Advertisement

Metallurgical Transactions A

, Volume 16, Issue 12, pp 2131–2165 | Cite as

Precipitation hardening

  • A. J. Ardell
Symposium on 50th Anniversary of the Introduction of Dislocations

Abstract

The topic of precipitation hardening is critically reviewed, emphasizing the influence of precipitates on the CRSS or yield strength of aged alloys. Recent progress in understanding the statistics of dislocation-precipitate interactions is highlighted. It is shown that Pythagorean superposition for strengthening by random mixtures of localized obstacles of different strengths is rigorously obeyed in the limit of very weak obstacles; this had been known previously as a result of computer simulation experiments. Some experimental data are discussed in light of this prediction. All of the currently viable mechanisms of precipitation hardening are reviewed. It is demonstrated that all versions of the theory of coherency hardening are woefully inadequate, while the theory of order hardening is capable of accurately predicting the contribution of γ′ precipitates to the CRSS of aged Ni-Al alloys. It is also convincingly shown that a new theory based on computer simulation experiments of the motion of dislocations through arrays of obstacles having a finite range of interaction cannot explain these same data, and is of doubtful validity in other instances for which its success has been proclaimed. A new theory of hardening by spinodal decomposition is proposed. It is based on the statistics of interaction between dislocations and diffuse attractive obstacles, and is shown to be in very good quantitative agreement with much of the limited data available. Some of the problems that remain to be addressed and solved are discussed.

Keywords

Metallurgical Transaction Slip Plane Edge Dislocation Dislocation Line Spinodal Decomposition 
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.

List of symbols

A

Amplitude of a composition modulation during spinodal decomposition.

a(ap) a(ap)

Lattice parameter of the matrix (precipitate).

B

Dimensionless variable in the order strengthening theory of Ardell, Munjal, and Chellman.

b bp

Burgers vectors of total (partial) dislocations.

C C0

Solute concentration (initial value) in atom fraction.

CG

A constant in an expression for the maximum interaction force in modulus hardening.

Csl, C’sl

Empirical constants in the theory of Schwarz and Labusch for energy conserving and energy storing interactions, respectively.

cij

Single crystal elastic moduli.

D

Spacing of the dislocation pair in order strengthening.

dI dII

Effective particle diameters for the leading (I) and trailing (II) dislocations of a pair at the critical configuration during order strengthening.

Fm

Maximum force of interaction that an obstacle can withstand.

Fmz

Maximum force of interaction between a precipitate and a dislocation on a slip plane at distance z from the particle center.

f

Volume fraction of precipitate.

G, G111

Shear modulus on the slip plane in the slip direction of the matrix of an fcc crystal.

Giso

Shear modulus of the matrix of an isotropic crystal.

Gp

Shear modulus of the precipitate.

ΔG GP

G

g

Distribution function of the variable contained within the parentheses.

h

Twice the amplitude of a zig-zag dislocation in the presence of attractive obstacles.

Jc

A constant in Cahn’s theory of spinodal de composition.

j

The number of dislocations in a procession during the shearing of ordered precipitates.

K

Force of interaction between two partial dislocations of Burgers vector bp.

k

Index representing successive obstacles encountered

L

Effective spacing of obstacles along a dislocation at the critical configuration.

LF

The Friedel spacing.

LM

The Mott spacing.

Ls

The square lattice spacing.

LI,LII

Effective spacings of obstacles along the leading and trailing dislocations of a pair at the critical configuration in order strengthening.

Edge length of a cube containing one obstacle on average.

l

Effective particle diameter for the trailing partial at the critical configuration in stackingfault strengthening.

m

An exponent appearing in equations for the maximum force and CRSS due to modulus hardening.

n

Number of obstacles contained within a dimensionless search area generated by circle rolling.

ns

Number of obstacles per unit area in the glide plane.

nv

Number of obstacles or precipitates per unit volume.

p

An adjustable parameter in the Hüther and Reppich theory of order strengthening by strong pair coupling.

q

An exponent in an empirical addition rule.

R(R *)

Radius (dimensionless radius) of a curved dislocation.

Rc(Rc*)

As above, at the critical breaking stress.

r

Radius of a spherical precipitate.

r0

Inner cut-off distance in the expression for the dislocation line energy.

rs

Planar radius of a spherical precipitate.

S(S *)

Area (dimensionless area) swept out by a dislocation in circle rolling.

Sc*

Dimensionless critical area swept out by a dislocation in circle rolling, containing one obstacle.

SF

Area swept out by a dislocation in Friedel statistics.

s0

Dimensionless, radius-independent search area at the critical configuration in circle rolling.

s0i

As above, but containing on average one obstacle of typei in a random mixture of distinct obstacles.

