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C N Tome - One of the best experts on this subject based on the ideXlab platform.
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elasto viscoplastic self consistent modeling of the ambient temperature plastic behavior of periclase deformed up to 5 4 gpa
Journal of Applied Physics, 2017Co-Authors: Feng Lin, C N Tome, Nadege Hilairet, Paul Raterron, Ahmed Addad, Julia Immoor, Hauke Marquardt, Lowell Miyagi, Sebastien MerkelAbstract:Anisotropy has a crucial effect on the mechanical response of Polycrystalline materials. Polycrystal anisotropy is a consequence of single crystal anisotropy and texture (crystallographic preferred orientation) development, which can result from plastic deformation by dislocation glide. The plastic behavior of Polycrystals is different under varying hydrostatic pressure conditions, and understanding the effect of hydrostatic pressure on plasticity is of general interest. Moreover, in the case of geological materials, it is useful for understanding material behavior in the deep earth and for the interpretation of seismic data. Periclase is a good material to test because of its simple and stable crystal structure (B1), and it is of interest to geosciences, as (Mg,Fe)O is the second most abundant phase in Earth's lower mantle. In this study, a Polycrystalline sintered sample of periclase is deformed at ∼5.4 GPa and ambient temperature, to a total strain of 37% at average strain rates of 2.26 × 10−5/s and 4....
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evaluation of self consistent Polycrystal plasticity models for magnesium alloy az31b sheet
International Journal of Solids and Structures, 2010Co-Authors: Huamiao Wang, B Raeisinia, S R Agnew, C N TomeAbstract:Various self-consistent Polycrystal plasticity models for hexagonal close packed (HCP) Polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed Polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the Polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.
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grain size effects on the tensile properties and deformation mechanisms of a magnesium alloy az31b sheet
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2008Co-Authors: A Jain, C N Tome, Ozgur Duygulu, Donald W Brown, S R AgnewAbstract:Abstract The grain size dependence of the tensile properties and the deformation mechanisms responsible for those properties are examined for Mg alloy, AZ31B, sheet. Specifically, the Hall–Petch effect and strain anisotropy ( r -value) are characterized experimentally, and interpreted using Polycrystal plasticity modeling. {1 0 . 2} extension twins, {1 0 . 1} contraction twins, and so-called “double-twins” are observed via microscopy and diffraction-based techniques, and the amount of twinning is found to increase with increasing grain size. For the sheet texture and tensile loading condition examined, {1 0 . 2} extension twinning is not expected, yet the Polycrystal plasticity model predicts the observed behavior, including this ‘anomalous’ tensile twinning. The analysis shows that the Hall–Petch strength dependence, of the Polycrystal as a whole, is primarily determined by the grain size dependence of the strength of the prismatic slip systems.
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mechanical response of zirconium i derivation of a Polycrystal constitutive law and finite element analysis
Acta Materialia, 2001Co-Authors: C N Tome, Ricardo A Lebensohn, P J Maudlin, G C KaschnerAbstract:Simulating the forming of anisotropic Polycrystals, such as zirconium, requires a description of the anisotropy of the aggregate and the single crystal, and also of their evolution with deformation (texture development and hardening). Introducing the anisotropy of the single crystal requires the use of Polycrystal models that account for inhomogeneous deformation depending on grain orientation. In particular, visco- plastic self-consistent models have been successfully used for describing strongly anisotropic aggregates. As a consequence, using a Polycrystal constitutive law inside finite element (FE) codes represents a considerable improvement over using empirical constitutive laws, since the former provides a physically based description of anisotropy and its evolution. In this work we develop a Polycrystal constitutive description for pure Zr deforming under quasi-static conditions at room and liquid nitrogen temperatures. We use tensile and compressive experimental data obtained from a clock-rolled Zr sheet to adjust the constitutive parameters of the Polycrystal model. Twinning is accounted for in the description. The Polycrystal model is implemented into an explicit FE code, assuming a full Polycrystal at the position of each integration point. The orientation and hardening of the individual grains associated with each element is updated as deformation proceeds. We report preliminary results of this methodology applied to simulate the three-dimensional deformation of zirconium bars deforming under four-point bend conditions to maximum strains of about 20%. A critical comparison between experiments and predictions is done in a second paper (Kaschner et al., Acta mater. 2001, 49(15), 3097-3107). Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.
