Matrix cracking

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. 

Matrix cracks begin to propagate at the matrix cracking stress (51,60)... 

A possible adjunct to the laminate design procedure is a specific laminate failure criterion that is based on the maximum strain criterion. In such a criterion, all lamina failure modes are ignored except for fiber failure. That is, matrix cracking is regarded as unimportant. The criterion is exercised by finding the strains in the fiber directions of each layer. When these strains exceed the fiber failure strain in a particular type of layer, then that layer is deemed to have failed. Obviously, more laminae of that fiber orientation are needed to successfully resist the applied load. That is, this criterion allows us to preserve the identity of the failing lamina or laminae so that more laminae of that type (fiber orientation) can be added to the laminate to achieve a positive margin of safety. 

Fig. 7. Fiber delamination, fiber pull-out and matrix cracks lead to a high energy dissipation and to good damage tolerance (SiC/SiC)ii...

There is increasing evidence in recent years in the fragmentation test of some brittle fiber-brittle matrix composites that a matrix crack is developed at the position of the fiber break. The presence of the matrix crack and its physical size are shown to alter the stress distributions at the fiber-matrix interface. As the applied strain... 

Effect of matrix cracking and interface debonding. J. Mater. Sci. 32, 633-641. 

Fig. 6.1. Model of crack fiber interaction in a simple composite, (a) In the uncracked composite, the fiber is gripped by the matrix, (b) A matrix crack is halted by the fiber. Increasing the load allows the crack to pass around the fiber without breaking the interfacial bond, (c) Interfacial shearing and lateral contraction of the fiber result in debonding and a further increment of crack extension, (d) After considerable debonding the fiber breaks at some weak spot within the matrix and further crack extension occurs, (e) The broken fiber end must be pulled out against the frictional grip of the matrix if total separation of the composite is to occur. After Harris (1980).

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... 

Xu. L.Y. (1996). Modifying stacking sequence design to delay delamination and matrix cracking in laminated composites - The multi dclamination interface design. J. Reinforced Plast. Composites 15, 230-248. 

How to Solve the Deactivation Problem. Solutions to the deactivation problem are difficult. The patent literature (42) has claims that either sodium, manganese or phosphorous added to alumina prevents deactivation by silica. In addition, removal of matrix silica from cracking catalyst formulations should prevent further deactivation because zeolitic silica, as we have shown, migrates more slowly. There is at least one patent relating to very high alumina matrix cracking catalysts (43). Another solution is to use more active SOx catalysts such as magnesia-based materials. 

The fractions were cracked at 560° and also at 500°C, with the exception of fraction 7 which did not vaporize completely at the lower temperature. The contributions of thermal and matrix cracking to the product yield were determined by cracking over -alumina and matrix respectively. Figure 1 shows that the zeolitic contribution to conversion decreases due to poorer access to zeolite pore structure, the thermal contribution decreases with increasing boiling point range, whereas the matrix contribution remains constant. 

However, the high matrix surface area of catalyst C made it possible to crack more heavy components than the other two catalysts, but the matrix cracking was too intense for this catalyst. Catalyst B showed the highest HCO yield of the... 

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