Skip to main content
SpringerLink
Log in
Book cover

Deformation and Fracture of High Polymers pp 501–541Cite as

On the Steady Propagation of a Crack in a Viscoelastic Sheet: Experiments and Analysis

  • Chapter

Abstract

In the following pages we present a continuum mechanical description of steady crack propagation in a linearly viscoelastic solid. The analysis is exact within the realm of linear viscoelasticity theory. Inasmuch as this colloquium deals with the deformation and fracture of high polymers from the molecular, microscopic, and macroscopic viewpoint, it is appropriate to recognize the complementary nature of the microscopic and the macro-continuum approach to polymer fracture. This remark seems essential because the later development contains assumptions which must appear rather gross to those who concern themselves with the microscopic or even atomistic aspect of the fracture process.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barenblatt, G. I., Entov, V. M., and Salganik, R. L., “Kinetics of Crack Propagation, General Considerations: Cracks Approaching Equilibrium Cracks”, Mech. Solids (Mekhan. Tverdogo Tela) 1 (5), English version p 82 (1966).

    Google Scholar 

  2. Barenblatt, G. I., Entov, V. M., and Salganik, R. L., “Kinetics of Crack Propagation: Conditions of Fracture and Long Term Strength”, ibid.,p 76.

    Google Scholar 

  3. Barenblatt, G. I., Entov, V. M., and Salganik, R. L., “Kinetics of Crack Propagation: A Note on the Rule of Summation of Damageabilities”, ibid., 2 (2), English version p 148 (1967).

    Google Scholar 

  4. Barenblatt, G. I., Entov, V. M., and Salganik, R. L., “Kinetics of Crack Propagation: Fluctuation Fracture”, ibid., 2, (1), English version p 122 (1967).

    Google Scholar 

  5. Barenblatt, G. I., Entov, V. M., and Salganik, R. L., “On the Influence of Vibrational Heating on the Fracture Propagation in Polymeric Materials”, Proceedings of the IUTAM Symposium in East Kilbride, June 25–28, 1968.

    Google Scholar 

  6. Barenblatt, G. I., Entov, V. M., and Salganik, R. L., “Some Problems of the Kinetics of Crack Propagation”, in Inelastic Behavior of Solids, Materials Science and Engineering Series, Kanninen, M. F., Adler, W. F., Rosenfield, A. R., and Jaffee, R. I. (Eds.), McGraw-Hill (1970).

    Google Scholar 

  7. Rivlin, R. S., and Thomas, A. G., “Rupture of Rubber, I. Characteristic Energy for Tearing”, J. Polymer Sci., 10 (3), 291 (1953).

    Article  CAS  Google Scholar 

  8. Thomas, A. G., “Rupture of Rubber, II. The Strain Concentration at an Incision”, J. Polymer Sci., 18, 177 (1955).

    Article  CAS  Google Scholar 

  9. Greensmith, H. W., and Thomas, A. G., “Rupture of Rubber, III. Determination of Tear Properties”, J. Polymer Sci., 18, 189 (1955).

    Article  CAS  Google Scholar 

  10. Greensmith, H. W., “Rupture of Rubber, IV. Tear Properties of Vulcanizates Containing Carbon Black”, J. Polymer Sci., 21, 175 (1956).

    Article  Google Scholar 

  11. Greensmith, H. W., Mullins, L., and Thomas, A. G., “Rupture of Rubber”, Trans. Soc. Rheology, 4, 179 (1960).

    Article  CAS  Google Scholar 

  12. Thomas, A. G., “Rupture of Rubber, VI. Further Experiments on the Tear Criterion”, J. Appl. Polymer Sci., 3 (8), 168 (1960).

    Article  CAS  Google Scholar 

  13. Greensmith, H. W., “Rupture of Rubber, VII. Effect of Rate Extension in Tensile Tests”, J. Appl. Polymer Sci., 3 (8), p 175 (1960).

    Article  CAS  Google Scholar 

  14. Mullins, L., “Rupture of Rubber, Part IX. Role of Hysteresis in the Tearing of Rubber”, Trans. Rubber Ind., 35, 213 (1959).