Ricardo A Lebensohn - One of the best experts on this subject based on the ideXlab platform.
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numerical implementation of non local Polycrystal plasticity using fast fourier transforms
Journal of The Mechanics and Physics of Solids, 2016Co-Authors: Ricardo A Lebensohn, A NeedlemanAbstract:Abstract We present the numerical implementation of a non-local Polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012) . Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influence of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc Polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of Polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.
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stress hot spots in viscoplastic deformation of Polycrystals
Modelling and Simulation in Materials Science and Engineering, 2010Co-Authors: Anthony D Rollett, Ricardo A Lebensohn, Michael A Groeber, Y Choi, Gregory S RohrerAbstract:The viscoplastic deformation of Polycrystals under uniaxial loading is investigated to determine the relationship between hot spots in stress and their location in relation to the microstructure. A 3D full-field formulation based on fast Fourier transforms for the prediction of the viscoplastic deformation of poly-crystals is used with rate-sensitive crystal plasticity. Two measured Polycrystalline structures are used to instantiate the simulations, as well as a fully periodic synthetic Polycrystal adapted from a simulation of grain growth. Application of (Euclidean) distance maps shows that hot spots in stress tend to occur close to grain boundaries. It is also found that low stress regions lie close to boundaries. The radial distribution function of the hot spots indicates clustering. Despite the lack of texture in the Polycrystals, the hot spots are strongly concentrated in ! 110 " orientations, which can account for the observed clustering. All three microstructures yield similar results despite significant differences in topology. (Some figures in this article are in colour only in the electronic version)
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simulation of micromechanical behavior of Polycrystals finite elements versus fast fourier transforms
Modelling and Simulation in Materials Science and Engineering, 2009Co-Authors: A Prakash, Ricardo A LebensohnAbstract:In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of Polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the Polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations. Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version.
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Elastic anisotropy and yield surface estimates of Polycrystals
International Journal of Solids and Structures, 2009Co-Authors: Renald Brenner, Ricardo A Lebensohn, Olivier CastelnauAbstract:Homogenization estimates based on the self-consistent scheme are customarily used to describe the plastic yielding of Polycrystals. Such estimates of the initial micro yield surface of a Polycrystal depend on the morphologic and crystallographic textures, the slip system geometry, the corresponding critical resolved shear stresses and the single crystal elastic anisotropy. The usual approach relies on a rather crude description of the stress field induced by the local elastic anisotropy. This deficiency is addressed and a new concept, i.e. a ‘‘probability” yield surface is proposed. Based on a statistical description of the local fields, the latter makes use of the average and the standard deviation of the resolved shear stress on the different slip systems within a given crystalline orientation. By comparing the homogenization estimates with full-field results, it is shown that the self-consistent scheme does not present intrinsic shortcomings regarding the prediction of the micro yield stress of Polycrystals with anisotropic elastic constitutive behaviour. On the contrary, it delivers realistic estimates if the local field fluctuations are taken into account in the yield criterion. The quantitative results obtained for cubic elasticity show a strong influence of the intragranular stress heterogeneity on the estimate of the micro yield stress.
