Crack geometry factor

In equation (5.66), fl is a crack-geometry factor—that is, an experimental parameter which reflects the fact that the cracks are formed close to a free surface, that because of the demands of crystal structure the profile of the radian or median cracks may be noncircular, and that there is mutual interaction between radials and median cracks that are simultaneously formed. 

Figure 3. Various solutions of crack geometry factors F and Fn applied in the asymmetric four point flexure configuration.

The estimation of the total lifetime of the structure is more complex - substantial crack growth will make the crack geometry change significantly this will have to be allowed for in the calculations by incorporating a correction factor, Y. 

The symmetric stress-intensity factor k, is associated ith the opening mode of crack extension in Figure 6-10. The skew/-symmetric stress-intensity factor l<2 is associated ith the fonward-shear mode. These plane-stress-intensity factors must be supplemented by another stress-intensity factor to describe the parallel-shear mode. The stress-intensity factors depend on the applied loads, body geometry, and crack geometry. For plane loads, the stress distribution around the crack tip can always be separated into symmetric and skew-symmetric distributions. 

Y Correction factor for configuration of specimen and crack geometry... 

A surface craze in a PMMA product breaks down and becomes a crack. Treat it as an edge crack of length a = 0.5 mm in a body of width w >a. What tensile stress stress intensity factor K = 1.12[Pg.498]

The index I denotes the mode I load case. T is a geometry factor that takes different geometries into account and is 1 for the case considered here. It will be discussed in greater detail below (see page 139). All other terms in the equations depend only on the spatial position so that only the stress intensity factor determines the stress level near the crack tip. The stress functions are singular because the distance from the crack tip r enters the denominator. Figures 5.5(a) and 5.5(b) show examples of the stress fields. The physical unit of the stress intensity factor K is MPa- /m according to equation (5.1) because the stress near the crack tip is proportional to the quotient of the stress intensity factor and the square root of the distance to the crack tip /r a oc Kfy/r. 

If the crack length a is not small compared to the extension of the component, the geometry factor can depend on the crack length Y = Y a). Table 5.1 lists some geometry factors for common crack configurations. It has to be kept in mind that the length of surface cracks is denoted by a, that of internal cracks by 2a. 

For the infinite geometries we used so far, the geometry factor is constant because a finite crack length does not cause a reduction of the infinite cross section. 

Although the critical crack length is an indicator of the crack sensitivity of a material, it is not a material parameter. This can be seen directly from equation (5.28) which contains the geometry factor Y. For this reason, analytically calculating Oc is frequently impossible. 

If the geometry factor Y is independent of the crack length - an assumption unfortunately not true in most cases -, we can take Y out of the integral and solve the integral.Otherwise, equation (10.10) must be integrated numerically. 

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