Abstract
An advanced, image-based crystal plasticity FE model is developed for predicting discrete twin formation and associated heterogeneous deformation in the single and polycrystalline microstructure of Magnesium. Twin formation is sensitive to the underlying microstructure and is responsible for the premature failure of Mg. The physics of nucleation, propagation, and growth of deformation-twins are considered in the CPFE formulation. The twin nucleation model is based on dissociation of sessile dislocations into stable twin loops, while propagation is assumed by layer-by-layer atoms shearing on twin planes and shuffling to reduce the energy barrier. A non-local FE-based computational framework is developed to implement the twin nucleation and propagation laws, which governs the explicit formation of each individual twin. The simulation matches satisfactorily with the experiments in the stress-strain-response and predicts heterogeneous twin formation with strain localization.
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References
Q. Yu, J. Zhang, Y. Jiang, Fatigue damage development in pure polycrystalline magnesium under cyclic tension compression loading. Mater. Sci. Eng. A 528(2526):7816–7826 (2011)
A. Staroselsky, L. Anand, A constitutive model for hcp materials deforming by slip and twinning: application to magnesium alloy az31b. Int. J. Plast 19, 843–1864 (2003)
S. Graff, W. Brocks, D. Steglich, Yielding of magnesium: from single crystal to polycrystalline aggregates. Int. J. Plast 23, 1957–1978 (2007)
A. Izadbakhsh, K. Inal, R.K. Mishra, M. Niewczas, New crystal plasticity constitutive model for large strain deformation in single crystals of magnesium. Model. Simul. Mater. Sci. Eng. 50, 2185–2202 (2011)
A. Izadbakhsh, K. Inal, R.K. Mishra, Crystal plasticity based finite element modelling of large strain deformation in am30 magnesium alloy. Model. Simul. Mater. Sci. Eng. 20, 035016 (2012)
J. Zhang, S.P. Joshi, Phenomenological crystal plasticity modeling and detailed micromechanical investigations of pure magnesium. J. Mech. Phys. Solids 60, 945–972 (2012)
H. Abdolvand, M.R. Daymond, Multi-scale modeling and experimental study of twin inception and propagation in hexagonal close-packed materials using a crystal plasticity finite element approach-part i: average behavior. J. Mech. Phys. Solids 61, 783–802 (2013)
M. Ardeljan, R.J. McCabe, I.J. Beyerlein, M. Knezevic, Explicit incorporation of deformation twins into crystal plasticity finite element models. Comput. Meth. App. Mech. Eng. 295, 396–413 (2015)
J. Cheng, S. Ghosh, A crystal plasticity fe model for deformation with twin nucleation in magnesium alloys. Int. J. Plast 67, 148–170 (2015)
M. Niewczas, Lattice correspondence during twinning in hexagonal close-packed crystals. Acta Mater. 58, 5848–5857 (2010)
G. Venkataramani, S. Ghosh, M.J. Mills, A size dependent CPFE model for creep and load-shedding in polycrystalline titanium alloys. Acta Mater. 55, 3971–3986 (2007)
A. Ma, F. Roters, D. Raabe, A dislocation density based constitutive model for crystal plasticity fem including geometrically necessary dislocations. Acta Mater. 54, 2169–2179 (2006)
C.J. Bettles, M.A. Gibson, Material rate dependence and localized deformation in crystalline solids. J. Miner. Met. Mater. Soc. 57(5), 46–49 (2005)
K.U. Kainer, Magnesium alloys and their applications (Wiley, Weinheim, 2003)
L.R. Barnett, Twinning and the ductility of magnesium alloys: part i: tension twins. Mater. Sci. Eng. A464, 1–7 (2007)
J. Cheng, S. Ghosh, Crystal plasticity fe modeling of discrete twin evolution in magnesium alloys. J. Mech. Phys. Solids (2017) (submitted)
M. Ghazisaeidi, W.A. Curtin, Analysis of dissociation of <c> and <c+a> dislocations to nucleate \( \left\{ { 10{\bar{\text{1}}\text{2}}} \right\} \) twins in mg. Model. Simul. Mater. Sci. Eng. 21:055007 (2013)
J.P. Hirth, J. Lothe. Theory of Dislocations, 2nd edn. (Wiley-Interscience, 1982)
J. Wang, J.P. Hirth, C.N. Tom, \( \left( {{\bar{\text{1}}}0 1 2} \right) \) twinning nucleation mechanisms in hexagonal-close-packed crystals. Acta Mater. 57:5521–5530 (2009)
A. Serra, R.C. Pond, D.J. Bacon, Computer simulation of the structure and mobility of twinning dislocations in hcp metals. Acta Metll. Mater. 39, 1469 (1991)
S. Keshavarz, S. Ghosh, Multi-scale crystal plasticity fem approach to modeling nickel based superalloys. Acta Mater. 61, 6549–6561 (2013)
Q. Yu, Z. Shan, L. Ju, X. Huang, L. Xiao, J. Sun, E. Ma, Strong crystal size effect on deformation twinning. Nat. Lett. 463, 08692 (2010)
J. Cheng, S. Ghosh, R.K. Mishra, Predicting the deformation anisotropy, tension-compression asymmetry and heterogeneity in mg alloy az31 using cpfe and discrete twin formation model. Acta Mater. (2017) (submitted)
A.S. Khan, A. Pandey, T. Gnaupel-Herold, R.K. Mishra, Mechanical response and texture evolution of az31 alloy at large strains for different strain rates and temperatures. Int. J. Plast 27, 688–706 (2011)
R.K. Mishra, K. Inal, Microstructure Data. Unpublished work (2013)
M.A. Groeber, M.A. Jackson, Dream.3d: a digital representation environment for the analysis of microstructure in 3d. Int. Mater. Manuf. Innov. 3 (2014)
Acknowledgements
This work has been supported by a GOALI research program sponsored by the National Science Foundation, Mechanics and Structure of Materials Program through Grant No. CMMI-1100818 (Program Manager: Dr. Kara Peters). The authors gratefully acknowledge this support. They thank their GOALI partner General Motors R&D for their support of this research. Computing support by the Homewood High Performance Compute Cluster (HHPC) and Maryland Advanced Research Computing Center (MARCC) is gratefully acknowledged.
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Cheng, J., Ghosh, S. (2017). Simulating Discrete Twin Evolution in Magnesium Using a Novel Crystal Plasticity Finite Element Model. In: Solanki, K., Orlov, D., Singh, A., Neelameggham, N. (eds) Magnesium Technology 2017. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-319-52392-7_26
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DOI: https://doi.org/10.1007/978-3-319-52392-7_26
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