Abstract
Calculations involving pile ups of dislocations, both analytical and numerical, using either discrete dislocations or continuous distribution of dislocations of infinitesimal Burgers vectors, are reviewed in the light of their effects on the relation between yield or flow stress and grain size. The limitations of the pileup models are discussed and some nonpileup theories of yielding are critically reviewed also. More critical experiments are still needed to reveal the fundamental mechanicm of yielding.
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E. O. Hall:Proc. Phys. Soc. London, 1951, vol.B64, p. 747.
N. J. Petch:J. Iron Steel lnst., 1953, vol.174, p. 25.
A. H. Cottrell:Trans. TMS-AIME, 1958, vol.212, p. 192.
J. D. Eshelby, F. C. Frank, and F. R. N. Nabarro:Phil. Mag., 1951, vol.42, p. 351.
Y. T. Chou andT. E. Mitchell:J. Appl. Phys., 1967, vol.38, p. 1535.
J. C. M. Li and G. C. T Liu:Phil. Mag., 1967, vol.15, p. 1059.
A. K. Head:Phil. Mag., 1959, vol.4, p. 295.
Y. T. Chou, E. Garofalo, and R.W. Whitmore:Acta Met., 1960, vol.8, p.480.
T.E. Mitchell, S.S. Hecker, and R.L. Smialek:Phys. Stat. Sol., 1965, vol.11, p. 585.
T.E. Mitchell:Phil. Mag., 1964, vol.10, p. 301.
Z.S. Basinski and T.E. Mitchell:Phil Mag., 1966, vol.13, p. 103.
Y. T. Chou:J. Appl. Phys., 1967, vol.38, p. 2080.
E. Jahnke and F. Emde:Tables of Functions with Formulas and Curves, Dover, New York, 1945.
G. Leibfried:Z. Phys., 1951, vol.130, p. 214.
A. K. Head and N. Louat:Austr. J. Phys., 1955, vol.8, p. 1.
A. N. Stroh:Proc. Roy. Soc, 1953, vol.A218, p. 391.
E. A. Guggenheim:Thermodynamics, p. 78, Interscience, New York, 1949.
L. D. Webster and H. H. Johnson:J. Appl Phys., 1965, vol.36, p. 1927.
Y. T. Chou and N. Louat: /.Appl. Phys., 1962, vol.33, p. 3312.
N. J. Muskhelishvili:Singular Integral Equations, Noordhoff, Groningen, Holland, 1953.
T. Yokobori and M. Ichikawa:J. Phys. Soc. Japan, 1964, vol.19, p. 2337;Int. J. Fracture Mech., 1965, vol.1, p. 129.
P. Chaudhari and R. O. Scattergood:Acta Met., 1966, vol.14, p. 685.
E. Smith:Acta Met., 1967, vol.15, p. 1193.
E. Smith:J. Appl. Phys., 1968, vol.39, p. 4865.
J. C. M. Li:Phil. Mag., 1969, vol.19, p. 189.
A. R. Rosenfield and G. T Hahn:Acta Met., 1968, vol.16, p. 755.
Y. T. Chou:Acta Met., 1965, vol.13, p. 779.
A. K. Head:Austr. J. Phys., 1960, vol.13, p. 278.
E. Smith:Acta Met., 1967, vol.15, p. 249.
D. M. Barnett:Acta Met., 1967, vol.14, p. 589.
D. M. Barnett and A. S. Tetelman:J. Mech. Phys. Solids, 1966, vol.14, p. 329;Can. J. Phys., 1967, vol. 45, p. 841.
Y. T. Chou:Can. J. Phys., 1967, vol.45, p. 559.
J. G. Kuang and T. Mura:J. Appl. Phys., 1968, vol.39, p. 109.
B. Noble:Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, New York, 1958.
R. W. Armstrong and A. K. Head:Acta Met., 1965, vol.13, p. 759.
Y. T. Chou:J. Appl Phys., 1966, vol.37, p. 2425.
J. P. Hirth and J. Lothe:Theory of Dislocations, p. 701, McGraw-Hill, Book Co., New York, 1968.
R. W. Armstrong, Y. T. Chou, R. M. Fisher, and N. Louat:Phil Mag., 1966, vol. 14, p. 943.
J. D. Eshelby:Phys. Stat. Sol., 1963, vol.3, p. 2057.
T. Yokobori and M. Ichikawa:Repts. Res. Inst. Strength Fracture Mater., Tohoku Univ., 1967, vol. 3, pp. 1–14.
E. Smith:Int. J. Eng. Sci, 1966, vol.4, p. 451.
N. Louat:Phil Mag., 1963, vol.8, p. 1219.
J. C. M. Li and C. D. Needham:J. Appl Phys., 1960, vol.31, p. 1318. 1158-VOLUME 1,MAY 1970
J. C. M. Li: unpublished results.
T. Hanaoka:J. Soc. Naval Architects Japan, 1953, no. 86, p. 91.
E. Smith:Proc. Roy. Soc, 1964, vol.A282, p. 422.
Y. T. Chou:Phys. Stat. Sol., 1967, vol.20, p. 285.
Y. T. Chou and D. M. Barnett:Phys. Stat. Sol., 1967, vol.21, p. 239.
R. C. Ku, A. J. McEvily, and T. L. Johnston:Met. Trans., in press.
P. J. Worthington and E. Smith:Acta Met., 1964, vol.12, p. 1277.
A. S. Keh:Direct Observation of Imperfections in Crystals, p. 213, Newkirk and Wernick, ed., Interscience, New York, 1962.
D. V. Wilson and J. A. Chapman:Phil. Mag., 1963, vol.8, p. 1543.
P. J. Worthington and E. Smith:Phil. Mag., 1964, vol.9, p. 211.
M. J. Marcinkowski and R. M. Fisher:Trans. TMS-AIME, 1965, vol.233, p.293.
J. D. Meakin and N. J. Petch: ASD-TDR-63-324, Orlando, Florida, 1963, p.243.
H. Conrad:Electron Microscopy and Strength of Crystals, Ed. by Thomas and Washburn, Interscience, 1963, p. 299.
A. A. Johnson:Phil. Mag., 1962, vol.7, p. 177.
H. Conrad, S. Feuerstein, and L. Rice:Mater. Sci. Eng., 1967, vol. 2, p. 157.
H. Conrad, S. Feuerstein, and L. Rice:Trans. Japan Inst. Metals, 1968, vol.9, Suppl.,p. 481.
R. P. Carreker, Jr., and W. R. Hibbard, Jr.:Acta Met., 1953, vol.1, p. 654.
R. P. Carreker, Jr.:AIME Trans., 1957, vol.209, p. 112.
R. P. Carreker, Jr. and W. R. Hibbard, Jr.:AIME Trans., 1957, vol. 209, p.1157.
Y. Ohba:Trans. Nat. Res. Inst. Metals, 1967, vol.9, p. 293.
D. J. Dingley and D. McLean:ActaMet, 1967, vol. 15, p. 885.
H. Conrad:Acta Met, 1963, vol. 11, p. 75.
H. Conrad:NPL Symp. Relation Substructure and Strength Metals and Alloys, p. 244, HMSO, London, 1963.
H. Conrad and B. Christ:Recovery and Recrystallization of Metals, p. 124, L. Himmel, ed., Interscience, New York, 1963.
J. C. M. Li:Trans. TMS-AIME, 1963, vol. 227, p. 247.
W. G. Johnston and J. J. Gilman:J. Appl. Phys., 1959, vol. 30, p. 129.
C. Crussard:NPL Symp. Relation Structure and Strength Metals Alloys, p.548, HMSO, London, 1963.
C. Crussard:J. Austr. Inst. Metals, 1963, vol. 8, p. 317.
E. Hornbogen:Trans. ASM, 1963, vol. 56, p. 16.
W. E. Carrington and D. McLean:Acta Met., 1965, vol. 13, p. 493.
J. C. Suits and B. Chalmers:Acta Met, 1961, vol. 9, p. 854.
N. F. Mott:J. Inst. Metals, 1946, vol. 72, p. 367.
J. C. M. Li:Direct Observation of Imperfections in Crystals, p. 234; Newkirk and Wernick, eds., Interscience, New York, 1962;J. Austr. Inst. Metals, 1963, vol. 8, pp. 206, 381.
R. M. Fisher, H. Hashimoto, and J. W. Negele: Sixth Inst. Congr. Electron Microscopy, Kyoto, 1966, p. 79.
T. L. Lin and D. McLean:Met Sci. J., 1968, vol. 2, p. 108.
Y. Ishida and M. H. Brown:Acta Met., 1967, vol. 15, p. 857.
Y. Ishida, T. Hasegawa, and F. Nagata:Trans. Japan Inst. Metals, 1968, vol.9 Suppl., p. 504.
D. V. Wilson:Met Sci. J., 1967, vol. 1, p. 40.
R. E. Hook:Met. Trans., 1970, vol. 1, p. 85.
R. S. Goodrich: Research Center, Jones and Laughlin Steel Corp., Pittsburgh, Pa., now at Department of Mech. Engr., Vanderbilt Univ., Nashville, Tenn.
