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Ultra-long cycle fatigue of high-strength carbon steels part II: estimation of fatigue limit for failure from internal inclusions
Materials Science and Engineering A356 (2003) 236 /244 www.elsevier.com/locate/msea
Ultra-long cycle fatigue of high-strength carbon steels part II: estimation of fatigue limit for failure from internal inclusions M.D. Chapetti a,b,*, T. Tagawa b, T. Miyata b a
INTEMA, University of Mar del Plata-CONICET, J.B. Justo 4302, B7608FDQ Mar del Plata, Argentina b Department of Material Science and Engineering, Nagoya University, Nagoya 464-8603, Japan Received 11 October 2002; received in revised form 12 February 2003
Abstract Ultra-long cycle fatigue fracture origins in high strength steels are mostly at non-metallic inclusions due to the influence of the trapped hydrogen. In the vicinity of a non-metallic inclusion at the fracture origin, an optically dark area (ODA) is often observed inside a fish-eye mark, which represents the particular morphology associated with mechanism of failure at an early stage: hydrogen assisted fatigue. From an analysis of several features involved in this mechanism of failure, as the development of the ODA, the threshold for pure fatigue propagation, as a function of crack length and inclusion size, an expression was deduced to estimate the internal fatigue limit, that is, the stress level below which fracture produced by cracks initiated from an internal inclusion is not found after 1010 cycles: DKth sInt ffi e 256 pffiffiffiffiffiffiffiffiffi Rmax i where DKth is the pure fatigue crack propagation threshold as a function of crack length estimated with the following expression: DKth 4 10 3 (HV 120)(3Rmax )1=3 i Otherwise
If DKth 510 MPa m1=2
1=2
DKth 10 MPa m
Rmax i
is the maximum radius of the non-metallic inclusions from which the crack initiates, in mm, and HV is the Vickers hardness, in kgf mm 2. The internal fatigue limit was estimated for several steels and compared with experimental results obtained from the literature for internal fatigue lives in the range of 108 /1010 cycles. Differences between the estimated internal fatigue limit and the experimental one ranged from 4 to /29%. # 2003 Published by Elsevier Science B.V. Keywords: High strength steels; Ultra-long fatigue life; Surface cracks; Internal cracks; Non-metallic inclusions
1. Introduction Fatigue fracture origins in ultra-long cycle fatigue in high strength steels are mostly at non-metallic inclusions due to the influence of the hydrogen trapped by them. In the vicinity of a non-metallic inclusion at the fracture origin, a dark area was often observed inside a fish-eye mark for specimens with a long fatigue life [1 /11], which represents the particular morphology associated with
* Corresponding author. E-mail address: [email protected] (M.D. Chapetti).
the mechanism of failure involved. Murakami and coworkers have named this area as ‘optically dark area’ (ODA), and the related mechanism of failure as ‘hydrogen embrittlement assisted by fatigue’ [1,3,4]. Fig. 1 illustrates the mechanism for ultra-long fatigue failure from internal non-metallic inclusions. In Part I of this study [12] some features related with creation of an ODA by hydrogen assisted fatigue was briefly reviewed, and pure fatigue crack propagation from surface and from internal inclusions was analyzed and modeled in high strength steels that show both types of crack initiation. It was concluded, in accordance with previous references, that any estimation of total fatigue life associated with the failure produced by cracks
0921-5093/03/$ - see front matter # 2003 Published by Elsevier Science B.V. doi:10.1016/S0921-5093(03)00136-9
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
Nomenclature a a0 area1/2 C* and m s Ds Dse DsInt e Dsth DK DKth DKthR HV ODA R Ri Rmax i se sInt e su
237
crack length initial crack length for pure fatigue propagation Murakami’s model parameter environmentally sensitive material-constants applied stress amplitude applied stress range surface fatigue limit range internal fatigue limit range threshold stress range for pure fatigue crack propagation applied stress intensity range (applied crack driving force) fatigue crack propagation threshold (function of crack length) mechanical threshold for long cracks (material constant for a given stress ratio R ) Vickers hardness optically dark area stress ratio (minimum stress/maximum stress) inclusion radius maximum inclusion radius surface fatigue limit amplitude internal fatigue limit amplitude ultimate tensile strength
initiated at internal inclusions will succeed only if the crack initiation period can be properly estimated. The crack initiation period is defined by the number of cycles necessary to create a crack length given by the optical dark area (ODA) [3 /12]. The number of cycles to form a crack length given by ODA size, is defined by the type and size of inclusion, the tensile residual stresses around it, the amount of hydrogen, the applied nominal stress range and amplitude, some particular features of the microstructure related to the hydrogen trapping places and the threshold for pure fatigue crack propagation. There exists very limited information about how parameters influence crack initiation period by hydrogen assisted fatigue. Thus, the aim of defining a proper model to estimate it is not an easy task. However, a threshold for pure fatigue propagation of internal cracks initiated at inclusions can be defined taking into account
Fig. 1. Scheme of the mechanism for super-long fatigue failure from internal inclusion with an initial hydrogen assisted fatigue crack initiation and early propagation.
the different geometrical and mechanical variables involved in the process. In this paper a model to estimate the threshold stress to obtain fatigue fracture from cracks initiated at internal inclusions (internal fatigue limit), is presented. The defined internal fatigue limit is obtained from: (a) the threshold for pure fatigue crack propagation, (b) the maximum inclusion size in the material, and (c) a defined critical size of the ODA.
2. Analysis of the ODA size As reviewed and analyzed in part I of this study [12], (1) the size of the ODA increases with an increase in fatigue life, (2) ODA cannot be found on the fracture surface of specimens failed at a small number of cycles, and (3) ODA size is independent of frequency. Besides, it seems that ODA size defines the critical crack length from which pure fatigue propagation takes place, and crack propagation inside the ODA is defined by hydrogen embrittlement assisted by fatigue. Between factors affecting the crack initiation from inclusions, the inclusion size plays an important role. The finite element calculations made by Brooksbank and Andrews [13 /15] to estimate the residual stress distributions surrounding inclusions in bearing steels have shown that the circumferential residual stresses are as high as 450 MPa at the matrix /inclusion interface (in the case of Al2O3 inclusions). This stress reduces to about 50 MPa at a distance from the matrix /inclusion
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interface equal to inclusion radius. The stress concentrations introduced by the inclusion have to be taken into account. In this case the inclusion is considered as a ‘porous’, for which the stress concentration is 2 and it banishes at a distance greater than its diameter [16]. The zone influenced by the inclusion can be conservatively confined to a sphere whose size is three times the size of the inclusion. Besides, according to studies of Taha et al. [17] the hydrogen resides at hydrostatic stress peak locations, in the highly stressed material. So, it is possible to assume a hydrogen embrittlement process assisted by fatigue will mainly take place inside a region as far as three times the inclusion radius Ri from the center of the inclusion. Another important factor defining the development of the ODA is the amount of hydrogen trapped around inclusions. The amount and its influence on crack initiation and early propagation by fatigue are far from being predictable at present. Besides, Furuya and coworkers [8] have shown that the fatigue lives were scattered and that scatter is caused by differences in inclusion size at the fracture origins. They also found scatter to be reduced significantly when the ODA size is considered as the initial size of the crack. This was also observed in related studies [1,3 /5] and supports the idea that size of the inclusion and influence of hydrogen embrittlement defines a threshold crack length for pure fatigue crack propagation, a0. This is supported by our analysis in Part I [12]. Finally, it is important to consider the work carried out by Furuya and coworkers on the influence of frequency (100, 600 and 20 kHz) on fatigue properties of JIS SNCM438 steels [8]. They found fatigue properties and ODA size to be independent of frequency. This support the idea that formation of the ODA requires a given number of cycles to be formed, and is related to the influence of alternating stress on the creation and movement of hydrogen trapping places. Fig. 2 shows experimental results of the ODA size against the number of cycles, obtained from references [5,8,24,28] for quenched and tempered JIS SUJ2, SCM435 and SNCM439 steels. The bold line corresponds to the following expression defined in this study to describe the relation between ODA and number of cycles (N ): pffiffiffiffiffiffiffiffiffi RODA areaj 0:25N 0:125 (1) pffiffiffiffiffiffiffiffiffi ODA Ri areajinclusion where area1/2 is the rout area parameter defined by Murakami [1,3,19]. The area1/2 parameter is used in our analysis, but we prefer to define the size of the inclusion by its radius Ri, supposing the inclusions to be spherical. We also prefer to deal with the crack length a, and define the size of ODA by its radius, RODA. Doing so, the following relations hold:
Fig. 2. Experimental ODA size results as a function of fatigue life [5,8,24,28]. Estimated ODA sizes from expression (1) are also shown.
pffiffiffiffiffiffiffiffiffi pffiffiffi area pa pffiffiffiffiffiffiffiffiffi pffiffiffi pRi areaj pffiffiffiffiffiffiffiffiffi inclusion pffiffiffi areajODA pRODA
(2a) (2b) (2c)
The minimum crack length is given by the inclusion radius (Ri), and the initial crack length for pure fatigue crack propagation (a0) is given by the ODA radius (RODA).
3. Estimation of the threshold to pure fatigue crack propagation The pure fatigue crack propagation threshold DKth for small cracks and defects can be evaluated using the area1/2 parameter model [18,19], which is based on threshold data for crack growth of specimens containing artificial defects ranging from 40 to 500 mm. The geometrical parameter (area1/2) was chosen in order to account for the maximum stress intensity factor for a 3D crack or defect. The following expression developed by Murakami and coworkers for surface cracks or defects allows us to estimate the threshold value [18,19]: pffiffiffiffiffiffiffiffiffi DKth 3:3 10 3 (HV 120)( area)1=3 (3) where HV is the Vickers hardness, in kgf mm 2, and area1/2 is in mm, giving DKth in MPa m1/2. In part I of this study the threshold for internal crack propagation was supposed to be given by the threshold for long crack (DKthR) for any crack length [12].
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However, the threshold for the propagation of internal short cracks depends on crack length. As for surface cracks, the internal cracks are not influenced by surface strain concentration and the development of a threshold for crack propagation is defined by the development of crack closure. Thus, the threshold for internal crack propagation takes a value between that one given by expression (3) and the threshold for long cracks, DKthR. This means that expression (3), if valid, would be conservative for internal cracks. It is necessary to analyze the limitation of expression (3) that is given by the propagation threshold for long cracks (DKthR), which is a material constant for a given stress ratio R , independent of crack length. Expression (3) gives a lineal relation with a slope equal to 1/3 in a log /log plot. Fig. 3 shows schematically the development of fatigue threshold as a function of area1/2 for two materials having different hardness. As mentioned in part I [12], DKth develops with crack length till a length that depends on the material. Murakami’s model works reasonably well in the short crack regime, where DKth develops. For short cracks, the threshold for crack propagation increases with hardness. However, for long cracks the threshold is constant and decreases with hardness [20] (see the two examples given in Fig. 3). This two opposite trend makes the crack depth, at which the transition takes place, to decreases as hardness increases (Fig. 3). Even though expression (3) seems to work well till a value of area1/2 of 1000 mm for low strength materials, the crack length (or the value of area1/2) at which the fatigue threshold for short crack equals the threshold for log cracks (DKthR) depends on material [21]. The higher the resistance of the material, the shorter is the crack length. Thus, it is necessary to define the upper limit for DKth for high strength steels. According to [19], this limit is obtained from expression (3) for (area)1/2 /100/
200 mm. At this (area)1/2 value, the threshold DKth for a material having a Vicker’s hardness of 600 kgf mm 2 is 11 /14 MPa m1/2. This value seems to be relatively high for high strength steels [22], so the upper value of DKth is defined to be equal to 10 MPa m1/2. Experimental measurement of the value of threshold fatigue crack propagation for long cracks is usually a difficult task but because of its relevant technological importance, more effort should be made to properly measure and estimate it. With expressions (3) and (2), we get the following to estimate DKth: DKth 4 10 3 (HV 120)a1=3
(4)
with a in mm and HV in kgf mm 2. For a given crack length for which expression (4) gives DKth values greater than 10 MPa m1/2, this value is considered as a pure fatigue threshold.
