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Crack and Contact Problems for Viscoelastic Bodies pp 259–311Cite as

Dynamic Viscoelastic Fracture

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 356))

Abstract

A semi-infinite crack in an infinite material body provides a canonical model with which to study the local crack-tip behavior of propagating cracks that avoids complicated analytical details arising in the consideration of finite length cracks in bounded bodies. Moreover, semi-infinite crack problems frequently admit analytical solutions with which one can examine precisely the behavior of relevant fracture parameters and calibrate alternative numerical schemes which must be employed in more complicated settings for which analytical solutions are not obtainable. These five chapters present analytical solution methods and results for a variety of dynamic, semi-infinite crack models within the context of linear viscoelasticity theory. In the introductory chapter, the general framework for constructing solutions to these semi-infinite crack problems is presented along with a discussion of the physical settings in which classical quasi-static analyses for elastic material models prove inadequate and which motivate the consideration of inertial effects and material viscoelasticity. The remaining chapters present detailed solutions to various canonical problems for both anti-plane shear and plane strain modes of deformation, and under both steady-state and transient crack propagation conditions. In particular, chapters 4 and 5 contain a description of a recently developed method for constructing solutions to dynamically accelerating, semi-infinite, anti-plane shear crack problems in viscoelastic material, and the result of applying the method to the case of an Achenbach-Chao material model.

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References

  1. Kaninnen, M.F. and C.H. Popelar: Advanced Fracture Mechanics, Oxford Univ. Press, New York 1985.

    Google Scholar 

  2. Ferry, J.D.: Viscoelastic Behaviour and Analysis of Composite Materials, 2nd Wiley, New York 1970.

    Google Scholar 

  3. Lockett, F.J.: Nonlinear Viscoelastic Solids, Academic Press, New York 1972.

    MATH  Google Scholar 

  4. Freund, L.B.: Dynamic Fracture Mechanics, Cambridge University Press, Cambridge 1990.

    Book  MATH  Google Scholar 

  5. Willis, J.R.: Accelerating Cracks and Related Problems, in: Elasticity, Mathematical Methods and Applications (Ed. G. Eason and R.W. Ogden ), Ellis Horwood Ltd., Chichester 1990, 397–409.

    Google Scholar 

  6. Graham, G.A.C.: The Correspondence Principle of Linear Viscoelasticity Theory for Mixed Boundary Value Problems Involving Time-dependent Boundary Regions, Quart. Appl. Math., 26 (1968), 167–174.

    MATH  Google Scholar 

  7. Schapery, R.A.: Correspondence Principles and a Generalized J Integral for Large Deformation and Fracture Analysis of Viscoelastic Media, Int. J. Frac., 25 (1984), 195–223.

    Article  Google Scholar 

  8. Golden, J.M. and G.A.C. Graham: Boundary Value Problems in Linear Viscoelasticity, Springer-Verlag, Berlin 1988.

    Book  MATH  Google Scholar 

  9. Willis, J.R.: Crack Propagation in Viscoelastic Media, J. Mech. Phys. Solids, 15 (1967), 229–240.

    Article  MATH  Google Scholar 

  10. Noble, B.: Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, New York 1958.

    MATH  Google Scholar 

  11. Walton, J.R.: On the Steady-State Propagation of an Anti-Plane Shear Crack in an Infinite General Linearly Viscoelastic Body, Quart. Appl. Math., 40 No. 1 (1982), 37–52.

    MathSciNet  MATH  Google Scholar 

  12. Fabrizio M. and A. Morro: Mathematical Problems in Linear Viscoelasticity, SIAM, Philadelphia 1992.

    Google Scholar 

  13. Atkinson, C. and R.D. List: A Moving Crack Problem in a Viscoelastic Solid, Int. J. Engng. Sci., 10 (1972), 309–322.

    Article  MATH  Google Scholar 

  14. Atkinson, C. and C.J. Coleman: On Some Steady-State Moving Boundary Problems in the Linear Theory of Viscoelasticity, J. Inst. Maths. Applics., 20 (1977), 85–106.

