Stress raisers, flaws and

FIGURE 10.1 Stresses near a crack of depth / and tip radius r. 

When the tip radius is much smaller than the depth of the flaw, as seems probable for the severe stress raisers responsible for fracture, Eq. (10.1) can be approximated by 

the breaking stress, denoted by is predicted to vary inversely with the depth of the flaw, /, in proportion to 1. This prediction has been tested for 

FIGURE 10.2 Fracture stresses for test pieces having cuts of depth /, exposed to ozone. (From Braden and Gent (1961).) 

FIGURE 10.3 Fatigue lives N for test pieces having initial cuts of depth /, subjected to repeated extensions to the indicated strains. 

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The areas where a test piece is attached to clamps and cut edges are preferential sites for cracking. It is generally good practice to coat clamped areas with an ozone resistant paint (which does not affect the rubber in any way) but cut edges are best left. For most purposes a Hypalon-based paint is satisfactory. Clamps, even when made of material such as aluminium, should be soaked in ozone prior to use. Any pattern or flaws on the test piece surface will also tend to act as stress raisers and show preferential cracking. 

However, real solids contain many flaws, which become stress raisers and initiate cracks at loads much below those required for the separation of an ideal body, even if only tensile forces are applied. The stressed system is unstable and cracks expand rapidly, accelerating to high propagation velocities only the bonds at the crack tips are breaking at any instant. 

We must recognize, however, that a tear that begins to propagate from an initial cut or flaw will soon develop a characteristic tip radius r of its own, independent of the sharpness of the initiating stress raiser (Thomas, 1958). It is therefore more appropriate to treat the product r as a characteristic fracture property of the material. Indeed, Irwin (1948, 1957) proposed that fracture occurs for different shapes of test piece and under varied loading conditions at a characteristic value of a stress intensity factor, Kc, defined as... 

This section is of particular interest as a consequence of the fact that almost all ceramics have flaws, many in form of microcracks or even cracks on a larger scale. These are outcomes of the fabrication techniques however, reducing such pores or cracks to a viable, minimal level is very costly. Many such cracks end at surfaces, where they act as stress raisers. Notches may also be considered as cracks, though the difference between notches and cracks is only a matter of size, not kind. Thus, the study of notched specimens has practical significance, because, in engineering components, fatigue starts mostly at the surface, at those places where stress-... 

Furthermore, the effect of a stress raiser is more significant in brittle than in ductile materials. For a ductile metal, plastic deformation ensues when the maximum stress exceeds the yield strength. This leads to a more uniform distribution of stress in the vicinity of the stress raiser and to the development of a maximum stress concentration factor less than the theoretical value. Such yielding and stress redistribution do not occur to any appreciable extent around flaws and discontinuities in brittle materials therefore, essentially the theoretical stress concentration results. 

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