Investigation of Friction and Surface Damage of Bearing ...

1

Investigation of Friction and Surface Damage of Bearing Steel in Cyclic Reciprocating Sliding Contact by Making Use of Fatigue Testing Machine

Yuya TANAKA1, Masahiro ENDO2, 3 and Shigeaki MORIYAMA2, 3

1 Graduate School of Engineering, Fukuoka University, Fukuoka 814-0180, Japan 2 Department of Mechanical Engineering, Fukuoka University, Fukuoka 814-0180, Japan

3 Institute of Materials Science and Technology, Fukuoka University, Fukuoka 814-0180, Japan

(Received 10 January 2017; received in revised form 3 April 2017; accepted 11 April 2017) Abstract: Rolling contact machine elements like bearing, gear wheel and railway rail have a problem of delamination failure such as flaking, pitting and shelling. It is known that this failure is closely related to shear-mode (mode II and mode III) as well as opening-mode (mode I) fatigue crack growth. In general, the shear-mode fatigue crack growth and its threshold behavior can be significantly influenced by the interaction of opposing crack faces. Therefore, understanding of the mechanism of friction and surface damage of crack faces is essential and a novel testing method that can estimate appropriately these properties is required. In this study, the influences of the cyclic reciprocating sliding contact with micro-scale relative motion on the frictional behavior and the surface damage of a bearing steel were studied under dry condition. The material investigated was a heat-treated high carbon-chromium bearing steel (JIS SUJ2). As a new friction and wear testing method, a cyclic ring-on-ring test was performed by making use of a hydraulic-controlled combined axial and torsional fatigue testing machine. The coefficient of kinetic friction was ranged from 0.4 to 1.0 and its average value was about 0.75. Keywords: Shear-mode fatigue crack growth, Bearing steel, Ring-on-ring test, Coefficient of kinetic friction, Damage of contact surface 1. Introduction Delamination failure is one of the most important engineering issues for rolling contact machine elements such as bearing, gear wheel and railway rail. For instance, to maintain the quality of high-integrity bearings, the statistical method and empirical rule based on the experiments with a large number of real products are employed for each redesign as affairs stand. However, this design procedure is time-consuming and costly, and even worse it has no applicability to massive products such as a bearing used for a wind generator. Consequently, an innovative change of design procedure is demanded all over the world. This demand is not only for bearing but also for other machine elements production. In specific, a new design method using fracture mechanics is required to achieve a rational design based on mechanics.

On the other hand, it is known that the delamination failure is highly related to shear-mode (mode II and mode III) as well as opening-mode (mode I) fatigue crack growth [1-4]. Generally, the mutual effect of opposing crack faces (i.e., crack face interference) can have a significant influence on the shear-mode fatigue crack propagation and the threshold behavior. In the literature, the shear-mode threshold stress intensity factor ranges, Kth, were reported, but there is the discrepancy in these values due to the different treatment of crack face interference [3-7]. Therefore, it is essential to understand the mechanism of friction and wear on crack faces. However, it is difficult to conduct a quantitative research for friction and wear on real crack faces in material. For this reason, a fundamental study with a relatively simple experimental setup is needed. Moreover, it is reasonable to carry out the tests with two surfaces to mimic the crack faces that undergo the cyclic reciprocating sliding contact. In our previous study [8], the

ring-on-ring test method, in which two end faces of cylinders were bilaterally contacted and relatively cyclically slid by using a servo-hydraulic combined axial and torsional high cycle fatigue testing machine, was developed. This procedure has some merits such as the non-existence of boundary edge of contact surfaces and the flexibility of settings for contact pressure, tangential force, relative displacement and cyclic frequency during the test. In addition, it is straightforward to define the coefficient of friction that represents frictional property between contact surfaces, and one can easily determine the coefficient as functions of contact pressure, number of cycles and relative displacement. In the previous study [8], the cyclic reciprocating relative slip contact tests for heat-treated Cr-Mo steel (JIS SCM435) were conducted with the micro-meter level of relative displacement.

In this study, the coefficients of kinetic friction of bearing steel were measured under comparatively high pressure condition because a very large pressure above 1 GPa is frequently imposed on the actual crack surface in bearings. Furthermore, the contact surfaces after the test were observed by using an optical microscope to inspect the relation between the surface roughness and the value of coefficient. 2. Experimental Method The material investigated was a JIS SUJ2 (high C-Cr bearing steel), which was held at 840 °C for 30 minutes, oil-hardened and then tempered at 170 °C. Table 1 shows the chemical composition in mass%. The Vickers hardness, HV, measured with a load of 9.8 N was 753. Figure 1 shows the shape and dimensions of the specimen. The end surfaces of hollow cylinders were finished by polishing with emery papers and then buffing with an alumina paste.

2

An MTS servo-hydraulic combined axial and torsional fatigue testing machine was used to conduct the ring-on-ring test, as shown by Fig. 2. This machine was designed to carry out the high cycle fatigue test in which axial force or displacement and torsional torque or angle were flexibly superimposed. The capacities are 100 kN for axial load and 1000 Nm for twisting moment. The operating frequency, f, can be applied up to 60 Hz.

In this experiment, the end faces of hollow cylinders shown in Fig. 1 were attached to each other and the static compressive axial force was applied. While maintaining this state, the sinusoidal displacement with constant angular amplitude, was applied by rotating the specimen at the driving side under the control of angular displacement, as illustrated in Fig. 2. The reciprocating relative sliding motion was generated on the contact surfaces. The test was conducted at room temperature under dry condition.

In this tests, the nominal contact pressure, p, was defined as

p = W / A (1) where W is the static compressive force measured by a load cell equipped in the testing machine, and A is the nominal contact area for which a value of 44.0 mm2 was used for the calculation. The tangential force, F, was defined as

F = T / r (2) where T is the twisting moment measured by the load cell, and r is the mean radius of hollow cylinder. Its nominal value of 7.0 mm was used. The relative displacement between the contact surfaces, S, was defined as

S = SD − SF (3) In this equation, SD and SF are the displacements of the driving side specimen and the fixed-end side specimen, respectively. These displacements were measured by a laser displacement meter (KEYENCE: LK-H020). A mirrored thin plate made from cermet tip was used as a target of laser light (cf. Fig. 2), and the target was attached to the jig made by a 3D-printer, as shown by Fig. 3. The material of jig was light ABS resin, so its inertia was negligibly small. The jig was mounted on the specimen surface with a distance of about 2 mm from the edge of hollow cylinder. 4-point support was used to fix the jig to the specimen (cf. Figs. 2 and 3).

The uniform contact on the contact surface is necessary during the test, but it was not so at the initial contact. Therefore, to attain the condition of uniform contact before starting the test, the contact condition was checked and adjusted by using a pressure-sensitive paper. Then, the contact surfaces were rubbed to each other under p = 25 MPa, = 10 deg, f = 1 Hz and the number of reciprocating cycles, N, ≈ 1000 cycles. Thereafter, uniform contact was checked by a pressure-sensitive paper again. Figure 4 shows the papers after checking the contact states. The

situation got better by only changing the relative position between the specimens (cf. Figs. 4 (a) and (b)). Furthermore, the uniform contact was achieved appropriately (cf. Fig.4 (c)). Accordingly, the contact surfaces were already worn by rubbing before the actual test. Finally, the tests were conducted after removing the debris from the contact surface.

Table 1 Chemical composition of SUJ2 in mass% C Si Mn P S Cu

1.01 0.25 0.34 0.017 0.007 0.10 Ni Cr Mo O2 Ti

0.05 1.41 0.03 5 ppm 20 ppm

Fig. 1 Shape and dimensions of specimen Fig. 2 Configuration of specimens and devices for measurement

Fig. 3 Shape of jig for a target of laser light

Advanced Experimental Mechanics, Vol.2 (2017), 82-86

Copyright Ⓒ 2017 JSEM

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Investigation of Friction and Surface Damage of Bearing Steel in Cyclic Reciprocating Sliding Contact by Making Use of Fatigue Testing Machine

Yuya TANAKA1, Masahiro ENDO2, 3 and Shigeaki MORIYAMA2, 3

1 Graduate School of Engineering, Fukuoka University, Fukuoka 814-0180, Japan 2 Department of Mechanical Engineering, Fukuoka University, Fukuoka 814-0180, Japan

3 Institute of Materials Science and Technology, Fukuoka University, Fukuoka 814-0180, Japan

(Received 10 January 2017; received in revised form 3 April 2017; accepted 11 April 2017) Abstract: Rolling contact machine elements like bearing, gear wheel and railway rail have a problem of delamination failure such as flaking, pitting and shelling. It is known that this failure is closely related to shear-mode (mode II and mode III) as well as opening-mode (mode I) fatigue crack growth. In general, the shear-mode fatigue crack growth and its threshold behavior can be significantly influenced by the interaction of opposing crack faces. Therefore, understanding of the mechanism of friction and surface damage of crack faces is essential and a novel testing method that can estimate appropriately these properties is required. In this study, the influences of the cyclic reciprocating sliding contact with micro-scale relative motion on the frictional behavior and the surface damage of a bearing steel were studied under dry condition. The material investigated was a heat-treated high carbon-chromium bearing steel (JIS SUJ2). As a new friction and wear testing method, a cyclic ring-on-ring test was performed by making use of a hydraulic-controlled combined axial and torsional fatigue testing machine. The coefficient of kinetic friction was ranged from 0.4 to 1.0 and its average value was about 0.75. Keywords: Shear-mode fatigue crack growth, Bearing steel, Ring-on-ring test, Coefficient of kinetic friction, Damage of contact surface 1. Introduction Delamination failure is one of the most important engineering issues for rolling contact machine elements such as bearing, gear wheel and railway rail. For instance, to maintain the quality of high-integrity bearings, the statistical method and empirical rule based on the experiments with a large number of real products are employed for each redesign as affairs stand. However, this design procedure is time-consuming and costly, and even worse it has no applicability to massive products such as a bearing used for a wind generator. Consequently, an innovative change of design procedure is demanded all over the world. This demand is not only for bearing but also for other machine elements production. In specific, a new design method using fracture mechanics is required to achieve a rational design based on mechanics.

On the other hand, it is known that the delamination failure is highly related to shear-mode (mode II and mode III) as well as opening-mode (mode I) fatigue crack growth [1-4]. Generally, the mutual effect of opposing crack faces (i.e., crack face interference) can have a significant influence on the shear-mode fatigue crack propagation and the threshold behavior. In the literature, the shear-mode threshold stress intensity factor ranges, Kth, were reported, but there is the discrepancy in these values due to the different treatment of crack face interference [3-7]. Therefore, it is essential to understand the mechanism of friction and wear on crack faces. However, it is difficult to conduct a quantitative research for friction and wear on real crack faces in material. For this reason, a fundamental study with a relatively simple experimental setup is needed. Moreover, it is reasonable to carry out the tests with two surfaces to mimic the crack faces that undergo the cyclic reciprocating sliding contact. In our previous study [8], the

ring-on-ring test method, in which two end faces of cylinders were bilaterally contacted and relatively cyclically slid by using a servo-hydraulic combined axial and torsional high cycle fatigue testing machine, was developed. This procedure has some merits such as the non-existence of boundary edge of contact surfaces and the flexibility of settings for contact pressure, tangential force, relative displacement and cyclic frequency during the test. In addition, it is straightforward to define the coefficient of friction that represents frictional property between contact surfaces, and one can easily determine the coefficient as functions of contact pressure, number of cycles and relative displacement. In the previous study [8], the cyclic reciprocating relative slip contact tests for heat-treated Cr-Mo steel (JIS SCM435) were conducted with the micro-meter level of relative displacement.

In this study, the coefficients of kinetic friction of bearing steel were measured under comparatively high pressure condition because a very large pressure above 1 GPa is frequently imposed on the actual crack surface in bearings. Furthermore, the contact surfaces after the test were observed by using an optical microscope to inspect the relation between the surface roughness and the value of coefficient. 2. Experimental Method The material investigated was a JIS SUJ2 (high C-Cr bearing steel), which was held at 840 °C for 30 minutes, oil-hardened and then tempered at 170 °C. Table 1 shows the chemical composition in mass%. The Vickers hardness, HV, measured with a load of 9.8 N was 753. Figure 1 shows the shape and dimensions of the specimen. The end surfaces of hollow cylinders were finished by polishing with emery papers and then buffing with an alumina paste.

2

An MTS servo-hydraulic combined axial and torsional fatigue testing machine was used to conduct the ring-on-ring test, as shown by Fig. 2. This machine was designed to carry out the high cycle fatigue test in which axial force or displacement and torsional torque or angle were flexibly superimposed. The capacities are 100 kN for axial load and 1000 Nm for twisting moment. The operating frequency, f, can be applied up to 60 Hz.

In this experiment, the end faces of hollow cylinders shown in Fig. 1 were attached to each other and the static compressive axial force was applied. While maintaining this state, the sinusoidal displacement with constant angular amplitude, was applied by rotating the specimen at the driving side under the control of angular displacement, as illustrated in Fig. 2. The reciprocating relative sliding motion was generated on the contact surfaces. The test was conducted at room temperature under dry condition.

In this tests, the nominal contact pressure, p, was defined as

p = W / A (1) where W is the static compressive force measured by a load cell equipped in the testing machine, and A is the nominal contact area for which a value of 44.0 mm2 was used for the calculation. The tangential force, F, was defined as

F = T / r (2) where T is the twisting moment measured by the load cell, and r is the mean radius of hollow cylinder. Its nominal value of 7.0 mm was used. The relative displacement between the contact surfaces, S, was defined as

S = SD − SF (3) In this equation, SD and SF are the displacements of the driving side specimen and the fixed-end side specimen, respectively. These displacements were measured by a laser displacement meter (KEYENCE: LK-H020). A mirrored thin plate made from cermet tip was used as a target of laser light (cf. Fig. 2), and the target was attached to the jig made by a 3D-printer, as shown by Fig. 3. The material of jig was light ABS resin, so its inertia was negligibly small. The jig was mounted on the specimen surface with a distance of about 2 mm from the edge of hollow cylinder. 4-point support was used to fix the jig to the specimen (cf. Figs. 2 and 3).

The uniform contact on the contact surface is necessary during the test, but it was not so at the initial contact. Therefore, to attain the condition of uniform contact before starting the test, the contact condition was checked and adjusted by using a pressure-sensitive paper. Then, the contact surfaces were rubbed to each other under p = 25 MPa, = 10 deg, f = 1 Hz and the number of reciprocating cycles, N, ≈ 1000 cycles. Thereafter, uniform contact was checked by a pressure-sensitive paper again. Figure 4 shows the papers after checking the contact states. The

situation got better by only changing the relative position between the specimens (cf. Figs. 4 (a) and (b)). Furthermore, the uniform contact was achieved appropriately (cf. Fig.4 (c)). Accordingly, the contact surfaces were already worn by rubbing before the actual test. Finally, the tests were conducted after removing the debris from the contact surface.

Table 1 Chemical composition of SUJ2 in mass% C Si Mn P S Cu

1.01 0.25 0.34 0.017 0.007 0.10 Ni Cr Mo O2 Ti

0.05 1.41 0.03 5 ppm 20 ppm

Fig. 1 Shape and dimensions of specimen Fig. 2 Configuration of specimens and devices for measurement

Fig. 3 Shape of jig for a target of laser light

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(a) (b)

(c) Fig. 4 The contact conditions on the same surfaces, (a) the worst contact condition before the rubbing, (b) the improved contact condition after adjusting by rotating the driving side specimen and (c) the uniform contact condition after the rubbing 3. Results and Discussion

3.1 Measurement of coefficient of kinetic friction Figure 5 (a) shows the change of the tangential force, F, and the relative displacement, S, as a function of time, t, which were measured under p = 100 MPa, f = 1 Hz, = 1 deg and N ≈ 100 cycles after the start of the test. The variation of S was approximately sinusoidal curve, but that of F was similar to rectangular waveform.

Figure 5 (b) shows the relationship between F and S in the dashed area of Fig. 5 (a). This relationship between F and S exhibited approximately a parallelogram hysteresis loop. The horizontal lines surrounded by the dotted frames in Fig. 5 (b) indicate the regions of entire slip happened all over the contact surfaces. An expected relationship between F and S for hollow tubular specimen calculated assuming a full adhesion is shown as a straight line in Fig. 5 (b). The vertical linear portion of experimentally-obtained relationship coincides with the calculated line. In this region, therefore, no virtual slippage is considered to take place. However, the initial point of the entire slip was not well-defined, suggesting the gradual start of slip on the contact surface. In this study, the coefficient of kinetic friction for the entire slip was defined as

k = Fkm / W (4) where Fkm is the mean value of tangential force during the entire slip.

Figure 6 shows the relationships between k and N that were observed under p = 100 MPa, f = 1 Hz and = 1 deg. They were measured at N = 10, 100, 1000 and 10000 cycles, respectively. As shown by Fig. 6, the coefficient

under this condition is almost constant and its value is about 0.8. Fig. 5 (a) Variation of tangential force, F, and relative displacement, S, as a function of time, t, and (b) relationship between F and S, which were observed at N = 100 cycles under p = 100 MPa, f = 1 Hz and = 1 deg Fig. 6 Relationship between k and N that were observed under p = 100 MPa, f = 1 Hz and = 1 deg

F vs S for complete adhesion (calculation)

(b)

Region of entire slip

k = 0.8

(a)

F S

4

3.2 Effects of test conditions In this study, the effects of the test conditions on the coefficient of friction were investigated. In particular, the tests were conducted under the respective test conditions in which only one of parameters of the test was changed from the basic setup. The basic setup was p = 100 MPa, f = 1 Hz and = 1 deg. These parameters were changed as p = 10 or 100 MPa, f = 0.1 or 1 Hz and = 1 or 5 deg. Figure 7 shows the test results as a function of N. As shown by Fig. 7, the coefficients, k, under p = 100 MPa are approximately same level and fall within a narrow band ranging from 0.6 to 0.9 (the average value of k ≈ 0.75), though the test frequency or sliding speed is appeared to have a little influence on the value of k. Furthermore, the sliding distance may exert almost no influence on k. On the other hand, it is appeared that k under p = 10 MPa have larger variation than under p = 100 MPa. In the following section, this variation is briefly discussed.

3.3 Observation of contact surfaces It is likely that the surface damage caused by prior rubbing under p = 25 MPa affects the actual test results under p = 10 MPa. For systematic investigation of the effect of this damage, however, further development of measuring techniques is necessary. In this paper, in order to seek the reason for the large scatter of the test results under p = 10 MPa, the contact surfaces were observed by using an optical microscope. Figures 8, 9 and 10 show the worn surfaces tested under p = 10 MPa, f = 1 Hz and = 1 deg. The mean values of the coefficient were about 0.95 for the surface shown by Fig. 8 and 0.5 for the surfaces shown by Figs. 9 and 10. Note that the surface roughness shown in Figs. 9 and 10 are apparently different from each other.

By comparing Fig. 8 with Fig. 9, the roughness of the surface exhibited by Fig. 8 is relatively higher. In general, the coefficient of friction becomes larger with increase of the surface roughness. At present, it is not clear that the difference of roughness caused the discrepancy of the coefficient in Fig. 7. Furthermore, the contact surface shown in Fig. 10 has the roughest surface but its coefficient value is the lowest. The surface roughness of the above worn surfaces was almost unchanged after removing debris on the surfaces by acetone with absorbent cotton probably because of strong adhesion. Therefore, it seems that under the condition of p = 10 MPa, the roughness does not have an influence on the kinetic coefficient.

In addition, as shown by Fig. 7, k under p = 10 MPa has a distinct and relatively large variation (i.e., 0.4 < k < 1.0). It is suspected that this result was caused by the lack of test samples. Note that the number of samples for each experimental condition is insufficient to statistically estimate the value of the coefficient for bearing steel under cyclic reciprocating sliding with dry condition. It is expected that the intermediate value of k (i.e., k ≈ 0.7) could be measured in the future experiments.

Fig. 7 Variation of coefficient of kinetic friction under different test condition Fig. 8 Worn surface observed at N = 104 cycles under the conditions of p = 10 MPa, f = 1 Hz, = 1 deg and k ≈ 0.95 Fig. 9 Worn surface observed at N = 104 cycles under the same condition with Fig. 8 and k ≈ 0.5

Y. TANAKA, M. ENDO and S. MORIYAMA

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(a) (b)

(c) Fig. 4 The contact conditions on the same surfaces, (a) the worst contact condition before the rubbing, (b) the improved contact condition after adjusting by rotating the driving side specimen and (c) the uniform contact condition after the rubbing 3. Results and Discussion

3.1 Measurement of coefficient of kinetic friction Figure 5 (a) shows the change of the tangential force, F, and the relative displacement, S, as a function of time, t, which were measured under p = 100 MPa, f = 1 Hz, = 1 deg and N ≈ 100 cycles after the start of the test. The variation of S was approximately sinusoidal curve, but that of F was similar to rectangular waveform.

