The brittle-to-ductile transition in cold-rolled tungsten sheets: the rate-limiting mechanism of plasticity controlling the BDT in ultrafine-grained tungsten
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Abstract
Abstract Conventionally produced tungsten (W) sheets are brittle at room temperature. In contrast to that, severe deformation by cold rolling transforms W into a material exhibiting room-temperature ductility with a brittle-to-ductile transition (BDT) temperature far below room temperature. For such ultrafine-grained (UFG) and dislocation-rich materials, the mechanism controlling the BDT is still the subject of ongoing debates. In order to identify the mechanism controlling the BDT in room-temperature ductile W sheets with UFG microstructure, we conducted campaigns of fracture toughness tests accompanied by a thermodynamic analysis deducing Arrhenius BDT activation energies. Here, we show that plastic deformation induced by rolling reduces the BDT temperature and also the BDT activation energy. A comparison of BDT activation energies with the trend of Gibbs energy of kink-pair formation revealed a strong correlation between both quantities. This demonstrates that out of the three basic processes, nucleation, glide, and annihilation, crack tip plasticity in UFG W is still controlled by the glide of dislocations. The glide is dictated by the mobility of the screw segments and therefore by the underlying process of kink-pair formation. Reflecting this result, a change of the rate-limiting mechanism for plasticity of UFG W seems unlikely, even at deformation temperatures well below room temperature. As a result, kink-pair formation controls the BDT in W over a wide range of microstructural length scales, from single crystals and coarse-grained specimens down to UFG microstructures.
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OpenAlex topics: Microstructure and mechanical properties · Fusion materials and technologies · Advanced materials and composites
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References (100+)
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1. Šesták B, Seeger A (1978) Gleitung und Verfestigung in kubisch-raumzentrierten Metallen und Legierungen (I). (paper in German language). Z. Metallkde. 69(4):195–20210.1515/ijmr-1978-690401 ↗
2. Anderson TL (2017) Fracture mechanics: fundamentals and applications, 4th edn. CRC Press, Boca Raton. https://doi.org/10.1201/978131537029310.1201/9781315370293 ↗
3. Smid I, Akiba M, Vieider G, Plöchl L (1998) Development of tungsten armor and bonding to copper for plasma-interactive components. J Nucl Mater. https://doi.org/10.1016/S0022-3115(98)00358-410.1016/S0022-3115(98)00358-4 ↗
4. Roberts SG, Hirsch PB, Booth AS, Ellis M, Serbena FC (1993) Dislocations, cracks and brittleness in single crystals. Phys Scr. https://doi.org/10.1088/0031-8949/1993/T49B/00610.1088/0031-8949/1993/T49B/006 ↗
5. Bitzek E, Gumbsch P (2013) Mechanisms of dislocation multiplication at crack tips. Acta Mater. https://doi.org/10.1016/j.actamat.2012.11.01610.1016/j.actamat.2012.11.016 ↗
6. Tarleton E, Roberts SG (2009) Dislocation dynamic modelling of the brittle–ductile transition in tungsten. Mag Philos. https://doi.org/10.1080/1478643090299261910.1080/14786430902992619 ↗
