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Role of \({\varvec{\alpha}} \to {\varvec{\varepsilon}} \to {\varvec{\alpha}}\) phase transformation on the spall behavior of iron at atomic scales

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Abstract

Shock compression of iron microstructures above a threshold stress results in a \(\alpha \left( {BCC} \right) \to \varepsilon \left( {HCP} \right)\) transformation, and the propagation of the release wave brings the metal back to the \(\alpha\) phase following the \(\varepsilon \to \alpha\) transformation. Predicting failure behavior under shock loading conditions (spallation) relies on understanding the evolution of defects in the microstructure as it undergoes the \(\alpha \to \varepsilon \to \alpha\) phase transformation. This study uses molecular dynamics (MD) simulations to investigate the role of defect evolution during the \(\alpha \to \varepsilon \to \alpha\) phase transformation on the spall strength values of single-crystal (sc) Fe microstructures. The MD simulations aim to characterize the \(\varepsilon\) phase fraction formed during shock compression and the defects during shock release for variations in loading orientations and shock stresses. The simulations are carried out for loading along the [100], [110], [111], and [112] orientations and for impact velocities ranging from 600 m/s to 1 km/s. The \(\varepsilon\) phase fractions during compression and defects (dislocations, twins) characterized during spall failure show an orientation dependence that affects the spall strength values. The lowest value for spall strength is observed for the \(110\) loading orientation that shows a high density of twins at the spall plane, whereas the highest value is observed for the \(100\) orientation and is associated with a \(\alpha \left( {BCC} \right) \to \gamma \left( {FCC} \right)\) transformation at the spall plane. The correlations of the spall strength values with the strain rates and with the \(\varepsilon\) phase fractions are discussed.

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References

  1. Meyers MA, Taylor Aimone C (1983) Dynamic fracture (spalling) of metals. Prog Mater Sci 28:1. https://doi.org/10.1016/0079-6425(83)90003-8

    Article  CAS  Google Scholar 

  2. Meyers MA (1994) Dynamic behavior of materials. John wiley & sons, New York

    Book  Google Scholar 

  3. Curran D, Seaman L, Shockey D (1987) Dynamic failure of solids. Phys Rep 147:253

    Article  CAS  Google Scholar 

  4. Whelchel RL, Kennedy GB, Dwivedi SK, Sanders TH, Thadhani NN (2013) Spall behavior of rolled aluminum 5083–H116 plate. J Appl Phys. https://doi.org/10.1063/1.4811452

    Article  Google Scholar 

  5. Kanel GI, Razorenov SV, Baumung K, Singer J (2001) Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point. J Appl Phys 90:136. https://doi.org/10.1063/1.1374478

    Article  CAS  Google Scholar 

  6. Kanel GI, Razorenov SV, Bogatch A, Utkin AV, Fortov VE, Grady DE (1996) Spall fracture properties of aluminum and magnesium at high temperatures. J Appl Phys 79:8310. https://doi.org/10.1063/1.362542

    Article  CAS  Google Scholar 

  7. Turley WD, Fensin SJ, Hixson RS et al (2018) Spall response of single-crystal copper. J Appl Phys. https://doi.org/10.1063/1.5012267

    Article  Google Scholar 

  8. Zaretsky EB, Kanel GI (2015) Yield stress, polymorphic transformation, and spall fracture of shock-loaded iron in various structural states and at various temperatures. J Appl Phys 117:195901. https://doi.org/10.1063/1.4921356

    Article  CAS  Google Scholar 

  9. Gilath I, Eliezer S, Dariel MP, Kornblit L (1988) Brittle-to-ductile transition in laser-induced spall at ultrahigh strain rate in 6061–T6 aluminum alloy. Appl Phys Lett 52:1207. https://doi.org/10.1063/1.99159

    Article  CAS  Google Scholar 

  10. Tamura H, Kohama T, Kondo K, Yoshida M (2001) Femtosecond-laser-induced spallation in aluminum. J Appl Phys 89:3520. https://doi.org/10.1063/1.1346996

