Overview of ageing and degradation issues in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 358

the magnitude of stress in subsequent cycles. However, the linear cumu-
lative damage rule, known as Miner's rule, assumes that the total life of
a component can be estimated by adding up the life fraction consumed
by each of the loading cycles. If N fi is the number of cycles to failure at
the i th cyclic loading and N i is the number of cycles experienced by the
structure then

N
N

∑

i
fi =

1 [1.18 ]

although Miner's rule is too simplistic and fails to predict the life when
notches are present. Further, it fails to predict the life when mean stress and
temperature are high or cyclic frequency is low where creep deformation
dominates over fatigue loading. In such situations a better approximation is
given by combining Robinson's rule for creep fracture with Minor's rule;

N

t

∑∑

N

i i

1, [1.19 ]

+

i

=

N t

fi

N

fi

where ( t fi ) and fracture time ( t i ) corresponding to the i th creep conditions.
It turns out that many materials exhibit deviations from this linear addi-
tion depending on whether it is cyclically hardening or softening. 13 In par-
ticular the predictions tend to be highly non-conservative for cyclically
softening materials.
Fatigue strength or life of structures can be improved by reducing the
mean positive stress, through appropriate design with no stress raisers and
by surface fi nish and modifi cations. In particular, case hardening by carbu-
rizing and nitriding as well as shot-peening, which increase surface residual
compressive stresses, result in distinct improvements in fatigue life. In com-
parison to pure metals, solid solution has been found to improve fatigue
strength. Other factors such as interstitials inducing strain ageing could also
improve fatigue life.
Environmental effects on creep-fatigue are quite complex and each case
needs to be considered separately. While Equation [1.19] gives an approxi-
mate assessment, the mechanistic explanations of high-temperature fatigue
effects are corrosion- or creep-related. Coffi n considered the time dependent
fatigue to be essentially SCC and formulated frequency-modifi ed fatigue
life-time correlations for crack initiation and propagation. 12 Manson pro-
posed a plasticity oriented fatigue model using a strain-range partitioning
method. 13 Fatigue crack growth assisted by creep cavitation at grain bound-
aries was considered by Majumdar and Maiya 14 to model high-temperature
fatigue crack growth.

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