5

Fig. 10 The roughest worn surface observed at N = 104 cycles under the same condition with Fig. 8 and k ≈ 0.5 4. Conclusions The cyclic reciprocating sliding contact experiment for JIS SUJ2 (high carbon-chromium bearing steel) was conducted to investigate the characteristics of friction and wear and the effects of the number of reciprocating cycles, test frequency, relative displacement and static load. The obtained results are summarized as follows:

1. The relationship between friction force, F, and relative displacement, S, exhibited nearly parallelogram hysteresis loop.

2. The slip on the surface started gradually. 3. The coefficient of kinetic friction was approximately

constant independently of the number of reciprocating cycles, N.

4. The test frequency, f, may have a little influence on the coefficient of kinetic friction.

5. The relative displacement, S, may have almost no influence on the coefficient of kinetic friction.

6. Under the condition with p = 10 MPa, the coefficient of kinetic friction had a relatively large variation ranging from 0.4 to 1.0.

7. Under the condition with p = 100 MPa, the coefficient of kinetic friction was about 0.75.

Nomenclature A nominal contact area [mm2] f test frequency [Hz] F tangential force [kN] N number of cycles [cycle] p nominal contact pressure [MPa] r mean radius of hollow cylinder [mm]

S relative displacement [m] SD displacement of the driving side specimen [m] SF displacement of the fixed-end side specimen [m] t time [sec] T twisting moment [Nm] W static compressive force [kN] angular amplitude [deg] k coefficient of kinetic friction Acknowledgement This work was partly supported by JSPS KAKENHI Grant Number JP16K06057 and the NSK Foundation for the Advancement of Mechatronics. References [1] Beretta, S., Boniardi, M., Carboni, M. and Desimone,

H.: Mode II fatigue failures at rail butt-welds, Engineering Failure Analysis, 12 (2005), 157-165.

[2] Lewis, M. W. J. and Tomkins, B.: A fracture mechanics interpretation of rolling bearing fatigue, J.Engineering Tribology, 226 (2012), 389-405.

[3] Otsuka, A., Fujii, Y. and Maeda, K.: A new testing method to obtain mode II fatigue crack growth characteristics of hard materials, Fatigue & Fracture of Engineering Materials & Structures, 27 (2004), 203-212.

[4] Matsunaga, H., Shomura, N., Muramoto, S. and Endo, M.: Shear mode threshold for a small fatigue crack in a bearing steel, Fatigue & Fracture of Engineering Materials & Structures, 34 (2010), 72-82.

[5] Fujii, Y., Maeda, K. and Otsuka, A.: A new test method for mode II fatigue crack growth in hard materials (in Japanese), J. JSMS, 50-10 (2001), 1108-1113.

[6] Toyama, K., Fukushima, Y. and Murakami, Y.: Mode II fatigue crack growth mechanism and threshold in a vacuum and air (in Japanese), J. JSMS, 55-8 (2006), 719-725.

[7] Matsunaga, H., Muramoto, S., Shomura, N. and Endo, M.: Shear mode growth and threshold of small fatigue cracks in SUJ2 bearing steel (in Japanese), J. JSMS, 58-9 (2009), 773-780.

[8] Endo, M., Saito, T., Moriyama, S., Okazaki, S. and Matsunaga, H.: Friction and wear properties of heat-treated Cr-Mo steel during reciprocating sliding contact with small relative motion, International Journal of Fracture Fatigue and Wear, 3 (2015), 215-220.

1

Fatigue Strength Evaluation of Ferritic-Pearlitic Ductile Cast Iron with Notches and Holes of Various Sizes

Tomohiro DEGUCHI1, Takashi MATSUO2,3, Hyojin KIM2,3, Tomohiro IKEDA4 and Masahiro ENDO2,3 1 Graduate School of Engineering, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan

2 Department of Mechanical Engineering, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan 3 Institute of Materials Science and Technology, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan

4 R&D Center HINODE, Ltd. Iwasaki, Harakoga, Miyaki-cho, Miyaki-gun, Saga, 849-0101, Japan

(Received 10 January 2017; received in revised form 27 March 2017; accepted 29 March 2017) Abstract: The fatigue strength of ductile cast iron is influenced by small defects such as graphite particles and casting defects in the material. Therefore, establishment of a reasonable predictive method of fatigue limit applicable to various shapes and sizes of defects is necessary to optimally design the ductile cast iron products. In this study, high cycle fatigue tests of sharply notched and drill-holed specimens as well as smooth specimens were performed for a ductile cast iron, JIS-FCD550, with ferrite and pearlite evenly distributed in the matrix. From the microscopic observation of the near-threshold crack growth behavior, it was revealed that the fatigue limit is determined by the threshold condition for propagation of a small crack emanating from a detrimental defect. A predictive method of the fatigue limit was presented based on a fracture mechanics approach that was composed of three different methods classified according to the defect size. Keywords: Ferritic-pearlitic ductile cast iron, Fatigue limit, Defects, area parameter model 1. Introduction Ductile cast iron has intrinsic defects such as graphite and casting defects in the structure, which dominantly control the fatigue strength. It is known that the fatigue limit of many metallic materials with small defects can successfully be predicted based on the area parameter model by using area as a geometrical parameter of defect and the Vickers hardness HV as a material parameter [1]. However, ductile cast irons have a vast number of graphite particles in the complex matrix structure. The measurement of HV of ductile cast iron is affected by soft graphite particles, so that evaluation of HV needs special considerations in applying the area parameter model to ductile cast irons. Namely, the true hardness of matrix near the detrimental defect, which does not contain the influence of soft graphite, is necessary. Endo and Yanase [2] proposed a method for estimation of the true values of HV for JIS-FCD400, JIS-FCD600 and JIS-FCD700, and showed that the fatigue limit can be predicted by areaparameter model. In common ductile cast irons, however, ferrite and pearlite are evenly distributed in the matrix structure, and the exact measurement of true HV is impossible in some cases. Accordingly, it is very important to establish the method for evaluation of material parameter applicable to all types of ferritic-pearlitic ductile cast irons. In addition, the area parameter model is valid only for materials containing relatively small defects and the prediction of fatigue limit for large-size defects such as real casting defects also needs to be considered. In this study, we investigated the fatigue limit of ductile cast iron FCD550 with a two-phase matrix of almost evenly distributed ferrite and pearlite phases by using specimens containing various artificial defects with a wide range of sizes. Physical meaning of the fatigue limit of ductile cast iron is discussed based on the observation of

small crack behavior. The purpose of this study is to present a simple yet useful method for prediction of the fatigue limit of ductile cast irons. 2. Experimental Procedures

2.1 Material and specimens The material investigated was an as-cast ductile cast iron FCD550. The chemical composition is listed in Table 1. The microstructure is given in Fig. 1. The area fractions in the microstructure were 10.5% for graphite, 45.3% for ferrite and 44.2% for pearlite. The ultimate tensile strength (UTS) σB was 552 MPa. The shapes and dimensions of smooth specimens are shown in Fig. 2. After lathe turning of specimens, the surface was finished with an emery paper up to #1000 and then by buffing with an alumina paste. Thereafter, a small hole or a circumferential notch was introduced as shown in Fig. 3. Before the fatigue test, the surface layer of about 10 μm in thickness was removed from the specimens by electro-polishing.

Fig. 1 Microstructure

Table 1 Chemical composition, wt.% C Si Mn P S Cu Mg

3.84 2.5 0.66 0.017 0.009 0.21 0.043

Advanced Experimental Mechanics, Vol.2 (2017), 87-91

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2.2 Fatigue testing machine A rotating bending fatigue test machine of uniform moment type with an operating speed of 50-67 Hz and a capacity of 100 Nm was used. The minimum step of stress level for determining the fatigue limit was 5 MPa. The tension-compression fatigue test of deeply notched specimens (Fig. 2(b)) was conducted at the operating speed of 35 Hz and the minimum step of stress level was 2.5 MPa because the stress amplitude became smaller than 100 MPa. 3. Results and Discussion

