0
Review Article

Atomistic Energetics and Critical Twinning Stress Prediction in Face and Body Centered Cubic Metals: Recent Progress

[+] Author and Article Information
Piyas Chowdhury

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 W. Green Street,
Urbana, IL 61801

Huseyin Sehitoglu

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 W. Green Street,
Urbana, IL 61801
e-mail: huseyin@illinois.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received March 8, 2017; final manuscript received November 19, 2017; published online January 19, 2018. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 140(2), 020801 (Jan 19, 2018) (19 pages) Paper No: MATS-17-1069; doi: 10.1115/1.4038673 History: Received March 08, 2017; Revised November 19, 2017

This paper recounts recent advances on the atomistic modeling of twinning in body-centered cubic (bcc) and face-centered cubic (fcc) alloy. Specifically, we have reviewed: (i) the experimental evidence of twinning-dominated deformation in single- and multi-grain microstructures, (ii) calculation of generalized planar fault energy (GPFE) landscapes, and (iii) the prediction of critical friction stresses to initiate twinning-governed plasticity (e.g., twin nucleation, twin–slip and twin–twin interactions). Possible avenues for further research are outlined.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Tucker, G. J. , and Foiles, S. M. , 2015, “ Quantifying the Influence of Twin Boundaries on the Deformation of Nanocrystalline Copper Using Atomistic Simulations,” Int. J. Plast., 65, pp. 191–205. [CrossRef]
Li, J. , Ngan, A. H. , and Gumbsch, P. , 2003, “ Atomistic Modeling of Mechanical Behavior,” Acta Mater., 51(19), pp. 5711–5742. [CrossRef]
Ogata, S. , Li, J. , and Yip, S. , 2005, “ Energy Landscape of Deformation Twinning in Bcc and Fcc Metals,” Phys. Rev. B, 71(22), p. 224102. [CrossRef]
Ogata, S. , Li, J. , and Yip, S. , 2002, “ Ideal Pure Shear Strength of Aluminum and Copper,” Science, 298(5594), pp. 807–811. [CrossRef] [PubMed]
Jin, Z. H. , Dunham, S. T. , Gleiter, H. , Hahn, H. , and Gumbsch, P. , 2011, “ A Universal Scaling of Planar Fault Energy Barriers in Face-Centered Cubic Metals,” Scr. Mater., 64(7), pp. 605–608. [CrossRef]
Chowdhury, P. , and Sehitoglu, H. , 2016, “ Mechanisms of Fatigue Crack Growth—A Critical Digest of Theoretical Developments,” Fatigue Fract. Eng. Mater. Struct., 39(6), pp. 652–674. http://onlinelibrary.wiley.com/doi/10.1111/ffe.12392/abstract
Remy, L. , 1977, “ Twin-Twin Interaction in FCC Crystals,” Scr. Metall., 11(3), pp. 169–172. [CrossRef]
Remy, L. , 1978, “ Kinetics of Fcc Deformation Twinning and Its Relationship to Stress-Strain Behaviour,” Acta Metall., 26(3), pp. 443–451. [CrossRef]
McPhie, M. , Berbenni, S. , and Cherkaoui, M. , 2012, “ Activation Energy for Nucleation of Partial Dislocation From Grain Boundaries,” Comput. Mater. Sci., 62, pp. 169–174. [CrossRef]
Warner, D. H. , Sansoz, F. , and Molinari, J. F. , 2006, “ Atomistic Based Continuum Investigation of Plastic Deformation in Nanocrystalline Copper,” Int. J. Plast., 22(4), pp. 754–774. [CrossRef]
M'Guil, S. , Wen, W. , Ahzi, S. , Gracio, J. J. , and Davies, R. W. , 2015, “ Analysis of Shear Deformation by Slip and Twinning in Low and High/Medium Stacking Fault Energy Fcc Metals Using the ϕ-Model,” Int. J. Plast., 68, pp. 132–149. [CrossRef]
Sun, C. Y. , Guo, N. , Fu, M. W. , and Wang, S. W. , 2016, “ Modeling of Slip, Twinning and Transformation Induced Plastic Deformation for TWIP Steel Based on Crystal Plasticity,” Int. J. Plast., 76, pp. 186–212. [CrossRef]
Müllner, P. , and Romanov, A. , 2000, “ Internal Twinning in Deformation Twinning,” Acta Mater., 48(9), pp. 2323–2337. [CrossRef]
Tadmor, E. B. , and Miller, R. E. , 2011, Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press, Cambridge, UK. [CrossRef]
Jo, M. , Koo, Y. M. , Lee, B.-J. , Johansson, B. , Vitos, L. , and Kwon, S. K. , 2014, “ Theory for Plasticity of Face-Centered Cubic Metals,” Proc. Natl. Acad. Sci., 111(18), pp. 6560–6565. [CrossRef]
Li, W. , Lu, S. , Hu, Q.-M. , Kwon, S. K. , Johansson, B. , and Vitos, L. , 2014, “ Generalized Stacking Fault Energies of Alloys,” J. Phys.: Condens. Matter, 26(26), p. 265005. [CrossRef] [PubMed]
Lebensohn, R. , and Tomé, C. , 1993, “ A Self-Consistent Anisotropic Approach for the Simulation of Plastic Deformation and Texture Development of Polycrystals: Application to Zirconium Alloys,” Acta Metall. Mater., 41(9), pp. 2611–2624. [CrossRef]
Chowdhury, P. B. , 2016, “Modeling Mechanical Properties–Linking Atomistics to Continuum,” Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, IL. https://www.ideals.illinois.edu/handle/2142/90474
Remy, L. , 1981, “ The Interaction Between Slip and Twinning Systems and the Influence of Twinning on the Mechanical Behavior of Fcc Metals and Alloys,” Metall. Trans. A, 12(3), pp. 387–408. [CrossRef]
Wang, J. , Anderoglu, O. , Hirth, J. P. , Misra, A. , and Zhang, X. , 2009, “ Dislocation Structures of Σ3 {112} Twin Boundaries in Face Centered Cubic Metals,” Appl. Phys. Lett., 95(2), p. 021908. [CrossRef]
Sutton, A. P. , and Balluffi, R. W. , 1995, “Interfaces in Crystalline Materials,” Phys. Today, 49(9), p. 88.
Kacher, J. , Eftink, B. , Cui, B. , and Robertson, I. , 2014, “ Dislocation Interactions With Grain Boundaries,” Curr. Opin. Solid State Mater. Sci., 18(4), pp. 227–243. [CrossRef]
Zhu, T. , Li, J. , Samanta, A. , Kim, H. G. , and Suresh, S. , 2007, “ Interfacial Plasticity Governs Strain Rate Sensitivity and Ductility in Nanostructured Metals,” Proc. Natl. Acad. Sci., 104(9), pp. 3031–3036. [CrossRef]
Karnthaler, H. , 1978, “ The Study of Glide on {001} Planes in Fcc Metals Deformed at Room Temperature,” Philos. Mag. A, 38(2), pp. 141–156. [CrossRef]
Wang, J. , and Huang, H. , 2006, “ Novel Deformation Mechanism of Twinned Nanowires,” Appl. Phys. Lett., 88(20), p. 203112. [CrossRef]
Asaro, R. J. , and Kulkarni, Y. , 2008, “ Are Rate Sensitivity and Strength Effected by Cross-Slip in Nano-Twinned Fcc Metals,” Scr. Mater., 58(5), pp. 389–392. [CrossRef]
Jin, Z.-H. , Gumbsch, P. , Ma, E. , Albe, K. , Lu, K. , Hahn, H. , and Gleiter, H. , 2006, “ The Interaction Mechanism of Screw Dislocations With Coherent Twin Boundaries in Different Face-Centred Cubic Metals,” Scr. Mater., 54(6), pp. 1163–1168. [CrossRef]
Miller, B. , Fenske, J. , Su, D. , Li, C.-M. , Dougherty, L. , and Robertson, I. M. , 2006, “ Grain Boundary Responses to Local and Applied Stress: An In Situ TEM Deformation Study,” Symposium EE at the MRS Fall Meeting, Boston, MA, Nov. 27–Dec. 1, Paper No. 0976-EE02-01. https://www.cambridge.org/core/journals/mrs-online-proceedings-library-archive/article/grain-boundary-responses-to-local-and-applied-stress-an-in-situ-tem-deformation-study/55FB9263A3D72D9E262E958195E3C04C
Frenkel, D. , and Smit, B. , 2001, Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, Cornwell, UK.
Christian, J. W. , and Mahajan, S. , 1995, “ Deformation Twinning,” Prog. Mater. Sci., 39(1), pp. 1–157. [CrossRef]
Beyerlein, I. J. , Zhang, X. , and Misra, A. , 2014, “ Growth Twins and Deformation Twins in Metals,” Annu. Rev. Mater. Res., 44, pp. 329–363. [CrossRef]
Zhu, Y. T. , Liao, X. , and Wu, X. , 2012, “ Deformation Twinning in Nanocrystalline Materials,” Prog. Mater. Sci., 57(1), pp. 1–62. [CrossRef]
Chowdhury, P. , Sehitoglu, H. , Maier, H. , and Rateick, R. , 2015, “ Strength Prediction in NiCo Alloys—The Role of Composition and Nanotwins,” Int. J. Plast., 79, pp. 237–258. https://doi.org/10.1016/j.ijplas.2015.07.002
Patriarca, L. , Abuzaid, W. , Sehitoglu, H. , Maier, H. J. , and Chumlyakov, Y. , 2013, “ Twin Nucleation and Migration in FeCr Single Crystals,” Mater. Charact., 75, pp. 165–175. [CrossRef]
Patriarca, L. , Abuzaid, W. , Sehitoglu, H. , and Maier, H. J. , 2013, “ Slip Transmission in Bcc FeCr Polycrystal,” Mater. Sci. Eng. A, 588, pp. 308–317. [CrossRef]
Cottrell, A. , and Bilby, B. , 1951, “ LX. A Mechanism for the Growth of Deformation Twins in Crystals,” London, Edinburgh, Dublin Philos. Mag. J. Sci., 42(329), pp. 573–581. [CrossRef]
Li, S. , Ding, X. , Deng, J. , Lookman, T. , Li, J. , Ren, X. , Sun, J. , and Saxena, A. , 2010, “ Superelasticity in Bcc Nanowires by a Reversible Twinning Mechanism,” Phys. Rev. B, 82(20), p. 205435. [CrossRef]
Harding, J. , 1967, “ The Yield and Fracture Behaviour of High-Purity Iron Single Crystals at High Rates Crystals of Strain,” Proc. R. Soc. London A, 299(1459), pp. 464–490. [CrossRef]
Kibey, S. , Liu, J. , Johnson, D. , and Sehitoglu, H. , 2007, “ Energy Pathways and Directionality in Deformation Twinning,” Appl. Phys. Lett., 91(18), p. 181916. https://doi.org/10.1063/1.2800806
Lagerlöf, K. , 1993, “ On Deformation Twinning in Bcc Metals,” Acta Metall. Mater., 41(7), pp. 2143–2151. [CrossRef]
Sleeswyk, A. , 1963, “ ½<111> Screw Dislocations and the Nucleation of {112}<111> Twins in the Bcc Lattice,” Philos. Mag., 8(93), pp. 1467–1486. [CrossRef]
Ogawa, K. , 1965, “ Edge Dislocations Dissociated in {112} Planes and Twinning Mechanism of Bcc Metals,” Philos. Mag., 11(110), pp. 217–233. [CrossRef]
