The effect of the residual stresses generated by surface finishing methods on the very high cycle fatigue behavior of matrix HSS

International Journal of Fatigue 33 (2011) 122–131

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The effect of the residual stresses generated by surface finishing methods on the very high cycle fatigue behavior of matrix HSS Yuuji Shimatani a, Kazuaki Shiozawa a,*, Takehiro Nakada b, Takashi Yoshimoto c, Liantao Lu d a

Graduate School of Science and Engineering, University of Toyama, Toyama 930-8555, Japan Yamaha Motor Co. Ltd., Shizuoka 438-8501, Japan c Kanazawa Institute of Technology, Ishikawa 921-8501, Japan d State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China b

a r t i c l e

i n f o

Article history: Received 29 November 2009 Received in revised form 12 July 2010 Accepted 15 July 2010 Available online 18 July 2010 Keywords: Very high cycle fatigue Subsurface crack Residual stress Inclusion Failure mode

a b s t r a c t To investigate the fatigue properties of matrix high-speed tool steel (0.7C–0.1W–3Mo–2V) under very high cycle fatigue regimes, cantilever-type rotating bending fatigue tests were carried out on hour-glass shaped specimens in an air atmosphere at room temperature. The specimen surfaces were finished by grinding and cutting processes which give different surface compressive residual stresses. Both specimen treatments showed a clear duplex S–N curve, composed of three types of failure mode depending on the stress amplitude. A map of the appearance of failure modes relating stress amplitude to residual stress was proposed. The dependence of the S–N curve on a critical size of inclusion at the crack origin was demonstrated by the estimation of crack growth rate from the S–N data. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction The fatigue behavior of materials in very high cycle fatigue (VHCF) regimes is of interest because of the general requirement to design for high reliability and efficiency in machines and structures. In several early studies, it has been noted that fatigue failure in high-strength steels occurs beyond the conventional fatigue limit of 107 cycles and leads to the elimination of the classical fatigue limit because that inclusions in matrix play an important role for crack initiation and the associated fatigue life [1–4]. An increased interest in this topic is demonstrated by a series of four international ‘‘very high cycle fatigue” conferences held since 1998 [5]. Some researchers have concentrated on high-carbon chromium bearing steel (JIS SUJ2, SAE52100 and 100Cr6) to investigate the fatigue behavior in VHCF regimes through the experimental studies with rotating bending fatigue tests [6–14], tension–compression tests including the effect of load ratio [15–20] and ultrasonic fatigue tests [21–26]. The VHCF characteristics of low-alloy steel (JIS SNCM439) [27–29] and high-speed tool steel (JIS SKH51) [30–32] have also been examined. Through these studies, it was clear that the characteristic mode of failure by fatigue of high-strength steels changed from surface crack induced failure mode (S-mode) at

* Corresponding author. E-mail address: [email protected] (K. Shiozawa). 0142-1123/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2010.07.009

high-stress amplitude and low-cycle regime to subsurface crack induced at low stress amplitude level and in a high-cycle regime, leading to a ‘‘two-stepwise” or ‘‘duplex” S–N curve. Non-metallic (Al2O3 or TiN) inclusions were observed at the crack initiation sites. Rough and granular faceted areas were found in the vicinity of the non-metallic inclusions at the internal crack initiation sites. These areas were named Granular Bright Facets (GBF) and a formation mechanism for GBF areas was described by a ‘dispersive decohesion of spherical carbide’ model by the authors [33,34]. This area is also named Optically Dark Area (ODA) [35,36] or Fine Granular Area (FGA) [37] and different mechanism for fracture process are proposed. Fracture mechanisms for appearance of the multi-stage fatigue life diagrams in the VHCF regime have been discussed, and it was emphasized to be primary importance of the subsurface crack initiation lives affected by different factors such as the density, size, location and distribution of non-metallic inclusions [38,39]. In a different approach from fatigue crack propagation, it is concluded that crack growth cannot be a significant portion of life in the VHCF range and initiation mechanism are of importance with subsurface initiation of cracking [40–42]. The authors note from detailed observation of fracture surfaces that the subsurface crack induced failure mode could be classified into two modes, namely failure without the GBF area (I-mode) and with GBF area (IG-mode) in the vicinity of an inclusion. The IG-mode failure occurs after about

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2.1. Testing material and specimens The matrix high-speed tool steel (Matrix HSS) used in the study was made by melting in an air atmosphere. The chemical composition (as mass percentage) of this steel is: 0.7C, 0.1 W, 3Mo, and 2 V. This material is a new development for improved fatigue properties, and is referred to as MHS10 in this paper. The alloy was heated in vacuum atmosphere at 1450 K and then gas-cooled, followed by three cycles of tempering heat treatment in a vacuum at 823 K which in turn was followed by further gas-cooling. The average Vickers hardness of the heat-treated alloy was 708 ± 12.8 HV.

