This work investigates the behavior of 316 stainless steel (SS) under stress-controlled low cycle fatigue loading. Several fatigue experiments are conducted under different environment such as in air at 300 °C and primary loop water conditions for a pressurized water reactor (PWR). Two different loading conditions are also employed to examine the effect of stress rate on material hardening and ratcheting. During PWR water test, actuator position measurements are used to determine the strain of the specimen. Under PWR environment, 316 SS is found to ratchet to a significantly greater degree compared with in air. At slow stress rate, higher amount of cyclic hardening is observed in 316 SS, and slow stress rate increases the rate of ratcheting. Results also indicate that 316 SS exhibits asymptotic strain response at higher stress loading which can cause material to behave very differently under same stress cyclic loading.
Under realistic loading conditions, nuclear reactor components are subjected to stress loading rather than strain loading, as in the case of conventional strain-controlled fatigue tests. In the low cycle fatigue regime, the life of reactor components is conventionally estimated by using S–N (strain–life) curves, which are estimated from strain-controlled fatigue test data. Thus, it is important to investigate material behavior under stress-controlled loading. Cyclic stress-controlled loading may result in ratcheting of strain-induced failure modes. Ratcheting can be defined as the progressive directional accumulation of permanent strain due to stress cycling [1,2]. The difference in peak true stress levels during tension and compression can lead to nonclosure of the hysteresis loop, which causes the shifting of the loop along the direction of the strain axis [3,4]. Ratcheting strain is a secondary deformation process that proceeds cycle by cycle. During stress cycling, the cumulative effect of fatigue damage and progressive ratcheting strain accumulation in a particular direction can severely deteriorate the performance of a component by continuous thinning out the cross-sectional area . It has been found that the ratcheting behavior has a close relation to the cyclic hardening/softening characteristics of the materials . Kang et al.  experimentally studied the uniaxial ratcheting behavior of both cyclic hardening and softening steels. They concluded that cyclic-hardening materials fail due to a combined effect of increasing ratcheting strain and low cycle fatigue, while cyclic softening materials fails due to a large ratcheting strain. In general, austenitic steel, such as 316 stainless steel (SS) and 304 SS, exhibits significant amount of cyclic hardening behavior. It has been found that ratcheting strain not only depends on the material but also the loading factors, such as stress level, loading history, stress rate, and loading path [3,7–11]. For time-dependent materials, stress rate plays an important role on ratcheting and should be taken into account . The elevated temperature coolant water of pressurized water reactor (PWR) has a detrimental effect on the fatigue strength of SS which is one of the major concerns for the long-term survivability of operating U.S. light water reactors (LWR). Many studies have been performed to examine the degree of reduction in fatigue life in the PWR environment. However, most of the studies have been performed under strain-controlled loading with varying strain amplitudes and strain rate. It is, therefore, important to investigate the effect of PWR environment on material ratcheting under stress-controlled loading. In this work, we investigate the behavior of 316 SS under stress-controlled loading. We also investigate the effect of stress rate and PWR environment on ratcheting behavior of 316 SS. Note that, in U.S. LWRs, 316 SS and other similar stainless steel grades are primarily used in the construction of hot leg, cold leg, and surge line pipes.
We performed stress-controlled fatigue experiments on 316 SS base metal under air at 300 °C and a PWR water coolant environment (water chemistry: 1000 ppm B as H3BO3, 2 ppm Li+ as LiOH, 20% H2/Bal. N2 cover gas, and dissolved oxygen <5 ppb) at 300 °C. Two loading rates were employed during the fatigue tests to determine the impact of loading rate on material behavior under air and PWR environment conditions. All the tests were conducted with small hourglass specimens. Experiments under air and PWR environment were conducted in separate test setups containing hydraulic-controlled mechanical testing system (MTS) test frames. The test setup used for in-air tests is shown in Fig. 1. An induction heating system was used to locally heat the specimen. Fifteen thermocouples spot welded to pull rod and specimen (nine on the specimen and six on the pull rod) were used to monitor and control the temperature. A precision high-temperature extensometer was used to measure the gauge-area strain during in-air tests.