Priestner, R. , and Leslie, W. , 1965, “ Nucleation of Deformation Twins at Slip Plane Intersections in BCC Metals,” Philos. Mag., 11(113), pp. 895–916. [CrossRef]
Venables, J. , 1961, “ Deformation Twinning in Face-Centred Cubic Metals,” Philos. Mag., 6(63), pp. 379–396. [CrossRef]
Venables, J. , 1974, “ On Dislocation Pole Models for Twinning,” Philos. Mag., 30(5), pp. 1165–1169. [CrossRef]
Sleeswyk, A. , 1974, “ Perfect Dislocation Pole Models for Twinning in the Fcc and Bcc Lattices,” Philos. Mag., 29(2), pp. 407–421. [CrossRef]
Mahajan, S. , and Chin, G. , 1973, “ Formation of Deformation Twins in Fcc Crystals,” Acta Metall., 21(10), pp. 1353–1363. [CrossRef]
Blewitt, T. , Coltman, R. , and Redman, J. , 1957, “ Low‐Temperature Deformation of Copper Single Crystals,” J. Appl. Phys., 28(6), pp. 651–660. [CrossRef]
Jin, Z. , and Bieler, T. R. , 1995, “ An In-Situ Observation of Mechanical Twin Nucleation and Propagation in TiAl,” Philos. Mag. A, 71(5), pp. 925–947. [CrossRef]
Karaman, I. , Sehitoglu, H. , Gall, K. , Chumlyakov, Y. , and Maier, H. , 2000, “ Deformation of Single Crystal Hadfield Steel by Twinning and Slip,” Acta Mater., 48(6), pp. 1345–1359. [CrossRef]
Vitek, V. , 1968, “ Intrinsic Stacking Faults in Body-Centred Cubic Crystals,” Philos. Mag., 18(154), pp. 773–786. [CrossRef]
Chowdhury, P. , Sehitoglu, H. , Abuzaid, W. , and Maier, H. , 2015, “ Mechanical Response of Low Stacking Fault Energy Co–Ni Alloys–Continuum, Mesoscopic and Atomic Level Treatments,” Int. J. Plast., 71, pp. 32–61. [CrossRef]
Chandran, M. , and Sondhi, S. , 2011, “ First-Principle Calculation of Stacking Fault Energies in Ni and Ni-Co Alloy,” J. Appl. Phys., 109(10), p. 103525. [CrossRef]
Zhou, X. , Johnson, R. , and Wadley, H. , 2004, “ Misfit-Energy-Increasing Dislocations in Vapor-Deposited CoFe/NiFe Multilayers,” Phys. Rev. B, 69(14), p. 144113. [CrossRef]
Pun, G. P. , and Mishin, Y. , 2012, “ Embedded-Atom Potential for Hcp and Fcc Cobalt,” Phys. Rev. B, 86(13), p. 134116. [CrossRef]
Siegel, D. J. , 2005, “ Generalized Stacking Fault Energies, Ductilities, and Twinnabilities of Ni and Selected Ni Alloys,” Appl. Phys. Lett., 87(12), p. 121901. [CrossRef]
Van Swygenhoven, H. , Derlet, P. , and Frøseth, A. , 2004, “ Stacking Fault Energies and Slip in Nanocrystalline Metals,” Nat. Mater., 3(6), pp. 399–403. [CrossRef] [PubMed]
Cai, T. , Zhang, Z. J. , Zhang, P. , Yang, J. B. , and Zhang, Z. F. , 2014, “ Competition Between Slip and Twinning in Face-Centered Cubic Metals,” J. Appl. Phys., 116(16), p. 163512. [CrossRef]
Tadmor, E. , and Bernstein, N. , 2004, “ A First-Principles Measure for the Twinnability of FCC Metals,” J. Mech. Phys. Solids, 52(11), pp. 2507–2519. [CrossRef]
Warner, D. H. , Curtin, W. A. , and Qu, S. , 2007, “ Rate Dependence of Crack-Tip Processes Predicts Twinning Trends in Fcc Metals,” Nat. Mater., 6(11), pp. 876–881. [CrossRef] [PubMed]
Kibey, S. A. , 2007, “Mesoscale Models for Stacking Faults, Deformation Twins and Martensitic Transformations: Linking Atomistics to Continuum,” Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, IL. http://adsabs.harvard.edu/abs/2007PhDT.......182K
Kalidindi, S. R. , 1998, “ Incorporation of Deformation Twinning in Crystal Plasticity Models,” J. Mech. Phys. Solids, 46(2), pp. 267–290. [CrossRef]
Staroselsky, A. , and Anand, L. , 1998, “ Inelastic Deformation of Polycrystalline Face Centered Cubic Materials by Slip and Twinning,” J. Mech. Phys. Solids, 46(4), pp. 671–696. [CrossRef]
Venables, J. , 1964, “ The Nucleation and Propagation of Deformation Twins,” J. Phys. Chem. Solids, 25(7), pp. 693–700. [CrossRef]
Pirouz, P. , 1989, “ On Twinning and Polymorphic Transformations in Compound Semiconductors,” Scr. Metall., 23(3), pp. 401–406. [CrossRef]
Miura, S. , Takamura, J. , and Narita, N. , 1968, “ Orientation Dependence of Flow Stress for Twinning in Silver Crystals,” Transactions of the Japan Institute of Metals, Sendai, Japan, p. 555.
Meyers, M. , Vöhringer, O. , and Lubarda, V. , 2001, “ The Onset of Twinning in Metals: A Constitutive Description,” Acta Mater., 49(19), pp. 4025–4039. [CrossRef]
Fischer, F. , Appel, F. , and Clemens, H. , 2003, “ A Thermodynamical Model for the Nucleation of Mechanical Twins in TiAl,” Acta Mater., 51(5), pp. 1249–1260. [CrossRef]
Tadmor, E. , and Hai, S. , 2003, “ A Peierls Criterion for the Onset of Deformation Twinning at a Crack Tip,” J. Mech. Phys. Solids, 51(5), pp. 765–793. [CrossRef]