2.2. Fatigue testing method The fatigue tests were performed in an open environment at room temperature using a four-axis cantilever-type rotating bending fatigue machine, which was operated at 3150 rev/min (equivalent to a frequency of f = 52.5 Hz). A photograph of this machine was shown in Fig. 3. This multi-type fatigue testing machine was originally developed by a research group in Japan [46] to perform fatigue tests efficiently, that is, to save the cost and time. The machine has two spindles driven one electric motor via a flat belt and each spindle has specimen holders at both ends. Therefore, four specimens can be tested simultaneously in cantilever-type rotating bending (load ratio R = 1). A weight applied to each specimen is suspended from the outer end of each specimen by means of a bearing and a helical spring. The residual stress distribution was measured by using X-ray diffraction equipment (Rigaku Corporation). The classical sin2u method was applied to the determination of residual stress along the specimen’s long axis, by using the diffraction pattern of the Fe(2 1 1) crystal plane obtained by Cr Ka radiation.

R7

Φ 10

2. Experimental procedures

Fig. 1 shows the microstructure of the heat-treated alloy observed by scanning electron microscopy (SEM), which was prepared by micro-etching. The observed material structure was approached a tempered martensitic structure consisting of an average prioraustenitic grain size of 15 lm. Large precipitated carbide particles (dark color) and fine particles (gray color) 0.3–1.3 lm in diameter (with an average of 0.6 lm) were observed distributed within the matrix. Hour-glass shaped specimens with a grip diameter of 10 mm and minimum diameter of 3 mm were used (Fig. 2). The elastic stress concentration factor, Kt, of these specimens was 1.06. After lathe machining and heat-treating, the specimen surface was finished by one of two processes. Cutting was done with a commercial cutting tool (N151.2-600-50E-P (CB20) Nachi-Fujikoshi Corp). The cutting conditions were a rotation speed of 250 rev/min and a sequence 0.06 mm/cut. The specimens finished by this process are referred to as MHS10-A or specimen-A. Grinding was done with a WA#60 wheel. The grinding conditions were a grinder-rotating speed of 3800 rev/min, a work-rotating speed of 750 rev/min and a sequence 0.005 mm/cut. The specimens finished by this process are referred to as MHS10-B or specimen-B. Technological developments of cutting tools in recent years mean that a hardened steel can be processed by a cutting tool instead of a grinding wheel. Therefore, one of the aims of this study was to investigate the effect of surface finishing by both processes on fatigue strength. The two processes develop significantly different residual stresses in the surface layer of specimen. To avoid the influence of surface roughness on the fatigue behavior results, the round-notched surface was polished with a series of emery papers up to mesh of #2000 and subsequently finished by buff polishing before fatigue testing.

Φ3

106 cycles and then the formation of a GBF area around a nonmetallic inclusion governs the failure in VHCF regime. The shape of the S–N curve depends on the appearance of three failure modes. Particularly, the two-stepwise S–N curve is formed because of transition from the S-mode to the IG-mode. Change in the failure modes depends not only on a stress amplitude level, and the applied stress ratio but also to compressive residual stresses on the surface layer of the specimen [13,19,20,43,44]. It has been reported that in rotating bending fatigue experiments using specimens with high surface compressive residual stresses produced by shot-peening, that compressive residual stresses could significantly increase the limit of stress amplitude for S-mode failure [45]. From the viewpoint of high efficiency, saving energy and minimizing the weight of structural elements, there is a demand for functional materials with high-strength, hardness, toughness, wear-resistance and fatigue resistance. To fulfill these requirements, high-speed tool steel (HSS) of the sort developed for cold dies is being used for functional machinery parts, and new increased fatigue resistance high-speed tool steels have been developed. Understanding the fatigue properties and fatigue failure mechanism of high-speed tool steel is important in the design of machine parts, and to provide clear requirement guidelines for developing new materials. The aim of this study is to clarify the VHCF properties of newly developed high-speed tool steels. Through an experimental investigation of the effects on rotating bending fatigue test results of inclusion size and residual stresses in the surface layer, the transition between failure modes has been investigated. The residual stresses in specimen surface layers are affected by surface finishing methods, so cut and ground finished specimens were prepared and a detailed examination was made on the effect of the choice of surface finishing method on VHCF lifetime.

