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Numerical study of geometric constraint and cohesive parameters in steady-state viscoelastic crack growth

International Journal of Fracture volume 141, pages 255–268 (2006)Cite this article

Abstract

This paper presents a finite element study of cohesive crack growth in a thin infinite viscoelastic strip to investigate the effects of viscoelastic properties, strip height, and cohesive model parameters on the crack growth resistance. The results of the study show that the dependence of the fracture energy on the viscoelastic properties for the strip problem is similar to that obtained for the infinite body problem even when the cohesive zone length is large compared to the height of the strip. The fracture energy also depends on the crack speed v through the dimensionless parameter v τ/L ∞ where L ∞ is the characteristic length of the cohesive zone and τ is the characteristic relaxation time of the bulk material. This relationship confirms that at least two properties of the fracture process must be prescribed accurately to model viscoelastic crack growth. In contrast, the fracture energy and crack speed are insensitive to the strip height even in situations where the growth of the dissipation zone is severely constrained by the strip boundaries. We observe that at high speeds, where the fracture energy asymptotically approaches the maximum value, the material surrounding the cohesive zone is in the rubbery (equilibrium) state and not the glassy state.

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References

  • GI Barenblatt (1962) ArticleTitleThe mathematical theory of equilibrium of crack in brittle fracture Adv Appl Mech 7 55–129 Occurrence Handle149728 Occurrence Handle10.1016/S0065-2156(08)70121-2

    Article  MathSciNet  Google Scholar 

  • R Christensen (1979) ArticleTitleA rate-dependent criterion for crack growth Int J Fract 15 3–21 Occurrence Handle10.1007/BF00115904

    Article  Google Scholar 

  • PG Gennes Particlede (1988) ArticleTitleFracture of a weakly crosslinked adhesive Comptes Rendus de l’Academie des Sciences, Serie II 307 1949–1953

    Google Scholar 

  • PG Gennes Particlede (1996) ArticleTitleSoft adhesives Langmuir 12 4497–4500 Occurrence Handle10.1021/la950886y

    Article  Google Scholar 

  • DS Dugdale (1960) ArticleTitleYielding of steel sheets containing slits J Mech Phys Solid 8 100–104 Occurrence Handle10.1016/0022-5096(60)90013-2 Occurrence Handle1960JMPSo...8..100D

    Article  ADS  Google Scholar 

  • AN Gent RP Petrich (1969) ArticleTitleAdhesion of viscoelastic materials to rigid substrates Proc Royal Soc London, Ser A 310 433–448 Occurrence Handle1969RSPSA.310..433G

    ADS  Google Scholar 

  • C-Y Hui DB Xu EJ Kramer (1992) ArticleTitleA fracture model for a weak interface in a viscoelastic material (small scale yielding analysis) J Appl Phys 72 3294–3304 Occurrence Handle10.1063/1.351451 Occurrence Handle1992JAP....72.3294H

    Article  ADS  Google Scholar 

  • A Jackson J Vincent R Turner (1988) ArticleTitleThe mechanical design of nacre Proc Royal Soc London, Ser B 234 415–440 Occurrence Handle1988RSPSB.234..415J Occurrence Handle10.1098/rspb.1988.0056

    Article  ADS  Google Scholar 

  • AJ Kinloch CC Lau JG Williams (1973) ArticleTitleMechanics of adhesive failure: I Proc Royal Soc London Ser A 332 385–399

    Google Scholar 

  • Klein PA, Nguyen TD (2005) Modeling crack dynamics under steady-state propagation conditions. (in preparation)

  • Knauss W (1973) On the steady propagation of a crack in a viscoelastic sheet: Experiments and analysis. In: Kausch HH, Hassell JA, Jaffee R (eds.) Deformation and fracture of high polymers. Plenum Press, New York, pp 501–541

  • W Knauss H Dietmann (1970) ArticleTitleCrack propagation under variable load histories in linearly viscoelastic solids Int J Eng Sci 8 643–656 Occurrence Handle10.1016/0020-7225(70)90049-2

