Page 136 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C003.fm Page 116 Monday, May 23, 2005 5:42 PM

116 Fracture Mechanics: Fundamentals and Applications

FIGURE 3.14 Double-edge-notched tension (DENT)
panel.

lengths. The latter is a calibration curve, which only applies to the material, specimen size, specimen
geometry, and temperature for which it was obtained. The Landes and Begley approach has obvious
disadvantages, since multiple specimens must be tested and analyzed to determine J in a particular
set of circumstances.
Rice et al. [13] showed that it was possible, in certain cases, to determine J directly from the
load displacement curve of a single specimen. Their derivations of J relationships for several
specimen configurations demonstrate the usefulness of dimensional analysis. 4
Consider a double-edge-notched tension panel of unit thickness (Figure 3.14). Cracks of length a
on opposite sides of the panel are separated by a ligament of length 2b. For this configuration, dA =
2da = −2db (see Footnote 1); Equation (3.16) must be modified accordingly:

P  ∆ ∂  P  ∆ ∂ 
J = 1  ∫   dP=− 1  ∫   dP (3.26)
2 0 a ∂  P 2 0 b ∂  P

In order to compute J from the above expression, it is necessary to determine the relationship between
load, displacement, and panel dimensions. Assuming an isotropic material that obeys a Ramberg-
Osgood stress-strain law (Equation (3.22)), the dimensional analysis gives the following functional
relationship for displacement:

 P a σ 
∆ Φ = b   σ o b bE o ; ; n   (3.27)
να;
;;

where Φ is a dimensionless function. For fixed material properties, we need only consider the load
and specimen dimensions. For reasons described below, we can simplify the functional relationship
for displacement by separating ∆ into elastic and plastic components:

∆ ∆ = el ∆ + p (3.28)

4 See Section 1.5 for a review of the fundamentals of dimensional analysis.