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Ali Nazari - One of the best experts on this subject based on the ideXlab platform.
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application of strain gradient Plasticity Theory to model charpy impact energy of functionally graded steels using modified stress strain curve data
Computational Materials Science, 2012Co-Authors: Ali NazariAbstract:Abstract Functionally graded ferritic and austenitic steels were produced through electroslag refining by setting the austenitic and carbon steels with appropriate thickness as electrode. Charpy impact energy of the specimen has been studied and modeled regarding the mechanism-based strain gradient Plasticity Theory. The hardness of each layer was related to the density of the dislocations of that layer and then by using a linear relation, the predicted hardness was related to its corresponding yield stress. Afterwards; by assuming Holloman relation for the corresponding stress–strain curves, tensile strengths and tensile strains of the constituent layer were determined via numerical method. By using load–displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress–strain curves from uniaxial tensile tests were modified. Charpy impact energy each layer was related to the corresponding area under modified stress–strain curve of that layer and finally by applying the rule of mixtures, Charpy impact energy of functionally graded steels was determined. The obtained results of the proposed model are in good agreement with the experimental ones.
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simulation charpy impact energy of functionally graded steels by modified stress strain curve through mechanism based strain gradient Plasticity Theory
Computational Materials Science, 2012Co-Authors: Ali NazariAbstract:Abstract In the present work, Charpy impact energy of functionally graded steels produced by electroslag remelting composed of graded ferritic or austenitic layers in both crack divider and crack arrester configurations has been modeled by finite element method. The yield stress of each layer was related to the density of the statistically stored dislocations of that layer and assuming by Holloman relation for the corresponding stress–strain curves, tensile strengths of the constituent layers were determined via numerical method. By using load–displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress–strain curves from uniaxial tensile tests were modified. The data used for each layer in finite element modeling were predicted modified stress–strain curves obtained from strain gradient Plasticity Theory. A relatively good agreement between experimental results and those obtained from simulation was observed.
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modeling charpy impact energy of functionally graded steel based on the strain gradient Plasticity Theory and modified stress strain curve data
Computational Materials Science, 2011Co-Authors: Ali NazariAbstract:Abstract Functionally graded ferritic and austenitic steels were produced through electroslag refining by setting the austenitic and carbon steels with appropriate thickness as electrode. Charpy impact energy of the specimen has been studied and modeled regarding the mechanism-based strain gradient Plasticity Theory. The yield stress of each layer was related to the density of the statistically stored dislocations of that layer and assuming Holloman relation for the corresponding stress–strain curves, tensile strengths of the constituent layer were determined via numerical method. By using load–displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress–strain curves from uniaxial tensile tests were modified. Charpy impact energy of each layer was related to the corresponding area under its modified stress–strain curve and finally by applying the rule of mixtures, Charpy impact energy of functionally graded steels was determined. The obtained results of the proposed model are in good agreement with the experimental ones.
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prediction charpy impact energy of bcc and fcc functionally graded steels in crack divider configuration by strain gradient Plasticity Theory
Computational Materials Science, 2011Co-Authors: Ali Nazari, Seyyed Mehdi Mojtahed NajafiAbstract:Abstract In the present study, the Charpy impact energy of bcc ferritic and fcc austenitic functionally graded steels produced by electroslag remelting process has been investigated. To produce functionally graded steels, an electrode consists of two different spot welded slices from plain carbon and austenitic stainless steels were utilized. Functionally graded steel containing graded layers of ferrite or austenite may be fabricated via diffusion of alloying elements during remelting stage. Charpy impact energy of the specimens has been obtained experimentally in crack divider configuration and modeled with mechanism-based strain gradient Plasticity Theory. In this regard, the density of the statistically stored dislocations and that of geometrically necessary dislocations was related to the Vickers hardness of each layer. Afterwards, the predicted Vickers hardness of each layer was related to its Charpy impact energy. Finally, Charpy impact energy of each specimen was calculated by using the rule of mixtures. The predicted Charpy impact energies are in good agreement with those obtained from the experiments.
