive behaviour of polyCrystal FCC metals under large plastic deformation. In order to be capable of predicting scale dependence, the heterogeneous deformation-induced evolution and distribution of geometrically necessary dislocations (GNDs) are incorporated into the phenomenological continuum theory of Crystal Plasticity. Consequently, the resulting boundary value problem accommodates, in addition to the ordinary stress equilibrium condition, a condition which sets the additional nodal degrees of freedom, the edge and screw GND densities, proportional (in a weak sense) to the gradients of Crystalline slip. Next to this direct coupling between microstructural dislocation evolutions and macroscopic gradients of plastic slip, another characteristic of the presented Crystal Plasticity model is the incorporation of the GND-effect, which leads to an essentially different constitutive behaviour than the statistically stored dislocation (SSD) densities. The GNDs, by their geometrical nature of locally similar signs, are expected to influence the plastic flow through a non-local back-stress measure, counteracting the resolved shear stress on the slip systems in the undeformed situation and providing a kinematic hardening contribution. Furthermore, the interactions between both SSD and GND densities are subject to the formation of slip system obstacle densities and accompanying hardening, accountable for slip resistance. As an example problem and without loss of generality, the model is applied to predict the formation of boundary layers and the accompanying size effect of a constrained strip under simple shear deformation, for symmetric double-slip conditions.
Yonggang Huang - One of the best experts on this subject based on the ideXlab platform.
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fracture of biCrystal metal ceramic interfaces a study via the mechanism based strain gradient Crystal Plasticity theory
International Journal of Plasticity, 2007Co-Authors: Amir Siddiq, S Schmauder, Yonggang HuangAbstract:Two continuum mechanical models of Crystal Plasticity theory namely, conventional Crystal Plasticity theory and mechanism-based Crystal Plasticity theory, are used to perform a comparative study of stresses that are reached at and ahead of the crack tip of a biCrystal niobium/alumina specimen. Finite element analyses are done for a stationary crack tip and growing cracks using a cohesive modelling approach. Using mechanism-based strain gradient Crystal Plasticity theory the stresses reached ahead of the crack tip are found to be two times larger than the stresses obtained from conventional Crystal Plasticity theory. Results also show that strain gradient effects strongly depend on the intrinsic material length to the size of plastic zone ratio (l/R0). It is found that the larger the (l/R0) ratio, the higher the stresses reached using mechanism-based strain gradient Crystal Plasticity theory. An insight into the role of cohesive strength and work of adhesion in macroscopic fracture is also presented which can be used by experimentalists to design better bimaterials by varying cohesive strength and work of adhesion.
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Fracture of biCrystal metal/ceramic interfaces: A study via the mechanism-based strain gradient Crystal Plasticity theory
International Journal of Plasticity, 2007Co-Authors: Amir Siddiq, S Schmauder, Yonggang HuangAbstract:Two continuum mechanical models of Crystal Plasticity theory namely, conventional Crystal Plasticity theory and mechanism-based Crystal Plasticity theory, are used to perform a comparative study of stresses that are reached at and ahead of the crack tip of a biCrystal niobium/alumina specimen. Finite element analyses are done for a stationary crack tip and growing cracks using a cohesive modelling approach. Using mechanism-based strain gradient Crystal Plasticity theory the stresses reached ahead of the crack tip are found to be two times larger than the stresses obtained from conventional Crystal Plasticity theory. Results also show that strain gradient effects strongly depend on the intrinsic material length to the size of plastic zone ratio (l/R0). It is found that the larger the (l/R0) ratio, the higher the stresses reached using mechanism-based strain gradient Crystal Plasticity theory. An insight into the role of cohesive strength and work of adhesion in macroscopic fracture is also presented which can be used by experimentalists to design better bimaterials by varying cohesive strength and work of adhesion.
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A conventional theory of strain gradient Crystal Plasticity based on the Taylor dislocation model
International Journal of Plasticity, 2007Co-Authors: Huamiao Wang, Chung-souk Han, Yonggang Huang, Kuo Chu Hwang, B. Liu, G. Ravichandran, Huajian GaoAbstract:Single Crystal metallic materials display strong size effects when the characteristic length of plastic deformation is on the order of microns. The classical Crystal Plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient Crystal Plasticity theory [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient Crystal Plasticity – I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188–1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient Crystal Plasticity – II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204–1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single Crystals. The intrinsic material length is identified from the Taylor dislocation model as l=α2(μτ0)2b, where μ is the shear modulus, τ0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical Crystal Plasticity theory due to geometrically necessary dislocations.
