sharper tip of the notch. Supposing that the notch is 100mm deep and thatR
¼10 nm,sloc/sovwill equal about 200. A well-known example is the linear
notch (scratch) applied on a glass pane by a diamond needle, which
enormously decreases the force needed to break the pane. A defect in a
crystal is generally of molecular dimension, i.e.,R&1nm.
Figure 17.7a relates in fact to a two-dimensional system, but also in
three dimensions the stress concentration around a small hole can in
principle be calculated. The figure is drawn for an experiment in which the
test piece is subject to uniaxial extension. Other loading modes can be used.
Uniaxial compression is frequently applied to solid foods; as mentioned, it
may lead to biaxial extension. Other tests invoke bending (as applied when
breaking a glass pane) or shearing. Although the mathematical relations are
somewhat different, the principles of fracture mechanics remain the same.
Crack Propagation. That sloc is higher thansfr is a necessary
condition for fracture to occur, but not a sufficient condition. It suffices for
fracture initiation, i.e., the formation of a small crack, but not for
spontaneous propagationof the crack. To explain this, energy relations
FIGURE17.7 Fracture in tension of a test piece containing a notch or crack. (a)
Geometry of the test piece. (b) Energies involved (W) as a function of crack length
(L).