Skip to main content
SpringerLink
Log in

Virtual texture analysis to investigate the deformation mechanisms in metal microstructures at the atomic scale

Journal of Materials Science Aims and scope Submit manuscript

Cite this article

Abstract

Understanding the deformation behavior of metallic materials at high strain rates requires the characterization of plasticity contributors, such as twins, phase transformed regions, and dislocations. However, predicting the contributions from phase transformation and twinning relies on a complete understanding of the selection of variants for various loading orientations and the evolution of their volume fractions. This manuscript presents a new virtual texture (VirTex) analysis approach to characterize phase transformation and twinning variants in deformed microstructures generated using molecular dynamics (MD) simulations. The VirTex method involves the construction of a rotation matrix to calculate the angle/axis pairs and misorientation angles for each atom in the microstructure. Any changes in the orientation angle from angle/axis pairs and/or structure types are analyzed to determine the nucleation and evolution of variants in the microstructure. The study uses shock deformed single-crystal Fe, Ta, and Cu to analyze the variant selections for phase transformation or twinning or both in BCC and FCC systems. In addition, the VirTex analysis is able to characterize the phase transformation and twinning variants in nanocrystalline Fe and Ta microstructures. Besides characterizing variants, orientation mapping also provides an accelerated and on-the-fly approach for quantifying twin fractions in MD microstructures.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10

Similar content being viewed by others

References

  1. Murr LE, Esquivel EV (2004) Observations of common microstructural issues associated with dynamic deformation phenomena: twins, microbands, grain size effects, shear bands, and dynamic recrystallization. J Mater Sci 39:1153–1168. https://doi.org/10.1023/B:JMSC.0000013870.09241.c0

    Article  CAS  Google Scholar 

  2. Meyers MA, Andrade UR, Chokshi AH (1995) The effect of grain size on the high-strain, high-strain-rate behavior of copper. Metall and Mater Trans A 26:2881–2893. https://doi.org/10.1007/BF02669646

    Article  Google Scholar 

  3. Wongwiwat K, Murr LE (1978) Effect of shock pressure, pulse duration, and grain size on shock-deformation twinning in molybdenum. Mater Sci Eng 35:273–285. https://doi.org/10.1016/0025-5416(78)90129-5

    Article  CAS  Google Scholar 

  4. Murr LE, Meyers MA, Niou CS, Chen YJ, Pappu S, Kennedy C (1997) Shock-induced deformation twinning in tantalum. Acta Mater 45:157–175. https://doi.org/10.1016/S1359-6454(96)00145-0

    Article  CAS  Google Scholar 

  5. Barker LM, Hollenbach RE (1974) Shock wave study of the α ⇄ ε phase transition in iron. J Appl Phys 45:4872–4887. https://doi.org/10.1063/1.1663148

    Article  CAS  Google Scholar 

  6. Crowhurst JC, Reed BW, Armstrong MR et al (2014) The α→ϵ phase transition in iron at strain rates up to ∼109 s−1. J Appl Phys 115:113506. https://doi.org/10.1063/1.4868676

    Article  CAS  Google Scholar 

  7. Garkushin GV, Naumova NS, Atroshenko SA, Razorenov SV (2016) Influence of the reversible α–ε phase transition and preliminary shock compression on the spall strength of Armco iron. Tech Phys 61:84–90. https://doi.org/10.1134/s1063784216010102

    Article  CAS  Google Scholar 

  8. Beason MT, Mandal A, Jensen BJ (2020) Direct observation of the hcp-bcc phase transition and melting along the principal Hugoniot of Mg. Phys Rev B 101:024110. https://doi.org/10.1103/PhysRevB.101.024110

    Article  CAS  Google Scholar 

  9. Jones DR, Morrow BM, Trujillo CP, GrayIII GT, Cerreta EK (2017) The α–ω phase transition in shock-loaded titanium. J Appl Phys 122:045902. https://doi.org/10.1063/1.4987146

    Article  CAS  Google Scholar 

  10. Milathianaki D, Boutet S, Williams GJ et al (2013) Femtosecond visualization of lattice dynamics in shock-compressed matter. Science 342:220–223. https://doi.org/10.1126/science.1239566