Kibey, S. A. , Wang, L.-L. , Liu, J. B. , Johnson, H. T. , Sehitoglu, H. , and Johnson, D. D. , 2009, “ Quantitative Prediction of Twinning Stress in Fcc Alloys: Application to Cu-Al,” Phys. Rev. B, 79(21), p. 214202. [CrossRef]
Ojha, A. , Sehitoglu, H. , Patriarca, L. , and Maier, H. , 2014, “ Twin Migration in Fe-Based Bcc Crystals: Theory and Experiments,” Philos. Mag., 94(16), pp. 1816–1840. [CrossRef]
Joos, B. , Ren, Q. , and Duesbery, M. , 1994, “ Peierls-Nabarro Model of Dislocations in Silicon With Generalized Stacking-Fault Restoring Forces,” Phys. Rev. B, 50(9), p. 5890. [CrossRef]
Schoeck, G. , 1994, “ The Generalized Peierls–Nabarro Model,” Philos. Mag. A, 69(6), pp. 1085–1095. [CrossRef]
Peierls, R. , 1940, “ The Size of a Dislocation,” Proc. Phys. Soc., 52(1), pp. 34–37. [CrossRef]
Nabarro, F. , 1947, “ Dislocations in a Simple Cubic Lattice,” Proc. Phys. Soc., 59(2), p. 256. [CrossRef]
Kibey, S. , Liu, J. , Johnson, D. , and Sehitoglu, H. , 2007, “ Predicting Twinning Stress in Fcc Metals: Linking Twin-Energy Pathways to Twin Nucleation,” Acta Mater., 55(20), pp. 6843–6851. [CrossRef]
Koning, M. D. , Miller, R. , Bulatov, V. , and Abraham, F. F. , 2002, “ Modelling Grain-Boundary Resistance in Intergranular Dislocation Slip Transmission,” Philos. Mag. A, 82(13), pp. 2511–2527. [CrossRef]
Hirth, J. P. , and Lothe, J. , 1982, Theory of Dislocations, Krieger Publishing Company, Malabar, FL.
Mahajan, S. , and Chin, G. , 1974, “ The Interaction of Twins With Existing Substructure and Twins in Cobalt-Iron Alloys,” Acta Metall., 22(9), pp. 1113–1119. [CrossRef]
Li, J. , 1960, “ The Interaction of Parallel Edge Dislocations With a Simple Tilt Dislocation Wall,” Acta Metall., 8(5), pp. 296–311. [CrossRef]
Li, J. , and Chalmers, B. , 1963, “ Energy of a Wall of Extended Dislocations,” Acta Metall., 11(4), pp. 243–249. [CrossRef]
Li, J. C. , and Needham, C. D. , 1960, “ Some Elastic Properties of a Screw Dislocation Wall,” J. Appl. Phys., 31(8), pp. 1318–1330. [CrossRef]
Neumann, P. , 1986, “ Low Energy Dislocation Configurations: A Possible Key to the Understanding of Fatigue,” Mater. Sci. Eng., 81, pp. 465–475. [CrossRef]
Lu, L. , Chen, X. , Huang, X. , and Lu, K. , 2009, “ Revealing the Maximum Strength in Nanotwinned Copper,” Science, 323(5914), pp. 607–610. [CrossRef] [PubMed]
Lu, L. , Shen, Y. , Chen, X. , Qian, L. , and Lu, K. , 2004, “ Ultrahigh Strength and High Electrical Conductivity in Copper,” Science, 304(5669), pp. 422–426. [CrossRef] [PubMed]
Deng, C. , and Sansoz, F. , 2009, “ Fundamental Differences in the Plasticity of Periodically Twinned Nanowires in Au, Ag, Al, Cu, Pb, and Ni,” Acta Mater., 57(20), pp. 6090–6101. [CrossRef]
Asaro, R. J. , and Suresh, S. , 2005, “ Mechanistic Models for the Activation Volume and Rate Sensitivity in Metals With Nanocrystalline Grains and Nano-Scale Twins,” Acta Mater., 53(12), pp. 3369–3382. [CrossRef]
Lu, L. , Schwaiger, R. , Shan, Z. , Dao, M. , Lu, K. , and Suresh, S. , 2005, “ Nano-Sized Twins Induce High Rate Sensitivity of Flow Stress in Pure Copper,” Acta Mater., 53(7), pp. 2169–2179. [CrossRef]
Wei, Q. , Cheng, S. , Ramesh, K. , and Ma, E. , 2004, “ Effect of Nanocrystalline and Ultrafine Grain Sizes on the Strain Rate Sensitivity and Activation Volume: Fcc Versus Bcc Metals,” Mater. Sci. Eng. A, 381(1), pp. 71–79. [CrossRef]
Jennings, A. T. , Li, J. , and Greer, J. R. , 2011, “ Emergence of Strain-Rate Sensitivity in Cu Nanopillars: Transition From Dislocation Multiplication to Dislocation Nucleation,” Acta Mater., 59(14), pp. 5627–5637. [CrossRef]
Lim, L. , 1984, “ Slip-Twin Interactions in Nickel at 573K at Large Strains,” Scr. Metall., 18(10), pp. 1139–1142. [CrossRef]
Evans, J. , 1974, “ Heterogeneous Shear of a Twin Boundary in α-Brass,” Scr. Metall., 8(9), pp. 1099–1103. [CrossRef]
Deng, C. , and Sansoz, F. , 2009, “ Size-Dependent Yield Stress in Twinned Gold Nanowires Mediated by Site-Specific Surface Dislocation Emission,” Appl. Phys. Lett., 95(9), p. 091914. [CrossRef]
Ezaz, T. , Sangid, M. D. , and Sehitoglu, H. , 2011, “ Energy Barriers Associated With Slip–Twin Interactions,” Philos. Mag., 91(10), pp. 1464–1488. [CrossRef]
Wu, Z. , Zhang, Y. , and Srolovitz, D. , 2009, “ Dislocation–Twin Interaction Mechanisms for Ultrahigh Strength and Ductility in Nanotwinned Metals,” Acta Mater., 57(15), pp. 4508–4518. [CrossRef]
Hartley, C. S. , and Blachon, D. L. , 1978, “ Reactions of Slip Dislocations at Coherent Twin Boundaries in Face‐Centered‐Cubic Metals,” J. Appl. Phys., 49(9), pp. 4788–4796. [CrossRef]
