Crack radial

Example 2.20 A cylindrical vessel with an outside radius of 20 mm and an inside radius of 12 mm has a radial crack 3.5 mm deep on the outside surface. If the vessel is made from polystyrene which has a critical stress intensity factor of 1.0 MN calculate the maximum permissible pressure in this vessel. 

The nano indentation technique can also be used to measure fracture toughness at small scales, by using the radial crack, which occurs when brittle materials are indented by a sharp indenter [72,73]. Lawn et al. [74] have shown that a simple relationship exists between the fracture toughness, Ag, and the lengths of the radial cracks, c, in the form of ... 

With a strong interfacial bond, when a fiber fractures, the high stresses in the matrix near the broken ends are relieved by the formation of a short radial crack in the resin. There is no interfacial debonding and corresponding friction at a sheared interface, but rather, the load is transferred to the fiber by elastic deformation of the resin. The lack of adhesive failure in this case is responsible for the relatively low emission observed. 

Lawn B. R., Evans A. G., Marshall D. B., 1980, Elastic-plastic indentation damage in ceramics. The median/radial crack system, J. Am. Ceram. Soc., 63, (9-10), 574-581. 

Fig. 6.2.9. Indentation /strength model system, (a) Vickers indenter, peak load P, generates median/radial crack, characteristic dimensions (value c0 at completion of contact cycle, with further post-indentation, supercritical extension to c0, if exposed to moisture), (b) Tensile field a in combination with residual ( ghost ) contact field, drives crack system to failure. (After Marshall and Lawn, 1980)...

As pointed out above, boron fiber is also a composite fiber like any other CVD-type fiber. During fracture, cracks frequently originate at pre-existing defects located at the boron/core interface or at the surface. Commonly, a radial crack originates at the boron/core interface and leads to a brittle fracture. 

Figure 18 Schematic of radial cracks due to (a) tangential thermal stress and (b) axial thermal stress. (From Ref. 29, courtesy of SAE.)...

Here stands for the applied tearing modulus in the case of radial crack growth. 

The three attrition mechanisms are in turn governed by different failure modes brittle, semibrittle, and ductile (Ghadiri, 1997). Brittle failure occurs when internal or surface cracks already exist and is dominant at low elastic deformation at the powder contact surface (Shipway and Hutchings, 1993). Semibrittle failure, at limited plastic deformation, is responsible for flaw initiation and occurs when the impact forces surpass the yield point. In fact, median and radial cracks cause particle fragmentation, and lateral cracks cause chipping. Soft materials are usually ductile and the mechanisms for particulate solids under ductile mode have not yet been elucidated (Ghadiri, 1997). 

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