Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-28T17:09:27.349Z Has data issue: false hasContentIssue false

Local microstructure and micromechanical stress evolution during deformation twinning in hexagonal polycrystals

Published online by Cambridge University Press:  07 February 2020

Mariyappan Arul Kumar*
Affiliation:
Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
Irene J. Beyerlein
Affiliation:
Department of Mechanical Engineering, Materials Department, University of California at Santa Barbara, Santa Barbara, California 93106, USA
*
a)Address all correspondence to this author. e-mail: marulkr@gmail.com, marulkr@lanl.gov
Get access

Abstract

Deformation twinning is a prevalent plastic deformation mode in hexagonal close-packed (HCP) materials, such as magnesium, titanium, and zirconium, and their alloys. Experimental observations indicate that these twins occur heterogeneously across the polycrystalline microstructure during deformation. Morphological and crystallographic distribution of twins in a deformed microstructure, or the so-called twinning microstructure, significantly controls material deformation behavior, ductility, formability, and failure response. Understanding the development of the twinning microstructure at the grain scale can benefit design efforts to optimize microstructures of HCP materials for specific high-performance structural applications. This article reviews recent research efforts that aim to relate the polycrystalline microstructure with the development of its twinning microstructure through knowledge of local stress fields, specifically local stresses produced by twins and at twin/grain–boundary intersections on the formation and thickening of twins, twin transmission across grain boundaries, twin–twin junction formation, and secondary twinning.

Type
REVIEW
Copyright
Copyright © Materials Research Society 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This section of Journal of Materials Research is reserved for papers that are reviews of literature in a given area.

References

Kim, N.J.: Critical assessment 6: Magnesium sheet alloys: Viable alternatives to steels? Mater. Sci. Technol. 30, 1925 (2014).CrossRefGoogle Scholar
Kulekci, M.K.: Magnesium and its alloys applications in automotive industry. Int. J. Adv. Manuf. Technol. 39, 851 (2008).CrossRefGoogle Scholar
Suh, B.C., Shim, M.S., Shin, K.S., and Kim, N.J.: Current issues in magnesium sheet alloys: Where do we go from here? Scr. Mater. 84–85, 1 (2014).CrossRefGoogle Scholar
Motta, A.T., Yilmazbayhan, A., da Silva, M.J.G., Comstock, R.J., Was, G.S., Busby, J.T., Gartner, E., Peng, Q., Jeong, Y.H., and Park, J.Y.: Zirconium alloys for supercritical water reactor applications: Challenges and possibilities. J. Nucl. Mater. 371, 61 (2007).CrossRefGoogle Scholar
Boyer, R.R.: Attributes, characteristics, and applications of titanium and its alloys. JOM 62, 21 (2010).CrossRefGoogle Scholar
Elias, C.N., Lima, J.H.C., Valiev, R., and Meyers, M.A.: Biomedical applications of titanium and its alloys. JOM 60, 46 (2008).CrossRefGoogle Scholar
Agnew, S.R. and Duygulu, O.: Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B. Int. J. Plast. 21, 1161 (2005).CrossRefGoogle Scholar
Wang, Y.N. and Huang, J.C.: The role of twinning and untwinning in yielding behavior in hot-extruded Mg–Al–Zn alloy. Acta Mater. 55, 897 (2007).CrossRefGoogle Scholar
Wronski, M., Arul Kumar, M., Capolungo, L., Madec, R., Wierzbanowski, K., and Tome, C.N.: Deformation behavior of CP-titanium: Experiment and crystal plasticity modeling. Mater. Sci. Eng., A 724, 289 (2018).CrossRefGoogle Scholar
Proust, G., Tome, C.N., Jain, A., and Agnew, S.R.: Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31. Int. J. Plast. 25, 861 (2009).CrossRefGoogle Scholar
Kumar, M.A., Beyerlein, I.J., and Tome, C.N.: A measure of plastic anisotropy for hexagonal close packed metals: Application to alloying effects on the formability of Mg. J. Alloys Compd. 695, 1488 (2017).CrossRefGoogle Scholar