Lee, T. , Robertson, I. , and Birnbaum, H. , 1990, “ An In Situ Transmission Electron Microscope Deformation Study of the Slip Transfer Mechanisms in Metals,” Metall. Trans. A, 21(9), pp. 2437–2447. [CrossRef]
Kulkarni, Y. , and Asaro, R. J. , 2009, “ Are Some Nanotwinned Fcc Metals Optimal for Strength, Ductility and Grain Stability?,” Acta Mater., 57(16), pp. 4835–4844. [CrossRef]
Müllner, P. , and Solenthaler, C. , 1997, “ On the Effect of Deformation Twinning on Defect Densities,” Mater. Sci. Eng. A, 230(1), pp. 107–115. [CrossRef]
El Kadiri, H. , and Oppedal, A. , 2010, “ A Crystal Plasticity Theory for Latent Hardening by Glide Twinning Through Dislocation Transmutation and Twin Accommodation Effects,” J. Mech. Phys. Solids, 58(4), pp. 613–624. [CrossRef]
Jin, Z.-H. , Gumbsch, P. , Albe, K. , Ma, E. , Lu, K. , Gleiter, H. , and Hahn, H. , 2008, “ Interactions Between Non-Screw Lattice Dislocations and Coherent Twin Boundaries in Face-Centered Cubic Metals,” Acta Mater., 56(5), pp. 1126–1135. [CrossRef]
Mahajan, S. , and Chin, G. , 1973, “ Twin-Slip, Twin-Twin and Slip-Twin Interactions in Co-8 wt.% Fe Alloy Single Crystals,” Acta Metall., 21(2), pp. 173–179. [CrossRef]
Alkan, S. , Chowdhury, P. , Sehitoglu, H. , Rateick, R. G. , and Maier, H. J. , 2016, “ Role of Nanotwins on Fatigue Crack Growth Resistance–Experiments and Theory,” Int. J. Fatigue, 84, pp. 28–39. [CrossRef]
Chowdhury, P. B. , Sehitoglu, H. , Rateick, R. G. , and Maier, H. J. , 2013, “ Modeling Fatigue Crack Growth Resistance of Nanocrystalline Alloys,” Acta Mater., 61(7), pp. 2531–2547. [CrossRef]
Chowdhury, P. , Sehitoglu, H. , and Rateick, R. , 2016, “ Recent Advances in Modeling Fatigue Cracks at Microscale in the Presence of High Density Coherent Twin Interfaces,” Curr. Opin. Solid State Mater. Sci., 20(3), pp. 140–150. [CrossRef]
Zhang, R. , Wang, J. , Beyerlein, I. , and Germann, T. , 2011, “ Twinning in Bcc Metals Under Shock Loading: A Challenge to Empirical Potentials,” Philos. Mag. Lett., 91(12), pp. 731–740. [CrossRef]
Shi, Z. , and Singh, C. V. , 2016, “ Competing Twinning Mechanisms in Body-Centered Cubic Metallic Nanowires,” Scr. Mater., 113, pp. 214–217. [CrossRef]
Estrin, Y. , and Mecking, H. , 1984, “ A Unified Phenomenological Description of Work Hardening and Creep Based on One-Parameter Models,” Acta Metall., 32(1), pp. 57–70. [CrossRef]
Jackson, P. , and Basinski, Z. , 1967, “ Latent Hardening and the Flow Stress in Copper Single Crystals,” Can. J. Phys., 45(2), pp. 707–735. [CrossRef]
Friedel, J. , 1955, “ CXXX. On the Linear Work Hardening Mate of Face-Centred Cubic Single Crystals,” Philos. Mag., 46(382), pp. 1169–1186. [CrossRef]
Lomer, W. , 1951, “ A Dislocation Reaction in the Face-Centred Cubic Lattice,” London, Edinburgh, Dublin Philos. Mag. J. Sci., 42(334), pp. 1327–1331. [CrossRef]
Garstone, J. , and Honeycombe, R. , 1957, Dislocations and Mechanical Properties of Crystals, Wiley, New York, p. 391.
Robertson, I. M. , 1986, “ Microtwin Formation in Deformed Nickel,” Philos. Mag. A, 54(6), pp. 821–835. [CrossRef]
Chowdhury, P. , Canadinc, D. , and Sehitoglu, H. , 2017, “ On Deformation Behavior of Fe-Mn Based Structural Alloys,” Mater. Sci. Eng.: R: Rep., 122, pp. 1–28. [CrossRef]
Yamakov, V. , Wolf, D. , Phillpot, S. R. , Mukherjee, A. K. , and Gleiter, H. , 2002, “ Dislocation Processes in the Deformation of Nanocrystalline Aluminium by Molecular-Dynamics Simulation,” Nat. Mater., 1(1), pp. 45–49. [CrossRef] [PubMed]
Shabib, I. , and Miller, R. E. , 2009, “ Deformation Characteristics and Stress–Strain Response of Nanotwinned Copper Via Molecular Dynamics Simulation,” Acta Mater., 57(15), pp. 4364–4373. [CrossRef]
Li, X. , Wei, Y. , Lu, L. , Lu, K. , and Gao, H. , 2010, “ Dislocation Nucleation Governed Softening and Maximum Strength in Nano-Twinned Metals,” Nature, 464(7290), pp. 877–880. [CrossRef] [PubMed]
Zhu, T. , and Gao, H. , 2012, “ Plastic Deformation Mechanism in Nanotwinned Metals: An Insight From Molecular Dynamics and Mechanistic Modeling,” Scr. Mater., 66(11), pp. 843–848. [CrossRef]
Chowdhury, P. B. , 2011, Fatigue Crack Growth (FCG) Modeling in the Presence of Nano-Obstacles, University of Illinois at Urbana-Champaign, Urbana, IL.
Chowdhury, P. , Sehitoglu, H. , and Rateick, R. , 2017, “ Damage Tolerance of Carbon-Carbon Composites in Aerospace Application,” Carbon, 126, pp. 382–393. https://doi.org/10.1016/j.carbon.2017.10.019
Rice, J. R. , 1992, “ Dislocation Nucleation From a Crack Tip: An Analysis Based on the Peierls Concept,” J. Mech. Phys. Solids, 40(2), pp. 239–271. [CrossRef]
