Page 380 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C008.fm Page 360 Monday, May 23, 2005 5:59 PM

360 Fracture Mechanics: Fundamentals and Applications

creep in metals, plots of J vs. da/dt fail to exhibit a single trend, but C* (which is a special case
of J ) correlates crack-growth data under different loading conditions (see Chapter 4).
v
The application of fracture mechanics to polymers presents additional problems for which both
J and J may be inadequate. At sufficiently high stresses, polymeric materials typically experience
v
irreversible deformation, such as yielding, microcracking, and microcrazing. This nonlinear material
behavior exhibits a different time dependence than viscoelastic deformation; computing pseudo
strains and displacements may not account for rate effects in such cases.
In certain instances, the J integral may be approximately applicable to polymers that exhibit
large-scale yielding. Suppose that there exists a quantity J that accounts for time-dependent yielding
y
in polymers. A conventional J test will reflect the material fracture behavior if J and J are related
y
through a separable function of time [10]:
t
J y J = φ () (8.23)
y
Section 8.1.5 outlines a procedure for determining J experimentally.
y
In metals, the J integral ceases to provide a single-parameter description of crack-tip conditions
when the yielding is excessive. Critical J values become geometry dependent when the single-
parameter assumption is no longer valid (see Chapter 3). A similar situation undoubtedly exists in
polymers: the single-parameter assumption becomes invalid after sufficient irreversible deformation.
Neither J nor J will give geometry-independent measures of fracture toughness in such cases.
y
Specimen size requirements for a single-parameter description of fracture behavior in polymers
have yet to be established, although there has been some research in this area (see Section 8.1.3
and Section 8.1.4).
Crack growth presents further complications when the plastic zone is large. Material near the
crack tip experiences nonproportional loading and unloading when the crack grows, and the J
integral is no longer path independent. The appropriate definition of J for a growing crack is unclear
in metals (Section 3.4.2), and the problem is complicated further when the material is rate sensitive.
The rate dependence of unloading in polymers is often different from that of loading.
In summary, the J integral can provide a rational measure of toughness for viscoelastic materials,
but the applicability of J data to structural components is suspect. When the specimen experiences
significant time-dependent yielding prior to fracture, J may give a reasonable characterization of
fracture initiation from a stationary crack, as long as the extent of yielding does not invalidate the
single-parameter assumption. Crack growth in conjunction with time-dependent yielding is a
formidable problem that requires further study.

8.1.2 PRECRACKING AND OTHER PRACTICAL MATTERS

As with metals, fracture toughness tests on polymers require that the initial crack be sharp.
Precracks in plastic specimens can be introduced by a number of methods, including fatigue and
razor notching.
Fatigue precracking in polymers can be very time consuming. The loading frequency must be
kept low in order to minimize hysteresis heating, which can introduce residual stresses at the crack tip.
Because polymers are soft relative to metals, plastic fracture toughness specimens can be
precracked by pressing a razor blade into a machined notch. Razor notching can produce a sharp
crack in a fraction of the time required to grow a fatigue crack, and the measured toughness is not
adversely affected if the notching is done properly [4].
Two types of razor notching are common: razor-notch guillotine and razor sawing. In the former
case, the razor blade is simply pressed into the material by a compressive force, while razor sawing
entails a lateral slicing motion in conjunction with the compressive force. Figure 8.4(a) and
Figure 8.4(b) are photographs of fixtures for the razor-notch guillotine and razor-sawing procedures,
respectively.