Page 87 - Biaxial Multiaxial Fatigue and Fracture

12 N. KOBE AND S. SAKURAI

Figure 12 shows relationships between the growth rate and surface length of cracks. Crack
growth rates in this figure were determined by the secant method [8]. In torsional fatigue tests
of base metal and axially welded specimens, crack growth rates decreased when cracks reached
about 0.5 mm long. In the uniaxial fatigue tests on all specimens and in the torsiona1 fatigue
test on circumferentially welded specimens, on the other hand, the cracks were relatively large
and reached about 2.0 mm long before the growth rates decreased.
X-shaped cracks were observed in the torsional fatigue tests of base metal [9] and axially
welded specimen with A&, = 0.7%, whereas cracks only propagated on one side of the
principal plane in the torsional fatigue test on the circumferentially welded specimen. Figure 13
shows the crack morphologies observed in the uniaxial and torsional fatigue tests. In a torsional
fatigue test, there are two equivalent principal planes. The minimum principal strain is the
compressive strain parallel to the crack and its absolute value is the same as the maximum
principal strain. Itoh [ 101 investigated the effect of the compressive strain parallel to the crack
by finite element analysis. It has been reported that the crack opening displacement in the
torsional condition, which corresponds to the case in Fig. 13(b), is smaller than that in a
uniaxial test. This is because the maximum principal stress acting on the crack initiated plane is
reduced when the minimum principal strain is small, i.e., its absolute value is large, due to the
effect of the Poisson ratio. Furthermore, when small X-shaped cracks form, cracks on two
equivalent principal planes affect each other and the stiffness around them also reduced so the
crack growth rate decreases. This is because a crack shows complicated growth behavior in the
early stage of life in the torsional test of base metal and axially welded specimen with A% =
0.7%.
On the other hand, a decrease in crack growth rate was observed when the crack length was
about 1 mm in the torsional test of the circumferentially welded specimen. This phenomenon
was also observed in the torsional fatigue test of the axially welded specimen with 4 = 0.5%.
as shown in Fig. 12. In these tests, the crack was relatively long when it was initiated and no X-
shaped cracks were observed. The crack propagated on one side of the principal plane with a
direction close to its initiated direction.

h
Q,

0 Crack length 2c (mm)

Fig. 12. Relationships between crack growth rate and crack length.