Abstract
Historically, the ability of crystal plasticity to incorporate the Schmid’s law at each integration point has been a powerful tool to simulate and predict slip-induced localization at the single and polycrystal levels. Unfortunately, this remarkable capability has not been replicated for materials where twinning becomes a noticeable deformation mechanism. The challenge resides mainly in the biased regional lattice transformation associated with twin formation in defiance of its obedience to threshold stress. Inspired by results from micromechanics, digital image correlation, and molecular dynamics, we developed an explicit twinning nucleation criterion based on hydrostatic stress gradient and volume fraction of twin inside a grain. Characteristic twin spacing parameter is used as a function of twin height to determine site-specific nucleation points in the case of multiple twins. This approach offered a good reproduction of the microstructure evolution and autocatalysis phenomenon as affected by twinning in a tricrystal system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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 (2003) 1843–1864.
H. El Kadiri, A. Oppedal, A crystal plasticity theory for latent hardening by glide twinning through dislocation transmutation and twin accommodation effects, Journal of the Mechanics and Physics of Solids 58 (2010) 613–624.
H. El Kadiri, J. Kapil, A. Oppedal, L. Hector Jr, S. R. Agnew, M. Cherkaoui, S. Vogel, The effect of twin–twin interactions on the nucleation and propagation of {1 0 1 \( \overline{2} \) } twinning in magnesium, Acta Materialia 61 (2013) 3549–3563 .
Q. Yu, J. Wang, Y. Jiang, R. J. McCabe, N. Li, C. N. Tomé, Twin–twin interactions in magnesium, acta materialia 77 (2014) 28–42.
L. Jiang, J. J. Jonas, A. A. Luo, A. K. Sachdev, S. Godet, Influence of {1 0 \( \overline{1} \) 2} extension twinning on the flow behavior of az31 mg alloy, Materials Science and Engineering: A 445 (2007) 302–309 .
B. M. Morrow, R. J. McCabe, E. K. Cerreta, C. N. Tomé, Observations of the atomic structure of tensile and compressive twin boundaries and twin–twin interactions in zirconium, Metallurgical and Materials Transactions A 45 (2014) 5891–5897.
K. D. Molodov, T. Al-Samman, D. A. Molodov, Profuse slip transmission across twin boundaries in magnesium, Acta Materialia 124 (2017) 397–409.
F. Wang, C. D. Barrett, R. J. McCabe, H. El Kadiri, L. Capolungo, S. R. Agnew, Dislocation induced twin growth and formation of basal stacking faults in {101-2} twins in pure mg, Acta Materialia 165 (2019) 471–485 .
D. W. Brown, A. Jain, S. R. Agnew, B. Clausen, Twinning and detwinning during cyclic deformation of mg alloy az31b, in: Materials science forum, volume 539, Trans Tech Publ, 2007, pp. 3407–3413.
B. M. Morrow, R. J. McCabe, E. K. Cerreta, C. N. Tomé, In-situ tem observation of twinning and detwinning during cyclic loading in mg, metallurgical and materials Transactions a 45 (2014) 36–40.
J. Wang, L. Liu, C. Tomé, S. Mao, S. Gong, Twinning and de-twinning via glide and climb of twinning dislocations along serrated coherent twin boundaries in hexagonal-close-packed metals, Materials Research Letters 1 (2013) 81–88.
J. Gilman, Mechanism of ortho kink-band formation in compressed zinc monocrystals, JOM 6 (1954) 621–629.
H. Rosenbaum, Non-basal slip and twin accommodation in zinc crystals, Acta Metallurgica 9 (1961) 742–748.
A. Fernández, A. Jérusalem, I. Gutiérrez-Urrutia, M. Pérez-Prado, Three-dimensional investigation of grain boundary–twin interactions in a mg az31 alloy by electron backscatter diffraction and continuum modeling, Acta Materialia 61 (2013) 7679–7692.
K. Hantzsche, J. Bohlen, J. Wendt, K. Kainer, S. Yi, D. Letzig, Effect of rare earth additions on microstructure and texture development of magnesium alloy sheets, Scripta Materialia 63 (2010) 725–730.
X. Huang, K. Suzuki, Y. Chino, Static recrystallization behavior of hot-rolled mg-zn-ce magnesium alloy sheet, Journal of Alloys and Compounds 724 (2017) 981–990.
H. El Kadiri, C. D. Barrett, J. Wang, C. N. Tomé, Why are {1 0 1 \( \overline{2} \)} twins profuse in magnesium?, Acta Materialia 85 (2015) 354–361 .
L. Zhang, Y. Han, Twins formation and their role in nanostructuring of zirconium, Materials Science and Engineering: A 523 (2009) 130–133.
A. Oppedal, H. El Kadiri, C. Tomé, G. Kaschner, S. C. Vogel, J. Baird, M. Horstemeyer, Effect of dislocation transmutation on modeling hardening mechanisms by twinning in magnesium, International Journal of Plasticity 30 (2012) 41–61.
P. Wu, X. Guo, H. Qiao, D. Lloyd, A constitutive model of twin nucleation, propagation and growth in magnesium crystals, Materials Science and Engineering: A 625 (2015) 140–145.
M. A. Kumar, A. Kanjarla, S. Niezgoda, R. Lebensohn, C. Tomé, Numerical study of the stress state of a deformation twin in magnesium, Acta Materialia 84 (2015) 349–358.
M. A. Kumar, I. J. Beyerlein, C. N. Tomé, Effect of local stress fields on twin characteristics in hcp metals, Acta Materialia 116 (2016) 143–154.
