Dislocation-based interpretation on the effect of the loading frequency on the fatigue properties of JIS S15C low carbon steel

International Journal of Fatigue 70 (2015) 328–341

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Dislocation-based interpretation on the effect of the loading frequency on the fatigue properties of JIS S15C low carbon steel Benjamin Guennec a,⇑, Akira Ueno b, Tatsuo Sakai b, Masahiro Takanashi c, Yu Itabashi c, Mie Ota d a

Graduate School of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan College of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan c Research Laboratory, Structural Strength Department, IHI Corporation, 1, Shin-Nakahara-Cho, Isogo-ku, Yokohama 235-8501, Japan d Research Organization of Science and Technology, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan b

a r t i c l e

i n f o

Article history: Received 8 May 2014 Received in revised form 18 August 2014 Accepted 12 October 2014 Available online 24 October 2014 Keywords: Frequency effect Low carbon steel Ultrasonic test Dislocation structure Seeger theory

a b s t r a c t Fatigue properties of low carbon steels are known to be particularly sensitive to the loading frequency. Indeed, literatures related to this field usually point out an increasing fatigue life with an increase of the loading frequency. The authors of the present paper have already reconfirmed such a general phenomenon in the case of JIS S15C (0.15%C) low carbon steel. In that paper, S–N properties under usual frequencies of 0.2–140 Hz can be successfully normalized by the lower yield stress at the individual frequency. Nevertheless, some irregularities have been detected on the fatigue property at 20 kHz. In order to clarify the physical meaning of such irregularities, we will compare fatigue properties at usual frequencies and ultrasonic frequency. In this work, the former experimental results were reintroduced and new discussions were developed by performing additional experiments and analyses paying an attention to microstructure and dislocation structure. Thus, it was found that the loading frequency effect at ultrasonic frequency is due to a particular behavior of B.C.C. ferrite under high strain rate. Such a behavior causes strain inhomogeneities at grain boundaries, and then facilitates the intergranular crack initiation mode rather than the usual intragranular one often reported at lower loading frequencies. Longer ultrasonic fatigue lives at ultrasonic frequency are directly related to this transition of the crack initiation mode. In addition, effects of the pearlitic volume fraction on the fatigue behavior have been also discussed in the present work. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Loading frequency effect on the fatigue properties of metallic materials have been an important subject and numerous researches have been carried out from various viewpoints by many researchers [1–5]. Among these works, it was commonly pointed out that a clear effect of loading frequency was found on the S–N properties of low carbon steels [6–9], i.e. the fatigue life tends to increase with an increase of the fatigue loading frequency. The authors of the present paper had also performed fatigue tests, in a previous work [10], for a wide range of loading frequency from 0.2 Hz to 20 kHz on the same steel of JIS S15C steel used here. S–N curves at respective frequencies, determined by using the JSMS standard JSMS-SD-11-07 [11], are shown in Fig. 1. Obviously, a similar trend depending on the loading frequency has been ⇑ Corresponding author. E-mail addresses: [email protected] (B. Guennec), [email protected]. ac.jp (T. Sakai). http://dx.doi.org/10.1016/j.ijfatigue.2014.10.006 0142-1123/Ó 2014 Elsevier Ltd. All rights reserved.

reconfirmed on the S–N property. Particularly, one can see that ultrasonic fatigue lives are significantly larger than corresponding results obtained at usual frequencies from 0.2 to 140 Hz. Nevertheless, some extent of fatigue life differences should be noted even inside this usual frequency range. These slight differences disappear in Fig. 2, where the stress amplitude was normalized by the lower yield stress under monotonous tensile tests at respective average strain rates induced during fatigue tests. The authors have decided to use the yield stress under monotonous tensile tests rather than cyclic yield stress in order to reach a wider applicability of the results for readers, as cyclic yield stress measures are not so common. The yield stress at 20 kHz was estimated in accordance with the regression between yield stress and strain rate found in the previous paper [10]. According to the Fig. 2, a common S–N curve is found in the usual frequency range. However, such a direct relation between the fatigue life and the yield stress cannot be verified for ultrasonic fatigue property, as a gap still exists in Fig. 2. In addition, the lattice local misorientation analysis has shown a clear irregularity

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obtained for sample fatigued at 20 kHz, which is certainly related to a rearrangement of the dislocations inside the ferrite phase. Thus, the fatigue properties of S15C steel at ultrasonic frequency remains not fully understood. The present work is focused on the fatigue properties of S15C steel at ultrasonic frequency. It was found that a drastic change of the fatigue behavior was caused at a certain critical frequency within 20 kHz depending on the temperature and the strain rate. Above this mentioned critical frequency, a change of the dislocation structure, strain inhomogeneities at grain boundaries and thus intergranular crack initiation mode are induced. Longer fatigue lives observed for fatigue tests at 20 kHz are directly related to this intergranular crack initiation. Fig. 2. Evaluation of yield stress variation influence on S–N properties [10].

2. Material and experimental procedure Material tested in the present study is exactly same as that in the previous work [10], extracted from a hot-rolled bar of JIS S15C steel. Chemical composition and mechanical properties are indicated in Tables 1 and 2, respectively. Microstructure of this steel observed by an optical microscope is presented in Fig. 3, where one can see a typical ferritic and pearlitic duplex microstructure usual for this kind of low carbon steels. Axial loading fatigue tests have been conducted at four different frequencies. (1) Using an ultrasonic fatigue device, displacement controlled tests at 20 kHz; (2) using an electro-magnetic type machine, stress controlled tests at 140 Hz; (3) finally, using a servo-hydraulic type machine, stress controlled tests at 20 Hz and (4) at 0.2 Hz. All fatigue tests were performed in air, at room temperature, with a stress ratio of R = 1. Due to the phenomenon of self-heating which occurs in the case of high frequency tests, specific procedures were accepted to avoid temperature rising of the specimen. An air-cooling system has been accepted for 140 Hz fatigue tests. In the case of ultrasonic tests, in addition to a similar air-cooling configuration, all the tests have been conducted under intermittent loading condition (110 ms of loading time followed by 2500 ms of rest time). Under these conditions, temperature of the specimen surface was kept below 40 °C. Configurations of fatigue specimens for respective types of machine are presented in Fig. 4. One can note that all specimens have a tested portion with a same diameter of 5 mm. In addition, after machining, specimens were electro-polished. By this way, we minimize the size effect and the residual stresses effect on the fatigue properties of S15C steel. Most of experiments conducted in the present work were performed to analyze the fatigue process before final fatigue failure. Due to the high frequency sensitivity of fatigue properties of S15C steel, for each loading frequency, we have chosen two

Fig. 1. S–N diagram of S15C steel under several loading frequencies [10].

Table 1 Chemical composition of S15C steel (mass%). C

Si

Mn

Cu

Ni

Cr

Fe

0.15

0.21

0.40

0.02

0.02

0.15

Bal.

Table 2 Mechanical properties of S15C steel. Mechanical property

Value

Lower yield stress (MPa) Tensile strength (MPa) Young modulus (GPa) Elongation (%) Reduction of area (%) Vickers hardness (HV)

273 441 207 40.2 65.8 161

Fig. 3. Microstructure of S15C steel [10], (a) along transversal axis and (b) along longitudinal axis.

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3. Experimental results 3.1. Distributions of grain size and local misorientation

Fig. 4. Shape and dimensions of fatigue specimens, (a) specimen used for servohydraulic type machine, (b) specimen used for electro-magnetic type machine and (c) specimen used for ultrasonic type machine.

particular stress levels defined by respective fatigue limits, estimated by the JSMS standard [11], obtained in our previous work [10] as follows; the first stress level is the fatigue limit plus 10 MPa, and the second one is the fatigue limit plus 30 MPa, respectively. The former one is hereafter denoted by Sw + 10 and the latter one by Sw + 30, respectively. Numerical values of these stress levels and corresponding values of fatigue lives Nf, obtained in accordance with bilinear S–N curves in Fig. 1 [10], are listed in Table 3 for each loading frequency. The experimental procedure in this work is based on several key points to explain the fatigue behavior of S15C steel in both low and high frequencies. Some experiments are conducted in correlation with the microstructure analysis, based on EBSD (Electron Beam Scattered Diffraction) scan, performed by a Hitachi SU6600 SEM equipped with HKL NordlysF camera for orientation acquisition. In addition, another important section will be dedicated to the dislocation structures found inside ferrite grains. These micrographs were obtained simultaneously using a JEOL JEM 2010 TEM and Hitachi HD-2700 STEM devices, with a 200 kV acceleration voltage each. Finally, fatigue slip bands formation on the specimen surface was analyzed at different stages of fatigue process before failure. Table 3 Numerical values of Sw + 10 and Sw + 30 stress levels and corresponding fatigue lives. Loading frequency f (Hz)

Sw (MPa)

At Sw + 10

At Sw + 30

0.2

178

ra = 188 MPa

ra = 208 MPa

Nf = 4.49  105 cycles 20

192

ra = 202 MPa

Nf = 2.03  105 cycles ra = 222 MPa Nf = 2.13  105 cycles ra = 230 MPa Nf = 1.90  105 cycles ra = 278 MPa Nf = 1.66  106 cycles

140

200

20,000

248

Nf = 5.57  105 cycles ra = 210 MPa Nf = 9.94  105 cycles ra = 258 MPa Nf = 1.43  107 cycles

In this section, the following two interesting aspects will be checked; (i) change of the grain size distribution and (ii) change of misorientation distribution caused by cyclic loadings. According to experimental results reported by Rittel et al. [12], a significant grain refinement was confirmed at very high strain rate of 103 s1. Even though possibility of such a refinement under ultrasonic fatigue tests performed here is low, due to an average strain rate of approximately 102 s1, we will check the grain size distribution of ferrite grains of S15C steel, using EBSD technique. In addition, we will analyze the local misorientation on the longitudinal section, since a similar study has already been carried out on the cross section in our previous paper [10]. All data accepted here come from EBSD scans obtained under the following procedures. In order to prepare the samples, OP-AA (Acidic Aluminum Oxide Polishing) method was first conducted and, then, 4 min. argon ion milling finishing was applied at 6 kV acceleration voltage. In order to get more reliable values of the grain size, an area of 300 lm  225 lm, larger than in the previous paper [10], has been considered. Nevertheless, in order to decrease the calculation time, a spatial step size of 0.5 lm between two adjacent points, rather than 0.3 lm in [10], has been used. Such a change can affect the local misorientation values [13]. However, the effect on misorientation value is supposed to be limited, since both step sizes are small compared to the 15 lm as the average grain size of the present material. The threshold value for grains boundaries is set as 5°, referring to Kamaya’s work [13,14] for local misorientation measurements of austenitic stainless steel. 3.1.1. Grain size distribution Aim of this section is to verify the change of grain size distribution after ultrasonic loadings. Thus, we will check here the grain size distributions before test and after ultrasonic fatigue test performed at both Sw + 10 and Sw + 30 stress levels, at 25% of respective fatigue lives. Distributions were analyzed in both transversal and longitudinal sections, as presented in Fig. 5(a) and (b), respectively. Calculation of each distribution here is based on four different sites of the same sample, by setting a grain size class as 1 lm width. Then, we have calculated the average occurrence frequency in each class over the four sites, and the distributions indicated in Fig. 5 have been finally obtained. As one can see in Fig. 5, in both transversal and longitudinal sections, grain size distributions are not influenced by fatigue loadings at ultrasonic frequency. Indeed, no significant difference was found among the respective distribution patterns. In addition, the average grain sizes found from these distributions, are listed in Table 4. We can thus presume that the slight change observed in Fig. 5 comes from a dispersion phenomenon of the grain size depending on the specimens, rather than any grain refinement process. In order to make an assessment of the influence of such slight changes, let us consider the Hall–Petch equation in Eq. (1), focusing to the lower yield stress as reported by Yokobori et al. [15] for a S15C steel.

ry ðDÞ ¼ r0 þ ky D1=2

ð1Þ 1/2

where ry = 90 MPa and ky = 21.6 MPa mm . A slight change from diameter D to diameter D + DD will induce:

ry ðD þ DDÞ ¼ r0 þ ky ðD þ DDÞ1=2 1

ry ðD þ DDÞ ¼ r0 þ ky D1=2  qffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ DDD

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except for the change of spatial step size, which is supposed to not affect significantly the misorientation values, as already mentioned earlier. In other words, misorientation patterns in [10] and in the present paper can be compared. Under these conditions, it is reported that the angular error for measurement of the local misorientation is less than 0.05° [16]. Some examples of local misorientation maps are depicted in Fig. 6. The case of a non-fatigued specimen is presented in Fig. 6(a); and fatigued configurations at the loading stage of 25%

Fig. 5. Grain size distributions of S15C ferrite grains, (a) in cross section and (b) in longitudinal section.

Table 4 Average grain size found from EBSD analysis. Section

Average grain size (lm) Transversal

Non-fatigued Stress level f = 20 kHz, N = 25% Nf

15.3 Sw + 10 14.7

Longitudinal Sw + 30 15.4

15.7 Sw + 10 15.3

Sw + 30 15.5

Assuming that term DD/D is close to 0, Taylor development up to 1st order gives:

ry ðD þ DDÞ  ry ðDÞ 

ky DD pffiffiffiffi 2D D

ð2Þ

According to numerical results in Table 4, changes of the average grain size are within a range of 0.6 lm. Numerical application of the last term in Eq. (2) gives the value of 7.3 MPa change, where D is taken equal to 15 lm. Comparing this value with the lower yield stress in quasi-static condition in Table 2, one can find that this change of 0.6 lm in grain size implies a variation of approximately 1.3% in lower yield strength. We can thus consider that such a change has a negligible influence on the fatigue properties of S15C steel. 3.1.2. Local misorientation in longitudinal section As described previously, a short analysis of the local misorientation will be conducted only in the longitudinal section, since a similar study has already been carried out in the transversal section in the authors’ former paper [10]. The main purpose here is to compare the local misorientation in the longitudinal section with the previous results obtained in the transversal section. Calculation of the local misorientation, for each map scan, is based exactly on the same procedure as explained in the former paper [10],

Fig. 6. Examples of S15C local misorientation maps of a-phase, (a) at initial stage, (b) f = 20 Hz, Sw + 30, N = 25% Nf and (c) f = 20 kHz, Sw + 30, N = 25% Nf.

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Fig. 7. Local misorientation distributions in longitudinal section, Sw + 30, S15C.

Nf are shown in Figs. 6(b) and (c), at f = 20 Hz and f = 20 kHz, respectively. Loading direction is horizontal for all maps. As indicated at the bottom edge of each map, color scale is representing a misorientation range from 0° to 1°. Since very few locations reveal misorientation value larger than 1° in each map, the color scale is adjusted to be sensitive in the range of 0–1° for the sake of convenience. One can see that general surface condition is good enough to provide meaningful results. The local misorientation distributions presented in Fig. 7 are based on the average of 4 different sites. In this work, a class width of 0.025° has been used. In accordance with the results presented in our previous work [10], one can see a clear decrease of the local misorientation values after fatigue loadings. In addition, ultrasonic fatigue tests at f = 20 kHz cause the largest decrease. However, it is noteworthy that peak of distribution after ultrasonic loadings in Fig. 7 does not reach as high occurrence levels as in the previous work [10]. This aspect can be attributed to the change of the sectional direction in these two studies. 3.2. Analysis of dislocation structures In order to analyze the dislocation structure of S15C steel in an effective way, one TEM and another STEM machines were used, as previously mentioned in the Section 2. Fatigue specimens at several loading stages have been sliced in the cross sectional direction within a suitable length to get a sufficient number of pieces. Based on this procedure, the analytical results can represent the general behavior of the entire specimen. To provide the samples, finishing methods were different between both devices. In the case of JEOL TEM, a perforation method by electrolytic polishing has been conducted, whereas FIB cut and argon ion milling at 500 V has been used for Hitachi STEM observations. Observation results and discussions on dislocation structures induced during cyclic loading at usual frequencies and ultrasonic frequency are given in this section. 3.2.1. Dislocation structure after fatigue tests at usual frequencies An overview of the dislocation structures found on specimens tested at the loading frequencies of f = 0.2 Hz and f = 140 Hz in the present work is depicted in Figs. 8 and 9, respectively. For both figures, specimens were fatigued up to 25% of the fatigue life at a stress level of Sw + 30. A clear subgrain structure within the whole grain is shown in Fig. 8(a). On the other hand, Fig. 8(b) represents a well-known ladder structure. Similar structures have been found at a loading frequency of f = 140 Hz, as indicated in Fig. 9. Thus, change of the loading frequency in the range of 0.2 to 140 Hz does not induce a significant effect on the dislocation structures of S15C steel. Weisse et al. [17] and Min et al. [18] have also reported such dislocation structures of low carbon steels after cyclic loadings in the same loading frequency range.

Fig. 8. Dislocation structures at f = 0.2 Hz (Sw + 30, 25% Nf; S15C), (a) cell structure and (b) ladder structure.

Let us also make a focus on the changes of the dislocation structure, and more particularly about the cell substructure, at the respective fatigue stages of 5%, 10% and 25% of fatigue life. Discussions here are based on micrographs in Fig. 10 observed at the respective stages for different specimens tested at f = 20 Hz, at stress level of Sw + 30. Even though the observations depicted in Fig. 10 are not taken from the same observation piece, some general trends have been detected within the number of pieces collected at the respective fatigue stages. At the stage of 5% Nf, cell structures are already initiated, but the dislocation walls are not so clear depending on the individual cell, as presented in Fig. 10(a). Thus, a lot of dislocations are widely distributed over some cells appearing as black areas. At the stage of 10% Nf, all the cell walls are more sharply formed, as one can see in Fig. 10(b). Finally, at the stage of 25% Nf, cell walls are entirely formed, as depicted in Fig. 10(c). Such a change of the dislocation wall density gives an important hint of the dislocation annihilation inside every cell due to the cyclic loading, as pointed out by Chai and Laird [19]. It is also found that this change of dislocation structure is certainly related to the S15C cyclic softening already verified in our previous work [10].

3.2.2. Dislocation structure induced by ultrasonic fatigue test The results obtained for specimens fatigued at the ultrasonic frequency of f = 20 kHz differ totally from the observations in the lower loading frequency range above. Fig. 11 represents the dislocation structures observed for a specimen fatigued at Sw + 30, up to 25% of fatigue life. One can find obviously that the structures obtained in Fig. 11(a) do not reveal clear walls. Details of this structure are given in Fig. 11(b), representing the area marked by the

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Fig. 9. Dislocation structures at f = 140 Hz (Sw + 30, 25% Nf; S15C), (a) cell structure and (b) ladder structure.

square in Fig. 11(a). One can see long screw segments belonging here to two different slip systems, with some dislocation forests occasionally formed. Such kinds of dislocation structure are induced by specific dislocation multiplication processes as reported by Saka et al. [20]. In this section, we will make a focus on the dislocation multiplication processes observed on iron samples, at an operative temperature of 120 °C or 90 °C, and compare these multiplication processes with dislocation structures obtained after cyclic loading at ultrasonic frequency here. Even though more recent in situ experiments are available, with a better observation resolution, the work of Saka et al. is an outstanding original result on dislocation multiplication mechanisms. Some dislocation multiplication processes described by Saka et al. have been observed in the dislocation observations of S15C steel after ultrasonic fatigue loadings, as shown in Figs. 12–14. These figures are composed of one TEM micrograph of S15C steel fatigued at f = 20 kHz up to 25% Nf, and a schematic illustration of the multiplication mechanism proposed by Saka et al., in (a) and (b), respectively. Presence of such particular multiplication processes after ultrasonic fatigue test at room temperature will be discussed in the Section 4. First particular multiplication process is due to jog J1 of the screw dislocation itself, which tends to retard the motion and thus to bow out the segment AJ1, as presented in the schematic illustration in Fig. 12(b). Fig. 12(a) shows a screw dislocation with a jog in the top square. In addition, one can also find a bowed out dislocation in the bottom square. Another possible multiplication process of the dislocations related to this particular long screw segment structure is depicted in Fig. 13, by a mechanism rather similar to the Frank-Read source.

Fig. 10. Change of the dislocation structures depending on the loading stage (f = 20 Hz, Sw + 30; S15C), (a) at 5% Nf, (b) at 10% Nf and (c) at 25% Nf.

Due to the interaction of two dislocations, the segment AB will bow out, as illustrated in Fig. 13(b). In order to better understand the overall situation, letters with similar meanings have been reproduced in the related STEM micrograph, in Fig. 13(a). Finally, let us focus on a multiplication process induced by a precipitate inside ferrite lattice. Indeed, such a precipitate will facilitate the cross-glide of screw dislocation. The two branches of the screw dislocation A and B rotate independently around the precipitate P, creating a new dislocation per each rotation, as presented in Fig. 14(b)(3). This aspect has been found in S15C STEM micrograph in the square, in Fig. 14(a). Thus, one can note that overall dislocation structure of S15C steel is extremely sensitive to the loading frequency. Conventional fatigue tests performed at 0.2–140 Hz induce similar dislocation structures with dislocation dipoles, particularly ladder or cell

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Fig. 11. Dislocation structure induced by ultrasonic loading, Sw + 30 at 25% Nf; S15C, (a) overview of the structure and (b) details on long screw segments. Fig. 12. Multiplication mechanism at super jogs on screw dislocations on S15C steel, (a) observation by TEM and (b) schematic illustration.

structures. On the other hand, ultrasonic loadings cause long screw dislocations with possibly some dislocations forests rather than clear walls. A detailed analysis of the dislocation multiplication processes at ultrasonic loading frequency has pointed out significant agreement with processes observed for iron uniformly deformed at low temperature [20]. 3.3. Fatigue slip band behavior Fatigue slip bands were observed depending on the loading stage, mainly using the plastic replica technique. Initial condition of the specimen surface was first observed by using a replica film and the result obtained by an optical microscope was indicated in Fig. 15. Since the specimens are polished by electrolytic method, some corrosion pits are formed on the surface. In order to remove as much as possible corrosion pits, alumina polishing up to 0.3 lm diameter has been performed. Nevertheless, a few pits are still present even after this process, as one can see in Fig. 15. It should be noted that the loading direction is adjusted to the vertical axis in the photograph. Main results concerning the formation of fatigue slip bands in the case of fatigue tests performed at usual frequency of 20 Hz are shown in Fig. 16. One can find in Fig. 16(a) that even at 10% Nf, some slight fatigue slip bands are already formed. Sasaki et al. [21] have also reported such a behavior for low carbon steel. At the loading stage of 25% Nf, fatigue slip bands were formed in numerous grains as shown in Fig. 16(b) and the density of the slip bands becomes high along the loading stage. In the next place, the

slip bands formations at frequencies of 0.2 Hz and 140 Hz are compared in Fig. 17 under a definite loading stage of 25% Nf at Sw + 30. Feature of slip band formation is almost same in both frequencies. However, the slip band density in Fig. 17 is a little lower than that at 20 Hz in the same loading stage of 25% Nf represented in Fig. 16(b). One can estimate the plastic strain amplitude Dep for any loading frequency based on the diagram of the stress amplitude against the plastic strain amplitude in the previous paper [10]. In accordance with this procedure, the plastic strain amplitude is given as follows; Dep = 833  106 at 0.2 Hz, Dep = 1020  106 at 20 Hz and Dep = 813  106 at 140 Hz. In such estimations, the largest value of Dep is found at 20 Hz, whereas both values at 0.2 Hz and 140 Hz are approximately 20% lower. This aspect may be a reason why the slip band density in Fig. 16(b) is higher than in both Fig. 17(a) and (b). Nevertheless, one can note that overall fatigue slip band formation is quite similar in the frequency range of 0.2–140 Hz. Observations of replica films for specimens fatigued at ultrasonic frequency were also undertaken by optical microscope. At both stress level Sw + 10 and Sw + 30, microscopic feature of the specimen surface shows that only a few localized grains have fatigue slip bands over the whole surface. Such a result is in a good agreement with the aspect that the macroscopic plastic strain during the ultrasonic test for S15C steel remains low, as reported by Zettl et al. [22]. However, photographs of these observations are not included here due to the restriction of pages.

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Fig. 13. Multiplication mechanism due to dislocation–dislocation interaction on S15C steel, (a) observation by STEM and (b) schematic illustration.

335

Fig. 14. Multiplication mechanism due to inclusion precipitate on S15C steel, (a) observation by STEM and (b) schematic illustration.

In order to investigate the slip band behavior at f = 20 kHz, some direct observations of the specimen surface were performed by SEM. Unlike the photographs taken from replica films, loading direction is horizontally oriented. Results at two different sites for a specimen fatigued at the stress level of Sw + 30, up to 25% of fatigue life are presented in Fig. 18. Two particular types of strain inhomogeneities have been detected. In the case of Type I, a distinct step is formed at only one edge of a grain, as shown in Fig. 18(a). On the other hand, in the case of Type II, an extruded step and an intruded step are formed at a pair of edges of a grain, as indicated in Fig. 18(b). Accordingly, the corresponding grain with the fatigue slip bands in Type I is a little bent, whereas a slight tilted deformation is found in the corresponding grain in Type II. 3.4. Microscopic observation of crack initiation behavior The crack initiation behavior has also been observed by SEM microscopy. Fig. 19 presents some pictures taken from a specimen fatigued at f = 0.2 Hz. Main crack initiation site is depicted in Fig. 19(a), where the crack is clearly initiated along slip bands. This intragranular crack initiation mechanism has been observed in a high majority of specimens failed in the usual frequency range of 0.2–140 Hz. Nevertheless, some secondary cracks tend to occur on the specimen surface revealing an intergranular crack, as shown in Fig. 19(b). Such type of crack initiation can be attributed to debonding of the weakened grain boundaries introduced during the process of the material fabrication. More discussions will be further made in Section 4.2.

Fig. 15. Replica observation of initial condition of specimen surface, S15C.

In the case of specimen fatigued at 20 kHz, the crack initiation mechanism was exclusively intergranular, as depicted in Fig. 20. The crack origin (crack initiation site) is represented by the arrow ‘‘O’’ and the crack grows along a grain boundary. The early stage crack tends to bifurcate along a pair of boundaries at the triple point ‘‘T’’ contacting three grains. It is a characteristic aspect that any slip band is not visible on the specimen surface in this micrograph.

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Fig. 16. Formation of fatigue slip bands, f = 20 Hz, Sw + 30; S15C, (a) at N = 10% Nf and (b) at N = 25% Nf.

Fig. 17. Formation of fatigue slip bands at N = 25% Nf, Sw + 30; S15C, (a) f = 0.2 Hz and (b) f = 140 Hz.

Such an intergranular crack initiation has already been reported in several literatures. Zhang et al. [23] have found that low carbon steel has an intergranular crack initiation for fatigue tests at an average strain rate of 300 s1. Wang et al. [24] have reported that iron at room temperature under ultrasonic loading has an intergranular crack initiation mechanism. Puskar [25] pointed out an intergranular crack initiation for an iron fatigued at ultrasonic frequency. Besides, at room temperature, crack initiation can also occur without any slip band on the specimen surface. It should be noted that a few severe strain inhomogeneities, without any visible fatigue slip band, have been found on direct observation of the specimen surface after 25% Nf at a stress level of Sw + 30. One typical example indicating such an inhomogeneity is depicted in Fig. 21, where no slip band is observed inside each grain at the surface. Making reference to the above discussion, this type of inhomogeneity is supposed to be induced along some grain boundaries in the long sequence of cyclic loadings, and the most severe site can be the crack initiation site leading the specimen to the fatigue failure.

rG, and a thermal component r⁄, as given in Eq. (3). The athermal component rG means the stress required for a gliding dislocation

4. Discussions 4.1. Seeger theory and related works This theory deals with a special plastic property of B.C.C. materials, first proposed by Seeger [26], in 1954. According to this theory, the flow stress r consists of a sum of an athermal component

to bow out and to overcome the elastic interaction with other dislocations. The thermal component r⁄, frequently so-called the ‘‘effective stress’’, is a supplement stress needed to allow screw dislocations to glide at a given temperature and strain rate. According to the analysis by Seeger [26], this thermal component is practically negligible above a transition temperature T0 (or below a transition strain rate e_ t ).

r ¼ rG þ r ðe_ ; TÞ

ð3Þ

The transition temperature T0 and the transition strain rate e_ t are linked each other, in accordance with Eq. (4).

U 0 ¼ kT 0 ln





qAbm0 ; e_ t

ð4Þ

where U0: activation energy for jog formation at zero stress, k: Boltzmann’s constant, q: density of mobile dislocations, A: displacement surface done by a dislocation after intersecting a screw dislocation, b: Burger vector norm, t0: Debye’s frequency. In most of related literatures, this particular phenomenon of B.C.C. materials has been studied under tensile tests, at low temperature such as 77 K (liquid nitrogen), for example. Thus, this particular region where r⁄ is not negligible has been so-called the ‘‘low temperature regime’’. Such a region can be reached at higher temperature, if a sufficiently high strain rate is applied to the material, in accordance with Eq. (4). In the present work, for the sake of

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Fig. 18. Direct observation of slip bands by SEM, f = 20 kHz, Sw + 30, N = 25% Nf; S15C, (a) Type I and (b) Type II.

coherency with such literatures, authors will use the same expression, even though all experiments, and particularly fatigue tests, are actually performed at room temperature. Those literatures have already discussed some particular properties of B.C.C. materials placed into this low temperature regime. One of these properties is related to the multiplication processes of dislocations, as clearly shown by Saka et al. [20], discussed in Section 3.3.2. Since B.C.C. structure introduces deep valleys into Peierls energy function aligned with Burgers vector b directions [27], dislocation multiplication processes can be affected. In the low temperature regime, dislocations tend to adopt low-energy configurations, and thus cannot overtake the amount of energy needed to glide in another valley. It leads to an essential property of dislocation motion in the low temperature regime: mobility of edge dislocations is higher than mobility of screw dislocations. For a Fe–Si alloy, Low and Turkalo [28] have found that edge dislocation mobility can reach a 25 times higher value than screw dislocation mobility in this domain. As a consequence, dislocation observations of a B.C.C. material placed into this low temperature regime show us long screw segments [28–30]. It is thus not possible to get a dislocation structure composed with clear screw and edge dipoles, as cell or ladder dislocation structures, if the gap of screw and edge dislocation mobilities is large enough. Recently, by means of in situ TEM observation, Caillard [31] has reported another screw dislocation displacement in pure iron at very low temperature based on ‘‘jerky motions’’, where the screw segment jumps over several Peierls valleys. Such a motion mechanism will not be further discussed here, as it was only detected in pure iron samples [32]. In order to confirm this theory in cyclic deformation, Mughrabi et al. [29] have performed fatigue tests, at room temperature, on

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Fig. 19. Crack initiation observation at f = 0.2 Hz, ra = 223.6 MPa, Nf = 1.12  105 cycles; S15C, (a) main crack initiation site and (b) secondary crack initiation site.

Fig. 20. Crack initiation site at f = 20 kHz, ra = 270 MPa, Nf = 1.67  106 cycles; S15C.

pure iron specimens. It has been found that dislocation structure is extremely sensitive to the strain rate, according to the Seeger theory. On the one hand, below the transition strain rate e_ t (approximately 104 s1 under these conditions), dislocation cell dipole structures can be clearly seen, which is a proof of equivalent screw/edge dislocation mobility. On the other hand, the same material fatigued at a strain rate higher than e_ t will show long screw dislocation structure, as depicted in Fig. 22. This structure is characteristic of the low temperature regime. This overall behavior of pure iron will be further discussed in Section 4.3. A second property affected by this low temperature regime is the fatigue crack initiation mechanism. Indeed, Magnin and Driver

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4.2. Effect of other chemical elements inside ferrite lattice

Fig. 21. Strain inhomogeneity at GB without slip bands (f = 20 kHz, Sw + 30, N = 25% Nf; S15C).

Fig. 22. Long screw dislocations after cyclic loading, e_ > e_ t , iron [29].

[33], Guiu et al. [34], Sommer et al. [35] and Mughrabi [36] have identified a transition of the crack initiation, in the case of pure iron. Outside the low temperature regime, intragranular crack initiation phenomenon has been reported, as illustrated in Fig. 23(a). Such a mechanism is due to the local stress concentration at slip bands. However, in the case where pure iron specimen is placed into the low temperature regime, intergranular crack initiation mechanism is predominant, as shown in Fig. 23(b). Such a transition is explained by a significant stress asymmetry and a large size change of the specimen by Magnin and Driver [33] in the low cycle fatigue regime. This change of size will be particularly effective at free surface of the specimen, implying plastic deformation. Since these deformations depend on the grain orientations, incompatible deformations at the grain boundaries occur, and thus this incompatible deformation tends to cause the intergranular crack initiation. Sommer et al. [37] have proposed also that this aspect could be related to highly inhomogeneous strain level between different grains, even though only a very small fraction of grains is plastically deformed.

The Seeger theory presented in the previous section has been widely studied for B.C.C. pure iron, due to the absence of other elements inside ferrite grains. Nevertheless, some publications are discussing about the influence of some additional elements inside ferrite grain based on the applicability of the Seeger theory. Addition of interstitial (or substitution) elements into a pure lattice is supposed to harden the material. This is the reason why the steel, iron plus solute carbon atoms, is significantly harder than pure iron due to the pinning of the dislocations. However, in a certain temperature range inside the low temperature regime, addition of carbon atoms will soften the material [38]. Sommer et al. [37] have observed this softening behavior for a 74 ppm carbon iron at a temperature of 220 K and a strain rate of 103 s1, under axial fatigue tests. Such a softening can be easily detected by in situ experiments, since mobility of screw segments will be drastically increased by addition of carbon atoms at a similar temperature [32,39]. Thus the gap between screw segment and edge segment mobilities will be significantly reduced. The reason of the effect of interstitial elements inside iron lattice on the dislocation mobilities has been an important subject with some controversies. Sato and Meshii [40] have pointed out a decrease of the activation energy of kink mechanism due to addition of interstitial elements. Solomon and McMahon [41] have considered these impurities as barriers to the motion of non-screw dislocations in the low temperature regime to explain their experimental results. Kuramoto et al. [42] have found a direct relation between the softening effect and the disappearance of the peak of dislocation activation area. Recently, Caillard [31] has found that the main mechanism related to this softening effect of carbon solute atoms, in a 110 ppmC iron, is due to the disappearance of the activation area peak, as proposed by Kuramoto et al. [42]. A similar conclusion has also been reported for Si, Ni or Cr additions at relatively low concentrations [43]. Such a softening effect has a direct consequence on the transition temperature T0 giving the temperature bound of the low temperature regime. In order to assess this transition temperature, one can undertake experiments on the strain rate sensitivity of the flow stress. To undertake this experiment, the flow stress difference from tensile tests carried out at two distinct strain rates is calculated. Such strain rate sensitivity in a function of the temperature presents a peak [44]. This peak means that the effective stress r⁄ is negligible for the lowest strain rate, but becomes significant for the highest strain rate. In other words, the transition temperature T0 is located at the peak temperature for a strain rate between the two distinct strain rates applied during tensile tests. According to Quesnel et al. [38] in Fig. 24, the higher the solute carbon composition up to 400 ppm is, the more distinct the shift to low temperature domain of the strain rate sensitivity is. Therefore, the higher the carbon solute element composition up to 400 ppm is, the lower the transition temperature T0 is. Based on the transition equation of the Seeger theory in Eq. (4), the transition strain rate e_ t of the ferrite grains in S15C steel will be higher than that for pure iron, at the same temperature. Such an important effect of the chemical composition for a-iron based metallic materials on the transition conditions was found by Magnin and Driver [33]. According to Table 1, ferrite grain lattice of S15C steel includes, in addition to carbon atoms, also Si, Mn and Cr solute atoms, inducing a shift of the transition condition to higher strain rates. Besides, Vaynman et al. [45] have discussed that the addition of nanosize precipitates inside B.C.C. lattice tends to decrease locally the Peierls stress over the length of a double kink pair along the dislocation. Due to the chemical composition of S15C steel, it seems reasonable to have a relatively high number of precipitates inside ferrite phase. Such a point is confirmed by the Fig. 14(a), where one can

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Fig. 24. Strain rate sensitivity of the flow stress, Fe–C system [38].

Fig. 23. Change of the crack initiation mode, iron [35], (a) intragranular initiation outside low temperature regime and (b) intergranular initiation inside low temperature regime.

see those precipitates. Since the Peierls stress is locally decreased, leading to a reduction of the activation energy U0, the transition strain rate e_ t tends to increase according to Eq. (4). Unfortunately, an estimation of this transition strain rate in the case of the ferrite grains in S15C steel is not given here, as it requires very specific experiments. In addition, it should be noted that addition of other elements has also a typical effect on the crack initiation, due to possible embrittlement of the grain boundaries. Indeed, it is usually reported that segregations of Mn [46], S [47] or P [48] impurities tend to weaken those grain boundaries. On the other hand, addition of carbon atoms tends to strengthen the grain boundaries by replacing the other segregation elements in the vicinity of grain boundary [49]. We have thus a competition of the segregation elements between carbon and other atoms at grain boundaries. According to the chemical composition listed in Table 1, it is thought that intergranular crack initiation mechanism is facilitated in the S15C steel studied in the present work compared with the pure iron. 4.3. Effect of high strain rate on the fatigue properties of S15C steel In our previous work [10], a slight change of fatigue strength of S15C steel in the usual frequency range of 0.2–140 Hz has been discussed from a wide variety of viewpoints. An increase of the strain rate will cause a higher yield stress. Thus, the strain rate has an important effect on the cyclic strain softening of S15C steel such that the plastic strain is affected. However, due to the drastic loss of local misorientation, a similar explanation is not suitable for fatigue tests conducted at the ultrasonic frequency.

The significant change of the dislocation structure and its arrangement observed in Section 3.2 causes the decrease of geometrically necessary dislocations (GND) density, and thus this change gives the reason of the drastic loss of local misorientation found in both transversal direction [10] and longitudinal direction, as reported in the Section 3.1.2 of the present paper. Instead of cell or ladder structure caused by fatigue loadings performed in the usual frequency range of 0.2–140 Hz, samples fatigued at 20 kHz reveal long segments of screw dislocations. Such a dislocation structure is peculiar to B.C.C. materials deformed at sufficiently low temperature and/or sufficiently high strain rate. Due to this change of dislocation structure, the effect of the strain rate on the fatigue properties of pure a-iron, is schematically depicted in Fig. 25. As already mentioned in Section 4.1, at room temperature, the transition strain rate e_ t is approximately 104 s1. At a strain rate lower than this transition value, mobilities of screw and edge components of dislocations are similar. Thus, dislocations dipoles can be formed as ladder or cell structures, and the fatigue crack tends to occur in the intragranular mode. If the average strain rate has overcome the transition strain rate, due to Peierls stress profile in B.C.C. lattice, mobility of the screw segment of dislocations becomes very low compared with the value for the non-screw segment. In such a circumstance, long screw segments are formed, and an intergranular fatigue crack initiation mechanism can act, as already discussed in Section 4.1. Such a change of the crack initiation mechanism causes a drastic increase of the fatigue life of a-iron [33,36]. In case of the S15C low carbon steel, even though the base matrix is also B.C.C. a-iron, we have to consider some complexities of the microstructure as follows; (1) the interstitial and substitution elements and precipitates inside the ferrite lattice; (2) the existence of cementite and thus a volume fraction of pearlite grains. As already discussed in Section 4.2, addition of such solute elements inside the ferrite lattice will macroscopically induce a softening effect in the low temperature regime compared with the case of pure iron. Indeed, addition of other solute elements and formation of precipitates inside ferrite phase will decrease the gap between screw and edge dislocation mobilities. This aspect is directly related with the decrease of the transition temperature T0 with an increase of carbon content as shown in Fig. 24, at a constant strain rate. Similarly, at the same temperature, the transition strain rate e_ t is increased by the effect of other elements inside the ferrite lattice, as already mentioned in Section 4.2. In the case of low carbon steels with carbon content higher than its solubility inside the ferrite lattice, volume fraction of pearlite

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Fig. 25. Strain rate effect on fatigue properties of pure a-iron.

grains is expected to have a significant effect on the athermal stress term rG of the flow stress, but the effective stress r⁄ is expected to keep negligible small. Indeed, fine lamellar structure of pearlite grains is supposed to prevent the formation of long segments of screw dislocations. Besides, one can note that most of the high misorientation values left after ultrasonic loadings are induced inside the pearlite grains in Fig. 6(c). Such an experimental evidence implies that dislocation structure in a-phase of pearlite grains is slightly affected by the ultrasonic loadings. In other words, the effective stress r⁄ of S15C steel is caused by B.C.C. a-phase in ferrite grains only. In addition, pearlite grains do not affect the behavior of adjacent ferrite grains in the low temperature regime, since long screw segments were observed in every ferrite grain in this work. In the case of S15C steel, a quick calculation based on the Fe-C phase diagram gives a volume fraction of pearlite grain of 16.9%. This result seems to be in a good agreement with the microstructure shown in Fig. 3. It is thus reasonable to consider that the small pearlite volume fraction inside S15C steel has a limited influence on the macroscopic effective stress r⁄. According to the above discussion, a scheme representing the strain rate effect on the fatigue properties of S15C steel is shown in Fig. 26. This schematic overview is roughly similar to the situation for pure iron. However, due to the dissolved elements and precipitates in the ferrite lattice, the transition strain rate e_ t has drastically increased. In accordance with results from dislocation micrographs, the transition is set between the corresponding average strain rate of fatigue tests performed at f = 140 Hz and f = 20 kHz, at room temperature. At a strain rate lower than the transition, dipole dislocation structures can be observed in ferrite grains, and the crack initiation mostly occurs due to slip bands, inducing an intragranular fatigue crack. The rare cases of intergranular crack initiation mode in this domain are certainly caused by diffusion of impurities increasing the segregation concentration along the grain boundaries. In other

Fig. 26. Strain rate effect on fatigue properties of S15C steel.

words, the fatigue crack tends to occur along the grain boundaries weakened by the impurities. On the other hand, at strain rate higher than the transition, mobilities of screw and edge dislocations are differ from each other. Thus, long segments of screw dislocations are formed, according to the Peierls stress profile. In this domain, crack initiation becomes exclusively intergranular. Such a change of crack initiation mode is the main reason why the S–N property in ultrasonic fatigue test differs significantly from that at usual frequencies, in a way similar to pure a-iron. Finally, it should be noted that this discussion is valid as long as the macroscopic behavior of the carbon steel studied in the low temperature regime is governed by the effective stress r⁄. As already mentioned, the effective stress r⁄ is caused by B.C.C. aphase in ferrite grains only, excluding the a-phase in pearlite grains due to its lamellar structure. In the case of S15C steel with a very slight pearlitic volume fraction, it seems reasonable to consider that its macroscopic behavior is governed by the effective stress r⁄. However, an increase of the pearlitic volume fraction reduces the effective stress r⁄ of the whole structural steel due to the decrease of ferritic volume fraction. Thus, fatigue properties of carbon steels with a higher content of carbon, i.e. higher volume fraction of pearlite, should be less sensitive to the peculiar behavior of ferrite grains, inducing a lower sensitivity to the loading frequency.

5. Conclusion In order to examine the effect of the loading frequency on the fatigue properties, fatigue tests were carried out in a wide frequency range of 0.2 Hz–20 kHz, by using the low carbon steel of S15C. A series of experimental aspects were discussed from a viewpoint of dislocation structure and crack initiation mechanism. Main results obtained in this work are summarized as follows; (1) No significant difference was found among the distributions representing the ferrite grain size before and after ultrasonic loadings. The strain rate applied during ultrasonic tests is not sufficient to cause a grain refinement in S15C steel. (2) Dislocation structure of S15C steel is extremely sensitive to the loading frequency. In the case of usual frequencies at 0.2–140 Hz, similar dislocation structures with dislocation dipoles are induced, as ladder or cell structures. On the other hand, ultrasonic loadings cause long segments of screw dislocations without clear wall. This dislocation rearrangement gives the reason of the drastic loss of lattice local misorientation in the ferrite phase. (3) The fatigue crack mostly occurs due to slip bands, inducing an intragranular fatigue crack at usual frequencies of 0.2– 140 Hz. On the other hand, this crack initiation behavior becomes exclusively intergranular for ultrasonic tests due to severe strain inhomogeneities at some grain boundaries. (4) According to the Seeger theory, any B.C.C. material is placed into the ‘‘low temperature regime’’ as the average strain rate of the fatigue loading exceeds a transition value. Based on dislocation structure, slip band formation and crack initiation behavior, the transition strain rate in the case of S15C steel is supposed to be within a range between fatigue tests at f = 140 Hz and f = 20 kHz, at room temperature. Consequently, the significantly higher fatigue strength of S15C steel at f = 20 kHz than usual frequencies is due to the transition of crack initiation mechanism, in a way similar to the case of pure a-iron. (5) The effective stress r⁄ is expected to be caused only by ferrite grains, excluding a-phase in pearlite grains due to its lamellar structure. Since the pearlitic volume fraction of

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S15C steel is very slight, its macroscopic behavior in the low temperature regime is governed by effective stress r⁄ of ferrite grains. However, an increase of the pearlitic volume fraction reduces the effective stress r⁄ of the structural steel due to the decrease of the ferritic volume fraction. Thus, fatigue properties of carbon steels with a higher content of carbon should be less sensitive to the peculiar behavior of ferrite grains, inducing a lower sensitivity to the loading frequency.

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