U0

Energy of interaction between an obstacle and a dislocation.

u

A dimensionless variable in the order hardening theory of Ardell, Munjal, and Chellman, equal to 2〈rs〉/LF.

V

A parameter related to the maximum force of interaction between a flexible edge dislocation and a spherical coherent precipitate.

wm(wp

Ribbon width of a stacking-fault in the matrix (precipitate).

Xi

Fraction of obstacles of typei in the slip plane; an areal concentration.

x

Spatial coordinate parallel to an initially straight dislocation line.

Y

An elastic modulus resisting lattice deformation during spinodal decomposition.

y

Spatial coordinate measuring the displacements of a dislocation from a straight line.

z

Distance between the center of a spherical precipitate and the slip plane of a dislocation,

α

A coefficient in the expression for the dislocation line tension.

βc

Dimensionless critical force exerted by a dislocation on an obstacle.

Γ

Line tension of a dislocation.

Γe, Γs

Line tension of a pure edge, screw dislocation.

γs

Energy of a matrix-precipitate interface created by slip.

γapb

Antiphase boundary energy on the slip plane of an ordered precipitate.

γsfm

Stacking-fault energy of the matrix.

γsfp

Stacking-fault energy of the precipitate.

〈γsf

Average stacking-fault energy of the matrix and precipitate phases.

Δγ γsfm− γ

sfP

Δ

Fractional misfit between the lattice parameters of the matrix and precipitate phases,

ε

Constrained strain; the fractional misfit between anin situ coherent precipitate and the matrix.ξ Z/r.

η

A measure of the lattice strains produced during spinodal decomposition.

η0

Parameter measuring the ratio of the obstacle range and the square root of its breaking strength.

θc

Critical angle through which the dislocation turns at an obstacle in,e.g., circle rolling.

Λ

Outer cut-off distance in the expression for the dislocation line energy.

λ

Wavelength of a composition modulation during spinodal decomposition.

v(vp

Poisson’s ratio of the matrix (precipitate).

ξ

Angle between the dislocation line and its Burgers vector.

τcc*)

CRSS (dimensionless CRSS) predicted theoretically

gTc**

Reduced theoretical CRSS; gTc/β c 3/2

gTo**

Experimentally determined value of gT c ** relevant to data on order hardening.

gTci(gTci*)

CRSS (dimensionless CRSS) predicted theoretically for obstacles of typei in a random mixture of distinct obstacles.

gTcc

Theoretically predicted CRSS due to chemical hardening.

gTcG

Theoretically predicted CRSS due to modulus hardening.

gTcO

Theoretically predicted CRSS due to order hardening.

gTcS

Theoretically predicted by CRSS due to hardening by spinodal decomposition.

gTce

Theoretically predicted CRSS due to coherency hardening.

gT

Theoretically predicted CRSS due to stackingfault strengthening.

gTss

Contribution of the solid solution matrix to the CRSS.

gT01, τ02

Contributions of Class 1 and Class 2 precipitates to the CRSS in alloys aged to contain bimodal γ′ particle size distributions.

gTt

Experimentally measured CRSS of a crystal.

Δτ

Contribution of precipitates to the CRSS determined experimentally.

ΔgT0

As above, in order strengthening,

Δτs

As above, in hardening by spinodal decomposition.

Δτε

As above, in coherency hardening.

ΔgTγ

As above, in stacking-fault strengthening.

θ

Angle between tangential directions of the dislocation line at successive obstacles in circle rolling.

θi

Similar to θ, but for obstacles of typei in a random mixture of distinct obstacles.

θo

Lower limit on θ which defines a boundary of the search area in circle rolling that contains one obstacle on average.

χ

A constant in the theory of coherency strengthening.

ψc

Critical breaking angle (cusp angle) included between adjacent arms of the dislocation at an obstacle.

ψw

The difference between the maximum and minimum values of ψc.

Ω(Ω*)

Range (dimensionless range) of interaction between an obstacle and a dislocation.