50 100 Fig. 1. Microstructure of materials tested.

Fig. 2. Shape and dimensions of specimen tested.

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Flat Belt

Electric Motor

Spindle

3.2. S–N curve characteristics

Holder Specimen

Bearing Helical Spring

Weight

the thickness. The reductions amounted to 1578 ± 126 MPa in specimen-A and 215 ± 13 MPa in specimen-B.

Photo Sensor Micro-Switch

Counter

Fig. 3. Four-axis cantilever-type rotating bending fatigue machine.

3. Experimental results 3.1. Residual stress distribution The residual stress distributions of the specimens (Fig. 4) were measured using X-ray diffraction as a function of depth from the surface. Electro-polishing was used to remove a layer of the surface about 5–10 lm thick before measurement. From these measured values, the maximum high compressive residual stress was determined in the near surface zone for specimens processed by both cutting and grinding. The average surface compressive residual stress of specimen-A (finished by cutting) was 2251 ± 214 MPa, significantly greater than that of specimen-B (finished by grinding) at 635 ± 48 MPa. The compressive residual stress decreased with depth from the specimen surface. The residual stress reached a zero value at about 100 lm below the surface for cutting-finished specimen-A and 20 lm for the grinding-finished specimen-B. Therefore, larger and deeper compressive residual stress layers are introduced by the cutting surface finishing than with grinding. The compressive residual stresses on the specimens were reduced by emery-paper polishing and buffing, removing about 10 lm from

Fig. 5a shows the S–N curve that was obtained from representative specimens formed by the two finishing processes. The stress amplitude, ra, is nominal stress on the specimen surface. From the examination of fracture surfaces by SEM (Section 3.3), the fatigue failure modes were classified into three types: a surface inclusion-induced failure mode (referred to as S-mode), a subsurface inclusion-induced failure mode without the GBF area (I-mode) and with the GBF area near an inclusion inside the fish-eye zone (IG-mode). From Fig. 5a, a clear duplex S–N curve exists in both specimens. The S-mode failure in specimen-A appeared at high-stress amplitude and after a low number of cycles, changing to the I-mode failure at a stress amplitude (ra) of about 1700 MPa, and then to the IG-mode at ra ffi 1200 MPa in low stress amplitude level and high cycles over a lifetime of more than 106 cycles. However, both Sand I-mode failures appeared in specimen-B over a wide range of values of ra (1100–750 MPa). The I-mode failure appeared at a ra value of about 1100 MPa and happened at a low stress amplitude level compared with specimen-A. The IG-mode failure in specimen-B occurred below a ra value of about 950 MPa. The appearance of the three failure modes is clearly separated by the stress amplitude level for specimen-A, but not in specimen-B. It is expected that the limiting stress amplitude marking the transition between failure modes is affected by compressive residual stress in the surface layer of the specimen and the size of any inclusions at the crack origin.

(a)

(b)

Fig. 4. Residual stress distribution of specimens measured by X-ray diffraction.

Fig. 5. S–N curves of specimens finished with different method, obtained from a cantilever-type rotating bending fatigue test; (a) nominal stress amplitude at surface vs. number of cycles to failure, Nf and (b) true stress amplitude at crack origin vs. Nf.

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3.3. SEM observation of fracture surface Fig. 6 shows SEM observations around a crack origin on the fracture surfaces of a cutting-finished specimen-A and a grinding-finished specimen-B. In Fig. 6, typical fracture surfaces of the Smode (a), I-mode (b) and IG-mode (c) are shown for both types of specimen. A non-metallic inclusion or a coarse carbide particle is present at the crack initiation site for the three failure modes. Aluminum oxide (Al2O3) and calcium oxide (CaO) were detected in the non-metallic inclusion by Electron Probe Micro Analyzer (EPMA), and vanadium carbide (VC) and molybdenum carbide (MoC) were detected at the site of the carbide particle. The nonmetallic inclusion on the fracture surface was seen to be exfoliated from the matrix, and the coarse carbide particles were separated and seen to remain on both fracture surfaces. In Fig. 6c, the GBF area formed around both the non-metallic inclusion and the coarse carbide particle at the crack initiation site on the fracture surface of the specimen that failed at low stress amplitude level and after a high number of cycles.

