Section 2.2.2. Application to Fracture
The hypothesis can be stated:
if the level of crack tip stress
intensity factor exceeds a critical value, unstable fracture will occur.
The concept is analogous to the criterion of stress at a point
reaching a critical value such as the yield strength. The value of the stress-intensity factor at which unstable crack
propagation occurs is called the fracture toughness and is given the symbol Kc. In equation form, the hypothesis states:
then catastrophic crack extension (fracture) occurs.
To verify the usefulness of the proposed hypothesis, consider
the results of a wide plate fracture study given in Figure
2.2.3 [Boeing, 1962]. These data
represent values of half crack length and gross section stress at
fracture. The stress-intensity factor
for the uniformly-loaded center-cracked finite-width panel is given by:
where W is the panel
width. Application of Equation 2.2.4
given in Figure 2.2.3 followed by averaging the
calculated fracture toughness values (except for those at the two smallest
crack lengths) gives the average fracture toughness curve shown. This example illustrates that the fracture
toughness concept can be used to adequately describe fractures that initiate at
gross sectional stress below 70% of the yield strength.
2.2.3. Results of a Wide Plate
Fracture Study Compared with a Fracture Toughness Curve Calculated Using the
Finite Width Plate Stress Intensity Factor Equation, Equation 2.2.4 (Data from
Note that since plastic deformation is assumed negligible in
the linear elastic analysis, Equation 2.2.3 is not expected to yield an
accurate approximation where the zone of plastic deformation is large compared
to the crack length and specimen dimensions.
Figure 2.2.3 shows that the relationship
derived on the basis of the Equation 2.2.3 hypothesis does not describe the
crack growth behavior for small cracks in plastic stress fields.