Beyerlein, I.J., Zhang, X.H., and Misra, A.: Growth twins and deformation twins in metals. Annu. Rev. Mater. Res. 44, 329 (2014).CrossRefGoogle Scholar
Partridge, P.G.: The crystallography and deformation modes of hexagonal close-packed metals. Metall. Rev. 12, 169 (1967).Google Scholar
Yoo, M.H.: Interaction of slip dislocations with twins in hcp metals. Trans. Metall. Soc. AIME 245, 2051 (1969).Google Scholar
Yoo, M.H.: Slip, twinning, and fracture in hexagonal close-packed metals. Metall. Trans. A 12, 409 (1981).CrossRefGoogle Scholar
Yoo, M.H. and Lee, J.K.: Deformation twinning in hcp metals and alloys. Philos. Mag. A 63, 987 (1991).CrossRefGoogle Scholar
Clark, W.A.T., Wagoner, R.H., Shen, Z.Y., Lee, T.C., Robertson, I.M., and Birnbaum, H.K.: On the criteria for slip transmission across interfaces in polycrystals. Scr. Metall. Mater. 26, 203 (1992).CrossRefGoogle Scholar
Hirth, J.P. and Lothe, J.: Theory of Dislocations, 2nd ed. (Krieger, Cambridge University Press, New York, USA, 1992).Google Scholar
Kuhlman-wilsdorf, D. and Hansen, N.: Geometrically necessary, incidental and subgrain boundaries. Scr. Metall. Mater. 25, 1557 (1991).CrossRefGoogle Scholar
Christian, J.W. and Mahajan, S.: Deformation twinning. Prog. Mater. Sci. 39, 1 (1995).CrossRefGoogle Scholar
Barnett, M.R., Nave, M.D., and Ghaderi, A.: Yield point elongation due to twinning in a magnesium alloy. Acta Mater. 60, 1433 (2012).CrossRefGoogle Scholar
Beyerlein, I.J., Capolungo, L., Marshall, P.E., McCabe, R.J., and Tome, C.N.: Statistical analyses of deformation twinning in magnesium (vol 90, pg 2161, 2010). Philos. Mag. 90, 4073 (2010).Google Scholar
Capolungo, L., Marshall, P.E., McCabe, R.J., Beyerlein, I.J., and Tome, C.N.: Nucleation and growth of twins in Zr: A statistical study. Acta Mater. 57, 6047 (2009).CrossRefGoogle Scholar
Kumar, M.A., Wroński, M., McCabe, R.J., Capolungo, L., Wierzbanowski, K., and Tomé, C.N.: Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study. Acta Mater. 148, 123 (2018).CrossRefGoogle Scholar
Wang, L.Y., Barabash, R., Bieler, T., Liu, W.J., and Eisenlohr, P.: Study of twinning in alpha-Ti by EBSD and laue microdiffraction. Metall. Mater. Trans. A 44, 3664 (2013).CrossRefGoogle Scholar
Wang, J., Beyerlein, I.J., and Tome, C.N.: An atomic and probabilistic perspective on twin nucleation in Mg. Scr. Mater. 63, 741 (2010).CrossRefGoogle Scholar
Wang, J., Yadav, S.K., Hirth, J.P., Tome, C.N., and Beyerlein, I.J.: Pure-shuffle nucleation of deformation twins in hexagonal-close-packed metals. Mater. Res. Lett. 1, 126 (2013).CrossRefGoogle Scholar
Barrett, C.D. and El Kadiri, H.: The roles of grain boundary dislocations and disclinations in the nucleation of $\left\{ {10\bar{1}2} \right\}$ twinning. Acta Mater. 63, 1 (2014).CrossRefGoogle Scholar
Hirth, J.P., Wang, J., and Tome, C.N.: Disconnections and other defects associated with twin interfaces. Prog. Mater. Sci. 83, 417 (2016).CrossRefGoogle Scholar
Hooshmand, M.S., Mills, M.J., and Ghazisaeidi, M.: Atomistic modeling of dislocation interactions with twin boundaries in Ti. Modell. Simul. Mater. Sci. 25, 045003 (2017).CrossRefGoogle Scholar
Ostapovets, A. and Groger, R.: Twinning disconnections and basal-prismatic twin boundary in magnesium. Modell. Simul. Mater. Sci. 22, 025015 (2014).CrossRefGoogle Scholar
Ostapovets, A. and Serra, A.: Characterization of the matrix-twin interface of a $\left( {10\bar{1}2} \right)$ twin during growth. Philos. Mag. 94, 2827 (2014).CrossRefGoogle Scholar
Wang, J., Beyerlein, I.J., and Hirth, J.P.: Nucleation of elementary $\left\{ {\bar{1}011} \right\}$ and $\left\{ {\bar{1}013} \right\}$ twinning dislocations at a twin boundary in hexagonal close-packed crystals. Modell. Simul. Mater. Sci. 20, 024001 (2012).CrossRefGoogle Scholar
Wang, J., Liu, L., Tome, C.N., Mao, S.X., and Gong, S.K.: Twinning and de-twinning via glide and climb of twinning dislocations along serrated coherent twin boundaries in hexagonal-close-packed metals. Mater. Res. Lett. 1, 81 (2013).CrossRefGoogle Scholar
