Matrix-crack bridging

Matrix cracking results in reduction in the laminate stiffness and strength. Stiffness reduction in CMCs is greater than that observed in polymer matrix composites due to lower ratio between fibre and matrix moduli. It also affects coefficients thermal expansion and vibration frequencies. A number of models have been suggested to estimate the effect of transverse macrocracks in the 90° plies and matrix cracks bridged by fibres in the 0° plies on the mechanical properties of cross-ply CMC laminates (Pryce and Smith, 1994 Daniel and Anastassopoulos, 1995 Lu and Hutchinson, 1995 Erdman and Weitsman, 1998 Birman and Byrd, 2001 Yasmin and Bowen, 2002 Birman and Weitsman, 2003). 

Figure 15. Transmission electron micrograph of functionalized carbon nanotubes. A nanotube bonded to a matrix crack bridge is pulled out of its outer shell (telescopic pull-out).

FESEM images of SWNT/epoxy fracture surface (a) Pulled out CNT bundles as long as 30-40 can be seen. Plastic deformation of the matrix is obvious. Scale bar is 2fj,m. (b) Fracture surface in lower magnification. The failure modes of the composite portion include SWNT pullout, matrix cracks bridged by SWNT. Scale bar is 10 / m. 

A partial answer to the first question has been provided by a theoretical treatment (1,2) that examines the conditions under which a matrix crack will deflect along the iaterface betweea the matrix and the reinforcement. This fracture—mechanics analysis links the condition for crack deflection to both the relative fracture resistance of the iaterface and the bridge and to the relative elastic mismatch between the reinforcement and the matrix. The calculations iadicate that, for any elastic mismatch, iaterface failure will occur whea the fracture resistance of the bridge is at least four times greater than that of the iaterface. For specific degrees of elastic mismatch, this coaditioa can be a conservative lower estimate. This condition provides a guide for iaterfacial desiga of ceramic matrix composites. 

In short fiber composites, energy absorption mechanisms, such as interfacial debonding and matrix cracking, most often occur at the fiber ends (Curtis et al., 1978). The damage model proposed by Bader et al. (1979) assumes that short fiber composites fail over a critical cross-section which has been weakened by the accumulation of cracks, since the short fibers bridging this critical zone are unable to carry the load. In fatigue loading, sudden fracture takes place as a direct result from the far-field effect of the composite, rather than due to the near field of the crack tip... 

Note that at CTc , some of the load is still carried by the matrix in the unbroken regions and that the maximum stress on the fibers is restricted to the bridging regions between single matrix cracks. Thus, Ofi, may be greater than the value obtained for unrestrained fibers. 

As discussed in the previous section, the toughening effect depends both on the matrix, where the shear bands are propagating, and the rubbery phase, which induces cavitation and crack bridging. 

A threshold of interfacial adhesion between both phases is needed to (a) promote the cavitation mechanism and (b) activate the crack-bridging mechanism. For rubbery particles, the former contributes much more than the latter to the total fracture energy. Adhesion is achieved by the use of functionalized rubbers that become covalently bonded to the matrix. Higher toughness values have been reported by the use of functionalized rubbers (Kinloch, 1989 Huang et al., 1993b). However, these experimental results also reflect the effect of other changes (particle size distribution,... 

The dispersion of SiC-coated MWCNTs increases the microhardness and fracture toughness of SiC. The SiC coating on MWCNTs at 1150°C is effective in improving the weak adhesion between MWCNTs and the SiC matrix. SiC-coated MWCNT/SiC composites show elastic behavior due to the crack-bridging effect of MWCNTs. 

Multiple matrix cracking perpendicular to the fibre axis was also reported by Blissett et al. (1997) for a UD Nicalon /CAS (calcium aluminosilicate) (Fig. 15.6). The density of these cracks increased with increasing AT but showed a reduction for AT> 800°C, which seemed to be consistent with the formation of strong silica bridging between the matrix and the fibres. 

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