For the PWR environment fatigue experiments, a specially designed pressurized water loop was used to create the PWR coolant water condition. In addition to the regular fatigue test frame, the test loop consists of various subsystems such as autoclave, preheater, heat exchanger, hydrogen and other cover gas supply, recirculating pump, feed water supply tank, etc. The test parameters were acquired using a NI-LabVIEW-based data acquisition system. Figure 2 shows the screenshot of the LabVIEW window showing various components of the test loop. The main fatigue test was conducted using a MTS test frame. Figure 3(a) shows the MTS test frame with pipe autoclave. Thermocouples were instrumented on outside of the autoclave to ascertain the temperature distribution along the length of the specimen and pull rod. Figure 3(b) shows the LabVIEW screenshot illustrating the schematic of autoclave, test specimen, and location of thermocouples with instantaneous thermocouple readings. For the PWR environment tests, an extensometer could not be used for gauge-area strain measurement due to a water-tight autoclave in the experimental assembly. To determine the strain of the specimens during the PWR environment tests, actuator position measurements from PWR water tests were used along with the position-strain mapping functions generated from the in-air fatigue tests. The test conditions along with Test IDs are presented in Table 1.
Two different stress inputs were used to perform fatigue tests on 316 SS. Figure 4 shows the stress input during ET-F43 and EN-F44 tests. As seen in the figure, stress input consists of an initial variable-amplitude block loading comprising 12 fatigue cycles with gradually increased stress amplitude followed by repeated cycles of constant-amplitude loading. The stress amplitude for the constant-amplitude loading was equal to the maximum stress amplitude (last cycle) during the variable-amplitude loading. This amplitude (216 MPa) was decided based on the stress amplitude during stabilized cycles of a previously (refer to ET-F41 test in Ref. ) conducted strain-controlled fatigue test (strain amplitude = ±0.5%). The stress rate during constant-amplitude loading was 43.2 MPa/s, which was selected such that the time period is the same as that of ET-F41 test. Note that the stress rate during variable-amplitude loading was 0.0432 MPa/s, which is 1000 times lower than the stress rate during constant-amplitude loading. This was done to mimic the initial slow heat-up of the nuclear reactor components during operation. The high stress rate (during constant-amplitude loading) after the initial variable-amplitude loading at low rate was done to complete the test within a reasonable time frame. The initial variable-amplitude block loading with gradually increased stress was applied to ensure that the test material does not deform too much within the first quarter cycle. As observed during a previously conducted tensile test (refer to ET-F04 test in Ref. ), a 2% deformation is observed after application of 197 MPa stress.
Another set of stress-controlled tests (ET-F45 and EN-F46) was conducted, where the stress rate was the same for both variable- and constant-amplitude loading. The employed stress rate was 0.0432 MPa/s. The stress input during ET-F45 and EN-F46 tests is shown in Fig. 5. These low stress rate tests were performed to examine the impact of loading rate on material behavior during constant-amplitude stress loading cycles. The time period per cycle was 20,000 s during low-rate constant-amplitude loading (ET-F45 and EN-F46), but only 20 s during high-rate constant-amplitude loading (ET-F43 and EN-F44).
Results and Discussion
Figure 6 shows the observed engineering strain during the entire ET-F43 test. The figure indicates that a significant amount of ratcheting strain occurs during the stress-controlled fatigue experiment with 316 SS. Although no mean stress was applied, the specimen still ratcheted up to 3% in the tensile direction. To determine the driving force behind ratcheting of the specimen, the mean true stresses during variable- and constant-amplitude loading of ET-F43 are plotted in Fig. 7. These figures show that the mean true stress during ET-F43 is in the tensile direction, which might have caused the material to ratchet in that direction. Figure 6 suggests that the rate of ratcheting was much higher during the initial phase (variable-amplitude loading) of the experiment. Careful observation also indicates that the observed strain amplitude was much higher during the last cycle of variable-amplitude loading than the first cycle of constant-amplitude loading. Note that the applied stress amplitude is same for both cases. This finding suggests that 316 SS shows rate-dependent behavior, particularly when the rate of loading changes. For example, the strain ratcheting rate was higher when the applied stress rate was lower during initial-variable loading, but when the applied stress rate was changed to a higher rate (during constant-amplitude loading), the observed strain ratcheting rate decreased. The slower strain ratcheting during higher rate constant-amplitude loading could be also due to work hardening associated with the higher rate strain ratcheting during the initial variable loading. This finding is very important for fatigue modeling of nuclear reactor components, as they are subjected to variable-rate stress–strain reversal, leading to a load-sequence effect on material performance. Also, this test result signifies the importance of stress analysis and fatigue modeling of reactor components based on both stress- and strain-controlled fatigue test data.
The observed strain during the ET-F45 test is shown in Fig. 8. As the stress rate during constant-amplitude loading of ET-F45 test was 1000 times lower than that of ET-F43, the experiment took exceptionally long, and the sample did not break even after 48 days. The experiment was stopped after 200 constant-amplitude loading cycles. Figure 9 shows the comparison between ratcheting strain during variable-amplitude block loading in-air tests ET-F43 and ET-F45. From the figure, a significant difference can be seen in ratcheting strain, although the loading conditions (stress amplitude and stress rate) were the same for both tests (during variable-amplitude loading). This finding indicates that the test material can behave very differently under the same stress cyclic loading. As can be seen in Fig. 6, during plastic deformation, material strain response becomes asymptotic at higher stress loading. A small amount of stress perturbation can cause huge plastic strain, which can further drive the ratcheting by increasing the mean true stress in the following loading cycle. These findings show the importance of conducting several stress-controlled fatigue tests under the same condition so that the variation in material behavior under stress loading can be incorporated into the material properties with a statistically good level of confidence. These findings also signify the complexity of conducting stress-controlled fatigue experiments.
Pressurized Water Reactor Tests.
During PWR environment tests, an extensometer could not be placed inside the water-tight autoclave for strain measurement. Thus, the axial deformation of the specimen must be measured or controlled by either frame crosshead displacement (i.e., stroke) or frame actuator position. Previously [13–15], we conducted PWR environment tests by controlling the crosshead displacement. To predict the strain from the crosshead displacement data of the PWR tests, we used stroke–strain mapping functions generated from in-air tests data, where the in-air tests were controlled by the same crosshead displacement used for PWR tests. The stroke-strain mapping functions from stoke-controlled in-air test data were generated by using a seventh-order polynomial. The details on stroke-strain calibration can be found in Refs.  and . In this work, we followed the similar method for position-strain calibration which was used to predict strain from actuator position measurements during PWR environment tests. Note that, we used actuator position measurements instead of stroke measurements, because during stress-controlled test, a significant amount of axial ratcheting of the specimen occurs in the tension direction, which is beyond the measurement range of the stroke sensor. To verify the position-strain calibration, we regenerated strain from the position data of in-air test ET-F43. The comparison between regenerated strain and actual measured strain from ET-F43 is shown in Fig. 10. As seen in the figures, the regenerated strain through position-strain mapping match the actual strain measurements with good accuracy.
Figure 11 shows the strain predicted from position data during PWR environment test EN-F44. The stress input during the PWR water test EN-F44 was the same as for the in-air test ET-F43. Initial observation of the strain data between ET-F43 (Fig. 6) and EN-F44 (Fig. 11) suggests that ratcheting is much higher in PWR water than in air. The strain predicted from actuator position data during PWR environment test EN-F46 is shown in Fig. 12. The stress input during this test was the same as that of the in-air test ET-F45, where the stress rate was 0.0432 MPa/s during both variable- and constant-amplitude loading. For EN-F44, the stress rate was 0.0432 MPa/s during variable-amplitude loading and 43.2 MPa/s during constant-amplitude loading. Due to the low (1000 times) stress rate during constant-amplitude loading of EN-F46, the experiment took exceptionally long, and the sample did not break even after 34 days. The test was stopped after 139 cycles. As seen in the comparison of the strain between ET-F43 (Fig. 6) and EN-F44 (Fig. 11), the comparison between ET-F45 (Fig. 8) and EN-F46 (Fig. 12) also indicates higher ratcheting in the case of the PWR water test. The comparison between Figs. 11 and 12 indicates that a significant difference in material ratcheting during variable-amplitude loading between the EN-F44 and EN-F46 tests, although the loading conditions (stress amplitude and stress rate) were the same for both tests during variable-amplitude loading. A similar observation was also made for the in-air tests. As discussed before, this kind of variation in material behavior under the same experimental condition could be due to the asymptotic plastic strain response at high stress level.
