Page 340 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C007.fm Page 320 Monday, May 23, 2005 5:54 PM

320 Fracture Mechanics: Fundamentals and Applications

7.4 J TESTING OF METALS

The current ASTM standard that covers J-integral testing is E 1820 [4]. This standard is actually
a generalized fracture toughness standard, as it also covers K and CTOD tests. The British Standard
Ic
BS 7448: Part 1 [10] is equivalent in scope to ASTM E 1820.
ASTM E 1820 has two alternative methods for J tests: the basic procedure and the resistance
curve procedure. The basic procedure entails monotonically loading the specimen to failure or to a
particular displacement, depending on the material behavior. The resistance curve procedure requires
that the crack growth be monitored during the test. The J integral is calculated incrementally in the
resistance curve procedure. The basic procedure can be used to measure J at fracture instability or
near the onset of ductile crack extension. The latter toughness value is designated by the symbol J .
Ic
7.4.1 THE BASIC TEST PROCEDURE AND J MEASUREMENTS
Ic
Measuring toughness near the onset of ductile crack extension J requires the determination of a
Ic
J resistance curve. If the basic procedure is used to generate such a resistance curve, the J values
on the R curve may be subject to error because they have not been corrected for crack growth. This
is of little consequence when measuring J , however, because the purpose of the R curve in this
Ic
instance is to extrapolate back to a J value where ∆a is small and a crack growth correction is not
necessary. If a J-R curve is to be used in a tearing instability analysis (see Chapter 9), the test
procedure in Section 7.4.2 should be applied.
Because crack growth is not monitored as a part of the basic test procedure, a multiple-specimen
technique is normally required to obtain a J-R curve. In such cases, a series of nominally identical
specimens are loaded to various levels and then unloaded. Different amounts of crack growth occur
in the various specimens. The crack growth in each sample is marked by heat tinting or fatigue
cracking after the test. Each specimen is then broken open and the crack extension is measured.
In addition to measuring crack growth, a J value must be computed for each specimen in order
to generate the R curve. For estimation purposes, it is convenient to divide J into elastic and plastic
components:
J J = el J + pl (7.7)

The elastic J is computed from the elastic stress intensity:

2
J = K 1( E −ν 2 ) (7.8)
el
where K is inferred from the load and crack size through Equation (7.4). If, however, side-grooved
specimens are used, the expression for K is modified:
P
K = fa W) (7.9)
(/
BB W
N
where B is the gross thickness and B is the net thickness (Figure 7.12). The basic procedure in
N
ASTM E 1820 includes a simplified method for computing J from the plastic area under the load-
pl
displacement curve: 3
η A
J = Bb pl (7.10)
pl
No

3 Since J is defined in terms of the energy absorbed divided by the net cross-sectional area, B N appears in the denominator.
For nonside-grooved specimens B N = B.