Page 290 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C006.fm Page 270 Monday, May 23, 2005 5:50 PM

270 Fracture Mechanics: Fundamentals and Applications

FIGURE 6.13 Cyclic stress-strain curve in a viscoelas-
tic material. Hysteresis results in absorbed energy, which
is converted to heat.

Of course there is a trade-off with rubber toughening, in that the increase in toughness and
ductility comes at the expense of yield strength. A similar trade-off between toughness and strength
often occurs in metals and alloys.
6.1.2.5 Fatigue

Time-dependent crack growth in the presence of cyclic stresses is a problem in virtually all material
systems. Two mechanisms control fatigue in polymers: chain scission and hysteresis heating [5].
Crack growth by chain scission occurs in brittle systems, where crack-tip yielding is limited.
A finite number of bonds are broken during each stress cycle, and measurable crack advance takes
place after sufficient cycles.
Tougher materials exhibit significant viscoelastic deformation and yielding at the crack tip. Figure 6.13
illustrates the stress-strain behavior of a viscoelastic material for a single load-unload cycle. Unlike
elastic materials, where the unloading and loading paths coincide and the strain energy is recovered,
a viscoelastic material displays a hysteresis loop in the stress-strain curve; the area inside this loop
represents the energy that remains in the material after it is unloaded. When a viscoelastic material
is subject to multiple stress cycles, a significant amount of work is performed on the material. Much
of this work is converted to heat, and the temperature in the material rises. The crack-tip region in a
polymer subject to cyclic loading may rise to well above T , resulting in local melting and viscous
g
flow of the material. The rate of crack growth depends on the temperature at the crack tip, which is
governed by the loading frequency and the rate of heat conduction away from the crack tip. Fatigue
crack growth data from small laboratory coupons may not be applicable to structural components
because heat transfer properties depend on the size and geometry of the sample.

6.1.3 FIBER-REINFORCED PLASTICS

This section focuses on the fracture behavior of continuous fiber-reinforced plastics, as opposed to
other types of polymer composites. The latter materials tend to be isotropic on the macroscopic
scale, and their behavior is often similar to homogeneous materials. Continuous fiber-reinforced
plastics, however, have orthotropic mechanical properties that lead to unique failure mechanisms
such as delamination and microbuckling.
The combination of two or more materials can lead to a third material with highly desirable
properties. Precipitation-hardened aluminum alloys and rubber-toughened plastics are examples of
materials whose properties are superior to those of the parent constituents. While these materials
form “naturally” through careful control of chemical composition and thermal treatments, the
manufacture of composite materials normally involves a somewhat more heavy-handed human
intervention. The constituents of a composite material are usually combined on a macroscopic scale
through physical rather than chemical means [20]. The distinction between composites and mul-
tiphase materials is somewhat arbitrary, since many of the same strengthening mechanisms operate
in both classes of material.