Page 285 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

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Fracture Mechanisms in Nonmetals 265

6.1.2 YIELDING AND FRACTURE IN POLYMERS

In metals, fracture and yielding are competing failure mechanisms. Brittle fracture occurs in materials
in which yielding is difficult. Ductile metals, by definition, experience extensive plastic deformation
before they eventually fracture. Low temperatures, high strain rates, and triaxial tensile stresses tend
to suppress yielding and favor brittle fracture.
From a global point of view, the foregoing also applies to polymers, but the microscopic details
of yielding and fracture in plastics are different from metals. Polymers do not contain crystallo-
graphic planes, dislocations, and grain boundaries; rather, they consist of long molecular chains.
Section 2.1 states that fracture on the atomic level involves breaking bonds, and polymers are no
exception. A complicating feature for polymers, however, is that two types of bond govern the
mechanical response: the covalent bonds between carbon atoms and the secondary van der Waals
forces between molecule segments. Ultimate fracture normally requires breaking the latter, but the
secondary bonds often play a major role in the deformation mechanisms that lead to fracture.
The factors that govern the toughness and ductility of polymers include the strain rate, tem-
perature, and molecular structure. At high rates or low temperatures (relative to T ) polymers tend
g
to be brittle, because there is insufficient time for the material to respond to stress with large-scale
viscoelastic deformation or yielding. Highly cross-linked polymers are also incapable of large-scale
viscoelastic deformation. The mechanism illustrated in Figure 6.4, where molecular chains over-
come van der Waals forces, does not apply to cross-linked polymers; primary bonds between chain
segments must be broken for these materials to deform.

6.1.2.1 Chain Scission and Disentanglement
Fracture, by definition, involves material separation, which normally implies severing bonds. In
the case of polymers, fracture on the atomic level is called chain scission.
Recall from Chapter 2 that the theoretical bond strength in most materials is several orders of
magnitude larger than the measured fracture stresses, but crack-like flaws can produce significant
local stress concentrations. Another factor that aids chain scission in polymers is that molecules
are not stressed uniformly. When a stress is applied to a polymer sample, certain chain segments
carry a disproportionate amount of load, which can be sufficient to exceed the bond strength. The
degree of nonuniformity in stress is more pronounced in amorphous polymers, while the limited
degree of symmetry in crystalline polymers tends to distribute stress more evenly.
Free radicals form when covalent bonds in polymers are severed. Consequently, chain scission
can be detected experimentally by means of electron spin resonance (ESR) and infrared spectros-
copy [9, 10].
In some cases, fracture occurs by chain disentanglement, where molecules separate from one
another intact. The likelihood of chain disentanglement depends on the length of molecules and
the degree to which they are interwoven. 3
Chain scission can occur at relatively low strains in cross-linked or highly aligned polymers, but
the mechanical response of isotropic polymers with low cross-link density is governed by secondary
bonds at low strains. At high strains, many polymers yield before fracture, as discussed below.
6.1.2.2 Shear Yielding and Crazing

Most polymers, like metals, yield at sufficiently high stresses. While metals yield by dislocation
motion along slip planes, polymers can exhibit either shear yielding or crazing.

3 An analogy that should be familiar to most Americans is the process of disentangling Christmas tree lights that have been
stored in a box for a year. For those who are not acquainted with this holiday ritual, a similar example is a large mass of
tangled strands of string; pulling on a single strand will either free it (chain disentanglement) or cause it to break (chain
scission).