Skip to main content
SpringerLink
Log in

Crazing in block copolymers and blends

  • Conference paper
  • First Online:
Crazing in Polymers

Part of the book series: Advances in Polymer Science ((POLYMER,volume 52-53))

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Abbreviations

A:

Area, B/kT

B:

Activation energy at zero stress

C:

Proportionality constant

Di :

Scale factor for velocity; i=1, interface convolution; i=2, repeated cavitation

E:

Young's modulus in general. With subscripts C, M, PB, PS, P: moduli of composite, matrix phase, polybutadiene, polystyrene, and particle, respectively

ΔG:

Activation energy

H:

Height of channel in which interface convolutes; craze tip opening displacement

K:

Bulk modulus in general. With subscript C, M, PB, PS, P: bulk moduli of composite, matrix phase, polybutadiene, polystyrene, and particle, respectively

KI :

Mode one stress intensity factor

KIC :

Critical stress intensity factor for propagation

N:

Surface density of crazable sites

Q:

Functional dependence of negative pressure on deviatric stress for cavity expansion

R:

Radius of particulate heterogeneity

T:

Absolute temperature

V:

Volume

W:

Toughness, total work to fracture

Y:

Yield stress in general. With subscript cr, craze-yield stress

Y(λn):

Tensile yield stress of polymer after uniaxial extension to an extension ratio of λn

Ŷ:

Athermal tensile yield stress of a glassy polymer

a:

Craze half length

b:

Craze half thickness at craze center

c:

Volume fraction

f:

f(x)=u(x)+k(x), final half thickness of craze cavity under the craze traction σc

g:

g(x), unconstrained half thickness of craze lentil after undergoing expansion

k:

k(x), primordial half thickness of craze cavity

n:

Total number of crazes, strain rate exponent in non-linear viscosity

n0 :

Total number of internal particulate heterogeneities

q:

Stress concentration factor

s:

Deviatoric (shear) stress

t:

Time in general. With subscripts f, in, inact: fracture, initiation, inactivation time

u:

(=uy) u(x), displacement of half craze cavity under craze traction σc

v:

Velocity of craze

w:

Width of sample in general. With subscripts l, s in the long and short direction

x:

Coordinate

y:

Coordinate

z:

Coordinate

Δ:

Mean distance between surface crazes

Δ:

Length of cavitational process zone

χ:

Surface free energy, surface tension

β:

Aspect ratio of a craze, =a/b

γ:

Volumetric coefficient of expansion in general. With subscripts C, M. PB, PS, P: composite, matrix, polybutadiene, polystyrene, particle, respectively

δ:

Mean distance between crazes in the volume

δ:

With subscripts, A, B: solubility parameter

δ:

With subscripts, A, B, solubility parameter

ε:

Uniaxial strain in general. With subscripts f, m, z: fracture, maximum at cavitation, and in the extension direction, respectively

λ:

Wave length of convoluted interface

λn :

Extension ratio

λ′n :

As defined in Eqn. (51)

ν:

Poisson's ratio of polystyrene. With subscripts C, M, P: composite, matrix, particle, respectively

ϱ:

Active craze front length per unit volume. With subscripts C, M, P: composite, matrix, particle, respectively

σ:

Negative pressure specifically. With subscripts c, e, i, m, P, ST, TH, ∞: craze traction, Mises equivalent, one of three principal stresses, maximum level of craze traction where cavitation in PB begins, negative pressure in particle, negative pressure due to one of three principal stresses, negative pressure due to thermal mismatch, uniaxial applied stress at the borders

σ:

With subscripts xx, yy, zz etc. for components of the local stress tensor

θ:

Ratio of slope of the falling to the rising part of the traction cavitation law

Θ:

Craze dilatation

τ:

Time constant

ξ:

Symbolic parameter describing defects. With subscripts e, i: extrinsic, intrinsic, respectively

η0 :

Non-linear viscosity coefficient

6 References

  1. Argon, A. S. in: “Glass: Science and Technology”, (eds.) Uhlmann, D. R., Kreidl, N. J., 79, New York, Academic Press, 1980

    Google Scholar 

  2. “Advances in Polymer Science”, (ed.) Kausch, H. H., E. J. Kramer, Chapter 1

    Google Scholar 

  3. “Advances in Polymer Science”, (ed.) Kausch, H. H., M. Dettenmaier, Chapter 2 (this volume)

