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VHCF properties and fatigue limit prediction of precipitation hardened 17-4PH stainless steel
International Journal of Fatigue 88 (2016) 205–216
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VHCF properties and fatigue limit prediction of precipitation hardened 17-4PH stainless steel Bernd M. Schönbauer a,b,c,⇑, Keiji Yanase a,b, Masahiro Endo a,b a
Department of Mechanical Engineering, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan Institute of Materials Science and Technology, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan c Institute of Physics and Materials Science, University of Natural Resources and Life Sciences (BOKU), Peter-Jordan-Str. 82, 1190 Vienna, Austria b
a r t i c l e
i n f o
Article history: Received 2 December 2015 Received in revised form 24 March 2016 Accepted 31 March 2016 Available online 1 April 2016 Keywords: 17-4PH stainless steel Fatigue limit Very high cycle fatigue pffiffiffiffiffiffiffiffiffiffi area parameter model Non-metallic inclusions
a b s t r a c t In this work, the very high cycle fatigue properties of precipitation-hardened chromium–nickel–copper stainless steel 17-4PH are investigated, and the factors determining the fatigue strength are discussed. In addition, fatigue test results on comparable materials reported in the literature are evaluated, and the influence of material hardness on the fatigue life and the endurance strength is quantified. Fractographic investigations show that fatigue fracture initiates predominantly from non-metallic inclusions at the surface and in the interior of specimens. It is found that the endurance limit at more than 1010 pffiffiffiffiffiffiffiffiffiffi loading cycles can be predicted by the area parameter model. The stress ratio dependency on the fatigue strength is determined with good accuracy using a simple method. Furthermore, the lower bound of the fatigue limit is predicted by the inclusion rating and use of the extreme value theory. In addition, the role of the optically dark areas observed around internal inclusions is discussed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Precipitation hardened stainless steel 17-4PH possesses excellent properties in terms of static and fatigue strengths, toughness, fabrication characteristics and heat treatment distortion. In particular, its resistance to corrosion is comparable to that of AISI 304 austenitic stainless steel in most environments. Therefore, it is widely used in applications where high strength as well as good corrosion resistance is required, e.g., in the aerospace, chemical, food-processing, paper and power industries. Some investigations on the fatigue properties of 17-4PH are reported in the literature. For instance, Wu and Lin [1,2] investigated the influence of temperature and cyclic loading frequency on the fatigue life for different heat treatments. Hsu and Lin [3] performed fatigue crack growth rate measurements at high temperatures with different frequencies. The corrosion fatigue behaviour was investigated by Viswanathan et al. [4], Lin and Lin [5] and Schönbauer et al. [6]. Nie and Mutoh [7] proposed a method to predict the fatigue strength of 17-4PH stainless steel by assuming that material failure initiates from the matrix based on the small crack model proposed by El Haddad et al. [8]. A similar approach was used by Schönbauer ⇑ Corresponding author at: Institute of Physics and Materials Science, University of Natural Resources and Life Sciences (BOKU), Peter-Jordan-Str. 82, 1190 Vienna, Austria. E-mail address: [email protected] (B.M. Schönbauer). http://dx.doi.org/10.1016/j.ijfatigue.2016.03.034 0142-1123/Ó 2016 Elsevier Ltd. All rights reserved.
et al. [6] for fatigue limit prediction in the presence of corrosion pits, which is applicable to different environments, stress ratios and a wide range of defect sizes. However, an extensive number of fatigue tests are required to determine all the material parameters necessary for the prediction. In laboratory tests, fatigue crack initiation in 17-4PH stainless steel is mainly observed at slip bands or non-metallic inclusions [1,6,7]. In actual components, surface discontinuities (e.g., scratches, pits, surface roughness, etc.) existing at critical locations can cause fatigue crack initiation. In the presence of compressive residual stresses at the surface of the material, fatigue failure from internal defects, such as non-metallic inclusions, becomes more dominant, especially in the very high cycle fatigue (VHCF) regime. Therefore, a simple model that can estimate the fatigue limit by taking the effect of small defects into account is essential for practical applications. pffiffiffiffiffiffiffiffiffiffi Murakami and Endo [9] proposed the area parameter model that can predict the fatigue limit using only two parameters: the square root of the projection area of a small defect or a crack perpffiffiffiffiffiffiffiffiffiffi pendicular to the loading direction ( area) and the Vickers hardness (HV). This model is based on the phenomenological fact that the fatigue limit is not a critical condition for crack initiation, but that it corresponds to the non-propagation of a small crack [10]. From this perspective, the fatigue limit in the presence of a small defect (e.g., a non-metallic inclusion) is determined by the
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Nomenclature b FGA Fj GBF HRC HV n N Nf ODA R RT S0 SEM SIF T V
factor for fatigue limit prediction dependent on location of defect fine granular area cumulative distribution function granular bright facet Rockwell hardness (C scale) Vickers hardness number of specimens number of cycles number of cycles to failure optically dark area stress ratio room temperature control surface area of specimens subjected to maximum stresses scanning electron microscope stress intensity factor return period prediction volume in which the maximum inclusion size is rated
threshold condition for propagation of a crack emanating from a defect. For this type of problem, fracture mechanics can be used and the stress intensity factor (SIF) can be calculated. Finally, a generalised expression of the fatigue limit rw is given as [11]:
