中南大学学报(英文版)

J. Cent. South Univ. (2012) 19: 1773-1779

DOI: 10.1007/s11771-012-1206-z

Effect of inclusion on high cycle fatigue response of a powder metallurgy tool steel

YAO Jun(姚君)1,2, QU Xuan-hui(曲选辉)1,2, Rafi-ud-din1,2, HE Xin-bo(何新波)1,2, ZHANG Lin(章林)1,2

1. State Key Laboratory for Advanced Metals and Materials

(University of Science and Technology Beijing), Beijing 100083, China;

2. School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract:

The high cycle fatigue response of a high V-alloyed powder metallurgy tool steel (AISI 11) with different inclusion sizes was studied. Two materials of this grade at a similar hardness of about HRC 60 were subjected to axial loading fatigue tests, tensile tests and fracture toughness measurements to investigate their mechanical properties. Large inclusion above 70 μm is indicated to be responsible for the tensile fracture which happens before yielding. The fatigue strength obtained up to 107 cycles is found to decrease from approximately 1 538 MPa to 1000 MPa with the inclusion size increasing above 30 μm. The internally induced crack initiation is mainly attributed to the surface compressive residual stress of 300-450 MPa. Fractographic evaluation demonstrates that the crack initiation and propagation controlling factors of the two materials are almost the same, indicating that the two factors would be insignificantly affected by the inclusion size level. Paris sizes of the two materials both show a tendency to decrease as the ratio of stress intensity factor of crack origin to factor of fish-eye increases. The investigation into the relationship between stress intensity factors and fatigue life of the two materials further indicates that the high cycle fatigue behavior of AISI 11 is controlled by crack propagation.

Key words:

powder metallurgy tool steel; high cycle fatigue; fractography; fish-eye; inclusion

1 Introduction

Powder metallurgy (PM) offers a versatile and efficient method to product excellent tool steels and engineering parts and components in many industries. In recent years, these PM tool steels working in interrupted metal cutting, stamping, blanking and in engine or aerospace industries have been subjected to more severe environment. They are always repeatedly exposed to stresses and strains because of the contact between tool and workpiece or the task of working under cyclic loading. So, it is necessary to study the performances of these PM tool steels in high cycle fatigue (HCF) regime in order to have a good knowledge of their fatigue characterization.

Fatigue failure is always induced by the most deleterious defects, which are the preferentially unsafe sites in hard- or low-ductility materials [1-5]. Inclusions, resulting from deoxidising additions, impurities or entrained exogenous materials, can be present in all commercial materials. They are often identified as common sites for fatigue crack nucleation and found at the center of fish-eye [6-9]. MURAKAMI et al revealed that inclusions exerted a significant influence on fatigue properties [1, 6, 10]. SHIOZAWA et al [11], KAZYMYROVYCH et al [12] and SOHAR et al [13] also found that they were very important to fatigue crack initiation and fatigue fracture in HCF regime. However, there is little information about the effect of inclusion on high cycle fatigue response of PM tool steels [2, 9, 14]. The detailed investigation into the fatigue behavior of AISI 11 with inclusion size less than 30 μm has been earlier presented [15]. The aim of this work is to make even more extensive study by comparing the fatigue response of AISI 11 with inclusion size of 10-30 μm and above 30 μm. Axial loading fatigue tests were performed at room temperature to obtain the fatigue properties and the important information of crack nucleation and propagation. Fractographic evaluation on the basis of linear fracture mechanics was employed to distinguish the propagation areas on the fracture surface of the failed specimens. In addition, the influence of surface residual stress measured by X-ray diffraction techniques on fatigue crack initiation was investigated.

