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
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 %).