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to failure (Nf). From the figure, the size of inclusions in specimen-A ranged from 5 to 19 lm with an average of 13.5 lm, which are independent of Nf. However, the size of inclusions in specimen-B ranged from 9 to 40 lm with an average of 23.2 lm, greater than that of specimen-A. The experimental data in Fig. 7a and b distinguishes non-metallic inclusions from coarse carbide particles at the crack origin. It is not clear why differences in size and kind of inclusion are seen between specimens-A and -B because the specimens were extracted from the same rod forging. The reason is possibly that crack initiation from large non-metallic inclusions near the surface layer is restricted by the high-compression residual stress and crack initiation site changes to internal coarse carbide particles at deeper locations. Fig. 7c shows the experimental p relationship between the size of inclusion at crack origin, areainc, and the depth of the inclusion, dinc. It is expected that the above speculation will be eventually verified from this type of result, but the non-uniform distribution of inclusions across the specimen section cannot be fully explained at the present time. 3.5. Change in surface residual stresses during fatigue cycles

3.4. Quantitative observations of the crack initiation site Fig. 7a shows the experimental relationship between the depth of a non-metallic inclusion or coarse carbide particle (hereafter, referred to as an inclusion) at the internal crack origin from the specimen surface, dinc, and number of cycles to failure Nf. The crack initiation sites in specimen-A range in depth from 73 to 200 lm below the specimen surface, being significantly deeper than the crack initiation sites in specimen-B: these range in depth from 34 to 86 lm. This difference in the subsurface crack initiation site depth between materials may relate to the residual stress distribution. A subsurface crack forms in the region where the compressive residual stress induced by the surface finishing has vanished. The cutter finished specimen-A types have a layer of compressive residual stress of about 100 lm and subsurface cracks initiate at the region below 100 lm depth. No correlation of dinc with Nf was identified. From the nature of the rotating bending fatigue test, when a stress gradient across the section of a specimen is applied, it is considered that the depth of subsurface crack initiation site affects the fatigue lifetime. From consideration of the true stress at the crack initiation site, rai, the difference in fatigue lifetime between specimens could not be explained and was still to be seen in Fig. 5b. The plan-area of an inclusion leading to crack initiation, areainc, was measured on the fracture surface. Fig. 7b shows the relationp ship between the size of inclusion, areainc, and number of cycles

Residual stresses near the specimen surface change with increasing number of fatigue cycles. In this study, the residual stress at the specimen surface was measured during fatigue cycles by using X-ray diffraction. Fig. 8a shows the experimentally determined relationship between residual stress on the surface of specimen-A and the fatigue life ratio N/Nf. The fatigue testing was interrupted at intervals for measurement. It can be seen from Fig. 8a that the compressive residual stress at the specimen surface is extremely relaxed at an early stage of the fatigue cycling and subsequently reaches a constant value after a fatigue life ratio of about 0.2. Residual stress retained on the surface of the specimen-A after fracture was measured on the specimen surface at 1 mm from the fracture point, and it was determined that this value was similar to the saturated residual stress during fatigue process shown in the figure. Fig. 8b shows the experimentally determined relationship between residual compressive stress retained rr, and the applied stress amplitude ra. The residual stress on the surface of the specimen-A which has a high compressive residual stress before the fatigue test decreases with increasing stress amplitude. However, the residual stress on the surface of specimen-B does not change during fatigue cycling, staying the same as before the fatigue test regardless of stress amplitude. Relaxation of the residual stress during the fatiguing process may result from plastic deformation,

Fig. 6. Typical SEM observations of crack initiation site on fracture surface for three types of failure mode (the scale of the micrographs is shown in left column except MHS10-B(a)).

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(a)

(a)

(b)

(b)

(c)

Fig. 8. Change in surface residual stress during fatigue cycles (a), and the experimental relationship between surface residual stress and applied stress amplitude (b). (Experimental plot with error bar shows an average, the maximum and the minimum value of five measurements. The other plot is the result of one or two measurement.)

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p areainc;s for surface inclusion ð1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DK inc;i ¼ 0:5ra ð1  dinc =rÞ p areainc;i for subsurface inclusion

DK inc;s ¼ 0:65ra

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DK GBF ¼ 0:5ra ð1  dinc =rÞ p areaGBF for GBF area

Fig. 7. Characteristics of crack initiation site; (a) experimental relationship between depth of inclusion at crack origin from specimen surface and number of cycles to failure, (b) experimental relationship between inclusion size at crack origin and number of cycles to failure, and (c) experimental relationship between size of inclusion and depth of inclusion. Note that experimental data in the figure (b) from surface crack initiation are distinguished by open marks and from the subsurface by solid marks. The data relating to metallic carbide (VC + MoC) at crack origins are marked by an asterisk ().

which occurs if the sum of the compressive residual stress and the applied compressive stress exceeds the compressive yield stress of the material. 4. Discussion 4.1. The stress intensity factor at the crack origin The initial stress intensity factor (SIF) range was calculated by using the formulae of Murakami and Endo [47], based on the measurements of the size of inclusion and the GBF area including the inclusion at a crack origin:

ð2Þ ð3Þ

where ra is the normal stress amplitude applied to the specimen, r is the radius of the minimum section of the specimen, dinc is the distance from the specimen surface to the center of inclusion at a crack p origin and areaGBF is the size of GBF area including the inclusion size. The effect of the stress gradient across the specimen section on the SIF was considered for the calculation. It is noted that Eqs. (2) and (3) are the same form but not the identical meaning. Subsurface crack initiates and propagates from an inclusion in case that I-mode failure occurs. On the other hand, IG-mode failure occurs after forming the GBF area around an inclusion, according as proposed ‘dispersive decohesion of spherical carbide’ model [33,34]. Then, to discuss the subsurface crack initiation and propagation behavior, it is necessary to take into account not only inclusion size but also GBF area size. Fig. 9 shows the relationship between the stress intensity factor range, DKinc,s, DKinc,i and DKGBF, and Nf obtained from specimens-A and -B. It can be seen from this figure that DKinc,s and DKinc,i decrease independently with increasing fatigue p life. All values of DKinc,s are above 3.5 MPa m. The threshold SIF p for surface crack growth, DKth,s, is estimated as 3.5 MPa m. Therefore, a surface crack cannot initiate and propagate at a surface inclusion below the DKth,s, and a fatigue limit for S-mode failure exists. p However, the value of DKinc,i is in the range of 6–2.3 MPa m and the GBF area was observed in the vicinity of all inclusions at the

Y. Shimatani et al. / International Journal of Fatigue 33 (2011) 122–131

Fig. 9. Relationship between stress intensity factor range at crack origin and number of cycles to failure.

p point of internal crack origination having DKinc,i below 4 MPa m. p The value of DKGBF is above 4 MPa m and larger than the DKinc,i. The formation of the GBF area is required for an internal crack initiation and propagation in low stress amplitude level, and it can be estimated that the threshold SIF of internal crack, DKth,i, which is the limit to initiate and propagate directly from an inclusion, is p 4 MPa m. Clear difference of values between DKth,s and DKth,i were obtained from this tested material, which is similar to the Ni–Cr– Mo low-alloy steel (SNCM439) reported previously [28,43]. It is observed from this figure that the values of DKinc,i, DKGBF and DKth,i are independent on the specimens tested, because internal crack initiation in the region is not affected by surface residual stress. Therefore, it is considered that the difference in fatigue lifetime between specimens failing in I-mode and IG-mode, as shown in the S– N curve, is not because of the effect of compressive residual stress on the specimen surface layer but more because of the size of subsurface inclusions at the crack origin. 4.2. Effect of inclusion size on fatigue life Murakami et al. [48] developed a model to estimate the fatigue limit of materials containing small inclusions. The fatigue limit, rw, for stress ratio R of –1 can be predicted using the Vickers hardness (HV) and the area of the inclusion in lm2 as in Eq. (4).

rw ¼ DðHV þ 120ÞðareaÞ1=12

ð4Þ

where D is a coefficient depending on the location of the inclusion at the crack origin. From this formula, it can be seen that the fatigue life of the materials is mainly controlled by the size of inclusion at crack origin and the hardness of materials. The difference in fatigue life between two different specimens with the same hardness is later discussed with relation to the effect of the size of inclusions in each specimen. Fig. 10 shows the relationship between the stress amplitude at the crack initiation site rai (=ra(1–2dinc/d)) multiplied by the (area)1/12 and Nf, where d is the minimum diameter of the specimen. It can be seen that there is no difference between specimens having different surface residual stresses. Fatigue lifetime can be approximated using Eq. (5).

frai ðareaÞ1=12 ga Nf ¼ C

ð5Þ

where rai is in MPa and the area is in lm2. From an approximation using least mean square data fitting, the parameters in Eq. (5) were estimated to be a = 3.51 and C = 2.85  1015 for specimens failing from surface inclusions, and a = 12.8 and C = 2.41  1047 for specimens failing from subsurface inclusions. Mayer et al. [26] used Eq. (5) to calculate fatigue lifetime from an ultrasonic fatigue test using

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Fig. 10. Evaluation of fatigue life by stress amplitude at crack initiation site multiplied with (area of inclusion)1/12.

100Cr6 steel, and a = 28.8 and C = 6.47  1098 for specimens failing from subsurface inclusions. From the above discussion, fatigue lifetimes of both specimens failing from surface and subsurface inclusions can be determined simply by the size of inclusion and the stress amplitude at the crack initiation site, though there are different residual stresses on the surface layer of each specimen. Surface residual stress does not affect on fatigue lifetime of the specimen failing from a surface inclusion because of the relaxation of the residual stress at an early stage during the fatigue cycles (see Section 3.5). The transition of the failure mode from S-mode to I-mode is different between specimens (see Fig. 10) and the effect of residual stress on the change of failure mode still remains. 4.3. Estimation of fatigue life by crack propagation law A fatigue crack propagation process initiated from a subsurface inclusion can be divided into three stages as reported by Shiozawa and Lu [19] and Akiniwa et al. [16]. The first stage is the formation of the GBF area by a mechanism described as the ‘decohesion of spherical carbide’ model [33,34]. After formation of an appropriate size in the GBF area (above DKth,i) to enable propagation as an ordinary crack, the crack propagates independently of the material microstructure and forms a ‘fish-eye’ as the second stage. After the subsurface crack reaches the specimen surface, the third stage is crack propagation as a surface crack. When the initial SIF at the subsurface inclusion is larger than DKth,i, the crack propagates without forming the GBF area, that is, an I-mode failure occurs. For an S-mode failure, a surface crack initiates and propagates at a surface inclusion. The fatigue cracks that occur in each stage are assumed to propagate according to the power law shown in Eq. (6), because the crack propagation mechanics at the stage of the GBF and the fish-eye area are not clear at the present time. It has been proposed by Tanaka [10] that coefficient, C, and exponent, m, in the Paris law of Eq. (6) were determined from the S–N data as an indirect method.

da ¼ CðDKÞm dN

ð6Þ

From the integration of Eq. (6) from inclusion size to final crack size and by approximation, as the final crack size is much larger than the inclusion size, the relationship between fatigue lifetime and initial SIF is given as Eq. (7) [10,28,43].

Nf 2 ðDK inc Þm pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ areainc ðm  2ÞC

ð7Þ

Fig. 11a shows the experimental relationship between DKinc and Nf/(area)1/2 derived from the S–N data taken from both speci-

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men-A and -B. The data reveals a strong linear relationship on a log–log plot for S-mode, I-mode and IG-mode failures. Further, it cannot be observed that there is any effect of residual stress in the specimen surface layer on surface and subsurface crack propagation behavior. Exponent m and coefficient C in the Paris law was obtained by the least square mean method (indicated by a solid line in this figure) and summarized in Table 1 for the three failure modes. Shiozawa et al. [43] have previously reported values of m = 15.2 and C = 5.08  1022 for the IG-mode failure of a Ni–Cr– Mo low-alloy steel (JIS SNCM439) by tension–compression axial loading fatigue testing. Values have been reported from an ultrasonic fatigue test of m = 14.2 and C = 3.44  1021 for JIS SUJ2 steel by Tanaka [10], and m = 14.5 and C = 4.86  1021 for 100Cr6 steel by Mayer et al. [26]. From the comparison of these values, the crack propagation rate in an IG-mode failure is similar for four types of high hardness steel and very slow as comparison with that of the S-mode failure. Fig. 11b shows the crack propagation rate, da/dN, against DK. It can be seen from the figure that the crack in the GBF area propagates very slowly compared with a surface crack between DKth,s and DKth,i. It is noted that the estimated value of m for the I- and IG-mode failure is very large as compared with the classical values of 2–7 for surface crack propagation. As contradictory works, Paris et al. [40–42] have proposed the Paris–Hertzberg– McClintock law using the effective SIF, DKeff, and m = 3 to describe the evolution of the growth rate law of the surface and subsurface crack in the VHCF regime, and showed a good correlation with experimental results.