7. Swinburne TD, Dudarev SL (2018) Kink-limited Orowan strengthening explains the brittle to ductile transition of irradiated and unirradiated bcc metals. Phys Rev Mater. https://doi.org/10.1103/PhysRevMaterials.2.07360810.1103/PhysRevMaterials.2.073608 ↗
8. Caillard D, Martin J-L (2003) Thermally activated mechanisms in crystal plasticity. Pergamon materials series 8. Pergamon, Oxford, GBR
9. Christian JW (2002) The theory of transformations in metals and alloys, 3rd edn. Pergamon, Oxford. https://doi.org/10.1016/B978-0-08-044019-4.X5000-410.1016/B978-0-08-044019-4.X5000-4 ↗
10. Hartmaier A, Gumbsch P (1999) The brittle-to-ductile transition and dislocation activity at crack tips. J Comput-Aided Mater Des. https://doi.org/10.1023/A:100870602289710.1023/A:1008706022897 ↗
11. Rice JR, Thomson R (1974) Ductile versus brittle behaviour of crystals. Philos Mag 1:2. https://doi.org/10.1080/1478643740821355510.1080/14786437408213555 ↗
12. Khantha M, Pope DP, Vitek V (1994) Dislocation screening and the brittle-to-ductile transition: a Kosterlitz–Thouless type instability. Phys Rev Lett. https://doi.org/10.1103/PhysRevLett.73.68410.1103/PhysRevLett.73.684 ↗
13. Hirsch PB, Roberts SG, Samuels J (1989) The brittle-ductile transition in silicon interpretation. Proc R Soc London Ser A. https://doi.org/10.1098/rspa.1989.000210.1098/rspa.1989.0002 ↗
14. Roberts SG (1996) In: Kirchner HO, Kubin LP, Pontikis V (eds) Computer simulation in materials science. Springer, Dordrecht, NLD, pp 409–433, https://doi.org/10.1007/978-94-009-1628-9_2210.1007/978-94-009-1628-9_22 ↗
15. Hartmaier A, Gumbsch P (2005) Thermal activation of crack-tip plasticity: The brittle or ductile response of a stationary crack loaded to failure. Phys Rev B. https://doi.org/10.1103/PhysRevB.71.02410810.1103/PhysRevB.71.024108 ↗
16. Cui Y, Po G, Ghoniem N (2016) Temperature insensitivity of the flow stress in body-centered cubic micropillar crystals. Acta Mater. https://doi.org/10.1016/j.actamat.2016.02.00810.1016/j.actamat.2016.02.008 ↗
17. Gumbsch P, Riedle J, Hartmaier A, Fischmeister H (1998) Controlling factors for the brittle-to-ductile transition in tungsten single crystals. Science. https://doi.org/10.1126/science.282.5392.129310.1126/science.282.5392.1293 ↗
18. Giannattasio A, Roberts SG (2007) Strain-rate dependence of the brittle-to-ductile transition temperature in tungsten. Philos Mag. https://doi.org/10.1080/1478643070125319710.1080/14786430701253197 ↗
19. Ast J, Schwiedrzik JJ, Wehrs J, Frey D, Polyakov MN, Michler J, Maeder X (2018) The brittle-ductile transition of tungsten single crystals at the micro-scale. Mater Des. https://doi.org/10.1016/j.matdes.2018.04.00910.1016/j.matdes.2018.04.009 ↗
20. Giannattasio A, Yao Z, Tarleton E, Roberts SG (2010) Brittle–ductile transitions in polycrystalline tungsten. Philos Mag. https://doi.org/10.1080/14786435.2010.50214510.1080/14786435.2010.502145 ↗
21. Németh AAN, Reiser J, Armstrong DEJ, Rieth M (2015) The nature of the brittle-to-ductile transition of ultra fine grained tungsten (W) foil. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2014.11.00510.1016/j.ijrmhm.2014.11.005 ↗
22. Rupp D, Weygand SM (2011) Loading rate dependence of the fracture toughness of polycrystalline tungsten. J Nucl Mater. https://doi.org/10.1016/j.jnucmat.2010.12.11810.1016/j.jnucmat.2010.12.118 ↗
23. Bonnekoh C, Hoffmann A, Reiser J (2018) The brittle-to-ductile transition in cold rolled tungsten: on the decrease of the brittle-to-ductile transition by 600 K to −65 °C. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2017.11.01710.1016/j.ijrmhm.2017.11.017 ↗
24. Lied P, Pantleon W, Bonnekoh C, Bonk S, Hoffmann A, Reiser J, Rieth M Comparison of K-doped and pure cold-rolled tungsten sheets: Tensile properties and ductile-to-brittle-transition. (manuscript under review)
25. Valiev RZ, Islamgaliev RK, Alexandrov V (2000) Bulk nanostructured materials from severe plastic deformation. Prog Mater Sci 1:2. https://doi.org/10.1016/S0079-6425(99)00007-910.1016/S0079-6425(99)00007-9 ↗
26. Kiener D, Fritz R, Alfreider M, Leitner A, Pippan R, Maier-Kiener V (2019) Rate limiting deformation mechanisms of bcc metals in confined volumes. Acta Mater. https://doi.org/10.1016/j.actamat.2019.01.02010.1016/j.actamat.2019.01.020 ↗
27. Bonk S, Hoffmann J, Hoffmann A, Reiser J (2018) Cold rolled tungsten (W) plates and foils: evolution of the tensile properties and their indication towards deformation mechanisms. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2017.09.00710.1016/j.ijrmhm.2017.09.007 ↗
28. Levin ZS, Srivastava A, Foley DC, Hartwig KT (2018) Fracture in annealed and severely deformed tungsten. Mater Sci Eng A. https://doi.org/10.1016/j.msea.2018.05.00410.1016/j.msea.2018.05.004 ↗
29. Reiser J, Hoffmann J, Jäntsch U, Klimenkov M, Bonk S, Bonnekoh C, Rieth M, Hoffmann A, Mrotzek T (2016) Ductilisation of tungsten (W): on the shift of the brittle-to-ductile transition (BDT) to lower temperatures through cold rolling. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2015.09.00110.1016/j.ijrmhm.2015.09.001 ↗
30. Ren C, Fang ZZ, Xu L, Ligda JP, Paramore JD, Butler BG (2019) An investigation of the microstructure and ductility of annealed cold-rolled tungsten. Acta Mater. https://doi.org/10.1016/j.actamat.2018.10.00210.1016/j.actamat.2018.10.002 ↗
31. Bonnekoh C, Jäntsch U, Hoffmann J, Leiste H, Hartmaier A, Weygand D, Hoffmann A, Reiser J (2019) The brittle-to-ductile transition in cold rolled tungsten plates: impact of crystallographic texture, grain size and dislocation density on the transition temperature. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2018.09.01010.1016/j.ijrmhm.2018.09.010 ↗
32. Ren C, Fang ZZ, Koopman M, Butler B, Paramore J, Middlemas S (2018) Methods for improving ductility of tungsten—a review. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2018.04.01210.1016/j.ijrmhm.2018.04.012 ↗
33. Butler BG, Paramore JD, Ligda JP, Ren C, Fang ZZ, Middlemas SC, Hemker KJ (2018) Mechanisms of deformation and ductility in tungsten—a review. Int J Refract Met Hard Mater 1:2. https://doi.org/10.1016/j.ijrmhm.2018.04.02110.1016/j.ijrmhm.2018.04.021 ↗
34. Duesbery MS, Xu W (1998) The motion of edge dislocations in body-centered cubic metals. Scr Mater. https://doi.org/10.1016/S1359-6462(98)00162-610.1016/S1359-6462(98)00162-6 ↗
35. Cheng GM, Jian WW, Xu WZ, Yuan H, Millett PC, Zhu YT (2013) Grain size effect on deformation mechanisms of nanocrystalline bcc metals. Mat Res Lett. https://doi.org/10.1080/21663831.2012.73958010.1080/21663831.2012.739580 ↗
