Open Access

ARTICLE

Analytical Models for Sliding Interfaces Associated with Fibre Fractures or Matrix Cracks

L. N. McCartney¹

1 Materials Division, National Physical Laboratory, Teddington, Middx. UK, TW11 0LW.

Computers, Materials & Continua 2013, 35(3), 183-227. https://doi.org/10.3970/cmc.2013.035.183

Abstract

Analytical stress transfer models are described that enable estimates to be made of the stress and displacement fields that are associated with fibre fractures or matrix cracks in unidirectional fibre reinforced composites. The models represent a clear improvement on popular shear-lag based methodologies. The model takes account of thermal residual stresses, and is based on simplifying assumptions that the axial stress in the fibre is independent of the radial coordinate, and similarly for the matrix. A representation for both the stress and displacement fields is derived that satisfies exactly the equilibrium equations, the required interface continuity equations for displacement and tractions, and all stress-strain equations except for the one that relates to axial deformation. In addition, the representation is such that the Reissner energy functional has a stationary value provided that averaged axial stress-strain relations for the fibre and matrix are satisfied. The improved representation is fully consistent with variational mechanics and provides both the stress and displacement distributions in the fibre and the matrix. For isolated or interacting fibre fractures or matrix cracks, interface sliding is considered where two types of condition are investigated. Firstly, it is assumed that the shear stress is uniform within the sliding region, and a small transition zone is included in the model in order that essential zero traction conditions can be satisfied on the crack surfaces. Secondly, it is assumed that stress transfer in the sliding region is controlled by Coulomb friction. Illustrative predictions are made for an example polymer composite, although the methodology presented is equally applicable to other types of composite (e.g. metal and ceramic matrix composites).

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