〈〉

Symbols denoting the average value of the quantity contained within. max, min, Subscripts denoting maximum, minimum, exp, experimental, and/or theoretical values of a theor parameter or variable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Wilm:Metallurgie, 1991, vol. 8, p. 225.Google Scholar
  2. 2.
    P. D. Merica, R. G. Waltenberg, and H. Scott:Trans. AIME, 1920, vol. 64, p. 41.Google Scholar
  3. 3.
    R. F. Mehl and L. K. Jetter:Age Hardening of Metals, American Society for Metals, Cleveland, OH, 1940, p. 342.Google Scholar
  4. 4.
    E. Orowan:Z. Phys., 1934, vol. 89, p. 634.CrossRefGoogle Scholar
  5. 5.
    G.I. Taylor:Proc. Roy. Soc. (London) A, 1934, vol. 145, p. 362.CrossRefGoogle Scholar
  6. 6.
    M. Polanyi:Z. Phys., 1934, vol. 89, p. 660.CrossRefGoogle Scholar
  7. 7.
    N.F. Mott and F.R.N. Nabarro:Proc. Phys. Soc., 1940, vol. 52, p. 86.CrossRefGoogle Scholar
  8. 8.
    E. Orowan:Symposium on Internal Stresses in Metals and Alloys, Session III Discussion, Institute of Metals, London, England, 1948, p. 451.Google Scholar
  9. 9.
    G.C. Smith:Prog. Metal Phys., 1950, vol. 1, p. 163.CrossRefGoogle Scholar
  10. 10.
    A. Kelly and R.B. Nicholson:Prog. Mater. Sci., 1963, vol. 10, p. 149.Google Scholar
  11. 11.
    L. M. Brown and R.K. Ham:Strengthening Methods in Crystals, A. Kelly and R. B. Nicholson, eds., Halsted Press Division, John Wiley & Sons, New York, NY, 1971, p. 9.Google Scholar
  12. 12.
    F.R.N. Nabarro:J. Less-Common Metals, 1972, vol. 28, p. 257.CrossRefGoogle Scholar
  13. 13.
    J. Friedel:Les Dislocations, Gauthier-Villars, Paris, France, 1956, p. 205.Google Scholar
  14. 14.
    J. Friedel:Electron Microscopy and Strength of Crystals, G. Thomas and J. Washbum, eds., Interscience, John Wiley & Sons, New York, NY, 1962, p. 605.Google Scholar
  15. 15.
    R.L. Fleischer and W. R. Hibbard, Jr.:The Relation between the Structure and Mechanical Properties of Metals, Her Majesty’s Stationery Office, London, England, 1963, p. 261.Google Scholar
  16. 16.
    R. Labusch:Z. Phys., 1962, vol. 167, p. 452.CrossRefGoogle Scholar
  17. 17.
    U.F. Kocks:Can. J. Phys., 1967, vol. 45, p. 737.Google Scholar
  18. 18.
    U.F. Kocks:Trans. Japan. Inst. Metals, 1968, vol. 9, supplement, p. 1.Google Scholar
  19. 19.
    J. E. Dorn, P. Guyot, and T. Stefansky:Physics of Strength and Plasticity, A.S. Argon, ed., M.I.T. Press, Cambridge, MA, 1969, p. 133.Google Scholar
  20. 20.
    U.F. Kocks:Phil. Mag., 1966, vol. 13, p. 541.CrossRefGoogle Scholar
  21. 21.
    A.J.E. Foreman and M. J. Makin:Phil. Mag., 1966, vol. 14, p. 911.CrossRefGoogle Scholar
  22. 22.
    J.W. Mrris, Jr. and D.H. Klahn:J. Appl. Phys., 1974, vol. 45, p. 2027.CrossRefGoogle Scholar
  23. 23.
    K. Hanson, J.W. Mrris and Jr.:J. Appl. Phys., 1975, vol. 46, p. 983.CrossRefGoogle Scholar
  24. 24.
    A. Melander:Scand. J. Metall., 1978, vol. 7, p. 109.Google Scholar
  25. 25.
    R. Labusch:J. Appl. Phys., 1977, vol. 48, p. 4550.CrossRefGoogle Scholar
  26. 26.
    N.F. Mott:Imperfections in Nearly Perfect Crystals, W. Shockley, J. H. Hollomon, R. Maurer, and F. Seitz, eds., John Wiley & Sons, New York, NY, 1952, p. 173.Google Scholar
  27. 27.
    B. Riddhagni and R.M. Asimow:J. Appl. Phys., 1968, vol. 39, p. 4144.CrossRefGoogle Scholar