2 Experimental

A kind of PM tool steel produced by hot isostatic pressing was used in the present experiments, whose chemical composition is 2.45C-5.25Cr-1.30Mo-9.75V-Fe (mass fraction, %). Steel A was acquired from Crucible Material Corporation (Crucible grade CPM 10V), and Steel B was under the same designation of AISI 11 but without inclusion control. The samples for mechanical tests were manufactured from the forged and soft- annealed master blocks. The materials were then austenitized at 1 120 °C for 15 min in vacuum and gas-quenched in uniform N2, and tempering was done triply at 540-550 °C for 2 h. As-tempered specimens were finally prepared with 15 μm diamond suspension to obtain the mirror-like finish in the longitudinal direction, and a surface layer of about 15 μm was polished off. A compressive residual stress (RS) of approximately 300-450 MPa was both detected at the narrowest section of the fatigue specimen surface of Steel A and Steel B, which was measured by X-ray diffraction (XRD) sin2Ψ techniques. The microstructure of the two materials was studied on a Zeiss SUPRA-55 scanning electron microscope (SEM) and a MSF-2M XRD. SEM and XRD results prove that they are both composed of fine dispersed carbides and tempered martensite, and there is no indication of insignificant amount of retained austenite.

The dimension of specimens used for axial fatigue and fracture toughness tests is indicated in Fig. 1. A resonant testing machine was employed to carry out axial loading fatigue experiments using samples as shown in Fig. 1(a). Each specimen was performed under 0.1 load ratio and 140 Hz working frequency to the final failure or to the maximum life of 107 cycles. The fatigue strengths of Steel A and Steel B at 107 cycles measured by stair-case method turn out to be 1 538 and 1 000 MPa, respectively. A servohydraulic testing machine was used to conduct fracture toughness and tensile tests. CT samples with the width of 20 mm as indicated in     Fig. 1(b) was chosen to measure the fracture toughness (KIC), and they were precracked by cyclic tensile process. Fractography was favored to investigate the fatigue nucleation sites and the fatigue strength controlling flaws on the fracture surface, the size of which was represented by equivalent diameter of a circular-like defect.

3 Results and discussion

3.1 Mechanical properties

Table 1 gives the mechanical properties of AISI 11. Though Steel A and Steel B at high hardness of about HRC 60-62 are both high strength steels with low ductility, their tensile strength and fatigue strength are much different from each other. Under monotonic loading condition, the tensile strength of Steel B is lower than that of Steel A, and it fractures before the yield stress reaches, which is illustrated in Fig. 2. Fractographic inspection is illustrated in Fig. 3(a), and it is indicated that there is no crack initiation on the tensile fracture surface of Steel A. On the contrary, it can be clearly seen from Fig. 3(b) that the poor performance of Steel B should be due to the occurrence of large crack origin. Energy dispersive spectrum (EDS) results show that Al2O3 inclusions larger than 70 μm are always identified as typical crack initiation sites, as well as VC primary carbides or carbide clusters of above 20 μm occasionally. So, the effect of large inclusions and carbides and carbide clusters on tensile properties of PM tool steels is particularly deleterious. On the basis of this investigation, it is roughly noted that the procedure of eliminating brittle inclusions less than 70 μm can significantly improve the performance of AISI 11 in static tensile loading.

Fig. 1 Fatigue and fracture toughness specimen geometry (Unit: mm): (a) Axial fatigue sample; (b) CT sample

In the cyclic loading cases, the fatigue strength at 107 cycles of Steel A and Steel B are measured to be 1 538 and 1 000 MPa, respectively. Such difference on fatigue strength of the two materials at a similar hardness should be closely related to the size of inclusion origin, which has been demonstrated in Refs. [1-2, 10, 12]. The fractographic examination results of the fatigue nucleation sites are shown in Fig. 4. The EDS spectra illustrate that the crack origins of Steel A and Steel B are both brittle non-metallic inclusions. But, the SEM micrographs indicate that their sizes are much different. The strength-controlling flaws of Steel A are 10-30 μm, while those of Steel B are above 30 μm. Therefore, it is noted that the fatigue strength of the investigated tool steel is very sensitive to inclusion size level, and it would decrease from about 1 538 MPa to 1 000 MPa when the inclusion is larger than 30 μm. In addition, the particularly deleterious effect of inclusion size on the cyclic properties of PM tool steels can be seen from  this point of view, which has already been reported for high-strength steels and conventional ones [3, 6, 10, 13-14, 16-17].

Table 1 Mechanical properties of studied materials

Fig. 2 Stress-strain curve of studied materials

Fig. 3 SEM micrographs of tensile fracture surface: (a) Steel A; (b) Steel B

3.2 Effect of residual stress

The brittle non-metallic inclusions are found to exert an important effect on the fatigue crack nucleation of the studied PM tool steel. However, MEURLING et al [14], GHANEM et al [18], FARRAHI and GHADBEIGI [19] reported that the fatigue strength and the endurance life were also affected by the surface RS resulting from the grinding and polishing process. SOHAR et al [20-21] further concluded that RS can change the actual applied stress along the specimen cross-section and correspondingly exercise influence over the location of crack initiating sites and the fatigue properties. According to MEURLING et al [14] and SOHAR et al [20-21], the fatigue strength was closely related to RS levels. Generally, in cyclic tensile-loading condition, the higher the compressive RS is, the more likely the internal initiation is prone to; accordingly, the higher the fatigue strength is obtained.

Fig. 4 SEM micrographs and EDS spectra of fatigue crack initiation: (a) and (b) Steel A; (c) and (d) Steel B

Steel A is demonstrated to mainly initiate from the interior inclusion (Fig. 5(a)), which has been described by YAO et al [15]. The inclusion origins of Steel B are always found to locate away from the specimen surface by 120-1 200 μm, and there are only a few cases fractured from surface. On the basis of Goodman equation, the location dependent fatigue strength of the surface layer σfs, as a function of RS, can be calculated by [15]

                   (1)

where σf and σb are the experimental determined fatigue strength and tensile strength, respectively, and σRS is the surface compressive RS of about 400 MPa. In the earlier work presented by YAO et al [15], the surface fatigue strength of Steel A was estimated to be approximately 1 925 MPa according to Eq. (1), which was found to be responsible for the occurrence of internal failure. The surface fatigue strength of Steel B turns out to be about  1 260 MPa, and it is higher than the measured value as well, suggesting that its dominated interior initiation is also encouraged by the surface compressive RS. Therefore, it is noted that the magnitude of compressive RS introduced from fatigue specimen preparing process plays an important role in determining the location of crack origin. Accordingly, it should also improve the fatigue strength of Steel A and Steel B by preventing the occurrence of the more dangerous surface crack initiation.

Fig. 5 SEM fatigue fracture morphologies of Steel B failed after 4.25×105 cycles at maximum stress of 1 200 MPa: (a) Internal fish-eye morphology; (b) Distinct zones of CI, CP1 and CP2 in fish-eye

3.3 Fatigue behavior

The fatigue crack propagation of Steel A with inclusion no larger than 30 μm was demonstrated to be mainly controlled by Paris-Law regime [15]. In the present work, the influence of inclusion above 30 μm on the fatigue response of Steel B was studied, and was even compared with that of Steel A for further understanding the fatigue behavior of AISI 11. The fish-eye area on the fracture surface of Steel B shown in Fig. 5(a) is divided into three zones according to the different fracture morphologies [15, 20]. Figure 5(b) shows that the crack initiation defect is "CI" and it is followed by zone "CP1" and "CP2" (CP1+ CP2=CP). For interior crack initiation, the stress intensity factor can be calculated by the following expression [14, 22]:

                              (2)

where 2σa and D represent the stress range and the crack equivalent diameter, respectively. Accordingly, the stress intensity factors of the three zones, ΔKCI, ΔKCP1 and ΔKCP2, were evaluated by Eq. (2). Figures 6 and 7 show the stress intensity factor ranges of crack origin (ΔKCI) and fish-eye (ΔKCP) for the failed specimens with the endurance life of 105-107 cycles, respectively. It can be seen from Fig. 6 that the values of ΔKCI for Steel A and Steel B are both above 4 MPa·m1/2. Figure 7 indicates that the ranges of ΔKCP for Steel A and Steel B are 10.6-13.3 MPa·m1/2 and 9.8-15.5 MPa·m1/2, respectively, which are similarly like each other and both show a good correlation with their KIC value. Therefore, it is noted that the crack initiation and propagation controlling factors of the two materials are not distinguished from each other in spite of the different inclusion size levels.