b ðHV þ 120Þ
rw ¼ pffiffiffiffiffiffiffiffiffiffi1=6 area
a 1R ; 2
ð1Þ
V0
control volume of specimens subjected to maximum stresses VHCF very high cycle fatigue y reduced variates j pffiffiffiffiffiffiffiffiffiffi area the square root of the projection area of a small defect or a crack perpendicular to the ffiloading direction pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi parea ffiffiffiffiffiffiffiffiffiffiInc inclusion size in terms of area pffiffiffiffiffiffiffiffiffiffi in terms of area parea ffiffiffiffiffiffiffiffiffiffimax maximum inclusion size pffiffiffiffiffiffiffiffiffi ffi areaODA ODA size in terms of area DK stress intensity factor range DKODA stress intensity factor range of an optically dark area DKth threshold stress intensity factor range DKth,lc threshold stress intensity factor range of a long cracks a exponent in the correction factor for the stress-ratio dependency of the fatigue limit Dr stress range (for fully reversed loading, also the compression part is taken into account) r nominal stress rw fatigue limit rwl lower bound of the scatter in the fatigue limit
pffiffiffiffiffiffiffiffiffiffi bending testing. The results are evaluated using the area parameter model to predict the fatigue strength of 17-4PH stainless steel for different stress ratios with a focus on addressing failure from non-metallic inclusions. Furthermore, the lower bound of the scatter in the fatigue limit is determined using statistics of extremes by analysing the defect size at crack initiation sites. 2. Material and experimental procedure
where the factor b is 1.43 for a surface defect/crack, 1.56 for an internal defect/crack and 1.41 for a subsurface defect just in contact pffiffiffiffiffiffiffiffiffiffi with the surface. Here, rw is in MPa, area is in lm and HV is in 2 kgf/mm . The influence of the stress ratio R can be taken into account by the correction factor {(1 R)/2}a, where a is given by:
a ¼ 0:226 þ HV 104 :
ð2Þ
This equation was initially derived based on the experimental results for two steels, and thereafter, it has successively been applied to a variety of steels [11]. However, it has been reported that the values of a determined experimentally for ductile cast iron [12], high strength steels [13] and turbine blade steels [14,15] were significantly different from those calculated using Eq. (2). The origin of fatigue fracture in the VHCF regime is often found in the interior of specimens. Non-metallic inclusions are regularly observed at the crack initiation sites [16], but failure can also originate from the matrix [17,18]. In the centre of a so-called ‘‘fish-eye” fracture, a fine grained area is often observed and appears dark when observed with an optical microscope and bright with a scanning electron microscope (SEM). Different explanations are provided to describe the formation of this area [19–21], which was named an ‘‘optically dark area” (ODA) by Murakami et al. [19,22], a ‘‘granular bright facet” (GBF) by Shiozawa et al. [23] and a ‘‘fine granular area” (FGA) by Sakai et al. [24]. Hereafter, the first expression (ODA) will be used in this work. For some high-strength steels in the VHCF regime, it is reported that the governing parameter for pffiffiffiffiffiffiffiffiffiffi the fatigue strength prediction according to Eq. (1) is the area of the ODA [19]. The use of the size of internal inclusions may lead to non-conservative results. In this investigation, the fatigue test results in the VHCF regime up to 1010 cycles to failure are reported. Tests were performed at three different R-ratios with ultrasonic fatigue testing and rotating
2.1. Material The material tested was precipitation-hardened chromium–nic kel–copper stainless steel 17-4PH that was hardened at 913 °C and age-hardened at 621 °C for 4 h (condition H1150). The chemical composition and the mechanical properties are given in Tables 1 and 2, respectively. The microstructure of the material is shown in Fig. 1. Equiaxed martensite laths are visible within the austenite grains. An average grain size of 11 lm was measured, independent of orientation. The number of inclusions per area was determined to be 23.1 per mm2 in the inspection area of 32 mm2. 2.2. Test setups Most tests were performed using an ultrasonic fatigue testing technique developed at BOKU [25,26], which stimulates specimens to resonance vibration at a frequency of approximately 20 kHz. This closed-loop controlled ultrasonic fatigue testing equipment ensures an accuracy of ±1% of the nominal displacement amplitude by using a vibration gauge at one end of the specimen that serves as the feed-back in a test generator. For tests performed under fully reversed loading (R = 1), only one end of a specimen is fixed to the resonance system and the other end vibrates freely. By superimposing a static force at this end of the specimen, tests at R – 1 can be performed. More details on the design of ultrasonic
Table 1 Chemical composition of the 17-4PH in weight %. C
Si
Mn
Cr
Cu
Ni
Nb + Ta
P
S
0.033
0.40
0.49
15.57
3.31
4.37
0.23
0.027
0.001
B.M. Schönbauer et al. / International Journal of Fatigue 88 (2016) 205–216 Table 2 Mechanical properties of the 17-4PH at room temperature. Tensile strength (MPa)
Yield strength (MPa)
Elongation (%)
Reduction of area (%)
Vickers hardness (kgf/mm2)
1030
983
21
61
352
207
measured at the surface using X-ray diffraction. To investigate the influence of annealing on the mechanical properties, tensile and hardness tests were performed both before and after heat treatment. After stress-relief annealing, the tensile strength and Vickers hardness were reduced by 3% and 1%, respectively, which was considered acceptable. The geometry for the rotating bending test specimens is shown in Fig. 2c. The control volume in which the maximum cyclic stress is higher than 95% of the nominal bending stress is 49 mm3 and the control surface area is 251 mm2. The surface of the specimens was ground and electropolished after machining. The residual stress measured on the surface after electropolishing was 6 ± 15 MPa. 3. Results 3.1. S–N data
Fig. 1. Microstructure of 17-4PH.
