Environmental Engineering Reference
In-Depth Information
p
p
1
1
−+
p
−+
p
2
2
a
a
f
o
[1.15]
N
for
2
p
≠
=
f
(
)
/
2
−
(
)
A
()
pp
p
p
)
Y
)
π
pp
and
⎛
⎜
⎞
⎟
1
a
f
ln
[1.16]
for
N
2
⎛
⎝
p
=
=
f
.
2
2
a
AY
()
Y
Y
o
)
π
Another important aspect of considering the crack growth versus
K
is to
examine the effects of superimposed environment such as corrosion and
radiation. The variation of d
a
/d
N
with
Δ
K
in these cases would shift the
threshold stress intensity range to lower values and the critical crack length
at fracture would be indicated by
K
ISCC
instead of
K
IC
.
In strain controlled fatigue tests for life evaluation, it may be noted that the
cyclic stress-strain curve leads to a hysteresis loop as depicted in Fig. 1.10a
where O-A-B is the initial loading curve
11
and, on unloading, the yielding
occurs at lower stress (point C as compared to A) which is known as the
Bauschinger effect. The material may undergo cyclic hardening or softening;
in rare cases it remains stable (Fig. 1.10b). This behaviour depends on the
initial metallurgical condition of the material. According to Fig. 1.10b, as the
number of cycles increases cyclic hardening leads to decreasing peak strains
while the peak strains increase in the case of cyclic softening. In general, the
hysteresis loop stabilizes after about 100 cycles and the stress-strain curve
obtained from cyclic loading will be different from that of monotonic load-
ing (Fig. 1.10c), but the stress-strain follows a power law relationship similar
to that in monotonic loading (Equation [1.3]):
Δ
Δ
σ
=
K
′
(
Δ
ε
)
n
′
,
[1.17 ]
ranges from 0.1 to 0.2 for many
metals and is given by the ratio of the parameters (
b
/
c
) (Equation [1.12b]).
In some cases fatigue ratchetting occurs resulting in an increase in strain as
a function of time when tested under a constant strain range (Fig. 1.11); this
is often referred to as cyclic creep.
12
In a stress controlled test with non-zero
mean stress, the shift in the hysteresis loop along the strain axis, as depicted
in Fig. 1.11, is attributed to thermally activated dislocation movement at
stresses well below the yield stress and/or due to dislocation pile up result-
ing in stress enhancement. Fatigue ratchetting may also occur in the pres-
ence of residual stress and in cases where microstructural inhomogeneities
exist such as in welded joints.
In real situations stresses change at random frequencies and, in gen-
eral, the percentage of life consumed in one cyclic loading depends on
where the cyclic hardening coeffi cient
n
′
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