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Mechanism-based strain gradient Crystal Plasticity—II. Analysis
Journal of the Mechanics and Physics of Solids, 2005Co-Authors: Chung-souk Han, Huajian Gao, Yonggang Huang, William D. NixAbstract:Abstract In part I of this series (Mechanism-based strain gradient Crystal Plasticity—I. Theory. J. Mech. Phys. Sol. (2005), accepted for publication), we have proposed a theory of mechanism-based strain gradient Crystal Plasticity (MSG-CP) to model the effect of inherent anisotropy of a Crystal lattice on size-dependent non-uniform plastic deformation at micron and submicron length scales. In the present paper, several example problems are investigated to show how Crystal anisotropy is reflected by the MSG-CP theory.
Surya R. Kalidindi - One of the best experts on this subject based on the ideXlab platform.
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Computationally efficient predictions of Crystal Plasticity based forming limit diagrams using a spectral database
International Journal of Plasticity, 2018Co-Authors: Akash Gupta, Mohamed Ben Bettaieb, Farid Abed-meraim, Surya R. KalidindiAbstract:Abstract The present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polyCrystalline metal sheets using a Taylor-type (full constraints) Crystal Plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak–Kuczynski model. The Crystal Plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of Crystal Plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in Crystal Plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).
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Crystal Plasticity finite element simulations using a database of discrete Fourier transforms
International Journal of Plasticity, 2015Co-Authors: Hamad F. Alharbi, Surya R. KalidindiAbstract:Abstract In recent work, we have demonstrated the viability and computational advantages of using a compact database of discrete Fourier transforms (DFTs) for facilitating Crystal Plasticity solutions in cubic polyCrystalline materials subjected to arbitrary deformation paths. This new DFT database approach allows for compact representation and fast retrieval of Crystal Plasticity solutions, which is found to be able to speed up the calculations by about two orders of magnitude. In this paper, we present the first successful implementation of this spectral database approach in a commercial finite element code to permit computationally efficient simulations of heterogeneous deformations using Crystal Plasticity theories. More specifically, the spectral database approach to Crystal Plasticity solutions was successfully integrated with the commercial finite element package ABAQUS through a user material subroutine, UMAT. Details of this new Crystal Plasticity spectral database-FE approach are demonstrated and validated through a few example case studies for selected deformation processes on face centered and body centered cubic metals. The evolution of the underlying Crystallographic texture and its associated macroscale anisotropic properties predicted from this new approach are compared against the corresponding results from the conventional Crystal Plasticity finite element method. It is observed that implementing the Crystal Plasticity spectral database in a FE code produced excellent predictions similar to the classical Crystal Plasticity FE method, but at a significantly faster computational speed and much lower computational cost.
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Crystal Plasticity simulations using discrete Fourier transforms
Acta Materialia, 2009Co-Authors: Marko Knezevic, Hamad F. Alharbi, Surya R. KalidindiAbstract:Abstract In this paper, we explore efficient representation of all of the functions central to Crystal Plasticity simulations in their complete respective domains using discrete Fourier transforms (DFTs). This new DFT approach allows for compact representation and fast retrieval of Crystal Plasticity solutions for a Crystal of any orientation subjected to any deformation mode. The approach has been successfully applied to a rigid–viscoplastic Taylor-type model for face-centered cubic polyCrystals. It is observed that the novel approach described herein is able to speed up the conventional Crystal Plasticity computations by two orders of magnitude. Details of this approach are described and validated in this paper through a few example case studies.
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Spectral calibration of Crystal Plasticity models
Acta Materialia, 2006Co-Authors: Surya R. Kalidindi, Hari K. Duvvuru, Marko KnezevicAbstract:A new and improved spectral framework are presented to capture efficiently the predictions for the stresses, the lattice spins, and the strain hardening rates in individual Crystals from the currently used Crystal Plasticity models as a function of the Crystal lattice orientation. The proposed methodology has been successfully applied to two classes of Crystal Plasticity models that incorporate very different types of interactions between the individual Crystals in the polyCrystal. The models used in this study include: (1) a Taylor-type fully constrained model; and (2) a micromechanical finite element Crystal Plasticity model where each Crystal is assumed to experience an average interaction with all other Crystals in the polyCrystal. Although the proposed method requires a one-time high computational cost in evaluating the relevant Fourier coefficients, it is expected to result in dramatic savings in computational time and effort in all subsequent computations.
Curt A Bronkhorst - One of the best experts on this subject based on the ideXlab platform.