    Google Scholar 

  4. Bucknall, C. B.: “Toughened Polymers”, London, Applied Science Publ. 1977

    Google Scholar 

  5. Kawai, H., et al., J. Macromol. Sci. — Phys. B17(3), 427 (1980)

    Google Scholar 

  6. Argon, A. S., et al.: in “Toughening of Plastics”, 16–1, London, Plastics and Rubber Institute, 1978

    Google Scholar 

  7. Argon, A. S. et al., in: “Deformation, Yield and Fracture of Polymers”, 28–1, London, Plastics and Rubber Institute, 1982

    Google Scholar 

  8. Argon, A. S., Bessonov, M. I.: Phil. Mag., 35, 917 (1977)

    Google Scholar 

  9. Wellinghoff, S. T., Baer, E.: J. Appl. Polymer Sci., 22, 2025 (1978)

    Google Scholar 

  10. Argon, A. S.: Acta Met., 27, 47 (1979)

    Google Scholar 

  11. Argon, A. S.: Phys. Chem. Solids, 43, 945 (1982)

    Google Scholar 

  12. Megusar, J., et al., in: Rapidly Solidified Amorphous and Crystalline Solids, (eds.) Kear, B. H., Giessen, B. C., and Cohen, M., New York, North Holland, 282, 1982

