Marko Knezevic - Academia.edu (original) (raw)

Papers by Marko Knezevic

Research paper thumbnail of A new spectral framework for crystal plasticity modeling of cubic and hexagonal polycrystalline metals

Crystal plasticity physics-based constitutive theories are used in understanding and predicting t... more Crystal plasticity physics-based constitutive theories are used in understanding and predicting the evolution of the underlying microstructure and the concomitant anisotropic stress-strain response in polycrystalline metals subjected to finite plastic strains. A new scheme for efficient crystal plasticity computations for both cubic and hexagonal polycrystalline metals subjected to arbitrary deformation modes has been developed in this thesis. This new computational scheme involves building material databases comprised of spectral coefficients. These spectral coefficients are computed using discrete Fourier transforms (DFTs) and allow for compact representation and fast retrieval of crystal plasticity solutions for a crystal of any orientation subjected to any deformation mode. The novel approach is able to speed up the conventional crystal plasticity computations by two orders of magnitude. Furthermore, mathematical procedures for delineation of property closures that identify the complete set of theoretically feasible combinations of macroscale effective properties has been developed for a broad set of mechanical properties. Subsequently, these constructs were used in microstructure design for identifying an optimal microstructure for selected performance criteria. And finally, hybrid processing recipes that transform a given initial microstructure into a member of the set of optimal microstructures that exhibit superior properties or performance characteristics have been described. Insights and tremendous potential of these novel materials knowledge systems are discussed and demonstrated through specific case-studies. The anisotropic stress-strain response measured in simple compression and simple tension tests in different sample directions on an annealed, strongly textured, AZ31 sheet has been studied. New insights into the mechanical response of this material were obtained by correlating the changes in the measured strain-hardening rates in the different experiments to the corresponding changes in the microstructure evolution are provided. Based on the experimental observations, a hypothesis is postulated for explaining the different morphologies of the extension and contraction twins, and the apparent tension/compression asymmetry exhibited by this alloy. The main elements of the hypothesis are then critically evaluated using finite element simulations of stress fields in various matrix-twin configurations subjected to a range of loading conditions.

Research paper thumbnail of Application of Microstructure Sensitive Design to FCC Polycrystals

Materials Science Forum, 2007

In this paper, we present the first successful design case studies in the application of microstr... more In this paper, we present the first successful design case studies in the application of microstructure sensitive design (MSD) methodology to optimize performance of structural components made from polycrystalline metals with hexagonal close-packed (hcp) crystal lattices. It is demonstrated that the underlying spectral framework of the MSD methodology facilitates an efficient consideration of the complete set of crystallographic textures in the design optimization. In order to accomplish this task a number of important enhancements had to be introduced to the MSD framework. The most significant enhancement is in the mathematical description of the design space, i.e. the texture hull. The advantages of the new approach described in this paper are illustrated with two specific design case studies involving different assumptions of symmetry at the sample scale. In both case studies presented, it is seen that the overall performance is strongly influenced by the crystallographic texture in the sample. Furthermore, the relevant property closures and performance maps accounting for the complete set of textures are also depicted. Published by Elsevier B.V.

Research paper thumbnail of Effect of age hardening on the deformation behavior of an Mg–Y–Nd alloy: In-situ X-ray diffraction and crystal plasticity modeling

Materials Science and Engineering: A, 2015

ABSTRACT The present study investigates the deformation behavior of an extruded Mg–Y–Nd (WE54) al... more ABSTRACT The present study investigates the deformation behavior of an extruded Mg–Y–Nd (WE54) alloy in as-extruded and aged conditions. Via age-hardening at 250 °C for 16 and 500 h or annealing treatments at 400 °C for 24 h, precipitates are formed within the grains or at the grain boundaries. To characterize microstructural changes with the age-hardening conditions, we employ electron-backscattered diffraction, transmission electron microscopy, and optical microscopy. In the as-extruded material, we observed an uncommonly low activity of {10-12}〈10-1-1〉 tension twinning in comparison with other Mg alloys. The tension twinning activity substantially increased after precipitation hardening and the accompanying reduction of alloying element concentration in solid solution. Consistent with the microstructural observations, the increase in twin activity clearly manifests in the compression flow curves. While the as-extruded and 16 h/250 °C samples exhibited a classical decreasing hardening rate throughout straining associated with crystallographic slip, the 500 h/250 °C and the 400 °C annealed sample featured a characteristic increase in the hardening rate associated with twinning. In order to determine the impact of the different heat treatments on the individual slip and twinning modes, in-situ energy-dispersive X-ray synchrotron diffraction experiments during loading and elasto-plastic self-consistent modeling were conducted. We find that plate-shape precipitates on the {10-10}α planes harden 〈a〉 basal slip more than the other slip systems, while the reduced solute concentration in the 500 h 250 °C and 24 h 400 °C samples results in a significant decrease in the critical resolved shear stress for {10-12}〈10-1-1〉 tension twinning.