  28. 28.
    R. Labusch:Phys. Stat. Sol., 1970, vol. 41, p. 659.CrossRefGoogle Scholar
  29. 29.
    R. Labusch:Acta Metall., 1972, vol. 20, p. 917.CrossRefGoogle Scholar
  30. 30.
    R. Schindlmayr and J. Schlipf:Phil. Mag., 1975, vol. 31, p. 13.CrossRefGoogle Scholar
  31. 31.
    U.F. Kocks, A. S. Argon, and M. F. Ashby:Prog. Mater. Sci., 1975, vol. 19, p. 1.CrossRefGoogle Scholar
  32. 32.
    R.B. Schwarz and R. Labusch:J. Appl. Phys., 1978, vol. 49, p. 5174.CrossRefGoogle Scholar
  33. 33.
    T. J. Koppenaal and D. Kuhlmann-Wilsdorf:Appl. Phys. Lett., 1964, vol. 4, p. 59.CrossRefGoogle Scholar
  34. 34.
    N. Büttner and E. Nembach: Deformation of Multi-Phase and Particle Containing Materials, Proc. 4th Risø Int. Symposium on Metallurgy and Materials Science, J.B. Bilde-Sørensen, N. Hansen, A. Horsewell, T. Leffers, and H. Lilholt, eds., Riseø National Laboratory, Roskilde, Denmark, 1983, p. 189.Google Scholar
  35. 35.
    G. Neite, M. Sieve, M. Mrotzek, and E. Nembach:Deformation of Multi-Phase and Particle Containing Materials, Proc. 4th Risø Int. Symposium on Metallurgy and Materials Science, J.B. Bilde-Sørensen, N. Hansen, A. Horsewell, T. Leffers, and H. Lilholt, eds., Risø National Laboratory, Roskilde, Denmark, 1983, p. 447.Google Scholar
  36. 36.
    A.J.E. Foreman and M.J. Makin:Can. J. Phys., 1967, vol. 45, p. 511.Google Scholar
  37. 37.
    K. Hanson, J.W. Mrris and Jr.:J. Appl. Phys., 1975, vol. 46, p. 2378.CrossRefGoogle Scholar
  38. 38.
    N. Louat:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds. Pergamon Press, Oxford, England, vol. 2, 1979, p. 941.Google Scholar
  39. 39.
    A. Melander:Phys. Stat. Sol.(a), 1977, vol. 43, p. 223.CrossRefGoogle Scholar
  40. 40.
    G. DeWit and J. S. Koehler:Phys. Rev., 1959, vol. 116, p. 1113.CrossRefGoogle Scholar
  41. 41.
    E. Nembach:Scripta Metall., 1982, vol. 16, p. 1261.CrossRefGoogle Scholar
  42. 42.
    C. Zener:Elasticity and Anelasticity of Metals, University of Chicago Press, Chicago, IL, 1948, p. 12.Google Scholar
  43. 43.
    J. Turley and G. Sines:J. Phys. D: Appl. Phys., 1971, vol. 4, p. 264.CrossRefGoogle Scholar
  44. 44.
    A. Kelly and G. W. Groves:Crystallography and Crystal Defects, Addison-Wesley, Reading, MA, 1970, p. 163.Google Scholar
  45. 45.
    H. Lilholt:Deformation of Multi-Phase and Particle Containing Materials, Proc. 4th Risøø Int. Symposium on Metallurgy and Materials Science, J.B. Bilde-Sørensen, N. Hansen, A. Horsewell, T. Leffers, and H. Lilholt, eds., Risø National Laboratory, Roskilde, Denmark, 1983, p. 381.Google Scholar
  46. 46.
    U. F. Kocks:Physics of Strength and Plasticity, A. S. Argon, ed., M.I.T. Press, Cambridge, MA, 1969, p. 143.Google Scholar
  47. 47.
    M. F. Ashby:Physics of Strength and Plasticity, A. S. Argon, ed., M.I.T. Press, Cambridge, MA, 1969, p. 113.Google Scholar
  48. 48.
    R. Ebeling and M. F. Ashby:Phil. Mag., 1966, vol. 13, p. 805.CrossRefGoogle Scholar
  49. 49.
    E. Nembach and M. Martin:Acta Metall, 1980, vol. 28, p. 1069.CrossRefGoogle Scholar
  50. 50.
    A. Kelly and M. E. Fine:Acta Metall., 1957, vol. 5, p. 365.CrossRefGoogle Scholar
  51. 51.
    S.D. Harkness and J.J. Hren:Metall. Trans., 1970, vol. 1, p. 43.Google Scholar
  52. 52.