The relationship between the stress intensity factor and the cycle number to failure of the Steel B failed specimens was investigated on a ΔK-lgNf graph.  Figure 8 shows that the fatigue life increases with decreasing the values of ΔKCI, and the threshold value for crack propagation (ΔKth) of 4.5 MPam1/2 is obtained from the corresponding fitted line. So, it is clearly noted that the fatigue behavior of Steel B in HCF regime is not controlled by crack nucleation stage because the values of ΔKCI are higher than ΔKth. It can be also seen from Fig. 8 that the fatigue life shows a tendency to increase as the changed values of (ΔKCP–ΔKCI) or (ΔKCP2-ΔKCI) increase, indicating that the crack propagation is dominated. In addition, as illustrated in Fig. 8, the gap of ΔKf2 and ΔKf2a are mostly within the range of 2-4 MPa·m1/2. It can be supposed that stages CP1 and CP2 are Paris and fast fatigue crack growth stages, respectively. All of these above conclusions agree well with the findings of Steel A, which have been revealed by YAO et al [15]. Therefore, a conclusion can be drawn that the high cycle fatigue behavior of Steel A and Steel B does not differ from each other. According to this consideration, it is noted that although the fatigue strength of AISI 11 is significantly affected by the various inclusion size level, the fatigue crack propagation is still mainly controlled by Paris-Law regime.

Fig. 6 Stress intensity factor of crack origin ΔKCI: (a) Steel A; (b) Steel B

Fig. 7 Stress intensity factor of fish-eye ΔKCP: (a) Steel A; (b) Steel B

Fig. 8 Relationship between stress intensity factor (ΔKCI, ΔKCP1 and ΔKCP2) and cycle number to failure for failed specimens of Steel B

The size of zone CP1 was connected with ΔKCI/ΔKCP for further understanding the fatigue behavior of AISI 11. Figure 9 clearly indicates that both the CP1 sizes of Steel A and Steel B show a tendency to decrease as the ratio of ΔKCI to ΔKCP increases. It is well-known that the lower ΔKth and the higher ΔKIC are, the smaller the Paris zone is, and vice versa. Provided that ΔKCI and ΔKCP are crack initiation and propagation controlling factors, respectively, they have a significant influence on CP1 size as well. From this point of view, Fig. 9 supports the assumption of CP1 to be Paris stage and demonstrates the combined effect of ΔKCI and ΔKCP on Paris size.

The detailed investigation indicates that both of the high cycle fatigue behavior of Steel A and Steel B is not determined by crack nucleation but is controlled by Paris-law regime. The inclusion size level is found to exert insignificant effect on the crack initiation and propagation controlling factors of the two materials. Zone CP1 is Paris stage, and it decreases with increasing the ratio of ΔKCI to ΔKCP.

Fig. 9 Relation between size of Paris zone and ?KCI/?KCP: (a) Steel A; (b) Steel B

4 Conclusions

1) Large inclusion above 70 μm is found to exert a harmful effect on the tensile properties. The fatigue strength with endurance life up to 107 cycles decreases from about 1 538 MPa to 1 000 MPa with the inclusion being larger than 30 μm. Internal inclusion causes fatigue crack initiation, probably due to the existence of surface compressive residual stress of 300-450 MPa.

2) The stress intensity factors of crack origin for the two materials are both above 4 MPa·m1/2. The values of fish-eye for Steel A and Steel B are 10.6-13.3 and 9.8-15.5 MPa·m1/2, respectively. Both of the crack initiation and propagation controlling factors show little connection with the inclusion size. The threshold value for crack propagation of Steel B is estimated to be    4.5 MPa·m1/2, and it is lower than the stress intensity factor of crack origin, suggesting that its fatigue behavior as well as that of Steel A is controlled by crack propagation stages.

3) Both the high cycle fatigue behaviors of Steel A and Steel B are mainly controlled by Paris-Law regime. The zone CP1 is demonstrated to be Paris stage, and it shows a tendency to decrease as the ratio of stress intensity factor of crack origin to factor of fish-eye increases.