Research paper thumbnail of Strain rate and temperature effects on the selection of primary and secondary slip and twinning systems in HCP Zr

Acta Materialia, 2015

ABSTRACT We investigate the temperature and rate dependence of slip, twinning, and secondary twin... more ABSTRACT We investigate the temperature and rate dependence of slip, twinning, and secondary twinning in high-purity hexagonal close packed α-Zr over a wide range of temperatures and strain rates (from 76 K to 673 K and 0.001 s−1 to 4500 s−1). To reliably identify the dominant deformation mechanisms for each condition, we employ electron-backscattered diffraction (EBSD), dislocation theory, multi-scale polycrystal constitutive modeling, and a thermally activated dislocation density evolution based hardening law. We demonstrate with direct comparison with measurement that the constitutive model, with a single set of intrinsic material parameters, can predict the underlying texture evolution, primary and secondary slip and twin activity, and twin volume fraction associated with the different loading orientations and applied temperatures and strain rates. We find that the twin is the preferred tension twin, either as a primary or secondary twin depending on the sample orientation, over the broad temperature and strain rate range tested. In contrast, we show that the preferred contraction twin, whether or , is sensitive to temperature but insensitive to strain rate and whether it is a primary or secondary twin. Based on the concomitant changes in the dominant slip mode predicted by the model and revealed by the texture development, we rationalize that the temperature-induced transition in contraction twinning is due to the increased predominance of basal 〈a〉 slip at high temperatures (>673 K). Last, our analysis implies that all twin modes studied are rate insensitive and so the strong influence of strain rate and temperature on twinning is due to the rate-sensitivity of slip.

Research paper thumbnail of A Comparison of Deformation Textures and Mechanical Properties Predicted by Different Crystal Plasticity Codes

Materials Processing and Texture, 2008

The public reporting burden for this collection of information is estimated to average 1 hour per... more The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

Research paper thumbnail of Anisotropic stress-strain response and microstructure evolution of textured α-uranium

Acta Materialia, 2000

The deformation behavior of wrought α-uranium is studied using electron backscattered diffraction... more The deformation behavior of wrought α-uranium is studied using electron backscattered diffraction and crystal plasticity modeling. We report stress–strain response and texture evolution for 12 different cases corresponding to tension and compression tests performed on three different initial textures: straight-rolled, clock-rolled and swaged α-uranium. It is seen that the response of α-uranium is highly anisotropic owing to its low-symmetry orthorhombic crystal structure and limited number of slip/twin systems. For modeling this complex system, we adapt a multiscale dislocation-based hardening law developed earlier for hexagonal metals and implement it within a viscoplastic self-consistent homogenization scheme. This hardening law performs well in capturing the anisotropic strain hardening and the texture evolution in all studied samples. Comparisons of simulations and experiments allow us to infer basic information concerning the various slip and twin mechanisms, their interactions, and their role on strain hardening and texture evolution in α-uranium.

Research paper thumbnail of A strain-rate and temperature dependent constitutive model for BCC metals incorporating non-Schmid effects: Application to tantalum–tungsten alloys

International Journal of Plasticity, 2014

ABSTRACT In this work, we present a multiscale physically based constitutive law for predicting t... more ABSTRACT In this work, we present a multiscale physically based constitutive law for predicting the mechanical response and texture evolution of body-centered cubic (BCC) metals as a function of strain-rate and temperature. In the model, deformation of individual single crystals results not only from the resolved shear stress along the direction of slip (Schmid law) but also from shear stresses resolved along directions orthogonal to the slip direction as well as the three normal stress components (non-Schmid effects). We account for coupled Schmid and non-Schmid effects through the modification of the resolved shear stress for both 1/2〈11¯1〉{110} and 1/2〈111¯〉{112} slip systems and the modification of the slip resistance for 1/2〈111¯〉{112} slip systems. The single crystal model is implemented into a self-consistent homogenization scheme containing a hardening law for crystallographic slip. The hardening law is based on the evolution of dislocation densities that incorporates strain-rate and temperature effects through the Peierls stress, thermally activated recovery, dislocation substructure formation and dislocation interactions. The polycrystal model is calibrated and validated using a set of mechanical and texture data collected on a tantalum-tungsten alloy, Ta-10W, at temperatures ranging from 298 K to 673 K and strain-rates from 10-3 to 2400 s-1. We show the model effectively captures the anisotropic hardening rate and texture evolution for all data using a single set of single-crystal hardening parameters. Comparisons between predictions and measured data allow us to discuss the role of slip on {110}{110} and {112}{112} in determining plasticity and texture evolution in Ta-10W.

Research paper thumbnail of In situ X-ray diffraction and crystal plasticity modeling of the deformation behavior of extruded Mg–Li–(Al) alloys: An uncommon tension–compression asymmetry

Acta Materialia, 2015

ABSTRACT The effects of alloying additions and grain size on the deformation behavior of two extr... more ABSTRACT The effects of alloying additions and grain size on the deformation behavior of two extruded Mg–4 wt.% Li and Mg–4 wt.% Li–1 wt.% Al alloys were studied. To determine the underlying deformation mechanisms, we employed a combination of texture analysis, in situ energy dispersive X-ray synchrotron diffraction and elasto-plastic self-consistent modeling. We show that both alloys exhibit two uncommon features: (1) low tension–compression asymmetry in yield strength and (2) a so-called positive asymmetry in which the compression yield strength is higher than the tension yield strength. Our analyses suggest that this unusual asymmetry arises because the addition of Li hinders the activation of {10-12}〈10-1-1〉 tension twinning. We also show that the increases in the yield stress and hardening rate with the addition of Al is a consequence of increases in the resistances to slip but a decrease in the resistance to {10-12}〈10-1-1〉 twinning.

Research paper thumbnail of Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models

Computer Methods in Applied Mechanics and Engineering, 2014

• Evolution of grain and grain boundary structure during plastic deformation is studied using cry... more • Evolution of grain and grain boundary structure during plastic deformation is studied using crystal plasticity.

Research paper thumbnail of Material-based design of the extrusion of bimetallic tubes

Computational Materials Science, 2014

Research paper thumbnail of Texture evolution and enhanced grain refinement under high-pressure-double-torsion

Materials Science and Engineering: A, 2014

ABSTRACT We present a severe plastic deformation process called high-pressure-double-torsion (HPD... more ABSTRACT We present a severe plastic deformation process called high-pressure-double-torsion (HPDT) for grain size refinement in metallic polycrystals. Like standard high-pressure torsion, HPDT monotonically imposes extreme plastic strains (⪢10) but via rotating both ends of the sample rather than one. Commercial purity Cu was subjected to HPT and HPDT for 1, 2, and 4 turns. The grain structure, hardness, and crystallographic texture were examined by transmission electron microscopy (TEM), Vickers microhardness tests, and X-ray diffraction (XRD) in both processes and compared in the mid-radius and at the edge of disks. We report that HPDT leads to finer grain sizes and higher hardness than HPT for the same number of turns. The measured textures exhibit typical shear components, which continuously strengthened with the plastic strain and also weakened with extreme grain refinement. These measurements also indicate that the texture gradients are lower in HPDT than HPT.

Research paper thumbnail of A new implementation of the spectral crystal plasticity framework in implicit finite elements

Mechanics of Materials, 2015

ABSTRACT We present a new implementation of a computationally efficient crystal plasticity model ... more 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.

Research paper thumbnail of Crystal plasticity simulations using discrete Fourier transforms

Acta Materialia, 2009

In this paper, we explore efficient representation of all of the functions central to crystal pla... more 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.

Research paper thumbnail of Spectral calibration of crystal plasticity models

Acta Materialia, 2006

A new and improved spectral framework are presented to capture efficiently the predictions for th... more 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.

Research paper thumbnail of Elastic–plastic property closures for hexagonal close-packed polycrystalline metals using first-order bounding theories

Acta Materialia, 2007

Property closures delineate the complete set of theoretically feasible combinations of macroscale... more Property closures delineate the complete set of theoretically feasible combinations of macroscale (homogenized) properties in a given material system. A novel spectral framework called microstructure sensitive design (MSD) was recently formulated and demonstrated to be capable of delineating elastic–plastic property closures in a number of composite material systems. In particular, it was successfully applied to cubic polycrystals, where it was assumed that the crystallographic texture had a dominant influence on the macroscale properties of interest. Application of these procedures to hexagonal polycrystals posed significant computational difficulties, because of the need to represent the texture in the hcp polycrystals in a much larger number of dimensions in the Fourier space compared with what was needed for the cubic polycrystals. This paper reports new computational schemes for delineating elastic–plastic closures for hcp polycrystals using the spectral framework of MSD. The primary focus of this paper continues to be on the influence of the crystallographic texture (in the hcp polycrystal) on the components of the macroscale anisotropic elastic stiffness, macroscale anisotropic tensile yield strength, and the macroscale R ratios (ratio of the transverse strains in tensile deformation mode) exhibited by the material.

Research paper thumbnail of Fast computation of first-order elastic–plastic closures for polycrystalline cubic-orthorhombic microstructures

Computational Materials Science, 2007

... the occurrence of the crystallographic orientation g in the sample,(1) where V denotes the to... more ... the occurrence of the crystallographic orientation g in the sample,(1) where V denotes the total sample volume and dV is the sum of all sub-volume elements in the sample that are associated with a lattice orientation that lies within an incremental invariant measure, dg, of the ...

Research paper thumbnail of Grain size and orientation distributions: Application to yielding of α-titanium

Acta Materialia, 2009

A method to incorporate grain size effects into crystal plasticity is presented. The classical Ha... more A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall–Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or variable grain size distributions. These deficiencies can be negated by incorporating both grain size and orientation characteristics into crystal plasticity theory. Augmented homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for rolled high-purity α-titanium are recovered through multi-section orientation imaging microscopy using chord length measurements to quantify grain size. It is illustrated that considerable variation in the grain size distribution occurs with lattice orientation in this material. Yield surface predictions calculated from the augmented and traditional models indicate that grain size distribution as a function of lattice orientation may play a significant role in explaining the large yield strength anisotropy of rolled α-titanium.

Research paper thumbnail of Towards Computationally Tractable Simulations of Metal Forming Processes With Evolving Microstructures

Volume 2: Processing, 2014

Research paper thumbnail of Grain Size and Orientation Distribution Function of High Purityα-Titanium

Materials Processing and Texture, 2008

... Grain Size and Orientation Distribution Function of High Purity α-Titanium ... Strain hardeni... more ... Grain Size and Orientation Distribution Function of High Purity α-Titanium ... Strain hardening regimes and microstructure evolution during large strain compression of high purity titanium. ... Soer, KE Aifantis, and JTM De Hosson, Incipient plasticity during nanoindentation at grain ...

Research paper thumbnail of Application of Microstructure Sensitive Design to FCC Polycrystals

Materials Science Forum, 2007

In this paper, we present the first successful design case studies in the application of microstr... more In this paper, we present the first successful design case studies in the application of microstructure sensitive design (MSD) methodology to optimize performance of structural components made from polycrystalline metals with hexagonal close-packed (hcp) crystal lattices. It is demonstrated that the underlying spectral framework of the MSD methodology facilitates an efficient consideration of the complete set of crystallographic textures in the design optimization. In order to accomplish this task a number of important enhancements had to be introduced to the MSD framework. The most significant enhancement is in the mathematical description of the design space, i.e. the texture hull. The advantages of the new approach described in this paper are illustrated with two specific design case studies involving different assumptions of symmetry at the sample scale. In both case studies presented, it is seen that the overall performance is strongly influenced by the crystallographic texture in the sample. Furthermore, the relevant property closures and performance maps accounting for the complete set of textures are also depicted. Published by Elsevier B.V.

