Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

High Strain Rate Metal Plasticity

  • Lewis J. LeaEmail author
  • Stephen M. Walley
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_219-1

Synonyms

Definitions

Adiabatic

Without the transfer of heat from the system to its surroundings.

BCC

Body-centered cubic, a Bravais lattice type adopted by metals.

Dislocation

Linear defect in a lattice arising from broken or mismatched bonds.

FCC

Face-centered cubic, a Bravais lattice type adopted by metals.

HCP

Hexagonal close packed, a Bravais lattice type adopted by metals.

HEL

Hugoniot elastic limit; the elastic limit in shock deformation.

Slip

Deformation resulting from dislocation motion.

Introduction

This section will discuss empirical observations and physical pictures describing the intermediate to high strain rate behavior of metals undergoing plastic deformation. While many other material types exist, bulk metals readily lend themselves to continuum modelling, which is not as readily applied to types such as composites, foams, or metamaterials. Twinning and failure are briefly discussed,...

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References

  1. Al’shitz V, Indenbom V (1975) Dynamic dragging of dislocations. Soviet Physics Uspekhi 18:1–20. https://doi.org/10.1070/PU1975v018n01ABEH004689 CrossRefGoogle Scholar
  2. Altshuler L, Bakanova A, Brazhnik M, Zhuchikhin V, Kormer S, Krupnikov K, Trunin R (1995) Shock Hugoniot of uranium measured at pressures through 4 TPa inclusive. Chem Phys Rep 14:205–207Google Scholar
  3. Altshuler L, Zeldovich Y, Styazhkin Y (1997) Investigation of isentropic compression and equations of state of fissionable materials. Physics Uspekhi 40:101–102CrossRefGoogle Scholar
  4. Anderson P, Hirth J, Lothe J (2017) Theory of dislocations, 3rd edn. Cambridge University Press, New YorkzbMATHGoogle Scholar
  5. Anderson T (1994) Fracture mechanics. CRC Press, Boca RatonGoogle Scholar
  6. Andrew S, Caliguri R, Eiselstein L (1992) Relationship between dynamic properties and penetration mechanisms of tungsten and depleted uranium penetrators. In: Persson A, Andersson K, Björck E (eds) Proceedings 13th international symposium ballistics, vol 3. National Defence Research Establishment, Sundyberg, pp 249–256Google Scholar
  7. Armstrong R (1967) Relation between the Petch friction stress and the thermal activation rate equation. Acta Metall 15:667–668. https://doi.org/10.1016/0001-6160(67)90118-6 CrossRefGoogle Scholar
  8. Armstrong R, Li Q (2015) Dislocation mechanics of high-rate deformations. Metall Mater Trans A 46:4438–4453. https://doi.org/10.1007/s11661-015-2779-6 CrossRefGoogle Scholar
  9. Armstrong R, Walley S (2008) High strain rate properties of metals and alloys. Int Mater Rev 53:105–128. https://doi.org/10.1179/174328008X277795 CrossRefGoogle Scholar
  10. Armstrong R, Arnold W, Zerilli F (2009) Dislocation mechanics of copper and iron in high rate deformation tests. J Appl Phys 105:023511. https://doi.org/10.1063/1.3067764 CrossRefGoogle Scholar
  11. Arrhenius S (1889) Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren. Z Phys Chem 4:226–248Google Scholar
  12. Asay J, Shahinpoor ME (1993) High-pressure shock compression of solids. Springer, New YorkzbMATHCrossRefGoogle Scholar
  13. Atkins A, Mai Y (1985) Elastic and plastic fractire. Ellis Horwood, LondonGoogle Scholar
  14. Austin R, McDowell D (2011) A dislocation-based constitutive model for viscoplastic deformation of FCC metals at very high strain rates. Int J Plast 27:1–24. https://doi.org/10.1016/j.ijplas.2010.03.002 CrossRefGoogle Scholar
