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A boundary integral method for a dynamic, transient mode I crack problem with viscoelastic cohesive zone

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Abstract

We consider the problem of the dynamic, transient propagation of a semi-infinite, mode I crack in an infinite elastic body with a nonlinear, viscoelastic cohesize zone. Our problem formulation includes boundary conditions that preclude crack face interpenetration, in contrast to the usual mode I boundary conditions that assume all unloaded crack faces are stress-free. The nonlinear viscoelastic cohesive zone behavior is motivated by dynamic fracture in brittle polymers in which crack propagation is preceeded by significant crazing in a thin region surrounding the crack tip. We present a combined analytical/numerical solution method that involves reducing the problem to a Dirichlet-to-Neumann map along the crack face plane, resulting in a differo-integral equation relating the displacement and stress along the crack faces and within the cohesive zone.

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Authors and Affiliations

  1. Department of Mathematics, Amherst College, Amherst, MA, 01002, USA

    Tanya L. Leise

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Jay R. Walton & Yuliya Gorb

Authors
  1. Tanya L. Leise
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  2. Jay R. Walton
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  3. Yuliya Gorb
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Corresponding author

Correspondence to Jay R. Walton.

Additional information

to appear Int. J. Frac., special issue devoted to the IUTAM Symposium: Dynamic Fracture and Fragmentation, 8–12 March 2009.

This work was supported in part by the Army Research Laboratory under contract number W911NF-04-2-00-11 and in part by award number KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).

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Leise, T.L., Walton, J.R. & Gorb, Y. A boundary integral method for a dynamic, transient mode I crack problem with viscoelastic cohesive zone. Int J Fract 162, 69–76 (2010). https://doi.org/10.1007/s10704-009-9385-9

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  • DOI: https://doi.org/10.1007/s10704-009-9385-9

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