Fan, H.D., Aubry, S., Arsenlis, A., and El-Awady, J.A.: The role of twinning deformation on the hardening response of polycrystalline magnesium from discrete dislocation dynamics simulations. Acta Mater. 92, 126 (2015).CrossRefGoogle Scholar
Fan, H.D., Aubry, S., Arsenlis, A., and El-Awady, J.A.: Grain size effects on dislocation and twinning mediated plasticity in magnesium. Scr. Mater. 112, 50 (2016).CrossRefGoogle Scholar
Lloyd, J.T.: A dislocation-based model for twin growth within and across grains. Proc. R. Soc. A 474, 20170709 (2018).CrossRefGoogle ScholarPubMed
Kondo, R., Tadano, Y., and Shizawa, K.: A phase-field model of twinning and detwinning coupled with dislocation-based crystal plasticity for HCP metals. Comput. Mater. Sci. 95, 672 (2014).CrossRefGoogle Scholar
Liu, C., Shanthraj, P., Diehl, M., Roters, F., Dong, S., Dong, J., Ding, W., and Raabe, D.: An integrated crystal plasticity-phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials. Int. J. Plast. 106, 203 (2018).CrossRefGoogle Scholar
Abdolvand, H., Daymond, M., and Mareau, C.: Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2. Int. J. Plast. 27, 1721 (2011).CrossRefGoogle Scholar
Ardeljan, M., McCabe, R.J., Beyerlein, I.J., and Knezevic, M.: Explicit incorporation of deformation twins into crystal plasticity finite element models. Comput. Methods Appl. Mech. Eng. 295, 396 (2015).CrossRefGoogle Scholar
Beyerlein, I.J. and Tome, C.N.: A probabilistic twin nucleation model for HCP polycrystalline metals. Proc. R. Soc. A 466, 2517 (2010).CrossRefGoogle Scholar
Kumar, M.A., Beyerlein, I.J., and Tome, C.N.: Effect of local stress fields on twin characteristics in HCP metals. Acta Mater. 116, 143 (2016).CrossRefGoogle Scholar
Kumar, M.A., Kanjarla, A.K., Niezgoda, S.R., Lebensohn, R.A., and Tome, C.N.: Numerical study of the stress state of a deformation twin in magnesium. Acta Mater. 84, 349 (2015).CrossRefGoogle Scholar
Niezgoda, S.R., Kanjarla, A.K., Beyerlein, I.J., and Tome, C.N.: Stochastic modeling of twin nucleation in polycrystals: An application in hexagonal close-packed metals. Int. J. Plast. 56, 119 (2014).CrossRefGoogle Scholar
Wang, H., Wu, P.D., Wang, J., and Tome, C.N.: A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms. Int. J. Plast. 49, 36 (2013).CrossRefGoogle Scholar
Abdolvand, H. and Wilkinson, A.J.: Assessment of residual stress fields at deformation twin tips and the surrounding environments. Acta Mater. 105, 219 (2016).CrossRefGoogle Scholar
Balogh, L., Niezgoda, S.R., Kanjarla, A.K., Brown, D.W., Clausen, B., Liu, W., and Tome, C.N.: Spatially resolved in situ strain measurements from an interior twinned grain in bulk polycrystalline AZ31 alloy. Acta Mater. 61, 3612 (2013).CrossRefGoogle Scholar
Basu, I., Fidder, H., Ocelik, V., and de Hosson, J.T.M.: Local stress states and microstructural damage response associated with deformation twins in hexagonal close packed metals. Crystals 8, 1 (2018).CrossRefGoogle Scholar
Kumar, M.A., Beyerlein, I.J., Lebensohn, R.A., and Tome, C.N.: Modeling the effect of neighboring grains on twin growth in HCP polycrystals. Modell. Simul. Mater. Sci. 25, 064007 (2017).CrossRefGoogle Scholar
Kumar, M.A., Beyerlein, I.J., McCabe, R.J., and Tome, C.N.: Grain neighbour effects on twin transmission in hexagonal close-packed materials. Nat. Commun. 7, 13826 (2016).CrossRefGoogle Scholar
Ma, Q., Li, B., Marin, E., and Horstemeyer, S.: Twinning-induced dynamic recrystallization in a magnesium alloy extruded at 450 °C. Scr. Mater. 65, 823 (2011).CrossRefGoogle Scholar
Ando, D., Koike, J., and Sutou, Y.: The role of deformation twinning in the fracture behavior and mechanism of basal textured magnesium alloys. Mater. Sci. Eng., A 600, 145 (2014).CrossRefGoogle Scholar
Niknejad, S., Esmaeili, S., and Zhou, N.Y.: The role of double twinning on transgranular fracture in magnesium AZ61 in a localized stress field. Acta Mater. 102, 1 (2016).CrossRefGoogle Scholar