  15. Averyanova T, Mirkin L, Pilipetskii N, Rustamov A (1965) The action of intense light beams on metal surfaces. J Appl Mech Tech Phys 6(6):54–57CrossRefGoogle Scholar
  16. Bai Y, Dodd B (1992) Adiabatic shear localisation, occurance, theories and applications. Pergamon Press, OxfordGoogle Scholar
  17. Basov N, Krokhin O, Sklizkov G (1967) Formation of shock waves with the aid of powerful laser radiation. JETP Lett 6:168–171Google Scholar
  18. Bauschinger J (1886) On the changes of the elastic limit and the strength of iron by straining in tension and in compression (in German). Mittheilungen aus dem Mechanisch-Technischen Laboboratorium der Koniglichen Technischen Hochschule in Munchen 13:1–115Google Scholar
  19. Benedick W (1965) Nitroguanidine explosive plane wave generator for producing low amplitude shock waves. Rev Sci Instrum 36:1309–1315CrossRefGoogle Scholar
  20. Bitzek E, Gumbsch P (2004) Atomistic study of drag, surface and inertial effects on edge dislocations in face-centered cubic metals. Mater Sci Eng A 387:11–15. https://doi.org/10.1016/j.msea.2004.01.092 CrossRefGoogle Scholar
  21. Bitzek E, Gumbsch P (2005) Dynamic aspects of dislocation motion: atomistic simulations. Mater Sci Eng A 400:40–44. https://doi.org/10.1016/j.msea.2005.03.047. dislocations 2004zbMATHCrossRefGoogle Scholar
  22. Brace W, Jones A (1971) Comparison of uniaxial deformation in shock and static loading of three rocks. J Geophys Res 76:4913–4921CrossRefGoogle Scholar
  23. Brailsford A (1972) Anharmonicity contributions to dislocation drag. J Appl Phys 43:1380–1393. https://doi.org/10.1063/1.1661329 CrossRefGoogle Scholar
  24. Brown L (2012) Constant intermittent flow of dislocations: central problems in plasticity. Mater Sci Technol 28:1209–1232. https://doi.org/10.1179/174328412X13409726212768 CrossRefGoogle Scholar
  25. Brown S, Kim K, Anand L (1989) An internal variable constitutive model for hot working of metals. Int J Plast 5:95–130. https://doi.org/10.1016/0749-6419(89)90025-9 zbMATHCrossRefGoogle Scholar
  26. Burgers J, Burgers W (1956) Dislocations in crystal lattices. In: Eirich FR (ed) Rheology. Academic Press, New York, pp 141–199Google Scholar
  27. Bush V, Conant J, Adams L (1946) Hypervelocity guns and the control of gun erosion. National Defense Research Committee, WashingtonGoogle Scholar
  28. Chhabildas L, Davison L, Horie Y (2005) High-pressure shock compression of solids. VIII: the science and technology of high-velocity impact. Springer, BerlinGoogle Scholar
  29. Cochran S, Banner D (1977) Spall studies in uranium. J Appl Phys 48:2729–2737CrossRefGoogle Scholar
  30. Cottrell A (1964) Theory of crystal dislocations. Blackie and Son, LondonzbMATHGoogle Scholar
  31. Couque H (2014) The use of the direct impact Hopkinson pressure bar technique to describe thermally activated and viscous regimes of metallic materials. Phil Trans R Soc A 372:20130218.  https://doi.org/10.1098/rsta.2013.0218 CrossRefGoogle Scholar
  32. Dandekar D, Martin A, Kelley J (1980) Deformation of depleted uranium – 0.78 titanium under shock compression to 11.0 GPa at room temperature. J Appl Phys 51:4784–4789CrossRefGoogle Scholar
  33. Davison L, Graham R (1979) Shock compression of solids. Phys Rep 55:255–379CrossRefGoogle Scholar
  34. Davison L, Shahinpoor ME (1998) High-pressure shock compression of solids III. Springer, BerlinCrossRefGoogle Scholar
  35. Davison L, Grady D, Shahinpoor M (1996) High-pressure shock compression of solids II: dynamic fracture and fragmentation. Springer, BerlinzbMATHCrossRefGoogle Scholar
  36. Davison L, Horie Y, Shahinpoor ME (1997) High-pressure shock compression of solids IV: response of highly porous solids to shock compression. Springer, BerlinCrossRefGoogle Scholar
  37. Davison L, Horie Y, Sekine Te (2003) High-pressure shock compression of solids V: shock chemistry with applications to meteorite impacts. Springer, BerlinCrossRefGoogle Scholar
  38. de Beaumont P, Leygonie J (1970) Vaporizing of uranium after shock loading. In: Proceedings fifth symposium (international) on detonation, Office of Naval Research, Arlington, pp 547–558Google Scholar
  39. Dimiduk D, Uchic M, Parthasarathy T (2005) Size-affected single-slip behavior of pure nickel microcrystals. Acta Mater 53:4065–4077. https://doi.org/10.1016/j.actamat.2005.05.023 CrossRefGoogle Scholar
  40. Dodd B, Bai Y (1987) Ductile fracture and ductility. Academic Press Inc., LondonGoogle Scholar
  41. Dodd B, Bai Y (2012) Adiabatic shear localization frontiers and advances. Elsevier, AmsterdamGoogle Scholar
  42. Eshelby J (1953) The equation of motion of a dislocation. Phys Rev 90:248–255.  https://doi.org/10.1103/PhysRev.90.248 MathSciNetzbMATHCrossRefGoogle Scholar
  43. Follansbee P, Kocks U (1988) A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metall 36:81–93. https://doi.org/10.1016/0001-6160(88)90030-2 CrossRefGoogle Scholar
  44. Follansbee P, Regazzoni G, Kocks U (1984) The transition to drag-controlled deformation in copper at high strain rates. Inst Phys Conf Ser 70:71–80Google Scholar
  45. Forquin P, Zinszner JL (2017) A pulse-shaping technique to investigate the behaviour of brittle materials subjected to plate-impact tests. Phil Trans R Soc A 375:20160333CrossRefGoogle Scholar
  46. Fortov V, Altshuler L, Trunin R, Funtikov A (2004) High-pressure shock compression of solids VII. Springer, BerlinCrossRefGoogle Scholar
  47. Fowles G, Duvall G, Asay J, Bellamy P, Feistman F, Grady D, Michaels T, Mitchell R (1970) Gas gun for impact studies. Rev Sci Instrum 41:984–996CrossRefGoogle Scholar
  48. Gao C, Zhang L (2012) Constitutive modelling of plasticity of fcc metals under extremely high strain rates. Int J Plast 32:121–133. https://doi.org/10.1016/j.ijplas.2011.12.001 CrossRefGoogle Scholar
  49. Gilman J (1960) The plastic resistance of crystals. Aust J Phys 13:327–346CrossRefGoogle Scholar
  50. Golubev V (2012) Strength and fracture of uranium, plutonium and several of their alloys under shock wave loading. EPJ Web Conf 26:02015CrossRefGoogle Scholar
  51. Gorham D (1991) An effect of specimen size in the high strain rate compression test. J Phys IV France 1(C3):411–418CrossRefGoogle Scholar
  52. Gorham D, Pope P, Field J (1992) An improved method for compressive stress-strain measurements at very high strain rates. Proc R Soc A 438:153–170.  https://doi.org/10.1098/rspa.1992.0099 zbMATHCrossRefGoogle Scholar
  53. Gorman JA, Wood DS, Vreeland T Jr (1969) Mobility of dislocations in aluminum. J Appl Phys 40:833–841. https://doi.org/10.1063/1.1657472 CrossRefGoogle Scholar
  54. Goto DM, Garrett RK, Bingert JF, Chen SR, Gray GT (2000) The mechanical threshold stress constitutive-strength model description of hy-100 steel. Metall Mater Trans A 31:1985–1996. https://doi.org/10.1007/s11661-000-0226-8 CrossRefGoogle Scholar
  55. Gould P, Goldthorpe B (2000) A path-dependent constitutive model for gilding copper. J Phys IV France 10 (Pr.9):39–44. https://doi.org/10.1051/jp4:2000907 Google Scholar
