High strain rate properties of metals and alloys

International Materials Reviews

Volumn 53, Issue 3, 2008, Pages 105-128

  Armstrong, R W ^a   Walley, S M ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Dislocation mechanics; High strain rates; Nanopolycrystals; Shock induced plasticity; Single crystals; Thermal activation

Indexed keywords

CHEMICAL ACTIVATION; COMPRESSION TESTING; DISLOCATIONS (CRYSTALS); POLYCRYSTALS; SENSITIVITY ANALYSIS; STRAIN RATE;

DISLOCATION MECHANICS; HIGH STRAIN RATES; NANOPOLYCRYSTALS; SHOCK INDUCED PLASTICITY; SPLIT HOPKINSON PRESSURE BAR (SHPB) MEASUREMENTS; THERMAL ACTIVATION;

SINGLE CRYSTALS;

EID: 44649180518     PISSN: 09506608     EISSN: None     Source Type: Journal    
DOI: 10.1179/174328008X277795     Document Type: Review

References (225)

1. J. Hopkinson: 'On the rupture of iron wire by a blow', Proc. Manch. Liter. Philos. Soc., 1872, 11, 40-45.
2. J. Hopkinson: 'Further experiments on the rupture of iron wire', Proc. Manch. Liter. Philos. Soc., 1872, 11, 119-121.
3. J. Hopkinson: 'Original papers', 2-'Scientific papers', 316-324; 1901, Cambridge, Cambridge University Press.
4. B. Hopkinson: 'The effects of momentary stresses in metals', Proc. R Soc. Lond, 1905, 74, 498-506.
5. B. Hopkinson: 'A method of measuring the pressure in the detonation of high explosives or by the impact of bullets', Philos. Trans. R Soc. Lond A, 1914, 213A, 437-456.
6. J. Niles, S. Nicolich, D. Doll and N. Rasmussen: 'Mitigating the shaped charge jet impact threat in main charge fill ammunition', in 'Advancements in energetic materials and chemical propulsion', (ed. K. K. Kuo and J. de Dios Rivera), 320-330; 2007, New York, Begell House, Inc.
7. A. G. A. Charpy: 'Note sur L'essai des métaux à la flexion par choc de barreaux entaillés', Mém. CR Soc. Ing. Civ. France, 1901, 848-877.
8. L. Toth, H.-P. Rossmanith and T. A. Siewert: 'Historical background and development of the Charpy test', in 'From Charpy to present impact testing', (ed. D. Francois and A. Pineau), 3-17; 2002, Amsterdam, Elsevier Science Ltd and European Society for Integrity of Structures.
9. H. Tresca: 'On further applications of the flow of solids', Proc. Inst. Mech. Eng., 1878, 30, 301-345.
10. W. Johnson: 'Henri Tresca as the originator of adiabatic heat lines', Int. J. Mech. Sci., 1987, 29, 301-310.
11. W. C. Unwin: 'On the yield point of iron and steel and the effect of repeated straining and annealing', Proc. R Soc. Lond., 1894, 57, 178-187.
12. R. W. Armstrong and F. J. Zerilli: 'Dislocation mechanics based viscoplasticity description of fee, bee, and hcp metal deformation and fracturing behaviors', in 'Proc. ASME Mater. Div.', MD-69-1, 417-428; 1995, New York, ASME.
13. A. W. McReynolds: 'Plastic waves in aluminum', Trans. Am. Inst. Min. Metall. Eng., 1949, 185, 32-45.
14. J. A. Ewing: 'On the measurements of small strains in the testing of materials and structures', Proc. R. Soc. Lond, 1895, 58, 123-142.
15. E. Orowan: 'Notch brittleness and the strength of materials', Trans. Inst. Eng. Shipb. Scotland, 1946, 89, 165-215.
16. J. S. Wark, J. F. Belak, G. W. Collins, J. D. Colvin, H. M. Davies, M. Duchaineau, J. H. Eggert, T. C. Germann, J. Hawreliak, A. Higginbotham, B. L. Holian, K. Kadau, D. H. Kalantar, P. S. Lomdahl, H. E. Lorenzana, M. A. Meyers, B. A. Remington, K. Rosolankova, R. E. Rudd, M. S. Schneider, J. Sheppard and J. S. Stolken: 'Picosecond X-ray diffraction from laser-shocked copper and iron', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP845, 286-291; 2006, New York, American Institute of Physics.
17. A. Considère: 'Mémoire sur l'emploi du fer et de l'acier dans les constructions', Ann. Ponts Chauss., 1885, 9, 574-775.
18. N. P. Sub and R. S. Lee: 'A dislocation model for the delayed yielding phenomenon', Mater. Sci. Eng., 1972, 10, 269-278.
19. W. P. Mason: 'Dislocation drag mechanisms and their effects on dislocation velocities', in 'Dislocation dynamics', (ed. A. R. Rosenfield et al.), 487-505; 1968, New York, McGraw-Hill Book Co.
20. A. N. Stroh: 'Force on a moving dislocation', Phys. Rev., 1962, 128,55-61.
21. J. P. Hirth and J. Lothe: 'Interaction between moving dislocations', in 'Dislocation dynamics', (ed. A. R. Rosenfield et al.), 231-254; 1968, New York, McGraw-Hill Book Co.
22. J. S. Rinehart and J. Pearson: 'Behavior of metals under impulsive loads'; 1954, Metals Park, OH, American Society of Metals.
23. M. A. Meyers: 'Dynamic behavior of materials'; 1994, New York, John Wiley and Sons, Inc.
24. M. Edwards: 'Properties of metals at high rates of strain', Mater. Sci. Technol, 2006, 22, 453-462.
25. Z. Jeffries: 'Effect of temperature, deformation, and grain size on the mechanical properties of metals', Trans. Am. Inst. Min. Metall. Eng., 1919, 60, 474-576.
26. F. Osmond and Ch. Frémont: 'Les propriétés mecanique du fer en cristaux isoles', CR Hebd Séances Acad. Sci. Paris, 1905, 141, 361-363.
