Crack geometry

We consider an equilibrium problem for a shell with a crack. The faces of the crack are assumed to satisfy a nonpenetration condition, which is an inequality imposed on the horizontal shell displacements. The properties of the solution are analysed - in particular, the smoothness of the stress field in the vicinity of the crack. The character of the contact between the crack faces is described in terms of a suitable nonnegative measure. The stability of the solution is investigated for small perturbations to the crack geometry. The results presented were obtained in (Khludnev, 1996b). 

The form of the solution for the bridging contribution is specific to the reinforcement and the crack geometry but is of the general form (35)... 

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... 

Fracture mechanics approach. Fracture mechanics provides the basis for many modern fatigue crack-growth studies. AK is the stress intensity range (kjnilx-kjnm) where K is the magnitude of the mathematically ideal crack-tip stress field in a homogeneous linear-elastic body and is a function of applied load and crack geometry. 

The results presented in Fig. 12 are at first sight rather surprising, since standard tests show that the fracture resistance of HIPS and other rubber-modified plastics increases with temperature. The difference between the two types of test lies in the extent of yielding. The fracture mechanics specimens were deseed to produce brittle fracture, with the minimum of yielding crack geometry, tip sharpness, specimen width, and specimen thickness were all chosen accordingly. The resistance to the initiation of brittle fracture follows the trends shown in Fig. 12. On the other hand, ductile fracture resistance increases with temperature, as the yield stress falls. Parvin and Williams measured A/c in 5 mm wide SEN cimens, and found that toughness increased with temperature above —60 °C. 

Figure 4. Fatigue crack growth rates in Ti-6-4 center crack geometry specimens, M(T) in the weld nugget. At stress ratio of 0.05 crack growth rates in the weld nugget are 4 times faster than the parent material, mill annealed Ti-6-4. Crack growth rates at R=0.8 were unaffected. Micrograph shows the weld nugget micro structure.

Comparison of Eqs. (7.11) and (7.13) clearly shows the influence of crack geometry on fatigue life. 

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 effect of crack geometry will be discussed further in Section 8.6.3. 

Figure 8.17 Double cantilever beam crack geometry.

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