References

[1] MURAKAMI Y, ENDO M. Quantitative evaluation of fatigue strength of metals containing various small defects or cracks [J]. Engineering Fracture Mechanics, 1983, 7: 1-15.

[2] DANNINGER H, WEISS B. The influence of defects on high cycle fatigue of metallic materials [J]. Journal Materials Processing Technology, 2003, 143/144: 179-184.

[3] ZHANG Guo-qing, SU Bing, PU Geng-qiang, WANG Cheng-tao. Fatigue properties of 48MnV steel with twin arc spraying 3Cr13 coatings [J]. Journal of Central South University of Technology, 2005, 12(2): 112-118.

[4] WILLIAMS J J, DENG X, CHAWLA N. Effect of residual surface stress on the fatigue behavior of a low-alloy powder metallurgy steel [J]. International Journal of Fatigue, 2007, 29: 1978-1984.

[5] MEDVEDEVA A, BERGSTROM J, GUNNARSSON S. Inclusions, stress concentrations and surface condition in bending fatigue of an H13 tool steel [J]. Steel Research, 2008, 79(5): 376-381.

[6] MURAKAMI Y, TAKADA M, TORIYAMA T. Super-long life tension-compression fatigue properties of quenched and tempered 0.46% carbon steel [J]. International Journal Fatigue, 1998, 16: 661-667.

[7] EKENGREN J, KAZYMYROVYCH V, BURMAN C, BERGSTR?M J. Relating gigacycle fatigue to other methods in evaluating the inclusion distribution of a H13 tool steel [C]// Fourth International Conference on Very High Cycle Fatigue. Michigan: TMS, 2007: 45-50.

[8] TCHUINDJANG J T, LECOMTE-BECKERS J. Fractography survey on high cycle fatigue failure: Crack origin characterization and correlations between mechanical tests and microstructure in Fe-C-Cr-Mo-X alloys [J]. International Journal Fatigue, 2007, 29: 713-728.

[9] SOHAR C R, BETZWAR-KOTAS A, GIERL C, WEISS B, DANNINGER H. PM tool steels push the edge in the fatigue tests [J]. Metal Powder Report, 2009, 64: 12-17.

[10] MURAKAMI Y, ENDO M. Effects of defects, inclusions and inhomogeneities on fatigue strength [J]. Fatigue, 1994, 16: 163-182.

[11] SHIOZAWA K, MORII Y, NISHINO S, LU L. Subsurface crack initiation and propagation mechanism in high-strength steel in a very high cycle fatigue regime [J]. International Journal of Fatigue, 2006, 28: 1521-1532.

[12] KAZYMYROVYCH V, EKENGREN J, BERGSTR?M J, BURMAN C. Evaluation of the giga-cycle fatigue strength, crack initiation and growth in high strength H13 tool steel [C]// Fourth International Conference on Very High Cycle Fatigue. Michigan: TMS, 2007: 209-215.

[13] SOHAR C R, BETZWAR-KOTAS A, GIERL C, WEISS B, DANNINGER H. Fatigue behavior of M2 and M42 high speed steel up to the gigacycle regime [J]. Kovove Materialy-Metallic Materials, 2009, 47: 147-158.

[14] MEURLING F, MELANDER A, TIDESTEN M, WESTIN L. In?uence of carbide and inclusion contents on the fatigue properties of high speed steels and tool steels [J]. International Journal Fatigue, 2001, 23: 215-224.

[15] YAO J, QU X H, HE X B, ZHANG L. Inclusion-controlled high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel [J]. Materials Science and Engineering A, 2011, 528: 4180-4186.

[16] YANG Z G, LI S X, LI Y D, LIU Y B, HUI W J, WENG Y Q. Relationship among fatigue life, inclusion size and hydrogen concentration for high-strength steel in the VHCF regime [J]. Materials Science and Engineering A, 2010, 527: 559-564.