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modeling fracture toughness of ferritic and austenitic functionally graded steel based on the strain gradient Plasticity Theory
Computational Materials Science, 2011Co-Authors: Ali NazariAbstract:Abstract Functionally graded ferritic and austenitic steels were produced through electroslag refining by setting the austenitic stainless steels and plain carbon steel with appropriate thickness as electrode. Fracture toughness of the specimen in terms of JIC was studied and modeled regarding the mechanism-based strain gradient Plasticity Theory. The yield stress of each layer was related to the density of the dislocations of that layer and assuming Holloman relation for the corresponding stress–strain curves, tensile strengths of the constituent layers were determined via numerical method. Fracture toughness of each layer was related to the corresponding area under stress–strain curve of that layer and finally by applying the rule of mixtures, fracture toughness of functionally graded steels was determined. The obtained results of the proposed model are in good agreement with the experimental ones.
Mitsutoshi Kuroda - One of the best experts on this subject based on the ideXlab platform.
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a higher order strain gradient Plasticity Theory with a corner like effect
International Journal of Solids and Structures, 2015Co-Authors: Mitsutoshi KurodaAbstract:Abstract A corner-like Plasticity model originally proposed as a size-independent Theory is extended to include a size effect resulting from plastic strain gradients. A method of solving boundary value problems at finite strains is also presented. The efficiency of the new Theory is demonstrated through two typical numerical examples: a constrained simple shear problem in which an infinitely long strip bounded by two hard materials is subjected to large shear under plane strain conditions, and a problem of shear band formation in plane strain tension.
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Theoretical and experimental study of forming-limit strain of half-hard AA1100 aluminium alloy sheet
Computational Materials Science, 2013Co-Authors: Ryoichi Chiba, Mitsutoshi Kuroda, Hiroshi Takeuchi, Tomoyuki Hakoyama, Toshihiko KuwabaraAbstract:Abstract The forming-limit diagram (FLD) of a half-hard aluminium alloy (AA1100-H24) sheet was obtained theoretically for linear strain paths using two different approaches: phenomenological Theory and crystal Plasticity Theory. For both approaches, the Marciniak–Kuczynski model was applied to the computation of the FLD. The Yld2000-2d yield function was used for the phenomenological analysis and a full-constraint Taylor-type model was adopted for the crystal Plasticity analysis. The experimental FLD was also obtained through the Marciniak in-plane stretching test. The theoretical predictability of the FLD was assessed by comparing the predicted FLDs with the experimental FLD. The comparison demonstrated that the phenomenological Theory could duplicate the experimental FLD on the left-hand side of the diagram but could not do so over the entire range on the right-hand side up to the equibiaxial stretching. The same was true when the Yld2000-2d yield function was determined based on numerically evaluated anisotropic properties instead of measured values. It was also shown that the crystal Plasticity Theory predicted higher forming-limit strains on the left-hand side and markedly lower limit strains on the right-hand side than the experimental strains except for the equibiaxial stretching.
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an alternative treatment of phenomenological higher order strain gradient Plasticity Theory
International Journal of Plasticity, 2010Co-Authors: Mitsutoshi Kuroda, Viggo TvergaardAbstract:Phenomenological higher-order strain-gradient Plasticity is here presented through a formulation inspired by previous work for strain-gradient crystal Plasticity. A physical interpretation of the phenomenological yield condition that involves an effect of second gradient of the equivalent plastic strain is discussed, applying a dislocation Theory-based consideration. Then, a differential equation for the equivalent plastic strain-gradient is introduced as an additional governing equation. Its weak form makes it possible to deduce and impose extra boundary conditions for the equivalent plastic strain. A connection between the present treatment and strain-gradient theories based on an extended virtual work principle is discussed. Furthermore, a numerical implementation and analysis of constrained simple shear of a thin strip are presented.
N A Fleck - One of the best experts on this subject based on the ideXlab platform.