    Article  CAS  Google Scholar 

  11. Wehrenberg CE, McGonegle D, Bolme C et al (2017) In situ X-ray diffraction measurement of shock-wave-driven twinning and lattice dynamics. Nature 550:496–499. https://doi.org/10.1038/nature24061

    Article  CAS  Google Scholar 

  12. Turneaure SJ, Renganathan P, Winey JM, Gupta YM (2018) Twinning and dislocation evolution during shock compression and release of single crystals: real-time X-ray diffraction. Phys Rev Lett 120:265503. https://doi.org/10.1103/PhysRevLett.120.265503

    Article  CAS  Google Scholar 

  13. Loveridge-Smith A, Allen A, Belak J et al (2001) Anomalous elastic response of silicon to uniaxial shock compression on nanosecond time scales. Phys Rev Lett 86:2349–2352. https://doi.org/10.1103/PhysRevLett.86.2349

    Article  CAS  Google Scholar 

  14. McGonegle D, Milathianaki D, Remington BA, Wark JS, Higginbotham A (2015) Simulations of in situ X-ray diffraction from uniaxially compressed highly textured polycrystalline targets. J Appl Phys. https://doi.org/10.1063/1.4927275

    Article  Google Scholar 

  15. Chen S, Li YX, Zhang NB et al (2019) Capture deformation twinning in mg during shock compression with ultrafast synchrotron X-ray diffraction. Phys Rev Lett 123:255501. https://doi.org/10.1103/PhysRevLett.123.255501

    Article  CAS  Google Scholar 

  16. Williams CL, Kale C, Turnage SA et al (2020) Real-time observation of twinning-detwinning in shock-compressed magnesium via time-resolved in situ synchrotron XRD experiments. Phys Rev Mater 4:83603. https://doi.org/10.1103/PhysRevMaterials.4.083603

    Article  CAS  Google Scholar 

  17. Morrow BM, Jones DR, Rigg PA, Gray GT, Cerreta EK (2018) In-situ experiments to capture the evolution of microstructure during phase transformation of titanium under dynamic loading. EPJ Web Conf 183:03020

    Article  Google Scholar 

  18. Albertazzi B, Ozaki N, Zhakhovsky V et al (2017) Dynamic fracture of tantalum under extreme tensile stress. Sci Adv 3:e1602705. https://doi.org/10.1126/sciadv.1602705

    Article  CAS  Google Scholar 

  19. Hwang H, Galtier E, Cynn H et al (2020) Subnanosecond phase transition dynamics in laser-shocked iron. Sci Adv. https://doi.org/10.1126/sciadv.aaz5132

    Article  Google Scholar 

  20. Kalantar DH, Belak JF, Collins GW et al (2005) Direct observation of the $\ensuremath{\alpha}\mathrm{\text{\ensuremath{-}}}\ensuremath{\epsilon}$ transition in shock-compressed iron via nanosecond X-ray diffraction. Phys Rev Lett 95:075502. https://doi.org/10.1103/PhysRevLett.95.075502

  21. Burgers W (1934) On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium. Physica 1:561–586

    Article  CAS  Google Scholar 

  22. Wang FM, Ingalls R (1998) Iron bcc-hcp transition: local structure from x-ray-absorption fine structure. Phys Rev B 57:5647–5654. https://doi.org/10.1103/PhysRevB.57.5647

    Article  CAS  Google Scholar 

  23. Takahashi T, Bassett WA (1964) High-pressure polymorph of iron. Science 145:483–486. https://doi.org/10.1126/science.145.3631.483

    Article  CAS  Google Scholar 

  24. Bassett W, Huang E (1987) Mechanism of the body-centered cubic—hexagonal close-packed phase transition in iron. Science 238:780–783

    Article  CAS  Google Scholar 

  25. Ishimatsu N, Miyashita D, Kawaguchi SI (2020) Strong variant selection observed in the α−ε martensitic transition of iron under quasihydrostatic compression along [111]α. Phys Rev B 102:054106. https://doi.org/10.1103/PhysRevB.102.054106

    Article  CAS  Google Scholar 

  26. Mishra A, Lind J, Kumar M, Dongare AM (2021) Understanding the phase transformation mechanisms that affect the dynamic response of Fe-based microstructures at the atomic scales. J Appl Phys. https://doi.org/10.1063/5.0069935