27. O. Brezina: 'Untersuchungen uber die zeitgesetze der unelastichen deformation bei zink and flusseisen', Phys. Z., 1923, 24, 338-344.
28. R. Becker: 'Elastische nachwirkung and plastizität', Z. Phys., 1925, 33, 185-213.
29. R. Becker: 'Über die plastizität amorpher and kristalliner fester körper', Phys. Z., 1925, 26, 919-925.
30. R. Becker: 'Plasticity, tenacity and recrystallization (in German)', Z. Tech. Phys., 1926, 7, 547-555.
31. H. Eyring: 'The activated complex in chemical reactions', J. Chem. Phys., 1935, 3, 107-115.
32. H. Eyring: 'Viscosity, plasticity, and diffusion as examples of absolute reaction rate theory', J. Chem. Phys., 1936, 4, 283-291.
33. W. Kauzmann: 'Flow of solid metals from the standpoint of the chemical rate theory', Trans. Am. Inst. Min. Metall. Eng., 1941, 143, 57-81.
34. F. Seitz and T. A. Read: 'Theory of the plastic properties of solids', J. Appl. Phys., 1941, 12, 100-118, 170-186, 470-486, 538-554.
35. E. Orowan: 'Zur kristallplastizitat. III: Uber den mechanismus des gleitvorganges', Z. Phys., 1934, 89, 634-659.
36. M. Polanyi: 'Uber eine art gitterstörung, die einen kristall plastich machen könnte', Z. Phys., 1934, 89, 660-664.
37. G. I. Taylor: 'The mechanism of plastic deformation of crystals. Part 1. Theoretical', Proc. R Soc. Lond A, 1934, 145A, 362ff.
38. E. Schmid and W. Boas: 'Kristallplastizitat'; 1935, Berlin, Julius Springer.
39. E. Orowan: 'Problems of plastic gliding', Proc. Phys. Soc. Lond., 1940, 52, 8-22.
40. J. M. Burgers and W. G. Burgers: 'Dislocations in crystal lattices', in 'Rheology'; (ed. F. R. Eirich), 141-199; 1956, New York, Academic Press.
41. C. Zener and J. H. Hollomon: 'Effect of strain rate upon plastic flow of steel', J. Appl. Phys., 1944, 15, 22-32.
42. G. I. Taylor: 'The testing of materials at high rates of mechanical loading', J. Inst. Civ. Eng., 1946, 26, 486-519.
43. C. S. Barrett and C. T. Haller, Jr: 'Twinning in polycrystalline magnesium', Trans. Am. Inst. Min. Metall. Eng., 1947, 171, 246-255.
44. G. I. Taylor: 'The use of flat-ended projectiles for determining dynamic yield strength. I. Theoretical considerations', Proc. R. Soc. Lond. A, 1948, 194A, 289-299.
45. A. C. Whiffin: 'The use of flat-ended projectiles for determining yield stress. II. Tests on various metallic materials', Proc. R Soc. Lond. A, 1948, 194A, 300-322.
46. W. E. Carrington and M. L. V. Gayler: 'The use of flat-ended projectiles for determining yield stress. III. Changes in microstructure caused by deformation at high striking velocities', Proc. R Soc. Lond. A, 1948, 194A, 323-331.
47. J. B. Hawkyard, D. Eaton and W. Johnson: 'The mean dynamic yield strength of copper and low-carbon steel at elevated temperature from measurements of the mushrooming of flatended projectiles', Int. J. Mech. Sci., 1968, 10, 929-948.
48. D. J. Chapman, D. D. Radford and S. M. Walley: '60 years of Taylor impact and its present use in the study of constitutive relations of materials', Unpublished article.
49. R. M. Davies: 'A critical study of the Hopkinson pressure bar', Philos. Trans. R Soc. Lond A, 1948, 240A, 375-457.
50. H. Kolsky: 'An investigation of the mechanical properties of materials at very high rates of strain', Proc. Phys. Soc. Lond. B, 1949, 62B, 676-700.
51. L. R. Oliver, R. W. Armstrong, R. J. Clifton and H. Kolsky: 'Cleavage of zinc crystals induced by stress waves', Nature, 1967, 216, 910.
52. T. von Karman and P. Duwez: 'The propagation of plastic deformation in solids', J. Appl. Phys., 1950, 21, 987-994.
53. R. W. Armstrong and F. J. Zerilli: 'Dislocation mechanics based analysis of material dynamics behavior', J. Phys. Fr. Colloq., 1988, 49, (C3), 529-534.
54. J. Harding, E. O. Wood and J. D. Campbell: 'Tensile testing of materials at impact rates of strain', J. Mech. Eng. Sci., 1960, 2, 88-96.
55. T. Nicholas: 'Tensile testing of materials at high rates of strain', Exp. Mech., 1981, 215, 177-185.
56. K. A. Hartley, J. Duffy and R. H. Hawley: 'The torsional Kolsky (split Hopkinson) bar', in "Metals handbook", 9th edn, Vol. 8, 218-228; 1985, Metals Park, OH, American Society for Metals.
57. P. S. Follansbee: 'The Hopkinson bar', in 'Metals handbook', 9th edn, Vol. 8, 198-203; 1985, Metals Park, OH, American Society for Metals.
58. G. T. Gray, III: 'Classic split-Hopkinson pressure bar testing', in 'ASM handbook', Vol. 8, 'Mechanical testing and evaluation', 462-476; 2000, Materials Park, OH, ASM International.
59. J. Klepaczko: 'Application of the split Hopkinson pressure bar to fracture dynamics', Inst. Phys. Conf. Ser., 1980, 47, 201-214.
60. J. E. Field, W. G. Proud, S. M. Walley and H. T. Goldrein: 'Review of experimental techniques for high rate deformation and shock studies', in 'New experimental methods in material dynamics and impact', (ed. W. K. Nowacki and J. R. Klepaczko), 109-177; 2001, Warsaw, Institute of Fundamental Technological Research.
61. B. W. Dunn: 'A photographic impact testing machine for measuring the varying intensity of an impulsive force', J. Franklin Inst., 1897, 144, 321-348.
62. K. S. Vecchio and F. Jiang: 'Improved pulse shaping to achieve constant strain rate and stress equilibrium in split Hopkinson pressure bar testing', Metall. Mater. Trans. A, 2007, 38A, 2655-2665.
63. F. Jiang and K. S. Vecchio: 'Dynamic effects in Hopkinson bar four-point bend fracture', Metall. Mater. Trans. A, 2007, 38A, 2896-2906.
64. D. A. Gorham, P. H. Pope and J. E. Field: 'Measurement of stress-strain properties of strong metals at very high strain rates', Inst. Phys. Conf. Ser., 1980, 47, 16-24.
65. D. A. Gorham, P. H. Pope and J. E. Field: 'An improved method for compressive stress-strain measurements at very high strain rates', Proc. R Soc. Lond. A, 1992, 438A, 153-170.
66. -1 using a miniaturized Hopkinson bar with dispersion corrections', Proc. 2nd Int. Symp. on 'Intense dynamic loading and its effects', (ed. G. Zhang and S. Huang), 378-383; 1992, Chengdu, Sichuan University Press.
67. D. Jia and K. T. Ramesh: 'A rigorous assessment of the benefits of miniaturization in the Kolsky bar system', Exp. Mech., 2004, 44, 445-454.
68. C. R. Siviour and J. L. Jordan: 'A miniaturized split Hopkinson pressure bar for very high strain rate testing', Technical Report AFRL-MN-EG-TR-2005- 7014, US Air Force Research Laboratory, Eglin, FL, USA, 2005.
69. J. L. Jordan, C. R. Siviour, J. R. Foley and E. N. Brown: 'Compressive properties of extruded PTFE', Polymer, 2007, 48, 4184-4195.
70. A. Seeger: 'Kristallplastizität', in 'Handbuch der physik VII/2, Crystal Physics II', (ed. S. Flugge), 1-210; 1958, Berlin, Springer.
71. A. R. Rosenfield, G. T. Hahn, A. L. Bement, Jr and R. I. Jaffee (eds.): 'Dislocation dynamics'; 1968, New York, McGraw-Hill Book Co.
72. F. J. Zerilli and R. W. Armstrong: 'Dislocation mechanics based constitutive relations for material dynamics calculations', J. Appl. Phys., 1987, 61, 1816-1825.
73. F. J. Zerilli and R. W. Armstrong: 'Dislocation-mechanics-based constitutive relations for material dynamics modeling: slip and deformation twinning in iron', in 'Shock waves in condensed matter', (ed. S. C. Schmidt and N. C. Holmes), 273-277; 1988, New York, Elsevier Sci. Publ. B.V.
74. F. J. Zerilli and R. W. Armstrong: 'Dislocation mechanics based constitutive relations for dynamic straining to tensile instability', in 'Shock compression of condensed matter - 1989', (ed. S. C. Schmidt et al.), 357-361; 1990, New York, Elsevier Sci. Publ. B.V.
75. F. J. Zerilli and R. W. Armstrong: 'Description of tantalum deformation behavior by dislocation mechanics based constitutive relations', J. Appl. Phys., 1990, 68, 1580-1591.
76. F. J. Zerilli and R. W. Armstrong: 'Modeling shock waves with dislocation mechanics based relations', in 'Shock compression of condensed matter - 1991', (ed. S. C. Schmidt et al.), 257-261; 1992, New York, Elsevier Sci. Publ. B.V.
77. F. J. Zerilli and R. W. Armstrong: 'Constitutive relations for titanium and Ti-6A1-4V', in 'Shock compression of condensed matter - 1995', (ed. S. C. Schmidt and W. C. Tao), 315-318; 1996, New York, American Institute of Physics.
78. F. J. Zerilli and R. W. Armstrong: 'Dislocation mechanics based analysis of material dynamics behavior: enhanced ductility, deformation twinning, shock deformation, shear instability, dynamic recovery', J. Phys. IV France Colloq., 1997, 7, (C3), 637-642.
79. R. W. Armstrong: 'Thermal activation-strain rate analysis (TASRA) for polycrystalline materials', J. Sci. Ind. Res. (Indian), 1973, 32, 591-598.
80. F. J. Zerilli: 'Dislocation mechanics based constitutive relations', Metall. Mater. Trans. A, 2004, 35A, 2547-2555.
81. R. W. Armstrong: 'Yield and flow stress dependence on polycrystal grain size', in 'Yield, flow and fracture of polycrystals', (ed. T. N. Baker), 1-31; 1983, Barking, Applied Science Publishers.
82. J. Klepaczko: 'Thermally activated flow and strain rate history effects for some polycrystalline fee metals', Mater. Sci. Eng., 1975, 18, 121-135.
83. D. E. Eakins and N. N. Thadhani: 'Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states', J. Appl. Phys., 2006, 100, 073503-1-073503-8.
84. D. Eakins and N. N. Thadhani: 'Analysis of dynamic mechanical behavior in reverse Taylor anvil-on-rod impact tests', Int. J. Impact Eng., 2007, 34, 1821-1834.
85. K. G. Hoge and A. K. Mukherjee: 'The temperature and strain rate dependence of the flow stress of tantalum', J. Mater. Sci., 1977, 12, 1666-1672.
86. S. R. Chen, G. T. Gray, III and S. R. Bingert: in 'Tantalum', (ed. E. Chen et al.), 173-184; 1996, Warrendale, PA, TMS.
87. F. J. Zerilli and R. W. Armstrong: 'Constitutive equation for hcp metals and high strength steels', in 'High strain rate effects on polymer, metal and ceramic matrix composites', (ed. Y. D. S. Rajapakse and J. R. Vinson), AD-Vol. 48, 121-126; 1995, New York, American Society of Mechanical Engineers.
88. R. W. Armstrong: 'Theory for the tensile ductile-brittle behavior of polycrystalline hcp materials, with application to beryllium', Acta Metall., 1968, 16, 347-355.
