Equilibrium cracks in composites reinforced with unidirectional fibres

• Published in: Journal of applied mathematics and mechanics 2006, Vol.70 (6), p.945-955
• Main Authors: Grekov, M.A., Morozov, N.F.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/j.jappmathmech.2007.01.011

A discrete-continuum approach, proposed by Novozhilov for analysing the equilibrium states of a brittle of crack in an isotropic body, is applied to a penny-shaped crack situated in a fibre-reinforced composite perpendicular to the fibres. The structural non-uniformity of the material is taken into account by the presence of unbroken fibres in the narrow part of the crack, adjoining the edge, and the different effect of the strength properties of the fibre and matrix on the limit state of the crack. Using this model, the range of dimensions of equilibrium cracks is established and an estimate is given of the critical size of the bridged part of the crack, corresponding to the onset of catastrophic fracture. It is shown that this dimension has the same value for a penny-shaped crack and for a crack under plane strain, does not depend on the form of the load and, under the condition of its smallness, is a brittle fracture characteristic of a fibre-reinforced material. The possibility of using this fracture model for two types of ceramics is analysed on the basis of experimental data.