Skip to main content

On the Plastic Behavior of Polycrystalline Aggregates

  • Chapter
Materials Science Research

Part of the book series: Materials Science Research ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. M. Clarebrough and M. E. Hargreaves, Work Hardening of Metals, Progress in Metal Physics 8, Chapter 1 (1959).

    Google Scholar 

  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. J. Friedel, Dislocation Interactions and Internal Strains, Internal Stresses and Fatigue in Metals, Elsevier Publishing Company, pp. 220–262 (1959).

    Google Scholar 

  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. 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. E. O. Hall, Twinning and Diffusionless Transformations in Metals, Butterworth and Co., Ltd., London, 1954.

    Google Scholar 

  7. W. Boas and E. Schmid, Über die Temperaturabhängigkeit der Kristallplastizität, Z. Phys. 61, pp. 767–781 (1930).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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. 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).

    Article  Google Scholar 

  11. S. Mader, Elektronenmikropische Untersuchung der Gleitlinienbildung auf Kupfereinkristallen, Z. Physik. 149, pp. 73–103 (1957).

    Article  Google Scholar 

  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. N. F. Mott, A Theory of Work-Hardening of Metal Crystals, Phil. Mag. 43, pp. 1151–1178 (1952).

    Google Scholar 

  14. A. H. Cottrell, The Time Laws of Creep, J. Mech. and Phys. Solids 1, pp. 53–63 (1952).

    Article  Google Scholar 

  15. J. Friedel, Les Dislocations, Gauthier-Villars, Paris, 1956.

    Google Scholar 

  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. N. F. Mott, The Work-Hardening of Metals, 1960 Inst. of Metals Lecture, Trans. AIME 218, pp. 962–968 (1960).

    Google Scholar 

  18. A. N. Stroh, Constrictions and Jogs in Extended Dislocations, Proc. Phys. Soc, London B, pp. 427–436 (1954).

    Google Scholar 

  19. A. F. Kocks, Polyslip in Single Crystals, Acta. Met. 8, pp. 345–352 (1960).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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. 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. 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. 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).

    Article  Google Scholar 

  25. V. G. Saada, Thesis, Faculty of Science, University of Paris, 1960.

    Google Scholar 

  26. G. Masing and J. Raffelsieper, Mechanische Erholung von Aluminium-Einkristallen, Z. Metallk. 41, pp. 65–70 (1950).

    Google Scholar 

  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. 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. H. Suzuki, S. Ikeda, and S. Takeuchi, Deformation of Thin Copper Crystals, J. Phys. Soc, Japan 11, pp. 382–393 (1956).

    Article  Google Scholar 

  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. B. Chalmers, The Plasticity of Polycrystalline Solids, Plastic Deformation of Crystalline Solids, Mellon Inst., Pittsburgh, 1950, pp. 193–196.

    Google Scholar 

  32. J. D. Livingston and B. Chalmers, Multiple Slip in Bicrystal Deformation, Acta Met. 5, pp. 322–327 (1957).

    Article  Google Scholar 

  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. 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).

    Article  Google Scholar 

  35. R. Clark and B. Chalmers, Mechanical Deformation of Aluminum Bicrystals, Acta Met. 2, pp. 80–86 (1954).

    Article  Google Scholar 

  36. C. Elbaum, Plastic Deformation of Aluminum Multicrystals, Trans. AIME 218, pp. 444–448 (1960).

    Google Scholar 

  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. R. J. Hartmann and E. Macherauch, Unterschung von Gleitvorgängen in Einzelkristalliten vielkristalliner Kupferproben, Z. Metallk. 51, pp. 694–699 (1960).

    Google Scholar 

  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. R. von Mises, Mechanik der Plastischen Formänderung von Kristallen, Z. ang. Math. und Mech. 8, pp. 161–185 (1928).

    Article  Google Scholar 

  41. G. Sachs, Zur Ableitung einer Fliessbedingung, Z. d. Ver. deut Ing. 72, pp. 734–736 (1928).

    Google Scholar 

  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).

    Article  Google Scholar 

  43. A. Kochendörfer, Plastische Eigenschaften von Kristallen, Springer, Berlin, 1941.

    Book  Google Scholar 

  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. 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. 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. 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. 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. 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)

    Article  Google Scholar 

  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. R. C. Deshpande, Inhomogeneous Deformation in Polycrystalline Metals, Trans. Indian Inst. of Metals 13, pp. 241–248 (1960).

    Google Scholar 

  52. C. S. Barrett and L. H. Levenson, The Structure of Aluminum after Compression, Trans. AIME 137, pp. 112–126 (1940).

    Google Scholar 

  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).

    Article  Google Scholar 

  54. U. F. Kocks, Polyslip in Polycrystals, Acta Met. 6, pp. 85–94 (1958).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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. R. A. Wilkins and E. S. Bunn, Copper and Copper Base Alloys, McGraw-Hill Book Co., Inc., New York, 1943.

    Google Scholar 

  58. C. Zener, A Theoretical Criterion for the Initiation of Slip Bands, Phys. Rev. 69, pp. 128–129 (1946).

    Article  Google Scholar 

  59. J. S. Koehler, On the Dislocation Theory of Plastic Deformation, Phys. Rev. 60, pp. 397–410 (1941).

    Article  Google Scholar 

  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. 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).

    Article  Google Scholar 

  62. D. A. Thomas and B. L. Averbach, The Early Stages of Plastic Deformation in Copper, Acta Met. 7, pp. 69–75 (1959).

    Article  Google Scholar 

  63. N. Brown and K. F. Lukens, Jr., Microstrain in Polycrystalline Metals, Acta Met. 9, pp. 106–111 (1961).

    Article  Google Scholar 

  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. J. D. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems, Proc. Roy. Soc. A241, pp. 376–396 (1957).

    Article  Google Scholar 

  66. E. Kröner, Zur Plastischen Verformung des Vielkristalls, Acta Met. 9, pp. 155–161 (1961).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

H. H. Stadelmaier W. W. Austin

Rights and permissions

Reprints and permissions

Copyright information

© 1963 Springer Science+Business Media New York

About this chapter

Cite this chapter

Dorn, J.E., Mote, J.D. (1963). On the Plastic Behavior of Polycrystalline Aggregates. In: Stadelmaier, H.H., Austin, W.W. (eds) Materials Science Research. Materials Science Research. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5537-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-5537-1_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-5539-5

  • Online ISBN: 978-1-4899-5537-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics