Cracks bridging

the subscripts c, m, and f represent composite, matrix, and fiber, respectively. And Y, V, and o are the Young s modulus, volume fraction, and fracture strength, respectively. Also, r is the radius of the fiber, G is the toughness, and Yf/y is the ratio of the fracture energy of the fiber to that of the interface. From this equation, we can determine that in order to increase fracture toughness, we must  

The third factor can be increased by decreasing the interfacial energy. An aftereffect of this decrease is the pullout of the fibers. Because this pullout consumes energy, it further increases the fracture toughness. 

Mechanism of crack bridging and deflection by rod-shaped grains. (From A. G. Evans and R. M. Cannon, Acta Metall., 34, 761-800,1986.) 

The effect of SiC whisker content on toughness enhancement in different matrices. (From P. Becher, Microstructural design of toughened ceramics, /. Am. Ceram. Soc., 74,255-269,1991.) 

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Furthermore, the model makes it possible to separate the contributions of the three toughening mechanisms as a function of temperature (Fig. 13.6). At high temperatures, the crack-bridging mechanism plays a minor role the void-growth mechanism is very sensitive to temperature and can be completely suppressed at low temperatures. Shear yielding is the main mechanism, except at very high test temperatures where cavitation plays the major role. The contribution of shear yielding depends on the difference between the test temperature and Tg, as discussed in Chapter 12. 

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,... 

From a mechanical point of view, a critical level of adhesion (chemical or physical) is required between TP and thermoset TS phases to insure stress and strain transfers and to favor ductile stretching of TP particles in the crack-bridging mechanism (Pearson, 1993 Hodgkin et al., 1998). 

Crack bridging by TP particles seems to be the main energy-dissipating mechanism. 

For the in-situ phase-separation process, an increase in the TP molar mass modifies the phase diagram (it lowers cnl), increases the viscosity - which is a drawback for processing and impregnation of composites - but increases the fracture energy associated with the crack-bridging mechanism. 

Sue et al. (1997) reported results for the same LC epoxy monomer cured with various hardeners. KIe values could be increased up to 1.89 MPa m1/2. Observations of fracture surfaces indicated that crack bridging, crack branching, and crack deflection were the main toughening mechanisms. 

Crack bridging is also complemented by the contribution of pullout of the failed whisker reinforcements. The pullout operation consumes energy which would otherwise contribute to the advancement of the crack front and thus enhances toughness. 

The important case of specimens with a fixed total thickness was considered in Ref. [40]. There are certain features of crack bifurcation under these conditions, such as that if the sample with a fixed total thickness has too large a number of layers there will be no bifurcation. Layer thickness and composition are important and efficient parameters to control the bifurcation in laminates. The effect is comparable with a crack bridging phenomenon [21], The bifurcation mechanism increases the laminate fracture toughness by approximately 1.5-2 times. 

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. 

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