4. Estimation of fatigue life for cracks initiated at internal non-metallic inclusions Eq. (4) gives the threshold DKth for pure fatigue crack propagation as a function of the crack length. Besides, the applied DK for a penny-shape internal crack can be estimated by the following equation [23]: DK
pffiffiffiffiffiffi 2 Ds pa p
(5)
From Eqs. (4) and (5), it is possible to relate threshold stress with crack length and hardness: Dsth × a1=6 3:55(HV 120)
(6)
With Dsth in MPa, a in mm and HV in kgf mm 2. Besides, expression (1) estimates the ODA size as a function of the total fatigue life. We have also addressed that the fatigue life necessary to develop the ODA is usually greater than 90% of the total fatigue life. If the number of cycles to create a crack length, given by the ODA size can be considered as an estimation of total fatigue life, an expression for total fatigue life as a function of the applied stress can be obtained by replacing the value of crack length for the ODA radius in Eq. (6): Dsth × N 1=48 4:473
Fig. 3. Fatigue threshold as a function of (area)1/2 parameter for two steels with different hardness.
239
(HV 120) 1=6
Ri
(7)
To define the value of Ri it is necessary to take into account the influence of statistical size distribution of inclusions inside materials. It is obvious that the largest inclusions are most detrimental to fatigue strength. Thus, Ri is given by the maximum radius of inclusions contained in the material, Rmax . i
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Fig. 4. Experimental fatigue life results for JIS SUJ2 Q/T steel from references [5] (rotating /bending tests) and [24] (tension /compression tests). Fatigue crack propagation life for surface and internal cracks estimated by using the procedure presented in part I of this study [12] for three different initial crack lengths, as well as total fatigue life estimated by expression (7), are shown.
Fig. 4 shows the experimental data obtained by Shiosawa et al. [5] for JIS SUJ2-QT steel from rotating /bending fatigue tests, which were analyzed in part I of this study, together with the experimental results obtained by Murakami et al. [24] for the same material but from tension /compression fatigue tests (both at R / /1). The estimated pure fatigue crack propagation life from crack of 0.02 mm and 0.035 mm in length, carried out by the methodology presented in part I of this study [12], as well as fatigue life given by expression (7), for an inclusion radius Ri /0.011 mm (equal to the maximum inclusion radius Rmax observed i by Shiozawa et al.) and 0.022 mm (twice Rmax ) are i shown. The slope of the estimated fatigue life seems to be in accordance with the trend shown by experimental results obtained by Murakami, which are well fitted by the curve corresponding to 2Rmax . i Two important features observed in Fig. 4 should be analyzed. The first one is that the experimental results from rotating /bending fatigue tests are at higher stresses and reveal a pronounced negative slop. At least two factors should be taken into account to explain the observed differences. The experimental results corresponding to rotating /bending tests are usually shown as a function of the nominal stress (at the surface of the specimens), but the initiation of cracks in this case takes
place at internal points located at distances between 0.05 and 0.23 mm from the surface of 3 mm diameter specimens [5]. Taking a depth of about 0.15 mm as an average, it is seen that for a fatigue life of 109 (at about 900 MPa) the stress at the position of the nucleated crack is about 90 MPa smaller, and for a fatigue life of about 106 (at about 1400 MPa) is about 150 MPa smaller. The difference increases as the depth at which the nucleation occurs increases. According to this analysis the slope of the data would reduce. This fact can be enhanced at intervals between 107 and 109. The other factor that have to be taken into account is that in terms of control volume testing one tension/ compression specimen is equivalent to testing 300 specimens in rotating /bending. The applied stress distribution in tension /compression fatigue test is uniform but it is linear in rotating /bending ones. In the tension/ compression fatigue test the control volume is relatively large and the probability of existence of larger inclusions is high, resulting in smaller fatigue strength. According to estimated fatigue lives, inclusions twice as great than those observed by Shiozawa could be found in tension/ compression tests of specimens with greater diameters. The other important feature is that the slope shown by the experimental results corresponding to tension/ compression tests and the estimated fatigue lives are small, and, even though it is possible to estimate fatigue life as a function of stress level, the stress range observed at the interval defined by 105 and 108 cycles is small. This small slope is a consequence of the increase of minimum crack length to pure fatigue crack growth as stress decreases (from expression (4)), and the simultaneous increase of the side of the ODA developed by hydrogen embrittlement assisted by fatigue (according to expression (1)), which consumes an increasing number of load cycles. The internal pure fatigue crack propagation threshold estimated by using the methodology presented in part I of this study for ai /0.02 mm agrees well with experimental results obtained by Shiozawa. ai /0.02 mm is about four times the radius of the inclusion from which the fracture process takes place at s /950 MPa (about 0.005 mm [5]). On the other hand, the estimated pure fatigue crack propagation threshold for ai /0.035 (three times the maximum inclusion radius Rmax observed by i Shiozawa, 0.0113 mm) agrees with experimental results obtained by Murakami. It is worth noting that even though the observed ODA size (Fig. 2) is at times greater than three times the inclusion size, in most cases the relation is smaller when comparing with the maximum observed inclusion radius. The maximum ODA size observed by Shiozawa is about 4.4 times the size of the inclusion from which the crack initiated but is 2.2 times the maximum inclusion size.
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
5. Estimation of the internal fatigue limit The internal fatigue limit for high strength steels is estimated as the threshold stress below which a crack length of three times the maximum inclusion radius cannot propagate. By replacing crack length by 3Rmax i (ath /a0 /3Rmax ) in expression (6), we get: i Int Dsth DsInt e 2se
3:55(HV 120) (3Rmax )1=6 i
(8)
It is necessary to consider the limitation of expression (4) to estimate the threshold for a crack length a / 3Rmax . We take DKth /10 MPa m1/2 as the upper limit i for DKth and rewrite expression (8) by using expression (5) with DK /DKth, a /3Rmax and Ds /2sInt i e : DKth sInt ffi e 256 pffiffiffiffiffiffiffiffiffi Rmax i
)1=3 DKth 4 10 3 (HV 120)(3Rmax i If DKth 510 MPa m1=2 DKth 10 MPa m1=2
size was 4.5 mm. The internal fatigue limit estimated by Eq. (9) is 735 MPa, greater than the surface fatigue limit. Fig. 5 shows the stress intensity factor range (DK ) as a function of crack length for cracks initiated from internal inclusions under different nominal stress levels for the JIS SUJ2 steel analyzed by Shiozawa et al. [5] (dashed lines). Above the threshold for pure fatigue propagation, DKth (bold line), cracks can propagate by pure fatigue. On the other hand, below DKth cracks could propagate by hydrogen assisted fatigue. Fig. 5 reveals that as the nominal stress level increases the size of the ODA decreases. Cracks could initiate and propagate from inclusions by pure fatigue for nominal stress level greater than 1000 MPa. This value can be considered as an upper limit for the experimental results obtained by Murakami [24] (see Fig. 4).
(9)
where Rmax is in mm and DKth is given by the following i expressions:
Otherwise
241
(10)
The internal fatigue limit was estimated by using expression (9) for several steels whose ultra-long fatigue properties where obtained from the literature [1,5,8,9,11,25 /29]. Table 1 shows the experimental and estimated results. Estimated results show different underestimations, which depends on the analyzed fatigue range, the available maximum inclusion size, type of fatigue test, specimen diameter and threshold for pure fatigue crack propagation. Difference ranged from /29 to 4%, and the less conservative ones are observed for tension/compression tests, highest analyzed fatigue lives ranges and greatest specimen diameters. From expression (9) we can get the following for Rmax : i DKth 262 144 (11) Rmax i 2sInt e By using expression (9), the maximum inclusion size that defines an internal fatigue limit (sInt e ) equals to the surface fatigue limit (se), can be estimated. With sInt e / se (1200 MPa for JIS SUJ2) and HV /750 [5], Rmax i results to be equal to 4.5 mm. Finally, results of the ultra-long cycle fatigue behavior of three spring steels studied by Abe and coworkers [26] are considered. For one of those steels (SUP 12 D1, HV /518) fracture from internal non-metallic inclusions was not observed and the surface fatigue limit was found to be 640 MPa. For this steel the maximum inclusion
6. Concluding remarks Fatigue fracture from internal inclusions depends on the type and size of inclusion, the tensile residual stresses around it, the amount of hydrogen in the material, some particular features of the microstructure related with the hydrogen trapping places and the threshold for pure fatigue crack propagation. In accordance with experimental results, ODA size increases as the applied stress level decreases, and thus, the internal fatigue life is a function of stress level (expression (7)). Expression (9) estimates the internal fatigue limit associated with a fatigue life of 1010 cycles. It also allows a proper maximum inclusion size to be defined for a given internal fatigue limit. Further experimental results are necessary in order to analyze the limitations of expressions (9) and (10) Fig. 6 shows the fatigue limit trend for steels as a function of its tensile strength su. For low and medium strength steels the fatigue limit is given by the surface fatigue limit se. The surface fatigue limit increases by increasing the tensile strength following a linear relation (e.g. se :/su/2 for R / /1), even for high strength steels. On the other hand, the internal fatigue limit sInt e is given by Rmax and DKth. DKth decreases as su increases [22], so i that sInt will obviously equals se at a given su, from e which the fatigue limit of the steel is given by the internal fatigue limit sInt e . As the inclusion size decreases the internal fatigue limit increases and the tensile strength till which the fatigue limit of the steel is given by the surface fatigue limit increases. Other factors are important for both fatigue limits: microstructure, hardness, residual stress distribution, type of inclusion, the amount of hydrogen in the material, and hydrogen trapping places, among others. For a better understanding and estimation of the fatigue behavior of high strength steels all these factors have to be considered.
242
DKth (MPa m1/2) Eq. (10)
sInt e (MPa) Eq. (9)
Difference (%)
31.4 40.5 11.3 5.8 28 9 11 14
10 10 10 7.1 10 7 7.12 8.75
457 402 762 752 608 597 550 599
/18 /17 /15 /28 /19 /17 /29 /18
/
11.5
8.07
609
/18
T-C
/
11
9.11
703
/16
R-B R-B T-C T-C T-C T-C T-C R-B R-B
24 23 35 34 28.4 16.6 10.7 270 161
13.5 13 20 19 16.3 9.4 6.1 152 91
536 625 498 581 620 646 707 252 334
/16 4 /8 0 /28 1 /2 /28 /21
Analyzed range (cycles)
/ / 2316 1950 1955 / / /
560 490 900 1050 750 720 780 730
108 5 /108 109 108 1010 4 /109 1010 5 /109
7 7 3 4 3 2.5 2.5 2.5
T-C T-C R-B T-C T-C T-C T-C T-C
55.6 71.9 20 10 50 / / /
500
/
740
1010
2.5
T-C
[29]
500
/
840
3 /109
2.5
[30] [30] [30] [30] [9] [26] [26] [27] [27]
441 528 441 528 590 516 528 275 360
1423 1730 1423 1730 / 1720 1764 :/800 :/1100
640 600 540 580 862 640 720 350 425
1010 1010 108 108 0.2 /108 108 108 5 /108 5 /108
6 6 6 6 2.5 6 4.5 10 10
Reference HV (kgf mm 2)
SCM435 0.46 Carbon SUJ2 SCM435 H SNCM439 42Cr /Mo Cr /V Cr /Si (54SC6) Cr /Si (55SC7) Cr /Si (55SC7) SUP7 SUP7 SUP7 SUP7 SUP10M SUP12 SWOSC-V KSFA80 KSFA110
[1] [11] [5] [25] [8] [29] [29] [29]
561 660 750 564 598 465 435 510
[29]
a
Testa area1/2 max (mm)
sInt e experimental (MPa)
Steel
su (MPa)
T /C, tension /compression; R /B, rotating /bending.
Specimen diameter (mm)
Rmax i (mm)
7.7 8.8 8.7 9.9 9.8 7.7 6.8 12.1 12.4
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
Table 1 Experimental and estimated data for several high strength steels
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
243
by cracks initiated from an internal inclusion is not found after 1010 cycles, was obtained as a function of the threshold for pure fatigue crack propagation and the maximum inclusion radius. (3) The internal fatigue limits was estimated for several high strength steels whose ultra-long fatigue properties were obtained from the literature. Estimations are in most cases conservative. Further experimental results are necessary in order to analyze the limitations of the define expression.
Acknowledgements One of the authors (M.D. Chapetti) wishes to express his thanks for funding provided by Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas (CONICET).
Fig. 5. Stress intensity factor range as a function of crack length for different nominal stress levels for JIS SUJ2 steel [5]. The threshold for pure fatigue crack propagation estimated by expression (10) is also shown.
7. Conclusions (1) The fatigue limit associated with crack initiation from internal non-metallic inclusions in high strength steels was analyzed in terms of the threshold for pure fatigue crack propagation as a function of crack length, the size of the inclusion from which the fracture process takes place, and the size of the optical dark area (ODA) associated with the early crack propagation by hydrogen assisted fatigue. (2) An expression to estimate the internal fatigue limit, i.e. the stress level below which fracture produced
Fig. 6. Fatigue limit as a function of tensile strength and the influence of some important parameters.
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Ultra-long cycle fatigue of high-strength carbon steels part II: estimation of fatigue limit for failure from internal inclusions M.D. Chapetti a,b,*, T. Tagawa b, T. Miyata b a
INTEMA, University of Mar del Plata-CONICET, J.B. Justo 4302, B7608FDQ Mar del Plata, Argentina b Department of Material Science and Engineering, Nagoya University, Nagoya 464-8603, Japan Received 11 October 2002; received in revised form 12 February 2003
Abstract Ultra-long cycle fatigue fracture origins in high strength steels are mostly at non-metallic inclusions due to the influence of the trapped hydrogen. In the vicinity of a non-metallic inclusion at the fracture origin, an optically dark area (ODA) is often observed inside a fish-eye mark, which represents the particular morphology associated with mechanism of failure at an early stage: hydrogen assisted fatigue. From an analysis of several features involved in this mechanism of failure, as the development of the ODA, the threshold for pure fatigue propagation, as a function of crack length and inclusion size, an expression was deduced to estimate the internal fatigue limit, that is, the stress level below which fracture produced by cracks initiated from an internal inclusion is not found after 1010 cycles: DKth sInt ffi e 256 pffiffiffiffiffiffiffiffiffi Rmax i where DKth is the pure fatigue crack propagation threshold as a function of crack length estimated with the following expression: DKth 4 10 3 (HV 120)(3Rmax )1=3 i Otherwise
If DKth 510 MPa m1=2
1=2
DKth 10 MPa m
Rmax i
is the maximum radius of the non-metallic inclusions from which the crack initiates, in mm, and HV is the Vickers hardness, in kgf mm 2. The internal fatigue limit was estimated for several steels and compared with experimental results obtained from the literature for internal fatigue lives in the range of 108 /1010 cycles. Differences between the estimated internal fatigue limit and the experimental one ranged from 4 to /29%. # 2003 Published by Elsevier Science B.V. Keywords: High strength steels; Ultra-long fatigue life; Surface cracks; Internal cracks; Non-metallic inclusions
1. Introduction Fatigue fracture origins in ultra-long cycle fatigue in high strength steels are mostly at non-metallic inclusions due to the influence of the hydrogen trapped by them. In the vicinity of a non-metallic inclusion at the fracture origin, a dark area was often observed inside a fish-eye mark for specimens with a long fatigue life [1 /11], which represents the particular morphology associated with
* Corresponding author. E-mail address: [email protected] (M.D. Chapetti).
the mechanism of failure involved. Murakami and coworkers have named this area as ‘optically dark area’ (ODA), and the related mechanism of failure as ‘hydrogen embrittlement assisted by fatigue’ [1,3,4]. Fig. 1 illustrates the mechanism for ultra-long fatigue failure from internal non-metallic inclusions. In Part I of this study [12] some features related with creation of an ODA by hydrogen assisted fatigue was briefly reviewed, and pure fatigue crack propagation from surface and from internal inclusions was analyzed and modeled in high strength steels that show both types of crack initiation. It was concluded, in accordance with previous references, that any estimation of total fatigue life associated with the failure produced by cracks
0921-5093/03/$ - see front matter # 2003 Published by Elsevier Science B.V. doi:10.1016/S0921-5093(03)00136-9
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Nomenclature a a0 area1/2 C* and m s Ds Dse DsInt e Dsth DK DKth DKthR HV ODA R Ri Rmax i se sInt e su
237
crack length initial crack length for pure fatigue propagation Murakami’s model parameter environmentally sensitive material-constants applied stress amplitude applied stress range surface fatigue limit range internal fatigue limit range threshold stress range for pure fatigue crack propagation applied stress intensity range (applied crack driving force) fatigue crack propagation threshold (function of crack length) mechanical threshold for long cracks (material constant for a given stress ratio R ) Vickers hardness optically dark area stress ratio (minimum stress/maximum stress) inclusion radius maximum inclusion radius surface fatigue limit amplitude internal fatigue limit amplitude ultimate tensile strength
initiated at internal inclusions will succeed only if the crack initiation period can be properly estimated. The crack initiation period is defined by the number of cycles necessary to create a crack length given by the optical dark area (ODA) [3 /12]. The number of cycles to form a crack length given by ODA size, is defined by the type and size of inclusion, the tensile residual stresses around it, the amount of hydrogen, the applied nominal stress range and amplitude, some particular features of the microstructure related to the hydrogen trapping places and the threshold for pure fatigue crack propagation. There exists very limited information about how parameters influence crack initiation period by hydrogen assisted fatigue. Thus, the aim of defining a proper model to estimate it is not an easy task. However, a threshold for pure fatigue propagation of internal cracks initiated at inclusions can be defined taking into account
Fig. 1. Scheme of the mechanism for super-long fatigue failure from internal inclusion with an initial hydrogen assisted fatigue crack initiation and early propagation.
the different geometrical and mechanical variables involved in the process. In this paper a model to estimate the threshold stress to obtain fatigue fracture from cracks initiated at internal inclusions (internal fatigue limit), is presented. The defined internal fatigue limit is obtained from: (a) the threshold for pure fatigue crack propagation, (b) the maximum inclusion size in the material, and (c) a defined critical size of the ODA.
2. Analysis of the ODA size As reviewed and analyzed in part I of this study [12], (1) the size of the ODA increases with an increase in fatigue life, (2) ODA cannot be found on the fracture surface of specimens failed at a small number of cycles, and (3) ODA size is independent of frequency. Besides, it seems that ODA size defines the critical crack length from which pure fatigue propagation takes place, and crack propagation inside the ODA is defined by hydrogen embrittlement assisted by fatigue. Between factors affecting the crack initiation from inclusions, the inclusion size plays an important role. The finite element calculations made by Brooksbank and Andrews [13 /15] to estimate the residual stress distributions surrounding inclusions in bearing steels have shown that the circumferential residual stresses are as high as 450 MPa at the matrix /inclusion interface (in the case of Al2O3 inclusions). This stress reduces to about 50 MPa at a distance from the matrix /inclusion
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interface equal to inclusion radius. The stress concentrations introduced by the inclusion have to be taken into account. In this case the inclusion is considered as a ‘porous’, for which the stress concentration is 2 and it banishes at a distance greater than its diameter [16]. The zone influenced by the inclusion can be conservatively confined to a sphere whose size is three times the size of the inclusion. Besides, according to studies of Taha et al. [17] the hydrogen resides at hydrostatic stress peak locations, in the highly stressed material. So, it is possible to assume a hydrogen embrittlement process assisted by fatigue will mainly take place inside a region as far as three times the inclusion radius Ri from the center of the inclusion. Another important factor defining the development of the ODA is the amount of hydrogen trapped around inclusions. The amount and its influence on crack initiation and early propagation by fatigue are far from being predictable at present. Besides, Furuya and coworkers [8] have shown that the fatigue lives were scattered and that scatter is caused by differences in inclusion size at the fracture origins. They also found scatter to be reduced significantly when the ODA size is considered as the initial size of the crack. This was also observed in related studies [1,3 /5] and supports the idea that size of the inclusion and influence of hydrogen embrittlement defines a threshold crack length for pure fatigue crack propagation, a0. This is supported by our analysis in Part I [12]. Finally, it is important to consider the work carried out by Furuya and coworkers on the influence of frequency (100, 600 and 20 kHz) on fatigue properties of JIS SNCM438 steels [8]. They found fatigue properties and ODA size to be independent of frequency. This support the idea that formation of the ODA requires a given number of cycles to be formed, and is related to the influence of alternating stress on the creation and movement of hydrogen trapping places. Fig. 2 shows experimental results of the ODA size against the number of cycles, obtained from references [5,8,24,28] for quenched and tempered JIS SUJ2, SCM435 and SNCM439 steels. The bold line corresponds to the following expression defined in this study to describe the relation between ODA and number of cycles (N ): pffiffiffiffiffiffiffiffiffi RODA areaj 0:25N 0:125 (1) pffiffiffiffiffiffiffiffiffi ODA Ri areajinclusion where area1/2 is the rout area parameter defined by Murakami [1,3,19]. The area1/2 parameter is used in our analysis, but we prefer to define the size of the inclusion by its radius Ri, supposing the inclusions to be spherical. We also prefer to deal with the crack length a, and define the size of ODA by its radius, RODA. Doing so, the following relations hold:
Fig. 2. Experimental ODA size results as a function of fatigue life [5,8,24,28]. Estimated ODA sizes from expression (1) are also shown.
pffiffiffiffiffiffiffiffiffi pffiffiffi area pa pffiffiffiffiffiffiffiffiffi pffiffiffi pRi areaj pffiffiffiffiffiffiffiffiffi inclusion pffiffiffi areajODA pRODA
(2a) (2b) (2c)
The minimum crack length is given by the inclusion radius (Ri), and the initial crack length for pure fatigue crack propagation (a0) is given by the ODA radius (RODA).
3. Estimation of the threshold to pure fatigue crack propagation The pure fatigue crack propagation threshold DKth for small cracks and defects can be evaluated using the area1/2 parameter model [18,19], which is based on threshold data for crack growth of specimens containing artificial defects ranging from 40 to 500 mm. The geometrical parameter (area1/2) was chosen in order to account for the maximum stress intensity factor for a 3D crack or defect. The following expression developed by Murakami and coworkers for surface cracks or defects allows us to estimate the threshold value [18,19]: pffiffiffiffiffiffiffiffiffi DKth 3:3 10 3 (HV 120)( area)1=3 (3) where HV is the Vickers hardness, in kgf mm 2, and area1/2 is in mm, giving DKth in MPa m1/2. In part I of this study the threshold for internal crack propagation was supposed to be given by the threshold for long crack (DKthR) for any crack length [12].
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
However, the threshold for the propagation of internal short cracks depends on crack length. As for surface cracks, the internal cracks are not influenced by surface strain concentration and the development of a threshold for crack propagation is defined by the development of crack closure. Thus, the threshold for internal crack propagation takes a value between that one given by expression (3) and the threshold for long cracks, DKthR. This means that expression (3), if valid, would be conservative for internal cracks. It is necessary to analyze the limitation of expression (3) that is given by the propagation threshold for long cracks (DKthR), which is a material constant for a given stress ratio R , independent of crack length. Expression (3) gives a lineal relation with a slope equal to 1/3 in a log /log plot. Fig. 3 shows schematically the development of fatigue threshold as a function of area1/2 for two materials having different hardness. As mentioned in part I [12], DKth develops with crack length till a length that depends on the material. Murakami’s model works reasonably well in the short crack regime, where DKth develops. For short cracks, the threshold for crack propagation increases with hardness. However, for long cracks the threshold is constant and decreases with hardness [20] (see the two examples given in Fig. 3). This two opposite trend makes the crack depth, at which the transition takes place, to decreases as hardness increases (Fig. 3). Even though expression (3) seems to work well till a value of area1/2 of 1000 mm for low strength materials, the crack length (or the value of area1/2) at which the fatigue threshold for short crack equals the threshold for log cracks (DKthR) depends on material [21]. The higher the resistance of the material, the shorter is the crack length. Thus, it is necessary to define the upper limit for DKth for high strength steels. According to [19], this limit is obtained from expression (3) for (area)1/2 /100/
200 mm. At this (area)1/2 value, the threshold DKth for a material having a Vicker’s hardness of 600 kgf mm 2 is 11 /14 MPa m1/2. This value seems to be relatively high for high strength steels [22], so the upper value of DKth is defined to be equal to 10 MPa m1/2. Experimental measurement of the value of threshold fatigue crack propagation for long cracks is usually a difficult task but because of its relevant technological importance, more effort should be made to properly measure and estimate it. With expressions (3) and (2), we get the following to estimate DKth: DKth 4 10 3 (HV 120)a1=3
(4)
with a in mm and HV in kgf mm 2. For a given crack length for which expression (4) gives DKth values greater than 10 MPa m1/2, this value is considered as a pure fatigue threshold.
4. Estimation of fatigue life for cracks initiated at internal non-metallic inclusions Eq. (4) gives the threshold DKth for pure fatigue crack propagation as a function of the crack length. Besides, the applied DK for a penny-shape internal crack can be estimated by the following equation [23]: DK
pffiffiffiffiffiffi 2 Ds pa p
(5)
From Eqs. (4) and (5), it is possible to relate threshold stress with crack length and hardness: Dsth × a1=6 3:55(HV 120)
(6)
With Dsth in MPa, a in mm and HV in kgf mm 2. Besides, expression (1) estimates the ODA size as a function of the total fatigue life. We have also addressed that the fatigue life necessary to develop the ODA is usually greater than 90% of the total fatigue life. If the number of cycles to create a crack length, given by the ODA size can be considered as an estimation of total fatigue life, an expression for total fatigue life as a function of the applied stress can be obtained by replacing the value of crack length for the ODA radius in Eq. (6): Dsth × N 1=48 4:473
Fig. 3. Fatigue threshold as a function of (area)1/2 parameter for two steels with different hardness.
239
(HV 120) 1=6
Ri
(7)
To define the value of Ri it is necessary to take into account the influence of statistical size distribution of inclusions inside materials. It is obvious that the largest inclusions are most detrimental to fatigue strength. Thus, Ri is given by the maximum radius of inclusions contained in the material, Rmax . i
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Fig. 4. Experimental fatigue life results for JIS SUJ2 Q/T steel from references [5] (rotating /bending tests) and [24] (tension /compression tests). Fatigue crack propagation life for surface and internal cracks estimated by using the procedure presented in part I of this study [12] for three different initial crack lengths, as well as total fatigue life estimated by expression (7), are shown.
Fig. 4 shows the experimental data obtained by Shiosawa et al. [5] for JIS SUJ2-QT steel from rotating /bending fatigue tests, which were analyzed in part I of this study, together with the experimental results obtained by Murakami et al. [24] for the same material but from tension /compression fatigue tests (both at R / /1). The estimated pure fatigue crack propagation life from crack of 0.02 mm and 0.035 mm in length, carried out by the methodology presented in part I of this study [12], as well as fatigue life given by expression (7), for an inclusion radius Ri /0.011 mm (equal to the maximum inclusion radius Rmax observed i by Shiozawa et al.) and 0.022 mm (twice Rmax ) are i shown. The slope of the estimated fatigue life seems to be in accordance with the trend shown by experimental results obtained by Murakami, which are well fitted by the curve corresponding to 2Rmax . i Two important features observed in Fig. 4 should be analyzed. The first one is that the experimental results from rotating /bending fatigue tests are at higher stresses and reveal a pronounced negative slop. At least two factors should be taken into account to explain the observed differences. The experimental results corresponding to rotating /bending tests are usually shown as a function of the nominal stress (at the surface of the specimens), but the initiation of cracks in this case takes
place at internal points located at distances between 0.05 and 0.23 mm from the surface of 3 mm diameter specimens [5]. Taking a depth of about 0.15 mm as an average, it is seen that for a fatigue life of 109 (at about 900 MPa) the stress at the position of the nucleated crack is about 90 MPa smaller, and for a fatigue life of about 106 (at about 1400 MPa) is about 150 MPa smaller. The difference increases as the depth at which the nucleation occurs increases. According to this analysis the slope of the data would reduce. This fact can be enhanced at intervals between 107 and 109. The other factor that have to be taken into account is that in terms of control volume testing one tension/ compression specimen is equivalent to testing 300 specimens in rotating /bending. The applied stress distribution in tension /compression fatigue test is uniform but it is linear in rotating /bending ones. In the tension/ compression fatigue test the control volume is relatively large and the probability of existence of larger inclusions is high, resulting in smaller fatigue strength. According to estimated fatigue lives, inclusions twice as great than those observed by Shiozawa could be found in tension/ compression tests of specimens with greater diameters. The other important feature is that the slope shown by the experimental results corresponding to tension/ compression tests and the estimated fatigue lives are small, and, even though it is possible to estimate fatigue life as a function of stress level, the stress range observed at the interval defined by 105 and 108 cycles is small. This small slope is a consequence of the increase of minimum crack length to pure fatigue crack growth as stress decreases (from expression (4)), and the simultaneous increase of the side of the ODA developed by hydrogen embrittlement assisted by fatigue (according to expression (1)), which consumes an increasing number of load cycles. The internal pure fatigue crack propagation threshold estimated by using the methodology presented in part I of this study for ai /0.02 mm agrees well with experimental results obtained by Shiozawa. ai /0.02 mm is about four times the radius of the inclusion from which the fracture process takes place at s /950 MPa (about 0.005 mm [5]). On the other hand, the estimated pure fatigue crack propagation threshold for ai /0.035 (three times the maximum inclusion radius Rmax observed by i Shiozawa, 0.0113 mm) agrees with experimental results obtained by Murakami. It is worth noting that even though the observed ODA size (Fig. 2) is at times greater than three times the inclusion size, in most cases the relation is smaller when comparing with the maximum observed inclusion radius. The maximum ODA size observed by Shiozawa is about 4.4 times the size of the inclusion from which the crack initiated but is 2.2 times the maximum inclusion size.
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
5. Estimation of the internal fatigue limit The internal fatigue limit for high strength steels is estimated as the threshold stress below which a crack length of three times the maximum inclusion radius cannot propagate. By replacing crack length by 3Rmax i (ath /a0 /3Rmax ) in expression (6), we get: i Int Dsth DsInt e 2se
3:55(HV 120) (3Rmax )1=6 i
(8)
It is necessary to consider the limitation of expression (4) to estimate the threshold for a crack length a / 3Rmax . We take DKth /10 MPa m1/2 as the upper limit i for DKth and rewrite expression (8) by using expression (5) with DK /DKth, a /3Rmax and Ds /2sInt i e : DKth sInt ffi e 256 pffiffiffiffiffiffiffiffiffi Rmax i
)1=3 DKth 4 10 3 (HV 120)(3Rmax i If DKth 510 MPa m1=2 DKth 10 MPa m1=2
size was 4.5 mm. The internal fatigue limit estimated by Eq. (9) is 735 MPa, greater than the surface fatigue limit. Fig. 5 shows the stress intensity factor range (DK ) as a function of crack length for cracks initiated from internal inclusions under different nominal stress levels for the JIS SUJ2 steel analyzed by Shiozawa et al. [5] (dashed lines). Above the threshold for pure fatigue propagation, DKth (bold line), cracks can propagate by pure fatigue. On the other hand, below DKth cracks could propagate by hydrogen assisted fatigue. Fig. 5 reveals that as the nominal stress level increases the size of the ODA decreases. Cracks could initiate and propagate from inclusions by pure fatigue for nominal stress level greater than 1000 MPa. This value can be considered as an upper limit for the experimental results obtained by Murakami [24] (see Fig. 4).
(9)
where Rmax is in mm and DKth is given by the following i expressions:
Otherwise
241
(10)
The internal fatigue limit was estimated by using expression (9) for several steels whose ultra-long fatigue properties where obtained from the literature [1,5,8,9,11,25 /29]. Table 1 shows the experimental and estimated results. Estimated results show different underestimations, which depends on the analyzed fatigue range, the available maximum inclusion size, type of fatigue test, specimen diameter and threshold for pure fatigue crack propagation. Difference ranged from /29 to 4%, and the less conservative ones are observed for tension/compression tests, highest analyzed fatigue lives ranges and greatest specimen diameters. From expression (9) we can get the following for Rmax : i DKth 262 144 (11) Rmax i 2sInt e By using expression (9), the maximum inclusion size that defines an internal fatigue limit (sInt e ) equals to the surface fatigue limit (se), can be estimated. With sInt e / se (1200 MPa for JIS SUJ2) and HV /750 [5], Rmax i results to be equal to 4.5 mm. Finally, results of the ultra-long cycle fatigue behavior of three spring steels studied by Abe and coworkers [26] are considered. For one of those steels (SUP 12 D1, HV /518) fracture from internal non-metallic inclusions was not observed and the surface fatigue limit was found to be 640 MPa. For this steel the maximum inclusion
6. Concluding remarks Fatigue fracture from internal inclusions depends on the type and size of inclusion, the tensile residual stresses around it, the amount of hydrogen in the material, some particular features of the microstructure related with the hydrogen trapping places and the threshold for pure fatigue crack propagation. In accordance with experimental results, ODA size increases as the applied stress level decreases, and thus, the internal fatigue life is a function of stress level (expression (7)). Expression (9) estimates the internal fatigue limit associated with a fatigue life of 1010 cycles. It also allows a proper maximum inclusion size to be defined for a given internal fatigue limit. Further experimental results are necessary in order to analyze the limitations of expressions (9) and (10) Fig. 6 shows the fatigue limit trend for steels as a function of its tensile strength su. For low and medium strength steels the fatigue limit is given by the surface fatigue limit se. The surface fatigue limit increases by increasing the tensile strength following a linear relation (e.g. se :/su/2 for R / /1), even for high strength steels. On the other hand, the internal fatigue limit sInt e is given by Rmax and DKth. DKth decreases as su increases [22], so i that sInt will obviously equals se at a given su, from e which the fatigue limit of the steel is given by the internal fatigue limit sInt e . As the inclusion size decreases the internal fatigue limit increases and the tensile strength till which the fatigue limit of the steel is given by the surface fatigue limit increases. Other factors are important for both fatigue limits: microstructure, hardness, residual stress distribution, type of inclusion, the amount of hydrogen in the material, and hydrogen trapping places, among others. For a better understanding and estimation of the fatigue behavior of high strength steels all these factors have to be considered.
242
DKth (MPa m1/2) Eq. (10)
sInt e (MPa) Eq. (9)
Difference (%)
31.4 40.5 11.3 5.8 28 9 11 14
10 10 10 7.1 10 7 7.12 8.75
457 402 762 752 608 597 550 599
/18 /17 /15 /28 /19 /17 /29 /18
/
11.5
8.07
609
/18
T-C
/
11
9.11
703
/16
R-B R-B T-C T-C T-C T-C T-C R-B R-B
24 23 35 34 28.4 16.6 10.7 270 161
13.5 13 20 19 16.3 9.4 6.1 152 91
536 625 498 581 620 646 707 252 334
/16 4 /8 0 /28 1 /2 /28 /21
Analyzed range (cycles)
/ / 2316 1950 1955 / / /
560 490 900 1050 750 720 780 730
108 5 /108 109 108 1010 4 /109 1010 5 /109
7 7 3 4 3 2.5 2.5 2.5
T-C T-C R-B T-C T-C T-C T-C T-C
55.6 71.9 20 10 50 / / /
500
/
740
1010
2.5
T-C
[29]
500
/
840
3 /109
2.5
[30] [30] [30] [30] [9] [26] [26] [27] [27]
441 528 441 528 590 516 528 275 360
1423 1730 1423 1730 / 1720 1764 :/800 :/1100
640 600 540 580 862 640 720 350 425
1010 1010 108 108 0.2 /108 108 108 5 /108 5 /108
6 6 6 6 2.5 6 4.5 10 10
Reference HV (kgf mm 2)
SCM435 0.46 Carbon SUJ2 SCM435 H SNCM439 42Cr /Mo Cr /V Cr /Si (54SC6) Cr /Si (55SC7) Cr /Si (55SC7) SUP7 SUP7 SUP7 SUP7 SUP10M SUP12 SWOSC-V KSFA80 KSFA110
[1] [11] [5] [25] [8] [29] [29] [29]
561 660 750 564 598 465 435 510
[29]
a
Testa area1/2 max (mm)
sInt e experimental (MPa)
Steel
su (MPa)
T /C, tension /compression; R /B, rotating /bending.
Specimen diameter (mm)
Rmax i (mm)
7.7 8.8 8.7 9.9 9.8 7.7 6.8 12.1 12.4
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
Table 1 Experimental and estimated data for several high strength steels
M.D. Chapetti et al. / Materials Science and Engineering A356 (2003) 236 /244
243
by cracks initiated from an internal inclusion is not found after 1010 cycles, was obtained as a function of the threshold for pure fatigue crack propagation and the maximum inclusion radius. (3) The internal fatigue limits was estimated for several high strength steels whose ultra-long fatigue properties were obtained from the literature. Estimations are in most cases conservative. Further experimental results are necessary in order to analyze the limitations of the define expression.
Acknowledgements One of the authors (M.D. Chapetti) wishes to express his thanks for funding provided by Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas (CONICET).
Fig. 5. Stress intensity factor range as a function of crack length for different nominal stress levels for JIS SUJ2 steel [5]. The threshold for pure fatigue crack propagation estimated by expression (10) is also shown.
7. Conclusions (1) The fatigue limit associated with crack initiation from internal non-metallic inclusions in high strength steels was analyzed in terms of the threshold for pure fatigue crack propagation as a function of crack length, the size of the inclusion from which the fracture process takes place, and the size of the optical dark area (ODA) associated with the early crack propagation by hydrogen assisted fatigue. (2) An expression to estimate the internal fatigue limit, i.e. the stress level below which fracture produced
Fig. 6. Fatigue limit as a function of tensile strength and the influence of some important parameters.
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