Page 421 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C009.fm Page 401 Monday, May 23, 2005 3:58 PM

Application to Structures 401

FIGURE 9.9 Applied J vs. applied load in an edge-cracked panel (Figure 9.1).

2
where P is in MN and J pl is in kJ/m . The elastic J is given by
K 2 Pf a W)/
2
2
(
J = el E I = BW E
2
From the polynomial expression in Table 2.4, f (a/W) = 0.770 for a/W = 0.125. Thus
2
(.
J = el 1000 P 0 770) 2 = 4 584 P 2
.
,
0 025 ) ( .m
(. 2 1 0 )(m 207 000MPa )
2
where P is in MN and J el is in kJ/m . The total J is the sum of J el and J pl :
J . P = 2 + 4 584 2 486 10 −8 P × 11
.
Figure 9.9 shows a plot of this equation. An analysis that includes the plastic zone correction
(Equation (9.33)) is also plotted for comparison.

9.3.1.3 Comparison with Experimental J Estimates
Typical equations for estimating J from a laboratory specimen have the following form:

K 2 η ∆ p
J = + p ∫ Pd∆ (9.35)
E b' 0 p

assuming unit thickness and a stationary crack. Equation (9.35) is convenient for experimental
measurements because it relates J to the area under the load vs. the load-line displacement curve.