Materials Transactions, Vol. 56, No. 12 (2015) pp. 2010 to 2016 2015 Japan Foundry Engineering Society Relationship between Fatigue Limit and Defect Size in Spheroidal Graphite Cast Iron with Different Graphite Spheroidization Ratios and Microstructures +1 Naoto Shiraki 1, Takuya Watanabe 1,+2 and Toshitake Kanno 2 1 Faculty of Engineering, Tokyo City University, Tokyo 158-8557, Japan 2 Kimura Chuzosho Co., LTD., Omaezaki 437-1615, Japan The purpose of this study is to investigate that effects of graphite spheroidization ratio and microstructure on the characteristics of fatigue limit in spheroidal graphite cast iron. Ferritic spheroidal graphite cast iron (FDI), pearlitic spheroidal graphite cast iron (PDI) and austempered spheroidal graphite cast iron (ADI) were used as specimens. The graphite spheroidization ratio was varied between 63³94% by the addition of a spheroidizing agent. Tensile test was carried out in air at room temperature. The experiment conformed to JIS (Japan Industrial Standards). Rotating bending fatigue test was also carried out using these materials. The experiment conformed also to JIS. Stress ratio R was ¹1, and the specimen used was type 1(JIS) with a diameter of 8 mm. The test was carried out in air at room temperature. The relationship between fatigue limit and graphite spheroidization ratio was investigated, as well as the correlation between fatigue limit and defect size. When the graphite spheroidization ratio was over 80%, the fatigue limit was not influenced. Fracture origins were micro-shrinkage, aggregate graphite, and unspheroidized graphite. When graphite spheroidization decreased, the ratio of unspheroidized graphite at the fracture origin increased. The defect size that transitioned from region I to II differed according to the microstructure: the defect size of PDI was the smallest, and that of FDI was larger than ADI. When there are no large defects in FDI, the fatigue limit can be estimated by tensile strength. However, in PDI and ADI, it must be estimated taking into account the size of existing defects in specimens. [doi:10.2320/matertrans.f-m2015826] (Received June 24, 2015; Accepted September 3, 2015; Published October 23, 2015) Keywords: graphite spheroidization, microstructure, spheroidal graphite cast iron, rotating bending fatigue test, fatigue limit, defect size, fracture origin 1. Introduction Spheroidal graphite cast iron has many excellent properties and is considered to be a promising structural material alternative to steel. In the Japanese Industrial Standard, spheroidal graphite cast iron is defined to have a graphite spheroidization ratio of 80% or more. 1) In addition, there s also a written description of tensile strength. For example spheroidal graphite cast iron (such as FCD700) has a tensile strength of 700 MPa or more. The spheroidal graphite cast iron is defined as having an approximately constant tensile strength with the graphite spheroidization ratio of 80% or more. On the other hand, spheroidal graphite cast iron contains graphite, which may become the origin of a fatigue fracture. 2) In addition, it is reported that unspheroidal graphite can become a fracture origin. 3) Materials with a graphite spheroidization ratio of 80% or more are categorized as the same material, while researchers do not yet fully understand how the spheroidizing ratio influences the fatigue strength. In other words, even in the case that the spheroidizing ratio satisfies the prescription, it is expected that stress concentration may be occured at the edge of the unspheroidal graphite or a coarse graphite grain may trigger fatigue fracture. This means that even if a spheroidizing ratio is large enough for providing a sufficient static strength, it may be not large enough to provide a satisfactory fatigue strength. Further, it is desired to establish a safe and simple method using for strength design because experimental determination of fatigue limit spends enormous time and effort. 4) Generally, +1 This Paper was Originally Published in Japanese in J. JFS 86 (2014) 454 460. +2 Graduate Student, Tokyo City University the fatigue limit of steels is said to be equal to 0.5 B (half of the tensile strength). However, the evaluation with only tensile strength may not always be sufficient because inherent defects in spheroidal graphite cast iron is large. 5) Murakami et al. proposed the four-parameters method to predict the fatigue limit in consideration of the hardness of the matrix and defect size in a material, and showed that the fatigue limit can be evaluated with a good accuracy for a material with a defect size of about 1,000 µm. 6) In this study, we performed a rotating bending fatigue test of ferritic spheroidal graphite cast iron, pearlitic spheroidal graphite cast iron, and austempered spheroidal graphite cast iron with different spheroidizing ratios obtained by different conditions of heat-treatment to study the influence of spheroidization ratio on the fatigue limit. In addition, we examined the correlation between fatigue limit and defect size which is dependent on the matrix. 2. Sample Materials Test ingots of 230 mm 190 mm 170 mm were prepared by melting 54 kg of metal in an electric furnace, and pouring it from the upper opening with a tapping temperature of 1773 K and a pouring temperature of 1653 K. The graphite spheroidization ratio of test materials was controlled by changing the quantity of a spheroidizing agent addition. Materials including four kinds of ferritic spheroidal graphite cast iron (FDI), five kinds of pearlitic spheroidal graphite cast iron (PDI), and four kinds of austempered spheroidal graphite cast iron (ADI) with different values of spheroidization ratio were prepared for the experiment. Table 1 shows the chemical components of the test materials. In addition, the name of each material is shown in conjunction with the graphite spheroidization ratio (e.g., FDI.94).