[17] LIU Y B, WANG Z G, LI Y D, CHEN S M, LI S X, HUI W J, WENG Y Q. Dependence of fatigue strength on inclusion size for high-strength steels in very high cycle fatigue regime [J]. Materials Science and Engineering A, 2010, 517: 180-184.

[18] GHANEM F, BRAHAM C, FITZPATRICK M E, SIDHOM H. Effect of near-surface residual stress and microstructure modification from machining on the fatigue endurance of a tool steel [J]. Journal of Materials Engineering and Performance, 2002, 11: 631-639.

[19] FARRAHI G H, GHADBEIGI H. An investigation into the effect of various surface treatments on fatigue life of a tool steel [J]. Journal of Materials Processing Technology, 2006, 174: 318-324.

[20] SOHAR C R, BETZWAR-KOTAS A, GIERL C, WEISS B, DANNINGER H. Fracrographic evaluation of gigacycle fatigue crack nucleation and propagation of a high Cr alloyed cold work tool steel [J]. Int J Fatigue, 2008, 30: 2191-2199.

[21] SOHAR C R, BETZWAR-KOTAS A, GIERL C, DANNINGER H, WEISS B. Gigacycle fatigue response of tool steels produced by powder metallurgy compared to ingot metallurgy tool steel [J]. International Journal of Materials Research, 2010, 101: 1140-1150.

[22] MURAKAMI Y. Stress intensity factors handbook [M]. Oxford: Pergamon Press, 1987: 668.

(Edited by YANG Bing)

Foundation item: Project(2007BAE51B05) supported by the National Key Technologies Research and Development Program of China

Received date: 2011-04-15; Accepted date: 2011-06-27

Corresponding author: QU Xuan-hui, Professor, PhD; Tel: +86-10-62332700; E-mail: quxh@ustb.edu.cn

Abstract: The high cycle fatigue response of a high V-alloyed powder metallurgy tool steel (AISI 11) with different inclusion sizes was studied. Two materials of this grade at a similar hardness of about HRC 60 were subjected to axial loading fatigue tests, tensile tests and fracture toughness measurements to investigate their mechanical properties. Large inclusion above 70 μm is indicated to be responsible for the tensile fracture which happens before yielding. The fatigue strength obtained up to 107 cycles is found to decrease from approximately 1 538 MPa to 1000 MPa with the inclusion size increasing above 30 μm. The internally induced crack initiation is mainly attributed to the surface compressive residual stress of 300-450 MPa. Fractographic evaluation demonstrates that the crack initiation and propagation controlling factors of the two materials are almost the same, indicating that the two factors would be insignificantly affected by the inclusion size level. Paris sizes of the two materials both show a tendency to decrease as the ratio of stress intensity factor of crack origin to factor of fish-eye increases. The investigation into the relationship between stress intensity factors and fatigue life of the two materials further indicates that the high cycle fatigue behavior of AISI 11 is controlled by crack propagation.

[1] MURAKAMI Y, ENDO M. Quantitative evaluation of fatigue strength of metals containing various small defects or cracks [J]. Engineering Fracture Mechanics, 1983, 7: 1-15.

[2] DANNINGER H, WEISS B. The influence of defects on high cycle fatigue of metallic materials [J]. Journal Materials Processing Technology, 2003, 143/144: 179-184.

[3] ZHANG Guo-qing, SU Bing, PU Geng-qiang, WANG Cheng-tao. Fatigue properties of 48MnV steel with twin arc spraying 3Cr13 coatings [J]. Journal of Central South University of Technology, 2005, 12(2): 112-118.

[4] WILLIAMS J J, DENG X, CHAWLA N. Effect of residual surface stress on the fatigue behavior of a low-alloy powder metallurgy steel [J]. International Journal of Fatigue, 2007, 29: 1978-1984.

[5] MEDVEDEVA A, BERGSTROM J, GUNNARSSON S. Inclusions, stress concentrations and surface condition in bending fatigue of an H13 tool steel [J]. Steel Research, 2008, 79(5): 376-381.

[6] MURAKAMI Y, TAKADA M, TORIYAMA T. Super-long life tension-compression fatigue properties of quenched and tempered 0.46% carbon steel [J]. International Journal Fatigue, 1998, 16: 661-667.