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heterogeneous deformation and texture development in halite Polycrystals comparison of different modeling approaches and experimental data
Tectonophysics, 2003Co-Authors: Ricardo A Lebensohn, P.r. Dawson, Hartmut Kern, Hansrudolf WenkAbstract:Modeling the plastic deformation and texture evolution in halite is challenging due to its high plastic anisotropy at the single crystal level and to the influence this exerts on the heterogeneity of deformation over halite Polycrystals. Three different assumptions for averaging the single crystal responses over the Polycrystal were used: a Taylor hypothesis, a self-consistent viscoplastic model, and a finite element methodology. The three modeling approaches employ the same single crystal relations, but construct the Polycrystal response differently. The results are compared with experimental data for extension at two temperatures: 20 and 100 degreesC. These comparisons provide new insights of how the interplay of compatibility and local equilibrium affects the overall plastic behavior and the texture development in highly anisotropic Polycrystalline materials. Neither formulation is able to completely simulate the texture development of halite Polycrystals while, at the same time, giving sound predictions of microstructural evolution. Results obtained using the finite element methodology are promising, although they point to the need for greater resolution of the individual crystals to capture the full impact of deformation heterogeneities. (C) 2003 Elsevier B.V All rights reserved.
F P E Dunne - One of the best experts on this subject based on the ideXlab platform.
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a spherical harmonic approach for the determination of hcp texture from ultrasound a solution to the inverse problem
Journal of The Mechanics and Physics of Solids, 2015Co-Authors: Bo Lan, M J S Lowe, F P E DunneAbstract:A new spherical convolution approach has been presented which couples HCP single crystal wave speed (the kernel function) with Polycrystal c-axis pole distribution function to give the resultant Polycrystal wave speed response. The three functions have been expressed as spherical harmonic expansions thus enabling application of the de-convolution technique to enable any one of the three to be determined from knowledge of the other two. Hence, the forward problem of determination of Polycrystal wave speed from knowledge of single crystal wave speed response and the Polycrystal pole distribution has been solved for a broad range of experimentally representative HCP Polycrystal textures. The technique provides near-perfect representation of the sensitivity of wave speed to Polycrystal texture as well as quantitative prediction of Polycrystal wave speed. More importantly, a solution to the inverse problem is presented in which texture, as a c-axis distribution function, is determined from knowledge of the kernel function and the Polycrystal wave speed response. It has also been explained why it has been widely reported in the literature that only texture coefficients up to 4th degree may be obtained from ultrasonic measurements. Finally, the de-convolution approach presented provides the potential for the measurement of Polycrystal texture from ultrasonic wave speed measurements.
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a generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed
Journal of The Mechanics and Physics of Solids, 2015Co-Authors: Bo Lan, M J S Lowe, F P E DunneAbstract:Abstract In this paper, the spherical harmonic convolution approach for HCP materials ( Lan et al., 2015 ) is extended into a generalised form for the principal purpose of bulk texture determination in cubic Polycrystals from ultrasonic wave speed measurements. It is demonstrated that the wave speed function of a general single crystal convolves with the Polycrystal Orientation Distribution Function (ODF) to make the resultant Polycrystal wave speed function such that when the three functions are expressed in harmonic expansions, the coefficients of any one function may be determined from the coefficients of the other two. All three Euler angles are taken into account in the description of the ODF such that the theorem applies for all general crystal systems. The forward problem of predicting Polycrystal wave speed with knowledge of single crystal properties and the ODF is solved for all general cases, with validation carried out on cubic textures showing strong sensitivity to texture and excellent quantitative accuracy in predicted wave speed amplitudes. Importantly, it is also revealed by the theorem that the cubic structure is one of only two crystal systems (the other being HCP) whose orientation distributions can be inversely determined from Polycrystal wave velocities by virtue of their respective crystal symmetries. Proof of principle is then established by recovering the ODFs of representative cubic textures solely from the wave velocities generated from a computational model using these texture inputs, and excellent accuracies are achieved in the recovered ODF coefficients as well as the resultant pole figures. Hence the methodology is argued to provide a powerful technique for wave propagation studies and bulk texture measurement in cubic Polycrystals and beyond.