36. Brunner D, Glebovsky V (2000) The plastic properties of high-purity W single crystals. Mater Lett. https://doi.org/10.1016/S0167-577X(99)00200-110.1016/S0167-577X(99)00200-1 ↗
37. Brunner D, Glebovsky V (2000) Analysis of flow-stress measurements of high-purity tungsten single crystals. Mater Lett. https://doi.org/10.1016/S0167-577X(00)00017-310.1016/S0167-577X(00)00017-3 ↗
38. Brunner D (2000) Comparison of flow-stress measurements on high-purity tungsten single crystals with the kink-pair theory. Mater Trans JIM 1:2. https://doi.org/10.2320/matertrans1989.41.15210.2320/matertrans1989.41.152 ↗
39. Hull D, Bacon DJ (2001) Introduction to dislocations, 5th edn. Butterworth-Heinemann, Oxford, GBR. https://doi.org/10.1016/B978-0-7506-4681-9.X5000-710.1016/B978-0-7506-4681-9.X5000-7 ↗
40. Taylor G (1992) Thermally-activated deformation of BCC metals and alloys. Prog Mater Sci. https://doi.org/10.1016/0079-6425(92)90004-Q10.1016/0079-6425(92)90004-Q ↗
41. Roberts SG, Booth AS, Hirsch PB (1994) Dislocation activity and brittle-ductile transitions in single crystals. Mater Sci Eng A. https://doi.org/10.1016/0921-5093(94)90962-810.1016/0921-5093(94)90962-8 ↗
42. Hartmaier A, Gumbsch P (2002) Scaling relations for crack-tip plasticity. Philos Mag A. https://doi.org/10.1080/0141861020824043210.1080/01418610208240432 ↗
43. Kubin LP (2013) Dislocations, mesoscale simulations and plastic flow, 1st edn. Oxford series on materials modelling. Oxford Univ. Press, Oxford, GBR10.1093/acprof:oso/9780198525011.001.0001 ↗
44. Ziebart U (1986) Experimentelle Untersuchungen zum Beitrag von Versetzungen zur inneren Reibung von Wolfram. Dissertation, Stuttgart, DEU
45. Ziebart U, Schultz H (1983) Dislocation relaxation peaks in high purity tungsten single crystals. J Phys Colloques. https://doi.org/10.1051/jphyscol:1983910410.1051/jphyscol:19839104 ↗
46. Glebovsky VG, Semenov VN, Lomeyko VV (1988) Influence of the crystallization conditions on the structural perfection of molybdenum and tungsten single crystals. J Cryst Growth. https://doi.org/10.1016/0022-0248(88)90353-310.1016/0022-0248(88)90353-3 ↗
47. Dorn JE, Rajnak S (1964) Nucleation of kink pairs and the Peierls mechanism of plastic deformation. Trans Metall Soc AIME 230:1052–1064
48. Ritchie IG, Fantozzi G (1992) In: Nabarro FRN (ed) Dislocations in solids, vol 9. Dislocations and dislocations. North-Holland, Amsterdam, pp 57–134
49. Blanter MS (2007) Internal friction in metallic materials: a handbook. Springer series in materials science 90. Springer, Berlin, DEU, https://doi.org/10.1007/978-3-540-68758-010.1007/978-3-540-68758-0 ↗
50. Seeger A (1956) On the theory of the low-temperature internal friction peak observed in metals. Philos Mag. https://doi.org/10.1080/1478643560824400010.1080/14786435608244000 ↗
51. Seeger A (1981) The temperature and strain rate dependence of the flow stress of body-centered cubic metals: a theory based on kink-kink interactions. Z Metallkde 72(6):369–380
52. Seeger A (1995) The flow stress of high-purity refractory body-centred cubic metals and its modification by atomic defects. J Phys IV France. https://doi.org/10.1051/jp4:199570410.1051/jp4:1995704 ↗
