Physical Chemistry of Foods

fracture is generally visible. In soft solids the situation is more complicated,
since fracture is generally preceded by local structure breakdown.
In several cases the material does not fracture but showsyielding. Also
during yielding a great number of bonds in some planes are broken, but at
the same time new bonds form (these are not necessarily of the same nature
as the original bonds). The specimen then is strongly deformed but remains
a continuous mass. This is often because liquid that is present between the
solid structural elements immediately flows to the tiny cracks formed.
Fracture and yielding both cause a sudden and significant change in
the mechanical properties of the specimen put under stress. Such a change is
often termedfailure. Other types of failure can occur. Consider, for instance,
the breaking of the stem of a flower without the stem being severed.
Buckling of two-dimensional structures is another example. It can occur
with the cell walls in cellular material when it is put under compressive stress
(see Section 17.5).
In the present section, we consider fracture mechanics. The theory
distinguishes threeregimes: linear-elastic, plastic-elastic, and time-dependent
fracture.

Linear-Elastic Fracture. This is also called brittle fracture. When
a homogeneous isotropic elastic test piece is put under stress, and the
magnitude of the stress applied is larger than the fracture stress of the
material, the test piece can break. For crystalline materials, the fracture
stress can be predicted from the known bond strengths and the geometry of
the crystal structure. However, it is generally observed that the
experimentally established fracture stress is much smaller than the
theoretical one, say, by two orders of magnitude. The discrepancy is
primarily due to the material being inhomogeneous, i.e., containing
imperfections or even tiny cracks at various sites. Virtually all materials
contain suchdefects. They give rise tostress concentration.
Consider the example illustrated in Figure 17.7a, i.e., a flat strip of
material put under elongational stress. To simulate a defect a small notch
has been applied. At the tip of the notch—and in principle the same applies
near a small imperfection—the stress will be larger than the overall stresssov
in the specimen at some distance away from the notch. The local stress then
is given by

sloc&sov 1 þ 2

L

R

! 0 : 5

ð 17 : 7 Þ

whereLis notch length andRis the radius of the tip of the notch. The stress
concentration can be considerable, the more so for a larger size and a