Crack propagation in fibre composites

In composites with a brittle matrix i. e., mainly in ceramic matrix composites, the aim is not to increase the strength, but the fracture toughness. The fracture strain of the matrix is usually smaller than that of the fibre, leading to crack propagation in the matrix when the load increases. 

It is crucial for the increase in fracture toughness that the crack is bridged by the fibre after the crack tip has propagated beyond the fibre (see figure 9.8). The fibres can transfer loads and thus hinder further opening of the crack. 

The load transfer between the crack surfaces results in a maximum of the stress in the part of the fibre that is situated within the crack. This stress has to be transferred to the matrix on both sides, in a region whose size is approximately that of the critical fibre length. If the stress in the fibre in this region exceeds the fracture stress, the fibre breaks. Fracture usually occurs at a defect, for example a surface defect or a local reduction in diameter. Because of this, fibre fracture occurs not always directly at the crack surface, but at an arbitrary position between the stress maximum near the crack surface and the region where the fibre stress has decreased markedly. The size of this region is 

The crack resistance is the higher, the larger the critical fibre length is. In a ceramic matrix composite, it is thus useful to have a low value of the interfacial shear stress. If fibres are shorter than the critical length, they will not break but will be pulled out on one side of the crack, if they are longer, they will fracture first and be pulled out afterwards. 

The energy dissipated on pull-out can be estimated as follows The force needed to pull out the fibre is 

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