Relationship between Fatigue Limit and Defect Size in Spheroidal Graphite Cast Iron Table 1 Chemical compositions of experimental materials,,,. Table 2 Comparison of microstructures, graphite spheroidization ratios, mean diameter of spheroidal graphite, and number of graphite at different graphite spheroidization ratios,,,. mass% Material C Si Mn P Mg S FDI.94 3.61 2.41 0.047 FDI.91 3.62 2.27 0.0 FDI.87 3.63 2.32 0.031 FDI.63 3.68 2.34 0.27 0.025 mass% Material C Si Mn P Mg S PDI.93 3.65 2.36 0.24 0.047 PDI.90 3.70 2.31 0.24 0.0 PDI.89 3.69 2.28 0.25 2 0.036 PDI.86 3.66 2.27 0.25 0.032 PDI.63 3.65 2.28 0.24 0.027 2011 FDI.94 FDI.91 FDI.87 FDI.63 Ratio of graphite spheroidization/% 94 91 87 63 Mean diameter of graphite/µm 36 42 31 Number of graphite in microstructure / /mm2 80 79 93 59 Microstructure 100 µm PDI.93 PDI.90 PDI.89 PDI.86 PDI.63 Ratio of graphite spheroidization/% 93 90 89 86 63 Mean diameter of graphite/µm 35 36 33 Number of graphite in microstructure / /mm2 81 62 66 64 61 mass% Material C Si Mn P Mg S ADI.92(1) 3.69 2.30 2 0.049 ADI.92(2) 3.74 2.30 0.27 0.039 ADI.87 3.66 2.31 6 0.037 ADI.79 3.68 2.30 0.25 0.032 Removing 10 mm of height from the lowermost part of each ingot, and the specimen for the tensile test and the rotating bending fatigue test was taken from a section of 70 mm from that height. Specimens from each ingot were roughly shaped into a round bar with a diameter of 18 mm and went through ferritization annealing, pearlite transformation normalizing annealing, and austempering processes, respectively. Ferritization annealing process includes holding at 1123 K for 18 ks in an atmospheric furnace, cooling at a speed of 8.3 10¹3 K/s and then 1.4 10¹2 K/s, and finally air-cooling. The pearlite transformation normalization steps consist of holding at 1203 K for 18 ks and air-cooling. The austempering process consists of holding at 1123 K for 3.6 ks (austenitizing annealing), an isothermal transformation process in a saltbath furnace at 648 K for 3.6 ks, and then air-cooling. The graphite spheroidization ratio was measured using the chucked portion of the specimens which went through the rotating bending fatigue test. An optical microscope was used in the measurement based on JIS G 5502. The JIS G 5502 prescribes the measurement of five viewing fields with a magnification of 100 times,1) but because we emphasize resolution in this study, the measurement was performed using 20 viewing fields per specimen with a magnification of 200 times so that the same area is covered each time. In consideration of the collection position of the ingot of the fatigue specimen, observation was chosen from three or more specimens for each material, and the average value thereof was defined as the ratio of graphite spheroidization. Table 2 summarizes the microstructures, the ratio of graphite Microstructure 100 µm ADI.92(1) ADI.92(2) ADI.87 ADI.79 Ratio of graphite spheroidization/% 92 92 87 79 Mean diameter of graphite/µm 44 40 40 Number of graphite in microstructure / /mm2 72 73 70 63 Microstructure 100 µm spheroidization, the diameter of spheroidal graphite, and the number of graphite per unit area of each material. The graphite spheroidization ratio of all test materials was in the range of 63 94%. The materials with a spheroidization ratio of less than 80%, which are not considered as spheroidal graphite cast iron, were also tested. Large differences were
2012 N. Shiraki, T. Watanabe and T. Kanno not observed in the diameter of spheroidal graphite and the number of graphite per unit area in each material. 3. Experimental Procedure 3.1 Tensile test In the tensile test, the shape and dimensions of tensile test specimens was compliant with the 14A tensile test specimen of JIS Z 2241, which has a diameter 8 mm in the parallel portion. 7) The tensile test was conducted in the atmosphere at room temperature using the AUTOGRAPH AG-Xplus and a crosshead displacement speed of 0.5 mm/min. The parallel portion of the specimens was polished using #400 abrasive paper, and a pair of foil type strain gauges of length 2 mm were attached to the left and right sides of the center of the parallel portion of the specimens. Young s modulus was calculated from the strain measured by the tensile test, and proof stress 0.2% was measured by the offset method. 3.2 Hardness test The hardness of the matrix of each material was obtained by the Vickers test. The specimen was polished using a #2000 abrasive paper, and the test surface was buff-polished with diamond paste of an average particle size of 0.25 µm. A micro-vickers hardness tester was used. The test conditions were an applied testing load of 1.96 N and 50 measurement points with load holding time of 15 sec. The average of 30 measurement points, from which the top and bottom 10 points were excluded, was defined as the hardness. 