Research paper thumbnail of A new spectral framework for crystal plasticity modeling of cubic and hexagonal polycrystalline metals

Crystal plasticity physics-based constitutive theories are used in understanding and predicting t... more Crystal plasticity physics-based constitutive theories are used in understanding and predicting the evolution of the underlying microstructure and the concomitant anisotropic stress-strain response in polycrystalline metals subjected to finite plastic strains. A new scheme for efficient crystal plasticity computations for both cubic and hexagonal polycrystalline metals subjected to arbitrary deformation modes has been developed in this thesis. This new computational scheme involves building material databases comprised of spectral coefficients. These spectral coefficients are computed using discrete Fourier transforms (DFTs) and allow for compact representation and fast retrieval of crystal plasticity solutions for a crystal of any orientation subjected to any deformation mode. The novel approach is able to speed up the conventional crystal plasticity computations by two orders of magnitude. Furthermore, mathematical procedures for delineation of property closures that identify the complete set of theoretically feasible combinations of macroscale effective properties has been developed for a broad set of mechanical properties. Subsequently, these constructs were used in microstructure design for identifying an optimal microstructure for selected performance criteria. And finally, hybrid processing recipes that transform a given initial microstructure into a member of the set of optimal microstructures that exhibit superior properties or performance characteristics have been described. Insights and tremendous potential of these novel materials knowledge systems are discussed and demonstrated through specific case-studies. The anisotropic stress-strain response measured in simple compression and simple tension tests in different sample directions on an annealed, strongly textured, AZ31 sheet has been studied. New insights into the mechanical response of this material were obtained by correlating the changes in the measured strain-hardening rates in the different experiments to the corresponding changes in the microstructure evolution are provided. Based on the experimental observations, a hypothesis is postulated for explaining the different morphologies of the extension and contraction twins, and the apparent tension/compression asymmetry exhibited by this alloy. The main elements of the hypothesis are then critically evaluated using finite element simulations of stress fields in various matrix-twin configurations subjected to a range of loading conditions.

Research paper thumbnail of Application of Microstructure Sensitive Design to FCC Polycrystals

Materials Science Forum, 2007

In this paper, we present the first successful design case studies in the application of microstr... more In this paper, we present the first successful design case studies in the application of microstructure sensitive design (MSD) methodology to optimize performance of structural components made from polycrystalline metals with hexagonal close-packed (hcp) crystal lattices. It is demonstrated that the underlying spectral framework of the MSD methodology facilitates an efficient consideration of the complete set of crystallographic textures in the design optimization. In order to accomplish this task a number of important enhancements had to be introduced to the MSD framework. The most significant enhancement is in the mathematical description of the design space, i.e. the texture hull. The advantages of the new approach described in this paper are illustrated with two specific design case studies involving different assumptions of symmetry at the sample scale. In both case studies presented, it is seen that the overall performance is strongly influenced by the crystallographic texture in the sample. Furthermore, the relevant property closures and performance maps accounting for the complete set of textures are also depicted. Published by Elsevier B.V.

Research paper thumbnail of Effect of age hardening on the deformation behavior of an Mg–Y–Nd alloy: In-situ X-ray diffraction and crystal plasticity modeling

Materials Science and Engineering: A, 2015

ABSTRACT The present study investigates the deformation behavior of an extruded Mg–Y–Nd (WE54) al... more ABSTRACT The present study investigates the deformation behavior of an extruded Mg–Y–Nd (WE54) alloy in as-extruded and aged conditions. Via age-hardening at 250 °C for 16 and 500 h or annealing treatments at 400 °C for 24 h, precipitates are formed within the grains or at the grain boundaries. To characterize microstructural changes with the age-hardening conditions, we employ electron-backscattered diffraction, transmission electron microscopy, and optical microscopy. In the as-extruded material, we observed an uncommonly low activity of {10-12}〈10-1-1〉 tension twinning in comparison with other Mg alloys. The tension twinning activity substantially increased after precipitation hardening and the accompanying reduction of alloying element concentration in solid solution. Consistent with the microstructural observations, the increase in twin activity clearly manifests in the compression flow curves. While the as-extruded and 16 h/250 °C samples exhibited a classical decreasing hardening rate throughout straining associated with crystallographic slip, the 500 h/250 °C and the 400 °C annealed sample featured a characteristic increase in the hardening rate associated with twinning. In order to determine the impact of the different heat treatments on the individual slip and twinning modes, in-situ energy-dispersive X-ray synchrotron diffraction experiments during loading and elasto-plastic self-consistent modeling were conducted. We find that plate-shape precipitates on the {10-10}α planes harden 〈a〉 basal slip more than the other slip systems, while the reduced solute concentration in the 500 h 250 °C and 24 h 400 °C samples results in a significant decrease in the critical resolved shear stress for {10-12}〈10-1-1〉 tension twinning.