    V. Gerold:Dislocations in Solids, F. R. N. Nabarro, ed., North-Holland, Amsterdam, The Netherlands, 1979, vol. 4, p. 220.Google Scholar
  53. 53.
    P. B. Hirsch and A. Kelly:Phil. Mag., 1965, vol. 12, p. 881.CrossRefGoogle Scholar
  54. 54.
    V. Gerold and K. Hartmann:Trans. Japan. Inst. Metals, 1968, vol. 9, supplement, p. 509.Google Scholar
  55. 55.
    P.C. J. Gallagher:Metall. Trans., 1970, vol. 1, p. 2429.Google Scholar
  56. 56.
    R. W. Weeks, S. R. Pati, M. F. Ashby, and P. Barrand:Acta Metall., 1969, vol. 17, p. 1403.CrossRefGoogle Scholar
  57. 57.
    M. Comninou and J. Dundurs:J. Appl. Phys., 1972, vol. 43, p. 2461.CrossRefGoogle Scholar
  58. 58.
    S. D. Gavazza and D. M. Barnett:Int. J. Engng. Sci., 1974, vol. 12, p. 1025. 59. G. Knowles and P. M. Kelly: Effect of Second-Phase Particles on the Mechanical Properties of Steel, The Iron and Steel Institute, London, England, 1971, p. 9.CrossRefGoogle Scholar
  59. 60.
    A. Melander and P. Å. Persson:Acta Metall., 1978, vol. 26, p. 267.CrossRefGoogle Scholar
  60. 61.
    E. Nembach:Phys. Stat. Sol.(a), 1983, vol. 78, p. 571.CrossRefGoogle Scholar
  61. 62.
    K.-H. Dünkeloh, G. Kralik, and V. Gerold:Z. Metallke, 1974, vol. 65, p. 773.Google Scholar
  62. 63.
    K. C. Russell and L. M. Brown:Acta Metall., 1972, vol. 20, p. 969.CrossRefGoogle Scholar
  63. 64.
    I. A. Ibrahim and A. J. Ardell:Mater. Sci. and Engr., 1978, vol. 36, p. 139.CrossRefGoogle Scholar
  64. 65.
    V. Gerold and H. Haberkorn:Phys. Stat. Sol., 1966, vol. 16, p. 675.CrossRefGoogle Scholar
  65. 66.
    H. Gleiter:Z. Angew. Physik, 1967, vol. 23, p. 108.Google Scholar
  66. 67.
    V. Gerold:Acta Metall., 1968, vol. 16, p. 823.CrossRefGoogle Scholar
  67. 68.
    B. Jansson and A. Melander:Scripta Metall., 1978, vol. 12, p. 497.CrossRefGoogle Scholar
  68. 69.
    H. Gleiter:Acta Metall., 1968, vol. 16, p. 829.CrossRefGoogle Scholar
  69. 70.
    V. Gerold and H.-M. Pham:Z. Metallik., 1980, vol. 71, p. 286.Google Scholar
  70. 71.
    V. Gerold and H.-M. Pham:Scripta Metall., 1979, vol. 13, p. 895.CrossRefGoogle Scholar
  71. 72.
    H. Wiedersich:Trans. Japan. Inst. Metals, 1968, vol. 9 supplement, p. 34.Google Scholar
  72. 73.
    J.D. Livingston:Trans. AIME, 1959, vol. 215, p. 566.Google Scholar
  73. 74.
    V. A. Phillips:Phil. Mag., 1965, vol. 11, p. 775.CrossRefGoogle Scholar
  74. 75.
    M. Witt and V. Gerold:Scripta Metall., 1969, vol. 3, p. 371.CrossRefGoogle Scholar
  75. 76.
    K. E. Amin, V. Gerold, and G. Kralik:J. Mater. Sci., 1975, vol. 10, p. 1519.CrossRefGoogle Scholar
  76. 77.
    I. A. Ibrahim and A. J. Ardell:Acta Metall., 1977, vol. 25, p. 1231.CrossRefGoogle Scholar
  77. 78.
    K. Matsuura, M. Kitamura, and K. Watanabe:Trans. Japan. Inst. Metals, 1978, vol. 19, p. 53.Google Scholar
  78. 79.
    H. Wendt and R. Wagner:Acta Metall., 1980, vol. 28, p. 709.CrossRefGoogle Scholar
  79. 80.
    S. R. Yeomans and P. G. McCormick:Mater. Sci. and Engr., 1978, vol. 34, p. 101.CrossRefGoogle Scholar
  80. 81.
    M. Hansen:Constitution of Binary Alloys, 2nd ed., McGraw-Hill Book Co., New York, NY, 1958, p. 596.Google Scholar
  81. 82.
    K. Nakajima and K. Numakura:Phil. Mag., 1965, vol. 12, p, 361.CrossRefGoogle Scholar
  82. 83.
