10¹¹ Gigacycle Fatigue Properties of High-strength Steel

Abstract

Fatigue tests were conducted up to 10¹¹ cycles on high-strength steel to clarify a fatigue limit. The fatigue limit of the high-strength steel was not confirmed by gigacycle fatigue tests up to 10¹⁰ cycles, while our previous study suggested that the fatigue limit was probably confirmed by those up to 10¹¹ cycles. However, the 10¹¹ cycles fatigue testing was challenging since it took 2 months even by using ultrasonic fatigue testing at 20 kHz. In this study, 3 specimens were tested beyond 10¹⁰ cycles. Although a test on a specimen was terminated at around 5 × 10¹⁰ cycles, 2 specimens reached 10¹¹ cycles without failure. In other word, no specimen failed above 10¹⁰ cycles. These results demonstrated the fatigue limit on high-strength steel in a gigacycle region. The fractured specimens below 10¹⁰ cycles revealed internal fractures originating from oxide-type inclusions. When the specimens failed in long-life regions, clear ODAs (Optically Dark Areas) were observed on the fracture surfaces at around the internal fracture origin, while the ODAs were obscure in case of failure in short-life regions. The runout specimens up to 10¹¹ cycles were forcibly fatigue-fractured at higher stress amplitudes in the short-life regions. As the result, the ODA was observed on the forcibly fatigue-fractured surface. This meant that small internal cracks existed in the runout specimens since the ODA was a trace of small internal crack growth. Namely, non-propagating cracks were the mechanism of the appearance of the fatigue limit.

1. Introduction

High-strength steels whose tensile strength exceeds approximately 1200 MPa¹⁾ show internal fractures,^{2,3,4,5,6,7,8)} resulting in the disappearance of conventional fatigue limits. Hence, gigacycle fatigue properties beyond 10⁹ cycles need to be considered in high-strength steels. A notable feature of gigacycle fatigue is the presence of internal fractures with distinctly different properties from ordinary surface fractures. These differences are observed in hydrogen effects,^9,10) size effects^11,12) and so on, as well as the disappearance of conventional fatigue limits. Moreover, although a major controlling factor of the surface fractures is strength, such as tensile strength and hardness, that of internal fractures is inclusion sizes at the fracture origins.^13,14)

Ultrasonic fatigue testing at 20 kHz is a powerful tool for evaluating internal fracture properties,^{15,16,17,18,19,20,21)} as it completes 10⁹ cycles in a day, rather than the 3–4 months needed with conventional 100-Hz testing. A point to note about ultrasonic fatigue testing concerns frequency effects. These are very small under conditions where internal fractures occur, so the results of ultrasonic fatigue testing show good agreement with those of conventional fatigue testing. The authors conducted 100-Hz fatigue tests up to 10¹⁰ cycles for three years, and compared the results with those at 20 kHz for a week. It was confirmed in several grades of high-strength steels that the fatigue test results showed good agreement provided that internal fractures occurred.^22,23,24) An accelerated fatigue testing method, which applies 10¹⁰ cycles in one week, was thus established, and this method enabled us to evaluate the internal fracture properties of various materials and under different conditions.^{8,9,10,11,12,13,25,26,27)} As a result of this research, a mass of experimental data has been accumulated on internal fracture properties.

Thereafter, the author embarked on research to elucidate the mechanisms of these internal fractures and to derive predictions of gigacycle fatigue strengths. These studies first required evaluations of the growth rates of small internal cracks.²⁸⁾ A beach mark method was then used to visualize internal crack growth. As a result of a huge number of pre-tests, the author succeeded in visualizing the crack growth of small internal cracks by using repeated two-step tests under ultrasonic fatigue testing.²⁹⁾ The evaluation results of the internal crack growth rates demonstrated that the crack growth of the small internal cracks controlled the internal fractures.³⁰⁾ On the basis of this mechanism, a new model was proposed to calculate the small internal crack growth lives,³¹⁾ from which predictions of the gigacycle fatigue strengths were derived.³²⁾

Previous research has suggested the presence of new fatigue limits in the gigacycle regions for internal fractures. Figure 1 shows an example in which each constant in the predictions is calculated by fitting to the experimental data.³²⁾ The details of the graph in Fig. 1 are explained below, but a key point is that open and solid marks clearly diverge at 10¹⁴ on the horizontal axis of N_f / $\sqrt{area}$_inc. N_f and $\sqrt{area}$_inc respectively indicate the number of cycles to failure and the inclusion size at the internal fracture origin. The inclusion size is the square root of the projected area on the fracture surface. The parameters of the horizontal and vertical axes indicate fatigue lives and loading forces, respectively, in which the effects of the inclusion size scattering were canceled out, so unique fatigue life curves are obtained. The open and solid marks indicate the data points for fractured and unfractured specimens, respectively, so this result seen in Fig. 1 suggests the presence of a fatigue limit. Although this fitting was performed on the experimental data for seven types of materials and five grades of steel, all the results showed the same pattern. The knee points of the fatigue life curves are calculated to be around 10⁹–10¹⁰ cycles by assuming that the inclusion sizes range from 20–100 μm. Although the previous 10¹⁰-cycle gigacycle fatigue tests could not confirm the fatigue limit, the 10¹¹-cycle versions were able to.

Fig. 1.

Typical result of fitting in the previous report.³²⁾

On the basis of the above, this study conducted 10¹¹-cycle gigacycle fatigue tests on high-strength steel and investigated the new fatigue limit. There were no previous reports on 10¹¹-cycle gigacycle fatigue test results, since even ultrasonic fatigue testing requires two months to reach 10¹¹ cycles.

2. Experimental Method

2.1. Materials

Table 1 shows the chemical compositions of the tested steel, which is a hot-rolled round bar of JIS-SCM440 low-alloy steel. The heat treatments applied were oil quenching after holding at 1153 K for 30 min and tempering by air cooling after holding at 473 K for 60 min. These heat treatments were conducted after pre-machining to round bars 12 mm in diameter. The Vickers hardness after heat treatment was HV604, which was equivalent to a tensile strength of 1969 MPa, assuming tensile strength to be equal to 3.26 HV.³³⁾ Tensile tests were not conducted in this study: the tensile properties of the similar JIS-SCM440 steel can be looked up.³⁴⁾ Figure 2 is a photo of the microstructure, which reveals prior-austenite grains. The microstructure was tempered martensite with a prior-austenite grain size of around 20 μm.

Table 1. Chemical compositions of the tested steel.

Steel	Element (mass%)
	C	Si	Mn	P	S	Cr	Mo
SCM440	0.40	0.21	0.71	0.009	0.009	0.96	0.16

Fig. 2.

Microstructure of the tested steel.

2.2. Fatigue Testing

Ultrasonic fatigue tests were conducted at 20 kHz. The machine used was a Shimadzu USF2000. The maximal cycle number tested was 10¹¹ cycles. The runout specimens were forcibly fatigue-fractured at a higher stress amplitude, at which internal fracture was expected. This forced fatigue fracture made it possible to inspect the inclusion sizes of the runout specimens by observing the fracture surface.²²⁾ Figure 3 shows the type of specimen used in these tests: it has an hourglass shape with a minimum diameter of 3 mm. The narrowed area of the specimens was finished with 1-μm grit powder to eliminate any machining flaws. The specimens were air-cooled during the fatigue tests to minimize any temperature increase. The air-cooling system consists of a vortex tube-type cooler and a 5.5 kW-class compressor. Under these conditions, the temperature increase was negligible even during continuous testing at 20 kHz, so intermittent tests¹⁹⁾ were not applied, i.e., all tests were conducted by continuous testing. These fatigue tests were conducted at room temperature in air with a stress ratio of R = –1.

Fig. 3.

Profiles of specimens in mm.

The fracture surfaces were observed using a scanning electron microscope (SEM) and an optical microscope (OM). Scanning electron microscopy is generally used for fracture surface observation, while the optical microscope takes clearer photos of optically dark areas (ODAs).^35,36,37) Although the fracture surfaces were too rough to allow direct OM observation, clear OM photos were created using commercially-available software to overlay several photos.

3. Experimental Results

Figure 4 shows the fatigue test results. The open and solid marks respectively indicate the data points of fractured and unfractured specimens. Arrows are attached to the unfractured data points, and the number alongside each arrow indicates the number of overlapped data points. The 10¹¹-cycle gigacycle fatigue tests were conducted at 680 MPa. Although a test on one specimen was terminated at around 5 × 10¹⁰ cycles, two specimens reached 10¹¹ cycles. A specimen was fractured at 8.37 × 10⁹ cycles. In summary, no specimen was fractured at above 10¹⁰ cycles.

Fig. 4.

Fatigue test results.

Figure 5 shows typical SEM images of fracture surfaces. All specimens ended in internal fractures originating from an oxide-type inclusion. In Fig. 5, one side of the fracture surfaces shows the inclusion, and the other side features a hole in which the inclusion had been embedded. This kind of fracture surface is frequently observed with oxide-type inclusions, since they are easily debonded from the matrix. In some cases, however, both sides of the fracture surfaces reveal inclusions, with the inclusions cracked. The inclusion sizes ranged from 14 to 35 μm, averaging 22 μm.

Fig. 5.

Typical SEM images of fracture surfaces at around the internal fracture origin. This specimen was fractured at 8.66 × 10⁷ cycles at 800 MPa.

Figure 6 shows typical OM photos of the fracture surfaces. (a) shows an example that fractured with a short-life of around 10⁶ cycles, and (b) shows a long-life example of around 10⁸ cycles. The fracture surface of Fig. 6(b) is the same as that shown in Fig. 5(a). A dark area around the inclusion is observed in Fig. 6(b). The dark area looks rough in the SEM image. On the other hand, the dark area is small and obscure in Fig. 6(a). The dark area is an ODA. In general, ODAs are not observed after short-life failure at around 10⁵ cycles, but they begin to appear at around 10⁶ cycles, and are clearly identifiable beyond 10⁷ cycles. The dark areas in Fig. 6 match this trend. Figure 7 shows the fracture surface of a specimen which was first load-cycled up to 10¹¹ cycles and then forcibly fatigue-fractured at a higher stress amplitude. In Fig. 7, the cycle number of the forcible fatigue-fracturing is close to that of Fig. 6(a), while a clear ODA is observed, as in Fig. 6(b). Although similar results, i.e., that ODAs were observed in the runout specimens after short-life forcible fatigue-fracturing, were reported in past studies,^22,35,36) this study confirms the same trend in the 10¹¹-cycle gigacycle fatigue test.

Fig. 6.

Typical OM photos of fracture surfaces at around the internal fracture origin. (a) is the specimen fractured at 3.01 × 10⁶ cycles at 920 MPa. (b) is the specimen fractured at 8.66 × 10⁷ cycles at 800 MPa.

Fig. 7.

OM photo of fracture surfaces at around the internal fracture origin. This specimen was first load-cycled up to 10¹¹ cycles at 680 MPa and then forcibly fatigue fractured at 2.48 × 10⁶ cycles at 890 MPa.

4. Discussion

The fatigue test results in Fig. 4 suggest the existence of a new fatigue limit, since no specimens failed at above 10¹⁰ cycles. To more clearly confirm the new fatigue limit, the analysis shown in Fig. 1 was applied to this test result. Figure 1 is the result of data-fitting as used to derive predictions in a previous study.³²⁾ The derivation started with the following original crack growth law which was applied to small internal cracks.   

$$\frac{d\sqrt{area}}{dN}=C{\left(\mathrm{\Delta }K\cdot {\sqrt{area}}^{\alpha }\right)}^m$$(1)

where $\sqrt{area}$ is crack size, ΔK is the stress intensity range and C, m and α are constants. ΔK was calculated using the following equation.   

$$\mathrm{\Delta }K=0.5\mathrm{\Delta }\sigma \sqrt{\pi \sqrt{area}},\mathrm{\hspace{0.17em} }\mathrm{\Delta }\sigma =2{\sigma }_a$$(2)

where σ_a is the stress amplitude. By integrating Eq. (1) in the range of $\sqrt{area}$ from an inclusion size $\sqrt{area}$_inc to double its size, i.e., 2$\sqrt{area}$_inc, the following equation is obtained.   

$${\left(\mathrm{\Delta }{K}_{inc}\cdot {\sqrt{area}}_{inc}^{\alpha }\right)}^m\left(\frac{N_f}{{\sqrt{area}}_{inc}}\right)=\frac{2^{1-m\left(\frac{1}{2}+\alpha \right)}-1}{C\left(1-m\left(\frac{1}{2}+\alpha \right)\right)}=D$$(3)

where D is a constant that simplifies the right-hand side of Eq. (3). Based on Eq. (3), the constants of C and m are determined by fitting the relationship between $\mathrm{\Delta }{K}_{inc}\cdot {\sqrt{area}}_{inc}^{\alpha }$ and N_f /$\sqrt{area}$_inc, and the constant α is determined by evaluating the R² values (coefficient of determination) of the fittings. Figure 1 is the result of this fitting.

Figure 8 shows the graph in Fig. 1 in which experimental data of this study are superimposed as diamond marks (♢ and ♦). The present results show a good agreement with previous experimental data. The runout data points indicated by solid diamond marks (♦) are located on an approximately horizontal line that shows the threshold value for the new fatigue limit obtained in the previous study. This result supports the presence of the new fatigue limit in that the data points of the 10¹¹-cycle fatigue tests reveal more clearly that the fitted line levels off at 10¹⁴ on the horizontal axis of N_f /$\sqrt{area}$_inc. Moreover, the new fatigue limits calculated in the previous study are valid, since the data points of the 10¹¹-cycle fatigue tests show good agreement with the threshold values indicated by the horizontal line. The existence of the new fatigue limit is thus confirmed in this study.

Fig. 8.

Present results plotted in a graph of Fig. 1.

Two mechanisms, crack initiations and non-propagating cracks, are considered for the presence of this fatigue limit. Although non-propagating cracks appear to be the cause of conventional surface fractures, it also seems likely to be the case in internal fractures. The reason is the fact that the runout specimen of the 10¹¹-cycle fatigue test shows an ODA as shown in Fig. 7. The specimen shown in Fig. 7 was first load-cycled up to 10¹¹ cycles and then forcibly fatigue-fractured at a higher stress amplitude, while the cycle number for forcible fatigue-fracturing is around 10⁶. The 10⁶-cycle is not enough to form clear ODAs, as shown in Fig. 6(a). The ODA seen in Fig. 7 was formed in the 10¹¹-cycle fatigue test. Moreover, a previous study using a beach mark method revealed ODAs to be evidence of small internal crack growth.³⁰⁾ The ODA in Fig. 7, therefore, means that a small internal non-propagating crack is present in the runout specimen. Non-propagating cracks are therefore the mechanism that creates the new fatigue limit.

5. Conclusion

This study carried out gigacycle fatigue tests up to 10¹¹ cycles on high-strength steel and investigated a new fatigue limit based on the occurrence of internal fractures. As a result, the following conclusions were obtained.

(1) Three specimens were fatigue-tested beyond 10¹⁰ cycles. Although the test for one specimen was terminated at around 5.0 × 10¹⁰ cycles, the two remaining specimens reached 10¹¹ cycles. No specimen was thus fractured above 10¹⁰ cycles, indicating the presence of a fatigue limit.

(2) All the fractured specimens revealed internal fractures that originated from oxide-type inclusions whose sizes ranged from 14–35 μm, averaging 22 μm.

(3) ODAs were observed using an optical microscope. Although they were small and obscure in short-life failure samples, clear ODAs were observed after failure in the long-life area. Clear ODAs were also observed in the runout specimen of the 10¹¹-cycle fatigue test after it had been forcibly fatigue-fractured at a higher stress amplitude with a short-life.

(4) The present results were compared with the previous experimental data by calculating the relationships between $\mathrm{\Delta }{K}_{inc}\cdot {\sqrt{area}}_{inc}^{\alpha }$ and N_f /$\sqrt{area}$_inc. The present results showed good agreement with the previous results, also revealing more clearly that the fitted line leveled off at 10¹⁴ of N_f /$\sqrt{area}$_inc. This result clarified the existence of the new fatigue limit and confirmed the validity of the new fatigue limit calculated in the previous study.

(5) The clear ODA observed in the runout specimen indicates the existence of a small internal crack, indicating non-propagating cracks to be the mechanism of occurrence of the new fatigue limit.

Acknowledgements

This study was supported in part by Kakenhi 18H03748.

References

• 1)   K.  Kanazawa,  T.  Abe and  S.  Nishijima: NRIM Fatigue Data Sheet Technical Document, No. 9, National Research Institute for Metals, Tokyo, (1989), 20 (in Japanese).
• 2)   Y.  Murakami: Metal Fatigue - Effects of Small Defects and Nonmetallic Inclusions, Yokendo, Tokyo, (1993), 73.
• 3)   P. H.  Frith: J. Iron Steel Inst., 180 (1955), 26.
• 4)   H.  Emura and  K.  Asami: Trans. Jpn. Soc. Mech. Eng. Ser. A, 55 (1989), 45 (in Japanese).
• 5)   S.  Nishijima and  K.  Kanazawa: Fatigue Fract. Eng. Mater. Struct., 22 (1999), 601.
• 6)   T.  Sakai,  M.  Takeda,  K.  Shiozawa,  Y.  Ochi,  M.  Nakajima,  T.  Nakamura and  N.  Oguma: J. Soc. Mater. Sci., Jpn., 49 (2000), 779 (in Japanese).
• 7)   T.  Sakai,  B.  Lian,  M.  Takeda,  K.  Shiozawa,  N.  Oguma,  Y.  Ochi,  M.  Nakajima and  T.  Nakamura: Int. J. Fatigue, 32 (2010), 497.
• 8)   T.  Abe,  Y.  Furuya and  S.  Matsuoka: Fatigue Fract. Eng. Mater. Struct., 27 (2004), 159.
• 9)   H.  Hirukawa,  Y.  Furuya and  M.  Hayakawa: Tetsu-to-Hagané, 93 (2007), 600 (in Japanese).
• 10)   H.  Hirukawa and  Y.  Furuya: Tetsu-to-Hagané, 99 (2013), 494 (in Japanese).
• 11)   Y.  Furuya: Tetsu-to-Hagané, 95 (2009), 426 (in Japanese).
• 12)   Y.  Furuya: Mater. Sci. Eng. A, 528 (2011), 5234.
• 13)   Y.  Furuya,  S.  Matsuoka,  T.  Kimura and  M.  Hayaishi: Tetsu-to-Hagané, 91 (2005), 630 (in Japanese).
• 14)   Y.  Furuya,  H.  Hirukawa,  T.  Kimura and  M.  Hayaishi: Metall. Mater. Trans. A, 38 (2007), 1722.
• 15)   W. P.  Mason: J. Acoust. Soc. Am., 28 (1956), 1207.
• 16)   H.  Ishii,  R.  Ebara,  Y.  Yamada and  K.  Minakawa: J. Soc. Mater. Sci., Jpn., 42 (1993), 1218 (in Japanese).
• 17)   C.  Bathias: Fatigue Fract. Eng. Mater. Struct., 22 (1999), 559.
• 18)   S. E.  Stanzl-Tschegg: Fatigue Fract. Eng. Mater. Struct., 22 (1999), 567.
• 19)   H.  Mayer: Int. Mater. Rev., 44 (1999), 1.
• 20)   H.  Mayer: Fatigue Fract. Eng. Mater. Struct., 39 (2016), 3.
• 21)  WES 1112: 2017, Standard test method for ultrasonic fatigue testing of metallic materials (in Japanese).
• 22)   Y.  Furuya,  S.  Matsuoka,  T.  Abe and  K.  Yamaguchi: Scr. Mater., 46 (2002), 157.
• 23)   T.  Abe,  Y.  Furuya and  S.  Matsuoka: Tetsu-to-Hagané, 88 (2002), 786 (in Japanese).
• 24)   Y.  Furuya,  T.  Abe and  S.  Matsuoka: Fatigue Fract. Eng. Mater. Struct., 26 (2003), 641.
• 25)   Y.  Furuya and  S.  Matsuoka: Trans. Jpn. Soc. Mech. Eng. Ser. A, 71 (2005), 1201 (in Japanese).
• 26)   Y.  Furuya: Trans. Jpn. Soc. Mech. Eng. Ser. A, 73 (2007), 957 (in Japanese).
• 27)   Y.  Furuya: Tetsu-to-Hagané, 99 (2013), 373 (in Japanese).
• 28)   K.  Tanaka and  Y.  Akiniwa: Fatigue Fract. Eng. Mater. Struct., 25 (2002), 775.
• 29)   Y.  Furuya: Mater. Lett., 112 (2013), 139.
• 30)   Y.  Furuya: Tetsu-to-Hagané, 101 (2015), 228 (in Japanese).
• 31)   Y.  Furuya: Tetsu-to-Hagané, 101 (2015), 494 (in Japanese).
• 32)   Y.  Furuya: Tetsu-to-Hagané, 102 (2016), 415 (in Japanese).
• 33)   S.  Nishijima,  A.  Ishii,  K.  Kanazawa,  S.  Matsuoka and  C.  Masuda: NRIM Fatigue Data Sheet Technical Document, No. 5, National Research Institute for Metals, Tokyo, (1989), 77 (in Japanese).
• 34)   Y.  Furuya and  S.  Matsuoka: Metall. Mater. Trans. A, 33 (2002), 3421.
• 35)   Y.  Murakami,  T.  Nomoto and  T.  Ueda: Fatigue Fract. Eng. Mater. Struct., 22 (1999), 581.
• 36)   Y.  Murakami,  N. N.  Yokoyama and  J.  Nagata: Fatigue Fract. Eng. Mater. Struct., 25 (2002), 735.
• 37)   T.  Nakamura and  H.  Oguma: J. Soc. Mater. Sci., Jpn., 60 (2011), 1066 (in Japanese).