Chemistry Reference
In-Depth Information
pore may lead to a blunting of the crack tip, resulting in a lower local stress
concentration. This will involve energy dissipation.
The force-deformation curve of a crispy cellular solid food product has a
jagged shape. We propose that the size of the force drops during fracture of a
cellular solid food is an important parameter in determining final crispness
perception. By using a force and sound sampling rate of 65 kHz, the fracture
and accompanying acoustic emission of individual beams and lamellae could be
determined in toasted rusk rolls and Cracotte crackers.
8,9
It could be concluded
that there is only a very low acoustic emission (or none at all) for a force drop
smaller than about 0.3 N; but for force drops larger than 3-6 N, products could
be graded as being more hard than crispy. It is likely that the exact numbers will
depend upon the product involved, as the boundary between when a product is
called primarily 'crispy' or 'hard' will be subjective and dependent upon the
product involved and what the consumers are used to. Nevertheless, based on
the numbers given above for the fracture force of an individual beam or
lamella, it is possible to make a rough estimate of the thickness of the beams
involved in an optimum crisp product.
7
Let us assume that the weakest parts of the structure of the crisp product are
square rectangular beams of length
200-500 mm, fixed at both ends, which
are deformed in bending. The relationship between the fracture stress and the
beam characteristics is
36
:
B
s
fracture
¼
E
e
¼
3
4
FL
bd
2
:
ð
3
Þ
Here,
s
fracture
is the fracture stress, E the Young's modulus of the beam,
e
the
fracture strain, F the fracture force, L the beam length, b the beam width and d
the beam thickness. For E
2
10
9
Nm
2
and
e
0.01,
11,12
the calculated
beam thickness is in the range 130-380 mm. Such a thickness is, however, likely
to be an overestimate for two reasons. Firstly, in using Equation (3), we neglect
any shear contribution to the resistance against bending of the beam, which is
not (fully) allowed for in view of the small length/diameter ratio of a large
proportion of the beams.
36
Secondly, the assumption that the applied force acts
on the middle of the beam is also a rough approximation. If loading would be
at one quarter of the end of the beam, the calculated beam thickness would be
about 30% less for the same fracture force. So, a better estimate of the lower
limit of the beam thicknesses calculated from Equation (3) is probably in the
range 50-100 mm. A similar calculation made for the lamellae between gas cells
results in similar film thicknesses. Vincent
34
has mentioned a value of 0.05 N as
the minimum force drop for a fracture event detectable by humans. Using this
number in a calculation according to Equation (3) gives a minimum beam
thickness of
E
E
70 mm, in accordance with the range just mentioned.
B
34.4.2 Need for Crack Stoppers
The conclusion that the crack has to grow at a speed 4300 m s
1
for acoustic
emission during the fracture of a crispy product has at first sight unexpected
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