New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

Zecevic, Miroslav; Lebensohn, Ricardo A.; Capolungo, Laurent

doi:10.1016/j.mechmat.2021.104208

Title: New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

Journal Article · 03 January 2022 · Mechanics of Materials

DOI: https://doi.org/10.1016/j.mechmat.2021.104208 · OSTI ID:1844163

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

This paper presents a new robust large-strain (LS) elasto-viscoplastic (EVP) formulation based on Fast Fourier Transforms (FFTs) for the prediction of the micro-mechanical response and microstructure evolution of polycrystalline and multiphase materials, with emphasis on the effect of strong crystallographic and/or morphologic anisotropy on localization of plastic deformation. In this work, the novel LS-EVPFFT formulation allows treatment of complex initial geometries and large deformations considering three grids of material points: a regular grid in the reference configuration, where FFTs can be performed; an irregular grid in the initial configuration, created by applying a stress-free displacement field to the reference regular grid; and an irregular grid in the current configuration, undergoing large strains and rotations as the material is loaded. Further numerical stability of the new formulation also required the use of a novel expression for the discrete modified Green’s operator, which reduces spurious field oscillations. After presenting and validating the new formulation by comparison with preexisting implementations and analytical solutions, LS-EVPFFT is applied to the prediction of slip and kink bands formation in polycrystalline columnar ice, and kink bands in single crystal zinc wires, showing good agreement with classic experiments. Finally, the model is used to study kink band formation during compression of Cu–Nb nano-metallic laminates (NMLs), in which accurate treatment of the complex geometry associated with the tortuosity of interfaces and large deformations become critical, showing consistency with corresponding micropillar experiments.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1844163

Report Number(s):: LA-UR-21-29080

Journal Information:: Mechanics of Materials, Journal Name: Mechanics of Materials Vol. 166; ISSN 0167-6636

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (54)

