Abstract
In this study, experimental investigations were conducted to create fatigue limit diagrams for NSSC180 ferritic stainless steel, which is used for automobile exhaust system parts, subjected to excess deformation, in order to clarify the relationship between the mean stress and fatigue limit. The fatigue tests were conducted under a fixed maximum stress, which allowed a fatigue design diagram to be obtained. The results indicated that the fatigue limit curve has a region where the effect of increasing the mean stress on the decrease in the fatigue limit is more moderate than that predicted by a modified Goodman line. Furthermore, it was found that a fatigue design based on static crack initiation is more appropriate than the modified Goodman line for higher values of mean stress.
This Paper was Originally Published in Japanese in J. Soc. Mater. Sci., Japan 72 (2023) 535–541.
1. Introduction
Automotive exhaust system components are often subjected to extremely high levels of plastic deformation. As illustrated in Fig. 1(a), under actual working conditions, such components are subjected to a cyclic load with a fixed maximum stress and an extremely high mean stress. Since the mean stress has a significant effect on the fatigue limit, the exhaust system components of automobiles are performed fatigue design to determine the usable region for practical safety by fatigue limit diagram showing the yield limit line based on the yield stress σY,Virgin for the virgin material, together with the modified Goodman line, as shown in Fig. 1(b). However, if the loading history in Fig. 1(a) is plotted on a fatigue limit diagram, the plotted points will appear as A or B in Fig. 1(b), which are outside the usable range for fatigue design. However, many components are currently in safe practical use under such loading conditions. This is because the fatigue limit diagram uses a yield limit line based on σY,Virgin, and does not consider the fact that the yield limit for a material subjected to excess deformation σmax also increases to σmax. However, there are only a few reports on fatigue limit diagrams for materials subjected to such excess deformation.1–4) On the other hand, there have been many reports on the fatigue limit for pre-strained materials, and it has been reported that the fatigue limit is affected by complex interactions among the amount of pre-strain, the type of material, and the stress ratio.5–13) For example, Kamaya et al. reported that for pre-strained materials, the fatigue life increases with increasing amount of pre-strain for the same stress amplitude. However, there is no experimental data available for extremely high mean stresses or for situations where the yield point changes. Consequently, applying fatigue design based on the general fatigue limit diagram for virgin materials to materials subjected to excess deformation is unreliable and may lead to overly safe or dangerous designs.
There are several design guidelines that consider the effect of mean stress. For example, the JIS E 420714) general rules for the strength of rolling-stock bogies specify that the effect of mean stress should be considered by using the allowable fatigue stress line based on the modified Goodman line, and the allowable yield stress line considering the maximum stress. The structural design standards for nuclear power components specified in ASME Boiler & Pressure Code Section III15) incorporate the effects of mean stress within the design fatigue curves. Although there are several design rules that consider the effects of mean stress, all are based on the modified Goodman line using the fatigue limit and tensile strength of virgin material and the allowable stress for material yield, and do not consider an increase in the yield limit for a material subjected to excess deformation.
It is extremely important for industry to clarify the fatigue design guidelines for materials subjected to excess deformation under realistic loads, because achieving carbon neutrality requires the production of lighter-weight and more compact automobiles to reduce carbon dioxide emissions.
In this study, ferritic stainless steel NSSC180, which is used for automotive exhaust system parts, was selected as the test material. The purpose of this study is to experimentally clarify the relationship between the mean stress and the fatigue limit by conducting fatigue tests under similar load conditions (fixed maximum stress and high mean stress) after being subjected to the same excess deformation as the actual machine. Based on the experimental results, a suitable method is discussed for creating fatigue limit diagrams for ferritic stainless steel subjected to excess deformation under fixed maximum stress conditions.
2. Specimens and Test Method
2.1 Specimens
The material used in this study was ferritic stainless steel NSSC180 (equivalent to SUS430J1L), whose chemical composition is shown in Table 1. This study used two different lots of steel, referred to as Lot 1 and Lot 2. The specimens were machined into the shapes shown in Fig. 2, and the R section of each was then mirror polished using emery paper (#600, #800, #1000, #1200, #1500, #2000) and alumina powder (3.0 µm, 1.0 µm). Hereinafter, these specimens are referred to as virgin material.
