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Non-uniform spacing of transverse cracks in symmetric composite laminates

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Abstract

We study multiple transverse cracking of symmetric laminates in the framework of the variational approach to fracture. Considering the Griffith model, we assume that several cracks can appear instantaneously through the whole thickness of the core layer, separating the bar in n elastic segments. We show that the energy minimization implies the bifurcation from solutions with uniform crack spacing to non uniformly spaced solutions, a phenomenon ignored in the literature for perfect systems. The stability of uniformly spaced solutions crucially depends on the concavity of the elastic compliance of each elastic segment as a function of the segment length. We compute this function and its derivatives numerically with domain-derivative techniques for a large set of geometric and material parameters. Our results indicate that the change of concavity and the related instability is a robust qualitative property that becomes quantitatively relevant in the case of laminates with thin and soft outer layers.

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Acknowledgements

The authors thank Blaise Bourdin and Jean-Jacques Marigo for their advice during this work.

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Authors and Affiliations

  1. DMAS, ONERA, F-59014, Lille, France

    Z. Karoui & J. Berthe

  2. CNRS, Institut Jean Le Rond d’Alembert, Sorbonne University, UMR 7190, 75005, Paris, France

    Z. Karoui & C. Maurini

  3. Université de Lille, CNRS, Centrale Lille, UMR 9013-LaMCube, Laboratoire de Mécanique, Multiphysiques, Multiéchelles, F-59000, Lille, France

    J. Berthe

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  1. Z. Karoui
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Correspondence to C. Maurini.

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Karoui, Z., Berthe, J. & Maurini, C. Non-uniform spacing of transverse cracks in symmetric composite laminates. Int J Fract 242, 191–206 (2023). https://doi.org/10.1007/s10704-023-00715-w

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