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On the Plastic Behavior of Polycrystalline Aggregates

  • John E. Dorn
  • Jim D. Mote
Part of the Materials Science Research book series (MSR)

Abstract

The complete understanding of the physical origin and nature of the plastic behavior of polycrystalline aggregates constitutes one of the major problems in materials science. It has as its major objective the predictions of the plastic behavior of polycrystals from the known behavior of single crystals. The possibility of making such a prediction rests on the tacit assumption that the mechanisms of plastic deformation in aggregates are substantially identical with those observed in single crystals. The steps involved in the solution are: (a) mechanisms of deformation in single crystals; (b) interactions at grain boundary; (c) statistical averaging; and (d) contained plasticity.

Keywords

Plastic Strain Slip System Tensile Axis Plastic Behavior Resolve Shear Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. M. Clarebrough and M. E. Hargreaves, Work Hardening of Metals, Progress in Metal Physics 8, Chapter 1 (1959).Google Scholar
  2. 2.
    A. Seeger, The Mechanism of Glide and Work-Hardening in Face-Centred Cubic and Hexagonal Close-Packed Metals, Dislocations and Mechanical Properties of Crystals, John Wiley and Sons, New York, pp. 243–329 (1957).Google Scholar
  3. 3.
    J. Friedel, Dislocation Interactions and Internal Strains, Internal Stresses and Fatigue in Metals, Elsevier Publishing Company, pp. 220–262 (1959).Google Scholar
  4. 4.
    G. Schoeck, Thermodynamic Principles in High-Temperature Materials, Mechanical Behavior of Materials at Elevated Temperatures, McGraw-Hill Book Company, Inc., New York, 1961, Chapter 5.Google Scholar
  5. 5.
    F. E. Hauser, P. R. Landon, and J. E. Dorn, Deformation and Fracture Mechanisms of Polycrystalline Magnesium at Low Temperatures, Trans. ASM 48, pp. 986–1002 (1956).Google Scholar
  6. 6.
    E. O. Hall, Twinning and Diffusionless Transformations in Metals, Butterworth and Co., Ltd., London, 1954.Google Scholar
  7. 7.
    W. Boas and E. Schmid, Über die Temperaturabhängigkeit der Kristallplastizität, Z. Phys. 61, pp. 767–781 (1930).CrossRefGoogle Scholar
  8. 8.
    T. S. Noggle and J. S. Koehler, Electron Microscopy of Aluminum Crystals Deformed at Various Temperatures, J. Appl. Phys. 28, pp. 53–62 (1957).CrossRefGoogle Scholar
  9. 9.
    J. Diehl, S. Mader, and A. Seeger, Gleitmechanismus und Oberflächenerscheinungen bei kubisch flächenzentrierten Metallen, Z. Metallkunde 46, pp. 650–657 (1955).Google Scholar
  10. 10.
    A. Seeger, J. Diehl, S. Mader, and R. Rebstock, Work-Hardening and Work-Softening of Face-Centred Cubic Metal Crystals, Phil. Mag. 2, pp. 323–350 (1957).CrossRefGoogle Scholar
  11. 11.
    S. Mader, Elektronenmikropische Untersuchung der Gleitlinienbildung auf Kupfereinkristallen, Z. Physik. 149, pp. 73–103 (1957).CrossRefGoogle Scholar
  12. 12.
    F. H. Blewitt, R. R. Coltman, and J. K. Redman, Work-Hardening in Copper Crystals, Report of a Conference on Defects in Crystalline Solids, Physical Society, London, pp. 369–382 (1955).Google Scholar
  13. 13.