3.1 Crack growth and non-propagation behavior The S-N diagrams of smooth, holed and circumferential-notched specimens are shown in Fig. 4. The results of specimens containing a sharp deep circumferential notch of 2500 m in depth were obtained by tension-compression fatigue tests, while those of all other specimens were obtained by rotating bending fatigue tests. The fatigue strength, including not only the fatigue limit but also the strength at a given cycles, tended to decrease as the defect size increased regardless of types of artificial defects. In smooth specimens, a great number of cracks emanated from various graphite particles. Figure 5 shows the growth and non-propagation behavior of the representative crack on the surface of a smooth specimen, which was successively observed by the replica method. The crack initiated before N = 104 cycles at a graphite particle and finally stopped propagation before N = 107 cycles after propagation and coalescence with other graphite particle．The crack length was not changed between N = 107 and N

t = 10, 100, 200 and 2500 m, = 5 and 50 m

10area t

d = h = 50, 200 and 500 m

4 3darea d h

(a) Circumferential notch (b) Drilled hole Fig. 3 Shapes and dimensions of artificial defects

(a) Rotating bending fatigue test

(b) Tension-compression fatigue test Fig. 2 Shapes and dimensions of specimens in mm

Fig. 4 S-N data

Fig. 5 Non-propagating cracks emanating from graphite particles on a surface of smooth specimen at fatigue limit of w0 = 260 MPa, which were Observed by replica method

3

= 108. The change in the crack length measured for other 8 cracks that were randomly chosen in the same specimen is shown in Fig. 6. None of those cracks changed their length between N = 107 and N = 108. In addition, Fig. 7 shows the growth and non-propagation behavior of a crack emanating from the hole edge of a holed specimen (d = h = 200 m) at fatigue limit. This crack also did not grow after 107 cycles. The non-propagation of cracks was also observed at the root of deep and shallow notches in notched specimens at each fatigue limit (Fig. 8). Therefore, all those cracks can be regarded as a non-propagating crack and it is concluded that the fatigue limit is determined by the threshold condition for

propagation of a crack, regardless of the type and size of defects

3.2 Prediction of fatigue limit of ductile cast iron The previous study [3] focused on the ultimate tensile strength (UTS) B instead of the Vickers hardness HV as a material parameter. Then the following form of predictive equation of the fatigue limit for various ductile cast irons was proposed by taking the concept of the area parameter model into account:

1/ 6

(0.34 170)( )

loc Bw

Farea

(1)

where Floc is the correction coefficient for the location of small defect being 1.43 for surface defects, 1.56 for internal defects and 1.41 for defects just in contact with the surface. w and B are in MPa and area is in μm. In the study [3], a predictive equation of fatigue limit for smooth specimens was also presented as:

0 0.25 110w B (2) Figure 9 shows a comparison of prediction by Eqs. (1) and (2) with the present experimental results for smooth specimen as well as specimens with artificial defects (cf. Figs. 2 and 3). The agreement is reasonably good. In Fig. 9, the data for the specimen with a 2500 m deep notch is not included because this defect is not in the category of small defects. It is seen that there is a critical size of defect that does not affect the fatigue strength. Defects with the areasmaller than about 80 m (region I), designated herein by

0area , are not harmful to the fatigue limit. As shown in Figs. 5 and 6, cracks initiated at graphite particles and stopped propagation at fatigue limit even in smooth specimen. Therefore, defects smaller than those non-propagating cracks are eventually harmless and these small defects can be regarded as a non-damaging defect. Figure 10 shows the non-propagating cracks observed at such non-damaging defects, which initiated at the same stress level as

Fig. 6 Relationship between length of cracks emanating from graphite particles and number of cycles

Fig. 8 Non-propagating cracks emanating from the circumferential notch at the fatigue limit, which were directly observed

Fig. 7 Non-propagating cracks observed at hole edge (d = h = 200 m) at fatigue limit of w = 220 MPa, which were Observed by replica method

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2.2 Fatigue testing machine A rotating bending fatigue test machine of uniform moment type with an operating speed of 50-67 Hz and a capacity of 100 Nm was used. The minimum step of stress level for determining the fatigue limit was 5 MPa. The tension-compression fatigue test of deeply notched specimens (Fig. 2(b)) was conducted at the operating speed of 35 Hz and the minimum step of stress level was 2.5 MPa because the stress amplitude became smaller than 100 MPa. 3. Results and Discussion