Yin, S.M., Yang, F., Yang, X.M., Wu, S.D., Li, S.X., and Li, G.Y.: The role of twinning-detwinning on fatigue fracture morphology of Mg–3% Al–1% Zn alloy. Mater. Sci. Eng., A 494, 397 (2008).CrossRefGoogle Scholar
Abdolvand, H. and Daymond, M.: 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 (2013).CrossRefGoogle Scholar
Abdolvand, H., Majkut, M., Oddershede, J., Wright, J., and Daymond, M.: 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 Mater. 93, 235 (2015).CrossRefGoogle Scholar
Abdolvand, H., Majkut, M., Oddershede, J., Schmidt, S., Lienert, U., Diak, B., Withers, P., and Daymond, M.: On the deformation twinning of Mg AZ31B: A three-dimensional synchrotron X-ray diffraction experiment and crystal plasticity finite element model. Int. J. Plast. 70, 77 (2015).CrossRefGoogle Scholar
Abdolvand, H., Wright, J., and Wilkinson, A.: Strong grain neighbour effects in polycrystals. Nat. Commun. 9, 171 (2018).CrossRefGoogle ScholarPubMed
Barnett, M.R.: Twinning and the ductility of magnesium alloys Part I: “Tension” twins. Mater. Sci. Eng., A 464, 1 (2007).CrossRefGoogle Scholar
Bieler, T., Wang, L., Beaudoin, A., Kenesei, P., and Lienert, U.: In situ characterization of twin nucleation in pure Ti using 3D-XRD. Metall. Mater. Trans. A 45, 109 (2014).CrossRefGoogle Scholar
El Kadiri, H., Kapil, J., Oppedal, A.L., Hector, L.G., Agnew, S.R., Cherkaoui, M., and Vogel, S.C.: The effect of twin-twin interactions on the nucleation and propagation of $\left\{ {10\bar{1}2} \right\}$ twinning in magnesium. Acta Mater. 61, 3549 (2013).CrossRefGoogle Scholar
Kumar, M.A., Clausen, B., Capolungo, L., McCabe, R.J., Liu, W., Tischler, J.Z., and Tome, C.N.: Deformation twinning and grain partitioning in a hexagonal close-packed magnesium alloy. Nat. Commun. 9, 4761 (2018).CrossRefGoogle Scholar
Lentz, M., Coelho, R.S., Camin, B., Fahrenson, C., Schaefer, N., Selve, S., Link, T., Beyerlein, I.J., and Reimers, W.: In-situ, ex-situ EBSD and (HR-)TEM analyses of primary, secondary and tertiary twin development in an Mg–4 wt% Li alloy. Mater. Sci. Eng., A 610, 54 (2014).CrossRefGoogle Scholar
Morrow, B.M., Mccabe, R.J., Cerreta, E.K., and Tome, C.N.: In situ TEM observation of twinning and detwinning during cyclic loading in Mg. Metall. Mater. Trans. A 45, 36 (2014).CrossRefGoogle Scholar
Shi, Z.Z., Zhang, Y.D., Wagner, F., Juan, P.A., Berbenni, S., Capolungo, L., Lecomte, J.S., and Richeton, T.: Variant selection of twins with low Schmid factors in cross grain boundary twin pairs in a magnesium alloy. IOP Conf. Ser.: Mater. Sci. Eng. 82, 012021 (2015).CrossRefGoogle Scholar
Stanford, N., Carlson, U., and Barnett, M.: Deformation twinning and the Hall–Petch relation in commercial purity Ti. Metall. Mater. Trans. A 39, 934 (2008).CrossRefGoogle Scholar
Wang, L., Eisenlohr, P., Yang, Y., Bieler, T.R., and Crimp, M.A.: Nucleation of paired twins at grain boundaries in titanium. Scr. Mater. 63, 827 (2010).CrossRefGoogle Scholar
Wang, L., Yang, Y., Eisenlohr, P., Bieler, T.R., Crimp, M.A., and Mason, D.E.: Twin nucleation by slip transfer across grain boundaries in commercial purity titanium. Metall. Mater. Trans. A 41, 421 (2010).CrossRefGoogle Scholar
Yang, H.J., Yin, S.M., Huang, C.X., Zhang, Z.F., Wu, S.D., Li, S.X., and Liu, Y.D.: EBSD study on deformation twinning in AZ31 magnesium alloy during quasi-in-situ compression. Adv. Eng. Mater. 10, 955 (2008).CrossRefGoogle Scholar
Yu, Q., Wang, J., Jiang, Y.Y., McCabe, R.J., Li, N., and Tome, C.N.: Twin-twin interactions in magnesium. Acta Mater. 77, 28 (2014).CrossRefGoogle Scholar
Fernández, A., Jérusalem, A., Gutiérrez-Urrutia, I., and Pérez-Prado, M.: Three-dimensional investigation of grain boundary–twin interactions in a Mg AZ31 alloy by electron backscatter diffraction and continuum modeling. Acta Mater. 61, 7679 (2013).CrossRefGoogle Scholar
Beyerlein, I.J. and Tome, C.N.: A dislocation-based constitutive law for pure Zr including temperature effects. Int. J. Plast. 24, 867 (2008).CrossRefGoogle Scholar
Beyerlein, I.J., McCabe, R.J., and Tome, C.N.: Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study. J. Mech. Phys. Solids 59, 988 (2011).CrossRefGoogle Scholar