  56. Gray III G (1994) Deformation twinning: influence of strain rate. In: Yoo MH, Wuttig M (Eds) Twinning in advanced materials. TMS, Warrendale, pp 337–349Google Scholar
  57. Gray III G (2012) High-strain-rate deformation: mechanical behavior and deformation substructures induced. Ann Rev Mater Res 42:285–303CrossRefGoogle Scholar
  58. Gray III G, Bourne N, Henrie B, Millett J (2003) Influence of shock-wave profile shape (triangular – Taylor-wave versus square-topped) on the spallation response of 316L stainless steel. J Phys IV France 110:773–778CrossRefGoogle Scholar
  59. Gray III G, Bourne N, Millett J, Lopez M (2004) Influence of shock-wave profile shape (‘Taylor-wave’ versus square-topped) on the shock-hardening and spallation response of 316L stainless steel. AIP Conf Proc 706:461–464CrossRefGoogle Scholar
  60. Gray III G, Cady C, McCabe R, Hixson R, Korzekwa D, Lopez M (2006) Influence of energetic-driven ’Taylor-wave’ shock-wave prestraining on the structure/property response of depleted uranium. J Phys IV France 134:909–914CrossRefGoogle Scholar
  61. Grunschel S, Clifton R, Jiao T (2012) Shearing resistance of aluminum at high strain rates and at temperatures approaching melt. AIP Conf Proc 1426:1335–1338. https://doi.org/10.1063/1.3686527 CrossRefGoogle Scholar
  62. Gurrutxaga-Lerma B, Shehadeh M, Balint D, Dini D, Chen L, Eakins D (2017) The effect of temperature on the elastic precursor decay in shock loaded FCC aluminium and BCC iron. Int J Plast 96:135–155. https://doi.org/10.1016/j.ijplas.2017.05.001 CrossRefGoogle Scholar
  63. Hall EO (1951) The deformation and ageing of mild steel: III discussion of results. Proc Phys Soc Sect B 64:747–753. https://doi.org/10.1088/0370-1301/64/9/303 CrossRefGoogle Scholar
  64. Hansen B, Beyerlein I, Bronkhorst C, Cerreta E, Dennis-Koller D (2013) A dislocation-based multi-rate single crystal plasticity model. Int J Plast 44:129–146. https://doi.org/10.1016/j.ijplas.2012.12.006 CrossRefGoogle Scholar
  65. Herrmann B, Landau A, Shvarts D, Favorsky V, Zaretsky E (2002) Modeling of uranium alloy response in plane impact and reverse ballistic experiments. AIP Conf Proc 620:1306–1309CrossRefGoogle Scholar
  66. Hirth J, Lothe J (1968) Theory of dislocations, 1st edn. McGraw-Hill, New-YorkzbMATHGoogle Scholar
  67. Holzer F (1965) Measurements and calculations of peak shock-wave parameters from underground nuclear detonations. J Geophys Res 70:893–905CrossRefGoogle Scholar
  68. Horie Y (2007) Shock wave science and technology reference library. 2: solids I. Springer, BerlinGoogle Scholar
  69. Horie Y (2009) Shock wave science and technology reference library. 3: solids II. Springer, BerlinGoogle Scholar
  70. Horie Y, Davison L, Thadhani N (2003) High-pressure shock compression of solids. VI: old paradigms and new challenges. Springer, New YorkGoogle Scholar
  71. Huang M, Riverz-Díaz-del Castillo P, Bouaziz O (2009) A constitutive model for high strain rate deformation in FCC metals based on irreversible thermodynamics. Mech Mater 41:982–988CrossRefGoogle Scholar
  72. Hugoniot H (1888) Mémoire sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits. 1 J École Polytech 57:3–97Google Scholar
  73. Hugoniot H (1889) Mémoire sur la propagation du mouvement dans les corps et spcialement dans les gaz parfaits. 2 J École Polytech 58:1–125Google Scholar
  74. Hugoniot H (1998) On the propagation of motion in bodies and in perfect gases in particular. In: Johnson JN, Chéret R (eds) Classic papers in shock compression science. Springer, Berlin, pp 161–358CrossRefGoogle Scholar
  75. Hunter A, Preston DL (2015) Analytic model of the remobilization of pinned glide dislocations from quasi-static to high strain rates. Int J Plast 70:1–29. https://doi.org/10.1016/j.ijplas.2015.01.008 CrossRefGoogle Scholar
  76. Huntington H (1955) Modification of the Peierls-Nabarro model for edge dislocation core. Proc Phys Soc Lond B 68:1043–1048zbMATHCrossRefGoogle Scholar
  77. Johnson J, Chéret R (1998) Classic papers in shock compression science. Springer, New-YorkzbMATHCrossRefGoogle Scholar
  78. Johnson P (1983) Tungsten versus depleted uranium for armour-piercing penetrators. Int J Refract Hard Metals 3:179–182Google Scholar
  79. Johnston W, Gilman J (1959) Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J Appl Phys 30:129–144. https://doi.org/10.1063/1.1735121 CrossRefGoogle Scholar
  80. Jones AH, Isbell WM, Maiden CI (1966) Measurement of the very high pressure properties of materials using a light gas gun. J Appl Phys 37:3493–3499CrossRefGoogle Scholar
  81. Jordan J, Siviour C, Sunny G, Bramlette C, Spowart J (2013) Strain rate-dependant mechanical properties of ofhc copper. J Mater Sci 48:7134–7141. https://doi.org/10.1007/s10853-013-7529-9 CrossRefGoogle Scholar
  82. Kamimura Y, Edagawa K, Takeuchi S (2012) Experimental evaluation of the Peierls stresses in a variety of crystals and their relation to the crystal structure. Acta mater 61:294–309CrossRefGoogle Scholar
  83. Kanel G, Fortov V, Razorenov S (2007) Shock waves in condensed-state physics. Physics-Uspekhi 50:771–781CrossRefGoogle Scholar
  84. Kanel GI (2014) Unusual behaviour of usual materials in shock waves. J Phys Conf Ser 500:012001CrossRefGoogle Scholar
  85. 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 90:136–143. https://doi.org/10.1063/1.1374478 CrossRefGoogle Scholar
  86. Klepaczko J (1975) Thermally activated flow and strain rate history effects for some polycrystalline FCC metals. Mater Sci Eng 18:121–135CrossRefGoogle Scholar
  87. Kocks U, Mecking H (2003) Physics and phenomenology of strain hardening: the FCC case. Prog Mater Sci 48:171–273. https://doi.org/10.1016/S0079-6425(02)00003-8 CrossRefGoogle Scholar
  88. Kocks U, Argon A, Ashby M (1975) Thermodynamics and kinetics of slip. Prog Mater Sci 19:1–288CrossRefGoogle Scholar
  89. Kocks UF, Tomé CN, Wenk HR (2000) Texture and anisotropy: preferred orientations in polycrystals and their effect on materials properties. Cambridge university Press, CambridgezbMATHGoogle Scholar
  90. Kozlov E, Litvinov B, Timofeeva L, Kurilo V, Orlov V (1996) Structural changes, phase transformations, and spalling in a sphere of delta-plutonium-gallium alloy in spherical stress waves. Phys Metals Metallog 81: 679–691Google Scholar
  91. Krehl P (2001) History of shock waves. In: Ben-Dor G, Igra O, Elperin T (eds) Handbook of shock waves vol 1. Academic Press, New York, pp 1–142. https://doi.org/10.1016/B978-012086430-0/50003-8 Google Scholar
  92. Krehl P (2009) History of shock waves, explosions and impact: a chronological and biographical reference. Springer, BerlinGoogle Scholar
  93. Krehl P (2011) Shock wave physics and detonation physics: a stimulus for the emergence of numerous new branches in science and engineering. Eur Phys J H 36:85–152CrossRefGoogle Scholar
  94. Krehl P (2015) The classical Rankine-Hugoniot jump conditions, an important cornerstone of modern shock wave physics: ideal assumptions vs. reality. Eur Phys J H 40:159–204CrossRefGoogle Scholar
  95. Kubin L, Madec R, Devincre B (2003) Dislocation intersections and reactions in FCC and BCC crystals. MRS Proc 779:25–36.  https://doi.org/10.1557/PROC-779-W1.6 Google Scholar
