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Asymptotic mechanical fields at the tip of a mode I crack in rubber-like solids
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
2014 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 10, 1923-1930 p.Article in journal (Refereed) Published
Abstract [en]

Asymptotic analyses of the mechanical fields in front of stationary and propagating cracks facilitate the understanding of the mechanical and physical state in front of crack tips, and they enable prediction of crack growth and failure. Furthermore, efficient modelling of arbitrary crack growth by use of XFEM (extended finite element method) requires accurate knowledge of the asymptotic crack tip fields. In the present work, we perform an asymptotic analysis of the mechanical fields in the vicinity of a propagating mode I crack in rubber. Plane deformation is assumed, and the material model is based on the Langevin function, which accounts for the finite extensibility of polymer chains. The Langevin function is approximated by a polynomial, and only the term of the highest order contributes to the asymptotic solution. The crack is predicted to adopt a wedge-like shape, i.e. the crack faces will be straight lines. The angle of the wedge and the order of the stress singularity depend on the hardening of the strain energy function. The present analysis shows that in materials with a significant hardening, the inertia term in the equations of motion becomes negligible in the asymptotic analysis. Hence, there is no upper theoretical limit to the crack speed.

Place, publisher, year, edition, pages
2014. Vol. 51, no 10, 1923-1930 p.
Keyword [en]
Asymptotic, Rubber, Elastomer, Fracture mechanics, Crack
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-145569DOI: 10.1016/j.ijsolstr.2014.01.030ISI: 000334982500005ScopusID: 2-s2.0-84896489402OAI: diva2:722987

QC 20140610

Available from: 2014-06-10 Created: 2014-05-23 Last updated: 2014-06-10Bibliographically approved

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Kroon, Martin
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Solid Mechanics (Dept.)
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