53. Hollang L, Hommel M, Seeger A (1997) The flow stress of ultra-high-purity molybdenum single crystals. Phys Status Solidi A. https://doi.org/10.1002/1521-396X(199704)160:2%3c329::AID-PSSA329%3e3.0.CO;2-O10.1002/1521-396X(199704)160:2%3c329::AID-PSSA329%3e3.0.CO;2-O ↗
54. Seeger A (2001) Why anomalous slip in body-centred cubic metals? Mater Sci Eng A. 1:2. https://doi.org/10.1016/S0921-5093(01)00958-310.1016/S0921-5093(01)00958-3 ↗
55. Guaranteed chem. composition for tungsten Plansee SE. https://www.plansee.com/de/werkstoffe/wolfram.html. Accessed 1 Nov 2018
56. Trefilov VI, Milman YV (1989) In: Bildstein H, Ortner HM (eds) 12th international plansee seminar '89: proceedings: high temperature and wear resistant materials in a world of changing technology. May 8th to 12th, 1989, Reutte, Tirol, Austria. Metallwerk Plansee, Reutte, AUT, pp 107–131
57. Wei Q, Kecskes LJ (2008) Effect of low-temperature rolling on the tensile behavior of commercially pure tungsten. Mater Sci Eng A. https://doi.org/10.1016/j.msea.2008.01.01310.1016/j.msea.2008.01.013 ↗
58. Lassner E, Schubert W-D (1999) Tungsten: properties, chemistry, technology of the element, alloys and chemical compounds. Kluwer Academic/Plenum Publishers, New York. https://doi.org/10.1007/978-1-4615-4907-910.1007/978-1-4615-4907-9 ↗
59. Hansen N, Barlow CY (2014) In: Laughlin DE, Hōno K (eds) Physical metallurgy, 5th edn. Elsevier, Amsterdam, NLD, pp 1681–1764, https://doi.org/10.1016/B978-0-444-53770-6.00017-410.1016/B978-0-444-53770-6.00017-4 ↗
60. Wiegleb G (2016) Gasmesstechnik in Theorie und Praxis. (textbook in German language). Springer Vieweg, Wiesbaden, DEU, https://doi.org/10.1007/978-3-658-10687-410.1007/978-3-658-10687-4 ↗
61. Harris DC (2015) Quantitative chemical analysis, 9th edn. W.H. Freeman and Company, New York, NY
62. ASTM International (2019) Test method for linear-elastic plane-strain fracture toughness KIc of metallic materials, 19th edn, West Conshohocken, PA, USA. ASTM International (E399)
63. Palacios T, Pastor JY (2015) Influence of the notch root radius on the fracture toughness of brittle metals: nanostructure tungsten alloy, a case study. Int J Refract Met Hard Mater. https://doi.org/10.1016/j.ijrmhm.2015.05.01210.1016/j.ijrmhm.2015.05.012 ↗
64. Kong BS, Shin JH, Jang C, Kim HC (2020) Measurement of fracture toughness of pure tungsten using a small-sized compact tension specimen. Materials. https://doi.org/10.3390/ma1301024410.3390/ma13010244 ↗
65. Abernethy RG, Gibson JSK-L, Giannattasio A, Murphy JD, Wouters O, Bradnam S, Packer LW, Gilbert MR, Klimenkov M, Rieth M, Schneider H-C, Hardie CD, Roberts SG, Armstrong DEJ (2019) Effects of neutron irradiation on the brittle to ductile transition in single crystal tungsten. J Nucl Mater. https://doi.org/10.1016/j.jnucmat.2019.15179910.1016/j.jnucmat.2019.151799 ↗
66. Lefort P (1978) Stress intensity factors for a circumferential crack emanating from a notch in a round tensile bar. Eng Fract Mech 1:2. https://doi.org/10.1016/0013-7944(78)90043-710.1016/0013-7944(78)90043-7 ↗
67. Damani R, Gstrein R, Danzer R (1996) Critical notch-root radius effect in SENB-S fracture toughness testing. J Eur Ceram Soc. https://doi.org/10.1016/0955-2219(95)00197-210.1016/0955-2219(95)00197-2 ↗
