Chemistry Reference
In-Depth Information
Considèere construction
β
α
1
2
Extension ratio
Λ
FIGURE 4.23
Sketch of conditions for yielding in tensile deformation.
The nominal stress (engineering stress)
5σ5
F/A
i
, and therefore:
σ 5σ
t
=Λ
(4-75)
d
σ
1
Λ
d
σ
t
Λ
2
σ
t
Λ
5
(4-76)
2
d
d
Λ
Since
d
A
5dΛ
, then at yield
d
d
d
σ
ε
5
0
5
(4-77)
d
Λ
and the yield condition is characterized by:
d
σ
t
d
Λ
5
σ
t
(4-78)
Λ
A maximum in the plot of
engineering
stress against strain occurs only if a
tangent can be drawn from
0 to touch the curve of
true
stress against the
extension ratio at a point, labeled
λ5
in
Fig. 4.23
. In this figure a second tangent
through the origin touches the curve at point
α
. This defines a minimum in the
usual plot of nominal stress against extension ratio where the orientation induced
by the deformation stiffens the polymer in the necked region. This phenomenon
is called
strain hardening
. The neck stabilizes and travels through the specimen
by incorporating more material from the neighboring tapered regions. As the ten-
sile deformation proceeds, the whole parallel gauge length of the specimen will
yield. If the true stress-extension ratio relation is such that a second tangent can-
not be drawn, the material will continue to thin until it breaks. Molten glass exhi-
bits this behavior.
The phenomenon of strain hardening in polymers is a consequence of orienta-
tion of molecular chains in the stretch direction. If the necked material is a
β