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experimental and computational studies of ultrasound wave propagation in hexagonal close packed Polycrystals for texture detection
Acta Materialia, 2014Co-Authors: Bo Lan, M J S Lowe, F P E DunneAbstract:Abstract Texture in hexagonal close-packed (hcp) Polycrystalline metals, often developed during thermomechanical processing, affects ultrasonic wave velocity. In this study, the relationship between bulk texture and ultrasonic wave velocity in aggregates of (predominantly) hcp grains is investigated using theoretical, numerical and experimental methods. A representative volume element methodology is presented, enabling the effects of texture on ultrasonic wave speed to be investigated in two-phase Polycrystals, and is employed to examine the ultrasonic response of random Polycrystals, textured Polycrystals and macro-zones often observed in titanium alloys. Numerical results show that ultrasonic wave speed varies progressively with changing texture, over a range of ∼200 m s −1 , within bounds set by the two extreme single-crystal orientations. Experimental ultrasound studies and full electron backscatter diffraction (EBSD) characterization are conducted on unidirectionally rolled and cross-rolled Ti–6Al–4V samples in three orthogonal directions. In addition, the EBSD-determined textures are incorporated within the Polycrystal model and predicted ultrasonic velocities compared directly with ultrasonic experiments. Good quantitative agreement is obtained and both the experimental and computed results demonstrate that ultrasonic velocity profiles exist for random, unidirectionally rolled and cross-rolled textures. The combined results indicate the possibility of the development of a methodology for bulk texture determination within Ti Polycrystal components using ultrasound.
Esteban P. Busso - One of the best experts on this subject based on the ideXlab platform.
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Effects of lattice misorientations on strain heterogeneities in FCC Polycrystals
Journal of the Mechanics and Physics of Solids, 2006Co-Authors: Ke-shen Cheong, Esteban P. BussoAbstract:Abstract It is well documented that the highly heterogeneous deformation behaviour and lattice rotation typically observed within grains in a Polycrystal are attributed to microstructural features such as grain structure, topology, size, etc. In this work, the effects of low- and high-angle grain boundaries on the mechanical behaviour of FCC Polycrystals are investigated using a micro-mechanical model based on crystal plasticity theory. The constitutive framework relies on dislocation mechanics concepts to describe the plastic deformation behaviour of FCC metallic crystals and is validated by comparing the measured and predicted local and macroscopic deformation behaviour in a thin Al–0.5% Mg Polycrystal tensile specimen containing a relatively small number of surface grains. Comparisons at the microscopic (e.g. local slip distribution) and macroscopic (e.g. average stress–strain response) levels elucidate the role of low-angle grain boundaries, which are found to have a profound effect on both the local and average deformation behaviour of FCC Polycrystals with a small number of grains. However, this effect diminishes when the number of grains increases and becomes negligible in bulk Polycrystals. In light of the widely accepted view that high-angle grain boundaries strongly influence the mechanical behaviour of very fine-grained metals, this work has shown that low-angle grain boundaries can also play an equally important role in the deformation behaviour of Polycrystals with a relatively small number of grains.
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a study of microstructural length scale effects on the behaviour of fcc Polycrystals using strain gradient concepts
International Journal of Plasticity, 2005Co-Authors: K S Cheong, Esteban P. Busso, A ArsenlisAbstract:Abstract Grain size is a critically important aspect of Polycrystalline materials and experimental observations on Cu and Al Polycrystals have shown that a Hall–Petch-type phenomenon does exist at the onset of plastic deformation. In this work, a parametric study is conducted to investigate the effect of microstructural and deformation-related length scales on the behaviour of such FCC Polycrystals. It relies on a recently proposed non-local dislocation-mechanics based crystallographic theory to describe the evolution of dislocation mean spacings within each grain, and on finite element techniques to incorporate explicitly grain interaction effects. Polycrystals are modeled as representative volume elements (RVEs) containing up to 64 randomly oriented grains. Predictions obtained from RVEs of Cu Polycrystals with different grain sizes are shown to be consistent with experimental data. Furthermore, mesh sensitivity studies revealed that, when there is a predominance of geometrically necessary dislocations relative to statistically stored dislocations, the Polycrystal response becomes increasingly mesh sensitive. This was found to occur especially during the early stages of deformation in Polycrystals with small grains.