    Article  CAS  Google Scholar 

  11. Moshe E, Eliezer S, Dekel E et al (1998) An increase of the spall strength in aluminum, copper, and metglas at strain rates larger than 107 s−1. J Appl Phys 83:4004. https://doi.org/10.1063/1.367222

    Article  CAS  Google Scholar 

  12. Eliezer S, Moshe E, Eliezer DAN (2002) Laser-induced tension to measure the ultimate strength of metals related to the equation of state. Laser Part Beams 20:87. https://doi.org/10.1017/S0263034602201123

    Article  CAS  Google Scholar 

  13. KT Ramesh (2008) Sprinr Handbook of Experimental Solid MechanicsSpringer US,

  14. Cottet F, Boustie M (1989) Spallation studies in aluminum targets using shock waves induced by laser irradiation at various pulse durations. J Appl Phys 66:4067. https://doi.org/10.1063/1.343991

    Article  CAS  Google Scholar 

  15. Cuq-Lelandais JP, Boustie M, Berthe L et al (2009) Spallation generated by femtosecond laser driven shocks in thin metallic targets. J Phys D: Appl Phys 42:065402

    Article  Google Scholar 

  16. Wei CT, Maddox BR, Stover AK, Weihs TP, Nesterenko VF, Meyers MA (2011) Reaction in Ni–Al laminates by laser-shock compression and spalling. Acta Mater 59:5276. https://doi.org/10.1016/j.actamat.2011.05.004

    Article  CAS  Google Scholar 

  17. Kanel GI (2014) Unusual behaviour of usual materials in shock waves. J Phys: Conf Ser 500:012001

    CAS  Google Scholar 

  18. Chevrier P, Klepaczko JR (1999) Spall fracture: mechanical and microstructural aspects. Eng Fract Mech 63:273. https://doi.org/10.1016/S0013-7944(99)00022-3

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Dongare AM, LaMattina B, Rajendran AM (2011) Atomic scale studies of spall behavior in single crystal Cu. Procedia Eng 10:3636. https://doi.org/10.1016/j.proeng.2011.04.598

    Article  CAS  Google Scholar 

  21. Dongare AM, Rajendran AM, LaMattina B, Zikry MA, Brenner DW (2010) Atomic scale studies of spall behavior in nanocrystalline Cu. J Appl Phys. https://doi.org/10.1063/1.3517827

    Article  Google Scholar 

  22. 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. https://doi.org/10.1063/1.4939867

    Article  Google Scholar 

  23. Suresh S, Lee SW, Aindow M, Brody HD, Champagne VK Jr, Dongare AM (2018) Unraveling the mesoscale evolution of microstructure during supersonic impact of aluminum powder particles. Sci Rep 8:10075. https://doi.org/10.1038/s41598-018-28437-3

    Article  CAS  Google Scholar 

  24. Galitskiy S, Ivanov DS, Dongare AM (2018) Dynamic evolution of microstructure during laser shock loading and spall failure of single crystal Al at the atomic scales. J Appl Phys. https://doi.org/10.1063/1.5051618

    Article  Google Scholar 

  25. 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. Comput Mater Sci. https://doi.org/10.1016/j.commatsci.2021.110668

    Article  Google Scholar 

  26. 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. https://doi.org/10.1016/j.commatsci.2017.12.032

    Article  CAS  Google Scholar 

  27. 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. https://doi.org/10.1063/5.0040802

    Article  Google Scholar 

  28. Jarmakani H, Maddox B, Wei CT, Kalantar D, Meyers MA (2010) Laser shock-induced spalling and fragmentation in vanadium. Acta Mater 58:4604. https://doi.org/10.1016/j.actamat.2010.04.027

    Article  CAS  Google Scholar 

  29. Grady DE (1988) The spall strength of condensed matter. J Mech Phys Solids 36:353. https://doi.org/10.1016/0022-5096(88)90015-4

    Article  Google Scholar 

  30. Kanel GI, Razorenov SV, Utkin AV et al (1993) Spall strength of molybdenum single crystals. J Appl Phys 74:7162. https://doi.org/10.1063/1.355032