H. Abdolvand, M. Majkut, J. Oddershede, J. P. Wright, M. R. Daymond, Study of 3-d stress development in parent and twin pairs of a hexagonal close-packed polycrystal: Part ii–crystal plasticity finite element modeling, Acta Materialia 93 (2015) 235–245.
J. Cheng, S. Ghosh, A crystal plasticity fe model for deformation with twin nucleation in magnesium alloys, International Journal of Plasticity 67 (2015) 148–170.
J. Cheng, S. Ghosh, Crystal plasticity finite element modeling of discrete twin evolution in polycrystalline magnesium, Journal of the Mechanics and Physics of Solids 99 (2017) 512–538.
J. Cheng, J. Shen, R. K. Mishra, S. Ghosh, Discrete twin evolution in mg alloys using a novel crystal plasticity finite element model, Acta Materialia 149 (2018) 142–153.
M. A. Kumar, I. J. Beyerlein, R. J. McCabe, C. N. Tome, Grain neighbour effects on twin transmission in hexagonal close-packed materials, Nature communications 7 (2016) 13826.
L. Jiang, M. A. Kumar, I. J. Beyerlein, X. Wang, D. Zhang, C. Wu, C. Cooper, T. J. Rupert, S. Mahajan, E. J. Lavernia, et al., Twin formation from a twin boundary in mg during in-situ nanomechanical testing, Materials Science and Engineering: A 759 (2019) 142–153.
L. Capolungo, P. Marshall, R. McCabe, I. Beyerlein, C. Tomé, Nucleation and growth of twins in Zr: a statistical study, Acta Materialia 57 (2009) 6047–6056.
E. El-Danaf, S. R. Kalidindi, R. D. Doherty, Influence of grain size and stacking-fault energy on deformation twinning in fcc metals, Metallurgical and Materials Transactions A 30 (1999) 1223–1233.
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 (2018) 203–227.
H. El Kadiri, C. D. Barrett, M. A. Tschopp, The candidacy of shuffle and shear during compound twinning in hexagonal close-packed structures, Acta Materialia 61 (2013) 7646–7659.
W. D. Russell, N. R. Bratton, R. D. Moser, Z. B. McClelland, C. D. Barrett, A. L. Oppedal, W. R. Whittington, H. Rhee, Y. Paudel, B. Paliwal, H. El Kadiri, In-situ characterization of the effect of twin-microstructure interactions on tensile-{1 0 \( \overline{1} \) 2} and contraction-{1 0 \( \overline{1} \) 1} nucleation, growth and damage in magnesium, (submitted) (2019).
G. Proust, C. N. Tomé, A. Jain, S. R. Agnew, Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy az31, International Journal of Plasticity 25 (2009) 861–880.
C. Barrett, F. Wang, S. Agnew, H. El Kadiri, Transmutation of basal dislocations by {1 0 \( \overline{1} \) 2} twinning in magnesium, in: Magnesium Technology 2017, Springer, 2017, pp. 147–152.
F. Wang, K. Hazeli, K. Molodov, C. Barrett, T. Al-Samman, D. Molodov, A. Kontsos, K. Ramesh, H. El Kadiri, S. Agnew, Characteristic dislocation substructure in 101 2 twins in hexagonal metals, Scripta Materialia 143 (2018) 81–85.
F. Wang, S. R. Agnew, Dislocation transmutation by tension twinning in magnesium alloy az31, International Journal of Plasticity 81 (2016) 63–86.
Y. Paudel, C. D. Barrett, M. A. Tschopp, K. Inal, H. El Kadiri, Beyond initial twin nucleation in hcp metals: micromechanical formulation for determining twin spacing during deformation, Acta Materialia 133 (2017) 134–146.
J. Baird, B. Li, S. Y. Parast, S. Horstemeyer, L. Hector Jr, P. Wang, M. Horstemeyer, Localized twin bands in sheet bending of a magnesium alloy, Scripta Materialia 67 (2012) 471–474.
Y. Paudel, J. Indeck, K. Hazeli, M. W. Priddy, K. Inal, H. Rhee, C. D. Barrett, W. R. Whittington, K. R. Limmer, H. El Kadiri, Characterization and modeling of {1 0 \( \overline{1} \) 2} twin banding in magnesium, Acta Materialia (under review) (2019).
M. Mamivand, M. A. Zaeem, H. El Kadiri, Shape memory effect and pseudoelasticity behavior in tetragonal zirconia polycrystals: A phase field study, International Journal of Plasticity 60 (2014) 71–86.
F. Lin, M. Marteleur, J. Alkorta, P. J. Jacques, L. Delannay, Local stress field induced by twinning in a metastable β titanium alloy, in: IOP Conference Series: Materials Science and Engineering, volume 219, IOP Publishing, 2017, p. 012031 .
R. A. Lebensohn, A. K. Kanjarla, P. Eisenlohr, An elasto-viscoplastic formulation based on fast fourier transforms for the prediction of micromechanical fields in polycrystalline materials, International Journal of Plasticity 32 (2012) 59–69.
H. Qin, J. J. Jonas, Variant selection during secondary and tertiary twinning in pure titanium, Acta Materialia 75 (2014) 198–211.
Acknowledgements
Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-15-2-0025. 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 US Government. The US 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
© 2020 The Minerals, Metals & Materials Society
About this paper
Cite this paper
Paudel, Y., Barrett, C.D., El Kadiri, H. (2020). Full-Field Crystal Plasticity Modeling of \( \mathbf{\{ 1\,0\,\overline{1}\, 2\}} \) Twin Nucleation. In: Jordon, J., Miller, V., Joshi, V., Neelameggham, N. (eds) Magnesium Technology 2020. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-030-36647-6_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-36647-6_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36646-9
Online ISBN: 978-3-030-36647-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)