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Mode I crack tip fields: strain gradient Plasticity Theory versus J2 flow Theory
2019Co-Authors: Martinez-paneda E, N A FleckAbstract:The mode I crack tip asymptotic response of a solid characterised by strain gradient Plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip Plasticity is suppressed when the material length scale $\ell$ of the gradient Theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient Plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk Plasticity and an outer J-field
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Mode I crack tip fields: Strain gradient Plasticity Theory versus J2 flow Theory
'Elsevier BV', 2019Co-Authors: Martinez-paneda E, N A FleckAbstract:The mode I crack tip asymptotic response of a solid characterised by strain gradient Plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip Plasticity is suppressed when the material length scale of the gradient Theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient Plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk Plasticity and an outer J-field
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a mathematical basis for strain gradient Plasticity Theory part ii tensorial plastic multiplier
Journal of The Mechanics and Physics of Solids, 2009Co-Authors: N A Fleck, J R WillisAbstract:Strain-gradient Plasticity theories are reviewed in which some measure of the plastic strain rate is treated as an independent kinematic variable. Dislocation arguments are invoked in order to provide a physical basis for the hardening at interfaces. A phenomenological, flow Theory version of gradient Plasticity is constructed in which stress measures, work-conjugate to plastic strain and its gradient, satisfy a yield condition. Plastic work is also done at internal interfaces and a yield surface is postulated for the work-conjugate stress quantities at the interface. Thereby, the Theory has the potential to account for grain size effects in polycrystals. Both the bulk and interfacial stresses are taken to be dissipative in nature and due attention is paid to ensure that positive plastic work is done. It is shown that the mathematical structure of the elasto-plastic strain-gradient Theory has similarities to conventional rigid-Plasticity Theory. Uniqueness and extremum principles are constructed for the solution of boundary value problems.
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strain gradient Plasticity Theory and experiment
Acta Metallurgica Et Materialia, 1994Co-Authors: N A Fleck, G M Muller, M F AshbyAbstract:Abstract Dislocation Theory is used to invoke a strain gradient Theory of rate independent Plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation Theory of Plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The Theory is a non-linear generalization of Cosserat couple stress Theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new Theory.
J R Willis - One of the best experts on this subject based on the ideXlab platform.
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a mathematical basis for strain gradient Plasticity Theory part ii tensorial plastic multiplier
Journal of The Mechanics and Physics of Solids, 2009Co-Authors: N A Fleck, J R WillisAbstract:Strain-gradient Plasticity theories are reviewed in which some measure of the plastic strain rate is treated as an independent kinematic variable. Dislocation arguments are invoked in order to provide a physical basis for the hardening at interfaces. A phenomenological, flow Theory version of gradient Plasticity is constructed in which stress measures, work-conjugate to plastic strain and its gradient, satisfy a yield condition. Plastic work is also done at internal interfaces and a yield surface is postulated for the work-conjugate stress quantities at the interface. Thereby, the Theory has the potential to account for grain size effects in polycrystals. Both the bulk and interfacial stresses are taken to be dissipative in nature and due attention is paid to ensure that positive plastic work is done. It is shown that the mathematical structure of the elasto-plastic strain-gradient Theory has similarities to conventional rigid-Plasticity Theory. Uniqueness and extremum principles are constructed for the solution of boundary value problems.
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interfaces within strain gradient Plasticity Theory and experiments
Acta Materialia, 2006Co-Authors: W A Soer, Katerina E Aifantis, Th J M De Hosson, J R WillisAbstract:Abstract In this paper, it is shown that the occurrence of dislocation pileups across grain boundaries, as well as subsequent emission to the adjacent grains, is captured theoretically by gradient Plasticity and confirmed experimentally by nanoindentation. From a theoretical point of view, this is accomplished (within a deformation Theory framework applicable to continued loading) by accounting for a specific interfacial term in the overall potential of the material, in terms of which its response, taken to conform to strain gradient Plasticity, is defined. The main features that result from the addition of this interfacial term are (i) significant size effects of Hall–Petch type in the overall stress–strain response of polycrystals and (ii) the determination of an analytical expression for the stress corresponding to the onset of dislocation transfer across interfaces. From an experimental point of view, the effective stress at which dislocation transfer takes place across an interface can be obtained from nanoindentations performed in close proximity to an Fe–2.2 wt.% Si grain boundary, since they exhibit a distinct strain burst that is related to the presence of the boundary. It is possible, therefore, to fit the theoretically determined analytical expression for the interfacial yield stress to the experimental data. From this fit, first estimates are obtained for key material parameters, namely the interfacial term and the internal length, that are required for the theoretical formulation. Dislocation mechanics are employed to provide physical insight of these parameters.
Rashid Abu K Alrub - One of the best experts on this subject based on the ideXlab platform.