3.3 Rotating bending fatigue test The shape and the dimensions of fatigue test specimens were compliant with the No. 1 test specimen of JIS Z 2274, which has a diameter of 8 mm in the parallel portion. 8) The number of the specimens was 12 23 for each material. Further, the parallel portion was mirror-polished using abrasive papers and by buff polishing. In the rotating bending fatigue test, Ono-type rotating bending fatigue testing machine (98 Nm) was used with a loading frequency of 47 rps at room temperature in the atmosphere. The number of repetitions for the fatigue test was 1 10 7 cycles for the FDI and PDI materials and 3 10 7 cycles for the ADI material. The approximation of S-N diagrams obtained by the rotating bending fatigue test and the fatigue limit were calculated in conformity with JSMS-SD-6-02. 9) The fracture origins and their peripheral areas of all specimens fractured after the fatigue test were observed using a scanning electron microscope. 4. Experimental Results and Discussion Table 3 summarizes the mechanical properties of each material evaluated by the tensile test and the hardness test. Large differences are not seen in the mechanical properties as far as the spheroidizing ratio is 80% or more in any material, but the decrease in the mechanical properties is seen in the material with the ratio of 80% or less. Figure 1 shows the relationship between the fatigue limit and the spheroidization ratio of each material evaluated by the rotating bending fatigue test. It is considered that the Table 3 Mechanical properties of spheroidal graphite cast iron at different graphite spheroidization ratios,,,. 0.2% Proof stress 0.2 /MPa Tensile strength B/MPa Elongation Reduction of area Young s modulus E/GPa Vickers hardness HV 0.2 FDI.94 235 371 30 25 149 192 FDI.91 236 370 29 24 150 190 FDI.87 242 375 28 24 153 191 FDI.63 240 341 13 10 142 195 0.2% Proof stress 0.2 /MPa Tensile strength B/MPa Elongation Reduction of area Young s modulus E/GPa Vickers hardness HV 0.2 PDI.93 634 1020 5 4 170 364 PDI.90 616 993 5 5 169 360 PDI.89 620 1001 5 4 168 361 PDI.86 618 1004 5 5 169 367 PDI.63 5 764 3 2 153 359 0.2% Proof stress 0.2 /MPa Tensile Elongation strength B/MPa Reduction of area Young s modulus E/GPa Vickers hardness HV 0.2 ADI.92(1) 719 902 6 6 158 414 ADI.92(2) 677 848 7 6 149 398 ADI.87 683 859 7 7 158 413 ADI.79 661 845 7 6 152 415 Fatigue limit, σ w / MPa 400 300 200 100 100 90 80 70 Ratio of graphite spheroidization / % ADI PDI FDI Fig. 1 Relationship between fatigue limit and graphite spheroidization ratio. influence of the graphite spheroidization ratio is not seen in the material with a spheroidization ratio of 80% or more. However, in the material with a spheroidization ratio of less than 80%, the fatigue limit decreased. In addition, the reason of the decrease in the fatigue limit of the FDI.91 material will be discussed later. The observation using an electron microscope (Fig. 2) showed that all fracture origins observed in this study were 60
Relationship between Fatigue Limit and Defect Size in Spheroidal Graphite Cast Iron 2013 (a) (b) (c) 100μm 100μm 100μm Fig. 2 Examples of fracture origins observed by SEM, (a) Micro-shrinkage (SEM image), (b) Aggregate graphite (back scattered electron image), (c) Unspheroidized graphite (back scattered electron image). (b) FDI.94 (a) PDI.93 PDI.90 FDI.91 PDI.89 FDI.87 PDI.86 FDI.63 PDI.63 0 20 40 60 80 100 Ratio of typical fracture origins / % 0 20 40 60 80 100 Ratio of typical fracture origins / % (c) ADI.92(1) ADI.92(2) ADI.87 ADI.79 0 20 40 60 80 100 Ratio of typical fracture origins / % Micro shrinkage Aggregate graphite Unspheroidizing graphite Fig. 3 Percentage of three kinds of fracture origins in each material,,,. either a micro-shrinkage cavity (Fig. 2(a)), Aggregate graphite (Fig. 2(b)), or unspheroidal graphite (Fig. 2(c)). Figure 3 shows the fraction of the kinds of fracture origins in a bar graph for each material. Micro-shrinkage cavity and aggregate graphite are often observed in the fracture origins in any material if the spheroidization ratio is 80% or more, while the percentage of fracture origins with unspheroidal graphite increases as the spheroidization ratio decreases. The reason is not clear why the micro-shrinkage cavity is often observed in the fracture origins of FDI materials if the spheroidizing ratio is 80% or more even though the ingots were made using the same conditions, but the following factors are considered to likely play a role. Judging from the fact that the starting point of a fatigue fracture is the largest defect size in a risk volume, it is considered that the shrinkage cavity is the largest among the existing defects in the FDI material, and that there would be a micro-shrinkage cavity that is greater in size than the aggregate graphite and the unspheroidal graphite (as shown in Table 4). The above results show that the fracture origin changes from the micro-shrinkage or aggregate graphite to the unspheroidizing graphite as the spheroidization ratio decreases. The fatigue limit decreases because the unspheroidizing graphite has larger defects than the micro-shrinkage and aggregate graphite inherent to the material. It is known that the fatigue limit of a material with a defect (crack) can be estimated using the 4-parameter model as shown in Fig. 4. 10) In other words, the relationship between
2014 N. Shiraki, T. Watanabe and T. Kanno the fatigue limit and defect size is classified into three regions as shown below. Region I: A region strongly ruled by mechanical properties Region II: A region strongly ruled by the resistance against the propagation of a small defect (crack) Region III: A region strongly ruled by the resistance against the propagation of a large defect (crack) In the case of steels, the size of defects and inclusions formed in the normal manufacturing process is as small as several 10 µm. Therefore, the fatigue limit is not affected by the size of defects and inclusions as far as the hardness is relatively small, and the proportional relationship of eq. (1) generally holds (in Region I) between the fatigue limit wi and the tensile strength B of the steel. 11) WI ¼ 0:5 B ð1þ On the other hand, spheroidal graphite cast iron has low strength graphite grains, which could be regarded as defects in same ways. In addition, there exists a micro-shrinkage with a size of several hundred µm as observed on the fractured surface. Because stress concentration occurs in a material containing defects of a size of several hundred µm or larger, it Fatigue limit, log σ w Region W σ B Defect size, log Region σ σ HV W area σ Region W ΔK Fig. 4 Schematic illustration of relationship between fatigue limit and pffiffiffiffiffiffiffiffiffi defect size, area (4 parameter model). th is known that, affected by the defect size and the hardness of the matrix, the fatigue limit becomes lower than the value predicted by eq. (1). Murakami et al. attempted to estimate the fatigue limit of a material containing defects of a size of several hundred µm or larger. 6) As a result, it was shown that the fatigue limit could be accurately estimated using eq. (2) for the material with defects of the size smaller than 1,000 µm (Region II). ðhv þ 120Þ WII ¼ pffiffiffiffiffiffiffiffiffi ð2þ 1=6 area HV is the Vickers hardness and is a coefficient, which depends on the position of a defect: it equals to 1.43 if the fracture p origin ffiffiffiffiffiffiffiffiffi exists near the surface or 1.56 if it exists in the inside. area, of which the unit is µm, is the square root of the area obtained by projecting the defect to the largest main stress surface. Therefore we measured the defect size at the origin of the fatigue fracture. In the measurement of the defect size in any fractured specimen, the fracture origin was approximated by a square, as shown in Fig. 5, disregarding the differences in the shape of fracture origins, and the p square ffiffiffiffiffiffiffiffiffi root of the area was assumed to be the defect size pffiffiffiffiffiffiffiffiffi area. In addition, by plotting the measured results with area on a gumbel paper, where the vertical axis shows the standardized variable and the cumulative distribution function and the horizontal axis shows the defect size area F¼50%. A tendency was observed that area F¼50% increased as the spheroidization ratio decreased. In the study, in the case of a spheroidization ratio 80% or more, the starting point of the fatigue fracture was a microshrinkage, an aggregate graphite, or unspheroidizing graphite of a size of approximately 100 600 µm, while an aggregate graphite or unspheroidizing graphite of a size of approximately 200 950 µm was the starting point in the case of a spheroidization ratio of less than 80%. It is estimated from the defect size that they belong to Region I or II in the 4- parameter method. Table 4(a) (c) shows the fatigue limit and (a) (b) (c) 100μm Fig. 5 SEM image and approximate rectangle area of fracture origins, (a) Micro-shrinkage, (b) Aggregate graphite, (c) Unspheroidized graphite.