    CAS  Google Scholar 

  15. Greensmith, H. W., “Rupture of Rubber, VIII. Comparison of Tear and Tensile Rupture Measurements”, J. Appl. Polymer Sci., 3, 183 (1960).

    Article  CAS  Google Scholar 

  16. Greensmith, H. W., “Rupture of Rubber, XI. Tensile Rupture and Crack Growth in a Noncrystallizing Rubber”, J. Appl. Polymer Sci., 8, 1113 (1964).

    Article  CAS  Google Scholar 

  17. Knauss, W. G., “The Time Dependent Fracture of Viscoelastic Materials”, Proceedings of the First International Conference on Fracture, (1965), Vol. 2, p 1139 See also Ph.D. Thesis, California Institute of Technology, Pasadena, California, 1963.

    Google Scholar 

  18. Knauss, W. G., “Stable and Unstable Crack Growth in Viscoelastic Media”, Trans. Soc. Rheology, 13 (3), 291 (1969).

    Article  CAS  Google Scholar 

  19. Mueller, H. K., and Knauss, W. G., “Crack Propagation in a Linearly Viscoelastic Strip”, J. Appl. Mech., 38, Series E (No. 2 ), 483 (1971).

    Google Scholar 

  20. Mueller, H. K., and Knauss, W. G., `The Fracture Energy and Some Mechanical Properties of a Polyurethane Elastomer“, Trans. Soc. Rheology, 15 (2), 217 (1971).

    Article  CAS  Google Scholar 

  21. Knauss, W. G., “Delayed Failure — the Griffith Problem for Linearly Viscoelastic Materials”, Intern. J. Fracture Mech.,6 (1), 7 (1970). See also, Fracture 1969,Proceedings of the International Conference on Fracture, Brighton (1969), p 894.

    Google Scholar 

  22. Kostrov, B. V., and Nikitin, L. V., “Some General Problems of Mechanics of Brittle Fracture”, Archiwum Mechaniki Stosowanej, 22 (6), English version p. 749 (1970).

    Google Scholar 

  23. Marshall, G. P., Culver, L. E., and Williams, J. G., “Crack and Craze Propagation in Polymers: A Fracture Mechanics Approach. I. Crack Growth in Polymethyl Methacrylate in Air”, in Plastics and Polymers, The Plastics Institute Transactions and Journal, Headington Hill Hall, Oxford (1969), p 75.

    Google Scholar 

  24. Marshall, G. P., Culver, L. E., and Williams, J. G., The Growth of Cracks and Crazes in Polystyrene: A Fracture Mechanics Approach, Imperial College of Science and Technology, Mechanical Engineering Department, London (1971).

    Google Scholar 

  25. Prandtl, L., “Ein Gedankenmodell fur den Zerreissvorgang spröder Körper”, ZAMM, 13, 129 (1933). See also Ludwig Prandtl, Gesammelte Abhandlungen, Erster Teil, Springer (1961).

    Google Scholar 

  26. Williams, M. L., “The Fracture of Viscoelastic Material”, in Fracture of Solids, Drucker and Gilman (Eds). Interscience Publishers (1963), p 157.

    Google Scholar 

  27. Williams, M. L., “The Kinetic Energy Contribution to Fracture Propagation in a Linearly Viscoelastic Material”, Intern. J. Fracture Mech., 4 (1), 69 (1968).

    Google Scholar 

  28. Williams, M. L., “Initiation and Growth of Viscoelastic Fracture”, ibid., 1 (4), 292 (1965).

    CAS  Google Scholar 

  29. Wnuk, M. P., and Knauss, W. G., “Delayed Fracture in Viscoelastic-plastic Solids”, Intern. J. Solids Structures, 6, 995 (1970).

    Article  Google Scholar 

  30. Wnuk, M. P., “Energy Criterion for Initiation and Spread of Fracture in Viscoelastic Solids”, South Dakota State University, Engineering Experiment Station Bulletin, No. 7 (April, 1968 ).