  96. Kuksin AY, Yanilkin AV (2013) Atomistic simulation of the motion of dislocations in metals under phonon drag conditions. Phys Solid State 55:1010–1019. https://doi.org/10.1134/S1063783413050193 CrossRefGoogle Scholar
  97. LaLone B, Gupta Y (2009) Elastic limit of x-cut quartz under shockless and shock wave compression: loading rate dependence. J Appl Phys 106:053526CrossRefGoogle Scholar
  98. Lea L (2018) Structural evolution in the dynamic plasticity of FCC metals. PhD Thesis, Cambridge University.  https://doi.org/10.17863/CAM.20971
  99. Lea L, Jardine A (2018) Characterisation of high rate plasticity in the uniaxial deformation of high purity copper at elevated temperatures. Int J Plast 41–52. https://doi.org/10.1016/j.ijplas.2017.11.006 CrossRefGoogle Scholar
  100. Leibfried G (1950) Über den einfluß thermisch angeregter Schallwellen auf die plastische deformation. Zeitschrift für Physik 127:344–356. https://doi.org/10.1007/BF01329831 MathSciNetzbMATHCrossRefGoogle Scholar
  101. Lothe J (1962) Theory of dislocation mobility in pure slip. J Appl Phys 33:2116–2125. https://doi.org/10.1063/1.1728907 CrossRefGoogle Scholar
  102. Magness L (2002) An overview of the penetration performances of tungsten and depleted uranium alloy penetrators: ballistic performances and metallographic examinations. In: Carleone J, Orphal D (eds) Proceedings of 20th international symposium on ballistics. National Defense Industrial Association, Lancaster, pp 1104–1111Google Scholar
  103. Maloy S, Gray III G, Cady C, Rutherford R, Hixson R (2004) The influence of explosive-driven ’Taylor-wave’ shock prestraining on the structure/property behavior of 304 stainless steel. Metall Mater Trans A 35:2617–2624CrossRefGoogle Scholar
  104. Marsh S (1980) LASL shock Hugoniot data. University of California Press, BerkeleyGoogle Scholar
  105. Meyers M (1994) Dynamic behavior of materials. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  106. Meyers M, Andrade U, Choksh I (1995) The effect of grain size on the high-strain, high-strain-rate behavior of copper, Metall Mater Trans A 26:2881–2893CrossRefGoogle Scholar
  107. Meyers M, Vöhringer O, Lubarda V (2001) The onset of twinning in metals: a constitutive description. Acta Mater 49:4025–4039. https://doi.org/10.1016/S1359-6454(01)00300-7 CrossRefGoogle Scholar
  108. Meyers M, Benson D, Vöhringer O, Kad B, Xue Q, Fu HH (2002) Constitutive description of dynamic deformation: physically-based mechanisms. Mater Sci Eng A 322:194–216. https://doi.org/10.1016/S0921-5093(01)01131-5 CrossRefGoogle Scholar
  109. Meyers MA, Aimone CT (1983) Dynamic fracture (spalling) of metals. Prog Mater Sci 28:1–96. https://doi.org/10.1016/0079-6425(83)90003-8 CrossRefGoogle Scholar
  110. Mitchell A, Nellis W, Moriarty J, Heinle R, Holmes N, Tipton R, Repp G (1991) Equation of state of aluminum, copper, molybdenum and lead at shock pressures up to 2.4 TPa (24 Mbar). J Appl Phys 69:2981–2986CrossRefGoogle Scholar
  111. Mullin S, Walker J, Weiss C, Leslie P (2005) Impact and penetration of B4C ceramic, aluminum and beryllium by depleted uranium rods at 2.0 km/s. In: Flis W, Scott B (eds) Proceedings of 22nd international symposium on ballistics. DEStech Publications Inc., Lancaster, pp 917–924Google Scholar
  112. Nabarro F (1980) Fifty-year study of the Peierls-Nabarro stress. Mater Sci Eng A XI:810–814Google Scholar
  113. Nabarro F (1989) The Peierls stress for a wide dislocation. Mater Sci Eng A 113:315–326CrossRefGoogle Scholar