    Article  Google Scholar 

  • BV Kostrov LV Nikitin (1970) ArticleTitleSome general problems of mechanics of brittle fracture Archiwum Mechaniki Stosowanej 22 749–776 Occurrence Handle0232.73110

    MATH  Google Scholar 

  • GA Maugin C Trimarco (1992) ArticleTitlePsuedomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture Acta Mechanica 94 1–28 Occurrence Handle0780.73014 Occurrence Handle1164929 Occurrence Handle10.1007/BF01177002

    Article  MATH  MathSciNet  Google Scholar 

  • H Mueller WG Knauss (1971) ArticleTitleCrack propagation in a linearly viscoelastic strip J Appl Mech 38 483–488

    Google Scholar 

  • A Needleman (1990) ArticleTitleAn analysis of decohesion along an imperfect interface Int J Solid Struct 42 21–40

    Google Scholar 

  • TD Nguyen S Govindjee PA Klein H Gao (2005) ArticleTitleA material force method for inelastic fracture J Mech Phys Solid 53 91–121 Occurrence Handle1086.74036 Occurrence Handle2106398 Occurrence Handle10.1016/j.jmps.2004.06.010 Occurrence Handle2005JMPSo..53...91N

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • P Rahulkumar A Jagota SJ Bennison S Saigal (2000) ArticleTitleCohesive element modeling of viscoelastic fracture: Application to peel testing of polymers Int J Solid Struct 37 1873–1897 Occurrence Handle1090.74676 Occurrence Handle10.1016/S0020-7683(98)00339-4

    Article  MATH  Google Scholar 

  • RA Schapery (1975a) ArticleTitleA theory of crack initiation and growth in viscoelastic media I. Theoretical development Int J Fract 11 141–159 Occurrence Handle10.1007/BF00034721

    Article  Google Scholar 

  • RA Schapery (1975b) ArticleTitleA theory of crack initiation and growth in viscoelastic media II. Approximate methods of analysis Int J Fract 11 369–388

    Google Scholar 

  • RA Schapery (1975c) ArticleTitleA theory of crack initiation and growth in viscoelastic media III. Analysis of continuous growth Int J Fract 11 549–562 Occurrence Handle10.1007/BF00116363

    Article  Google Scholar 

  • JC Simo TJR Hughes (1998) Computational inelasticity Springer-Verlag New York Occurrence Handle0934.74003

    MATH  Google Scholar 

  • V Tvergaard JW Hutchinson (1992) ArticleTitleThe relation between crack growth resistance and fracture process parameters in elastic-plastic solids J Mech Phys Solids 40 1377–1397 Occurrence Handle0775.73218 Occurrence Handle10.1016/0022-5096(92)90020-3 Occurrence Handle1992JMPSo..40.1377T

    Article  MATH  ADS  Google Scholar 

  • JR Walton (1990) ArticleTitleThe dynamic energy release rate for a steadily propagating Mode I crack in an infinite, linearly viscoelastic body J Appl Mech 57 343–353 Occurrence Handle0729.73162

    MATH  Google Scholar 

  • ML Williams (1965) ArticleTitleInitiation and growth of viscoelastic fracture Int J Fract 1 292–310

    Google Scholar 

  • DB Xu C-Y Hui EJ Kramer (1992) ArticleTitleInterface fracture and viscoelastic deformation in finite size specimens J Appl Phys 72 3305–3316 Occurrence Handle10.1063/1.352342 Occurrence Handle1992JAP....72.3305X

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Mechanics of Materials, Sandia National Laboratories, P.O. Box 0969, Livermore, CA, 94551, USA

    T. D. Nguyen

  2. Center of Mechanics, ETH Zurich, CLA J 27, Tannenstr. 3, CH-8092, Zurich, Switzerland

    S. Govindjee

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  1. T. D. Nguyen
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  2. S. Govindjee
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Correspondence to T. D. Nguyen.

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Nguyen, T.D., Govindjee, S. Numerical study of geometric constraint and cohesive parameters in steady-state viscoelastic crack growth. Int J Fract 141, 255–268 (2006). https://doi.org/10.1007/s10704-006-0080-9

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  • DOI: https://doi.org/10.1007/s10704-006-0080-9

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