    N. F. Mott, A Theory of Work-Hardening of Metal Crystals, Phil. Mag. 43, pp. 1151–1178 (1952).Google Scholar
  14. 14.
    A. H. Cottrell, The Time Laws of Creep, J. Mech. and Phys. Solids 1, pp. 53–63 (1952).CrossRefGoogle Scholar
  15. 15.
    J. Friedel, Les Dislocations, Gauthier-Villars, Paris, 1956.Google Scholar
  16. 16.
    A. Seeger, Theorie der Kristallplastizität, I. Grundzüge der Theorie, Z. Naturforsch. 9A, pp. 758–774 (1954); II. Die Grundstruktur der dichtest gepackten Metalle und ihr Einfluss auf die plastische Verfomung, Z. Naturforsch. 9A, pp. 856-870 (1954); III. Die Temperatur-und Geschwindigkeitsabhängigkeit der Kristallplastizität, Z. Naturforsch. 9A, pp. 870-881 (1954); The Generation of Lattice Defects by Moving Dislocations and Its Application to the Temperature Dependence of the Flow-Stress of F.C.C. Crystals, Phil. Mag. 46, pp. 1194-1217 (1955).Google Scholar
  17. 17.
    N. F. Mott, The Work-Hardening of Metals, 1960 Inst. of Metals Lecture, Trans. AIME 218, pp. 962–968 (1960).Google Scholar
  18. 18.
    A. N. Stroh, Constrictions and Jogs in Extended Dislocations, Proc. Phys. Soc, London B, pp. 427–436 (1954).Google Scholar
  19. 19.
    A. F. Kocks, Polyslip in Single Crystals, Acta. Met. 8, pp. 345–352 (1960).CrossRefGoogle Scholar
  20. 20.
    J. E. Bailey and P. B. Hirsch. The Dislocation Distribution Flow-Stress, and Stored Energy in Cold-Worked Polycrystalline Silver, Phil. Mag. 5, pp. 485–497 (1960).CrossRefGoogle Scholar
  21. 21.
    A. H. Cottrell, The Intersection of Gliding Screw Dislocations, Dislocations and Mechanical Properties of Crystals, John Wiley and Sons, Inc., New York, pp. 509–512 (1957).Google Scholar
  22. 22.
    A. Seeger, S. Mader, and K. Kronmüller, Theory of Work-Hardening in F.C.C. and H.C.P. Single Crystals, Electron Microscopy and Strength of Crystals, Interscience New York, pp. 665–712 (1963).Google Scholar
  23. 23.
    S. K. Mitra and J. E. Dorn, On the Nature of Strain Hardening in Face-Centered Cubic Metals, Trans. AIME 224, pp. 1062–1071 (1963).Google Scholar
  24. 24.
    Z. S. Basinski, Thermically Activated Glide in Face-Centered Cubic Metals and Its Application to the Theory of Strain Hardening, Phil. Mag. 4, pp. 393–432 (1959).CrossRefGoogle Scholar
  25. 25.
    V. G. Saada, Thesis, Faculty of Science, University of Paris, 1960.Google Scholar
  26. 26.
    G. Masing and J. Raffelsieper, Mechanische Erholung von Aluminium-Einkristallen, Z. Metallk. 41, pp. 65–70 (1950).Google Scholar
  27. 27.
    K. Lücke and H. Lange, Über die Form der Verfestigungskurve von Reinstaluminium-Kristallen und die Bildung von Deformationsbändern, Z. Metallk. 43, pp. 55–66 (1952).Google Scholar
  28. 28.
    F. D. Rossi, Stress-Strain Characteristics and Slip-Band Formation in Metal Crystals: Effect of Crystal Orientation, Trans. AIME 200, p. 1009 (1954).Google Scholar
  29. 29.
    H. Suzuki, S. Ikeda, and S. Takeuchi, Deformation of Thin Copper Crystals, J. Phys. Soc, Japan 11, pp. 382–393 (1956).CrossRefGoogle Scholar
  30. 30.
    H. Lange and K. Lücke, Störungen der Gleitung bei Aluminium Kristallen, I. Untersuchung der Verfestigung und des Laue-Asterismus, Z. Metallk. 44, pp. 183–191 (1953); II. Mikroskopische Untersuchung des Gleitlinienbildes und Diskussion des Verformungsmechanisms, Z. Metallk. 44, pp. 514-527 (1953).Google Scholar