    Article  MATH  Google Scholar 

  15. Atkinson, C.: A Note on Some Dynamic Crack Problems in Linear Viscoelasticity, Arch. Mech. Stos., 31 (1979), 829–849.

    MATH  Google Scholar 

  16. Atkinson, C. and C.H. Popelar: Antiplane Dynamic Crack Propagation in a Viscoelastic Strip, J. Mech. Phys. Solids, 27 (1979), 431–439.

    Article  MATH  Google Scholar 

  17. Popelar, C.H. and C. Atkinson: Dynamic Crack Propagation in a Viscoelastic Strip, J. Mech. Phys. Solids, 28 (1980), 79–83.

    Google Scholar 

  18. Walton, J.R.: The Dynamic Steady-State Propagation of an Anti-Plane Shear Crack in a General Lineâ ly Viscoelastic Layer, J. Appl. Mech., 52 (1985), 853–856.

    Article  MathSciNet  MATH  Google Scholar 

  19. Walton, J.R.: The Dynamic Energy Release Rate for a Steadily Propagating Anti-Plane Shear Crack in a Linearly Viscoelastic Body, J. Appl. Mech., 54 (1987), 635–641.

    Article  MATH  Google Scholar 

  20. Herrmann, J.M. and J.R. Walton: On the Energy Release Rate for Dynamic Transient Anti-Plane Shear Crack Propagation in a General Linear Viscoelastic Body, J. Mech. Phys. Solids, 37 (1989), 619–645.

    Article  MathSciNet  MATH  Google Scholar 

  21. Schovanec L. and J.R. Walton: The Dynamic Energy Release Rate for Two Parallel Steadily Propagating Mode III Cracks in a Viscoelastic Body, Int. J. Frac., 41 (1989), 133–155.

    Article  MathSciNet  Google Scholar 

  22. Walton, J.R.: The Dynamic Energy Release Rate for a Steadily Propagating Mode I Crack in an Infinite Linear Viscoelastic Body, J. Appl. Mech., 57 (1990), 343–353.

    Article  MATH  Google Scholar 

  23. Gakov, F.D.: Boundary Value Problems, Pergamon Press, London 1966.

    Google Scholar 

  24. Titchmarsh, E.C.: Introduction to the Theory of Fourier Integrals, Oxford Univ. Press, London 1975.

    Google Scholar 

  25. Goleniewski, G.: Dynamic Crack Growth in a Viscoelastic Material, Int. J. Frac., 37 No. 3 (1988), R39 - R44.

    Article  Google Scholar 

  26. Achenbach, J.D. and Z.P. Bazant: Elastodynamic Near Tip Stress and Displacement Fields for Rapidly Propagating Cracks in Orthotropic Materials, J. Appl. Mech., 42 No. 1 (1975), 183–189.

    Article  MATH  Google Scholar 

  27. Achenbach, J.D.: Wave Propagation in Elastic Solids, North-Holland, Amsterdam 1973.

    MATH  Google Scholar 

  28. Herrmann, J.M. and J.R. Walton: On the Energy Release Rate for Dynamic Transient Mode I Crack Propagation in a General Linear Viscoelastic Body, Quart. Appl. Math., (52) No. 2 (1994), 201–228.

    MathSciNet  Google Scholar 

  29. Herrmann, J.M. and J.R. Walton: [ 1988 ], A Comparison of the Dynamic Transient Anti-Plane Shear Crack Energy Release Rate for Standard Linear Solid and Power-Law Type Viscoelastic Materials, in: Elastic-Plastic Failure Modelling of Structures with Applications, Eds. D. Hui and T.J. Kozik, ASME PVP-Vol 141 (1988), 1–11.

    Google Scholar 

  30. Boume, J.P. and J.R. Walton: On a Dynamically Accelerating Crack in an Achenbach-Chao Viscoelastic Solid, Int. J. Engng. Sci., 31 No. 4 (1993), 569–581

    Article  Google Scholar 

  31. Walton, J.R. and J.M. Herrmann: A New Method for Solving Dynamically Accelerating Crack Problems: Part 1. The Case of a Semi-Infinite Mode III Crack in Elastic Material Revisited, Quart. Appl. Math., 50 No. 2 (1992), 373–387.