3.1 Crack growth and non-propagation behavior The S-N diagrams of smooth, holed and circumferential-notched specimens are shown in Fig. 4. The results of specimens containing a sharp deep circumferential notch of 2500 m in depth were obtained by tension-compression fatigue tests, while those of all other specimens were obtained by rotating bending fatigue tests. The fatigue strength, including not only the fatigue limit but also the strength at a given cycles, tended to decrease as the defect size increased regardless of types of artificial defects. In smooth specimens, a great number of cracks emanated from various graphite particles. Figure 5 shows the growth and non-propagation behavior of the representative crack on the surface of a smooth specimen, which was successively observed by the replica method. The crack initiated before N = 104 cycles at a graphite particle and finally stopped propagation before N = 107 cycles after propagation and coalescence with other graphite particle．The crack length was not changed between N = 107 and N

t = 10, 100, 200 and 2500 m, = 5 and 50 m

10area t

d = h = 50, 200 and 500 m

4 3darea d h

(a) Circumferential notch (b) Drilled hole Fig. 3 Shapes and dimensions of artificial defects

(a) Rotating bending fatigue test

(b) Tension-compression fatigue test Fig. 2 Shapes and dimensions of specimens in mm

Fig. 4 S-N data

Fig. 5 Non-propagating cracks emanating from graphite particles on a surface of smooth specimen at fatigue limit of w0 = 260 MPa, which were Observed by replica method

3

= 108. The change in the crack length measured for other 8 cracks that were randomly chosen in the same specimen is shown in Fig. 6. None of those cracks changed their length between N = 107 and N = 108. In addition, Fig. 7 shows the growth and non-propagation behavior of a crack emanating from the hole edge of a holed specimen (d = h = 200 m) at fatigue limit. This crack also did not grow after 107 cycles. The non-propagation of cracks was also observed at the root of deep and shallow notches in notched specimens at each fatigue limit (Fig. 8). Therefore, all those cracks can be regarded as a non-propagating crack and it is concluded that the fatigue limit is determined by the threshold condition for

propagation of a crack, regardless of the type and size of defects

3.2 Prediction of fatigue limit of ductile cast iron The previous study [3] focused on the ultimate tensile strength (UTS) B instead of the Vickers hardness HV as a material parameter. Then the following form of predictive equation of the fatigue limit for various ductile cast irons was proposed by taking the concept of the area parameter model into account:

1/ 6

(0.34 170)( )

loc Bw

Farea

(1)

where Floc is the correction coefficient for the location of small defect being 1.43 for surface defects, 1.56 for internal defects and 1.41 for defects just in contact with the surface. w and B are in MPa and area is in μm. In the study [3], a predictive equation of fatigue limit for smooth specimens was also presented as:

0 0.25 110w B (2) Figure 9 shows a comparison of prediction by Eqs. (1) and (2) with the present experimental results for smooth specimen as well as specimens with artificial defects (cf. Figs. 2 and 3). The agreement is reasonably good. In Fig. 9, the data for the specimen with a 2500 m deep notch is not included because this defect is not in the category of small defects. It is seen that there is a critical size of defect that does not affect the fatigue strength. Defects with the areasmaller than about 80 m (region I), designated herein by

0area , are not harmful to the fatigue limit. As shown in Figs. 5 and 6, cracks initiated at graphite particles and stopped propagation at fatigue limit even in smooth specimen. Therefore, defects smaller than those non-propagating cracks are eventually harmless and these small defects can be regarded as a non-damaging defect. Figure 10 shows the non-propagating cracks observed at such non-damaging defects, which initiated at the same stress level as

Fig. 6 Relationship between length of cracks emanating from graphite particles and number of cycles

Fig. 8 Non-propagating cracks emanating from the circumferential notch at the fatigue limit, which were directly observed

Fig. 7 Non-propagating cracks observed at hole edge (d = h = 200 m) at fatigue limit of w = 220 MPa, which were Observed by replica method

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the fatigue limit of smooth specimen but stopped propagation because of the stress level lower than the threshold level predicted by Eq. (1). Prediction line based on area parameter model (Eq. (1)) agreed well with the experimental results for the artificial defects with area of between about 80 m and 1000 m (region II). In the case of notched specimen containing a deep notch with the depth of 2500 m, the fatigue limit can no longer be predicted by Eq. (1). This is because the notch size is sufficiently large beyond the region II, and the threshold stress intensity factor (SIF) range, Kth should be a material constant, which is Kth for a long crack, Kth,lc. The translation between the fatigue limit range w = 2w and the threshold range Kth can be made by using the following formula derived based on the linear elastic fracture mechanics analysis [1, 4]:

I max 00.65K area (3) where KImax is the maximum value of SIF along the front of a three-dimensional surface crack with the arbitrary shape existing in a semi-infinite body with a Poisson’s ratio of 0.3 under remote tensile stress 0. Another expression of Eq. (1) for the region II is given as follows by setting KImax = Kth / 2 and 0 = w ∕ 2 = w given by Eq. (1) with Floc = 1.43:

3 1/ 33.3 10 (0.34 170)( )th BK area (4) where Kth is in MPa m , B is in MPa and area is in m. The experimental values of Kth are calculated by substituting 2w into 0 in Eq. (3). On the other hand, the Kth-value for a deep notch of 2500 m in depth is calculated to be Kth,lc = 13.5 MPa m with the fatigue limit range of 0 = 2w = 105 MPa based on the Benthem and Koiter equation [5]. According to the previous studies [6-8], the Kth,lc-value was obtained to be 10-12 MPa m for ferritic–pearlitic DCIs based on the fatigue crack growth

tests using a CT specimen at a stress ratio of R = 0.1. The value of Kth,lc = 13.5 MPa m obtained at R = -1 in this study is thought to be reasonable considering the effect of stress ratio. Figure 11 shows the relationship between Kth and area . The experimental data for 2500 m deep notch is not plotted in Fig. 11 since the value of area cannot be defined. The transition value of area ( )transarea which means the boundary between region II and III is obtained to be about 1500 m by putting Kth,lc = 13.5 MPa m into Eq. (4) with B = 552 MPa. In the region III of

transarea area , where Kth is constant, the fatigue limit can in general be predicted based on the conventional

Fig. 11 Relationship between Kth and area

Fig. 9 Relationship between fatigue limit and area of artificial defect

Fig. 10 Non-propagating cracks emanating from drilled hole (d = h = 50 m, area = 46.3 m) and circumferential notch ( = 5 m, t = 10 m, area = 31.6 m) at the fatigue limit of w0 = 260 MPa, N = 108, which are directly observed

5

fracture mechanics approach established for large (long) cracks. 4. Conclusions The fatigue strength of ferritic and pearlitic ductile cast iron containing a defect with a wide range of sizes was investigated. The principal results and conclusions are as follows: (1) From the microscopic observation of crack growth, it is

revealed that the fatigue limit is determined by the threshold condition for propagation of a crack emanating from the largest defect, regardless of type and size of defect.

(2) The effect of defects on the fatigue limit can be classified

into three regions depending on the defect size. In the first region where the area of defect is smaller than about 80 m, comparable to the size of non-propagating crack present in smooth specimen, the defect can be regarded as a non-damaging defect and the fatigue limit is the same as that of smooth specimen.

(3) In the second region where the area of defect is

between about 80 m and 1500 m, the fatigue limit can be quantitatively predicted based on the area parameter model in terms of a geometrical parameter of defects

area and a material parameter, i.e. tensile strength B. (4) In the third region in which the area of defect is greater

than about 1500 m, the threshold stress intensity factor range, Kth becomes a material constant (Kth,lc = 13.5 MPa m ) and the fatigue limit can be estimated based on the conventional fracture mechanics approach.

Nomenclature notch root radius [m] t depth of circumferential notch [m] d diameter of hole [m] h depth of hole [m] N number of cycles [cycles] B ultimate tensile strength [MPa] w fatigue limit of specimen containing artificial

defect [MPa] w0 fatigue limit of smooth specimen [MPa] F, Floc correction coefficient [-]

Kth threshold stress intensity factor (SIF) range [ MPa m ]

Kth,lc Kth for a long crack [ MPa m ] area square root of the area which occupied by

projecting a defect or a crack onto the maximum tensile plane [m]

0area area at the boundary between region I and II [m]

transarea area at the boundary between region II and III [m]

References [1] Murakami, Y.: Metal Fatigue: Effects of Small Defects

and Nonmetallic Inclusions, Elsevier (2002). [2] Endo, M. and Yanase, K.: Effects of small defect,

matrix structures and loading conditions on the fatigue strength of ductile cast irons, Theor. Appl. Fract. Mec., 69 (2014), 34-43.