Effect of Stress Rate on Material Behavior.
As discussed in the experimental section, the applied stress rate was the same during the variable-amplitude loading for all the tests, while it was different during constant-amplitude loading. The stress rate during constant-amplitude loading of ET-F43 and EN-F44 was 43.5 MPa/s, while a 1000 times lower stress rate (0.0432 MPa/s) was employed during constant-amplitude loading of ET-F45 and EN-F46 tests. Comparisons between strain data from ET-F43 (Fig. 6) and ET-F45 (Fig. 8) shows that the strain at the beginning of the constant-amplitude loading was different, which was due to the difference in ratcheting strain after the initial variable-amplitude loading (see Fig. 9). To compare the effect of stress rate on material behavior, therefore, the engineering strain responses during constant-amplitude loading were normalized by subtracting the initial strain (i.e., strain after the initial variable-amplitude loading). Figure 13(a) plots the normalized engineering strain versus fatigue cycles of ET-F43 and ET-F45. Similarly, Fig. 13(b) plots the same factors from constant-amplitude loading of PWR tests EN-F44 and EN-F46. From both figures, it can be concluded that under lower stress rate as well as for longer fatigue cycles, material hardens more. The normalized ratcheting strain as a function of fatigue cycles is plotted in Fig. 14 for both in-air and PWR tests. The plot indicates that material ratchets at a higher rate under lower stress rate, a finding that is somewhat conflicting if the conclusion is made only based on the material hardening observed from Fig. 13. One would expect slower ratcheting as material hardens, as in the case of the low stress rate test, but it is not always the case.
Effect of Pressurized Water Reactor Environment on Material Behavior.
To investigate the effect of the PWR environment on material behavior, ratcheting strain during variable-amplitude loading of all four stress-controlled tests is plotted as a function of fatigue cycles in Fig. 15. Note that the stress input for all four cases is the same during variable-amplitude loading. As seen in Fig. 15, the ratcheting strain at the end of variable-amplitude loading is higher for the two PWR tests (EN-F44 and EN-F46) than the two in-air tests (ET-F43 and ET-F45). However, there is substantial variation in the ratcheting strain values irrespective of the environment. Ratcheting strain for ET-F45 (in-air) is 2.65 times higher than ET-F43 (in-air), while ratcheting strain for EN-F46 (PWR) is 3.43 times higher than EN-F44 (PWR). There is also significant variation in material response at the initial stage of the stress-controlled fatigue test. The effect of the PWR environment on material behavior during constant-amplitude loading was also investigated. Figure 14 compares the normalized ratcheting strain between ET-F43 and EN-F44, which are high stress rate (43.2 MPa/s) tests, and between ET-F45 and EN-F46, which are low stress rate (0.0432 MPa/s) tests. In both cases, the test material experiences higher ratcheting under the PWR environment. The life of the EN-F44 (PWR) specimen is also reduced by 13% compared to the ET-F43 specimen (in-air).
In this work, stress-controlled fatigue experiments are conducted on 316 SS under different stress rate and different environment such as in-air at 300 °C and PWR water coolant at 300 °C. Since an extensometer cannot be used due to a water tight autoclave in the PWR test assembly, actuator position measurements are used to predict strain of the specimen. 316 SS is found to exhibit stress rate-dependent material behavior, particularly when the rate of loading changes. This signifies the importance of stress analysis and fatigue modeling of nuclear reactor components based on both stress- and strain-controlled fatigue test data, as they are subjected to variable-rate stress–strain reversal, leading to load-sequence effect on material performance. It is also found that 316 SS can behave very differently under same stress cyclic loading due to the asymptotic strain response at higher stress loading. A small amount of stress perturbation can cause huge plastic deformation, which can further drive the ratcheting by increasing the mean true stress in the following loading cycles. It is, therefore, important to conduct several stress-controlled fatigue tests under the same condition so that the variation in material behavior under stress loading can be incorporated into the material properties with a statistically good level of confidence. PWR environment fatigue test results indicate substantial effect of PWR water condition and loading rate on ratcheting strain. PWR environment is found to drive ratcheting of the material at a faster rate and to a higher value.
U.S. Department of Energy, Program Manager Dr. Keith Leonard (Light Water Reactor Sustainability Program Under the Work Package of Environmental Fatigue Study).