Research paper thumbnail of Strain rate and temperature effects on the selection of primary and secondary slip and twinning systems in HCP Zr

Acta Materialia, 2015

ABSTRACT We investigate the temperature and rate dependence of slip, twinning, and secondary twin... more ABSTRACT We investigate the temperature and rate dependence of slip, twinning, and secondary twinning in high-purity hexagonal close packed α-Zr over a wide range of temperatures and strain rates (from 76 K to 673 K and 0.001 s−1 to 4500 s−1). To reliably identify the dominant deformation mechanisms for each condition, we employ electron-backscattered diffraction (EBSD), dislocation theory, multi-scale polycrystal constitutive modeling, and a thermally activated dislocation density evolution based hardening law. We demonstrate with direct comparison with measurement that the constitutive model, with a single set of intrinsic material parameters, can predict the underlying texture evolution, primary and secondary slip and twin activity, and twin volume fraction associated with the different loading orientations and applied temperatures and strain rates. We find that the twin is the preferred tension twin, either as a primary or secondary twin depending on the sample orientation, over the broad temperature and strain rate range tested. In contrast, we show that the preferred contraction twin, whether or , is sensitive to temperature but insensitive to strain rate and whether it is a primary or secondary twin. Based on the concomitant changes in the dominant slip mode predicted by the model and revealed by the texture development, we rationalize that the temperature-induced transition in contraction twinning is due to the increased predominance of basal 〈a〉 slip at high temperatures (>673 K). Last, our analysis implies that all twin modes studied are rate insensitive and so the strong influence of strain rate and temperature on twinning is due to the rate-sensitivity of slip.

Research paper thumbnail of A Comparison of Deformation Textures and Mechanical Properties Predicted by Different Crystal Plasticity Codes

Materials Processing and Texture, 2008

The public reporting burden for this collection of information is estimated to average 1 hour per... more The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

Research paper thumbnail of Anisotropic stress-strain response and microstructure evolution of textured α-uranium

Acta Materialia, 2000

The deformation behavior of wrought α-uranium is studied using electron backscattered diffraction... more The deformation behavior of wrought α-uranium is studied using electron backscattered diffraction and crystal plasticity modeling. We report stress–strain response and texture evolution for 12 different cases corresponding to tension and compression tests performed on three different initial textures: straight-rolled, clock-rolled and swaged α-uranium. It is seen that the response of α-uranium is highly anisotropic owing to its low-symmetry orthorhombic crystal structure and limited number of slip/twin systems. For modeling this complex system, we adapt a multiscale dislocation-based hardening law developed earlier for hexagonal metals and implement it within a viscoplastic self-consistent homogenization scheme. This hardening law performs well in capturing the anisotropic strain hardening and the texture evolution in all studied samples. Comparisons of simulations and experiments allow us to infer basic information concerning the various slip and twin mechanisms, their interactions, and their role on strain hardening and texture evolution in α-uranium.

Research paper thumbnail of A strain-rate and temperature dependent constitutive model for BCC metals incorporating non-Schmid effects: Application to tantalum–tungsten alloys

International Journal of Plasticity, 2014

ABSTRACT In this work, we present a multiscale physically based constitutive law for predicting t... more ABSTRACT In this work, we present a multiscale physically based constitutive law for predicting the mechanical response and texture evolution of body-centered cubic (BCC) metals as a function of strain-rate and temperature. In the model, deformation of individual single crystals results not only from the resolved shear stress along the direction of slip (Schmid law) but also from shear stresses resolved along directions orthogonal to the slip direction as well as the three normal stress components (non-Schmid effects). We account for coupled Schmid and non-Schmid effects through the modification of the resolved shear stress for both 1/2〈11¯1〉{110} and 1/2〈111¯〉{112} slip systems and the modification of the slip resistance for 1/2〈111¯〉{112} slip systems. The single crystal model is implemented into a self-consistent homogenization scheme containing a hardening law for crystallographic slip. The hardening law is based on the evolution of dislocation densities that incorporates strain-rate and temperature effects through the Peierls stress, thermally activated recovery, dislocation substructure formation and dislocation interactions. The polycrystal model is calibrated and validated using a set of mechanical and texture data collected on a tantalum-tungsten alloy, Ta-10W, at temperatures ranging from 298 K to 673 K and strain-rates from 10-3 to 2400 s-1. We show the model effectively captures the anisotropic hardening rate and texture evolution for all data using a single set of single-crystal hardening parameters. Comparisons between predictions and measured data allow us to discuss the role of slip on {110}{110} and {112}{112} in determining plasticity and texture evolution in Ta-10W.

Research paper thumbnail of In situ X-ray diffraction and crystal plasticity modeling of the deformation behavior of extruded Mg–Li–(Al) alloys: An uncommon tension–compression asymmetry

Acta Materialia, 2015

ABSTRACT The effects of alloying additions and grain size on the deformation behavior of two extr... more ABSTRACT The effects of alloying additions and grain size on the deformation behavior of two extruded Mg–4 wt.% Li and Mg–4 wt.% Li–1 wt.% Al alloys were studied. To determine the underlying deformation mechanisms, we employed a combination of texture analysis, in situ energy dispersive X-ray synchrotron diffraction and elasto-plastic self-consistent modeling. We show that both alloys exhibit two uncommon features: (1) low tension–compression asymmetry in yield strength and (2) a so-called positive asymmetry in which the compression yield strength is higher than the tension yield strength. Our analyses suggest that this unusual asymmetry arises because the addition of Li hinders the activation of {10-12}〈10-1-1〉 tension twinning. We also show that the increases in the yield stress and hardening rate with the addition of Al is a consequence of increases in the resistances to slip but a decrease in the resistance to {10-12}〈10-1-1〉 twinning.

Research paper thumbnail of Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models

Computer Methods in Applied Mechanics and Engineering, 2014

• Evolution of grain and grain boundary structure during plastic deformation is studied using cry... more • Evolution of grain and grain boundary structure during plastic deformation is studied using crystal plasticity.

Research paper thumbnail of Material-based design of the extrusion of bimetallic tubes

Computational Materials Science, 2014

Research paper thumbnail of Texture evolution and enhanced grain refinement under high-pressure-double-torsion

Materials Science and Engineering: A, 2014

ABSTRACT We present a severe plastic deformation process called high-pressure-double-torsion (HPD... more ABSTRACT We present a severe plastic deformation process called high-pressure-double-torsion (HPDT) for grain size refinement in metallic polycrystals. Like standard high-pressure torsion, HPDT monotonically imposes extreme plastic strains (⪢10) but via rotating both ends of the sample rather than one. Commercial purity Cu was subjected to HPT and HPDT for 1, 2, and 4 turns. The grain structure, hardness, and crystallographic texture were examined by transmission electron microscopy (TEM), Vickers microhardness tests, and X-ray diffraction (XRD) in both processes and compared in the mid-radius and at the edge of disks. We report that HPDT leads to finer grain sizes and higher hardness than HPT for the same number of turns. The measured textures exhibit typical shear components, which continuously strengthened with the plastic strain and also weakened with extreme grain refinement. These measurements also indicate that the texture gradients are lower in HPDT than HPT.

Research paper thumbnail of A new implementation of the spectral crystal plasticity framework in implicit finite elements

Mechanics of Materials, 2015

ABSTRACT We present a new implementation of a computationally efficient crystal plasticity model ... more 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.

Research paper thumbnail of Crystal plasticity simulations using discrete Fourier transforms

Acta Materialia, 2009

In this paper, we explore efficient representation of all of the functions central to crystal pla... more 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.

Research paper thumbnail of Spectral calibration of crystal plasticity models

Acta Materialia, 2006

A new and improved spectral framework are presented to capture efficiently the predictions for th... more 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.

Research paper thumbnail of Elastic–plastic property closures for hexagonal close-packed polycrystalline metals using first-order bounding theories

Acta Materialia, 2007

Property closures delineate the complete set of theoretically feasible combinations of macroscale... more Property closures delineate the complete set of theoretically feasible combinations of macroscale (homogenized) properties in a given material system. A novel spectral framework called microstructure sensitive design (MSD) was recently formulated and demonstrated to be capable of delineating elastic–plastic property closures in a number of composite material systems. In particular, it was successfully applied to cubic polycrystals, where it was assumed that the crystallographic texture had a dominant influence on the macroscale properties of interest. Application of these procedures to hexagonal polycrystals posed significant computational difficulties, because of the need to represent the texture in the hcp polycrystals in a much larger number of dimensions in the Fourier space compared with what was needed for the cubic polycrystals. This paper reports new computational schemes for delineating elastic–plastic closures for hcp polycrystals using the spectral framework of MSD. The primary focus of this paper continues to be on the influence of the crystallographic texture (in the hcp polycrystal) on the components of the macroscale anisotropic elastic stiffness, macroscale anisotropic tensile yield strength, and the macroscale R ratios (ratio of the transverse strains in tensile deformation mode) exhibited by the material.

Research paper thumbnail of Fast computation of first-order elastic–plastic closures for polycrystalline cubic-orthorhombic microstructures

Computational Materials Science, 2007

... the occurrence of the crystallographic orientation g in the sample,(1) where V denotes the to... more ... the occurrence of the crystallographic orientation g in the sample,(1) where V denotes the total sample volume and dV is the sum of all sub-volume elements in the sample that are associated with a lattice orientation that lies within an incremental invariant measure, dg, of the ...

Research paper thumbnail of Grain size and orientation distributions: Application to yielding of α-titanium

Acta Materialia, 2009

A method to incorporate grain size effects into crystal plasticity is presented. The classical Ha... more A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall–Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or variable grain size distributions. These deficiencies can be negated by incorporating both grain size and orientation characteristics into crystal plasticity theory. Augmented homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for rolled high-purity α-titanium are recovered through multi-section orientation imaging microscopy using chord length measurements to quantify grain size. It is illustrated that considerable variation in the grain size distribution occurs with lattice orientation in this material. Yield surface predictions calculated from the augmented and traditional models indicate that grain size distribution as a function of lattice orientation may play a significant role in explaining the large yield strength anisotropy of rolled α-titanium.

Research paper thumbnail of Towards Computationally Tractable Simulations of Metal Forming Processes With Evolving Microstructures

Volume 2: Processing, 2014

Research paper thumbnail of Grain Size and Orientation Distribution Function of High Purityα-Titanium

Materials Processing and Texture, 2008

... Grain Size and Orientation Distribution Function of High Purity α-Titanium ... Strain hardeni... more ... Grain Size and Orientation Distribution Function of High Purity α-Titanium ... Strain hardening regimes and microstructure evolution during large strain compression of high purity titanium. ... Soer, KE Aifantis, and JTM De Hosson, Incipient plasticity during nanoindentation at grain ...

Research paper thumbnail of Application of Microstructure Sensitive Design to FCC Polycrystals

Materials Science Forum, 2007

In this paper, we present the first successful design case studies in the application of microstr... more In this paper, we present the first successful design case studies in the application of microstructure sensitive design (MSD) methodology to optimize performance of structural components made from polycrystalline metals with hexagonal close-packed (hcp) crystal lattices. It is demonstrated that the underlying spectral framework of the MSD methodology facilitates an efficient consideration of the complete set of crystallographic textures in the design optimization. In order to accomplish this task a number of important enhancements had to be introduced to the MSD framework. The most significant enhancement is in the mathematical description of the design space, i.e. the texture hull. The advantages of the new approach described in this paper are illustrated with two specific design case studies involving different assumptions of symmetry at the sample scale. In both case studies presented, it is seen that the overall performance is strongly influenced by the crystallographic texture in the sample. Furthermore, the relevant property closures and performance maps accounting for the complete set of textures are also depicted. Published by Elsevier B.V.