89. Y. V. R. K. Prasad, N. M. Madhava and R. W. Armstrong: 'The strengthening of hcp materials due to the presence of grain boundaries', in 'Grain boundaries in engineering materials', 67-75; 1975, Baton Rouge, LA, Claitor's Press.
90. P. Rodriguez, R. W. Armstrong and S. L. Mannan: 'The dependence of activation area on grain size in cadmium', Trans. Ind Inst. Met., 2003, 56, 189-196.
91. P. Rodriguez: 'Grain size dependence of the activation parameters for plastic deformation: influence of crystal structure, slip system, and rate-controlling dislocation mechanism', Metal!. Mater. Trans. A, 2004, 35A, 2697-2705.
92. T. Zhu, J. Li, A. Samanta, H. G. Kim and S. Suresh: 'Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals', Proc. Nat!. Acad. Sci., 2007, 104, 3031-3036.
93. Z. Q. Wang, I. J. Beyerlein and R. LeSar: 'The importance of cross-slip in high-rate deformation', Model. Simul. Mater. Sci. Eng., 2007, 15, 675-690.
94. Z. Q. Wang, I. J. Beyerlein and R. LeSar: 'Dislocation motion in high strain-rate deformation', Philos. Mag., 2007, 87, 2263-2279.
95. R. W. Armstrong and P. Rodriguez: 'Flow stress/strain rate/grain size coupling for fcc nanopolycrystals', Philos. Mag., 2006, 86, 5787-5796.
96. R. J. Asaro and S. Suresh: 'Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins', Acta Mater., 2005, 53, 3369-3382.
97. M. A. Meyers, A. Mishra and D. J. Benson: 'Mechanical properties of nanocrystalline materials', Prog. Mater. Sci., 2006, 51, 427-556.
98. H. Conrad: 'Plastic deformation kinetics in nanocrystalline fcc metals based on the pile-up of dislocations', Nanotechnology, 2007, 18, 325701.
99. J. J. Gilman: 'The plastic response of solids', in 'Dislocation dynamics', (ed. A. R. Rosenfield et al.), 3-25; 1968, New York, McGraw-Hill Book Co.
100. G. Z. Voyiadjis and F. H. Abed: 'Thermomechanical response of metals with different crystal structures at high strain rates and temperatures', in 'Dislocations, plasticity, damage, and metal forming: material response and multiscale modeling', (ed. A. S. Khan and A. R. Khoei), 382-384; 2005, Fulton, MD, Neat Press.
101. G. Z. Voyiadjis and F. H. Abed: 'Microstructural based models for bee and fcc metals with temperature and strain rate dependency', Mech. Mater., 2005, 37, 355-378.
102. F. H. Abed and G. Z. Voyiadjis: 'A consistent modified Zerilli - Armstrong flow stress model for BCC and FCC metals at elevated temperatures', Acta Mech., 2005, 175, 1-18.
103. G. R. Johnson and W. H. Cook: 'A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures', Proc. 7th Int. Symp. on 'Ballistics', The Hague, The Netherlands, 1983, American Defense Preparedness Association, 541-547.
104. G. R. Johnson and W. H. Cook: 'Fracture characteristics of three metals subjected to various strains, strain rates, temperatures, pressures', Eng. Fract. Mech., 1985, 21, 31-48.
105. B. Langrand, P. Geoffrey, J.-L. Petitniot, J. Fabis, E. Markiewicz and P. Drazetic: 'Identification technique of constitutive model parameters for crashworthiness modeling', Aerospace Sci. Technol., 1999, 4, 215-227.
106. S. Nemat-Nasser, Y.-F. Li and J. B. Isaacs: 'Experimental/ computational valuation of flow stress at high strain rates with application to adiabatic shear banding', Mech. Mater., 1994, 17, 111-134.
107. R. E. Reed, H. D. Guberman and R. W. Armstrong: 'Effect of neutron irradiation on the temperature dependence of the flow stress of niobium single crystals', Phys. Status Sol., 1970, 37, 647-655.
108. P. S. Follansbee and U. F. Kocks: 'A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable', Acta Metall., 1988, 36, 81-93.
109. G. T. Gray, III, S. R. Chen and K. S. Vecchio: 'Influence of grain size on the constitutive response and substructure evolution of Monel 400', Metall. Mater. Trans. A, 1999, 30A,1235-1247.
110. B. Holmedal: 'On the formulation of the mechanical threshold stress model', Acta Mater., 2007, 55, 2739-2746.
111. D. J. Steinberg, S. G. Cochran and M. W. Guinan: 'A constitutive model for metals Applicable at high strain rates', J. Appl. Phys., 1980, 51, 1498-1504.
112. S. R. Bodner and Y. Partom: 'Constitutive equations for elastoviscoplastic strain-hardening materials', J. AppE Mech., 1975, 42, 385-389.
113. B. A. Remington, P. Allen, E. M. Bringa, J. Hawreliak, D. Ho, K. T. Lorenz, H. Lorenzana, J. M. McNaney, M. A. Meyers, S. W. Pollaine, K. Rosolankova, B. Sadik, M. S. Schneider, D. Swift, J. Wark and B. Yaakobi: 'Material dynamics under extreme conditions of pressure and strain rate', Mater. Sci. Technol., 2006, 22, 474-488.
114. T. C. Germann, D. Tanguy, B. L. Holian, P. S. Lomdahl, M. Mareschal and R. Ravelo: 'Dislocation structure behind a shock front in fcc perfect crystals: atomistic simulation results', Metall. Mater. Trans. A, 2004, 35A, 2609-2615.
115. K. Kadau, T. C. Germann, P. S. Lomdahl, B. L. Holian, D. Kadau, P. Entel, M. Kreth, F. Westerhoff and D. E. Wolf: 'Molecular-dynamics study of mechanical deformation in nanocrystalline aluminum', Metal!. Mater. Trans. A, 2004, 35A, 2719-2723.
116. R. A. Lebensohn, E. M. Bringa and A. Caro: 'A viscoplastic micromechanical model for the yield strength of nanocrystalline materials', Acta Mater., 2007, 55, 261-271.