(a)

(b)

Table 1 Exponent and constant in a Paris law relationship obtained from the S–N data. Failure mode

m

C

S-mode I-mode IG-mode

3.17 29.1 12.4

1.24  1011 7.06  1032 1.69  1019

The fatigue life Nf, for the specimens failing by S-, I- and IGmode can be estimated from Eq. (7) using the inclusion size at the crack origin and obtained values of m and C. Fig. 12 shows the S–N curves for three failure modes estimated as a parameter of inclusion size. The horizontal line in Fig. 12a and b is the estimated fatigue limit for S-mode and I-mode failures, taking p p DKth,s = 3.5 MPa m and DKth,i = 4.0 MPa m from experimental values. It can be understood from this figure that the distribution of the experimental results plotted arises from the difference of inclusion size at the crack origin. Fig. 13 shows a comparison between the predicted and the experimentally determined fatigue life. From this it can be seen that the agreement is fairly good (within a factor of three) and there is no difference between specimens having different residual compressive stresses in the surface layer. 4.4. Effect of surface residual stress on failure mode The difference of fatigue strength between the two specimen types used in this study could be explained by the inclusion size at the crack initiation site. However, the difference in stress amplitude level changing the failure mode between specimens cannot be explained by inclusion size (Fig. 10), and it is necessary to consider the effect of surface residual stress on the transition between failure modes. The effect of surface residual stress on transition of the failure mode has been examined, and a map of failure mode has been proposed by the authors [13,19,20,28,43]. In outline form, this idea is as follows: if the size of surface inclusion is same as that of subsurface one, the value of SIF of surface inclusion, DKinc,s, calculated from Eq. (1) is usually larger that of subsurface inclusion, DKinc,i, calculated from Eq. (2). The relation between SIF and stress amplitude is represented schematically in Fig. 14a as a dot-dashed line for surface inclusion and a dashed line for subsurface. Above the threshold SIF of surface crack growth, DKth,s (at point A in the figure), S-mode failure occurs. Below the stress amplitude at point A, subsurface cracks can start to grow after the SIF of the subsurface inclusion reaches the threshold SIF of subsurface crack growth, DKth,i (>DKth,s) , with the formation of a GBF area around a subsurface inclusion. Therefore, S-mode failure occurs in the region of high-stress amplitude and changes to IG-mode failure at low stress amplitude levels. In this case, only two failure modes appear on an S–N curve and I-mode failure will not be observed at any stress amplitude level contrary to experimental facts (Fig. 5a). To explain the experimental result, it is necessary to add the effect of compressive residual stress on the specimen surface to the above discussion. It is assumed that the residual stress, rr, acts on the fatigue behavior as a mean stress effect and stress range in tensile side affects the crack initiation and propagation, according to the experimental facts [20]. Based on the assumption, initial SIF of the surface inclusion, DKinc,s is rewritten to DK inc;s as Eq. (8) [10,43]:

DK inc;s ¼ 0:65ðra þ rr Þ Fig. 11. Relationship between stress intensity factor range for inclusion and number of cycles to failure divided by the inclusion size (a) and estimated crack propagation rate vs. stress intensity factor range (b).

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p areainc;s

ð8Þ

In addition, it is considered that the surface residual stress affects only surface inclusions and does not affect subsurface inclusions. Therefore, the SIF of the subsurface inclusion does not

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(b)

109

Number of cycles to failure, Prediction, Nf, pre

(a)

8

10

Surface Subsurface MHS10-A MHS10-B

107 106 105

Factor of 3

104 103 3 10

104

105

106

107

10 8

109

Number of cycles to failure, cycles, Experiment Nf,exp Fig. 13. Comparison between fatigue lives predicted by the fatigue crack growth law and experimental one.

(a)

(c)

(b)

Fig. 12. S–N curves as a parameter of inclusion size calculated by the fatigue crack growth law derived from the S–N data: (a) S-mode failure, (b) I-mode failure, and (c) IG-mode failure.

change without regard to the existence of residual stress on surface layer. The compressive residual stress on the surface layer reduces the SIF of a surface inclusion, DKinc,s , toDK inc;s (as indicated solid line in Fig. 14b). The line DK inc;s intersects the dashed line of DKinc,i at point B. The failure mode changes from S-mode to I-mode at a stress amplitude corresponding to point B, because DKinc,i is larger than DKth,i, and a subsurface crack can initiate and propagate at a subsurface inclusion without forming a GBF area. The value of DKinc,i becomes equal to the DKth,i at point C as stress amplitude decreases. Below this stress amplitude, a subsurface crack cannot directly initiate and propagate from an inclusion, and the formation of a GBF area around an inclusion is required for initiation and propagation of the subsurface crack, in other words, the IGmode failure appears. Therefore, because of the existence of com-

Fig. 14. Schematic representation for changing the failure mode: (a) no residual stress in a specimen and (b) effect of compressive residual stress on surface layer.

pressive residual stresses on a specimen surface layer, three types of failure mode, that is S-, I- and IG, will occur depending on the applied stress amplitude level. The type of failure mode that appears will be affected by competition between the surface and subsurface crack propagation rates, difference in size of inclusions between the surface and subsurface zone, and the amount of residual stress on the surface layer. Fig. 15 summarizes the above discussion with a map for the transition of failure modes, showing a relationship between the stress amplitude occurring at the transition of failure mode and compressive residual stress on the specimen surface layer. For

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Fig. 15. Map of the failure mode relating stress amplitude to compressive residual stress on surface layer of the specimen.

the calculation, the following assumptions are made: mean inclusion size of 13.5 lm for specimen-A and 22.8 lm for specimen-B, mean depth of subsurface inclusion of 148 lm for specimen-A p and 55.3 lm for specimen-B, DKth,s = 3.5 MPa m, and p DKth,i = 4.0 MPa m, which are obtained by experiment. The calculated result is indicated by a solid line for specimen-A and a dashed line for specimen-B. At the region of small surface compressive residual stress, S-mode and IG-mode failures occur and the transition stress amplitude from S-mode to IG-mode failure increases with increasing compressive residual stress. At the region of large surface compressive residual stress I-mode and IG-mode failures occur and the stress amplitude at the change in failure mode is constant because of the transition that occurs at DKinc,i = DKth,i. The appearance of the failure modes is complex in the middle region of surface compressive residual stress. Basically, three kinds of failure modes occur depending on stress amplitude level. However, it is possible for IG-mode or I-mode failure to occur instead of S-mode, because of the competition between surface and subsurface crack propagation rate as discussed above. Hence, the map of failure modes is classified into five zones with three failure modes. Experimental results for the stress amplitudes producing a change in failure mode were plotted in Fig. 15. Data for specimen-A are shown in this figure as parameters of compressive residual stress measured before and after the fatigue test. Stress amplitudes causing the change from S-mode to I-mode failure for Specimen-A obtained by experiment agree with the calculated results if the values of compressive residual stress relaxation during fatigue cycling are used, as shown by the arrows in the figure. The transition from I-mode to IG-mode for specimen-A is not affected by the surface residual stress. Stress amplitudes changing from Smode to I-mode and from I-mode to IG-mode failure obtained by experiment for specimen-B show good agreement with those calculated. The value of compressive residual stress measured on the surface of specimen-B is common to the values related to the appearance of all three failure modes, and this is a reason why the three failure modes appear in a wide range of stress amplitudes from 1100 to 700 MPa for specimen-B as shown in the S–N curve in Fig. 5a. 5. Conclusions To examine the effect of surface residual stress and inclusion size on fatigue properties of matrix high-speed tool steel resulting from a very high cycle fatigue regime, a cantilever-type rotating bending fatigue test was carried out using specimens which were made with different surface finishing processes. The results obtained from this study are summarized as follows:

(1) Residual compressive stress in the surface layer of a specimen finished with a cutting tool was larger than that finished with a grinding tool. (2) The large residual compressive stress relaxed and decreased at an early stage of fatigue cycling and subsequently decreased to an almost constant value after a fatigue life ratio of about 0.2. The relaxation behavior was dependent on stress amplitude level. (3) Both specimens showed a clear duplex S–N curve, composed of three types of failure mode depending on the stress amplitude, namely, a surface inclusion-induced failure mode, and a subsurface inclusion-induced failure mode without and with the formation of a GBF area. (4) Aluminum-oxide type non-metallic and MC-type carbide inclusions were observed at both surface and subsurface crack initiation sites. There was no difference in fatigue lifetime between the presence of a non-metallic inclusion and a large carbide particle at the crack origin. A GBF area was observed in the vicinity of the non-metallic and the carbide particle inclusions at the crack initiation site in the very high-cycle regime, but no difference in morphology was distinguished. (5) It is possible to explain the effect of size of non-metallic and carbide particle inclusion on fatigue lifetime by using the relationship of {rai(area)1/12}aNf = C. (6) Fatigue life was estimated by an analytical integration of crack propagation rate assuming the Paris power law and deriving from the S–N data. S–N curves depending on the size of non-metallic inclusion and carbide particle give a fairly good agreement with the experimental results. Experimental scatter in the S–N curve depended on the size of non-metallic inclusion and carbide particles at the crack origin. (7) The appearance of three types of failure mode and the stress amplitudes responsible for changing the failure mode in the S–N curve could be explained by the effect of compressive residual stress in the specimen surface layer. A map relating stress amplitude with compressive residual stress for transition of failure mode was proposed based on fracture mechanics.

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