Page 383 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C008.fm Page 363 Monday, May 23, 2005 5:59 PM

Fracture Testing of Nonmetals 363

yields, it often experiences strain softening followed by strain hardening. The yield strength is
defined at the peak stress prior to strain softening, as Figure 8.5 illustrates. Because the flow
properties are rate dependent, the ASTM K standard for plastics requires that the time to reach
Ic
σ in a tensile test coincide with the time to failure in the fracture test to within ±20%.
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The size requirements for metals (Equation (8.25)) have been incorporated into the ASTM K Ic
standard for plastics, apparently without assessing the suitability of these criteria for polymers.
Recall from Chapter 2 and Chapter 7 the purported reasons for the K size requirements:
Ic
• The plastic zone should be small compared to in-plane dimensions to ensure the presence
of an elastic singularity zone ahead of the crack tip.
• The plastic zone (supposedly) should be small compared to the thickness to ensure
predominantly plane strain conditions at the crack tip.
In recent years, the second requirement has been called into question. As discussed in Section 2.10,
the apparent thickness dependence of fracture toughness in metals is a result of the mixture of two
fracture morphologies: flat fracture and shear fracture. Moreover, plane strain conditions can exist
near the crack tip even in the fully plastic regime; the plastic zone need not be small r elative to
thickness to ensure high triaxiality near the cr ack tip.
Section 7.2.2 discusses the shortcomings of the ASTM E 399 test procedure and validity require-
ments when applied to metals. Many of these issues also apply to polymer testing. For example, the
5% secant method often introduces an artificial size dependence in K , as described below.
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Figure 8.6 shows the effect of specimen width on K values for a rigid polyvinyl chloride
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(PVC) and a polycarbonate (PC) [4]. In most cases, the specimens were geometrically similar, with
W = 2B and a/W = 0.5. For specimen widths greater that 50 mm in the PC, the thickness was fixed
at 25 mm, which corresponds to the plate thickness. The size dependence in K is a direct result
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of inferring P from a 5% secant construction (Figure 7.13).
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As discussed in Section 7.2, nonlinearity in the load-displacement curve can come from two
sources: stable crack growth and crack-tip yielding (or crazing). In the former case, a 5% deviation
from linearity corresponds to the crack growth through approximately 2% of the specimen ligament.
For materials that exhibit a rising crack-growth resistance curve, the 2% crack growth criterion
results in a size-dependent K , as Figure 7.17 illustrates. For materials that fracture without prior
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stable crack growth, nonlinearity in the load-displacement curve is largely due to yielding or crazing
at the crack tip. In such cases, 5% nonlinearity corresponds to the point at which the crack-tip
plastic zone (or damage zone) is on the order of a few percent of the specimen ligament. The
measured K is proportional to W a − until the specimen size is sufficient for fracture to occur
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before a 5% nonlinearity is achieved.
In the case of PVC and PC (Figure 8.6), the nonlinearity in the load-displacement curve is
likely due to crack-tip yielding or crazing. Note that K is more size dependent in the PC than
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in the PVC. The ASTM E 399 size requirements for in-plane dimensions appear to be adequate
for the latter but not for the former when K is defined by a 5% secant construction. The different
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behavior for the two polymer systems can be partially attributed to strain-softening effects.
Figure 8.7 shows the stress-strain curves for these two materials. Note that the PC exhibits
significant strain softening, while the rigid PVC stress-strain curve is relatively flat after yielding.
Strain softening probably increases the size of the yielded zone. If one defines σ as the lower
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flow stress plateau, the size requirements are more restrictive for materials that strain soften.
Figure 8.6(b) shows the E 399 in-plane requirements corresponding to the lower yield strength;
in the polycarbonate. Even with this adjustment, however, the E 399 methodology is not sufficient
to ensure a size-independent fracture toughness estimate in the PC. That is not to say that the
fracture toughness is actually more sensitive to the specimen size in the PC. Rather, the real
problem is that the 5% secant construction introduces an artificial size dependence in the toughness
estimate K .
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