Enhanced Plasticity via Kinking in Cubic Metallic Nanolaminates: Enhanced Plasticity via Kinking in Cubic Metallic Nanolaminates Nizolek, Thomas; Mara, Nathan A.; Beyerlein, Irene J. Advanced Engineering Materials, Vol. 17, Issue 6 https://doi.org/10.1002/adem.201400324	journal	October 2014
Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis Hughes, Thomas J. R.; Winget, James International Journal for Numerical Methods in Engineering, Vol. 15, Issue 12 https://doi.org/10.1002/nme.1620151210	journal	December 1980
A computational scheme for linear and non‐linear composites with arbitrary phase contrast Michel, J. C.; Moulinec, H.; Suquet, P. International Journal for Numerical Methods in Engineering, Vol. 52, Issue 12 https://doi.org/10.1002/nme.275	journal	September 2001
Computational homogenization of elasticity on a staggered grid: COMPUTATIONAL HOMOGENIZATION OF ELASTICITY ON A STAGGERED GRID Schneider, Matti; Ospald, Felix; Kabel, Matthias International Journal for Numerical Methods in Engineering, Vol. 105, Issue 9 https://doi.org/10.1002/nme.5008	journal	October 2015
FFT-based homogenization for microstructures discretized by linear hexahedral elements: FFT-BASED HOMOGENIZATION USING LINEAR HEXAHEDRAL ELEMENTS Schneider, Matti; Merkert, Dennis; Kabel, Matthias International Journal for Numerical Methods in Engineering, Vol. 109, Issue 10 https://doi.org/10.1002/nme.5336	journal	August 2016
Numerical modelling of bifurcation and localisation in cohesive-frictional materials de Borst, René pure and applied geophysics, Vol. 137, Issue 4 https://doi.org/10.1007/BF00879040	journal	December 1991
Strain-rate sensitivity of zinc sheet Wagoner, R. H. Metallurgical and Materials Transactions A, Vol. 15, Issue 6 https://doi.org/10.1007/BF02644721	journal	June 1984
Processing and Deformation Behavior of Bulk Cu–Nb Nanolaminates Nizolek, T.; Mara, N. A.; Beyerlein, I. J. Metallography, Microstructure, and Analysis, Vol. 3, Issue 6 https://doi.org/10.1007/s13632-014-0172-2	journal	November 2014
The AFRL Additive Manufacturing Modeling Challenge: Predicting Micromechanical Fields in AM IN625 Using an FFT-Based Method with Direct Input from a 3D Microstructural Image Cocke, Carter K.; Rollett, Anthony D.; Lebensohn, Ricardo A. Integrating Materials and Manufacturing Innovation, Vol. 10, Issue 2 https://doi.org/10.1007/s40192-021-00211-w	journal	May 2021
Yield surfaces for textured polycrystals—I. Crystallographic approach Lequeu, Ph.; Gilormini, P.; Montheillet, F. Acta Metallurgica, Vol. 35, Issue 2 https://doi.org/10.1016/0001-6160(87)90250-1	journal	February 1987
The elastic constants of zinc between 4.2° and 670°K Alers, G. A.; Neighbours, J. R. Journal of Physics and Chemistry of Solids, Vol. 7, Issue 1 https://doi.org/10.1016/0022-3697(58)90180-X	journal	October 1958
Strain localization in ductile single crystals Asaro, R. J.; Rice, J. R. Journal of the Mechanics and Physics of Solids, Vol. 25, Issue 5 https://doi.org/10.1016/0022-5096(77)90001-1	journal	October 1977
Modelling of texture evolution for materials of hexagonal symmetry—I. Application to zinc alloys Philippe, M. J.; Wagner, F.; Mellab, F. E. Acta Metallurgica et Materialia, Vol. 42, Issue 1 https://doi.org/10.1016/0956-7151(94)90066-3	journal	January 1994
Kink band propagation and broadening in ductile matrix fiber composites: Experiments and analysis Moran, P. M.; Shih, C. F. International Journal of Solids and Structures, Vol. 35, Issue 15 https://doi.org/10.1016/S0020-7683(97)00138-8	journal	May 1998
A numerical method for computing the overall response of nonlinear composites with complex microstructure Moulinec, H.; Suquet, P. Computer Methods in Applied Mechanics and Engineering, Vol. 157, Issue 1-2 https://doi.org/10.1016/S0045-7825(97)00218-1	journal	April 1998
Finite deformation plasticity based on the additive split of the rate of deformation and hyperelasticity Fish, Jacob; Shek, Kamlun Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 1-2 https://doi.org/10.1016/S0045-7825(99)00415-6	journal	October 2000
N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform A. Lebensohn, R. Acta Materialia, Vol. 49, Issue 14 https://doi.org/10.1016/S1359-6454(01)00172-0	journal	August 2001
Modeling slip, kink and shear banding in classical and generalized single crystal plasticity Forest, S. Acta Materialia, Vol. 46, Issue 9 https://doi.org/10.1016/S1359-6454(98)00012-3	journal	May 1998
Length-scale-dependent deformation mechanisms in incoherent metallic multilayered composites Misra, A.; Hirth, J. P.; Hoagland, R. G. Acta Materialia, Vol. 53, Issue 18 https://doi.org/10.1016/j.actamat.2005.06.025	journal	October 2005
Modeling texture, twinning and hardening evolution during deformation of hexagonal materials Proust, G.; Tomé, C. N.; Kaschner, G. C. Acta Materialia, Vol. 55, Issue 6 https://doi.org/10.1016/j.actamat.2006.11.017	journal	April 2007
Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper Lebensohn, Ricardo A.; Brenner, Renald; Castelnau, Olivier Acta Materialia, Vol. 56, Issue 15 https://doi.org/10.1016/j.actamat.2008.04.016	journal	September 2008
Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals Lebensohn, R. A.; Montagnat, M.; Mansuy, P. Acta Materialia, Vol. 57, Issue 5 https://doi.org/10.1016/j.actamat.2008.10.057	journal	March 2009
Bulk texture evolution of Cu–Nb nanolamellar composites during accumulative roll bonding Carpenter, J. S.; Vogel, S. C.; LeDonne, J. E. Acta Materialia, Vol. 60, Issue 4 https://doi.org/10.1016/j.actamat.2011.11.045	journal	February 2012
Modeling void growth in polycrystalline materials Lebensohn, Ricardo A.; Escobedo, Juan P.; Cerreta, Ellen K. Acta Materialia, Vol. 61, Issue 18 https://doi.org/10.1016/j.actamat.2013.08.004	journal	October 2013
Strain fields induced by kink band propagation in Cu-Nb nanolaminate composites Nizolek, T. J.; Begley, M. R.; McCabe, R. J. Acta Materialia, Vol. 133 https://doi.org/10.1016/j.actamat.2017.04.050	journal	July 2017
Validation of micro-mechanical FFT-based simulations using High Energy Diffraction Microscopy on Ti-7Al Tari, Vahid; Lebensohn, Ricardo A.; Pokharel, Reeju Acta Materialia, Vol. 154 https://doi.org/10.1016/j.actamat.2018.05.036	journal	August 2018
Intragranular localization induced by softening crystal plasticity: Analysis of slip and kink bands localization modes from high resolution FFT-simulations results Marano, Aldo; Gélébart, Lionel; Forest, Samuel Acta Materialia, Vol. 175 https://doi.org/10.1016/j.actamat.2019.06.010	journal	August 2019
Use of composite voxels in FFT-based homogenization Kabel, Matthias; Merkert, Dennis; Schneider, Matti Computer Methods in Applied Mechanics and Engineering, Vol. 294 https://doi.org/10.1016/j.cma.2015.06.003	journal	September 2015
A new visco-plastic self-consistent formulation implicit in dislocation-based hardening within implicit finite elements: Application to high strain rate and impact deformation of tantalum Zecevic, Miroslav; Knezevic, Marko Computer Methods in Applied Mechanics and Engineering, Vol. 341 https://doi.org/10.1016/j.cma.2018.07.027	journal	November 2018
Validation of a numerical method based on Fast Fourier Transforms for heterogeneous thermoelastic materials by comparison with analytical solutions Anglin, B. S.; Lebensohn, R. A.; Rollett, A. D. Computational Materials Science, Vol. 87 https://doi.org/10.1016/j.commatsci.2014.02.027	journal	May 2014
DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale Roters, F.; Diehl, M.; Shanthraj, P. Computational Materials Science, Vol. 158 https://doi.org/10.1016/j.commatsci.2018.04.030	journal	February 2019
Spectral methods for full-field micromechanical modelling of polycrystalline materials Lebensohn, Ricardo A.; Rollett, Anthony D. Computational Materials Science, Vol. 173 https://doi.org/10.1016/j.commatsci.2019.109336	journal	February 2020
Fourier-based schemes for computing the mechanical response of composites with accurate local fields Willot, François Comptes Rendus Mécanique, Vol. 343, Issue 3 https://doi.org/10.1016/j.crme.2014.12.005	journal	March 2015
DBFFT: A displacement based FFT approach for non-linear homogenization of the mechanical behavior Lucarini, S.; Segurado, J. International Journal of Engineering Science, Vol. 144 https://doi.org/10.1016/j.ijengsci.2019.103131	journal	November 2019
An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials Lebensohn, Ricardo A.; Kanjarla, Anand K.; Eisenlohr, Philip International Journal of Plasticity, Vol. 32-33 https://doi.org/10.1016/j.ijplas.2011.12.005	journal	May 2012
A spectral method solution to crystal elasto-viscoplasticity at finite strains Eisenlohr, P.; Diehl, M.; Lebensohn, R. A. International Journal of Plasticity, Vol. 46 https://doi.org/10.1016/j.ijplas.2012.09.012	journal	July 2013
Modeling the texture evolution of Cu/Nb layered composites during rolling Hansen, B. L.; Carpenter, J. S.; Sintay, S. D. International Journal of Plasticity, Vol. 49 https://doi.org/10.1016/j.ijplas.2013.03.001	journal	October 2013
Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials Shanthraj, P.; Eisenlohr, P.; Diehl, M. International Journal of Plasticity, Vol. 66 https://doi.org/10.1016/j.ijplas.2014.02.006	journal	March 2015
A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics Berbenni, Stéphane; Taupin, Vincent; Djaka, Komlan Sénam International Journal of Solids and Structures, Vol. 51, Issue 23-24 https://doi.org/10.1016/j.ijsolstr.2014.08.009	journal	November 2014
Spectral implementation of an adaptive moving mesh method for phase-field equations Feng, W. M.; Yu, P.; Hu, S. Y. Journal of Computational Physics, Vol. 220, Issue 1 https://doi.org/10.1016/j.jcp.2006.07.013	journal	December 2006
Filtering material properties to improve FFT-based methods for numerical homogenization Gélébart, Lionel; Ouaki, Franck Journal of Computational Physics, Vol. 294 https://doi.org/10.1016/j.jcp.2015.03.048	journal	August 2015
Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms Lebensohn, Ricardo A.; Needleman, Alan Journal of the Mechanics and Physics of Solids, Vol. 97 https://doi.org/10.1016/j.jmps.2016.03.023	journal	December 2016
Predicting the 3D fatigue crack growth rate of small cracks using multimodal data via Bayesian networks: In-situ experiments and crystal plasticity simulations Rovinelli, Andrea; Sangid, Michael D.; Proudhon, Henry Journal of the Mechanics and Physics of Solids, Vol. 115 https://doi.org/10.1016/j.jmps.2018.03.007	journal	June 2018
A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals Berbenni, Stéphane; Taupin, Vincent; Lebensohn, Ricardo A. Journal of the Mechanics and Physics of Solids, Vol. 135 https://doi.org/10.1016/j.jmps.2019.103808	journal	February 2020
Kink band and shear band localization in anisotropic perfectly plastic solids Nizolek, Thomas J.; Pollock, Tresa M.; McMeeking, Robert M. Journal of the Mechanics and Physics of Solids, Vol. 146 https://doi.org/10.1016/j.jmps.2020.104183	journal	January 2021
Elastic Constants of Artificial and Natural Ice Samples by Brillouin Spectroscopy Gammon, P. H.; Kiefte, H.; Clouter, M. J. Journal of Glaciology, Vol. 29, Issue 103 https://doi.org/10.1017/S0022143000030355	journal	January 1983
Rate-controlling processes in the creep of polycrystalline ice Duval, P.; Ashby, M. F.; Anderman, I. The Journal of Physical Chemistry, Vol. 87, Issue 21 https://doi.org/10.1021/j100244a014	journal	October 1983
A type of Plastic Deformation new in Metals Orowan, E. Nature, Vol. 149, Issue 3788 https://doi.org/10.1038/149643a0	journal	June 1942
Tensile behavior and flow stress anisotropy of accumulative roll bonded Cu-Nb nanolaminates Nizolek, Thomas; Beyerlein, Irene J.; Mara, Nathan A. Applied Physics Letters, Vol. 108, Issue 5 https://doi.org/10.1063/1.4941043	journal	February 2016
Strength and plasticity of nanolaminated materials Wang, Jian; Zhou, Qing; Shao, Shuai Materials Research Letters, Vol. 5, Issue 1 https://doi.org/10.1080/21663831.2016.1225321	journal	July 2016
Variational Principles for Scattering Processes. I Lippmann, B. A.; Schwinger, Julian Physical Review, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRev.79.469	journal	August 1950
A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion Jin, Xiaoqing; Keer, Leon M.; Wang, Qian Journal of Applied Mechanics, Vol. 78, Issue 3 https://doi.org/10.1115/1.4003238	journal	February 2011
Polycrystal Plasticity: Comparison Between Grain - Scale Observations of Deformation and Simulations Pokharel, Reeju; Lind, Jonathan; Kanjarla, Anand K. Annual Review of Condensed Matter Physics, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031113-133846	journal	March 2014
Theory of disclinations: IV. Straight disclinations deWit, Roland Journal of Research of the National Bureau of Standards Section A: Physics and Chemistry, Vol. 77A, Issue 5 https://doi.org/10.6028/jres.077A.036	journal	September 1973

Similar Records

Generalized grain boundary constitutive description implemented in a strain-gradient large-strain FFT-based formulation: Application to nano-metallic laminates

Journal Article · 2024 · Journal of the Mechanics and Physics of Solids · OSTI ID:2446817

Zecevic, Miroslav; Lebensohn, Ricardo A.; Capolungo, Laurent

Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates

Journal Article · 2022 · Journal of the Mechanics and Physics of Solids · OSTI ID:1908481

Zecevic, Miroslav; Lebensohn, Ricardo A.; Capolungo, Laurent

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Journal Article · 2023 · International Journal of Plasticity · OSTI ID:1922795

Cocke, Carter K.; Mirmohammad, H.; Zecevic, Miroslav; +4 more

Related Subjects

36 MATERIALS SCIENCE
Anisotropy
FFT-Based methods
Kink bands
Nano-metallic laminates
Polycrystalline materials
Strain localization

Title: New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

Citation Formats

References (54)

Similar Records

Related Subjects