Intrinsic flaw sizes

Estimate the intrinsic flaw size in these materials assuming they were tested under (a) plane stress and (b) plane strain. Assume v = 0.3. Comment on your result. Which of these two materials will be more suitable for use in an application where the ability to withstand extensive abuse is a requirement ... 

Since fatigue failure of rubber is envisioned as growth of intrinsic flaws, measurement of fatigue lifetimes (e.g., deformation cycles to failure) can provide a measure of the intrinsic flaw size (Gent et al., 1964 Lake andLindley, 1965 Lake, 1983). Table 3.4 includes the flaw sizes determined from the fatigue life of these sample NR compounds (Choi and Roland, 1996). 

TABLE 3.4 Intrinsic Flaw Size of Natural Rubbers (Choi and Roland, 1996 ... 

TABLE IV Intrinsic Flaw Size of Natnral Rubber... 

Dynamic fatigue is more widely recognized as a cause of fracture, and most handbooks provide fatigue data in the form of S-N curves, as illustrated in Fig. 8.20. These curves usually flatten out beyond 10 cycles, in which case it is possible to define a fatigue endurance limit, i.e. the minimum st ress required to cause failure within 10 cycles. Both the static and the dynamic tests reflect the response of the material to the small defects that are present in the unnotched specimens, and in a sense are measuring the distribution of intrinsic flaw sizes as much as the fracture resistance of the polymer. Consequently, when the component is to be used in a critical application, there is a good case for mounting a full-scale fracture mechanics study. 

As may be seen, the shear strength, Xf, is always less than the tensile butt joint strength, o-f, and the latter rises to much greater values for thin adhesive layers. However, the relative values of o-f, Xf and P depend upon the values of Ea, the intrinsic flaw size, a, and the local stress concentration effects. Ratios obtained with a particular adhesive/substrate combination will not therefore generally hold for others. 

Broutman and McGarry [17] thus obtained intrinsic flaw sizes of 50 jim for PMMA and of 620 jum for PS. Berry [13] reports values of between 62 and 95 /xm for PMMA. These values seem to be very high and no direct optical observations of such flaws have been reported. They are also two to three orders of magnitude larger than the diameters of microcracks found in PMMA and listed in Table 8.3. The microcracks are assumed to have dimensions comparable to those of a globular substructure which may be responsible for their appearance under stress. The intrinsic flaws must have a different significance, therefore, and may only develop at a stress level close to o. ... 

In the Irwin approach, as with the Griffith approach, strength is found to depend on a combination of a material property (intrinsic) and a flaw size (extrinsic). In the linear elastic fracture mechanics approach, however, the material property is T or R and it has a component that depends on the microstructure of the material. Thus, if the mechanisms that increase T for a material can be identified, an approach is available to increase the reliability of brittle materials. It is this philosophy that has been a major driving force in the recent production of ceramics with higher strengths and toughnesses than had previously been considered possible. 

The values determined for the inherent flaws only represent effective sizes, corresponding to a given degree of stress concentration [289]. This stress concentration also depends on the shape of a crack (e.g., bluntness), as well as the dissipative capacity of the material itself [290]. While compounding variables such as crosslink density strongly affect the failure properties of rubber, their influence on the intrinsic defect size is more modest [287,288,291].The measured flaw size is unaffected by temperature [281], although it can vary with carbon black type... 

---