Rice, J. R. , and Thomson, R. , 1974, “ Ductile Versus Brittle Behaviour of Crystals,” Philos. Mag., 29(1), pp. 73–97. [CrossRef]
deCelis, B. , Argon, A. S. , and Yip, S. , 1983, “ Molecular Dynamics Simulation of Crack Tip Processes in Alpha‐Iron and Copper,” J. Appl. Phys., 54(9), pp. 4864–4878. [CrossRef]
Chowdhury, P. B. , Sehitoglu, H. , and Rateick, R. G. , 2014, “ Predicting Fatigue Resistance of Nano-Twinned Materials—Part I: Role of Cyclic Slip Irreversibility and Peierls Stress,” Int. J. Fatigue, 68, pp. 277–291. [CrossRef]
Chowdhury, P. B. , Sehitoglu, H. , and Rateick, R. G. , 2014, “ Predicting Fatigue Resistance of Nano-Twinned Materials—Part II: Effective Threshold Stress Intensity Factor Range,” Int. J. Fatigue, 68, pp. 292–301. [CrossRef]
Xie, C. , Fang, Q. H. , Liu, X. , Guo, P. C. , Chen, J. K. , Zhang, M. H. , Liu, Y. W. , Rolfe, B. , and Li, L. X. , 2016, “ Theoretical Study on the { 1 ¯ 012} Deformation Twinning and Cracking in Coarse-Grained Magnesium Alloys,” Int. J. Plast., 82, pp. 44–61. https://doi.org/10.1016/j.ijplas.2016.02.001
Otsuka, K. , and Wayman, C. M. , 1999, Shape Memory Materials, Cambridge University Press, Cambridge, UK. [PubMed] [PubMed]
Chowdhury, P. , Patriarca, L. , Ren, G. , and Sehitoglu, H. , 2016, “ Molecular Dynamics Modeling of NiTi Superelasticity in Presence of Nanoprecipitates,” Int. J. Plast., 81, pp. 152–167. [CrossRef]
Lai, W. , and Liu, B. , 2000, “ Lattice Stability of Some Ni-Ti Alloy Phases Versus Their Chemical Composition and Disordering,” J. Phys.: Condens. Matter, 12(5), p. L53. [CrossRef]
Chowdhury, P. , and Sehitoglu, H. , 2016, “ Significance of Slip Propensity Determination in Shape Memory Alloys,” Scr. Mater., 119, pp. 82–87. https://doi.org/10.1016/j.scriptamat.2016.03.017
Chowdhury, P. , and Sehitoglu, H. , 2017, “ Deformation Physics of Shape Memory Alloys–Fundamentals at Atomistic Frontier,” Prog. Mater. Sci., 88, pp. 49–88. [CrossRef]
Mirzaeifar, R. , Gall, K. , Zhu, T. , Yavari, A. , and DesRoches, R. , 2014, “ Structural Transformations in NiTi Shape Memory Alloy Nanowires,” J. Appl. Phys., 115(19), p. 194307. [CrossRef]
Mutter, D. , and Nielaba, P. , 2013, “ Simulation of the Shape Memory Effect in a NiTi Nano Model System,” J. Alloys Compd., 577(Suppl. 1), pp. S83–S87. [CrossRef]
Chowdhury, P. , Ren, G. , and Sehitoglu, H. , 2015, “ NiTi Superelasticity Via Atomistic Simulations,” Philos. Mag. Lett., 95(12), pp. 1–13. https://doi.org/10.1080/09500839.2015.1123819
Chowdhury, P. , and Sehitoglu, H. , 2016, “ A Revisit to Atomistic Rationale for Slip in Shape Memory Alloys,” Prog. Mater. Sci., 85, pp. 1–42. https://doi.org/10.1016/j.pmatsci.2016.10.002
Wang, F. , and Agnew, S. R. , 2016, “ Dislocation Transmutation by Tension Twinning in Magnesium Alloy AZ31,” Int. J. Plast., 81, pp. 63–86. [CrossRef]
El Kadiri, H. , Baird, J. C. , Kapil, J. , Oppedal, A. L. , Cherkaoui, M. , and Vogel, S. C. , 2013, “ Flow Asymmetry and Nucleation Stresses of Twinning and Non-Basal Slip in Magnesium,” Int. J. Plast., 44, pp. 111–120. [CrossRef]
Ishii, A. , Li, J. , and Ogata, S. , 2016, “ Shuffling-Controlled Versus Strain-Controlled Deformation Twinning: The Case for HCP Mg Twin Nucleation,” Int. J. Plast., 82, pp. 32–43. https://doi.org/10.1016/j.ijplas.2016.01.019
Ngan, A. , 1995, “ A Critique on Some of the Concepts Regarding Planar Faults in Crystals,” Philos. Mag. Lett., 72(1), pp. 11–19. [CrossRef]
Zimmerman, J. A. , Gao, H. , and Abraham, F. F. , 2000, “ Generalized Stacking Fault Energies for Embedded Atom FCC Metals,” Modell. Simul. Mater. Sci. Eng., 8(2), p. 103. [CrossRef]
Kibey, S. , Liu, J. B. , Johnson, D. D. , and Sehitoglu, H. , 2006, “ Generalized Planar Fault Energies and Twinning in Cu–Al Alloys,” Appl. Phys. Lett., 89(19), p. 191911. https://doi.org/10.1063/1.2387133
Cai, W. , and Bulatov, V. V. , 2004, “ Mobility Laws in Dislocation Dynamics Simulations,” Mater. Sci. Eng.: A, 387–389, pp. 277–281. [CrossRef]
Devincre, B. , Kubin, L. , Lemarchand, C. , and Madec, R. , 2001, “ Mesoscopic Simulations of Plastic Deformation,” Mater. Sci. Eng.: A, 309–310, pp. 211–219. [CrossRef]
Amodeo, R. , and Ghoniem, N. , 1990, “ Dislocation Dynamics—I: A Proposed Methodology for Deformation Micromechanics,” Phys. Rev. B, 41(10), p. 6958. [CrossRef]
Kocks, U. F. , Argon, A. S. , and Ashby, M. F. , 1975, Thermodynamics and Kinetics of Slip, Pergamon Press, Oxford, UK.
Clayton, J. D. , 2010, Nonlinear Mechanics of Crystals, Springer Science & Business Media, New York. [PubMed] [PubMed]

