Crack matrix

The descriptions presented in the foregoing sections are concerned mainly with composites containing brittle fibers and brittle matrices. If the composite contains ductile fibers or matrix material, the work of plastic deformation of the composite constituents must also be taken into account in the total fracture toughness equation. If a composite contains a brittle matrix reinforced with ductile libers, such as steel wire-cement matrix systems, the fracture toughness of the composite is derived significantly from the work done in plastically shearing the fiber as it is extracted from the cracked matrix. The work done due to the plastic flow of fiber over a distance on either side of the matrix fracture plane, which is of the order of the fiber diameter d, is given by (Tetelman, 1969)... 

FIGURE 6-9 Schematic representations of the progression of oxidation in a crack/matrix/fiber coating region shown in the elliptical region in Figure 6-8. Source Luthra, 1997b. 

Ochiai, S. (1999) Interfacial debonding in single fibre-composite with a cracked matrix - Part 1 Debonding during cooling. International Journal of Materials and Product Technology, 14, 147-166. 

The problem of the fibre orientation was also examined by Mashima etal. (1990), who tested tensioned specimens reinforced with unidirectional or bi-directional systems of polypropylene fibres. Because the polypropylene fibres behave differently in the cracked matrix, other fracture mechanisms were considered than those proposed for steel ones. Tests on glass fibres are mentioned in Section 8.4.3. 

I n FRC composites, the major role played by the fibres occurs in the post-cracking zone, in which the fibres bridge across the cracked matrix. In a well-designed composite the fibres can serve two functions in this zone ... 

Post-multiple cracking range, during which the fibres are being stretched or pulled out of the cracked matrix. 

For >> 2 c sufficient embedded length is available to develop a stress equal to the fibre strength, and the failure will be predominantly by fibre fracture. For I ll(, the fibres are so short that they wiii pull out before sufficient stress is developed to cause fibre failure. These strength efficiency factors for a cracked matrix (Eqs 4.11 and 4,12) are smaller than those derived by Kelly (Eqs 4.3 and 4.4) for a composite with a ductile, uncracked matrix. 

A regression analysis of flexural strength results [7,18,19] indicates that this equation provides a good description of the experimental data (Figure 4.12). Laws [19] has questioned the validity of Eq. 4.42, since the cracked matrix cannot provide any contribution to strength. She demonstrated that while one can derive Eq. 4.42 to describe the flexural strength, this has nothing to do with the rule of mixtures (see Section 4.7). 

The reduction in elastic strain energy of the matrix after cracking, AUm-The increase in elastic strain energy of the fibres after matrix cracking, AUf, due to load transfer from the cracked matrix to the fibre. 

A series of events can take place in response to the thermal stresses (/) plastic deformation of the ductile metal matrix (sHp, twinning, cavitation, grain boundary sliding, and/or migration) (2) cracking and failure of the brittle fiber (5) an adverse reaction at the interface and (4) failure of the fiber—matrix interface (17—20). 

Fig. 14. Reinforcement and crack tip kiteractions ki a particulate composite (a) coarse particles ki a strong particle—matrix kiterface, and (b) fine particles ki...

Fig. 17. Variety of subcritical damage mechanisms in fiber-reinforced composites, that lead to a highly diffuse damage 2one. (a) Fiber cracking, (b) matrix...

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