Table 1 Chemical composition of NSSC 180 [mass%].
Static tensile tests and fatigue tests were performed using a hydraulic Servo pulser EHF-ED10T-20L manufactured by Shimadzu Corporation. Both types of tests were conducted at room temperature in air with a load speed of 100 N/s for the static tensile tests. The fatigue tests were conducted at a frequency of f = 1–20 Hz, a stress ratio of R = −1, and a maximum number of fatigue cycles of N = 1 × 107 cycles. A Dynastrain 344-01201-01 gauge displacement meter with a gauge length of 12.5 mm manufactured by Shimadzu Corporation was used to measure the strain. Scanning electron microscopy (SEM) observations of the fracture surface were performed using an electron microscope TM4000 manufactured by Hitachi Corporation. Hardness measurements were conducted with a retention time of 10 s and an indentation force of 9.8 N using a Vickers hardness tester HMV-G manufactured by Shimadzu Corporation.
Figure 3 shows the fatigue test procedure under fixed maximum stress conditions used in this study. First, the maximum stress σmax above the yield point is determined from the static tensile test results (Fig. 3(i)). The virgin material is then statically loaded with σmax, and fatigue tests are carried out at various stress amplitudes with σmax as the maximum stress (Figs. 3(ii)-(a), (ii)-(b)). Because the maximum stress is fixed, the mean stress σm also changes as the stress amplitude σa changes. Namely, σmax becomes the new yield point after loading σmax against the yield point of the virgin material, and the broken/unbroken test results are plotted on the yield limit line for the new σmax, as indicated by the dashed lines and square symbols in Fig. 3(iii). In this study, σmax values of 370, 410, 430, 450, and 470 MPa were chosen, and the measured fatigue limits were plotted on a fatigue limit diagram. Hereinafter, specimens subjected to excess deformation by loading at σmax = 370, 410, 430, 450, and 470 MPa are referred to as ExD-370, ExD-410, ExD-430, ExD-450 and ExD-470, respectively. The stress values are calculated based on the minimum diameter of the virgin material before loading, and the effect of cross-sectional shrinkage is not considered.
3. Experimental Results
3.1 Static tensile test results
Figure 4 shows the static tensile test results for the virgin material. The vertical and horizontal axes indicate the applied stress and strain, respectively. It can be seen that the yield point and tensile strength for Lot 1 and Lot 2 are σY = 400 MPa, σB = 519 MPa, and σY = 335 MPa, σB = 500 MPa, respectively. The NSSC180 steel used in this study was highly ductile and exceeded the measurement range of the displacement meter, so a sharp increase in stress occurred only just before breaking (area outlined by ellipse in the figure).
The same static tensile test was conducted on ExD-450 in Lot 1, and the results are shown in Fig. 5. The tensile strength is seen to be 520 MPa, indicating that excess deformation has little effect on the tensile strength.
3.2 Fatigue test results
Fatigue tests were carried out on the virgin material (Lot 1) and ExD-450 to determine the fatigue limit for a stress ratio of R = −1, and the results are shown in Fig. 6. The fully reversed fatigue limits for the virgin material and ExD-450 were 323 and 290 MPa, respectively. Thus, the fatigue limit decreases when the specimen is subjected to excess deformation. Here, the fatigue limit is defined as the average of the minimum stress amplitude for a broken specimen and the maximum stress amplitude for an unbroken specimen.
3.3 Hardness test results
Next, the fatigue tests were conducted on virgin material (Lot 1), ExD-450 subjected to excess deformation only, and ExD-450 (ExD-450 + Run-out) unbroken up to 107 cycles with a stress amplitude of σa = 150 MPa, and a hardness measurement of the R section cross-section was performed to investigate the effect of excess deformation and cyclic load on specimen hardness. As seen in Fig. 7, an average hardness value of 200 points was measured at random positions on the cross-section with the minimum diameter. It can also be seen that the hardness of ExD-450 was larger than that for the virgin material, indicating that work hardening occurs when the specimen is subjected to excess deformation. On the other hand, there is little difference between the results for ExD-450 and ExD-450 + Run-out, indicating that no further work hardening occurs under additional fatigue loading.
3.4 Fatigue limit diagram under fixed maximum stress condition
Fatigue tests were conducted on ExD-370, ExD-410, ExD-430, ExD-450, and ExD-470 for various stress amplitudes. Figure 8 shows the relationship between the stress and strain for ExD-430 at a stress amplitude of 150 MPa as a representative example. The solid line shows the relationship for increasing stress of up to σmax = 430 MPa. The dashed line shows the relationship under subsequent cyclic loading at a fixed maximum stress, where the stress is seen to cycle on the unloading elastic line. Figure 9 shows the observed fracture surface for this specimen following breaking after Nf = 3.9 × 105 cycles, which indicates that fracture originates at multiple points on the surface. Similar results were obtained for all tested specimens.
Figure 10 shows all fatigue test results obtained in this study plotted on a fatigue limit diagram. The vertical and horizontal axes are normalized by the tensile strength of each lot to evaluate differences in tensile strength between lots. A modified Goodman line using the fully reversed fatigue limit for the virgin material (Lot 1), with σw = 323 MPa and σB = 519 MPa, is also shown. In the range of mean stress σm/σB between 0.4 and 0.6, there existed experimental data that were unbroken even when the experimental data were considered to be on the danger side for the modified Goodman line. In addition, ExD-470, which was subjected to the largest excess deformation, exhibits fracture for all stress amplitudes, even for small values below the modified Goodman line. The reason for this was investigated by specimen surface observations by SEM.
Figure 11 shows SEM images of the surfaces of the virgin material, ExD-430, ExD-450, and ExD-470. For the former three specimens, polishing marks but no clear cracks are observed, whereas the latter specimen exhibits Luders bands running at 45° to the loading direction and clear cracks exceeding 100 µm in length around the entire circumference of the R section. Therefore, for NSSC180, an applied stress of 470 MPa causes too much deformation just before static fracture, and so it is assumed that the specimen fractured despite the small stress amplitude in the subsequent fatigue test. Therefore, the static crack initiation limit stress was defined as 460 MPa (equivalent to 3.6% plastic strain), which is midway between the stress values for ExD-450 and ExD-470.
Finally, Fig. 12 shows a summary of the results obtained in the present study. From these results, fatigue design guidelines for NSSC180 subjected to excess deformation under fixed maximum stress conditions can be discussed. The red line in the figure shows the boundary between broken and unbroken specimens as the fatigue limit line, and it can be divided into three areas. First, for a mean stress up to the intersection of the yield limit line and the modified Goodman line for the virgin material (Area I), fatigue design based on the general modified Goodman line is appropriate. Next, for a mean stress above point A, it can be seen that there is an area (Area II) where the effect of the mean stress increase on the fatigue limit decrease is less severe than the modified Goodman line. This is thought to be due to the fact that the dislocation density in the material increased under the influence of the initial excess deformation, and work hardening occurred, which suppressed dislocation movement under cyclic stress during the fatigue test. However, a detailed quantitative analysis regarding this point is left for future work. Furthermore, for a mean stress above the intersection of the fatigue limit line in Area II (point B) and the static crack initiation limit line (Area III), it can be seen that fatigue design based on the static crack initiation limit line is more appropriate than that based on the modified Goodman line.
From the above results, fatigue design based on the modified Goodman line and the initial yield limit line provides an extremely safe evaluation due to the presence of unbroken areas despite the stress amplitude being higher than that for the general modified Goodman line. However, it should be noted that when the static crack initiation limit line is exceeded, the specimen will break even at stresses below the modified Goodman line.
4. Conclusion
In this study, the relationship between the mean stress and the fatigue limit was investigated for ferritic stainless steel NSSC180, which is used for automotive exhaust system parts. Fatigue tests were performed under fixed maximum stress conditions for specimens subjected to excess deformation. The results showed that an area existed where the effect of increasing mean stress on the decrease in the fatigue limit was more relaxed than predicted using the modified Goodman line based on the mechanical properties of the virgin material, and that for higher mean stress, fatigue design based on the static crack initiation limit line was more appropriate.
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