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706 Polymers, Mechanical Behavior

under a given loading profile, it will most likely undergo
deformation by shear if allowed, since its resistance to
that mode of deformation is less than that in tension. It
should be noted that the bulk modulus is not infinity even
for good elastomers; however, the volume of the bulk
modulus, B, for such systems far exceeds the values of
E or G.

IV. EFFECT OF TEMPERATURE ON
STRESS–DEFORMATION BEHAVIOR

Let us now address how macromolecular systems may
respond to external variables, one of the most important
being temperature. Let us assume at the beginning that we
are deforming a high molecular weight un-cross-linked
FIGURE 10 Generalized stress–strain curves showing the effect
amorphous system such as un-cross-linked high molecu-
of temperature.
lar weight polybutadiene (a rubbery system under ambient
conditions). If we were to undertake the uniaxial deforma-
tion of samples of this material and carry out the loading of and hence we will not refer to the term B in the present
each sample at the same rate of deformation, the general discussion.
stress–strain behavior that would be observed at different If modulus is plotted versus temperature based on the
temperatures might be as shown in Fig. 10. We would find stress–strain experiment described above for the un-cross-
that at low temperatures (i.e., well below the glass transi- linked high-molecular-weight amorphous material, the
tion temperature T g of the system) the material displays a general behavior is as shown in Fig. 11. There are two
high modulus and relatively low strain to break (i.e., brittle rather distinct regions that are not strongly dependent on
behavior). (Not all amorphous polymers display brittle be- temperature, whereas there are two others that show a
havior below T g ; some may display ductile behavior if the considerable dependence on temperature, particularly the
deformation conditions are suitable.) Above the glass tran- lower temperature region. The lowest region, A, which is
◦
sition temperature (approximately −90 C for amorphous not strongly dependent on temperature would display a
cis-1,4-polybutadiene), a lower modulus is observed, and modulus nearly equivalent to that of organic glass (10 –
9
it continually decreases but not necessarily in a monotonic 10 Pa), and hence this region is known as the glassy state
10
manner with temperature. The important point here is that
temperature strongly influences the mechanical response
of a macromolecular material, and it is therefore necessary
to understand this thermomechanical response. One com-
mon way of illustrating this dependence on temperature
is by a thermomechanical spectrum, which is the plot of a
given mechanical property versus temperature. Although
many such parameters could be selected, such as the en-
ergytorupture,stressatbreak,andstrainatbreak,theseare
ultimate properties and their values are often influenced
by the presence of molecular orientation as well as defects
in the material (voids, cracks, etc.). Thus, they are not al-
ways truly representative of the inherent macromolecular
system before deformation. This is also often true of the
yield stress and yield strain values. However, a principal
means of illustrating the behavior dependence of the ini-
tial structure on the variable of temperature is to utilize
the low-deformation parameter of modulus. If the test is in
tension the value of E would be plotted, whereas if it were
FIGURE 11 Typical plot of log Young’s modulus E versus tem-
in shear (torsion) the value of G would be the appropriate perature for a high-molecular-weight un-cross-linked amorphous
variable. Generally, bulk deformations are not common, polymer.