    MathSciNet  MATH  Google Scholar 

  32. Ravi-Chandar, K. Knauss, W.G.: Dynamic Crack-Tip Stresses Under Stress Wave Loading-A Comparison of Theory and Experiment, Int. J. Frac., 20 (1982), 209–222.

    Article  Google Scholar 

  33. Ravi-Chandar, K. Knauss, W.G.: An Experimental Investigation into Dynamic Fracture: I. Crack Initiation and Arrest, ibid., 25 (1984), 247–262.

    Google Scholar 

  34. Ravi-Chandar, K. Knauss, W.G.: An Experimental Investigation into Dynamic Fracture: II. Microstructural Aspects, ibid., 26 (1984), 65–80.

    Google Scholar 

  35. Ravi-Chandar, K. Knauss, W.G.: An Experimental Investigation into Dynamic Fracture: III. On Steady-State Crack Propagation and Crack Branching, ibid., 26 (1984), 141–154.

    Google Scholar 

  36. Knauss, W.G.: On the Steady Propagation of a Crack in a Viscoelastic Sheet: Experiments and Analysis, in: Deformation and Fracture of High Polymers, H.H. Kausch R. Jaffee, eds.,Plenum Press, New York (1973), 501–541.

    Chapter  Google Scholar 

  37. Schapery, R.A.: A Theory of Crack Initiation and Growth in Viscoelastic Media I. Theoretical Development, I.t. J. Frac., 11 No. 1 (1975), 141–159.

    Article  Google Scholar 

  38. Barenblatt, G.I.: The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, in: Advances in Applied Mechanics, vol. VII, Academic Press, New York (1962), 55–129.

    Google Scholar 

  39. Kostrov, B.V. and L.V. Nikitin: Some General Problems of Mechanics of Brittle Fracture, Arch. Mech. Stos., 22 (1970), 749–775.

    MATH  Google Scholar 

  40. Mueller, H.K. and W.G. Knauss: Crack Propagation in a Viscoelastic Strip, J. Appl. Mech., (93) Series E (1971), 483–488.

    Google Scholar 

  41. Schovanec, L. and J.R. Walton: The Energy Release Rate for a Quasi-Static Mode I Crack in a Nonhomogeneous Linearly Viscoelastic Body, Engng. Frac. Mech., (28) No. 4 (1987), 445–454.

    Article  Google Scholar 

  42. Kostrov, B.V.: Unsteady Propagation of Longitudinal Shear Cracks, Appl. Math. and Mech. (PMM), (30) (1966), 1241–1248.

    Google Scholar 

  43. Burridge, R.: An Influence Function for the Intensity Factor in Tensile Fracture, Int. J. Engng. Sci., (14) (1976), 725–734.

    Google Scholar 

  44. Willis, J.R.: Accelerating Cracks and Related Problems, in: Elasticity, Mathematical Methods and Applications, G. Eason and R.W. Ogden, Ed.’s, Ellis Horwood Ltd., Chichester (1990), 397–409.

    Google Scholar 

  45. Achenbach, J.D. and C.C. Chao: A Three-Parameter Viscoelastic Model Particularly Suited for Dynamic Problems, J. Mech. Phys. Solids, (10) (1962), 245–252.

    Google Scholar 

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Authors and Affiliations

  1. Texas A&M University, College Station, TX, USA

    J. R. Walton

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Editors and Affiliations

  1. Simon Fraser University, Canada

    G. A. C. Graham

  2. Texas A & M University, USA

    J. R. Walton

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© 1995 Springer-Verlag Wien

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Walton, J.R. (1995). Dynamic Viscoelastic Fracture. In: Graham, G.A.C., Walton, J.R. (eds) Crack and Contact Problems for Viscoelastic Bodies. International Centre for Mechanical Sciences, vol 356. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2694-3_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2694-3_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82686-7

  • Online ISBN: 978-3-7091-2694-3

  • eBook Packages: Springer Book Archive

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