Stress intensity factor approach

The problem of a crack situated well away from any interface will be considered first, followed by the far more complex problem of a crack at, or very close to, an interface. 

The parameter K is the stress intensity factor and relates the magnitude of the stress intensity local to the crack in terms of the applied loadings and geometry of the structure in which the crack is located. 

A crack may be stressed in three different modes, denoted I, II and III, as depicted in Fig. 7.3 superposition of the three modes constitutes the general case of crack loading. The cleavage or tensile-opening mode, mode I, is technically the most important since it is the most commonly encountered and usually the one which most often results in failure. However, crack propagation in joints is often constrained to the adhesive layer, regardless of the orientation of the adhesive layer to the applied loads. Thus, in the case of joint fracture attention must sometimes be given to modes II and III, as well as mode I. 

For the mode I case the crack tip stresses may be developed from Equation 7.11 to yield the expressions below, and it should be noted that analogous expressions may be developed for the other two modes. 

Note that in the plane 0 = 0° the shear stress is zero hence for 0 = 0° the stresses crn, 0-22,0-33 are the principal stresses o-i, 0 2 and 0-3, respectively. 

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The energy method of Griffith and the stress intensity factor approach of Irwin are, perhaps, the most basic and often used of the fracture criteria. Therefore, they have been emphasized in this article. However, the reader should be aware that other approaches to the problem have gained considerable popularity in recent years, foremost among them the J-integral (19) and the crack-opening displacement methods (20). These two criteria have been extensively applied to the fracture of metals for which crack tip plasticity is significant. 

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 approach is invalid. The most conunon test methods are shown in Fig. 1. 

Fracture mechanics A J KINLOCH Basis energy balance and stress-intensity factor approaches... 

In the late 1950s Irwin developed the stress intensity factor approach (this is different to stress intensity used in pressure vessel stress analysis). Consider a structural component containing a sharp crack, subjected to a load applied in a direction normal to the crack surface (known as Mode I loading) as shown in Figure B.4. The normal stress in the y direction, Oy, at a point located at an angle 0 and at a distance r from the crack tip, can be expressed as... 

It is evident from even this brief discussion of applying the stress intensity factor approach to cracks in adhesive joints that many problems arise and have yet to be fully resolved. Therefore, it is not surprising that many workers have... 

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... 

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