Abstract
Mechanical twinning is a form of inelastic deformation in magnesium and other hexagonal close-packed (hcp) metals, which has a significant effect on material behavior. Magnesium’s high strength-to-weight ratio has led to its interest in structural, automotive, and armor applications, requiring a comprehensive understanding of twinning’s effect on material response. Past studies have taken either a microscopic approach, through atomistic simulations, or a macroscopic approach, through simplified pseudo-slip models. However, twins interact across the mesoscale, forming collectively across grains with complex local morphology propagating into bulk behavior. With the goal of describing twinning’s mesoscale behavior, we propose a model where twinning is treated using a phase-field approach, while slip is considered using crystal plasticity, with lattice reorientation, twinning length scale, and twin-slip interactions all accounted. We present GPU accelerated simulations on polycrystalline solids and summarize the insights gained from these studies and the implications on the macroscale behavior of hcp materials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
B. Li, E. Ma, Atomic shuffling dominated mechanism for deformation twinning in magnesium, Physical Review Letters 103 (3) (2009) 1–4. https://doi.org/10.1103/PhysRevLett.103.035503.
A. J. Cao, Y. G. Wei, Formation of fivefold deformation twins in nanocrystalline face-centered-cubic copper based on molecular dynamics simulations, Applied Physics Letters 89 (4) (2006) 2004–2007. https://doi.org/10.1063/1.2243958.
A. Datta, U. V. Waghmare, U. Ramamurty, http://dx.doi.org/10.1016/j.scriptamat.2008.09.018Density functional theory study on stacking faults and twinning in Ni nanofilms, Scripta Materialia 60 (2) (2009) 124–127. https://doi.org/10.1016/j.scriptamat.2008.09.018.
V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee, H. Gleiter, Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation, Nature Materials 1 (1) (2002) 45–48. https://doi.org/10.1038/nmat700.
S. R. Agnew, M. H. Yoo, C. N. Tomé, Application of texture simulation to understanding mechanical behavior of Mg and solid solution alloys containing Li or Y, Acta Materialia 49 (20) (2001) 4277–4289. https://doi.org/10.1016/S1359-6454(01)00297-X.
S. Graff, W. Brocks, D. Steglich, Yielding of magnesium: From single crystal to polycrystalline aggregates, International Journal of Plasticity 23 (12) (2007) 1957–1978. https://doi.org/10.1016/j.ijplas.2007.07.009.
A. Staroselsky, L. Anand, A constitutive model for hcp materials deforming by slip and twinning: Application to magnesium alloy AZ31B, International Journal of Plasticity 19 (10) (2003) 1843–1864 https://doi.org/10.1016/S0749-6419(03)00039-1.
S. R. Kalidindi, Incorporation of Deformation Twinning in Models, International Journal of Plasticity 46 (2) (1998) 267–290.
J. D. Clayton, J. Knap, A phase field model of deformation twinning: Nonlinear theory and numerical simulations, Physica D: Nonlinear Phenomena 240 (9-10) (2011) 841–858. http://dx.doi.org/10.1016/j.physd.2010.12.012https://doi.org/10.1016/j.physd.2010.12.012.
Y. Chang, D. M. Kochmann, A variational constitutive model for slip-twinning interactions in hcp metals: Application to single- and polycrystalline magnesium, International Journal of Plasticity 73 (2015) 39–61. https://doi.org/10.1016/j.ijplas.2015.03.008.
I. J. Beyerlein, A. Hunter, Understanding dislocation mechanics at the mesoscale using phase field dislocation dynamics, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374 (2066). https://doi.org/10.1098/rsta.2015.0166.
C. Liu, P. Shanthraj, M. Diehl, F. Roters, S. Dong, J. Dong, W. Ding, D. Raabe, An integrated crystal plasticity-phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials, International Journal of Plasticity 106 (December 2017) (2018) 203–227. DOIurlhttps://doi.org/10.1016/j.ijplas.2018.03.009.
H. Zhou, K. Bhattacharya, Accelerated computational micromechanics, arXivhttp://arxiv.org/abs/2010.06697arXiv:2010.06697.
I. J. Beyerlein, R. J. McCabe, C. N. Tomé, Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study, Journal of the Mechanics and Physics of Solids 59 (5) (2011) 988–1003. https://doi.org/10.1016/j.jmps.2011.02.007.