[7] EKENGREN J, KAZYMYROVYCH V, BURMAN C, BERGSTR?M J. Relating gigacycle fatigue to other methods in evaluating the inclusion distribution of a H13 tool steel [C]// Fourth International Conference on Very High Cycle Fatigue. Michigan: TMS, 2007: 45-50.

[8] TCHUINDJANG J T, LECOMTE-BECKERS J. Fractography survey on high cycle fatigue failure: Crack origin characterization and correlations between mechanical tests and microstructure in Fe-C-Cr-Mo-X alloys [J]. International Journal Fatigue, 2007, 29: 713-728.

[9] SOHAR C R, BETZWAR-KOTAS A, GIERL C, WEISS B, DANNINGER H. PM tool steels push the edge in the fatigue tests [J]. Metal Powder Report, 2009, 64: 12-17.

[10] MURAKAMI Y, ENDO M. Effects of defects, inclusions and inhomogeneities on fatigue strength [J]. Fatigue, 1994, 16: 163-182.

[11] SHIOZAWA K, MORII Y, NISHINO S, LU L. Subsurface crack initiation and propagation mechanism in high-strength steel in a very high cycle fatigue regime [J]. International Journal of Fatigue, 2006, 28: 1521-1532.

[12] KAZYMYROVYCH V, EKENGREN J, BERGSTR?M J, BURMAN C. Evaluation of the giga-cycle fatigue strength, crack initiation and growth in high strength H13 tool steel [C]// Fourth International Conference on Very High Cycle Fatigue. Michigan: TMS, 2007: 209-215.

[13] SOHAR C R, BETZWAR-KOTAS A, GIERL C, WEISS B, DANNINGER H. Fatigue behavior of M2 and M42 high speed steel up to the gigacycle regime [J]. Kovove Materialy-Metallic Materials, 2009, 47: 147-158.

[14] MEURLING F, MELANDER A, TIDESTEN M, WESTIN L. In?uence of carbide and inclusion contents on the fatigue properties of high speed steels and tool steels [J]. International Journal Fatigue, 2001, 23: 215-224.

[15] YAO J, QU X H, HE X B, ZHANG L. Inclusion-controlled high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel [J]. Materials Science and Engineering A, 2011, 528: 4180-4186.

[16] YANG Z G, LI S X, LI Y D, LIU Y B, HUI W J, WENG Y Q. Relationship among fatigue life, inclusion size and hydrogen concentration for high-strength steel in the VHCF regime [J]. Materials Science and Engineering A, 2010, 527: 559-564.

[17] LIU Y B, WANG Z G, LI Y D, CHEN S M, LI S X, HUI W J, WENG Y Q. Dependence of fatigue strength on inclusion size for high-strength steels in very high cycle fatigue regime [J]. Materials Science and Engineering A, 2010, 517: 180-184.

[18] GHANEM F, BRAHAM C, FITZPATRICK M E, SIDHOM H. Effect of near-surface residual stress and microstructure modification from machining on the fatigue endurance of a tool steel [J]. Journal of Materials Engineering and Performance, 2002, 11: 631-639.

[19] FARRAHI G H, GHADBEIGI H. An investigation into the effect of various surface treatments on fatigue life of a tool steel [J]. Journal of Materials Processing Technology, 2006, 174: 318-324.

[20] SOHAR C R, BETZWAR-KOTAS A, GIERL C, WEISS B, DANNINGER H. Fracrographic evaluation of gigacycle fatigue crack nucleation and propagation of a high Cr alloyed cold work tool steel [J]. Int J Fatigue, 2008, 30: 2191-2199.

[21] SOHAR C R, BETZWAR-KOTAS A, GIERL C, DANNINGER H, WEISS B. Gigacycle fatigue response of tool steels produced by powder metallurgy compared to ingot metallurgy tool steel [J]. International Journal of Materials Research, 2010, 101: 1140-1150.

[22] MURAKAMI Y. Stress intensity factors handbook [M]. Oxford: Pergamon Press, 1987: 668.