    P.A. Flinn, G.M. McManus, and J.A. Rayne:J. Phys. Chem. Solids, 1960, vol. 15, p. 189.CrossRefGoogle Scholar
  83. 84.
    Z. S. Basinski, W. Hume-Rothery, and A. L. Sutton:Proc. Roy. Soc. (London) A, 1955, vol. 229, p. 459.CrossRefGoogle Scholar
  84. 85.
    Z. S. Basinski and J. W. Christian:J. Inst. Metals, 1952, vol. 80, p. 659.Google Scholar
  85. 86.
    W. B. Pearson:A Handbook of Lattice Spacings and Structures of Metals and Alloys, Pergamon Press, Oxford, England, 1958, p. 733.Google Scholar
  86. 87.
    R.D. Dragsdorf:J. Appl. Phys., 1960, vol. 31, p. 434.CrossRefGoogle Scholar
  87. 88.
    H. Haberkorn:Mater. Sci. and Engr., 1968/69, vol. 3, p. 302.CrossRefGoogle Scholar
  88. 89.
    N.J. Long, M.H. Loretta, and C.H. Lloyd:Acta Metall., 1980, vol. 28, p. 709.CrossRefGoogle Scholar
  89. 90.
    H. Haberkorn:Phys. Stat. Sol., 1966, vol. 15, p. 153.CrossRefGoogle Scholar
  90. 91.
    H. Haberkorn and V. Gerold:Phys. Stat. Sol., 1966, vol. 15, p. 167.CrossRefGoogle Scholar
  91. 92.
    P. B. Hirsch and F. J. Humphries:Physics of Strength and Plasticity, A.S. Argon, ed., M.I.T. Press, Cambridge, MA, 1969, p. 189.Google Scholar
  92. 93.
    H. Gleiter and E. Hornbogen:phhys. Stat. Sol., 1965, vol. 12, p. 235.CrossRefGoogle Scholar
  93. 94.
    J.L. Castagné:J. de Physique, 1966, vol. 27, pp. C3–233.Google Scholar
  94. 95.
    R. K. Ham:Trans. Japan. Inst. Metals, 1968, vol. 9 supplement, p. 52.Google Scholar
  95. 96.
    P. Guyot:Phil. Mag., 1971, vol. 24, p. 987.CrossRefGoogle Scholar
  96. 97.
    D. Raynor and J. M. Silcock:Metal Sci. J., 1970, vol. 4, p. 121.Google Scholar
  97. 98.
    W. Hüther and B. Reppich:Z. Metallkde, 1978, vol. 69, p. 628.Google Scholar
  98. 99.
    J. M. Oblak, D. F. Paulonis, and D. S. Duvall:Metall. Trans., 1974, vol. 5, p. 143.CrossRefGoogle Scholar
  99. 100.
    J. Greggi and W. A. Soffa:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds., Pergamon Press, Oxford, England, 1979, vol. 1, p. 651.Google Scholar
  100. 101.
    A. J. Ardell, V. Munjal, and D. J. Chellman:Metall. Trans. A, 1976, vol. 7A, p. 1263.Google Scholar
  101. 102.
    A. J. Ardell:Metal. Sci. J., 1980, vol. 14, p. 221.CrossRefGoogle Scholar
  102. 103.
    V. Munjal and A.J. Ardell:Acta Metall., 1975, vol. 23, p. 513.CrossRefGoogle Scholar
  103. 104.
    N.T. Travina and G.I. Nosova:Phys. Met. Metallogr., 1970, vol. 29, p. 119.Google Scholar
  104. 105.
    V.A. Phillips:Acta Metall., 1966, vol. 14, p. 1533.CrossRefGoogle Scholar
  105. 106.
    M. Gröhlich, P. Haasen, and G. Frommeyer:Scripta Metall., 1982, vol. 16, p. 367.CrossRefGoogle Scholar
  106. 107.
    M.M. Dawance, D.H. Ben Israel, and M.E. Fine:Acta Metall., 1964, vol. 12, p. 705.CrossRefGoogle Scholar
  107. 108.
    M.C. Chaturvedi, D.J. Lloyd, and D.W. Chung:Metal Sci. J., 1976, vol. 10, p. 373.Google Scholar
  108. 109.
    L. K. Singhal and J. W. Martin:Acta Metall., 1968, vol. 16, p. 947.CrossRefGoogle Scholar
  109. 110.
    A. Melander and P.Å. Persson:Metal Sci. J., 1978, vol. 13,p. 391.Google Scholar
  110. 111.
    J. L. Castagné, F. Lecroisey, and A. Pineau:C. R. Acad. Sci. Paris, 1968, vol. 266, p. 510.Google Scholar
  111. 112.
    A. Pineau, F. Lecroisey, J.L. Castagné, and M. Sindzingre:Acta Metall., 1969, vol. 17, p. 905.CrossRefGoogle Scholar
  112. 113.