Capolungo, L. and Beyerlein, I.J.: Nucleation and stability of twins in hcp metals. Phys. Rev. B 78, 024117 (2008).CrossRefGoogle Scholar
Beyerlein, I.J. and Arul Kumar, M.: The stochastic nature of deformation twinning: Application to HCP materials. In Handbook of Materials Modeling, Andreoni, S. and Yip, S., eds. (Springer Nature, Switzerland, 2018).Google Scholar
McCabe, R.J., Proust, G., Cerreta, E.K., and Misra, A.: Quantitative analysis of deformation twinning in zirconium. Int. J. Plast. 25, 454 (2009).CrossRefGoogle Scholar
Khosravani, A., Fullwood, D.T., Adams, B.L., Rampton, T.M., Miles, M.P., and Mishra, R.K.: Nucleation and propagation of $\left\{ {10\bar{1}2} \right\}$ twins in AZ31 magnesium alloy. Acta Mater. 100, 202 (2015).CrossRefGoogle Scholar
Clausen, B., Tome, C.N., Brown, D.W., and Agnew, S.R.: Reorientation and stress relaxation due to twinning: Modeling and experimental characterization for Mg. Acta Mater. 56, 2456 (2008).CrossRefGoogle Scholar
Kumar, M.A., Capolungo, L., McCabe, R.J., and Tomé, C.N.: Characterizing the role of adjoining twins at grain boundaries in hexagonal close packed materials. Sci. Rep. 9, 3846 (2019).CrossRefGoogle Scholar
Kacher, J. and Minor, A.M.: Twin boundary interactions with grain boundaries investigated in pure rhenium. Acta Mater. 81, 1 (2014).CrossRefGoogle Scholar
Simkin, B.A., Ng, B.C., Crimp, M.A., and Bieler, T.R.: Crack opening due to deformation twin shear at grain boundaries in near-gamma TiAl. Intermetallics 15, 55 (2007).CrossRefGoogle Scholar
Yang, F., Yin, S.M., Li, S.X., and Zhang, Z.F.: Crack initiation mechanism of extruded AZ31 magnesium alloy in the very high cycle fatigue regime. Mater. Sci. Eng., A 491, 131 (2008).CrossRefGoogle Scholar
Lu, J., Wu, L., Sun, G., Luo, K., Zhang, Y., Cai, J., Cui, C., and Luo, X.: Microstructural response and grain refinement mechanism of commercially pure titanium subjected to multiple laser shock peening impacts. Acta Mater. 127, 252 (2017).CrossRefGoogle Scholar
Yu, Q., Jiang, Y., and Wang, J.: Cyclic deformation and fatigue damage in single-crystal magnesium under fully reversed strain-controlled tension–compression in the [100] direction. Scr. Mater. 96, 41 (2015).CrossRefGoogle Scholar
Yu, Q., Zhang, J., and Jiang, Y.: Fatigue damage development in pure polycrystalline magnesium under cyclic tension–compression loading. Mater. Sci. Eng. A 528, 7816 (2011).CrossRefGoogle Scholar
Gong, M., Xu, S., Jiang, Y., Liu, Y., and Wang, J.: Structural characteristics of $\left\{ {\bar{1}012} \right\}$ non-cozone twin-twin interactions in magnesium. Acta Mater. 159, 65 (2018).CrossRefGoogle Scholar
Lentz, M., Risse, M., Schaefer, N., Reimers, W., and Beyerlein, I.J.: Strength and ductility with $\left\{ {1\bar{0}11} \right\} – \left\{ {1\bar{0}12} \right\}$ double twinning in a magnesium alloy. Nat. Commun. 7, 11068 (2016).CrossRefGoogle Scholar
Mokdad, F., Chen, D.L., and Li, D.Y.: Single and double twin nucleation, growth, and interaction in an extruded magnesium alloy. Mater. Des. 119, 376 (2017).CrossRefGoogle Scholar
Shi, Z.Z., Zhang, Y.D., Wagner, F., Richeton, T., Juan, P.A., Lecomte, J.S., Capolungo, L., and Berbenni, S.: Sequential double extension twinning in a magnesium alloy: Combined statistical and micromechanical analyses. Acta Mater. 96, 333 (2015).CrossRefGoogle Scholar
Liu, Y., Li, N., Kumar, M.A., Pathak, S., Wang, J., McCabe, R.J., Mara, N.A., and Tome, C.N.: Experimentally quantifying critical stresses associated with basal slip and twinning in magnesium using micropillars. Acta Mater. 135, 411 (2017).CrossRefGoogle Scholar
Ye, J., Mishra, R.K., Sachdev, A.K., and Minor, A.M.: In situ TEM compression testing of Mg and Mg–0.2 wt% Ce single crystals. Scr. Mater. 64, 292 (2011).CrossRefGoogle Scholar
Aydiner, C.C., Bernier, J.V., Clausen, B., Lienert, U., Tome, C.N., and Brown, D.W.: Evolution of stress in individual grains and twins in a magnesium alloy aggregate. Phys. Rev. B. 80, 024113 (2009).CrossRefGoogle Scholar
