Time-Dependent Fracture. (This is not an established term.) In
this regime, which is frequently observed in soft-solid foods, the whole test
piece shows lasting deformation and hence structural breakdown before
fracture occurs. Because of this, the fracture phenomena will depend on time
scale. The resulting fragments do not fit each other at all.
We will first consider theenergy relationsfor fracture. The total work
done upon deformation of the test piece would be given by
Wtot¼WelþWveþWstrðþWfrÞð 17 : 11 ÞHereWelis theelastic energy stored; its amount is proportional to the size of
the test piece for a given stress. The last term, i.e., the net work of fracture, is
put between parentheses, because it is derived fromWel, which thereby will
decrease. In linear-elastic fracture, the sum ofWelandWfris even constant
as soon as the fracture propagates spontaneously. In time-dependent
fracture, where fracture propagation can be slow, the sum is not constant (a)
because the material is viscoelastic and part of the energy is dissipated
during its transport to the crack tip, and (b) some elastic energy will be
added to the system after fracture has started, since deformation is still
going on.
The other two terms in the equation refer to theenergy dissipated into
heat; its amount is larger for a larger test piece. Somewhat arbitrarily, it has
been split into two terms.Wverefers to what happens in ahomogeneous
viscoelastic material. As discussed in Section 17.1.1 under ‘‘Time effects,’’
the stressrelaxation timetis an essential parameter if its value is in the range
of the values of 1/Capplied. At low values ofC, there is enough time for
part of the stress to relax, implying thatsremains low and also thatsfris
small. See Figure 17.6a, where the maximum in each curve roughly coincides
with fracture. At low C values, the proportion of the energy that is
dissipated (i.e.,Wve/Wtot) is larger; hence the amount of energy storedWelis
smaller for a given value ofe; so fracture will occur at a largerevalue. This is
seen in Figure 17.6a, and also in frame (b), since a higher stress causes a
largerCvalue. All these effects are stronger for materials having a larger
value of tand(at a givenCvalue).
The termWstrbecomes important forinhomogeneous materialsat large
deformation. Presumably, the energy dissipation is mainly caused by friction
between structural elements due to inhomogeneous deformation. Moreover,
immediate irreversible bond breaking can contribute. It is difficult to predict
how total energy dissipation will depend on strain rate. This is because the
deformation will change the structure and thus the rheological properties of
the material. Altogether, increasing values ofCnearly always cause an
increase insfr, albeit to a widely variable extent.