  114. Neuman F (1964) Momentum transfer and cratering effects produced by giant laser pulses. Appl Phys Lett 4:167–169CrossRefGoogle Scholar
  115. Olmsted D, Hector L, Curtin W, Clifton R (2005) Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys. Modell Simul Mater Sci Eng 13:371–388CrossRefGoogle Scholar
  116. Orowan E (1940) Problems of plastic gliding. Proc Phys Soc 52:8–22CrossRefGoogle Scholar
  117. Parameswaran VR, Urabe N, Weertman J (1972) Dislocation mobility in aluminum. J Appl Phys 43:2982–2986. https://doi.org/10.1063/1.1661644 CrossRefGoogle Scholar
  118. Peach M, Koehler J (1950) The forces exerted on dislocations and the stress fields produced by them. Phys Rev 80:436–439MathSciNetzbMATHCrossRefGoogle Scholar
  119. Petch NJ (1953) The cleavage strength of polycrystals. J Iron Steel inst 174:25–28Google Scholar
  120. Preston D, Tonks D, Wallace D (2003) Model of plastic deformation for extreme loading conditions. J Appl Phys 93:211–220. https://doi.org/10.1063/1.1524706 CrossRefGoogle Scholar
  121. Ragan C, Silbert M, Diven B (1977) Shock compression of molybdenum to 2.0 TPa by means of a nuclear explosion. J Appl Phys 47:2860–2870CrossRefGoogle Scholar
  122. Ragan III C (1984) Shock-wave experiments at threefold compression. Phys Rev A 29:1391–1402CrossRefGoogle Scholar
  123. Rankine W (1870) On the thermodynamic theory of waves of finite longitudinal disturbance. Phil Trans R Soc Lond 160:277–288CrossRefGoogle Scholar
  124. Reed B (2015) The physics of the Manhattan Project. Springer, BerlinzbMATHGoogle Scholar
  125. Regazzoni G, Kocks U, Follansbee P (1987) Dislocation kinetics at high strain rates. Acta Metall 35:2865–2875. https://doi.org/10.1016/0001-6160(87)90285-9 CrossRefGoogle Scholar
  126. Remington T, Remington B, Hahn E, Meyers M (2017) Deformation and failure in extreme regimes by high-energy pulsed lasers: a review. Mater Sci Eng A 688:429–458CrossRefGoogle Scholar
  127. Rittel D, Zhang L, Osovski S (2017) The dependence of the Taylor – Quinney coefficient on the dynamic loading mode. J Mech Phys Solids 107:96–114. https://doi.org/10.1016/j.jmps.2017.06.016 CrossRefGoogle Scholar
  128. Roos A, De Hosson J, Cleveringa H, Van der Giessen E (1999) Fast-moving dislocations in high strain rate deformation. University Library Groningen. http://hdl.handle.net/11370/a0c6e779-88a6-4b96-909c-c01c42284332
  129. Salvado F, Teixeira-Dias F, Walley S, Lea L, Cardoso J (2017) A review on the strain rate dependency of the dynamic viscoplastic response of FCC metals. Prog Mater Sci 88:186–231. https://doi.org/10.1016/j.pmatsci.2017.04.004 CrossRefGoogle Scholar
  130. Sorensen B, Kimsey K, Zukas J, Frank K (1998) A penetration model for steel-jacketed depleted uranium penetrators. In: Levine H (ed) Structures under extreme loading conditions. PVP, vol 361. American Society of Mechanical Engineers, New York, pp 331–338Google Scholar
  131. Stokes E (1848) On a difficulty in the theory of sound. Philos Mag (Ser 3) 33:349–356Google Scholar
  132. Strachan A, Çağ ın T, Goddard WA (2001) Critical behavior in spallation failure of metals. Phys Rev B 63:060103.  https://doi.org/10.1103/PhysRevB.63.060103
  133. Swift D, Hawreliak J, Braun D, Kritcher A, Glenzer S, Collins G, Rothman S, Chapman D, Rose S (2012) Gigabar material properties experiments on NIF and OMEGA. AIP Conf Proc 1426:477–480CrossRefGoogle Scholar
  134. Taylor G (1934) The mechanism of plastic deformation of crystals. Proc R Soc Lond A 145:362–404zbMATHCrossRefGoogle Scholar
  135. Taylor G, Quinney H (1934) The latent energy remaining in a metal after cold working. Proc R Soc Lond A 143:307–326.  https://doi.org/10.1098/rspa.1934.0004 CrossRefGoogle Scholar