  31. 31.
    B. Chalmers, The Plasticity of Polycrystalline Solids, Plastic Deformation of Crystalline Solids, Mellon Inst., Pittsburgh, 1950, pp. 193–196.Google Scholar
  32. 32.
    J. D. Livingston and B. Chalmers, Multiple Slip in Bicrystal Deformation, Acta Met. 5, pp. 322–327 (1957).CrossRefGoogle Scholar
  33. 33.
    R. L. Fleischer and W. A. Backofen, Effects of Grain Boundaries in Tensile Deformation at Low Temperatures, Trans. AIME 218, pp. 243–251 (1960).Google Scholar
  34. 34.
    K. J. Aust and N. K. Chen, Effect of Orientation Difference on the Plastic Deformation of Aluminum Bicrystals, Acta Met. 2, pp. 632–638 (1954).CrossRefGoogle Scholar
  35. 35.
    R. Clark and B. Chalmers, Mechanical Deformation of Aluminum Bicrystals, Acta Met. 2, pp. 80–86 (1954).CrossRefGoogle Scholar
  36. 36.
    C. Elbaum, Plastic Deformation of Aluminum Multicrystals, Trans. AIME 218, pp. 444–448 (1960).Google Scholar
  37. 37.
    F. D. Rossi and C. H. Mathewson, A Study of the Plastic Behavior of High-Purity Aluminum Single Crystals at Various Temperatures, Trans. AIME 188, pp. 1159–1167 (1950).Google Scholar
  38. 38.
    R. J. Hartmann and E. Macherauch, Unterschung von Gleitvorgängen in Einzelkristalliten vielkristalliner Kupferproben, Z. Metallk. 51, pp. 694–699 (1960).Google Scholar
  39. 39.
    S. K. Mitra, P. W. Osborne, and J. E. Dorn, On the Intersection Mechanism of Plastic. Deformation in Aluminum Single Crystals, Trans. AIME 221, pp. 1206–1213 (1961).Google Scholar
  40. 40.
    R. von Mises, Mechanik der Plastischen Formänderung von Kristallen, Z. ang. Math. und Mech. 8, pp. 161–185 (1928).CrossRefGoogle Scholar
  41. 41.
    G. Sachs, Zur Ableitung einer Fliessbedingung, Z. d. Ver. deut Ing. 72, pp. 734–736 (1928).Google Scholar
  42. 42.
    H. L. Cox and D. G. Sopwith, Effect of Orientation on Stresses in Single Crystals and of Random Orientation on Strength of Polycrystalline Aggregates, Proc. Phys. Soc. 49, pp. 134–151 (1937).CrossRefGoogle Scholar
  43. 43.
    A. Kochendörfer, Plastische Eigenschaften von Kristallen, Springer, Berlin, 1941.CrossRefGoogle Scholar
  44. 44.
    E. A. Calnan and C. J. B. Clews, Deformation Textures in Face-Centered Cubic Metals, Phil. Mag. 41, pp. 1085–1100 (1950).Google Scholar
  45. 45.
    S. B. Batdorf and B. Budiansky, A Mathematical Theory of Plasticity Based on the Concept of Slip, NACA Tech. Note. No. 1871.Google Scholar
  46. 46.
    G. I. Taylor, Plastic Strain in Metals, J. Inst. Met. 62, pp. 307–324 (1938); Analysis of Plastic Strain in a Cubic Crystal, Stephen Timoshenko 60th Anniversary, Volume 5, pp. 218-224; Strains in Crystalline Aggregates, Deformation and Flow of Solids, Madrid, 1955, pp. 3-12.Google Scholar
  47. 47.
    J. F. W. Bishop and R. Hill, A Theory of the Plastic Distortion of a Polycrystalline Aggregate under Combined Stresses, Phil. Mag. 42, pp. 414–427 (1951); A Theoretical Derivation of the Plastic Properties of a Polycrystalline Face-Centered Metal, Phil. Mag. 42, pp. 1298-1307 (1951).Google Scholar
  48. 48.
    J. F. W. Bishop, A Theoretical Examination of the Plastic Deformation of Crystals by Glide, Phil. Mag. 44, pp. 51–64 (1953).Google Scholar