H. F. Ryan and J. Suiter:Phil. Mag., 1964, vol. 10, p. 727.
H. F. Ryan and J. Suiter:Acta Met., 1966, vol. 14, p. 847.
D. G. Brandon:Trans. Japan Inst Metals, 1968, vol. 9 Suppl., p. 497.
R. E. Hook and J. P. Hirth:Trans. Japan Inst. Metals, 1968, vol. 9 Suppl., p.778.
A. H. Cottrell:NPL Symp. Relation Structure and Strength Metals Alloys, p. 456, HMSO, London, 1963.
J. H. Westbrook:Met Rev., 1964, vol. 9, p. 415.
S. Floreen and J. H. Westbrook:Acta Met., 1969, vol. 17,p. 1175.
A. U. Seybolt and J. H. Westbrook:ActaMet., 1964, vol. 12, p. 449.
M. Braunovic, C. W. Haworth, and R. T. Weiner:Met. Sci. J., 1968, vol. 2, p. 67.
J. G. Y. Chow and S. B. McRickard:Phi Mag., 1963, vol. 8, p. 2097.
H. Wagenblast and A. C. Damask:J. Phys. Chem. Solids, 1962, vol. 23, p. 212.
D. Hull and I. L. Mogford:Phil Mag., 1958, vol. 3, p. 1213.
M. Yajima and M. Ishii:Trans. Japan Inst. Metals, 1968, vol. 9 Suppl., p. 325.
J. J. Gilman:J. Appl Phys., 1965, vol. 36, p. 3195.
N. J. Petch:Phil Mag., 1958, vol. 3, p. 1089.
H. Conrad and G. Schoeck:Acta Met, 1960, vol. 8, p. 791.
B. J. Brindley and J. T. Barnby:Acta Met, 1966, vol. 14, p. 1765.
A. A. Johnson:Acta Met, 1960, vol. 8, p. 737.
A. T. Churchman:J. Inst. Metals, 1960, vol. 88, p. 221.
M. A. Adams, A. C. Roberts, and R. E. Smallman:Acta Met., 1960, vol. 8, 328.
M. J. Marcinkowski and H. A. Lipsitt:Acta Met., 1962, vol. 10, p. 95.
F. E. Hauser, P. R. Landon, and J. E. Dorn:AIME Trans., 1956, vol. 206, p.589.
J. Heslop and N. J. Petch:Phil. Mag., 1958, vol. 3, p. 1128.
J. D. Campbell and J. Harding:Response of Metals to High Velocity Deformation, p. 51, Shewmon and Zackay, eds., Interscience, New York, 1961.
M. Castagna, A. Ferro, F. S. Rossi, J. Sebille, and G. Szabo-Miszenti:Mem. Sci. Rev. Met., 1966, vol. 63, p. 555.
J. Gouzou:Acta Met., 1964, vol. 12, p. 785.
J. C. M. Li:Dislocation Dynamics, p. 87, A. R. Rosenfieldet al, eds., McGraw-Hill Book Co., New York, 1968.
1. Gokyu and J. Kihara:Trans. Japan Inst. Metals, 1968, vol. 9 Suppl., p.427.
J. F. Butler:Acta Met., 1962, vol. 10, p. 258.
G.T.Hahn:Acta Met., 1962, vol. 10, p.727.
K. M. Prewo: Ph.D. dissertation, Columbia University, 1969.
J. C. M. Li:Can. J. Phys., 1967, vol. 45, p. 493.
T. W. Chou: Ph.D. dissertation, Stanford University, l969;Met.Trans., in press.
E. Smith:Scripta Met., 1969, vol. 3, p. 415.
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N.J. Y. T. CHOU, formerly with E.C. Bain Laboratory for Fundamental Research, U.S. Steel Corporation, Monroeville, Pa.
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Li, J.C.M., Chou, Y.T. The role of dislocations in the flow stress grain size relationships. Metall Trans 1, 1145–1159 (1970). https://doi.org/10.1007/BF02900225
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DOI: https://doi.org/10.1007/BF02900225