    Article  CAS  Google Scholar 

  31. Dandekar DP, Weisgerber WJ (1999) Shock response of a heavy tungsten alloy. Int J Plast 15:1291. https://doi.org/10.1016/S0749-6419(99)00041-8

    Article  CAS  Google Scholar 

  32. 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 

  33. Escobedo JP, Cerreta EK, Dennis-Koller D (2014) Effect of crystalline structure on intergranular failure during shock loading. JOM 66:156. https://doi.org/10.1007/s11837-013-0798-6

    Article  CAS  Google Scholar 

  34. de Rességuier T, Hallouin M (2008) Effects of the α−εphase transition on wave propagation and spallation in laser shock-loaded iron. Phys Rev B. https://doi.org/10.1103/PhysRevB.77.174107

    Article  Google Scholar 

  35. Ashitkov SI, Zhakhovsky VV, Inogamov NA, Komarov PS, Agranat MB, Kanel GI (2017) The behavior of iron under ultrafast shock loading driven by a femtosecond laser. AIP Conf Proc 1793:100035. https://doi.org/10.1063/1.4971660

    Article  Google Scholar 

  36. Mahajan S (1970) Effects of existing substructure on shock-twinning behaviour of iron. Physica Status Solidi (a) 2(2):217–223. https://doi.org/10.1002/pssa.19700020205

    Article  CAS  Google Scholar 

  37. Mahajan S, Bartlett AF (1971) Influence of prior mechanical and thermal treatments on shock-induced substructures in molybdenum. Acta Metall 19:1111. https://doi.org/10.1016/0001-6160(71)90043-5

    Article  CAS  Google Scholar 

  38. Christian JW, Mahajan S (1995) Deformation twinning. Prog Mater Sci 39:1. https://doi.org/10.1016/0079-6425(94)00007-7

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  40. Hsiung LM, Lassila DH (2000) Shock-induced deformation twinning and omega transformation in tantalum and tantalum–tungsten alloys. Acta Mater 48:4851. https://doi.org/10.1016/S1359-6454(00)00287-1

    Article  CAS  Google Scholar 

  41. 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. https://doi.org/10.1023/B:JMSC.0000013870.09241.c0

    Article  CAS  Google Scholar 

  42. Florando JN, Barton NR, El-Dasher BS, McNaney JM, Kumar M (2013) Analysis of deformation twinning in tantalum single crystals under shock loading conditions. J Appl Phys 113:083522. https://doi.org/10.1063/1.4792227

    Article  CAS  Google Scholar 

  43. Chen CQ, Florando JN, Kumar M, Ramesh KT, Hemker KJ (2014) Incipient deformation twinning in dynamically sheared bcc tantalum. Acta Mater 69:114. https://doi.org/10.1016/j.actamat.2014.01.046

    Article  CAS  Google Scholar 

  44. Florando JN, El-Dasher BS, Chen C et al (2016) Effect of strain rate and dislocation density on the twinning behavior in tantalum. AIP Adv 6:045120. https://doi.org/10.1063/1.4948528

    Article  CAS  Google Scholar 

  45. Bancroft D, Peterson EL, Minshall S (1956) Polymorphism of Iron at high pressure. J Appl Phys 27:291. https://doi.org/10.1063/1.1722359

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  47. 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 

  48. Wang SJ, Sui ML, Chen YT et al (2013) Microstructural fingerprints of phase transitions in shock-loaded iron. Sci Rep 3:1086. https://doi.org/10.1038/srep01086

    Article  CAS  Google Scholar 

  49. 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. https://doi.org/10.1016/j.scriptamat.2009.01.014

    Article  CAS  Google Scholar 

  50. 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. https://doi.org/10.1134/s1063784216010102

    Article  CAS  Google Scholar 

  51. Righi G, Ruestes CJ, Stan CV et al (2021) Towards the ultimate strength of iron: spalling through laser shock. Acta Mater. https://doi.org/10.1016/j.actamat.2021.117072

