Chemistry Reference
In-Depth Information
NOMINAL STRAIN
FIGURE 4.22
Tensile stress
strain curve and test specimen appearance for a polymer which yields and
cold draws.
partially crystalline materials becomes vanishingly small near
T
m
, as the crystal-
lites that hold the macromolecules in position are melted out. Yield stresses are
rate dependent and increase at faster deformation rates.
The shear component of the applied stress appears to be the major factor in
causing yielding. The uniaxial tensile stress in a conventional stress
strain exper-
iment can be resolved into a shear stress and a dilational (negative compressive)
stress normal to the parallel sides of test specimens of the type shown in
Fig. 4.22
. Yielding occurs when the shear strain energy reaches a critical value
that depends on the material, according to the von Mises yield criterion, which
applies fairly well to polymers.
Yield and necking phenomena can be envisioned usefully with the Consid
`
ere
construction shown in
Fig. 4.23
. Here the initial conditions are initial gauge
length and cross-sectional area
l
i
and
A
i
, respectively, and the conditions at any
instant in the tensile deformation are length
l
and cross-sectional area
A
, when the
force applied is
F
. The true stress,
σ
t
, defined as the force divided by the corre-
sponding instantaneous cross-sectional area
A
i
, is plotted against the extension
ratio,
1, as defined in
Fig. 4.14
). If the deformation takes
place at constant volume then:
Λ
(
Λ5
1/10
5
A
2
A
i
l
i
5
Al
(4-74)
