Page 433 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C009.fm Page 413 Monday, May 23, 2005 3:58 PM

Application to Structures 413

FIGURE 9.18 Schematic plot of crack driving force vs. applied stress.

Figure 9.18 is a schematic plot of the fracture driving force vs. the applied stress. The applied
J can be converted to an equivalent K through the following relationship:

JE
K = (9.59)
J
1 −ν 2
In the linear elastic range, K = K and stresses near the crack tip are characterized by a 1/ r
J
I
singularity (Chapter 2). In the elastic-plastic range, the plot of K vs. stress deviates from linearity
J
and a 1/ r stress singularity no longer exists. Note that K is a special case of K , the stress-
J
eff
intensity factor adjusted for plasticity effects (Section 2.8). However, K has a sounder theoretical
J
basis than K values estimated from the Irwin plastic zone correction or the strip-yield model.
eff
Following the approach of the original derivation of the FAD from the strip-yield model, let
us define a K ratio as follows:
K
K = K I J (9.60)
r
Figure 9.19 is a schematic plot of K vs. applied stress. In the limit of small applied stresses, linear
r
elastic conditions prevail and K = 1. This ratio decreases as the applied stress increases.
r
Next, we normalize the horizontal axis by introducing a load ratio:
σ
L = σ ref (9.61)
r
YS

where s is the reference stress, which was introduced in Section 9.3.2. Traditionally, the reference stress
ref
has been based on yield load or limit load solutions for the configuration of interest (Equation (9.42)).
However, this approach introduces geometry dependence into the FAD curve. Section 9.4.4 presents
an alternative definition of s .
ref
The final step in creating the FAD is introducing a cut-off value L r(max) on the horizontal axis.
This cutoff represents a limit load criterion.