[3] Deguchi, T., Matsuo, T., Takemoto, S., Ikeda, T. and Endo, M.: Effects of graphite and artificial defects on the fatigue strength of ferritic-pearlitic ductile cast iron, Asia-Pacific Conference on Fracture and Strength 2016, (2016), 149-150.

[4] Murakami, Y. and Endo, M.: Quantitative evaluation of fatigue strength of metals containing various small defects or cracks, Eng. Fract. Mech., 17 (1983), 1-15.

[5] Benthem, J. P. and Koiter, W. T.: Asymptotic Approximations to Crack Problems. In: Mechanics of Fracture, Vol. 1: Methods of Analysis and Solutions of Crack Problems (Sih, G. C. ed.), Noordhoff. International Publishers, Leyden (1973), 131-178.

[6] Ito, I., Sugiyama, Y., Asami, K. and Yamada, S.: Fatigue crack propagation characteristics of spheroidal graphite cast iron, J. Soc. Mater. Sci., Japan, 36 (1987), 369-375.

[7] Sugiyama, Y., Asami, K. and Kuroiwa, H.: Fatigue crack propagation characteristics of spheroidal graphite cast irons with various dual phase matrix microstructures, Trans. Jap. Soc. Mech. Eng. A, 56 (1990), 482-487.

[8] Yamabe, J. and Kobayashi, M.: Effect of hardness and stress ratio on threshold stress intensity factor ranges for small cracks and long cracks in spheroidal cast irons, The Japan Society of Mechanical Engineers, Journal of Solid Mechanics and Materials Engineering, 1-5 (2007), 667-678.

T. DEGUCHI, T. MATSUO, H. KIM, T. IKEDA and M. ENDO

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the fatigue limit of smooth specimen but stopped propagation because of the stress level lower than the threshold level predicted by Eq. (1). Prediction line based on area parameter model (Eq. (1)) agreed well with the experimental results for the artificial defects with area of between about 80 m and 1000 m (region II). In the case of notched specimen containing a deep notch with the depth of 2500 m, the fatigue limit can no longer be predicted by Eq. (1). This is because the notch size is sufficiently large beyond the region II, and the threshold stress intensity factor (SIF) range, Kth should be a material constant, which is Kth for a long crack, Kth,lc. The translation between the fatigue limit range w = 2w and the threshold range Kth can be made by using the following formula derived based on the linear elastic fracture mechanics analysis [1, 4]:

I max 00.65K area (3) where KImax is the maximum value of SIF along the front of a three-dimensional surface crack with the arbitrary shape existing in a semi-infinite body with a Poisson’s ratio of 0.3 under remote tensile stress 0. Another expression of Eq. (1) for the region II is given as follows by setting KImax = Kth / 2 and 0 = w ∕ 2 = w given by Eq. (1) with Floc = 1.43:

3 1/ 33.3 10 (0.34 170)( )th BK area (4) where Kth is in MPa m , B is in MPa and area is in m. The experimental values of Kth are calculated by substituting 2w into 0 in Eq. (3). On the other hand, the Kth-value for a deep notch of 2500 m in depth is calculated to be Kth,lc = 13.5 MPa m with the fatigue limit range of 0 = 2w = 105 MPa based on the Benthem and Koiter equation [5]. According to the previous studies [6-8], the Kth,lc-value was obtained to be 10-12 MPa m for ferritic–pearlitic DCIs based on the fatigue crack growth

tests using a CT specimen at a stress ratio of R = 0.1. The value of Kth,lc = 13.5 MPa m obtained at R = -1 in this study is thought to be reasonable considering the effect of stress ratio. Figure 11 shows the relationship between Kth and area . The experimental data for 2500 m deep notch is not plotted in Fig. 11 since the value of area cannot be defined. The transition value of area ( )transarea which means the boundary between region II and III is obtained to be about 1500 m by putting Kth,lc = 13.5 MPa m into Eq. (4) with B = 552 MPa. In the region III of

transarea area , where Kth is constant, the fatigue limit can in general be predicted based on the conventional

