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A bridging law and its application to the analysis of toughness of carbon nanotube-reinforced composites and pull-out of fibres grafted with nanotubes

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Abstract

Bridging laws are essential in predicting the mechanical behaviour of conventional short-fibre-reinforced composites and the emerging nanofibre-reinforced composites. In this paper, we first review some studies on the toughness of carbon nanotube-reinforced composites that is induced by the pull-out of the nanotubes from the matrix, and on the development of the corresponding bridging laws. A close examination of the available bridging laws for carbon nanotubes reveals that some fundamental issues need to be further addressed. We propose a simple nonlinear and smooth bridging law to describe the pull-out force–displacement behaviour of carbon nanotubes from a matrix. This law contains only two material parameters, reflects the basic features of the pull-out experiments, and is easy to use. We then use this bridging law to calculate the fracture toughness of carbon nanotube-reinforced nanocomposites and predict the pull-out force–displacement response of conventional short fibres that are grafted with carbon nanotubes. Some parametric studies are conducted to reveal the influence of various parameters at the nano- and micro-scale on these properties.

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Acknowledgments

J. Wang and L. Tong thank the support of the China Scholarship Council and the Australian Research Council via Discovery Project Grant (DP130103958). J. Wang also thanks the support of the National Natural Science Foundation of China (Grant Nos. 11232001 and 11521202). Miss Linjuan Wang is thanked for assistance with numerical calculations and figures.

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems and Center for Applied Physics and Technology, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China

    Jianxiang Wang

  2. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    Jianxiang Wang & Liyong Tong

  3. School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK

    Bhushan L. Karihaloo

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  1. Jianxiang Wang
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Wang, J., Tong, L. & Karihaloo, B.L. A bridging law and its application to the analysis of toughness of carbon nanotube-reinforced composites and pull-out of fibres grafted with nanotubes. Arch Appl Mech 86, 361–373 (2016). https://doi.org/10.1007/s00419-015-1100-x

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