    Article  Google Scholar 

  27. Smith RF, Eggert JH, Swift DC et al (2013) Time-dependence of the alpha to epsilon phase transformation in iron. J Appl Phys. https://doi.org/10.1063/1.4839655

    Article  Google Scholar 

  28. Liu H, Lin F, Liu P et al (2021) Variant selection of primary–secondary extension twin pairs in magnesium: an analytical calculation study. Acta Mater 219:117221

    Article  CAS  Google Scholar 

  29. Dougherty LM, Gray Iii GT, Cerreta EK, McCabe RJ, Field RD, Bingert JF (2009) Rare twin linked to high-pressure phase transition in iron. Scripta Mater 60:772–775. https://doi.org/10.1016/j.scriptamat.2009.01.014

    Article  CAS  Google Scholar 

  30. Mackenchery K, Valisetty RR, Namburu RR, Stukowski A, Rajendran AM, Dongare AM (2016) Dislocation evolution and peak spall strengths in single crystal and nanocrystalline Cu. J Appl Phys 119:044301. https://doi.org/10.1063/1.4939867

    Article  CAS  Google Scholar 

  31. Agarwal G, Dongare AM (2018) Defect and damage evolution during spallation of single crystal Al: comparison between molecular dynamics and quasi-coarse-grained dynamics simulations. Comput Mater Sci 145:68–79. https://doi.org/10.1016/j.commatsci.2017.12.032

    Article  CAS  Google Scholar 

  32. Germann TC, Holian BL, Lomdahl PS, Ravelo R (2000) Orientation dependence in molecular dynamics simulations of shocked single crystals. Phys Rev Lett 84:5351–5354. https://doi.org/10.1103/PhysRevLett.84.5351

    Article  CAS  Google Scholar 

  33. Davila LP, Erhart P, Bringa EM et al (2005) Atomistic modeling of shock-induced void collapse in copper. Appl Phys Lett 86:161902

    Article  Google Scholar 

  34. Wang K, Xiao S, Deng H, Zhu W, Hu W (2014) An atomic study on the shock-induced plasticity and phase transition for iron-based single crystals. Int J Plast 59:180–198

    Article  CAS  Google Scholar 

  35. Echeverria MJ, Galitskiy S, Mishra A, Dingreville R, Dongare AM (2021) Understanding the plasticity contributions during laser-shock loading and spall failure of Cu microstructures at the atomic scales. Comp. Mater. Sci. 198:110668. https://doi.org/10.1016/j.commatsci.2021.110668

  36. Ma K, Chen J, Dongare AM (2021) Role of pre-existing dislocations on the shock compression and spall behavior in single-crystal copper at atomic scales. J. Appl. Phys. 129:175901. https://doi.org/10.1063/5.0040802

  37. Chen J, Hahn EN, Dongare AM, Fensin SJ (2019) Understanding and predicting damage and failure at grain boundaries in BCC Ta. J Appl Phys 126:165902. https://doi.org/10.1063/1.5111837

    Article  CAS  Google Scholar 

  38. Higginbotham A, Suggit MJ, Bringa EM et al (2013) Molecular dynamics simulations of shock-induced deformation twinning of a body-centered-cubic metal. Phys Rev B 88:104105. https://doi.org/10.1103/PhysRevB.88.104105

    Article  CAS  Google Scholar 

  39. Gunkelmann N, Bringa EM, Tramontina DR et al (2014) Shock waves in polycrystalline iron: plasticity and phase transitions. Phys Rev B 89:140102. https://doi.org/10.1103/PhysRevB.89.140102

    Article  CAS  Google Scholar 

  40. Lu CH, Hahn EN, Remington BA, Maddox BR, Bringa EM, Meyers MA (2015) Phase transformation in tantalum under extreme laser deformation. Sci Rep 5:15064. https://doi.org/10.1038/srep15064. https://www.nature.com/articles/srep15064#supplementary-information

  41. Hahn EN, Fensin SJ (2019) Influence of defects on the shock Hugoniot of tantalum. J Appl Phys 125:215902. https://doi.org/10.1063/1.5096526

    Article  CAS  Google Scholar 

  42. Zhang RF, Wang J, Beyerlein IJ, Germann TC (2011) Twinning in bcc metals under shock loading: a challenge to empirical potentials. Philos Mag Lett 91:731–740. https://doi.org/10.1080/09500839.2011.615348