    V. Martens and E. Nembach:Acta Metall., 1975, vol. 23, p. 149.CrossRefGoogle Scholar
  113. 114.
    B. Reppich, P. Schepp, and G. Wehner:Acta Metall., 1982, vol. 30, p. 95.CrossRefGoogle Scholar
  114. 115.
    A. Thompson and J. A. Brooks:Acta Metall., 1982, vol. 30, p. 2197.CrossRefGoogle Scholar
  115. 116.
    B. Noble, S.J. Harris, and K. Dinsdale:Metal Sci. J., 1982, vol. 16, p. 425.CrossRefGoogle Scholar
  116. 117.
    M. Rembges, P. Haasen, and L. Schultz:Z. Metallke, 1976, vol. 67, p. 330.Google Scholar
  117. 118.
    J. W. Goodrum and B. G. LeFevre:Metall. Trans. A, 1977, vol. 8A, p. 939.Google Scholar
  118. 119.
    W. Hüther and B. Reppich:Mater. Sci. and Engr., 1979, vol. 39, p. 247.CrossRefGoogle Scholar
  119. 120.
    M.C. Chaturvedi and D.W. Chung:Metall. Trans. A, 1981, vol. 12A, p. 77.Google Scholar
  120. 121.
    G.G. Brown and J.A. Whiteman:J. Aust. Inst. Metals, 1969, vol. 14, p. 217.Google Scholar
  121. 122.
    D. H. Jack and R. W. K. Honeycombe:Acta Metall., 1972, vol. 20, p. 787.CrossRefGoogle Scholar
  122. 123.
    I.O. Smith and M.G. White:Metall. Trans. A, 1976, vol. 7A, p. 293.Google Scholar
  123. 124.
    R. Taillard and A. Pineau:Mater. Sci. and Engr., 1982, vol. 56, p. 219.CrossRefGoogle Scholar
  124. 125.
    A.J. Ardell and R.B. Nicholson:J. Phys. Chem. Solids, 1966, vol. 27, p. 1793.CrossRefGoogle Scholar
  125. 126.
    D. J. Chellman and A. J. Ardell:Acta Metall., 1974, vol. 22, p. 577.CrossRefGoogle Scholar
  126. 127.
    A. J. Ardell:Acta Metall., 1968, vol. 16, p. 511.CrossRefGoogle Scholar
  127. 128.
    E.Z. Vintaikin:Sov. Phys. Dokl., 1966, vol. 11, p. 91.Google Scholar
  128. 129.
    H. Pottebohm, G. Neite, and E. Nembach:Mater. Sci. and Engr., 1983, vol. 60, p. 189.CrossRefGoogle Scholar
  129. 130.
    A. J. Ardell, D. J. Chellman, and V. Munjal:Proc. 4th Int. Conf. on the Strength of Metals and Alloys, Lab. de Phys. du Solide, eds., Nancy, France, 1976, vol. 1, p. 209.Google Scholar
  130. 131.
    R.F. Decker and J.R. Mihalisin.Trans.ASM, 1969,vol. 62,p. 481.Google Scholar
  131. 132.
    B. A. Parker:J. Aust. Inst. Metals, 1969, vol. 14, p. 321.Google Scholar
  132. 133.
    P. Haasen and R. Labusch:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds., Pergamon Press, Oxford, England, 1979, vol. 1, p. 639.Google Scholar
  133. 134.
    E. Nembach:Z. Metallke, 1981, vol. 72, p. 401.Google Scholar
  134. 135.
    B. Reppich:Acta Metall., 1982, vol. 30, p. 87.CrossRefGoogle Scholar
  135. 136.
    I.M. Lifshitz and V.V. Slyozov:J. Phys. Chem. Solids, 1961, vol. 19, p. 35.CrossRefGoogle Scholar
  136. 137.
    C. Wagner:E. Elektrochem., 1961, vol. 65, p. 581.Google Scholar
  137. 138.
    A. Melander and B. Jansson:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds., Pergamon Press, Oxford, England, 1979, vol. 1, p. 627.Google Scholar
  138. 139.
    V. Munjal and A. J. Ardell:Acta Metall., 1976, vol. 24, p. 827.CrossRefGoogle Scholar
  139. 140.
    E. Nembach and C.-K. Chow:Mater. Sci. and Engr., 1978, vol. 36, p. 271.CrossRefGoogle Scholar
  140. 141.
    D. J. Chellman and A. J. Ardell:Proc. 4th Int. Conf. on the Strength of Metals and Alloys, Lab. de Phys. du Solide, eds., Nancy, France, 1976, vol. l,p. 219.Google Scholar
  141. 142.
