Stress intensity factor approach geometry factors

As discussed above, many of the most severe problems associated with a stress intensity factor approach to cracking along, or close to, interfaces may be circumvented if a combined interfacial stress intensity factor, is defined and therefore only a single geometry factor, Qi, has to be determined. This approach has been adopted by several workers [10,34,35,52] and values of Qi... 

The boundary layer approach is used to investigate the mode I plane strain fields near the crack. The symmetry of the problem allows consideration of only half the geometry (see Fig. 7), which consists of an initial blunted crack of radius n with traction-free surfaces along the crack. Along the boundary of the remote region at a distance R with R % 200rt, the mode I elastic field at stress intensity factor Ki is prescribed [8,22],... 

Various approaches have been developed to obtain analytical and numerical expressions for the stress intensity factor associated with a wide variety of crack and loading geometries. These solutions are useful not only in developing fracture toughness testing techniques, but also in understanding the interaction of cracks with structure at all scale levels. 

Note that the stress approaches infinity as the crack tip is approached, since the denominator factor, (27tr) , approaches infinity with r going to zero. The literature contains expressions for K (and a) for a large number of crack and loading geometries and both numerical and experimental procedures exist for determining the stress-intensity factor in actual, specific geometries. From Eq. (8.49), it is possible to express critical stress as ... 

Rates of CF crack propagation are uniquely defined by the linear elastic fracture mechanics stress intensity factor range that combines the effects of applied load, crack size, and geometry 17,40. The similitude principle states that fatigue and CF cracks grow at equal rates when subjected to equal values of AK [6-S]. The dal N versus AK relationship may be complex however, an effective approach is based on a power (or Paris) relationship of the form [4/]... 

The energy balance approach is generally the most applicable to flexible joints, since away from the crack tip the adhesive or substrates may not exhibit linear-elastic behaviour and so the stress intensity factor is invalid. Of course, in those cases where linear-elastic behaviour is observed then either approach may in principle be adopted. Essentially, to obtain an expression for the value of the adhesive fracture energy, Gc, for a particular geometry requires a solution to the left-hand side of Equation 7.3 to be deduced. 

A major feature of the continuum fracture mechanics approach is that the plane strain values of the fracture energy or the stress intensity factor for a given mode of loading should be independent of the geometry of the specimen employed for their evaluation. This is obviously required if the values of Gc and... 

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