68. Schwalbe K-H, Neale B (1995) A procedure for determining the fracture behaviour of materials: the unified fracture mechanics test method EFAM GTP 94. Fat Frac Eng Mat Struct. https://doi.org/10.1111/j.1460-2695.1995.tb01185.x10.1111/j.1460-2695.1995.tb01185.x ↗
69. Murakami Y (ed) (1987) Stress intensity factors handbook. Pergamon Press, Oxford, GBR
70. Rice JR, Paris PC, Merkle JG (1973) In: Kaufman JG, Swedlow JL, Corten HT, Srawley JE, Heyer RH, Wessel ET, Irwin GR (eds) Progress in flaw growth and fracture toughness testing. ASTM International, West Conshohocken, PA, USA
71. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech. https://doi.org/10.1115/1.360120610.1115/1.3601206 ↗
72. European Structural Intergrity Society (1992) ESIS procedure for determining the fracture behaviour of materials: TC1 Subcommittee on Fracture Mechanics Testing Standards, Delft, NLD (ESISP2-92)
73. EricksonKirk MA, EricksonKirk MT, Rosinski S, Spanner J (2009) A comparison of the tanh and exponential fitting methods for Charpy V-notch energy data. Int J Press Vessels Pip. https://doi.org/10.1115/1.310998710.1115/1.3109987 ↗
74. Viehrig H-W, Zurbuchen C, Schindler H-J, Kalkhof D (2010) Application of the Master Curve approach to fracture mechanics characterisation of reactor pressure vessel steel. Wissenschaftlich-Technische Berichte, Dresden, DEU
75. Campbell RW, Dickinson CD (1963) In: Ault GM, Barclay WF, Munger HP (eds) High temperature materials II: Proceedings of technical conference on high temperature materials II. Conference held in Cleveland, Ohio, April 26–27, 1961. Interscience Publishers, New York, NY, USA, pp 655–668
76. Stephens JR (1964) Effects of interstitial impurities on the low-temperature tensile properties of tungsten. NASA Technical Note, Washington D.C.
77. Pan Z, Kecskes LJ, Wei Q (2014) The nature behind the preferentially embrittling effect of impurities on the ductility of tungsten. Comput Mater Sci. https://doi.org/10.1016/j.commatsci.2014.06.03610.1016/j.commatsci.2014.06.036 ↗
78. Hu Y-J, Fellinger MR, Bulter BG, Wang Y, Darling KA, Kecskes LJ, Trinkle DR, Liu Z-K (2017) Solute-induced solid-solution softening and hardening in bcc tungsten. Acta Mater. https://doi.org/10.1016/j.actamat.2017.09.01910.1016/j.actamat.2017.09.019 ↗
79. Samolyuk GD, Osetsky YN, Stoller RE (2013) The influence of transition metal solutes on the dislocation core structure and values of the Peierls stress and barrier in tungsten. J Phys Condens Matter. https://doi.org/10.1088/0953-8984/25/2/02540310.1088/0953-8984/25/2/025403 ↗
80. Rupp D, Weygand SM (2010) Anisotropic fracture behaviour and brittle-to-ductile transition of polycrystalline tungsten. Philos Mag. https://doi.org/10.1080/14786435.2010.50419810.1080/14786435.2010.504198 ↗
81. Meyers MA (1994) Dynamic behavior of materials. Wiley, New York. https://doi.org/10.1002/978047017227810.1002/9780470172278 ↗
82. Riedle J (1995) Bruchwiderstand in Wolfram-Einkristallen: Einfluß der kristallographischen Orientierung, der Temperatur und der Lastrate: (PhD-thesis in German language). Dissertation. Fortschritt-Berichte VDI Reihe 18, Mechanik, Bruchmechanik 184. VDI-Verl., Stuttgart, DEU