117. A. Cao, E. M. Bringa and M. A. Meyers: 'Shock compression of monocrystalline copper: atomistic simulations', Metall. Mater. Trans. A, 2007, 38A, 2681-2688.
118. P. Rodriguez and R. W. Armstrong: 'Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals', Bull. Mater. Sci. (Ind.), 2006, 29, 717-720.
119. A. S. Argon and S. Yip: 'The strongest size', Philos. Mag. Lett., 2006, 86, 713-720.
120. J. M. Krafft, A. M. Sullivan and G. R. Irwin: 'Relationship between the fracture ductility transition and strain hardening characteristics of a low carbon steel', J. App!. Phys, 1957, 28, 379-380.
121. A. H. Cottrell: 'Theory of brittle fracture in steel and similar metals', Trans. TMS-AIME, 1958, 212, 192-203.
122. N. J. Petch: 'The ductile-brittle transition in the fracture of alphairon', Philos. Mag., 1958, 3, 1089-1127.
123. J. D. Campbell, R. H. Cooper and T. J. Fischhof: 'The dynamics of non-uniform plastic flow in low-carbon steel', in 'Dislocation dynamics', 723-746; 1968, New York, McGraw-Hill Book Co.
124. A. R. Rosenfield, E. Votava and G. T. Hahn: 'Dislocations and the ductile-brittle transition', in 'Ductility', 63-85; 1968, Metals Park, OH, American Society of Metals.
125. R. W. Armstrong: 'The (cleavage) fracture strength of pre-cracked polycrystals', Eng. Fract. Mech., 1987, 28, 529-538.
126. R. W. Armstrong, G. R. Irwin and X. J. Zhang: 'Microstructural mechanics description of cleavage fracturing', in 'Cleavage fracture: George R. Irwin Symposium', 51-58; 1998, Warrendale, PA, TMS.
127. R. Sandstrom and Y. Bergstrom: 'Relationship between Charpy V transition temperature in mild steel and various material parameters', Met. Sci., 1984, 18, 177-186.
128. G. R. Irwin: 'Fracture', in 'Encyclopedia of physics VI', (ed. S. Flugge), 551-590; 1958, Berlin, Springer.
129. G. R. Irwin: 'Fracture mechanics', in 'Metals handbook', Vol. 8, 439-458; 1985, Metals Park, OH, American Society of Metals.
130. J. F. Kalthoff: 'On the measurement of dynamic fracture toughness - a review of recent work', Int. J. Fract., 1985, 27, 277-298.
131. G. S. Pisarenko, A. Y. Krasowsky, V. A. Vainshtock, I. V. Kramerenko and V. N. Krasiko: 'The combined micro- and macro-fracture mechanics approach to engineering problems of strength', Eng. Fract. Mech., 1987, 28, 539-554.
132. M. S. Wechsler: 'Radiation embrittlement in the pressure-vessel steels of nuclear power plants', J. Met., 1989, 41, (12), 7-14.
133. J. D. Landes: 'Fracture mechanics and the nuclear industry', Metall. Trans. A, 1990, 21A, 1097-1104.
134. N. J. Petch and R. W. Armstrong: 'Work hardening in cleavage fracture toughness', Acta Metal!. Mater., 1989, 37, 2279-2285.
135. H. C. Rogers: 'Adiabatic shearing: a review', Ann. Rev. Mater. Sci., 1979, 9, 283-311.
136. S. P. Timothy: 'The structure of adiabatic shear bands in metals: a critical review', Acta Metall., 1987, 35, 301-306.
137. S. M. Walley: 'Shear localization: a historical overview', Metall. Mater. Trans. A, 2007, 38A, 2629-2654.
138. Y. Bai and B. Dodd: 'Adiabatic shear localization: occurrence, theories and applications', 1992; Oxford, Pergamon Press.
139. R. W. Armstrong, R. C. Batra, M. A. Meyers and T. W. Wright (eds.): 'Shear instabilities and viscoplasticity theories', Mech. Mater., 1994, 17, 83-328.
140. Q. Wei: 'Strain rate effects in the ultrafine grain and nanocrystalline regimes - influence on some constitutive responses', J. Mater. Sci., 2007, 42, 1709-1727.
141. R. W. Armstrong and F. J. Zerilli: 'Dislocation mechanics aspects of plastic instability and shear banding', Mech. Mater., 1994, 17, 319-327.
142. N. J. Petch and R. W. Armstrong: 'The tensile test', Acta Metall. Mater., 1990, 3, 2695-2700.
143. G. Z. Voyiadjis and F. H. Abed: 'A coupled temperature and strain rate dependent yield function for dynamic deformation of bee metals', Int. J. Plast., 2006, 22, 1398-1431.
144. G. Z. Voyiadjis and F. H. Abed: 'Transient localizations in metals using microstructure-based yield surfaces', Model. Simul. Mater. Sci. Eng., 2007, 15, 583-595.
145. L. P. Kubin, Ph. Spiesser and Y. Estrin: 'Computer simulation of the low temperature instability of plastic flow', Acta Metall., 1982, 30, 385-394.
146. A. Marchand and J. Duffy: 'An experimental study of the formation process of adiabatic shear bands in a structural steel', J. Mech. Phys. Sol., 1988, 36, 251-283.
147. M. A. Meyers, Y.-J. Chen, F. D. S. Marquis and D. S. Kim: 'High strain, high-strain-rate behavior of tantalum', Metall. Mater. Trans. A, 1995, 26A, 2493-2501.
148. Y.-J. Chen, M. A. Meyers and V. F. Nesterenko: 'Spontaneous and forced shear localization in high-strain-rate deformation of tantalum', Mater. Sci. Eng. A, 1999, A268, 70-82.
149. T. W. Wright: 'The physics and mathematics of adiabatic shear bands'; 2002, Cambridge, Cambridge University Press.
150. V. F. Nesterenko: 'Dynamics of heterogeneous materials'; 2001, New York, Springer-Verlag.
151. R. C. Batra and L. Chen: 'Effect of viscoplastic relations on the instability strain, shear band initiation strain, and the strain corresponding to the minimum shear band spacing, and the band width in a thermo-viscoplastic material', Int. J. Plast., 2001, 17, 1465-1489.