    Article  CAS  Google Scholar 

  43. Ravelo R, Germann TC, Guerrero O, An Q, Holian BL (2013) Shock-induced plasticity in tantalum single crystals: interatomic potentials and large-scale molecular-dynamics simulations. Phys Rev B. https://doi.org/10.1103/PhysRevB.88.134101

    Article  Google Scholar 

  44. Hahn EN, Fensin SJ (2019) Influence of defects on the shock Hugoniot of tantalum. J Appl Phys 125:215902

    Article  Google Scholar 

  45. Agarwal G, Dongare AM (2019) Deformation twinning in polycrystalline Mg microstructures at high strain rates at the atomic scales. Sci Rep 9:3550. https://doi.org/10.1038/s41598-019-39958-w

    Article  CAS  Google Scholar 

  46. Agarwal G, Dongare AM (2016) Shock wave propagation and spall failure in single crystal Mg at atomic scales. J Appl Phys 119:145901. https://doi.org/10.1063/1.4944942

    Article  CAS  Google Scholar 

  47. Bolesta AV, Fomin VM (2017) Molecular dynamics simulation of shock-wave loading of copper and titanium. AIP Conf Proc 1893:020008. https://doi.org/10.1063/1.5007446

    Article  CAS  Google Scholar 

  48. Zong H, Ding X, Lookman T, Sun J (2016) Twin boundary activated α → ω phase transformation in titanium under shock compression. Acta Mater 115:1–9. https://doi.org/10.1016/j.actamat.2016.05.037

    Article  CAS  Google Scholar 

  49. Flanagan TJ, Vijayan S, Galitskiy S et al (2020) Shock-induced deformation twinning and softening in magnesium single crystals. Mater Des 194:108884

    Article  CAS  Google Scholar 

  50. Wu Z, Francis M, Curtin W (2015) Magnesium interatomic potential for simulating plasticity and fracture phenomena. Model Simul Mater Sci Eng 23:015004

    Article  CAS  Google Scholar 

  51. Kelchner CL, Plimpton SJ, Hamilton JC (1998) Dislocation nucleation and defect structure during surface indentation. Phys Rev B 58:11085–11088. https://doi.org/10.1103/PhysRevB.58.11085

    Article  CAS  Google Scholar 

  52. Stukowski A (2012) Structure identification methods for atomistic simulations of crystalline materials. Model Simul Mater Sci Eng. https://doi.org/10.1088/0965-0393/20/4/045021

    Article  Google Scholar 

  53. Honeycutt JD, Andersen HC (1987) Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. J Phys Chem 91:4950–4963

    Article  CAS  Google Scholar 

  54. Tsuzuki H, Branicio PS, Rino JP (2007) Structural characterization of deformed crystals by analysis of common atomic neighborhood. Comput Phys Commun 177:518. https://doi.org/10.1016/j.cpc.2007.05.018

    Article  CAS  Google Scholar 

  55. Ackland G, Jones A (2006) Applications of local crystal structure measures in experiment and simulation. Phys Rev B 73:054104

    Article  Google Scholar 

  56. Stukowski A (2014) Computational analysis methods in atomistic modeling of crystals. JOM 66:399. https://doi.org/10.1007/s11837-013-0827-5

    Article  CAS  Google Scholar 

  57. Stukowski A, Bulatov VV, Arsenlis A (2012) Automated identification and indexing of dislocations in crystal interfaces. Model Simul Mater Sci Eng. https://doi.org/10.1088/0965-0393/20/8/085007

    Article  Google Scholar 

  58. Stukowski A, Albe K (2010) Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Model Simul Mater Sci Eng. https://doi.org/10.1088/0965-0393/18/8/085001

    Article  Google Scholar 

  59. Larsen PM, Schmidt S, Schiøtz J (2016) Robust structural identification via polyhedral template matching. Model Simul Mater Sci Eng. https://doi.org/10.1088/0965-0393/24/5/055007

    Article  Google Scholar 

  60. Jc E, Tang MX, Fan D, Wang L, Luo SN (2018) Deformation of metals under dynamic loading: characterization via atomic-scale orientation mapping. Comput Mater Sci 153:338–347. https://doi.org/10.1016/j.commatsci.2018.06.020