83. Magnusson AW, Baldwin WM Jr (1957) Low temperature brittleness. J Mech Phys Solids. https://doi.org/10.1016/0022-5096(57)90003-010.1016/0022-5096(57)90003-0 ↗
84. Harmon EL (1960) Investigation of the properties of tungsten and its alloys. WADD Technical Report, Wright-Patterson Air Force Base, OH, USA
85. Chilton AC, Wronski AS (1969) The effects of strain rate and pressurization on the ductile-brittle transition temperature of polycrystalline sintered tungsten. J Less Common Metals. https://doi.org/10.1016/0022-5088(69)90071-X10.1016/0022-5088(69)90071-X ↗
86. Andresen PL (2016) In: Féron D, Staehle RW (eds) Stress corrosion cracking of nickel-based alloys in water-cooled nuclear: The coriou effect. Woodhead Publishing, Duxford, GBR, pp 169–238, https://doi.org/10.1016/B978-0-08-100049-6.00005-710.1016/B978-0-08-100049-6.00005-7 ↗
87. Hahn GT, Hoagland RG, Rosenfield AR (1971) The variation of K1C with temperature and loading rate. Metall Trans A. https://doi.org/10.1007/BF0266334610.1007/BF02663346 ↗
88. Kocks UF, Argon AS, Ashby MF (1975) Thermodynamics and kinetics of slip, 1st edn. Progress in materials science 19. Pergamon Press, Oxford, GBR
89. Po G, Cui Y, Rivera D, Cereceda D, Swinburne TD, Marian J, Ghoniem N (2016) A phenomenological dislocation mobility law for bcc metals. Acta Mater. https://doi.org/10.1016/j.actamat.2016.08.01610.1016/j.actamat.2016.08.016 ↗
90. Seeger A (2002) Peierls barriers, kinks, and flow stress: recent progress. Z Metallkde. https://doi.org/10.3139/146.02076010.3139/146.020760 ↗
91. Anderson PM, Hirth JP, Lothe J (2017) Theory of dislocations, 3rd edn. Cambridge Univ. Press, New York
92. Arsenault RJ (1975) In: Arsenault RJ (ed) Plastic deformation of materials. Academic Press, New York, NY, USA, pp 1–99, https://doi.org/10.1016/B978-0-12-341806-7.50008-810.1016/B978-0-12-341806-7.50008-8 ↗
93. Seeger A (1957) Dislocations and mechanical properties of crystals. In: Fisher JC
94. (ed) International conference held at Lake Placid, September 6-8, 1956. Wiley, New York, NY, USA, pp 243-329
95. Schulze V, Vöhringer O (2001) In: Buschow KHJ (ed) Encyclopedia of materials: Science and technology. Pergamon, Oxford, GBR, pp 7050–7064, https://doi.org/10.1016/B0-08-043152-6/01250-X10.1016/B0-08-043152-6/01250-X ↗
96. Šesták B, Seeger A (1978) Gleitung und Verfestigung in kubisch-raumzentrierten Metallen und Legierungen (II). (paper in German language). Z. Metallkde. 69(6):355–36310.1515/ijmr-1978-690601 ↗
97. Caillard D (2018) Geometry and kinetics of glide of screw dislocations in tungsten between 95K and 573K. Acta Mater. https://doi.org/10.1016/j.actamat.2018.09.00910.1016/j.actamat.2018.09.009 ↗
98. Gröger R, Bailey AG, Vitek V (2008) Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of ½%3c111%3e screw dislocations at 0 K. Acta Mater, https://doi.org/10.1016/j.actamat.2008.07.01810.1016/j.actamat.2008.07.018 ↗
99. Srivastava K, Gröger R, Weygand D, Gumbsch P (2013) Dislocation motion in tungsten: Atomistic input to discrete dislocation simulations. Int J Plast. https://doi.org/10.1016/j.ijplas.2013.01.01410.1016/j.ijplas.2013.01.014 ↗
100. Marichal C, Swygenhoven H, van Petegem S, van Borca C (2013) 110 slip with 112 slip traces in bcc Tungsten. Sci Rep. https://doi.org/10.1038/srep0254710.1038/srep02547 ↗