152. T. Rabczuk, P. M. A. Areias and T. Belytschko: 'A simplified mesh-free method for shear bands with cohesive surfaces', Int. J. Numer. Meth. Eng., 2007, 69, 993-1021.
153. F. J. Zerilli and R. W. Armstrong: 'Dislocation mechanics based constitutive equation incorporating dynamic recovery and applied to thermomechanical shear instability', in 'Shock compression of condensed matter - 1997', (ed. S. C. Schmidt et al.), CP 429, 215-218; 1998, Melville, NY, American Institute of Physics.
154. R. W. Armstrong, C. S. Coffey and W. L. Elban: 'Adiabatic heating at a dislocation pile-up avalanche', Acta Metall., 1982, 30, 2111-2118.
155. R. W. Armstrong and W. L. Elban: 'Temperature rise at a dislocation pile-up breakthrough', Mater. Sci. Eng. A, 1989, A122, L1-L3.
156. R. W. Armstrong and W. R. Grise: 'Hot spots from dislocation pile-up avalanches', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP 845, 1033-1036; 2006, Melville, NY, American Institute of Physics.
157. M. A. Meyers, G. Subhash, B. K. Kad and L. Prasad: 'Evolution of microstructure and shear-band formation in α-titanium', Mech. Mater., 1994, 17, 175-193.
158. K.-H. Hartmann, H.-D. Kunze and L. W. Meyer: 'Metallurgical effects on impact loaded materials', in 'Shock-wave and high-strain-rate phenomena in metals', (ed. M. A. Meyers and L. E. Murr), 325-337; 1981, New York, Marcel Dekker.
159. W. H. Holt, W. Mock, Jr, W. G. Soper, C. S. Coffey, V. Ramachandran and R. W. Armstrong: 'Reverse-ballistic impact study of shear plug formation and displacement in Ti6A14V alloy', J. Appl. Phys., 1993, 73, 3753-3759.
160. F. Martinez, L. E. Murr, A. Ramirez, S. M. Lopez and S. M. Gaytan: 'Dynamic deformation and adiabatic shear microstructures associated with ballistic plug formation and fracture in Ti6A14V targets', Mater. Sci. Eng. A, 2007, A454-A455, 581-589.
161. L. S. Magness, Jr: 'High strain rate deformation behaviors of kinetic energy penetrator materials during ballistic impact', Mech. Mater., 1994, 17, 147-154.
162. L. Zernow and E. J. Chapyak: 'Direct experimental evidence of melting on a shear band in a molybdenum shaped charge slug', in 'Metallurgical and materials applications of shock-wave and high-strain-rate phenomena', (ed. L. E. Murr et al.), 479-486; 1995, Amsterdam, Elsevier Science B.V.
163. S. Pappu and L. E. Murr: 'Hydrocode and microstructural analysis of explosively formed penetrators', J. Mater. Sci., 2002, 37, 233-248.
164. C. Kennedy and L. E. Murr: 'Comparison of tungsten heavy-alloy rod penetration into ductile and hard metal targets: microstructural analysis and computer simulations', Mater. Sci. Eng. A, 2002, A325, 131-143.
165. O. L. Valerio-Flores, L. E. Murr, V. Hernandez and S. Quinones: 'Observations and simulations of the low velocity-to-hypervelocity impact crater transition for a range of penetrator densities into thick aluminum targets', J. Mater. Sci., 2004, 39, 6271-6289.
166. C. Pizana, L. E. Murr, M. T. Baquera, I. A. Anchondo, A. Putrevu, C. Y. Pina, T. C. Tamoria, H. C. Chen and S. J. Cytron: 'Solid-state flow, mechanical alloying, and melt-related phenomena for [001] single-crystal W ballistic rod penetrators interacting with steel targets', Mater. Sci. Eng. A, 2006, A428, 301-313.
167. S. Dey, T. Borvik, O. S. Hopperstad and M. Langseth: 'On the influence of constitutive relation in projectile impact in steel plates', Int. J. Impact Eng., 2007, 34, 464-486.
168. R. G. McQueen, S. P. Marsh, J. W. Taylor and W. J. Carter: 'The equation of state of solids from shock-wave studies', in 'High velocity impact phenomena', (ed. R. Kinslow), Chapter 6, 293-417, 515-568; 1970, New York, Academic Press.
169. C. S. Smith: 'Metallographic studies of metals after explosive shock', Trans. TMS-AIME, 1958,212, 574-589.
170. J. Weertman and P. S. Follansbee: 'Dislocation dynamics and plastic shock waves', Mech. Mater., 1988, 7, 177-189.
171. G. T. Gray, III: 'Shock wave testing of ducUles', in 'ASM materials handbook', Vol. 8, 'Mechanical testing', 530-538; 2000, Materials Park, OH, ASM International.
172. E. M. Bringa, K. Rosolankova, R. E. Rudd, B. A. Remington, J. S. Wark, M. Duchaineau, D. H. Kalantar, J. Hawreliak and J. Belak: 'Shock deformation of face-centered-cubic metals on subnanosecond timescales', Nat. Mater., 2006, 5, 805-809.
173. R. J. Jensen, P. A. Rigg, M. D. Knudsen, R. S. Hixson, G. T. Gray, III, B. H. Sensor and F. J. Cherna: 'Dynamic compression of iron single crystals', in 'Shock compression of condensed matter-2005', (ed. M. D. Furnish et al.), CP845, Part 1, 232-235; 2006, Melville, NY, American Institute of Physics.
174. P. S. Follansbee, G. Regazzoni and U. F. Kocks: 'The transition in drag-controlled deformation in copper at high strain rates', Inst. Phys. Conf Ser. 1984, 70, 71-80.
175. R. W. Armstrong, V. Ramachandran and F. J. Zerilli: 'Dislocation mechanics description of dynamic plasticity and fracturing properties', in 'Advances in materials and applications', (ed. P. R. Rao), 201-229; 1994, New Delhi, Wiley Eastern, Ltd.
