interpreted as representing the inherent effectivedefect length Ldefof the
material, i.e., the size of inhomogeneities that are responsible for stress
concentration. In several cases, good agreement between Ldef and
microscopically observed inhomogeneities has been obtained. For instance,
the defect length in concentrated starch gels agrees well with the size of the
partly swollen starch granules in the gel (e.g., about 0.1 mm).
Equation (17.12) is valid for an ideally elastic material. Some sugar
glasses do fit the prerequisites and show an even steeper curve than curve 2
in Figure 17.9. But most soft solids behave differently. Some gels come close
to the ideal relation: for instance, curves 2 and 4 fit reasonably well for a
10 %potato starch gel. Many materials give relations of the general shape of
curve 3. That means that these materials are notch sensitive and show
defects of a length far greater than molecular. However, Eq. (17.12) cannot
be used to predict relations.
Theextent of notch sensitivity, i.e., the steepness of decrease ofsprwith
notch length, varies considerably. The factors affecting it are not fully
understood. Some factors that decrease notch sensitivity are following:
A larger inherent defect length. This is because the curve starts at a
higherLvalue. Compare curves 2 and 3 in Figure 17.9.
A lower yield stress. As mentioned, a low yield stress leads to a
relatively thick zone around the crack where yielding occurs, hence
to blunting of the crack tip, hence to decreased stress concentration.
More pronounced anisotropy. The anisotropy meant implies that the
forces keeping the material together vary with direction. Consider a
fibrous material like muscle tissue. If it is put under tension in the
direction of the fibers, and a small notch is made perpendicular to
the fibers, hardly any stress concentration occurs. This is because the
breaking stress in the direction of the fibers is quite high, whereas
the fibers can easily be torn apart if the stress is perpendicular to
their direction. Thus only a small fraction of the elastic energy
applied to one fiber can be transmitted to other ones, and each fiber
will have to break separately. The relation betweensfrandLthen
will be close to that of curve 1 in Figure 17.9.Question
Consider an isotropic material that exhibits elastic-plastic fracture. Will its yield
stress be higher or lower than its fracture stress, or is the difference unimportant?