    Google Scholar 

  31. Wnuk, M. P., “Effects of Time and Plasticity on Fracture”, Brit. J. Appl. Phys., Series 2, 2, 1245 (1969).

    Google Scholar 

  32. Knauss, W. G., “The Mechanics of Polymer Fracture”, Appl. Mech. Reviews (January, 1973).

    Google Scholar 

  33. Jones, W. J., North American Rockwell Corp., Rocketdyne Division, McGregor, Texas, personal communication.

    Google Scholar 

  34. Williams, M. L., Landel, R. F., and Ferry, J. D., “The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glassforming Liquids”, J. Am. Chem. Soc., 77, 3701–3707 (1955).

    Article  CAS  Google Scholar 

  35. Kambour, R. P., “Mechanism of Fracture in Glassy Polymers. I. Fracture Surfaces in Poly-methyl methacrylate”, J. Polymer Sci., Part A, 3, 1713 (1965).

    CAS  Google Scholar 

  36. Kambour, R. P., “Mechanism of Fracture in Glassy Polymers, II. Survey of Crazing Response During Crack Propagation in Several Polymers”, J. Polymer Sci., Part A-2, 4, 17 (1966).

    Article  CAS  Google Scholar 

  37. Kambour, R. P., “Mechanism of Fracture in Glassy Polymers, III. Direct Observation of the Craze Ahead of the Propagating Crack in Poly(methyl methacrylate) and Polystyrene”, J. Polymer Sci., Part A-2, 4, 349 (1966).

    Article  CAS  Google Scholar 

  38. Kaelble, D. H., Physical Chemistry of Adhesion, Interscience Publishers, John Wiley and Sons, New York (1971).

    Google Scholar 

  39. McClintock, F. A., Plasticity Aspects of Fracture, in Fracture, an Advanced Treatise, Liebowitz, H. (Ed.), Academic Press, New York (1971), Vol 3, p 47.

    Google Scholar 

  40. Broek, D., A Study on Ductile Fracture,National Lucht-en Ruimtevaartlaboratorium, NLR TR 71021 U, The Netherlands.

    Google Scholar 

  41. Dugdale, D. S., “Yielding of Steel Sheets Containing Slits”, Jour. Mech. Phys. Solids, 8, 100 (1960).

    Article  Google Scholar 

  42. Barenblatt, G. I., `The Mathematical Theory of Equilibrium Cracks in Brittle Fracture“, in Advances in Applied Mechanics, Academic Press (1962), Vol. 7, p 55.

    Google Scholar 

  43. England, A. H., Complex Variable Methods in Elasticity, Wiley-Interscience, New York (1971).

    Google Scholar 

  44. Rice, J. R., Mathematical Analysis in the Mechanics of Fracture, Liebowitz, H. (Ed.), Academic Press, New York (1971), Vol 2, p 192.

    Google Scholar 

  45. Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, J.R.M. Radok Transl.; Noordhoff Ltd., Groningen (1963).

    Google Scholar 

  46. Lake, G. J., and Thomas, A. G., “The Strength of Highly Elastic Materials”, Proc. Roy. Soc., London, Series A, Math. and Phys. Sci., 300 (1460), 108 (1967).

    Article  CAS  Google Scholar 

  47. Bueche, F., and Halpin, J. C., “Molecular Theory for the Tensile Strength of Gum Elastomers”, J. Appl. Phys., 35 (1), 36 (1964).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. California Institute of Technology, Pasadena, California, USA

    W. G. Knauss

Authors
  1. W. G. Knauss
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Materials Sciences Department, Battelle-Institut e. V., Frankfurt/Main, Germany

    H. Henning Kausch

  2. Organic and Polymeric Materials Department, Battelle Memorial Institute, Columbus Laboratories, USA

    John A. Hassell

  3. Department of Physics and Metallurgy, Battelle Memorial Institute, Columbus Laboratories, USA

    Robert I. Jaffee

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer Science+Business Media New York

About this chapter

Cite this chapter

Knauss, W.G. (1973). On the Steady Propagation of a Crack in a Viscoelastic Sheet: Experiments and Analysis. In: Kausch, H.H., Hassell, J.A., Jaffee, R.I. (eds) Deformation and Fracture of High Polymers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1263-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-1263-6_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1265-0

  • Online ISBN: 978-1-4757-1263-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation