Mechanics of Materials
Study on Extremely-Low-Cycle Fatigue of Fe–15Mn–10Cr–8Ni–4Si Alloy
2023 Volume 64 Issue 2 Pages 548-554
Details
2023 Volume 64 Issue 2 Pages 548-554
The extremely-low-cycle fatigue behavior and post-fatigue microstructure of an Fe–15Mn–10Cr–8Ni–4Si austenitic alloy were investigated under a strain rate and maximum strain amplitude of 0.5%/s and 10%, respectively, in the axial direction. The results can be summarized as follows. (1) A steel damper made of Fe–15Mn–10Cr–8Ni–4Si alloy can withstand approximately 15 swings back even if the structure is distorted by approximately 10% due to a large earthquake. (2) The εpa–Nf relationship of the Fe–15Mn–10Cr–8Ni–4Si alloy demonstrated a linear relationship, and it was confirmed that Manson-Coffin rule holds. (3) Even in an extremely-low-cycle fatigue test with a strain rate of 0.5%/s, the test specimen temperature did not exceed 40°C under all test conditions. Therefore, the ε phase was formed in the fatigue test under all test conditions. (4) Various facets and secondary cracks were observed in the fatigue propagation region of the fracture surface. Accordingly, it was inferred that most of the main cracks propagated at the γ/ε interface and the secondary cracks merged. Consequently, the fatigue crack could not propagate linearly, and the generation of the secondary cracks caused a decrease in the displacement at the tip of the crack when the stress was redistributed, thus extending the fatigue life.
This Paper was Originally Published in Japanese in J. Soc. Mater. Sci., Japan 70 (2021) 751–757.
Fig. 6 Total strain amplitude and number of cycles to failure.
Japan is an earthquake-prone country, and hydraulic, rubber, and steel dampers are installed in newly constructed structures to prepare for large earthquakes. Steel dampers are less expensive than other types of dampers and are often used to reinforce existing structures as seismic reinforcements, thus requiring excellent low-cycle fatigue characteristics. Recently, the γ → ε transformation in Fe–Mn–Si (FMS) alloys was observed to be effective in improving low-cycle fatigue properties, and new applications such as vibration dampers for buildings have emerged.1,2) The authors investigated low-cycle fatigue properties of various Fe–Mn–Si-based alloys with systematically varied stacking fault energy.3–13) In this study, we developed an iron-based vibration-damping alloy (Fe–15Mn–10Cr–8Ni–4Si alloy) that protects the structure of skyscrapers from long-period seismic tremors.6) Fe–15Mn–10Cr–8Ni–4Si alloys, which were initially developed from iron-based shape memory alloys, improve fatigue life owing to the reversible deformation of ε-martensite during cyclic deformation processes, and exhibit low-cycle fatigue properties 10 times longer than those of ordinary steel owing to the generation of γ-twin deformation.9)
However, tremor analyses of recent large earthquakes have reported that they occurred at extremely high strain rates.14) Long-period oscillations in earthquakes have a period ranging from a few seconds to approximately 10 s and some percentage of strain amplitude. However, recently, actual measurements have demonstrated that the frequency of S-waves varies with the distance from the epicenter, with extremely short frequencies of approximately 0.4 s and frequencies at intervals of 1 s observed in the Kumamoto earthquake, which caused extensive damage.14) Assuming a strain amplitude of 1%, a period of 1 s is 4%/s in terms of strain rate, which is 80 times higher than the strain rate in a normal low-cycle test (0.5%/s), and adds extremely large and fast vibrations to the structure.
The test condition commonly used for low-cycle fatigue is a maximum axial strain amplitude (Δεtl/2) of approximately 2%.15) Tests conducted at higher strains are referred to as extremely-low-cycle fatigues. To ensure the usefulness of FMS alloys in large earthquakes, it is necessary to understand their ultra-low-cycle fatigue properties. Therefore, in this study, for the sake of comparison with basic data, extremely-low-cycle fatigue tests involving a strain rate of 0.5%/s and maximum strain amplitude of 10%, converted to the axial direction, were conducted in general low-cycle fatigue tests to analyze the behavior of deformed microstructures and their effects during the fatigue damage process.
The specimen material was Fe–15Mn–10Cr–8Ni–4Si (mass%). An Fe–15Mn–10Cr–8Ni–4Si alloy was prepared from 10-kg ingots using vacuum induction melting, rolled at 1273 K, annealed at 1273 K/1 h, and water-cooled. The metallurgical structure before the test was a single phase of austenite (γ), and the average size of the crystal grains was 95 µm.9) Fatigue specimen were machined so that the specimen longitudinal axis was aligned along the former rolling direction.
Normally, low-cycle fatigue tests are conducted on smooth cylindrical specimens with extensometers attached along the axial direction at a controlled maximum axial strain amplitude of approximately 2%. If a strain greater than 2% is applied, the test cannot be performed because the change into a barrel shape, resulting in deviation from the controlled strain and buckling under some test conditions. For such extremely-low-cycle fatigue testing, an hourglass-shaped round bar specimen is used, an extensometer is attached along the radial direction, and the fatigue test is conducted using the radial strain as the control strain. Hourglass-shaped fatigue specimens with a minimum diameter of 6 mm, as shown in Fig. 1, were also used in this experiment, and a servo-hydraulic fatigue testing machine with a capacity of 50 kN was employed under double-swinging (stress ratio R = −1) conditions. The maximum strain amplitude in the radial direction (Δεtd/2) was set at 5%, 4%, 3%, and 2%, and the test speed was 0.5%/sec. Figure 2 shows the specimen mounting conditions for the very low cycle fatigue test. A thermocouple was mounted directly under the extensometer to measure the temperature change during the test, and the temperature of the specimen was measured. The following equation was used to convert radial strain to axial strain.
| \begin{equation} \varepsilon_{ta} = (\sigma_{a}/E)(1 - 2\nu) + 2(\varDelta\varepsilon_{ed}/2) \end{equation} | (1) |
Schematic diagram of a fatigue specimen.
Fatigue test condition with radial extensometer attached.
After conducting the fatigue test, the fracture surface was observed in detail using Field Emission Scanning Electrion Microscopes (FE-SEM) to determine the fracture initiation point and fracture-surface aspect. A 2-mm section was cut from the fracture surface on one side, and a 2-mm-thick slice was buffed and polished from the cut surface for microstructural analysis. This analysis was performed using a ferrite meter FMP30 (Helmut Fischer) and an X-ray diffraction (XRD) system (SmartLab, Rigakus).
Figure 3 shows the relationship between the strain amplitude and fracture life, where ○ represents the total strain (εta = Δεtl/2), △ denotes the plastic strain (εpa), and □ refers to the elastic strain (εea = εta − εpa). The solid marks represent the results of the ultra-low-cycle fatigue test, whereas the open marks represent the results of the low-cycle fatigue test. The εpa-Nf relationship can be expressed as εpa = Cp/NfKp. This relationship is called the Manson-Coffin rule and is the most fundamental relationship in low-cycle fatigue.16–18) The analytical values in the figure are those obtained for the low-cycle fatigue data. Kp and Cp are 0.51 and 0.83, respectively. Cp is usually in the range from 0.1 to 0.5, which is a high value for the εpa-Nf relationship. Kp is approximately 0.3 for a low-strength carbon-steel tempered material and gradually increases to 0.5–0.6 as the tempered material becomes higher in strength. In this test piece, this parameter exhibited a relatively high value. The εea-Nf relationship can be expressed as εea = Ce/NfKe, where Ke and Ce are 0.24 and 0.028, respectively. In a previous study,12) a comparison was made between the test specimen, high Mn steel (shape memory alloy) of the same series, and SUS304 steel. The reported values are close to those of an Fe–30Mn–4Si–2Al alloy of the same series (Ke = 0.26, Ce = 0.038).
Strain amplitude and number of cycles to failure.
Figure 4 shows the hysteresis loops at Nf/2 for each strain test condition. The radial strain was converted to axial strain using eq. (1). The strain at the point where the unloading process of the hysteresis loop intersects with zero stress in the figure is εpa; however, the plastic strain was large for all strain conditions. The stress component was larger in compression than in tension under each strain test condition, and slightly asymmetric between the tension and compression sides. In this specimen, epsilon martensite was formed by tensile deformation; however, during the cyclic process, the formed epsilon phase underwent a reverse transformation to the original γ phase and returned to the original flat surface. Furthermore, it is established that compressive deformation also produces the epsilon phase, however, reversal of the deformation direction (compressive to tensile) results in reverse transformation; thereafter, similar microstructural changes occur repeatedly and reversibly.6) This (ε ↔ γ) reversible microstructural change is responsible for the excellent low-cycle fatigue properties of Fe-based shape memory alloys, thereby affecting their extremely low-cycle fatigue properties.
Stress-strain hysteresis loops at half-life cycle Nf/2 for obtained of total strain amplitudes: 10%, 8%, 6%, and 4%.
Figure 5 shows cyclic softening and hardening curves. For all test conditions, cyclic hardening occurred at the beginning of the test, followed by slight hardening.
Stress amplitude σa plotted as a function of the number of cycles N, obtained of total strain amplitudes: 10%, 8%, 6%, and 4%.
Figure 6 shows the relationship between the total strain amplitude and fracture life for various steels. The results for Kamaya’s SUS316 steel19) are represented by △. The results for this test specimen are indicated by circles. The solid marks represent the results of the extremely-low-cycle fatigue tests conducted in this experiment, and the open marks represent the results of the low-cycle fatigue tests. Gray marks were made at a constant frequency of 0.0625 Hz based on the results of the extremely-low-cycle fatigue test described in a previous report.13) When the test was conducted with εta = 10%, the difference in terms of the strain rate was 0.5%/s in this test and 2.5%/s in the aforementioned previous report, i.e., five times faster than in this test. The data for the total strain amplitude and number of repetitions are listed in Table 1. The test results for the solid and open marks are almost continuous. The fatigue properties of the specimens were not adversely affected by the high strain rate test conditions described in the abovementioned previous report, and the cyclic life of the specimens tended to be slightly longer. The low-cycle fatigue life of the test specimen was approximately five times longer than that of Type-316 steel. When the data for SUS316 steel were extended to εta = 10%, the number of iterations decreased significantly. The extremely-low-cycle fatigue life (εta = 10%) of this test specimen is much higher than that of SUS316 steel (no data plot, but extended △ data), and even if the structure is subjected to approximately 10% strain by a large earthquake, the Fe–15Mn–10Cr–8Ni–4Si alloy steel damper can withstand approximately 15 cycles (Nf/2) of shaking.
Total strain amplitude and number of cycles to failure.
Figure 7 shows the temperature variation of the specimen during repeated ultra-low-cycle fatigue tests. The specimen temperatures started near room temperature (26°C) for all test conditions and increased during the test according to the order of increasing test strain. At εta = 10%, the specimen temperature increased to a maximum of 35.8°C, although remained almost constant at 35°C until fracture. At εta = 8%, the specimen temperature increased to a maximum of 33.8°C, after which it gradually decreased and remained almost constant at 32°C until fracture. At εta = 6%, the specimen temperature reached a maximum of 32.4°C, however, remained almost constant at 32°C until fracture. At εta = 4%, the specimen temperature remained nearly constant at 28°C until fracture.
Test specimen temperature changes during extremely-low-cycle fatigue test.
Figures 8 and 9 depict the fracture-surface observations of an extremely-low-cycle fatigue specimen that failed at εta = 10%. In the Optical Microscope (OM) image shown in Fig. 8, the fatigue-fracture area was classified into three regions: fatigue-fracture area itself, which is curved around the starting point in contact with the surface; dimples, which are ductile-fracture areas outside the fatigue-fracture area; and shear lip, which is the shear-fracture area at the final fracture. Figure 9 shows the SEM image of the fatigue initiation point. Striations peculiar to fatigue-fracture surfaces were observed in the fatigue-fracture region of the low-cycle fatigue; however, such striations could not be distinguished in the extremely-low-cycle fatigue test. On the fracture surface of low-cycle tests, the fatigue failure zone is usually the fatigue crack growth zone that propagates from Mode I to Mode II, and the crack propagates perpendicular to the stress axis, resulting in a flat fracture surface. However, grain-dependent facet-like irregularities were observed on the fracture-surface of the specimen under extremely-low-cycle fatigue near the starting point, and many secondary cracks were observed in the fatigue fracture zone. The fracture surfaces of the specimens under different strain conditions also demonstrated facet-like irregularities in the fatigue fracture zone, and numerous secondary cracks were observed in all specimens, although the fatigue fracture and dimpled zones differed in percentage. In previous studies on ultra-low-cycle fatigue of SUS316 and SFVQ1A steels, it was reported that multiple internal fractures originating from inclusions were observed on the fatigue fracture surface.19,20) The specimens indicated no internal fracture in any of the strain-controlled tests, demonstrating that the fracture-surface phase of the specimens was different from that of the other alloys.
Optical micrographs showing fracture surfaces.
SEM micrographs showing fracture surfaces: (a) Low magnification show fatigue-fracture area; (b) High magnification show around the fatigue crack initiation site.
Two approaches to analyze low-cycle fatigue damage have been discussed: 1) surface cracks and 2) damage that accumulates inside the material (hereafter referred to as bulk damage). Kikukawa et al.21) applied a maximum plastic strain amplitude of 6% to S20C steel to consider the effects of surface and bulk cracks and compared the changes in life after surface removal and annealing treatments. The results revealed that surface crack initiation and growth dominate fatigue life. In addition, Murakami et al.22) reported that in load-controlled tests of S45C steel (equivalent to a plastic strain amplitude of 2%), the fatigue life was almost 100% dominated by crack growth according to the observation of crack growth from holes as small as 40 µm in diameter. Furthermore, the Manson-Coffin rule, which describes fatigue life as a function of plastic strain amplitude and phase, can be explained using the relationship between the crack growth rate and crack length. Komotori et al.23) showed that fatigue damage (fatigue life) is governed by crack propagation and that the Manson-Coffin rule is equivalent to life evaluation using crack propagation by observing such crack propagation from the pit in S20C steel and pure iron. In the plastic strain amplitude and fracture life shown in Fig. 3, the number of cycles decreased in the extremely-low-cycle fatigue region compared to the analytical value for low-cycle fatigue (Manson-Coffin rule). Although it is not possible to separate and analyze the crack initiation and propagation lives of the specimens in the extremely-low-cycle fatigue regime, the Manson-Coffin rule holds in the low-cycle fatigue regime, suggesting that crack propagation is also dominant in the extremely-low-cycle regime. The fatigue fracture zone shown in Fig. 8 extended approximately 3 mm from the starting point, and the fracture life was 32 times. Therefore, if the crack propagates evenly, 100 µm corresponds to one propagation, which is approximately equal to the size of a grain. Regarding the reason for the larger stress component on the compression side in Fig. 4, the crack growth life was dominant in the extremely-low-cycle test, which suggests that the crack propagated considerably at Nf/2. The hysteresis loop may have become asymmetric because of the cyclic ε → γ transformation during compression, although the tensile stress was reduced when cracks were included.
Figure 10 shows the results of ferrite meter measurements. Magnetic phases were detected in all the tests. This trend increased with increasing strain amplitude, except for the test results for εta = 8%. Therefore, it is clear that a martensitic (α′) phase was formed during the cyclic testing of BCC in all specimens.
The results measured by the ferrite meter.
Figure 11 shows the results of XRD analysis. Deformation-induced martensitic (ε), austenitic (γ), and α′ phases of HCP were detected in all the specimens. The test specimen had a single phase of γ before the test, and ε and α′ phases were generated during the fatigue test. The deformation-induced ε-martensitic transformation was determined by the difference between the deformation temperature and the Ms point, which is the starting temperature of the martensitic transformation. Figure 12 schematically shows the temperature dependence of the deformation-induced martensitic transformation on the yield stress. Just above the Ms point, the yield was dominated by the stress-assisted martensitic transformation (stress-assisted γ → ε), and the yield stress demonstrated a positive temperature dependence. As the temperature increased, the yield became dominated by sliding deformation, and the yield stress indicated a negative temperature dependence; however, a strain-induced martensitic transformation (strain-induced γ → ε) occurred in which martensite was formed with dislocations as nuclei. These martensitic transformations (γ → ε) or the boundary temperatures at which the positive and negative temperature dependences of the yield stress change are denoted by Msσ. Note that Msσ < T < Md, where specimen temperature T is the temperature range in which strain-induced martensitic transformation occurs, together with the upper limit Md for the temperature at which deformation-induced martensitic transformation occurs. Previous studies demonstrated that fatigue life is improved when deformation occurs in the temperature range in which strain-induced martensitic transformation occurs. The specimens in this study were designed to have a high fatigue life in the temperature range from room temperature to approximately 100°C, with Ms = −40°C, Msσ = 40°C, and Md = 80°C. The deformation microstructure differed depending on the test conditions with different strain amplitudes at high strain rates, as described in a previous report.13) The γ and ε phases were detected at εta = 4% and 8%, respectively; at εta = 10%, the γ phase and some twin deformation were present; however, no ε phase was present. Under the constant-frequency condition reported in Ref. 13), the specimen temperature was heated to 70°C owing to the higher strain rate at εta = 10%, but 70°C was within the range given by Msσ < T < Md. However, considering that the specimen temperature was measured directly under the extensometer and not at the crack tip, a specimen temperature of 70°C was considered to be within the error range, no strain-induced martensitic transformation occurred, and no ε phase was formed. In this experiment, as shown in Fig. 7, the specimen temperature never exceeded 40°C under all the test conditions, and the epsilon phase was formed during cyclic deformation.
The results measured by XRD.
Plasticity mechanisms in the various ΔG γ → ε regions.
The crack propagation mechanism of the same series of alloys (this test specimen was developed from the Fe–30Mn–4Si–2Al alloy) can be considered the cause of this excellent fatigue property according to the following explanation. Let us first discuss the facets and secondary cracks observed in the fatigue-fracture zone on the fracture surface. Figure 13 shows the EBSD results near the fracture surface of the Fe–30Mn–4Si–2Al alloy fractured in a low-cycle fatigue test, as observed in previous report (5). In Fig. 13(b), white represents the γ phase and gray represents the ε phase. The crack propagated preferentially in the ε phase. Referring to the crystal orientation map in Figure (a), the reversible deformation of γ/ε occurred at the crystal wall of the most easily deformable ε phase. When the limit of repeated deformation was exceeded, the crack propagated in zigzag because the crystallographic grain changed, the crystallographic walls of the easily deformable ε phase presented different orientations, and the crack could not propagate following a straight line. The cracks branched during the propagation process, and branching due to crack bifurcation was observed. Considering these observations, the facets on the fracture surface in extremely-low-cycle fatigue are the crystalline walls of the ε-phase and are considered to be cracks formed beyond the limit of cyclic deformation. The facet steps are considered to be traces of the main crack propagation at the crystal wall of the epsilon phase, which is the most easily deformed phase, depending on the grain size. Multiple subcracks are considered traces of cracks formed by crack branching.
The microstructure developed near the crack’s tip in the low-cycle fatigue fractured sample of Fe–30Mn–4Si–2Al alloy:5) (a) IPF + IQ map and (b) correspondent phase map showing the crack propagation inside the e-martensite.
Ju et al.11) conducted crack growth tests on the Fe–30Mn–4Si–2Al alloy in which the ε phase was formed. These authors pointed out that the ε-phase exerts a dual effect: 1) it inhibits crack growth by suppressing the localization of plastic strain due to repetitive motion of partial dislocations, 2) it induces crack closure due to roughness of the fracture surface, mitigating secondary crack stress at the main crack tip, and promoting crack growth due to secondary crack coalescence. The fatigue-fracture surface of this specimen exhibited almost no flat areas, and facet-like irregularities and numerous secondary cracks were observed. Therefore, it is inferred that most of the main cracks propagated at the γ/ε interface, and the secondary cracks coalesced. Two processes of crack strengthening were applied to the secondary crack formation. The first process was stress redistribution, resulting from the release of residual stress at the crack tip during secondary crack propagation.24) This behavior increases the resistance of the main crack to fatigue propagation through a crack-tip shielding mechanism.25) The second process shows that the crack-tip opening displacement decreases with the opening of the secondary crack.
In the fatigue tests of this specimens, crack propagation life was dominant, and various facets and secondary cracks were observed in the fatigue propagation region of the fracture surface (Fig. 8, Figs. 9). This suggests that the fatigue life is extended because the cracks cannot propagate linearly through the γ/ε interface of the main crack, and the secondary-crack formation results in stress redistribution and reduced crack-tip aperture displacement.
The deformation structure of the Fe–15Mn–10Cr–8Ni–4Si alloy, developed as a damper material, was examined during the fatigue damage process using ultra-low-cycle fatigue tests at a strain rate of 0.5%/s and a maximum strain amplitude of 10% in the axial direction. The obtained results can be summarized as follows:
This work was supported by JSPS KAKENHI (grant number JP20K04170).