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on the numerical implementation of the higher order strain gradient dependent Plasticity Theory and its non classical boundary conditions
Finite Elements in Analysis and Design, 2015Co-Authors: Mahmood Ettehad, Rashid Abu K AlrubAbstract:Abstract The higher-order gradient Plasticity Theory is successful in explaining the size effects encountered at the micron and submicron length scale. Due to the incorporation of spatial gradients of one or more internal variables in these theories and the associated non-classical boundary conditions, special types of elements in the finite element method maybe necessary. This makes the numerical implementation of this higher-order Theory not straightforward. In this paper, a robust but straightforward numerical implementation of higher-order gradient-dependent Plasticity theories is presented. The novelty of this paper is in (1) the application of the meshless methods, particularly the moving weighted least square method, combined with the finite element method for the numerical computation of plastic strain gradients, and (2) the numerical implementation of different types of higher-order microscopic boundary conditions at internal/external surfaces, interfaces, and moving elastic–plastic boundaries. The proposed numerical implementation algorithms can be easily adapted in the implementation of any form of higher-order gradient-dependent constitutive models. Examples of applying the current numerical approach is demonstrated for capturing mesh-objective shear band formation and size effect and boundary layer formation in thin films on elastic substrates and metal matrix composites with embedded elastic inclusions through the consideration of stiff, intermediate, and soft interfaces.
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modeling the particle size and interfacial hardening effects in metal matrix composites with dispersed particles at decreasing microstructural length scales
International Journal for Multiscale Computational Engineering, 2009Co-Authors: Rashid Abu K AlrubAbstract:The focus of this paper is on incorporating the particle size effect and the effect of particlematrix interfacial properties on the average onset of Plasticity and strain hardening rates of metal matrix composites reinforced with hard, stiff, or soft particles. In order to achieve this objective, a higher-order gradient Plasticity Theory that explicitly includes the effect of interfacial energy at particle-matrix interfaces is formulated within the frameworks of virtual power and thermodynamic laws. The derived higher-order gradient Plasticity Theory also takes into account large variations in plastic strain tensor and effective plastic strain; namely, the gradient of plastic strain, the gradient of the effective plastic strain, and the accumulation of plastic strain gradients. Moreover, unlike the majority of the existing gradient Plasticity theories in the literature, it is shown that the matrix nonlocal yield condition as well as a yield-like condition for the particle-matrix interface can be directly derived from the principle of virtual power without any further constitutive assumptions. Also, in this work the interfaces dissipate energy similar to the bulk material during plastic deformation. The interfacial yield condition takes into consideration the particle type (soft, stiff, hard) through the incorporation of the particle-matrix interfacial yield strength and interfacial hardening in case of dislocation transmission across the interface (i.e. shearing of particles). The proposed higher-order gradient Plasticity Theory is shown to be qualitatively successful in predicting the increase in the average yield strength, strain hardening rates, and flow stress as the particle size decreases and the particle interfacial strength increases.
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a physically based gradient Plasticity Theory
International Journal of Plasticity, 2006Co-Authors: Rashid Abu K Alrub, George Z VoyiadjisAbstract:Abstract The intent of this work is to derive a physically motivated mathematical form for the gradient Plasticity that can be used to interpret the size effects observed experimentally. The step of translating from the dislocation-based mechanics to a continuum formulation is explored. This paper addresses a possible, yet simple, link between the Taylor’s model of dislocation hardening and the strain gradient Plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result, a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. Comparisons are made of this Theory with experiments on micro-torsion, micro-bending, and micro-indentation size effects.
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gradient Plasticity Theory with a variable length scale parameter
International Journal of Solids and Structures, 2005Co-Authors: George Z Voyiadjis, Rashid Abu K AlrubAbstract:The definition and magnitude of the intrinsic length scale are keys to the development of the gradient Plasticity Theory that incorporates size effects. However, a fixed value of the material length-scale is not always realistic and different problems could require different values. Moreover, a linear coupling between the local and nonlocal terms in the gradient Plasticity Theory is not always realistic and that different problems could require different couplings. This work addresses the proper modifications required for the full utility of the current gradient Plasticity theories in solving the size effect problem. It is shown that the current gradient Plasticity theories do not give sound interpretations of the size effects in micro-bending and micro-torsion tests if a definite and fixed length scale parameter is used. A generalized gradient Plasticity model with a non-fixed length scale parameter is proposed based on dislocation mechanics. This model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled (or to the way in which the statically stored and geometrically necessary dislocations are coupled). In addition a physically-based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.