Guo, Y., Abdolvand, H., Britton, T.B., and Wilkinson, A.J.: Growth of $\left\{ {11\bar{2}2} \right\}$ twins in titanium: A combined experimental and modelling investigation of the local state of deformation. Acta Mater. 126, 221 (2017).CrossRefGoogle Scholar
Abdolvand, H. and Wilkinson, A.: On the effects of reorientation and shear transfer during twin formation: Comparison between high resolution electron backscatter diffraction experiments and a crystal plasticity finite element model. Int. J. Plast. 84, 160 (2016).CrossRefGoogle Scholar
Ardeljan, M., Beyerlein, I., McWilliams, B., and Knezevic, M.: Strain rate and temperature sensitive multi-level crystal plasticity model for large plastic deformation behavior: Application to AZ31 magnesium alloy. Int. J. Plast. 83, 90 (2016).CrossRefGoogle Scholar
Kumar, M.A., Beyerlein, I.J., Lebensohn, R.A., and Tome, C.N.: Role of alloying elements on twin growth and twin transmission in magnesium alloys. Mater. Sci. Eng., A 706, 295 (2017).CrossRefGoogle Scholar
Ardeljan, M. and Knezevic, M.: Explicit modeling of double twinning in AZ31 using crystal plasticity finite elements for predicting the mechanical fields for twin variant selection and fracture analyses. Acta Mater. 157, 339 (2018).CrossRefGoogle Scholar
Kanjarla, A.K., Lebensohn, R.A., Balogh, L., and Tome, C.N.: Study of internal lattice strain distributions in stainless steel using a full-field elasto-viscoplastic formulation based on fast Fourier transforms. Acta Mater. 60, 3094 (2012).CrossRefGoogle Scholar
Lebensohn, R.A., Kanjarla, A.K., and Eisenlohr, P.: An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int. J. Plast. 32–33, 59 (2012).CrossRefGoogle Scholar
Simmons, G. and Wang, H.: Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (MIT Press, Cambridge, London, 1971).Google Scholar
Kocks, U.F., Tomé, C.N., and Wenk, H.R.: Texture and Anisotropy—Preferred Orientations in Polycrystals and Their Effect on Materials Properties (Cambridge University Press, Cambridge, UK, 2000); pp. 285290.Google Scholar
Knezevic, M., Zecevic, M., Beyerlein, I.J., Bingert, J.F., and McCabe, R.J.: Strain rate and temperature effects on the selection of primary and secondary slip and twinning systems in HCP Zr. Acta Mater. 88, 55 (2015).CrossRefGoogle Scholar
Wang, L., Barabash, R.I., Yang, Y., Bieler, T.R., Crimp, M.A., Eisenlohr, P., Liu, W., and Ice, G.E.: Experimental characterization and crystal plasticity modeling of heterogeneous deformation in polycrystalline alpha-Ti. Metall. Mater. Trans. A 42, 626 (2011).CrossRefGoogle Scholar
Qin, H., Jonas, J.J., Yu, H.B., Brodusch, N., Gauvin, R., and Zhang, X.Y.: Initiation and accommodation of primary twins in high-purity titanium. Acta Mater. 71, 293 (2014).CrossRefGoogle Scholar
Barnett, M.R., Keshavarz, Z., Beer, A.G., and Ma, X.: Non-Schmid behaviour during secondary twinning in a polycrystalline magnesium alloy. Acta Mater. 56, 5 (2008).CrossRefGoogle Scholar
Guo, C.F., Xin, R.L., Ding, C.H., Song, B., and Liu, Q.: Understanding of variant selection and twin patterns in compressed Mg alloy sheets via combined analysis of Schmid factor and strain compatibility factor. Mater. Sci. Eng., A 609, 92 (2014).CrossRefGoogle Scholar
Shi, Z.Z., Zhang, Y.D., Wagner, F., Juan, P.A., Berbenni, S., Capolungo, L., Lecomte, J.S., and Richeton, T.: On the selection of extension twin variants with low Schmid factors in a deformed Mg alloy. Acta Mater. 83, 17 (2015).CrossRefGoogle Scholar
Juan, P.A., Pradalier, C., Berbenni, S., McCabe, R.J., Tome, C.N., and Capolungo, L.: A statistical analysis of the influence of microstructure and twin-twin junctions on twin nucleation and twin growth in Zr. Acta Mater. 95, 399 (2015).CrossRefGoogle Scholar
Lebensohn, R.A. and Tome, C.: A study of the stress state associated with twin nucleation and propagation in anisotropic materials. Philos. Mag. A 67, 187 (1993).CrossRefGoogle Scholar
