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Fracture Toughness Testing of Metals 327
where r is the plastic rotational factor, a constant between 0 and 1 that defines the relative position
p
of the apparent hinge point. The mouth-opening displacement is measured with a clip gage. In the
case of an SE(B) specimen, knife edges are often attached in order to hold the clip gage, so that
Equation (7.21) must take account of the knife-edge height z. The compact specimen is usually
designed such that z = 0. The plastic component of V is obtained from the load-displacement curve
by constructing a line parallel to the elastic loading line, as illustrated in Figure 3.6. The plastic
rotational factor is given by
.
r = 044 (7.22a)
p
for the SE(B) specimen and
a 2 a 12 / a
r = p . + 04 1 2 o + o + −05 . o + 2 05 . (7.22b)
b b o b o
o
for the compact specimen. The original British standard for CTOD tests, BS 5762:1979, applied
only to SE(B) specimens and specified r = 0.40.
p
The crack-mouth-opening displacement V on an SE(B) specimen is not the same as the load-
line displacement ∆. The latter displacement measurement is required for J estimation because A pl
in Figure 7.23 represents the plastic energy absorbed by the specimen. The CTOD standard utilizes
V because this displacement is easier to measure in SE(B) specimens. If r is known, however, it
p
p
is possible to infer J from a P-V curve or CTOD from a P-∆ curve [5, 6]. The compact specimen
simplifies matters somewhat because V = ∆ as long as z = 0.
When using the resistance curve procedure in ASTM E 1820, the CTOD equation must
continually be updated with the current crack size. For the ith measurement point in the test, CTOD
is given by
K 2 ( − ν ) [ 2 r ( W a − ) ∆ a+ i] V
1
δ = () i + pi () i pi () (7.23)
i
() σ E () [ i ]
2 YS r pi ( W a − i ) a + z +
where a is the current crack length and ∆ a i a = i a − o . The stress-intensity factor K i () is computed
i
using the current crack length. For compact specimens, the rotational factor must also be continually
updated to account for crack growth:
a 2 a 12 / a
r pi () = . + 04 1 2 i + i + − 05 . i + 2 05 (7.24)
.
b b i b i
i
Equation (7.23) and Equation (7.24) do not appear in ASTM E 1290.
When the material exhibits ductile crack extension, the above procedure can be used to generate
a d -R curve. The CTOD near the onset of ductile crack extension, d , can be inferred from the
Ic
resistance curve in a manner very similar to the J measurement (Figure 7.24). The slope of the
Ic
blunting line and exclusion lines for a d -R curve is M , where M is assumed to equal 1.4 unless
δ
δ
an experimental measurement of the blunting line slope has been made. The provisional initiation
toughness d is defined at the intersection between the d -R curve, defined by a power-law fit within
Q