    R. Wagner:Czech. J. Phys. B, 1981, vol. 31, p. 198.CrossRefGoogle Scholar
  142. 143.
    J.W. Cahn:Acta Metall., 1963, vol. 11, p. 1275.CrossRefGoogle Scholar
  143. 144.
    M. Kato, T. Mori, and L. H. Schwartz:Acta Metall., 1980, vol. 28, p. 285.CrossRefGoogle Scholar
  144. 145.
    D. N. Ghista and W. D. Nix:Mater. Sci. and Engr., 1969, vol. 3, p. 293.CrossRefGoogle Scholar
  145. 146.
    Y. Hanai, T. Miyazaki, and H. Mori:J. Mater. Sci., 1979, vol. 14, p. 599.Google Scholar
  146. 147.
    B. Ditchek and L. H. Schwartz:Proc. 4th Int. Conf. on the Strength of Metals and Alloys, Lab. de Phys. du Solide, eds., Nancy, France, 1976, vol. 2, p. 593.Google Scholar
  147. 148.
    M. Kato, T. Mori, and L. H. Schwartz:Mater. Sci. and Engr., 1981, vol. 51, p. 25.CrossRefGoogle Scholar
  148. 149.
    D.L. Douglass and T. W. Barbee:J. Mater. Sci, 1969, vol. 4, p. 121.CrossRefGoogle Scholar
  149. 150.
    R.W. Carpenter:Acta Metall., 1967, vol. 15, p. 1297.CrossRefGoogle Scholar
  150. 151.
    L.H. Schwartz and J. T. Plewes:Acta Metall., 1974, vol. 22,p. 911.CrossRefGoogle Scholar
  151. 152.
    B.G. LeFevre, A.T. D’Annessa, and D. Kalish:Metall. Trans. A, 1978, vol. 9A, p. 577.Google Scholar
  152. 153.
    E. P. Butler and G. Thomas:Acta Metall., 1970, vol. 18, p. 347.CrossRefGoogle Scholar
  153. 154.
    R.J. Livak and G. Thomas:Acta Metall., 1971, vol. 19, p. 497.CrossRefGoogle Scholar
  154. 155.
    S.D. Dahlgren:Metall. Trans. A, 1977, vol. 8A, p. 347.Google Scholar
  155. 156.
    T. Miyazaki, E. Yajima, and H. Suga:Trans. Japan. Inst. Metals, 1971, vol. 12, p. 119.Google Scholar
  156. 157.
    R. Wagner:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds., Pergamon Press, Oxford, England, 1979, vol. 1, p. 645.Google Scholar
  157. 158.
    A. Datta and W. A. Soffa:Acta Metall., 1976, vol. 24, p. 987.CrossRefGoogle Scholar
  158. 159.
    P. Kratochvíl, M. Saxlová, and J. Pešička:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds., Pergamon Press, Oxford, England, 1979, vol. 1, p. 687.Google Scholar
  159. 160.
    V. I. Dotsenko, P. Kratochvíl, J. Pešička, and B. Wielke:Czech. J. Phys.B, 1981, vol. 31, p. 209.CrossRefGoogle Scholar
  160. 161.
    A.W. Thompson and J.C. Williams:Metall. Trans. A, 1984, vol. 15A, p. 931.Google Scholar
  161. 162.
    J. Greggi and W. A. Soffa:Scripta Metall., 1980, vol. 14, p. 649.CrossRefGoogle Scholar
  162. 163.
    P. Kratochvíl and P. Haasen:Scripta Metall., 1982, vol. 16, p. 197.CrossRefGoogle Scholar
  163. 164.
    B. Ditchek and L.H. Schwartz:Ann. Rev. Mater. Sci., R. A. Huggins, R. H. Bube, and D. A. Vermilyea, eds., Annual Reviews Inc., Palo Alto, CA, 1979, vol. 9, p. 219.Google Scholar
  164. 165.
    A. J. Bradley, W. F. Cox, and H. J. Goldschmidt:J. Inst. Metals, 1941, vol. 67, p. 189.Google Scholar
  165. 166.
    E.J. Lee and A.J. Ardell:Strength of Metals and Alloys, Proc. 5th Int. Conf. on the Strength of Metals and Alloys, P. Haasen, V. Gerold, and G. Kostorz, eds., Pergamon Press, Oxford, England, 1979, vol. 1, p. 633.Google Scholar

Copyright information

© The Metallurgical of Society of AIME 1985

Authors and Affiliations

  • A. J. Ardell
    • 1
  1. 1.Department of Materials Science and EngineeringUniversity of CaliforniaLos Angeles

Personalised recommendations