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Section 4.2.3.0. Crack Growth Resistance – Tearing Fracture
As illustrated in Figures 4.2.2c and d, when the crack extends
by a tearing mode of fracture, which
typically occurs in thin metal sheets or in tough materials, the crack
extension is essentially slow and stable. The failure condition for tearing fractures depends on the crack
growth resistance (KR)
behavior of the material and the applied stress-intensity factor K, which in turn depends on the crack
and structural configurations. Figure 4.2.7 describes the observations that lead to
the development of the crack growth resistance curve (KR vs. Da). Figure 4.2.7 a
and b present the tearing behavior as a function of
applied stress and the corresponding stress-intensity factor,
respectively. Figure
4.2.7c presents the crack growth resistance curve that is a composite of the three stress-intensity factor curves shown
in Figure 4.2.7b.
Note that the composite was created by using the amount of physical
crack movement observed in each case as the independent variable. As implied by the data points on the crack
growth resistance curve in Figure 4.2.7c, the
stress-intensity factor level associated with material failure is not
necessarily constant.

Figure 4.2.7. Schematic Illustration of Tearing Fracture Behavior and the
Development of a Crack Growth Resistance Curve ( R-Curve)
Shown in Figure 4.2.8 is a
resistance curve for a 7475 aluminum alloy described as a function effective
crack length [Margolis, et al., 1975].
The effective crack length is the sum of the physical crack length and
the plastic zone size corresponding to the current crack length and loading
conditions.

Figure 4.2.8. KR Curve
from 7475 Alloy, 16 Inch Wide Panels, 0.5 Inch Thick [Margolis, et al., 1975]
Indeed, while the shape of the resistance curve is basically independent
of crack length or other geometrical effects, the fracture level is a function
of crack length (see Figure 4.2.9). To account for this variation in fracture
critical level, a two parameter failure criterion was required. However, before introducing the two
parameter criteria that are used for more accurate estimates, approximate
single parameter criteria for tearing failures are presented.

Figure 4.2.9. Schematic Illustration of Tearing Fracture
Behavior Which Further Defines the Change in Critical Level of Fracture
Toughness as a Function of Crack Length (also see Figure 4.2.7)