Page 209 - Academic Press Encyclopedia of Physical Science and Technology 3rd Polymer

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718 Polymers, Mechanical Behavior

FIGURE 24 Generalized plot of the log of Young’s modulus versus temperature contrasting the effect of levels of
crystallinity ranging from 0 to 50%.

matrix material, whereas glass, carbon, or graphite fibers The phenomenon of crazing may not always be
or other materials serve as fiber components that are gener- induced; rather, yielding by shear can be promoted,
ally stiff (high modulus) relative to the polymeric matrix. (Recall that yielding indicates plastic deformation and
This is a higly complex area in terms of how these fillers energy dissipation, which add to the toughness of a given
or fibers influence mechanical properties, but a few impor- material.) Softer phase particulates are often placed in
tant points can be made. In addition, there is a considerable the matrix for purposes of promoting toughness by one or
literature available. both of the mechanisms indicated above. The price that
As stated above, there are two categories of particulate- is paid for placing a soft component into a hard matrix
filled systems that we will address here. The first is a is that the modulus and yield stress will be sacrificed to
soft filler in a hard matrix component, an example be- some degree by the presence of the softer species.
ing a rubber particle or a void in a glassy polymer. In The second system is a hard phase located in a soft ma-
this case, if a stress is applied along some specific axis, trix, such as a glass sphere placed within an elastomeric
such as in tension, the filler particle serves as a stress
concentrator; that is, the stress field is altered in the gen-
eral locality of the matrix near the filler particle (Fig. 25).
Mechanics show that the soft filler will concentrate the
stress to a maximum point at the equatorial region of the
particle–matrix interface (Fig. 25). This forces the matrix
material to undergo shear yielding or crazing—two im-
portant mechanisms by which energy dissipation occurs
and which can promote a higher degree of toughening
of the initial matrix system. An example of the crazing
mechanism is shown in Fig. 26, where rubber particles
FIGURE 25 Schematic showing the relative stress levels around
in a glassy polystyrene matrix have promoted localized
a hole that has been placed in a tensile sample loaded with the
crazing in the equatorial regions. Without the presence of stress σ 0 along the x axis. The relative numbers on the contours
these rubber particles, polystyrene would show low strain imply the stress intensity factor above that of σ 0 . Note that the
to break and relatively low toughness, in contrast to the highest value is located at the equators and is a factor of 3. In the
rubber-modified version. There are other ways in which case of a spherical inclusion, the stress levels change in a similar
way except that the maximum value is a factor of 2 at the equator.
rubber-toughening morphologies can be induced such as
[Reprinted with permission from Nielsen, L. E. (1974). “Mechani-
in high-impact polystyrene, but they are outside the scope cal Properties of Polymers and Composites,” Vol. 2, Dekker, New
of this article. York. Copyright 1974 Marcel Dekker.]