176. F. J. Zerilli and R. W. Armstrong: 'The effect of dislocation drag on the stress-strain behavior of fcc metals', Acta Mater., 1992, 40, 1803-1808.
177. G. T. Gray III, E. Cerreta, C. A. Yablinsky, L. B. Addessio, B. L. Henrie, B. H. Sencer, M. Burkett, P. J. Maudlin, S. A. Maloy, C. P. Trujillo and M. F. Lopez: 'Influence of shock pre-straining and grain size on the dynamic-tensile-extrusion response of copper: experiments and simulation', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP845, Part 2, 7725-7728; 2006, Melville, NY, American Institute of Physics.
178. R. W. Armstrong: 'Strength and ductility of metals', Trans. Ind. Inst. Met., 1997, 50, 521-531.
179. M. A. Meyers: 'A mechanism for dislocation generation in shock-wave deformation', Scr. Metall., 1978, 12, 21-26.
180. M. A. Shehadeh, H. M. Zbib and T. D. de la Rubia: 'Modelling the dynamic deformation and patterning in fcc single crystals at high strain rates: dislocation dynamics plasticity analysis', Philos. Mag., 2005, 85, 1667-1685.
181. M. A. Shehadeh, H. M. Zbib and T. Diaz de la Rubia: 'Multiscale dislocation dynamics simulations of shock compression in copper single crystal', Int. J. Plast., 2005, 21, 2369-2390.
182. M. A. Shehadeh, E. M. Bringa, H. M. Zbib, J. M. McNaney and B. A. Remington: 'Simulation of shock-induced plasticity including homogeneous and heterogeneous dislocation nucleations', Appl. Phys. Lett, 2006, 89, 171918.
183. R. W. Armstrong (transl. J. Boileau): 'Roles possibles des dislocations dans les detonations par choc dans les cristeaux energetique', Rev. Scient. Tech. Defence, 1992, 16, (2), 162-165.
184. F. A. Bandak, R. W. Armstrong, A. S. Douglas and D. H. Tsai: 'Dislocation structures for shock strengthening', in 'Shock compression of condensed matter - 1991', (ed. S. C. Schmidt et al.), 559-561; 1992, New York, Elsevier Sci. Publ. B.V.
185. F. A. Bandak, R. W. Armstrong and A. S. Douglas: 'Dislocation structure for one-dimensional strain in a shocked crystal', Phys. Rev. B, 1992, 46B, 3228-3235.
186. F. A. Bandak, D. H. Tsai, R. W. Armstrong and A. S. Douglas: 'Formation of nanodislocation dipoles in shock-compressed crystals', Phys. Rev. B, 1993, 47B, 11681-11687.
187. R. W. Armstrong, W. Arnold and F. J. Zerilli: 'Dislocation mechanics of shock induced plasticity', Metall. Mater. Trans. A, 2007, 38A, 2605-2610.
188. J. W. Swegle and D. E. Grady: 'Shock viscosity and the prediction of shock wave rise times', J. Appl. Phys., 1985, 58, 692-701.
189. T. Zhu, J. Li, A. Samanta, A. Leach and K. Gall: 'Temperature and strain-rate dependence of surface dislocation nucleation', Phys. Rev. B, Unpublished article.
190. M. A. Tschopp and D. L. McDowell: 'Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading', J. Mech. Phys. Sol., to be published.
191. W. Arnold: 'Dynamisches Werkstoffverhalten von Armco-Eisen
192. L. E. Murr, M. A. Meyers, C.-S. Niou, Y.-J. Chen, S. A. Pappu and C. Kennedy: 'Shock induced deformation twinning in tantalum', Acta Mater., 1997, 45, 157-175.
193. M. A. Meyers: 'Dynamic deformation and failure', in 'Mechanics and materials: fundamentals and linkages', (ed. M. A. Meyers et al.), Chapter 14, 489-594; 1999, New York, John Wiley and Sons, Inc.
194. B. Y. Cao, M. A. Meyers, D. H. Lassila, M. S. Schneider, Y. B. Xu, D. H. Kalantar and B. A. Remington: 'Defect substructures in plate impacted and laser shocked monocrystalline copper', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP845, Part 2, 1145-1148; 2006, Melville, NY, American Institute of Physics.
195. B. Y. Cao, M. A. Meyers, D. H. Lassila, M. S. Schneider, Y. B. Xu, D. H. Kalantar and B. A. Remington: 'Effect of shock compression method on the defect structure in single crystal copper', Mater. Sci. Eng. A, 2005, A409, 270-281.
196. H. Jarmakani, J. M. McNaney, M. S. Schneider, D. Orlikowski, J. H. Nguyen, B. Kad and M. A. Meyers: 'Dynamic response of [single crystalline] copper subjected to quasi-isentropic gas-gun driven loading', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP845, Part 2, 1319-1322; 2006, Melville, NY, American Institute of Physics.
197. H. Jarmakani, J. M. McNaney, M. S. Schneider, D. Orlikowski, J. H. Nguyen, B. Kad and M. A. Meyers: 'Dynamic response of single crystalline copper subjected to quasi-isentropic, gas-gun loading', Mater. Sci. Eng. A, 2007, A463, 249-262.
198. R. W. Armstrong, W. Arnold and F. J. Zerilli: 'Dislocation mechanics under extreme pressures', in 'Shock compression of condensed matter - 2007', (ed. M. L. Elert et al.), CP955, Part 1, 623-626; 2007, Melville, NY, American Institute of Physics.
199. L. E. Murr and E. V. Esquivel: 'Observations of common microstructural issues associated with dynamic deformation phenomena: twins, microbands, grain size effects, shear bands, and dynamic recrystallization', J. Mater. Sci., 2004, 39, 1153-1168.
200. R. W. Armstrong and F. J. Zerilli: 'Deformation twinning: from atomic modeling to shock wave loading', in 'Advances in twinning', (ed. S. Ankem and C. S. Pande), 67-81; 1999, Warrendale, PA, TMS.