    Article  CAS  Google Scholar 

  61. White TG, Tikku A, Alves Silva MF, Gregori G, Higginbotham A, Eakins DE (2017) Identifying deformation mechanisms in molecular dynamics simulations of laser shocked matter. J Comput Phys 350:16–24. https://doi.org/10.1016/j.jcp.2017.08.040

    Article  CAS  Google Scholar 

  62. Bartók AP, Kondor R, Csányi G (2013) On representing chemical environments. Phys Rev B 87:184115

    Article  Google Scholar 

  63. Thompson AP, Swiler LP, Trott CR, Foiles SM, Tucker GJ (2015) Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials. J Comput Phys 285:316

    Article  CAS  Google Scholar 

  64. Wood MA, Thompson AP (2018) Extending the accuracy of the SNAP interatomic potential form. J Chem Phys 148:241721

    Article  Google Scholar 

  65. Behler J (2011) Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J Chem Phys 134:074106

    Article  Google Scholar 

  66. Huo H, Rupp M (2017) Unified representation for machine learning of molecules and crystals. arXiv preprint arXiv:1704.06439 13754

  67. Lazar EA, Han J, Srolovitz DJ (2015) Topological framework for local structure analysis in condensed matter. Proc Natl Acad Sci 112:E5769

    Article  CAS  Google Scholar 

  68. Drautz R (2019) Atomic cluster expansion for accurate and transferable interatomic potentials. Phys Rev B 99:014104. https://doi.org/10.1103/PhysRevB.99.014104

    Article  CAS  Google Scholar 

  69. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO – the Open Visualization Tool. Modelling Simul. Mater. Sci. Eng. 18:015012

  70. Barton NR, Dawson PR (2001) A methodology for determining average lattice orientation and its application to the characterization of grain substructure. Metall Mater Trans A 32:1967–1975

    Article  Google Scholar 

  71. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1–19. https://doi.org/10.1006/jcph.1995.1039

    Article  CAS  Google Scholar 

  72. Menache A (2011) Understanding motion capture for computer animation. Elsevier

    Google Scholar 

  73. Virtanen P, Gommers R, Oliphant TE et al (2020) SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods. https://doi.org/10.1038/s41592-019-0686-2

    Article  Google Scholar 

  74. Gunkelmann N, Bringa EM, Kang K, Ackland GJ, Ruestes CJ, Urbassek HM (2012) Polycrystalline iron under compression: plasticity and phase transitions. Phys Rev B. https://doi.org/10.1103/PhysRevB.86.144111

    Article  Google Scholar 

  75. Mishra A, Kunka C, Echeverria MJ, Dingreville R, Dongare AM (2021) Fingerprinting shock-induced deformations via diffraction. Sci Rep 11:1

    Article  Google Scholar 

  76. de Rességuier T, Hallouin M (2008) Effects of the α−ε phase transition on wave propagation and spallation in laser shock-loaded iron. Phys Rev B 77:174107

    Article  Google Scholar 

  77. Righi G, Ruestes CJ, Stan CV et al (2021) Towards the ultimate strength of iron: spalling through laser shock. Acta Materialia 117072

Download references

Acknowledgements

“This material is based upon work supported by the Department of Energy, National Nuclear Security Administration under Award No. DE-NA0003857. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Nuclear Security Administration. The authors also acknowledge the computational facility at the University of Connecticut, Storrs campus.”

Author information

Authors and Affiliations

  1. Materials Science and Engineering, Institute of Materials Science, University of Connecticut, Storrs, CT, 06269, USA

    Avanish Mishra, Marco J. Echeverria, Ke Ma, Shayani Parida, Ching Chen, Sergey Galitskiy & Avinash M. Dongare

Authors
  1. Avanish Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco J. Echeverria
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ke Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shayani Parida
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ching Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sergey Galitskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Avinash M. Dongare
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Avinash M. Dongare.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Handling Editor: M. Grant Norton.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 2220 kb)

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, A., Echeverria, M.J., Ma, K. et al. Virtual texture analysis to investigate the deformation mechanisms in metal microstructures at the atomic scale. J Mater Sci 57, 10549–10568 (2022). https://doi.org/10.1007/s10853-022-07108-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-022-07108-9

search

Navigation