Introduction
High temperature equipment is generally subjected to cyclic loadings
during operation.1-5 Hence, the failure mechanism of
these kinds of equipment is complicated and often with mixed damages
modes of creep, fatigue, as well as their interactions. Under realistic
loading conditions, such as nuclear reactor components, stress loading
is considered to be more common than strain loading.6Cyclic creep commonly refers to the progressive change of mean strain
during the cyclic plastic deformation of a material between fixed stress
limits, which belongs to creep-fatigue interactive
behaviour.7 Therefore, cyclic creep response of
materials should be an essential consideration for the component’s
design.
The cumulative deformation for cyclic creep is time-dependent, which is
similar to ratcheting.8,9 According to previous
studies, the strain rate can be greatly influenced by a series of test
parameters, such as stress amplitude, stress ratio, and duration under
hold stress. With the increase of duration under peak stress, a
transition in dominant damage type from fatigue to creep can be found,
and the fracture mode transformed from brittle to ductile failure
correspondingly.10 Moreover, research results of
9-12% Cr steel showed that the strain rate in cyclic creep was between
those under ratcheting fatigue and static creep, i.e., the creep damage
was more significant than fatigue damage, and the pure creep rate
determined the upper rate of the cyclic creep.11Similar performances can be found in some nickel-based alloy such as
GH720Li alloy12 and MA754 alloy.13However, research on the cyclic creep response of a nickel-based super
alloy DZ125 under different gradients of stress amplitudes and
temperatures showed that cyclic creep led to accelerate the strain
accumulation compared with static creep, and the ratcheting fatigue rate
was reported to be the upper rate of the cyclic creep, even if the
duration under peak stress was as long as 240
minutes.14 Cases where fatigue damage dominates could
also be found on pure metal copper15 and AMg6
alloy.16In
addition, a material appears opposite results at different temperature,
such as Cr-Mo-V steel was observed cyclic creep acceleration at room
temperature and cyclic creep retardation at 550℃
respectively.17 Therefore, cyclic creep performances
deserve more attention, and the underlying deformation mechanism should
be further studied.
For creep-dominated cases, the anelasticity produced during unloading of
cyclic creep is the main reason to retard the creep rate. Researchers
have found that the anelasticity occurs if a material undergoes a sudden
change in loading and requires time to attain a new equilibrium
configuration.18 Zhang et al.19analysed the
anelastic
strain of 9-12% Cr steel during different valley stress holding stages
alongside with changed stress amplitudes, stress ratios, and peak stress
durations. The results indicated that magnitude of anelastic strain
increased with the increasing stress amplitude, peak stress duration and
decreasing stress ratio. On the other hand, the research by Gaudin et
al.20 on 316 austenitic stainless steel found the
reversibility of plastic strain reversibility, which inhibited cyclic
creep below a threshold stress. Rao et al.21 justified
the relationship between the dislocation distribution and the anelastic
behaviour by using a back stress division approach, together with
observations from transmission electron microscopy (TEM). In addition,
some microscopic mechanisms on the anelastic behaviour of pure metal and
alloy also have been proposed, such as the bowing of dislocations
between precipitates,22 the grain boundary reverse
slip due to the relaxation of dislocation pile-ups,23the reverse movement of dislocations in sub-grain,24and the reverse bending of sub-grain boundaries.25,26More recently, Hosseini et al.27 proposed a simplified
model of 9-12%Cr steel for the movement of dislocation pile-ups based
on the effective stress concept.
Due to its good mechanical properties at elevated temperatures,
2.25Cr-1Mo steel has been extensively used in pressure vessels and
pipeline systems in petroleum and power industries. The mechanical
behaviour of 2.25Cr-1Mo steel under static creep, low cycle fatigue, and
creep-fatigue interaction conditions have been studied by
Klueh,28 Jaske,29 and Challenger et
al.30,31 Kschinka and Stubbins32conducted uniaxial fatigue and creep-fatigue tests at 565°C in both air
and vacuum environments to understand the effects of waveform and
environment on the fatigue behaviour of a forged bainitic 2.25Cr-lMo
steel. Although large amounts of data have been available on
creep-fatigue interaction of 2.25Cr-lMo steel, most of them are based on
strain-controlled tests. Research on cyclic creep under
stress-controlled and anelastic behaviour of 2.25Cr-1Mo steel has rarely
been reported, and corresponding failure mechanism is still inexplicit
as yet.
In this study, a series of uniaxial stress-controlled cyclic creep tests
on bainite 2.25Cr-1Mo steel at 455°C in air are conducted, and the
strain accumulation processes under different unloading conditions are
analysed through the stress-strain curves. Specific attention is paid to
the effect of unloading rate and duration under valley stress on the
anelastic behaviour. Moreover, scanning electron microscopy (SEM)
observations of fracture surfaces are performed to identify the failure
mechanism. A life prediction method for cyclic creep under different
unloading conditions is proposed based on the ductile exhaustion theory.
Experimental procedure
2.1 Material
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The material used for this study is a bainite 2.25Cr-1Mo steel, with
cyclic properties being reported in an earlier work.33The steel was normalized at 950 °C for 6 hours, and followed by
tempering at 690 °C for 6 hours. Then simulated post-weld heat treatment
was done at 690 °C for 8 hours, which was aimed to release residual
stress. Fig. 1 (a) presents the microstructural morphology of the steel
under an optical microscope (OP), and the metallographic structure is
mainly granular bainite. The chemical composition of the steel is shown
in Table 1. The material was machined into cylindrical test specimens
for static creep and cyclic creep tests, with a diameter of and a gauge
length of 50 mm, and the dimension specification is shown in Fig. 1 (b).
Table 1 The chemical composition of the bainite 2.25Cr-1Mo steel (wt
%).