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Enhanced fictitious crack model accounting for material drawn into the cohesive zone: physically based crack closure criterion

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Abstract

According to the fictitious crack model, the crack width is infinitely thin at crack initiation and with further loading the crack opens, but no material exists in the cohesive zone. Despite that, the crack is assumed to able to sustain a load. While this is possible at the atomic level, it is not a realistic assumption for the macroscopic behavior we are considering. Invoking the mass conservation law and by postulating a relation between the porosity f of the cohesive zone and the damage variable \(\kappa _{n}\), which is that part of the damage variable \((\kappa )\) that is related to opening of the crack, it is shown that the fictitious crack model can be enhanced so that it accounts for material that is drawn into the cohesive zone. In turn, the amount of material present in the cohesive zone implies a consistent and physically based crack closure criterion. The concepts are first discussed in detail for uniaxial loading and then generalized to arbitrary loadings.

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Acknowledgments

Stimulating discussions with Adj. Prof. Johan Tryding, Lund University, Sweden and TetraPak, Lund, Sweden are greatly appreciated.

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Authors and Affiliations

  1. Division of Solid Mechanics, Lund University, 22100, Lund, Sweden

    Niels Saabye Ottosen & Matti Ristinmaa

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  1. Niels Saabye Ottosen
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  2. Matti Ristinmaa
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Correspondence to Niels Saabye Ottosen.

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Ottosen, N.S., Ristinmaa, M. Enhanced fictitious crack model accounting for material drawn into the cohesive zone: physically based crack closure criterion. Int J Fract 199, 199–211 (2016). https://doi.org/10.1007/s10704-016-0105-y

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  • DOI: https://doi.org/10.1007/s10704-016-0105-y

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