Environmental Engineering Reference
In-Depth Information
ε
t
c
1
σ
t
/
ε
Total
b
Elastic
1
Plastic
N
t
1
2
N
t
Reversals to failure (log scale)
1. 7
Δ
ε
vs N curve showing plastic and elastic strain regimes.
11
fatigue (HCF) regions, corresponding to the plastic and elastic deforma-
tion ranges, respectively. LCF is characterized by macroscopic cyclic plastic
strains and is generally limited to less than 10
4
cycles. LCF is controlled by
the ductility and HCF by the strength of the material, and thus, cold-work
and radiation hardening (both of which result in reduced ductility) result in
decreased fatigue life in the LCF range while being benefi cial in the HCF
range, especially at low stresses/strains. Figure 1.7 shows a typical fatigue
life plot as strain range (
) against number of failure cycles (
N
f
) along with
the corresponding stress-strain loops (broad in LCF and narrow in HCF).
In the high cycle region corresponding to HCF, the Basquin equation relates
the applied stress (
Δ
ε
Δ
σ
) to the number of cycles:
N
f
(
Δ
σ
)
p
=
C
or in terms of strains
N
f
(
E
Δ
ε
)
p
=
C
,
[1.10 ]
where
C
and
p
are material constants. LCF with inelastic strains is often
described by the Coffi n-Manson equation
Δ
ε
=
2
A
(2
N
f
)
c
[1.11 ]
where
A
, a function of the ductility, and
c
(
0.7) are material con-
stants and
N
f
is the number of stress/strain reversals. The Coffi n-Manson
equation is seen to be valid for many materials over a broad range of tem-
perature, environment, stress history and microstructural conditions. The
complete fatigue curve can be described by combining the LCF and the HCF
−
0.5 to
−
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