    Google Scholar 

  13. Argon, A. S., Hannoosh, J. G.: Phil. Mag., 36, 1195 (1977)

    Google Scholar 

  14. Argon, A. S., Salama, M. M.: Phil. Mag., 36, 1217 (1977)

    Google Scholar 

  15. Donald, A. M., Kramer, E. J.: Phil. Mag., 43, 857 (1981)

    Google Scholar 

  16. Argon, A. S., et al.: J. Polymer Sci., 19, 253 (1981)

    Google Scholar 

  17. Murray, J., Hull, D.: J. Polymer Sci., (Part A-2) 8, 1521 (1970)

    Google Scholar 

  18. Murray, J., Hull, D.: Polymer Letters, 8, 159 (1970)

    Google Scholar 

  19. Brown, N.: Phil. Mag., 32, 1041 (1975)

    Google Scholar 

  20. Haward, R. N., Thackray, G.: Proc. Roy. Soc. A302, 453 (1968)

    Google Scholar 

  21. Argon, A. S.: Phil. Mag., 28, 839 (1973)

    Google Scholar 

  22. Lauterwasser, B. D., Kramer, E. J.: Phil. Mag. 39, 469 (1979)

    Google Scholar 

  23. Argon, A. S., Salama, M. M.: Mater. Sci. Engng., 23, 219 (1976)

    Google Scholar 

  24. Kambour, R. P.: Polymer Sci. Macromol. Rev., 7, 1 (1973)

    Google Scholar 

  25. Sternstein, S. S., Ongchin, L.: Polymer Prepr., 10, 117 (1969)

    Google Scholar 

  26. Argon, A. S.: J. Macromol. Sci.-Phys., B8(3–4), 573 (1973)

    Google Scholar 

  27. Argon, A. S.: Pure Appl. Chem., 43, 247 (1975)

    Google Scholar 

  28. Bucknall, C. B.: J. Mater., 4, 214 (1969)

    Google Scholar 

  29. Bucknall, C. B. et al.: J. Mater. Sci., 7, 1443 (1972)

    Google Scholar 

  30. Oxborough, R. J., Bowden, P. B.: Phil. Mag., 28, 547 (1973)

    Google Scholar 

  31. Oxborough, R. J., Bowden, P. B.: Phil. Mag., 30, 171 (1974)

    Google Scholar 

  32. Bates, F. S. et al.: Macromolecules, in the press

    Google Scholar 

  33. Green, A. E., Zerna, W.: “Theoretical Elasticity”, 346, Oxford, Clarendon Press, 1954

    Google Scholar 

  34. Andrews, E. H., Bevan, S.: Polymer, 13, 337 (1972)

    Google Scholar 

  35. Bevan, S.: J. Appl. Polymer Sci., 27, 4263 (1982)

    Google Scholar 

  36. Verheulpen-Heymans, N., Bauwens, J. C.: J. Mater. Sci., 11, 1 (1976); Ibid., 11, 7 (1976)

    Google Scholar 

  37. Beahan, P. et al.: Phil. Mag., 24, 1267 (1971)

    Google Scholar 

  38. Brown, H. R., Kramer, E. J.: J. Macromol. Sci. Phys., B19, 487 (1981)

    Google Scholar 

  39. Schwier, C. E.: “Crazing in Block Copolymers”, Ph. D. Thesis, M.I.T., Cambridge, Mass. 1983

    Google Scholar 

  40. Andersson, H., Bergkvist, H.: J. Mech. Phys. Solids, 18, 1 (1970)

    Google Scholar 

  41. Bird, R. J. et al.: Polymer, 12, 742 (1971)

    Google Scholar 

  42. Doyle, M.J. et al.: Proc. Roy. Soc., A329, 137 (1972)

    Google Scholar 

  43. Doyle, M. J.: J. Maters. Sci., 17, 760 (1982)

    Google Scholar 

  44. Murray, J., Hull, D.: J. Polymer Sci., (Part A-2) 8, 583 (1970)

    Google Scholar 

  45. Doyle, M. J.: J. Mater. Sci., 17, 204 (1982)

    Google Scholar 

  46. Helfand, E., Wasserman, Z. R. in: “Developments in Block Copolymers”, (ed.) Goodman, I., London, Appl. Sci. Publ., 99, 1982; Macromolecules, 11, 960 (1978)

    Google Scholar 

  47. Meier, D. J.: J. Polymer Sci., C26, 81 (1969)

    Google Scholar 

  48. Krause, S.: Macromolecules, 3, 84 (1970)

    Google Scholar 

  49. Cohen, R. E.: ACS Symposium Series, 193, 489 (1982)

    Google Scholar 

  50. Argon, A. S. et al.: J. Polymer Sci., 19, 253 (1981)

    Google Scholar 

  51. Kawai, E. et al., in: “Progress in Polymer Science, Japan”, (eds.) Imahori, K., and Iwakura, Y., vol. 4, New York, Halstead Press, 1972

    Google Scholar 

  52. Leibler, L.: Macromol. Chem., Rapid Communication, 2, 393 (1981)

    Google Scholar 

  53. Reiss, G. et al.: J. Macromol. Sci., B17(2), 355 (1980)

    Google Scholar 

  54. Gebizlioglu, O. S. et al.: SPE-ANTEC, 40, 126 (1982)

    Google Scholar 

  55. Echte, A.: Angew. Makromol. Chem., 58/59, 175 (1977)

    Google Scholar 

  56. Argon, A. S. in: “Polymeric Materials, Relationship Between Structure and Mechanical Behavior”, 411, Metals Park, Ohio, ASM, 1975

    Google Scholar 

  57. Bohn, L.: Angew. Makromol. Chem., 20, 129 (1971)

    Google Scholar 

  58. Ferry, J. D.: “Viscoelastic Properties of Polymers”, (2nd. Ed.), 586, New York, J. Wiley and Sons, 1970

    Google Scholar 

  59. Goodier, J. N.: ASME Trans., 55, 39 (1933)

    Google Scholar 

  60. Eshelby, J. D.: Proc. Roy. Soc., A 241, 376 (1957)

    Google Scholar 

  61. Mura, T.: “Micromechanics of Defects in Solids”, The Hague, Martinus Nijhoff Publ., 1982

    Google Scholar 

  62. Chow, T. S.: J. Polymer Sci.-Phys., 16, 959 (1978)

    Google Scholar 

  63. Chow, T. S.: J. Polymer Sci.-Phys., 16, 967 (1978)

    Google Scholar 

  64. Argon, A. S. et al.: J. Appl. Phys., 39, 1899 (1968)

    Google Scholar 

  65. Turley, S. G., Keskkula, H.: Polymer, 21, 466 (1980)

    Google Scholar 

  66. Gebizlioglu, O. S., Tanaka, T.: to be published

    Google Scholar 

  67. Gebizlioglu, O. S. et al.: Polymer Preprints, 22, (No. 2), 257 (1981)

    Google Scholar 

  68. Cunningham, M. et al.: to be published

    Google Scholar 

  69. Broutman, J. J., Panizza, G.: Int. J. Poly. Mater., 1, 95 (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    A. S. Argon, R. E. Cohen, O. S. Gebizlioglu & C. E. Schwier

Authors
  1. A. S. Argon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. E. Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. S. Gebizlioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. E. Schwier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

H. H. Kausch

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Argon, A.S., Cohen, R.E., Gebizlioglu, O.S., Schwier, C.E. (1983). Crazing in block copolymers and blends. In: Kausch, H.H. (eds) Crazing in Polymers. Advances in Polymer Science, vol 52-53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024060

Download citation

  • DOI: https://doi.org/10.1007/BFb0024060

  • Received:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12571-6

  • Online ISBN: 978-3-540-38652-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation