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Nucleation and Development of Multiple Cracks in Thin Composite Fibers via the Inverse-Deformation Approach

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Abstract

We study the nucleation and development of crack patterns in thin composite fibers under tension in this work. A fiber comprises an elastic core and an outer layer of a weaker brittle material. In recent tensile experiments on such composites, multiple cracks were observed to develop simultaneously on the outer layer. We propose here a simple one-dimensional model to predict such phenomena using the inverse-deformation approach to fracture. We idealize the problem as two axially loaded rods coupled by a linear interfacial condition. The latter can be regarded as an adhesive that resists slip between the two materials. One rod is modeled as a brittle material, and the other a linearly elastic material, both undergoing finite deformations.

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Acknowledgements

We thank Phoebus Rosakis, Patrick Farrell, David Bindel, Maximilian Ruth, and Gokul Nair for useful conversations.

Funding

This work was supported in part by the National Science Foundation through grant DMS-2006586, which is gratefully acknowledged.

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Authors and Affiliations

  1. Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY, 14853, USA

    Arnav Gupta & Timothy J. Healey

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Timothy J. Healey

Authors
  1. Arnav Gupta
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  2. Timothy J. Healey
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Both authors contributed equally to the paper.

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Correspondence to Arnav Gupta.

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The authors declare no competing interests.

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Dedicated to the memory of Jerry Ericksen and his many deep contributions to continuum mechanics

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Gupta, A., Healey, T.J. Nucleation and Development of Multiple Cracks in Thin Composite Fibers via the Inverse-Deformation Approach. J Elast (2023). https://doi.org/10.1007/s10659-023-10019-8

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