Figure 5 (b) shows the relationship between F and S in the dashed area of Fig. 5 (a). This relationship between F and S exhibited approximately a parallelogram hysteresis loop. The horizontal lines surrounded by the dotted frames in Fig. 5 (b) indicate the regions of entire slip happened all over the contact surfaces. An expected relationship between F and S for hollow tubular specimen calculated assuming a full adhesion is shown as a straight line in Fig. 5 (b). The vertical linear portion of experimentally-obtained relationship coincides with the calculated line. In this region, therefore, no virtual slippage is considered to take place. However, the initial point of the entire slip was not well-defined, suggesting the gradual start of slip on the contact surface. In this study, the coefficient of kinetic friction for the entire slip was defined as

k = Fkm / W (4) where Fkm is the mean value of tangential force during the entire slip.

Figure 6 shows the relationships between k and N that were observed under p = 100 MPa, f = 1 Hz and = 1 deg. They were measured at N = 10, 100, 1000 and 10000 cycles, respectively. As shown by Fig. 6, the coefficient

under this condition is almost constant and its value is about 0.8. Fig. 5 (a) Variation of tangential force, F, and relative displacement, S, as a function of time, t, and (b) relationship between F and S, which were observed at N = 100 cycles under p = 100 MPa, f = 1 Hz and = 1 deg Fig. 6 Relationship between k and N that were observed under p = 100 MPa, f = 1 Hz and = 1 deg

F vs S for complete adhesion (calculation)

(b)

Region of entire slip

k = 0.8

(a)

F S

4

3.2 Effects of test conditions In this study, the effects of the test conditions on the coefficient of friction were investigated. In particular, the tests were conducted under the respective test conditions in which only one of parameters of the test was changed from the basic setup. The basic setup was p = 100 MPa, f = 1 Hz and = 1 deg. These parameters were changed as p = 10 or 100 MPa, f = 0.1 or 1 Hz and = 1 or 5 deg. Figure 7 shows the test results as a function of N. As shown by Fig. 7, the coefficients, k, under p = 100 MPa are approximately same level and fall within a narrow band ranging from 0.6 to 0.9 (the average value of k ≈ 0.75), though the test frequency or sliding speed is appeared to have a little influence on the value of k. Furthermore, the sliding distance may exert almost no influence on k. On the other hand, it is appeared that k under p = 10 MPa have larger variation than under p = 100 MPa. In the following section, this variation is briefly discussed.

3.3 Observation of contact surfaces It is likely that the surface damage caused by prior rubbing under p = 25 MPa affects the actual test results under p = 10 MPa. For systematic investigation of the effect of this damage, however, further development of measuring techniques is necessary. In this paper, in order to seek the reason for the large scatter of the test results under p = 10 MPa, the contact surfaces were observed by using an optical microscope. Figures 8, 9 and 10 show the worn surfaces tested under p = 10 MPa, f = 1 Hz and = 1 deg. The mean values of the coefficient were about 0.95 for the surface shown by Fig. 8 and 0.5 for the surfaces shown by Figs. 9 and 10. Note that the surface roughness shown in Figs. 9 and 10 are apparently different from each other.

By comparing Fig. 8 with Fig. 9, the roughness of the surface exhibited by Fig. 8 is relatively higher. In general, the coefficient of friction becomes larger with increase of the surface roughness. At present, it is not clear that the difference of roughness caused the discrepancy of the coefficient in Fig. 7. Furthermore, the contact surface shown in Fig. 10 has the roughest surface but its coefficient value is the lowest. The surface roughness of the above worn surfaces was almost unchanged after removing debris on the surfaces by acetone with absorbent cotton probably because of strong adhesion. Therefore, it seems that under the condition of p = 10 MPa, the roughness does not have an influence on the kinetic coefficient.

In addition, as shown by Fig. 7, k under p = 10 MPa has a distinct and relatively large variation (i.e., 0.4 < k < 1.0). It is suspected that this result was caused by the lack of test samples. Note that the number of samples for each experimental condition is insufficient to statistically estimate the value of the coefficient for bearing steel under cyclic reciprocating sliding with dry condition. It is expected that the intermediate value of k (i.e., k ≈ 0.7) could be measured in the future experiments.

Fig. 7 Variation of coefficient of kinetic friction under different test condition Fig. 8 Worn surface observed at N = 104 cycles under the conditions of p = 10 MPa, f = 1 Hz, = 1 deg and k ≈ 0.95 Fig. 9 Worn surface observed at N = 104 cycles under the same condition with Fig. 8 and k ≈ 0.5

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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.

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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

Y. TANAKA, M. ENDO and S. MORIYAMA

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