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A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

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Abstract

A new linear elastic and perfectly brittle interface model for mixed mode is presented and analysed. In this model, the interface is represented by a continuous distribution of springs which simulates the presence of a thin elastic layer. The constitutive law for the continuous distribution of normal and tangential initially-linear-elastic springs takes into account possible frictionless elastic contact between adherents once a portion of the interface is broken. A perfectly brittle failure criterion is employed for the springs, which enables the study of crack onset and propagation. This interface failure criterion takes into account the variation of the interface fracture toughness with the fracture mode mixity. A unified way to represent several phenomenological both energy and stress based failure criteria is introduced. A proof relating the energy release rate and tractions at an interface point (not necessarily a crack tip point) is introduced for this interface model by adapting Irwin’s crack closure technique for the first time. The main advantages of the present interface model are its simplicity, robustness and computational efficiency, even in the presence of snap-back and snap-through instabilities, when the so-called sequentially linear (elastic) analysis is applied. This model is applied here in order to study crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads. Firstly, this model is used to obtain analytical predictions about interface crack onset, while investigating a single fibre embedded in a matrix which is subjected to uniform remote transverse loads. Then, numerical results provided by a 2D boundary element analysis show that a fibre-matrix interface failure is initiated by the onset of a finite debond in the neighbourhood of the interface point where the failure criterion is first reached (under increasing proportional load); this debond further propagates along the interface in mixed mode or even, in some configurations, with the crack tip under compression. The analytical predictions of the debond onset position and associated critical load are used for several parametric studies of the influence of load biaxiality, fracture-mode sensitivity and brittleness number, and for checking the computational procedure implemented.

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Notes

  1. It is easy to see that \(\chi \) gives the position of the center of the normalized Mohr circumference and its characteristic values are \(\chi =1\) (equibiaxial tension), \(\chi =0.5\) (uniaxial tension), \(\chi =0\) (equibiaxial tension-compression or pure shear stress), \(\chi =-0.5\) (uniaxial compression) and \(\chi =-1\) (equibiaxial compression). It is useful to realize that \(\phi ^\infty =\frac{\pi }{2}\left( \chi -\frac{1}{2}\right) \).

  2. There are several misprints in Eqs. (27)–(31) in Távara et al. (2011) corrected herein.

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Acknowledgments

The study was supported by the Junta de Andalucía and European Social Fund (Projects of Excellence TEP-2045, TEP-4051 and P12-TEP-1050), The Spanish Ministry of Education and Science (Projects TRA2006-08077 and MAT2009-14022) and Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (Projects MAT2012-37387 and DPI2012-37187).

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  1. Grupo de Elasticidad y Resistencia de Materiales, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain

    Vladislav Mantič, Luis Távara, Antonio Blázquez, Enrique Graciani & Federico París

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  1. Vladislav Mantič
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Mantič, V., Távara, L., Blázquez, A. et al. A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads. Int J Fract 195, 15–38 (2015). https://doi.org/10.1007/s10704-015-0043-0

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