201. R. W. Armstrong and F. J. Zerilli: 'Dislocation mechanics aspects of shock-wave and high-strain-rate phenomena', in 'Fundamental issues and applications of shock-wave and high-strain-rate phenomena', (ed. K. P. Staudhammer et al.), Chapter 15, 115-124; 2001, Oxford, Elsevier Sci. Publ.
202. V. F. Moiseev and V. I. Trefilov: 'Change of the deformation mechanism (slip vs twinning) in polycrystalline alpha-iron', Phys. Status Sol., 1966, 18, 881-895.
203. N. M. Madhava, P. J. Worthington and R. W. Armstrong: 'Discontinuous twinning during essentially elastic compression of steel', Philos. Mag., 1972, 25, 519-522.
204. J. B. McKirgan: 'Microstructurally-based EPIC simulations of Taylor impact tests', MSc thesis, University of Maryland, College Park, MD, USA, 1990.
205. G. T. Gray, III: 'Deformation twinning in Al-4.8 wt% Mg', Acta Metall., 1988, 36, 1745-1754.
206. L. E. Murr, E. A.Trillo, S. Pappu and C. Kennedy: 'Adiabatic shear bands and examples of their role in severe plastic deformation', J. Mater. Sci., 2002, 37, 3337-3360.
207. J. F. C. Lins, H. R. Z. Sandim, H.-J. Kestenbach, D. Raabe and K. S. Vecchio: 'A microstructural investigation of adiabatic shear bands in an interstitial free steel', Mater. Sci. Eng. A, 2007, A457, 205-218.
208. Q. Xue, E. K. Cerreta and G. T. Gray, III: 'Microstructural characteristics of post-shear localization in cold-rolled 316L stainless steel', Acta Mater., 2007, 55, 691-704.
209. B. Y. Yang, M. A. Meyers, D. H. Lassila, M. S. Schneider, Y. B. Xu, D. H. Kalantar and B. A. Remington: 'Defect substructures in plate impacted and laser shocked monocrystalline copper', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP 845, 1145-1148; 2006, Melville, NY, American Institute of Physics.
210. E. V. Esquivel and L. E. Murr: 'Deformation effects in shocked metals and alloys', Mater. Sci. Technol., 2006, 22, 438-452.
211. L. E. Murr and C. Pizana: 'Dynamic recrystallization: the dynamic deformation regime', Metall. Mater. Trans. A, 2007, 38A, 2611-2628.
212. S. N. Medyanik, W. K. Liu and S. Li: 'On criteria for dynamic adiabatic shear band propagation', J. Mech. Phys. Sol., 2007, 55, 1439-1461.
213. S. A. Quinones and L. E. Murr: 'Correlations of computed simulations with residual hardness mapping and microstructural observations of high velocity and hypervelocity impact craters in copper', Phys. Status Sol. (a), 1998, 166, 763-789.
214. J. M. Wells and R. M. Brannon: 'Advances in X-ray computed tomography diagnostics of ballistic impact damage', Metall. Mater. Trans. A, 2007, 38A 2943-2949.
215. L. Seaman: 'Fracture and fragmentation under shock loading', in 'Shock and vibration computer programs', (ed. W. Pilkey and B. Pilkey), 563-577; 1975, Charlottesville, VA, University of Virginia.
216. L. Seaman, D. R. Curran and D. A. Shockey: 'Computational models for ductile and brittle fracture', J. Appl. Phys., 1976, 47, 4814-4826.
217. V. I. Romanchenko and G. V. Stepanov: 'Dependence of the critical stress on the loading time parameters during spall in copper, aluminum and steel', J. Appl. Mech. Tech. Phys. (Russ.), 1980, 21, 555-561.
218. V. Panov, R. Vignjevic, N. Bourne and J. Millet: 'Material modeling at high strain rate', in 'Shock compression of condensed matter-2005', (ed. M. D. Furnish et al.), CP845, Part 1, 646-649; 2006, New York, American Institute of Physics.
219. D. E. Grady: 'The statistical fragmentation theory of N.F. Mott', in 'Shock compression of condensed matter - 2003', (ed. M. D. Furnish et al.), CP 706, Part 1, 455-458; 2004, Melville, NY, American Institute of Physics.
220. R. M. Brannon, J. M. Wells and O. E. Strack: 'Validating theories for brittle damage', Metall. Mater.Trans. A, 2007, 38A, 2861-2868.
221. M. D. Furnish, W. M. Trott, J. Mason, J. Podsednik, W. D. Reinhart and C. Hall: 'Assessing mesoscale material response via high-resolution line-imaging VISAR', in 'Shock compression of condensed matter - 2003', (ed. M. D. Furnish et al.), CP706, Part 2, 1159-1162; 2004, Melville, NY, American Institute of Physics.
222. M. D. Furnish, W. D. Reinhart, W. M. Trott, L. C. Chhabildas and T. J. Vogler: 'Variability in dynamic properties of tantalum: spall, Hugoniot elastic limit and attenuation', in 'Shock compression of condensed matter - 2005', (ed. M. D. Furnish et al.), CP 845, 615-618; 2006, Melville, NY, American Institute of Physics.
223. S. R. Greenfield, J. L. Casson and A. C. Koskelo: 'Nanosecond interferometric studies of surface deformation induced by laser irradiation', Proc. SPIE - Int. Soc. Opt. Eng., 2000, 3902, 108-117.
224. A. C. Koskelo, S. R. Greenfield, D. Greening and D. Swift: 'New windows into shocks at the mesoscale', in 'Shock compression of condensed matter - 2003', (ed. M. D. Furnish et al.), CP706, Part 1, 239-242; 2004, Melville, NY, American Institute of Physics.
225. A. C. Koskelo, S. R. Greenfield, K. McClellan, D. Byler, R. Dickerson, D. Paisley, S. Luo, D. Swift, D. Tonks and P. Peralta: 'Dynamics of the onset of damage in metals under shock loading', in 'Shock compression of condensed matter - 2007', (ed. M. L. Elert et al.), CP955, Part 1, 557-560; 2007, Melville, NY, American Institute of Physics.