Figures

Grahic Jump Location
Fig. 1

A perspective on the goal of using atomistics to develop physically based theories that can capture the phenomenology of deformation, and thus formulate strategies for property enhancement in novel alloys of wide technological importance

Grahic Jump Location
Fig. 2

(a) The Co-Ni crystal under ⟨111⟩ tension plastically deforms predominantly via twinning and twin-slip interactions as confirmed by DIC, EBSD, and TEM [52]. (b) Co-Ni compressed along the ⟨001⟩ orientation demonstrates parallel twinning as the primary deformation mechanism [52]. (c) The deformation of electrodeposited nanocrystalline (as indicated by EBSD analysis) Ni-Co alloys with pre-existent annealing twins shows a strong composition effect [52]. The deformation behavior is found to be characterized by massive slip–twin boundary interactions via electron microscopy.

Grahic Jump Location
Fig. 3

(a) Fe-Cr single crystal under [01¯0] tension deforms via interacting deformation twins as evidenced in DIC, EBSD, and SEM analyses [34]. (b) The deformation mechanism of Fe-Cr single crystal under [101] begins with slip activities followed by twin nucleation, which causes a stress drop [34]. Subsequently, twin–twin interactions give rise to hardening as substantiated by DIC, EBSD, and TEM techniques. (c) Polycrystalline Fe-Cr stress–strain response is found to be governed by massive strain transfer across grain boundaries [35] (as confirmed by combined EBSD and DIC studies).

