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An analysis of competing toughening mechanisms in layered and particulate solids

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Abstract

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus \(90^{\circ }\) symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic–plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale.

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Notes

  1. The dimension of the square finite elements near the crack tips has been fixed to 1/20th the vertical distance between the semi-infinite cracks.

  2. Recall that \(\phi <0\) implies upwards kinking, whereas \(\phi >0\) will give downwards kinking, as explained by Lo (1978).

  3. We note in passing that the limit \(R_0 /d\ll 1\) corresponds to an elastic–brittle solid. We anticipate that the degree of toughening associated with the deviations in crack path are comparable to that determined for the choice \(R_0 /d=1\).

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Acknowledgments

The authors are grateful to DARPA for their financial support through Grant W91CRB-10-1-005 titled “A micro-cellular solids approach to thermo-structural materials with controlled architecture”.

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  1. Cambridge University Engineering Department, Trumpington Street, Cambridge, CB2 1PZ, UK

    Giovanni Noselli, Vikram S. Deshpande & Norman A. Fleck

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  1. Giovanni Noselli
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  2. Vikram S. Deshpande
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  3. Norman A. Fleck
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Correspondence to Giovanni Noselli.

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Noselli, G., Deshpande, V.S. & Fleck, N.A. An analysis of competing toughening mechanisms in layered and particulate solids. Int J Fract 183, 241–258 (2013). https://doi.org/10.1007/s10704-013-9890-8

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  • DOI: https://doi.org/10.1007/s10704-013-9890-8

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