M. Ortiz, L. Stainier, The variational formulation of viscoplastic constitutive updates, Computer Methods in Applied Mechanics and Engineering 171 (3-4) (1999) 419–444. https://doi.org/10.1016/S0045-7825(98)00219-9.
C. Carstensen, K. Hackl, A. Mielke, Non-convex potentials and microstructures in finite-strain plasticity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 458 (2018) (2002) 299–317. https://doi.org/10.1098/rspa.2001.0864.
S. Conti, M. Ortiz, Minimum principles for the trajectories of systems governed by rate problems, Journal of the Mechanics and Physics of Solids 56 (5) (2008) 1885–1904. https://doi.org/10.1016/j.jmps.2007.11.006.
H. MOULINEC, P. SUQUET, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, Comptes rendus de l’Académie des sciences. Série II, Mécanique, physique, chimie, astronomie 318 (11) (1994) 1417–1423.
K. Bhattacharya, P. M. Suquet, A model problem concerning recoverable strains of shape-memory polycrystals, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461 (2061) (2005) 2797–2816. https://doi.org/10.1098/rspa.2005.1493.
R. A. Lebensohn, A. Needleman, Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms, Journal of the Mechanics and Physics of Solids 97 (2016) 333–351. https://doi.org/10.1016/j.jmps.2016.03.023.
S. Berbenni, V. Taupin, R. A. Lebensohn, A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals, Journal of the Mechanics and Physics of Solids 135 (2020) 1–23. https://doi.org/10.1016/j.jmps.2019.103808.
J. C. Michel, H. Moulinec, P. Suquet, A computational method based on augmented lagrangians and fast fourier transforms for composites with high contrast, CMES - Computer Modeling in Engineering and Sciences 1 (2) (2000) 79–88. https://doi.org/10.3970/cmes.2000.001.239.
E. W. Kelley, W. F. Hosford, Plane-Strain Compression of Magnesium and Magnesium Alloy Crystals, Transactions of the Metallurgical Society of AIME (1969) 9.
Y. Chang, J. T. Lloyd, R. Becker, D. M. Kochmann, Modeling microstructure evolution in magnesium: Comparison of detailed and reduced-order kinematic models, Mechanics of Materials 108 (2017) 40–57. https://doi.org/10.1016/j.mechmat.2017.02.007.
J. Wang, J. P. Hirth, C. N. Tomé, -1 0 1 2) twinning nucleation mechanisms in hexagonal-close-packed crystals, Acta Materialia (18) 5521–5530. https://doi.org/10.1016/j.actamat.2009.07.047.
V. I. Levitas, V. A. Levin, K. M. Zingerman, E. I. Freiman, Displacive phase transitions at large strains: Phase-field theory and simulations, Physical Review Letters 103 (2) (2009) 1–4. https://doi.org/10.1103/PhysRevLett.103.025702.
M. L. Kronberg, A structural mechanism for the twinning process on [1012] in hexagonal close packed metals, Acta Metallurgica 16 (1) (1968) 29–34. https://doi.org/10.1016/0001-6160(68)90068-0.
J. Zhang, S. P. Joshi, Phenomenological crystal plasticity modeling and detailed micromechanical investigations of pure magnesium, Journal of the Mechanics and Physics of Solids 60 (5) (2012) 945–972. https://doi.org/10.1016/j.jmps.2012.01.005.
A. D. Tutcuoglu, A. Vidyasagar, K. Bhattacharya, D. M. Kochmann, Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals, Journal of the Mechanics and Physics of Solids 122 (2019) 590–612. https://doi.org/10.1016/j.jmps.2018.09.032.
Acknowledgements
We gratefully acknowledge discussions with Hao Zhou on the development of the numerical method. The research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Minerals, Metals & Materials Society
About this paper
Cite this paper
Ocegueda, E., Bhattacharya, K. (2022). Phase-Field Modeling of Deformation Twinning and Dislocation Slip Interaction in Polycrystalline Solids. In: Maier, P., Barela, S., Miller, V.M., Neelameggham, N.R. (eds) Magnesium Technology 2022. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-030-92533-8_51
Download citation
DOI: https://doi.org/10.1007/978-3-030-92533-8_51
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-92532-1
Online ISBN: 978-3-030-92533-8
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)