Table 4 Comparison of experimental fatigue limits, average defect sizes, fatigue limits estimated by eqs. (1) and (2) and estimated accuracies w/ wi, w/ wii,,,. Fatigue limit determined by S-N curve w/mpa /µm area F¼50% by eq. (1) wi /MPa by eq. (2) wii /MPa FDI.94 200 256 186 177 1.08 1.13 FDI.91 170 314 185 170 0.92 1.00 FDI.87 200 236 188 179 1.07 1.12 FDI.63 160 494 171 160 0.94 1.00 Fatigue limit determined by S-N curve w/mpa /µm area F¼50% by eq. (1) wi /MPa by eq. (2) wii /MPa PDI.93 285 203 510 285 0.56 1.00 PDI.90 295 223 497 279 0.59 1.06 PDI.89 295 232 501 277 0.59 1.06 PDI.86 295 221 502 283 0.59 1.04 PDI.63 215 470 2 246 0.56 0.88 Fatigue limit determined by S-N curve w/mpa Relationship between Fatigue Limit and Defect Size in Spheroidal Graphite Cast Iron 2015 /µm area F¼50% by eq. (1) wi /MPa by eq. (2) wii /MPa ADI.92(1) 335 254 451 331 0.74 1.01 ADI.92(2) 335 319 424 309 0.79 1.08 ADI.87 335 245 430 332 0.78 1.01 ADI.79 310 365 423 312 0.73 0.99 w/ wi w/ wi w/ wi w/ wii w/ wii w/ wii the average defect size area F¼50% of the material; the fatigue limit estimated using eq. (1) as a function of tensile strength B; and the fatigue limit estimated using eq. (2) as a function of both average defect size area F¼50% and the hardness HV of the matrix. Table 4 also shows w/ wi and w/ wii assuming that the estimate accuracy of the fatigue limit is given by the ratio between the fatigue limit, which is obtained from the S-N diagram, and the estimate value. The evaluation is in a safe side if the ratio exceeds 1, while in a dangerous side if less than 1. The estimate is rated as precise as the ratio comes close to 1. If we pay an attention to the average defect size, it is found the size is large in all materials when the spheroidizing ratio is less than 80%. This probably suggests that the fracture origin changes from the microshrinkage or aggregate graphite to the unspheroidizing graphite. It is thought that the fatigue limit decreases as a result. Paying an attention to the estimated fatigue limit by eq. (1) (Region I) and eq. (2) (Region II) in the 4-parameter method, good results are obtained for the fatigue limit of FDI.94 and FDI.87 materials using eq. (1). On the other hand, in the FDI.91 and FDI.63 materials, of which the average defect size is larger than that of FDI.94 and FDI.87, good results are obtained using eq. (2). In other words, even in the FDI materials having comparable mechanical properties, the fatigue limit cannot be simply estimated from the tensile strength by using eq. (1) due to the difference in the inherent defect size, indicating an estimation in consideration of the defect size is needed. It is judged that in the PDI and ADI materials excluding PDI.63, good results are obtained in Fatigue limit, σ w / MPa 1000 PDI ADI FDI 6μm 26μm 180μm 100 1 10 100 1000 Defect size, area / μm pffiffiffiffiffiffiffiffiffi Fig. 6 Relationship between fatigue limit and defect size, area in each materials (4 parameter model based on experimental results). estimating the fatigue limit using eq. (2). The estimation for the PDI.63 materials is on the dangerous side even using eq. (2) presumably because of a notch effect at the edges of graphite grains. Based on the results of fatigue limit and defect size, Fig. 6 shows the 4-parameter model of each material used in this study. From the accuracy of estimating the fatigue limit of the materials shown in Table 4, judgment was made to decide if they belonged to Region I or Region II. By using the tensile strength for the material in Region I and the hardness of the matrix in Region II, the value for the 4-parameter model for
2016 N. Shiraki, T. Watanabe and T. Kanno each material was subtracted from the estimated fatigue limit obtained using eq. (2). Then the defect size that shows the transition from Region I to Region II is shown by the arrow and dash line for each material. In addition, the defect size from which the transition to Region III (the domain strongly ruled by the resistance against the propagation of a large defect (crack)) assumed to 1,000 µm, which is said to be the application limit of Region II, is shown by the two-dot chain line. The defect size domain (approximately 100 600 µm) that corresponds to a spheroidization ratio of 80% or more as evaluated in this study is shown by the hatched area in the figure. Paying an attention to the hatched area and the defect size which shows the transition from Region I to Region II in Fig. 6, the FDI materials belong either to Region I or Region II, while both of the PDI and ADI materials evaluated in this study, of which defects being much larger than the transition defect size (6 µm, 26 µm), belong to Region II. In addition, the transition defect size of the PDI and ADI materials is smaller than the diameter of spheroidal graphite of the spheroidal graphite cast iron used in this study. This suggests that, even if the inherent micro-shrinkage is very small and the ratio of graphite spheroidization is large, any inherent graphite of which the size is greater than that of the transition defect size may become the starting point of fatigue fracture. The transition defect size of each material depends on the matrix. The size increases in the order of PDI, ADI, and FDI. In other words, it can be said that the fatigue limit of FDI materials without large inherent defects is estimated from the tensile strength using eq. (1). However, in PDI and ADI materials of which the transition defect size is smaller than that of FDI materials, the fatigue limit cannot be simply predicted from the tensile strength in any event and it is necessary to consider the inherent defect size including the diameter of spheroidal graphite and the spheroidization ratio. 5. Conclusions By carrying out the rotating bending fatigue test for the spheroidal graphite cast iron with different matrices and ratios of graphite spheroidization, the following conclusions were obtained. (1) If the graphite spheroidization ratio is 80% or more, the fatigue limit is not affected by graphite spheroidization ratio. (2) In any material, if the spheroidizing ratio is 80% or more, mainly micro-shrinkage and aggregate graphite are found at the fracture origins and the ratio of the fracture origins with unspheroidizing graphite increases as the spheroidizing ratio decreases. (3) In any material, the defect size from parameter which transition occurs from Region I to Region II depends on the matrix and increases in the order of PDI, ADI, and FDI. (4) It can be considered that, in the FDI material without large inherent defects, the fatigue limit is estimated from the tensile strength. However, in the PDI and ADI materials, it is considered necessary to estimate the fatigue limit in consideration of inherent defect size including the diameter of spheroidal graphite and the spheroidization ratio. REFERENCES 1) JIS G 5502: Spheroidal Graphite Iron Castings, (2007). 2) T. Shiota and S. Komatsu: J. JFS 54 (1982) 434 439. 3) Y. Sugiyama, K. Asami and H. Wakasa: J. JFS 66 (1994) 666 671. 4) K. Ohji: Hakai-Kyodo-Gaku, (Ohmsha, 1985) p. 194. 5) H. Tamura, Y. Sugiyama and T. Kimura: J. JFS 69 (1997) 234 239. 6) Y. Murakami: Metal Fatigue, Effects of Small Defects and Nonmetallic Inclusions, (Yokendo, 1993) p. 43. 7) JIS Z 2241: Method of Tensile Test for Metallic Materials, (2011). 8) JIS Z 2274: Method of Rotating Bending Fatigue Testing of Metals, (1978). 9) JSMS-SD-6-02: Standard Evaluation Method of Fatigue Reliability for Metallic Materials, Standard Regression Method of S-N Curves, (2002). 10) Y. Sugiyama, K. Asami and S. Matsuoka: Trans. JSME(A) 58 (1992) 2287 2292 (in Japanese). 11) H. Nakazawa and H. Honma: Kinzoku-no-Hiroukyodo, (Yokendo, 1982) p. 10.