Bridging zone

Fig. 10.1 Schematic of the development of a bridging zone due to the presence of a weak fiber/matrix interface.

Currently, mathematical tools are available only for the modeling of cohesive or bridging zones for cracks in linear-elastic solids, although the closure pressure function p(u) or p(u,t) can itself be nonlinear. We first review some basic approaches for the modeling of cohesive zones, beginning with time-independent bridging and then discuss the relationship between cohesive zones and crack growth at elevated temperature primarily based on some recent or just-completed studies.29,30,32,33... 

Kb accordingly represents the toughening provided by the bridging zone. If failure of the composite occurs at Keff = Kc (the fracture toughness), then the fracture resistance, KR is given by... 

Another mathematical approach to modeling cohesive zones is to consider the crack tip fully shielded, that is Keff = 0, rather than partially shielded as in the case considered above. In this case, a cohesive zone lies in front of a traction free crack (Zone 1). This is the classical Barenblatt-Dugdale model in which the stress-intensity factor at the end of the cohesive zone is now zero that is, stress singularities are completely removed by the cohesive forces.29 The requirement of complete shielding results in a cusp-shaped cohesive zone or bridging zone profile. This approach has advantages, particularly for the elevated temperature case, in that the cohesive zone can... 

The model is formulated in terms of an integral equation which is solved with the condition at the boundary of the open crack and the bridging zone (.x — 0) that 6(0) = 5C. It is interesting to note that the structure of the rate-dependent problem is such that, aside from the material parameters, the solution is completely determined for a given crack velocity. For a given velocity, the value of the applied stress intensity factor, K, and the length of the cohesive zone, L, that maintains this condition is determined. Selected results are presented below. 

Fig. 2. Magnetic orbitals cf>Cu and 4>vo in the bridging zone of CuVO(fsa)2en CH3OH (from Ref. 36)...

In relation (4.27), Cq refers to the penny-shaped flaw size at the moment of crack initiation. Kq is an intensity factor chosen as Kq = 2 MPa.m. The bridging-zone length, Db, prior to critical fracture, has a bridging stress, p, assumed to be constant. For the derivation of Eq. (4.27), the reader should consult the work of Chien-Wei Li et al. [34]. The estimated p for the FG, medium and... 

Fig. 4.70 a Critical bridging stress decreases with grain width b Variation of bridging zone length with average grain width [34]. With kind permission of John Wiley and Sons... 

There is usually a crack bridging zone just behind the crack tip, with a small (sub-millimetre) microcrack region at the crack tip, and the cracking process zone extends over several mm. This is the cracking mechanism in some largegrained ceramics, and in whisker reinforced ceramics. See crack bridging toughness. 

Fibre bridging zone, in which stress is transferred by frictional slip of the fibres. 

At the beginning, while the opening of the crack is small, the length of the bridging zone behind the crack face increases as the crack progresses, and... 

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