components can be found in [27]. The test environment was laboratory air at 90 °C by placing the specimen in a test chamber and blowing air around the specimen that was heated using a coil. A thermo-couple was attached to the specimen and temperature adjustment was provided by closed-loop control which ensured a constant temperature with an accuracy of ±1 °C. Furthermore, rotating bending tests were performed at room temperature with a test frequency of 67 Hz at Fukuoka University. 2.3. Test specimens The specimen geometries for ultrasonic fatigue testing at R = –1 and R – –1 are shown in Fig. 2a and b, respectively. The control volume and control surface area in the gauge length (which was 10 mm in length), i.e., the volume and surface area subjected to a constant stress during fatigue testing, are 126 mm3 and 126 mm2, respectively. The surface of specimens was ground over the gauge length with abrasive paper up to a grade of #4000, and stressrelief annealing was conducted in a vacuum at 600 °C for one hour afterwards. A compressive residual stress of 65 ± 29 MPa was
Fatigue tests were performed at R = 1, 0.05 and 0.4. The S–N data are shown in Fig. 3, in which the stress on the ordinate is expressed by the range, Dr. Most tests were performed at approximately 20 kHz using an ultrasonic fatigue technique, and six rotating bending tests (R = 1) were conducted. Additionally, one specimen was tested at 5 Hz using an ultrasonic fatigue test specimen, as shown in Fig. 2b, at R = 0.4 using a servohydraulic testing machine. No significant influence associated with the testing method and specimen geometry on the fatigue life was found. The fatigue strength decreases as the stress ratio R increases. A fatigue limit was not determined since fatigue failure occurred after more than 1010 loading cycles. 3.2. Fractography The fracture surfaces of the failed specimens were analysed using a SEM. For most ultrasonic fatigue test specimens, a nonmetallic inclusion was found at the crack initiation site, see Fig. 4a–c. At R = 1, all the specimens failed as a result of internal inclusions. Two of them were located slightly below the surface of the specimen, see Fig. 4b (labelled as ‘‘Subsurface” in Fig. 3). At R = 0.05, all the specimens failed from interior inclusions, except one in which failure resulted from a surface inclusion. At R = 0.4, crack initiation from surface and interior inclusions was observed. At one of these crack initiation sites, a structural inhomogeneity was found, see Fig. 4d. This inhomogeneity was analysed using energy dispersive X-ray spectroscopy and a high amount of chromium and niobium was detected. Furthermore, cup-and-cone like
Fig. 2. Specimen geometries for ultrasonic fatigue testing at (a) R = 1 and (b) R – 1 and (c) rotating bending testing (dimensions in mm).
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Fig. 3. S–N test results for different R-ratios. Run-out specimens are marked with arrows.
fractures occurred in two specimens, which exhibited large degrees of plastic deformation during failure (see Fig. 5). These appeared similar to fracture surfaces observed in tensile tests. Although fatigue failure took place after more than 107 cycles, no distinct fatigue features were observable on the fracture surfaces. The cup-and-cone like fracture is often observed during fatigue testing of ductile steels at high stress ratios (cf. [14,18,28,29]) and is associated with cyclic creep/ratcheting. For more details, we refer to Schönbauer et al. [6]. To investigate any influence of test frequency and temperature on the fracture mode, an additional test was performed at 5 Hz at room temperature (RT). Again, a cup-and-cone like fracture occurred, and the fatigue life was consistent with the ultrasonic fatigue test results (see the x-marked
diamond symbol in Fig. 3). Although only one specimen was tested under these conditions, the result clearly shows that the aforementioned fracture mode is independent of the test procedure and the temperature for the investigated range (5 Hz–20 kHz and RT–90 °C). Thirteen inclusions at the crack initiation site of the specimens which failed during ultrasonic fatigue testing were analysed using energy dispersive X-ray spectroscopy. The chemical composition of these inclusions was determined to be calcium aluminate x(CaO) Al2O3, mostly containing MgO or, less often, MnO. Examples of the respective non-metallic inclusions are shown in Fig. 6. The relationship between the size and location for all the inclusions, which was measured at the fracture surfaces of ultrasonic fatigue test specimens, is shown in Fig. 7. The crack initiation sites are almost uniformly distributed. However, it is clear that crack initiation at the surface is preferred at R = 0.4. As mentioned in Section 2.3, residual stresses of 65 ± 29 MPa were measured on the surface of the ultrasonic fatigue specimens. These compressive residual stresses resulted in crack initiation at internal inclusions, as observed for tests at low stress ratios. However, it is known that high R-ratios cause the relaxation of residual stresses [30] because the maximum stress experienced during cyclic loading approaches the yield strength of the material. This fact may explain the frequent observation of surface crack initiation at R = 0.4. As shown in Fig. 3, the rotating bending fatigue test results are comparable to those obtained using the ultrasonic fatigue testing technique. However, exclusive surface failure is apparent because of the presence of the maximum bending stress at the surface of specimen. In Fig. 8, the fracture surface of a rotating bending specimen is shown. The location of the crack initiation in the highmagnification image is marked by an arrow. No inclusion was observed, but a small shallow pit is visible in the area believed to be the fracture origin. Fig. 9 shows images taken at the different surface areas of specimens where the fatigue cracks and slip bands initiated. The pictures at the top were selectively taken at N = 1.00 107 cycles, in
Fig. 4. Crack initiation sites for tests conducted at f = 20 kHz: (a) surface inclusion (Dr = 610 MPa, R = 0.4, Nf = 4.03 105 cycles), (b) subsurface inclusion (Dr = 1200 MPa, R = 1, Nf = 2.51 107 cycles), (c) fish-eye fracture (Dr = 1120 MPa, R = 1, Nf = 1.78 108 cycles) and (d) surface inhomogeneity (Dr = 600 MPa, R = 0.4, Nf = 4.34 106 cycles).
B.M. Schönbauer et al. / International Journal of Fatigue 88 (2016) 205–216
Fig. 5. Cup-and-cone like fatigue fracture (Dr = 610 MPa, R = 0.4, Nf = 1.89 107 cycles): (a) fractured specimen with high plastic deformation and (b) fracture surface.
which 97% of the total fatigue life was already consumed. The pictures at the bottom show the same areas after fatigue failure at Nf = 1.03 107 cycles. The crack initiation site where final failure occurred was unfortunately not observed at N = 1.00 107 cycles. In Fig. 9a, the crack initiation and propagation from a small pit is visible. Such pits probably originate from inclusions during electropolishing of specimens. A small pit is also shown in Fig. 9b with slip bands in its vicinity. No cracking was observed after N = 1.00 107 cycles, but a small crack initiated prior to specimen failure. The evolution of the slip bands is also visible in Fig. 9c, but no distinct cracking is observed. These observations suggest that crack initiation mainly took place at shallow pits that formed during electropolishing. It is important to note that even after N = 107 cycles, there is steady progress of fatigue damage, such as crack propagation and slip bands evolution. Thus, it should be recognised that for the investigated 17-4PH stainless steel, the true fatigue limit to determine infinite life cannot be calibrated with the 107 load cycles that is conventionally employed in laboratory tests for steels. The defect size on the fracture surface for the rotating bending test specimens was not clearly measureable for most of the specimens because the crack initiation area was deformed during fracture. However, it was apparent that the fracture origin sites were located at the surface. Optically dark areas (ODAs) were observable around inclusions when the failure originated in the interior of ultrasonic fatigue specimens at all stress ratios. Their size was not easily measureable
209
Fig. 7. Size and location of non-metallic inclusions on the fracture surfaces.
because the border between the ODA and the neighbouring ‘‘fish-eye” region is blurred. Therefore, SEM micrographs, as well as light microscopic images were used to measure the size of the ODAs, as shown in Fig. 10. pffiffiffiffiffiffiffiffiffiffi The area of the ODAs and inclusions measured at the fracture surfaces are plotted versus the number of cycles to failure in Fig. 11. Although the ODA size increases with number of cycles to failure (shown by a dashed line), the mean value of the inclusion size is constant (shown by a solid line).
4. Discussion 4.1. Comparison with literature In the following, the fatigue test results are compared with the data reported in the literature. The material properties and specimen sizes are summarised in Table 3. For investigations in which the Rockwell hardness (HRC) was quoted, the values were converted into Vickers hardnesses (HV) according to the international standard ISO 18265 [31]. In Fig. 12, the S–N data at R = 1 measured in the present investigation are compared with those reported by Viswanathan et al. [4] and Nie and Mutoh [7]. Viswanathan et al. performed deflection controlled reversed bending tests on material with the same heat treatment condition as used in the present investigation. The
Fig. 6. Non-metallic inclusions: (a) CaOAl2O3, (b) CaO–MgO–Al2O3 and (c) CaO–MnO–Al2O3.
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This can suppress crack initiation at the surface, which is usually the preferred crack initiation site for failure up to 107 cycles. Consequently, failure occurs from internal inclusions, which consume a much higher number of load cycles for crack initiation and small crack growth. Similar observations were made by Ochi et al. [32], who systematically investigated the influence of residual stresses on the fatigue behaviour of high-strength steels. In the present investigation, it is assumed that the determined fatigue strength in the VHCF regime is not significantly affected by residual stresses because the data at R = 0.4 (where the relaxation of residual stresses is expected due to high maximum stresses) show good correlation for failure from the surface and the interior (see Fig. 3). 4.2. Influence of stress ratio R
Fig. 8. Fracture surface from the rotating bending specimen at Dr = 1100 MPa for Nf = 3.69 107 cycles (arrow marks crack initiation site).
results by Nie and Mutoh were obtained using an electrodynamic vibration fatigue testing machine at 100 Hz. Their heat treatment was slightly different (H1025), and consequently, the material hardness was higher. As is seen in Fig. 12, the endurance strengths at 108 cycles are comparable for all three investigations. The fatigue life determined by Nie and Mutoh is considerably longer than those reported by Viswanathan et al., and the data obtained in the present study lies in between. Wu and Lin [1] performed fatigue testing on 17-4PH stainless steel with different heat treatments. A commercial closed-loop servohydraulic test machine was used for experiments at R = 0.1. In Fig. 13, their results obtained with materials in heat treat conditions of H900 and H1150 are compared with the present investigation at R = 0.05. Significantly different S–N data were obtained for the different heat treatments. The data point of the specimen that failed from the surface at approximately 105 cycles in the present study lies in between those data. No investigations in the VHCF regime are reported by Wu and Lin [1]. To investigate the influence of material hardness on the fatigue life, the data are plotted in a modified S–N diagram in Fig. 14 where the stress range Dr is normalised by (HV + 120) in accordance with Eq. (1). With this approach, much better data consistency is achieved. In the approach by Murakami and Endo [9], the material hardness is used only to predict the fatigue limit. However, the current findings suggest that the material hardness can also be used for comparison of the fatigue life time for similar materials and loading conditions. When the influence of the hardness is taken into account, the fatigue strength for the data reported by Nie and Mutoh agree well with the other researchers’ data, although their data are slightly lower at N > 107. Normalising the stress range by (HV + 120) leads to good congruency for the results tested under different heat treatment conditions by Wu and Lin at R = 0.1. Furthermore, the surface failure at R = 0.05 obtained in the present investigation correlates very well with their data. However, there is still a significant gap in the fatigue life between surface and interior crack initiation. As already discussed in Section 3.2, compressive residual stresses were measured in the ultrasonic fatigue test specimens.
The R-ratio dependency in Eq. (1) is expressed by the term {(1 R)/2}a, in which the exponent a was originally determined using specimens containing artificial defects [33]. In this investigation, the determination of the value of a using fractographic information on non-metallic inclusions is studied. Fig. 15 shows the pffiffiffiffiffiffiffiffiffiffi1=6 value of rw area =fb ðHV þ 120Þg as a function of (1 R)/2 on a double-logarithmic graph, where b is 1.43 for surface defects, 1.56 for internal defects and 1.41 for subsurface defects just in contact with the surface (cf. Eq. (1)). In the figure, the data for inclusions observed on the fracture surfaces are plotted using solid symbols. The data for unbroken specimens are also plotted using pffiffiffiffiffiffiffiffiffiffi open symbols, for which the value of area of the inclusions was determined by breaking specimens in the subsequent fatigue tests at higher stress levels. In Fig. 15, a straight solid line is drawn through the lowest solid symbols. It is noted that these data points represent failure at approximately 1010 cycles, and therefore, should be representative for the endurance limit in the VHCF regime. A value of a = 0.421 is determined from the slope of the line. The coefficient of determination is r2 = 0.991, which shows that the regression line adequately fits the data. In addition, a horizontal dashed line at the ordinate value of 1 is plotted, which represents the predicted fatigue limit at R = –1 according to Eq. (1). It is noted that at R = 1 (i.e., (1 R)/2 = 1), all the data points lie above this line. As will be reported in a forthcoming paper, additional fatigue tests with specimens containing small circumferential notches with depths of 10 lm and 30 lm were performed at the same three R-ratios of 1, 0.05 and 0.4. The values of a = 0.434 determined in those tests is only 3% higher than that obtained from non-metallic inclusions. Therefore, we may conclude that the appropriate fractographic investigation of specimens which failed from nonmetallic inclusions in the VHCF regime is suitable for the determination of the exponent a. The determined value of a = 0.421 is significantly higher than the values of a = 0.261 according to Eq. (2) with HV = 352. This equation has successfully been used for estimating the value of a in a number of steels since it was initially derived based on experimental data for only two steels. However, some investigations have reported that the value of a differed significantly from those calculated by Eq. (2). For example, Furuya and Abe [13] reported a value of a = 0.5 for several steels and Kovacs et al. [14] found a = 0.546 for a martensitic 12% Cr steel. Although these investigations do not consider the defect size for determination of a (i.e., only the fatigue limit is plotted versus (1 R)/2), their results are in better agreement with the present findings than those from Eq. (2). Nevertheless, it would be very helpful to develop a simple formula similar to Eq. (2) that is based on many experimental results obtained using different materials in the future.
B.M. Schönbauer et al. / International Journal of Fatigue 88 (2016) 205–216
211
Fig. 9. Surface areas of a rotating bending specimen after cyclic loading at Dr = 1200 MPa. Images show cracks and slip bands at N = 1.00 107 cycles (top) and after failure at Nf = 1.03 107 (bottom).