    Article  Google Scholar 

  52. 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

    Article  CAS  Google Scholar 

  53. Bowden HG, Kelly PM (1967) The crystallography of the pressure induced phase transformations in iron alloys. Acta Metall 15:1489. https://doi.org/10.1016/0001-6160(67)90180-0

    Article  CAS  Google Scholar 

  54. 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

    Article  CAS  Google Scholar 

  55. 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 

  56. Jensen BJ, GTG III, RS Hixson, (2009) Direct measurements of the α-ϵ transition stress and kinetics for shocked iron. J Appl Phys 105:103502. https://doi.org/10.1063/1.3110188

    Article  CAS  Google Scholar 

  57. Kalantar DH, Collins GW, Colvin JD et al (2006) In situ diffraction measurements of lattice response due to shock loading, including direct observation of the α–ε phase transition in iron. Int J Impact Eng 33:343. https://doi.org/10.1016/j.ijimpeng.2006.09.050

    Article  Google Scholar 

  58. Hawreliak J, Colvin JD, Eggert JH et al (2006) Analysis of the x-ray diffraction signal for the $\ensuremath{\alpha}\text{\ensuremath{-}}ϵ$ transition in shock-compressed iron: simulation and experiment. Phys Rev B 74:184107. https://doi.org/10.1103/PhysRevB.74.184107

    Article  CAS  Google Scholar 

  59. 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 

  60. Wang K, Chen J, Zhang X, Zhu W (2017) Interactions between coherent twin boundaries and phase transition of iron under dynamic loading and unloading. J Appl Phys 122:105107

    Article  Google Scholar 

  61. 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 130:215902. https://doi.org/10.1063/5.0069935

    Article  CAS  Google Scholar 

  62. Amadou N, De Resseguier T, Dragon A, Brambrink E (2020) Effects of orientation, lattice defects and temperature on plasticity and phase transition in ramp-compressed single crystal iron. Comput Mater Sci. https://doi.org/10.1016/j.commatsci.2019.109318

    Article  Google Scholar 

  63. 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 

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

    Article  CAS  Google Scholar 

  65. 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 

  66. Mishra A, Kunka C, Echeverria MJ, Dingreville R, Dongare AM (2021) Fingerprinting shock-induced deformations via diffraction. Sci Rep 11:9872. https://doi.org/10.1038/s41598-021-88908-y

    Article  CAS  Google Scholar 

  67. Avanish Mishra MJ, Echeverria KM et al (2022) Virtual texture analysis to investigate the deformation mechanisms in metal microstructures at the atomic-scale. J Mater Sci. https://doi.org/10.1007/s10853-022-07108-9

    Article  Google Scholar 

  68. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modell Simul Mater Sci Eng. https://doi.org/10.1088/0965-0393/18/1/015012

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  74. Dongare A, Rajendran A, LaMattina B, Zikry M, Brenner D (2009) Atomic scale simulations of ductile failure micromechanisms in nanocrystalline Cu at high strain rates. Phys Rev B. https://doi.org/10.1103/PhysRevB.80.104108

    Article  Google Scholar 

  75. Smith RF, Eggert JH, Rudd RE, Swift DC, Bolme CA, Collins GW (2011) High strain-rate plastic flow in Al and Fe. J Appl Phys. https://doi.org/10.1063/1.3670001

    Article  Google Scholar 

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Acknowledgements

A.M.D would like to acknowledge financial support from the Department of Energy, National Nuclear Security Administration under Award No. DE-NA0003857. This study also acknowledges discussions with Dr. Avanish Mishra. 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 support from the high-performance computing center at the University of Connecticut, Storrs campus.

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  1. Department of Materials Science and Engineering, Institute of Materials Science, University of Connecticut, 97 North Eagleville Road, Storrs, CT, 06269, USA

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Ma, K., Dongare, A.M. Role of \({\varvec{\alpha}} \to {\varvec{\varepsilon}} \to {\varvec{\alpha}}\) phase transformation on the spall behavior of iron at atomic scales. J Mater Sci 57, 12556–12571 (2022). https://doi.org/10.1007/s10853-022-07381-8

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