  49. 49.
    W. Boas and M. E. Hargreaves, On the Inhomogeneity of Plastic Deformation in the Crystals of an Aggregate, Proc. Roy. Soc. A193, pp. 89–97 (1948)CrossRefGoogle Scholar
  50. 50.
    V. M. Urie and H. L. Wain, Plastic Deformation of Coarse-Grained Aluminum, J. Inst. Metals 81, pp. 153–159 (1952–1953).Google Scholar
  51. 51.
    R. C. Deshpande, Inhomogeneous Deformation in Polycrystalline Metals, Trans. Indian Inst. of Metals 13, pp. 241–248 (1960).Google Scholar
  52. 52.
    C. S. Barrett and L. H. Levenson, The Structure of Aluminum after Compression, Trans. AIME 137, pp. 112–126 (1940).Google Scholar
  53. 53.
    J. F. W. Bishop, A theory of the Tensile and Compressive Textures of Face-Centered Cubic Metals, J. Mech. and Phys. Solids 3, pp. 130–142 (1954).CrossRefGoogle Scholar
  54. 54.
    U. F. Kocks, Polyslip in Polycrystals, Acta Met. 6, pp. 85–94 (1958).CrossRefGoogle Scholar
  55. 55.
    S. Howe and C. Elbaum, The Relation between the Plastic Deformation of Aluminium Single Crystals and Polycrystals, Phil. Mag. 6, pp. 37–48 (1961).CrossRefGoogle Scholar
  56. 56.
    J. E. Dorn, P. Pietrokowsky, and T. E. Tietz, The Effect of Alloying Elements and the Plastic Properties of Aluminum Alloys, Trans. AIME 188, 933–943 (1950).Google Scholar
  57. 57.
    R. A. Wilkins and E. S. Bunn, Copper and Copper Base Alloys, McGraw-Hill Book Co., Inc., New York, 1943.Google Scholar
  58. 58.
    C. Zener, A Theoretical Criterion for the Initiation of Slip Bands, Phys. Rev. 69, pp. 128–129 (1946).CrossRefGoogle Scholar
  59. 59.
    J. S. Koehler, On the Dislocation Theory of Plastic Deformation, Phys. Rev. 60, pp. 397–410 (1941).CrossRefGoogle Scholar
  60. 60.
    J. D. Eshelby, F. C. Frank, and F. R. N. Nabarro, The Equilibrium of Linear Arrays of Dislocations, Phil. Mag. 42, pp. 351–364 (1951).Google Scholar
  61. 61.
    A. N. Stroh, The Formation of Cracks as a Result of Plastic Flow, Proc. Roy. Soc. 223, pp. 404–414 (1954); A Theory of Fracture of Metals, Advances in Physics 6, pp. 418-465 (1957).CrossRefGoogle Scholar
  62. 62.
    D. A. Thomas and B. L. Averbach, The Early Stages of Plastic Deformation in Copper, Acta Met. 7, pp. 69–75 (1959).CrossRefGoogle Scholar
  63. 63.
    N. Brown and K. F. Lukens, Jr., Microstrain in Polycrystalline Metals, Acta Met. 9, pp. 106–111 (1961).CrossRefGoogle Scholar
  64. 64.
    B. Budiansky, Z. Hashin, and J. S. Sanders, Jr., The Stress Field of a Slipped Crystal and the Early Plastic Behavior of Polycrystalline Materials, Plasticity, Proc. of Second Symposium on Naval Structural Mechanics, Pergamon Press, London, 1960.Google Scholar
  65. 65.
    J. D. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems, Proc. Roy. Soc. A241, pp. 376–396 (1957).CrossRefGoogle Scholar
  66. 66.
    E. Kröner, Zur Plastischen Verformung des Vielkristalls, Acta Met. 9, pp. 155–161 (1961).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1963

Authors and Affiliations

  • John E. Dorn
    • 1
  • Jim D. Mote
    • 1
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Research Metallurgist, Lawrence Radiation LaboratoryUniversity of CaliforniaBerkeleyUSA

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