Fig. 10. SEM and optical micrographs of a fish-eye fracture with ODA around a non-metallic inclusion (Dr = 1060 MPa, R = 1, Nf = 7.54 108 cycles).
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Fig. 11. Size of the ODAs and non-metallic inclusions at the crack initiation sites.
Fig. 12. Comparison of the S–N test results at R = -1 with the data reported by Viswanathan et al. [4] and Nie and Mutoh [7].
4.3. Prediction of fatigue strength In the following sections, the fatigue data are evaluated using pffiffiffiffiffiffiffiffiffiffi Eq. (1) with the inclusion size, areaInc , a Vickers hardness of HV = 352 and a = 0.421 for the present steel, which yields:
b ð352 þ 120Þ
rw ¼ pffiffiffiffiffiffiffiffiffiffi 1=6 areaInc
0:421 1R : 2
ð3Þ
The results are plotted using a modified S–N diagram, as shown in Fig. 16, in which the nominal stress r is divided by the predicted fatigue limit rw (note that either the stress range or amplitude must be used for both r and rw). As seen, no failures are observed below r/rw = 1. The prediction according to Eq. (3) is conservative even for the data obtained at more than Nf = 1010 cycles to failure and works well for all three R-ratios. The solid and dashed lines show the trends for fatigue failure from the surface and the interior, respectively. In calculations of rw for the rotating bending specimens, the size of the crack initiation sites is estimated to be the mean size of the non-metallic pffiffiffiffiffiffiffiffiffiffi inclusions (in terms of areaÞ because the fracture origins were the small pits that formed from inclusions during electropolishing (see Section 3.2). It is reported by Murakami et al. [19] that the fatigue limit prediction for high-strength steels according to Eq. (3) can be pffiffiffiffiffiffiffiffiffiffi non-conservative when the inclusion size, areaInc , is used. In this pffiffiffiffiffiffiffiffiffiffi case, the use of the ODA size, areaODA , which is the size of the ODA including the inclusion, leads to reasonable results. Based on this
Fig. 13. Comparison of the S–N test results at R = 0.05 with data reported by Wu and Lin at R = 0.1 [1]. The run-out specimens are marked with arrows.
consideration, the fatigue limit is re-estimated for the present material using the following equation:
rw ¼
0:421 1:56 ð352 þ 120Þ 1 R : pffiffiffiffiffiffiffiffiffiffi 1=6 2 areaODA
ð4Þ
Table 3 Comparison of material properties and specimen sizes of different investigations.
a
Investigation
Condition for heat treatment
Tensile strength (MPa)
Yield strength (MPa)
Vickers hardness HV (kgf/mm2)
Control volume V0 (mm3)
Control surface area S0 (mm2)
Test frequency (Hz)
Present investigation
H1150
1030
983
352
126 49a
126 251
20000 67
Viswanathan et al. [4]
H1150
–
–
328 (34 HRC)
–
1500
12
Nie and Mutoh [7]
H1025
1073
1056
390
6a
26a
100
Wu and Lin [1]
H900 H1150
1414 966
1387 880
448 (45.5 HRC) 315 (32.5 HRC)
509
339
20
Volume/surface in which the stress is higher than 95% of the nominal stress.
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213
Fig. 14. Modified S–N data from the present investigation and the literature [1,4,7]. The run-out specimens are marked with arrows.
Fig. 16. Modified S–N diagram. Fig. 15. Influence of the stress ratio R on the fatigue limit.
As shown by the dot-dashed line in Fig. 16, the fatigue strength is underestimated by approximately 40% if the ODA is considered. It is mentioned in Section 3.2 that the border between the ODA and the subsequent fracture surface of the fish-eye features was not clearly distinguishable (see Fig. 10). Therefore, the measured size of the ODAs may be too large. However, even if the ODA sizes are overestimated from the micrographs and corrected smaller sizes are used instead, the prediction would still be highly conservative. This raises a question about the difference between the mechanical effects of the ODAs observed in 17-4PH stainless steel and in other materials. Shiozawa et al. [20,23] first noted that the SIF of the inclusions usually decreases with the number of cycles to failure, whereas the SIF is nearly constant for ODAs. Furthermore, they mentioned that the value of the SIF range DK at the border of the ODA is almost equal to the threshold SIF range of a long crack DKth,lc. This means that ODA formation takes place until DK reaches the threshold for a long crack and conventional crack propagation starts afterwards.