Barnett, M.R., Keshavarz, Z., Beer, A.G., and Atwell, D.: Influence of grain size on the compressive deformation of wrought Mg–3Al–1Zn. Acta Mater. 52, 5093 (2004).CrossRefGoogle Scholar
Ecob, N. and Ralph, B.: The effect of grain-size on deformation twinning in a textured zinc alloy. J. Mater. Sci. 18, 2419 (1983).CrossRefGoogle Scholar
Ghaderi, A. and Barnett, M.: Sensitivity of deformation twinning to grain size in titanium and magnesium. Acta Mater. 59, 7824 (2011).CrossRefGoogle Scholar
Jain, A., Duygulu, O., Brown, D.W., Tome, C.N., and Agnew, S.R.: Grain size effects on the tensile properties and deformation mechanisms of a magnesium alloy, AZ31B, sheet. Mater. Sci. Eng., A 486, 545 (2008).CrossRefGoogle Scholar
Kang, S., Jung, J.G., Kang, M., Woo, W., and Lee, Y.K.: The effects of grain size on yielding, strain hardening, and mechanical twinning in Fe–18Mn–0.6C–1.5Al twinning-induced plasticity steel. Mater. Sci. Eng., A 652, 212 (2016).CrossRefGoogle Scholar
Kumar, M.A., Beyerlein, I.J., and Tome, C.N.: Grain size constraints on twin expansion in hexagonal close packed crystals. J. Appl. Phys. 120, 155105 (2016).CrossRefGoogle Scholar
Lentz, M., Behringer, A., Fahrenson, C., Beyerlein, I.J., and Reimers, W.: Grain size effects on primary, secondary, and tertiary twin development in Mg–4 wt% Li (−1 wt% Al) alloys. Metall. Mater. Trans. A 45, 4737 (2014).CrossRefGoogle Scholar
Liu, X., Nuhfer, N.T., Warren, A.P., Coffey, K.R., Rohrer, G.S., and Barmak, K.: Grain size dependence of the twin length fraction in nanocrystalline Cu thin films via transmission electron microscopy based orientation mapping. J. Mater. Res. 30, 528 (2015).CrossRefGoogle Scholar
Rahman, K.M., Vorontsov, V.A., and Dye, D.: The effect of grain size on the twin initiation stress in a TWIP steel. Acta Mater. 89, 247 (2015).CrossRefGoogle Scholar
Stanford, N. and Barnett, M.R.: Fine grained AZ31 produced by conventional thermo-mechanical processing. J. Alloys Compd. 466, 182 (2008).CrossRefGoogle Scholar
Tsai, M.S. and Chang, C.P.: Grain size effect on deformation twinning in Mg–Al–Zn alloy. Mater. Sci. Technol. 29, 759 (2013).CrossRefGoogle Scholar
Kumar, M.A. and Beyerlein, I.J.: Influence of plastic properties on the grain size effect on twinning in Ti and Mg. Mater. Sci. Eng., A 771, 138644 (2020).CrossRefGoogle Scholar
Xin, R.L., Liang, Y.C., Ding, C.H., Guo, C.F., Wang, B.S., and Liu, Q.: Geometrical compatibility factor analysis of paired extension twins in extruded Mg–3Al–1Zn alloys. Mater. Des. 86, 656 (2015).CrossRefGoogle Scholar
Jiang, L. and Jonas, J.J.: Effect of twinning on the flow behavior during strain path reversals in two Mg (+Al, Zn, Mn) alloys. Scr. Mater. 58, 803 (2008).CrossRefGoogle Scholar
Jiang, L., Jonas, J.J., Luo, A.A., Sachdev, A.K., and Godet, S.: Influence of $\left\{ {10\bar{1}2} \right\}$ extension twinning on the flow behavior of AZ31 Mg alloy. Mater. Sci. Eng., A 445, 302 (2007).CrossRefGoogle Scholar
Yu, Q., Wang, J., Jiang, Y.Y., McCabe, R.J., and Tome, C.N.: Co-zone $\left\{ {\bar{1}012} \right\}$ twin interaction in magnesium single crystal. Mater. Res. Lett. 2, 82 (2014).CrossRefGoogle Scholar
Kumar, M.A., Gong, M., Beyerlein, I., Wang, J., and Tomé, C.N.: Role of local stresses on co-zone twin-twin junction formation in HCP magnesium. Acta Mater. 168, 353 (2019).CrossRefGoogle Scholar
Sun, Q., Zhang, X., Ren, Y., Tan, L., and Tu, J.: Observations on the intersection between $\left\langle {10\bar{1}2} \right\rangle$ twin variants sharing the same zone axis in deformed magnesium alloy. Mater. Charact. 109, 160 (2015).CrossRefGoogle Scholar
Morrow, B.M., Cerreta, E.K., McCabe, R.J., and Tome, C.N.: Toward understanding twin–twin interactions in hcp metals: Utilizing multiscale techniques to characterize deformation mechanisms in magnesium. Mater. Sci. Eng., A 613, 365 (2014).CrossRefGoogle Scholar
Mokdad, F., Chen, D.L., and Li, D.Y.: Twin-twin interactions and contraction twin formation in an extruded magnesium alloy subjected to an alteration of compressive direction. J. Alloys Compd. 737, 549 (2018).CrossRefGoogle Scholar