  136. Taylor J (1968) Hypervelocity impact phenomena. Academic Press, New YorkGoogle Scholar
  137. Thunborg S Jr, Ingram G, Graham R (1964) Compressed gas gun for controlled planar impacts over a wide velocity range. Rev Sci Instrum 35:11–14CrossRefGoogle Scholar
  138. Tinder R, Trzil J (1973) Millimicroplastic burst phenomena in zinc monocrystals. Acta Metall 21:975–989. https://doi.org/10.1016/0001-6160(73)90154-5 CrossRefGoogle Scholar
  139. Trunin R (1998) Shock compression of condensed materials. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  140. Uchic M, Dimiduk D, Wheeler R, Shade P, Fraser H (2006) Application of micro-sample testing to study fundamental aspects of plastic flow. Scr Mater 54:759–764. https://doi.org/10.1016/j.scriptamat.2005.11.016 CrossRefGoogle Scholar
  141. Viswanathan UK, Dey GK, Asundi MK (1993) Precipitation hardening in 350 grade maraging steel. Metall Trans A 24:2429–2442. https://doi.org/10.1007/BF02646522 CrossRefGoogle Scholar
  142. Voce E (1948) The relationship between stress and strain for homogeneous deformation. J Inst Metals 74: 537–562Google Scholar
  143. Voronov F, Vereshchagin L (1961) The influence of hydrostatic pressure on the elastic properties of metals. 1: Experimental data. Phys Metals Metallog 11:111–118Google Scholar
  144. Walker J, Mullin S, Weiss C, Leslie P (2006) Penetration of boron carbide, aluminum, and beryllium alloys by depleted uranium rods: modeling and experimentation. Int J Impact Eng 33:826–836CrossRefGoogle Scholar
  145. Walley S, Field J (2016) Elastic wave propagation in materials. In: Reference module in materials science and materials engineering. Elsevier, Amsterdam. https://doi.org/10.1016/B978-0-12-803581-8.02945-3 CrossRefGoogle Scholar
  146. Walley S, Field J, Pope P, Safford N (2000) Comparison of two methods of measuring the rapid temperature rises in split Hopkinson bar specimens. Rev Sci Instrum 71:1766–1771CrossRefGoogle Scholar
  147. Weertman J (1961) Response of metals to high velocity deformation. Interscience, New-YorkGoogle Scholar
  148. Weertman J, Weertman J (1980) Moving dislocations. In: Nabarro FR ed Dislocations in solids vol 3. North-Holland Publ. Co., Amsterdam, pp 1–60zbMATHGoogle Scholar
  149. Weiss J, Richeton T, Louchet F, Chmelik F, Dobron P, Entemeyer D, Lebyodkin M, Lebedkina T, Fressengeas C, McDonald R (2007) Evidence for universal intermittent crystal plasticity from acoustic emission and high-resolution extensometry experiments. Phys Rev B 76:224110.  https://doi.org/10.1103/PhysRevB.76.224110 CrossRefGoogle Scholar
  150. Wickham L, Schwarz K, Stölken J (1999) Rules for forest interactions between dislocations. Phys Rev Lett 83:4574–4577.  https://doi.org/10.1103/PhysRevLett.83.4574 CrossRefGoogle Scholar
  151. Yoshiaki K, Yoshio H (1975) Lattice thermal conductivity of crystals containing dislocations. J Phys Soc Jpn 38:471–479.  https://doi.org/10.1143/JPSJ.38.471 CrossRefGoogle Scholar
  152. Zerilli F, Armstrong R (1987) Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys 61:1816–1825. https://doi.org/10.1063/1.338024 CrossRefGoogle Scholar
  153. Zhernokletov M (1998) Shock compression and isentropic expansion of natural uranium. High Temp 36:214–221Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The Cavendish LaboratoryUniversity of CambridgeCambridgeUK

Section editors and affiliations

  • Filipe Teixeira-Dias
    • 1
  1. 1.The University of Edinburgh - School of EngineeringEdinburghUK