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thermodynamic theory of Crystal Plasticity formulation and application to polyCrystal fcc copper
Journal of The Mechanics and Physics of Solids, 2020Co-Authors: Charles K C Lieou, Curt A BronkhorstAbstract:Abstract We present a thermodynamic description of Crystal Plasticity. Our formulation is based on the Langer-Bouchbinder-Lookman thermodynamic dislocation theory (TDT), which asserts the fundamental importance of an effective temperature that describes the state of configurational disorder and therefore the dislocation density of the Crystalline material. We extend the TDT description from isotropic Plasticity to Crystal Plasticity with many slip systems. Finite-element simulations show favourable comparison with experiments on polyCrystal fcc copper under uniaxial compression, tension, and simple shear. The thermodynamic theory of Crystal Plasticity thus provides a thermodynamically consistent and physically rigorous description of dislocation motion in Crystals. We also discuss new insights about the interaction of dislocations belonging to different slip systems.
Marko Knezevic - One of the best experts on this subject based on the ideXlab platform.
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A new implementation of the spectral Crystal Plasticity framework in implicit finite elements
Mechanics of Materials, 2015Co-Authors: Miroslav Zecevic, Rodney J. Mccabe, Marko KnezevicAbstract:Abstract We present a new implementation of a computationally efficient Crystal Plasticity model in an implicit finite element (FE) framework. In recent publications, we have reported a standalone version of a Crystal Plasticity model based on fast Fourier transforms (FFTs) and termed it the spectral Crystal Plasticity (SCP) model. In this approach, iterative solvers for obtaining the mechanical response of a single Crystal of any Crystallographic orientation subjected to any deformation mode are replaced by a database of FFTs that allows fast retrieval of the solution. The standalone version of the code facilitates simulations of relatively simple monotonic deformation processes under homogeneous boundary conditions. In this paper, we present a new model that enables simulations of complex, non-monotonic deformation process with heterogeneous boundary conditions. For this purpose, we derive a fully analytical Jacobian enabling an efficient coupling of SCP with implicit finite elements. In our implementation, an FE integration point can represent a single Crystal or a polyCrystalline material point whose meso-scale mechanical response is obtained by the mean-field Taylor-type homogenization scheme. The finite element spectral Crystal Plasticity (FE-SCP) implementation has been validated for several monotonic loading conditions and successfully applied to rolling and equi-channel angular extrusion deformation processes. Predictions of the FE-SCP simulations compare favorably with experimental measurements. Details of the FE-SCP implementation and predicted results are presented and discussed in this paper.
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A high-performance computational framework for fast Crystal Plasticity simulations
Computational Materials Science, 2014Co-Authors: Marko Knezevic, Daniel J. SavageAbstract:Abstract We present a new computational framework aimed at dramatically reducing time needed for Crystal Plasticity simulations. The framework is based on a combination of the recently developed numerical implementations of Crystal Plasticity in the spectral representation for obtaining the response of single Crystals and specialized computer hardware that integrates a graphics-processing unit (GPU). Following a divide and conquer approach adapted here from a fast GPU8 method for matrix operations, we describe a new GPU based implementation of the spectral Crystal Plasticity and demonstrate its performances through a few example case studies involving a Taylor-type polyCrystalline model. Using a single GPU card, the novel framework described herein provides speedup factors exceeding three orders of magnitude over the conventional Crystal Plasticity numerical schemes.
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Crystal Plasticity simulations using discrete Fourier transforms
Acta Materialia, 2009Co-Authors: Marko Knezevic, Hamad F. Alharbi, Surya R. KalidindiAbstract:Abstract In this paper, we explore efficient representation of all of the functions central to Crystal Plasticity simulations in their complete respective domains using discrete Fourier transforms (DFTs). This new DFT approach allows for compact representation and fast retrieval of Crystal Plasticity solutions for a Crystal of any orientation subjected to any deformation mode. The approach has been successfully applied to a rigid–viscoplastic Taylor-type model for face-centered cubic polyCrystals. It is observed that the novel approach described herein is able to speed up the conventional Crystal Plasticity computations by two orders of magnitude. Details of this approach are described and validated in this paper through a few example case studies.
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Spectral calibration of Crystal Plasticity models
Acta Materialia, 2006Co-Authors: Surya R. Kalidindi, Hari K. Duvvuru, Marko KnezevicAbstract:A new and improved spectral framework are presented to capture efficiently the predictions for the stresses, the lattice spins, and the strain hardening rates in individual Crystals from the currently used Crystal Plasticity models as a function of the Crystal lattice orientation. The proposed methodology has been successfully applied to two classes of Crystal Plasticity models that incorporate very different types of interactions between the individual Crystals in the polyCrystal. The models used in this study include: (1) a Taylor-type fully constrained model; and (2) a micromechanical finite element Crystal Plasticity model where each Crystal is assumed to experience an average interaction with all other Crystals in the polyCrystal. Although the proposed method requires a one-time high computational cost in evaluating the relevant Fourier coefficients, it is expected to result in dramatic savings in computational time and effort in all subsequent computations.