Gong, M., Xu, S., Xie, D., Wang, S., Wang, J., Schuman, C., and Lecomte, J-S.: Steps and $\left\{ {11\bar{2}1} \right\}$ secondary twinning associated with $\left\{ {11\bar{2}2} \right\}$ twin in titanium. Acta Mater. 164, 776 (2019).CrossRefGoogle Scholar
Martin, E., Capolungo, L., Jiang, L.A., and Jonas, J.J.: Variant selection during secondary twinning in Mg–3% Al. Acta Mater. 58, 3970 (2010).CrossRefGoogle Scholar
Mu, S.J., Jonas, J.J., and Gottstein, G.: Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy. Acta Mater. 60, 2043 (2012).CrossRefGoogle Scholar
Xu, S., Zhou, P., Liu, G., Xiao, D., Gong, M., and Wang, J.: Shock-induced two types of $\left\{ {10\bar{1}2} \right\}$ sequential twinning in titanium. Acta Mater. 165, 547 (2019).CrossRefGoogle Scholar
Xu, S., Toth, L.S., Schuman, C., Lecomte, J.S., and Barnett, M.R.: Dislocation mediated variant selection for secondary twinning in compression of pure titanium. Acta Mater. 124, 59 (2017).CrossRefGoogle Scholar
Bao, L., Schuman, C., Le, Q.C., Lecomte, J.S., Zhang, Z.Q., Philippe, M.J., Cui, J.Z., and Esling, C.: A novel method for predicting variant selection during primary, secondary and tertiary twinning in titanium. Mater. Lett. 132, 162 (2014).CrossRefGoogle Scholar
Wang, S., Schuman, C., Bao, L., Lecomte, J.S., Zhang, Y., Raulot, J.M., Philippe, M.J., Zhao, X., and Esling, C.: Variant selection criterion for twin variants in titanium alloys deformed by rolling. Acta Mater. 60, 3912 (2012).CrossRefGoogle Scholar
Qin, H. and Jonas, J.J.: Variant selection during secondary and tertiary twinning in pure titanium. Acta Mater. 75, 198 (2014).CrossRefGoogle Scholar
Xu, S., Gong, M., Schuman, C., Lecomte, J-S., Xie, X., and Wang, J.: Sequential twinning stimulated by other twins in titanium. Acta Mater. 132, 57 (2017).CrossRefGoogle Scholar
Zhou, P., Xu, S., Xiao, D., Jiang, C., Hu, Y., and Wang, J.: Shock-induced $\left\{ {11\bar{2}1} \right\} \to \left\{ {11\bar{2}2} \right\}$ double twinning in titanium. Int. J. Plast. 112, 194 (2019).CrossRefGoogle Scholar
Xu, S., Gong, M., Jiang, Y., Schuman, C., Lecomte, J-S., and Wang, J.: Secondary twin variant selection in four types of double twins in titanium. Acta Mater. 152, 58 (2018).CrossRefGoogle Scholar
Basha, D.A., Somekawa, H., and Singh, A.: Crack propagation along grain boundaries and twins in Mg and Mg–0.3 at.% Y alloy during in-situ straining in transmission electron microscope. Scr. Mater. 142, 50 (2018).CrossRefGoogle Scholar
Liu, L., Wu, H.C., Wang, J., Gong, S.K., and Mao, S.X.: Twinning-dominated nucleation, propagation and deflection of crack in molybdenum characterized with in situ transmission electron microscopy. Philos. Mag. Lett. 94, 225 (2014).CrossRefGoogle Scholar
Xu, D. and Han, E.: Relationship between fatigue crack initiation and activated $\left\{ {10\bar{1}2} \right\}$ twins in as-extruded pure magnesium. Scr. Mater. 69, 702 (2013).CrossRefGoogle Scholar
Liu, Y., Li, N., Shao, S., Gong, M., Wang, J., McCabe, R.J., Jiang, Y., and Tomé, C.N.: Characterizing the boundary lateral to the shear direction of deformation twins in magnesium. Nat. Commun. 7, 11577 (2016).CrossRefGoogle ScholarPubMed
Liu, Y., Tang, P.Z., Gong, M.Y., McCabe, R.J., Wang, J., and Tomé, C.N.: Three dimensional character of $\left\{ {1\bar{0}12} \right\}$ deformation twin in Mg. Nat. Commun. 10, 3308 (2019).CrossRefGoogle Scholar
Gong, M., Liu, G., Wang, J., Capolungo, L., and Tomé, C.N.: Atomistic simulations of interaction between basal 〈a〉 dislocations and three-dimensional twins in magnesium. Acta Mater. 155, 187 (2018).CrossRefGoogle Scholar
Cheng, J.H. and Ghosh, S.: A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys. Int. J. Plast. 67, 148 (2015).CrossRefGoogle Scholar
Jiang, L., Kumar, M.A., Beyerlein, I.J., Wang, X., Zhang, D., Wu, C., Cooper, C., Rupert, T.J., Mahajan, S., Lavernia, E.J., and Schoenung, J.M.: Twin formation from a twin boundary in Mg during in-situ nanomechanical testing. Mater. Sci. Eng. A 759, 142 (2019).CrossRefGoogle Scholar