Grahic Jump Location
Fig. 4

Nucleation of a twin embryo through the pole mechanism in fcc lattice is proposed to be controlled by a simultaneous process of mobile jog formation and dislocation loop expansion [4446]. Expanding slip loops from two adjoining planes eventually interconnect to form a continuous spiral, ultimately leading to the twin nucleation.

Grahic Jump Location
Fig. 5

An illustration of twin nucleation model via pole mechanism in bcc lattice [30,36]. An expanding slip loop stemming from sessile dislocation (pole) cross-slips into a perpendicular plane. Subsequently, the dislocation continues to revolve around the pole assisted by further cross-slips and hence generates layers of stacking faults, i.e., the twin embryo.

Grahic Jump Location
Fig. 6

The dissociation of a screw dislocation with three-fold core in bcc materials into three fraction dislocations under applied stress [4043]. Two of the fractional dislocations (the most stress ones) cross-glide and become parallel to the third one, thereby forming a three-layer twin nucleus.

Grahic Jump Location
Fig. 7

Full dislocations dissociate into partials connected by intrinsic stacking faults [47]. Two extended dislocations from adjoining planes form a two-layer fault, i.e., an extrinsic stacking fault. Interaction between two extrinsic stacking faults leads ultimately to twin formation.

Grahic Jump Location
Fig. 8

The atomistic configuration of a deformation twin produced from lattice shearing induced by consecutive glide of slip [52]

Grahic Jump Location
Fig. 9

To generate a γ surface, crystal blocks consisting of atoms are rigidly sheared in atomic simulations. The atomic structures of the perfect lattice and the one corresponding to an intrinsic stacking fault are shown [52] as computed from DFT simulations.

Grahic Jump Location
Fig. 10

Evolution of energy barriers for various slip–twin interaction mechanisms with respect to the number of incident slip (nslip) and the predicted frictional stresses (τCRSStwin−slip) [105]

Grahic Jump Location
Fig. 11

(a) GSFE for Co-Ni alloys, which represents the energy pathway for the nucleation of an extended dislocation [52] connected by an intrinsic stacking fault. (b) GPFE for Co-Ni alloys [52] as an example. The GPFE represents the twinning energy pathway encompassing the formation of a single-layer intrinsic stacking fault first, then a two-layer extrinsic stacking fault, and finally a three-layer twin nucleus. Further shearing on consecutive planes results in the twin growth (migration) process. (c) Comparison among the GSFE and GPFE in bcc Fe and Fe-Cr alloys. There are two distinct types of twin boundaries in bcc alloys, namely, isosceles and reflective ones [71], which are favored differently from one material (e.g., Fe) to another (e.g., Fe-Cr).

Grahic Jump Location
Fig. 12

(a) Relative sizes of the fault energetics (GSFE and GPFE) and their implication regarding the preference for a certain defect nucleation for fcc lattice [3,5860] and (b) possible shapes of fault energy surfaces and the likely defect mechanism scenario in bcc lattice

Grahic Jump Location
Fig. 13

Modeling of twin–slip interaction based on dislocation mechanics whereby a propagating three-layer twin approaches a dislocation dipole arrangement [52]. The atomistic contributions are considered in the form of GPFE representing the discrete lattice during the process.

Grahic Jump Location
Fig. 14

Five different types of slip–twin boundary interaction mechanisms studied in molecular dynamics simulations: transmission [23], incorporation [27] (shown after 1.3 picoseconds from the beginning, to) Lomer lock formation [25], transmission-incorporation [98] and multiplication [94]

Grahic Jump Location
Fig. 15

The “tracing atom” method for computing the extrinsic magnitude of γus from molecular dynamics simulations [104]. The convergence criteria of the energy parameter are obtained at high l and low w, which are the length and width of the tracing area, respectively.

Grahic Jump Location
Fig. 16

Fault energy profile for various slip-coherent twin boundary interaction mechanism in fcc Cu [94]. Incorporation process has the lowest energy barrier while the blockage case has the highest. The curves designated “baseline” represents the GSFE profile for bulk lattice shearing (i.e., absence of residual slip br). The reason the GSFE curves specific to the reactions are elevated is that br creates local stress, which makes glide difficult for subsequent incidence.

Grahic Jump Location
Fig. 17

An approaching twin consisting of three (a/6)[111¯]  type twinning partials intercept a pre-existent twin boundary [71] in bcc Fe-Cr alloy. The resultant reaction is the incorporation of the twinning partials on the boundary leaving a residual dislocation (br) behind at the interception site. Depending on the magnitude of br (which can be obtained by modulating the Schmid factor or changing single crystal loading direction), the GSFE profile will be altered as shown on the right.

Grahic Jump Location
Fig. 18

Comparison between the predicted twin–twin interaction stress (τCRSStwin−twin) and the experimental one in several bcc alloys [71]

Grahic Jump Location
Fig. 19

Comparison between the predicted and experimental critical resolved shear stresses in polycrystalline NiCo alloys (in the presence of annealing twins) [52]

Grahic Jump Location
Fig. 20

Molecular dynamics simulation of polycrystalline deformation behaviors. From left to right: Nucleation of twins from grain boundaries in nanocrystalline Al [115]; a nanocrystalline Cu structure with annealing twins, which upon deformation results in massive slip–interface interactions [117]; Shockley partials emerging from grain boundaries in Cu [116].

Grahic Jump Location
Fig. 21

Study of crack-tip twinning behavior using atomistics concept. Competition between twin and slip nucleation from a crack is correlated with the relative size/shape of GSFE/GPFE curves [59,60,69,123].

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In