Fig. 11 Relationship between Kth and area

Fig. 9 Relationship between fatigue limit and area of artificial defect

Fig. 10 Non-propagating cracks emanating from drilled hole (d = h = 50 m, area = 46.3 m) and circumferential notch ( = 5 m, t = 10 m, area = 31.6 m) at the fatigue limit of w0 = 260 MPa, N = 108, which are directly observed

5

fracture mechanics approach established for large (long) cracks. 4. Conclusions The fatigue strength of ferritic and pearlitic ductile cast iron containing a defect with a wide range of sizes was investigated. The principal results and conclusions are as follows: (1) From the microscopic observation of crack growth, it is

revealed that the fatigue limit is determined by the threshold condition for propagation of a crack emanating from the largest defect, regardless of type and size of defect.

(2) The effect of defects on the fatigue limit can be classified

into three regions depending on the defect size. In the first region where the area of defect is smaller than about 80 m, comparable to the size of non-propagating crack present in smooth specimen, the defect can be regarded as a non-damaging defect and the fatigue limit is the same as that of smooth specimen.

(3) In the second region where the area of defect is

between about 80 m and 1500 m, the fatigue limit can be quantitatively predicted based on the area parameter model in terms of a geometrical parameter of defects

area and a material parameter, i.e. tensile strength B. (4) In the third region in which the area of defect is greater

than about 1500 m, the threshold stress intensity factor range, Kth becomes a material constant (Kth,lc = 13.5 MPa m ) and the fatigue limit can be estimated based on the conventional fracture mechanics approach.

Nomenclature notch root radius [m] t depth of circumferential notch [m] d diameter of hole [m] h depth of hole [m] N number of cycles [cycles] B ultimate tensile strength [MPa] w fatigue limit of specimen containing artificial

defect [MPa] w0 fatigue limit of smooth specimen [MPa] F, Floc correction coefficient [-]

Kth threshold stress intensity factor (SIF) range [ MPa m ]

Kth,lc Kth for a long crack [ MPa m ] area square root of the area which occupied by

projecting a defect or a crack onto the maximum tensile plane [m]

0area area at the boundary between region I and II [m]

transarea area at the boundary between region II and III [m]

References [1] Murakami, Y.: Metal Fatigue: Effects of Small Defects

and Nonmetallic Inclusions, Elsevier (2002). [2] Endo, M. and Yanase, K.: Effects of small defect,

matrix structures and loading conditions on the fatigue strength of ductile cast irons, Theor. Appl. Fract. Mec., 69 (2014), 34-43.

[3] Deguchi, T., Matsuo, T., Takemoto, S., Ikeda, T. and Endo, M.: Effects of graphite and artificial defects on the fatigue strength of ferritic-pearlitic ductile cast iron, Asia-Pacific Conference on Fracture and Strength 2016, (2016), 149-150.

[4] Murakami, Y. and Endo, M.: Quantitative evaluation of fatigue strength of metals containing various small defects or cracks, Eng. Fract. Mech., 17 (1983), 1-15.

[5] Benthem, J. P. and Koiter, W. T.: Asymptotic Approximations to Crack Problems. In: Mechanics of Fracture, Vol. 1: Methods of Analysis and Solutions of Crack Problems (Sih, G. C. ed.), Noordhoff. International Publishers, Leyden (1973), 131-178.

[6] Ito, I., Sugiyama, Y., Asami, K. and Yamada, S.: Fatigue crack propagation characteristics of spheroidal graphite cast iron, J. Soc. Mater. Sci., Japan, 36 (1987), 369-375.

[7] Sugiyama, Y., Asami, K. and Kuroiwa, H.: Fatigue crack propagation characteristics of spheroidal graphite cast irons with various dual phase matrix microstructures, Trans. Jap. Soc. Mech. Eng. A, 56 (1990), 482-487.

[8] Yamabe, J. and Kobayashi, M.: Effect of hardness and stress ratio on threshold stress intensity factor ranges for small cracks and long cracks in spheroidal cast irons, The Japan Society of Mechanical Engineers, Journal of Solid Mechanics and Materials Engineering, 1-5 (2007), 667-678.

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