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discrete dislocation density modelling of single phase fcc Polycrystal aggregates
Acta Materialia, 2004Co-Authors: Ke-shen Cheong, Esteban P. BussoAbstract:A new dislocation-mechanics based crystallographic theory has been developed to model the mechanical behaviour of single-phase FCC Polycrystal aggregates. In the theory, dislocations are discretised into edge and screw components with intrinsically different relative mobilities and are subject to different dynamic recovery processes. The theory has been implemented within a finite-strain and rate-dependent constitutive framework, and applied to a thin Polycrystal Cu specimen to investigate the effect of intragranular lattice misorientations on deformation behaviour. These misorientations are representative of low angle grain boundaries, which are known to play an important role in the microstructural evolution of Polycrystals under monotonic and cyclic deformation. This study reveals that the presence of these misorientations strengthen the material response by suppressing and re-distributing the localisation of slip within the grains, as well as inhibiting the formation of sub-grains. Through the discretisation of dislocations, the model also predicts a higher proportion of edge dislocations in the vicinities of localised slip regions.
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a study of microstructural length scale effects on the behaviour of fcc Polycrystals using strain gradient concepts
Journal Name: International Journal of Plasticity vol. 21 no. 9 September 1 2005 pp. 1797-1814, 2004Co-Authors: K S Cheong, Esteban P. Busso, A ArsenlisAbstract:Grain size is a critically important aspect of Polycrystalline materials and experimental observations on Cu and Al Polycrystals have shown that a Hall-Petchtype phenomenon does exist at the onset of plastic deformation. In this work, a parametric study is conducted to investigate the effect of microstructural and deformation-related length scales on the behavior of such FCC Polycrystals. It relies on a recently proposed non-local dislocation-mechanics based crystallographic theory to describe the evolution of dislocation mean spacings within each grain, and on finite element techniques to incorporate explicitly grain interaction effects. Polycrystals are modeled as representative volume elements (RVEs) containing up to 64 randomly oriented grains. Predictions obtained from RVEs of Cu Polycrystals with different grain sizes are shown to be consistent with experimental data. Furthermore, mesh sensitivity studies revealed that, when there is a predominance of geometrically necessary dislocations (GNDs) relative to statistically-stored dislocations (SSDs), the Polycrystal response becomes increasingly mesh sensitive. This was found to occur specially during the early stages of deformation in Polycrystals with small grains.
S R Agnew - One of the best experts on this subject based on the ideXlab platform.
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evaluation of self consistent Polycrystal plasticity models for magnesium alloy az31b sheet
International Journal of Solids and Structures, 2010Co-Authors: Huamiao Wang, B Raeisinia, S R Agnew, C N TomeAbstract:Various self-consistent Polycrystal plasticity models for hexagonal close packed (HCP) Polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed Polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the Polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.
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grain size effects on the tensile properties and deformation mechanisms of a magnesium alloy az31b sheet
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2008Co-Authors: A Jain, C N Tome, Ozgur Duygulu, Donald W Brown, S R AgnewAbstract:Abstract The grain size dependence of the tensile properties and the deformation mechanisms responsible for those properties are examined for Mg alloy, AZ31B, sheet. Specifically, the Hall–Petch effect and strain anisotropy ( r -value) are characterized experimentally, and interpreted using Polycrystal plasticity modeling. {1 0 . 2} extension twins, {1 0 . 1} contraction twins, and so-called “double-twins” are observed via microscopy and diffraction-based techniques, and the amount of twinning is found to increase with increasing grain size. For the sheet texture and tensile loading condition examined, {1 0 . 2} extension twinning is not expected, yet the Polycrystal plasticity model predicts the observed behavior, including this ‘anomalous’ tensile twinning. The analysis shows that the Hall–Petch strength dependence, of the Polycrystal as a whole, is primarily determined by the grain size dependence of the strength of the prismatic slip systems.