It was shown in Fig. 11 that the size of the inclusions that pffiffiffiffiffiffiffiffiffiffi caused failure, areaInc , is independent of the number of cycles pffiffiffiffiffiffiffiffiffiffi to failure, Nf, but the size of the ODAs, areaODA , increases with Nf. However, it is obvious from Fig. 16 that Nf is depending on the size of inclusions or ODAs and the nominal stress according to Eqs. (3) and (4). In order to calculate the SIF ranges for inclusions and ODAs, following formulae [11] were used:
DK ¼ 0:65 Dr
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi p area;
ð5Þ
for surface inclusions and:
DK ¼ 0:5 Dr
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi p area;
ð6Þ
for internal inclusions and ODAs. The DK values were normalised by the experimentally determined R-ratio dependency {(1 R)/2}0.421 and plotted against the number of cycles to failure, Nf, in Fig. 17. Although the normalised DK values for inclusions decrease with Nf, the values for the ODAs are nearly constant, with a mean value
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As seen from Fig. 18, as well as Fig. 16, the inclusion size is the determining parameter for the threshold conditions. Nevertheless, it is obvious in Fig. 18 that the SIF range of ODAs, DKODA, is not a constant value, but in fact depends on the size. It is interesting that the size-dependency of DKODA follows the same slope of 1/3 that is characterised by Eq. (7), although the values of DKODA are approximately 40% higher than DKth (as shown by the dot-dashed line in Fig. 18). The reason for this behaviour is unclear at present, and further investigations are necessary to gain more insight on the role of ODAs for threshold conditions. 4.4. Extreme value distribution of inclusion size and estimation of the lower bound of the fatigue limit
Fig. 17. SIF range normalised by {(1 R)/2}0.421 vs. number of cycles to failure, Nf.
p of approximately 8 MPa m. However, the threshold SIF range for pffiffiffiffiffi long cracks for the present material is DK th;lc ¼ 6:7 MPa m at R = 1, which has previously been determined by Schönbauer et al. [6] (shown by the dashed line in Fig. 17). Consequently, the assumption that ODAs tend to grow until their SIF ranges reach a value comparable to the threshold for a long crack is not convincing for the present results. It is well known that the threshold SIF range, DKth, is dependent on the crack length or defect size when their sizes are small compared to long cracks. Therefore, the relationship between the SIF ranges normalised by the R-ratio dependency {(1 R)/2}0.421 and the size of the internal inclusions and ODAs are plotted in Fig. 18. The solid straight line shows the threshold SIF ranges for small internal cracks or defects, which pffiffiffiffiffiffiffiffiffiffi was calculated according to the area parameter model [11] as:
pffiffiffiffiffiffiffiffiffiffi1=3 1 R 0:421 area : 2
Non-metallic inclusions are found to be the most critical intrinsic defects and determine the fatigue failure in the investigated 17-4PH stainless steel. Therefore, the distribution of inclusion size is analysed based on the extreme value theory [34]. Using this method, the lower bound of the fatigue limit can be predicted according to the expected maximum inclusion size as proposed by Murakami [11]. Details on the theory and procedure exercised in what follows are well described in the literature [11,34–36]. It can be assumed that the fatigue failure of a specimen pffiffiffiffiffiffiffiffiffiffi originates at the largest inclusion with a size of areamax in a conpffiffiffiffiffiffiffiffiffiffi trol volume V0. The values of areamax measured for inclusions found at the fracture origins for n specimens during fatigue testing pffiffiffiffiffiffiffiffiffiffi can be classified in ascending order as areamax;1 . . . pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi areamax;j . . . areamax;n . With this, the cumulative distribution function Fj (%) and the reduced variates yj can be calculated from:
Fj ¼
j 100ð%Þ; nþ1
yj ¼ ln ln
j : nþ1
ð8Þ ð9Þ
Eq. (7) is a corresponding expression to Eq. (4). Additionally, the pffiffiffiffiffi threshold SIF range for long cracks, DK th;lc ¼ 6:7 MPa m, is plotted as a dotted line.
In Fig. 19, the data are plotted in an extreme value distribution diagram. Additionally, the return period T = 1/(1 F) = V/V0 and the prediction volume V, i.e., the volume in which the maximum inclusion size is rated, are indicated. The straight line in Fig. 19 can be expressed by the following equation:
Fig. 18. Stress intensity factor range normalised by {(1 R)/2}0.421 vs. internal pffiffiffiffiffiffiffiffiffiffi inclusion/ODA size, area.
Fig. 19. Extreme value distribution of the inclusion size.
DK th ¼ 2:77 103 ð352 þ 120Þ
ð7Þ
B.M. Schönbauer et al. / International Journal of Fatigue 88 (2016) 205–216
pffiffiffiffiffiffiffiffiffiffi areamax ¼ l y þ m;
ð10Þ
where:
T 1 ffi lnðTÞ ðwhen V 0 VÞ; y ¼ ln ln T
0:421 1:41 ð352 þ 120Þ 1 R : pffiffiffiffiffiffiffiffiffiffi 1=6 2 areamax
5. The lower bound of the fatigue limit can be predicted using the inclusion rating and the extreme value theory.
ð11Þ References
where l and m are the material parameters, which are measured to be l = 2.33 and m = 11.14, respectively. By substituting T = V/V0 into pffiffiffiffiffiffiffiffiffiffi Eq. (11), the maximum inclusion size for areamax of an arbitrary prediction volume V can be calculated using Eq. (10). This type of material shows a scatter in the fatigue strength because of inclusions. If the extreme case is assumed that an inclupffiffiffiffiffiffiffiffiffiffi sion with the predicted maximum value of areamax is located just below the surface (i.e., the most harmful position), the lower bound of the scatter in the fatigue limit, rwl, can be calculated as [11]:
rwl ¼
215
ð12Þ
The endurance limit at R = 1 for 1010 cycles is found to be approximately 1000 MPa in the present investigation (see Fig. 12). The maximum size of the non-metallic inclusions found pffiffiffiffiffiffiffiffiffiffi at 26 fracture surfaces in this study was areamax ¼ 18:5 lm, as shown in Fig. 19. This inclusion has a potential to reduce the fatigue limit to rwl = 818 MPa at R = 1 if it is located just below the surface. For large volumes, for instance V = 100 V0 (T = 100) and pffiffiffiffiffiffiffiffiffiffi V = 1000 V0 (T = 1000), the expected value of areamax is calculated to be 21.8 lm and 27.2 lm according to Eq. (10); and the lower bound rwl could result in 796 MPa and 767 MPa, respectively, which is considerably smaller than the aforementioned value of 1000 MPa. Therefore, it is important to recognise that the lower bound is not a fixed material constant, but a value that is dependent on the number of specimens or the overall control volume of the machine parts or structural components.
5. Conclusions In this work, the fatigue properties of precipitation hardened c hromium–nickel–copper stainless steel 17-4PH were investigated. Experiments were performed at three different stress ratios in the VHCF regime up to more than 1010 cycles to failure. Fractographic investigations were conducted to identify the crack initiation sites. The data obtained were compared with data from the literature pffiffiffiffiffiffiffiffiffiffi and evaluated using the area parameter model. The following results were found: 1. Ultrasonic fatigue failure preferably originates from nonmetallic inclusions at the surface and in the interior of specimens. For rotating bending fatigue specimens with electropolished surfaces, crack initiation occurs from small pits that are probably formed from surface inclusions during electropolishing. pffiffiffiffiffiffiffiffiffiffi 2. The fatigue strength can be estimated according to the area parameter model by using the Vickers hardness, HV, and the square root of the projection area of non-metallic inclusions pffiffiffiffiffiffiffiffiffiffi perpendicular to the loading direction, area. 3. The stress ratio dependency of the fatigue limit can be a described by the term 1R . The exponent of a can be deter2 mined appropriately from the fractographic investigations on the specimens failed from non-metallic inclusions. 4. Optically dark areas (ODAs) are formed during failure from internal inclusions. The stress intensity factor range at the border of ODA, DKODA, is correlated to the size-dependent threshold value for propagation of small cracks, DKth. However, the values of DKODA are approximately 40% higher than the calculated value of DKth.
[1] Wu J-H, Lin C-K. Tensile and fatigue properties of 17-4PH stainless steel at high temperatures. Metall Mater Trans A 2002;33:1715–24. [2] Wu J-H, Lin C-K. Influence of frequency on high-temperature fatigue behavior of 17-4PH stainless steels. Mater Trans, JIM 2003;44:713–21. [3] Hsu K-C, Lin C-K. Influence of frequency on the high-temperature fatigue crack growth behavior of 17-4PH stainless steels. Mater Trans, JIM 2007;48:490–9. [4] Viswanathan R, Wittig JE, Syrett BC. Corrosion fatigue o 17-4PH turbine blade steel in chloride environments. In: Jaffe RI, editor. Proceedings of EPRI conference on corrosion fatigue of steam turbine blade materials. Palo Alto, Ca: Pergamon Press; 1981. [5] Lin C-K, Lin C-P. Corrosion fatigue behavior of 17-4PH stainless steel in different tempers. In: Reuter WG, Pascik RS, editors. Fatigue and fracture mechanics. West Conshohocken, PA: ASTM International; 2002. p. 598–613. [6] Schönbauer BM, Stanzl-Tschegg SE, Perlega A, Salzman RN, Rieger NF, Turnbull A, et al. The influence of corrosion pits on the fatigue life of 17-4PH steam turbine blade steel. Eng Fract Mech 2015;147:158–75. [7] Nie D, Mutoh Y. Fatigue limit prediction of the matrix of 17-4PH stainless steel based on small crack mechanics. J Press Vessel-Technol ASME 2013;135. [8] Haddad MHE, Topper TH, Smith KN. Prediction of non propagating cracks. Eng Fract Mech 1979;11:573–84. [9] Murakami Y, Endo M. Effect of hardness and crack geometries on DKth of small cracks emanating from small defect. In: Miller KJ, de Los Rios ER, editors. The behavior of short fatigue crack. London: Mechanical Engineering Publications; 1986. p. 275–93. [10] Murakami Y, Endo M. Quantitative evaluation of fatigue strength of metals containing various small defects or cracks. Eng Fract Mech 1983;17:1–15. [11] Murakami Y. Metal fatigue, effects of small defects and nonmetallic inclusions. Elsevier; 2002. [12] Endo M, Ikeda K. Prediction of the fatigue strength of nodular cast iron under combined loading. Int J Mod Phys B 2006;20–27:3817–23. [13] Furuya Y, Abe T. Effect of mean stress on fatigue properties of 1800 MPa-class spring steel. Mater Des 2011;32:1101–7. [14] Kovacs S, Beck T, Singheiser L. Influence of mean stresses on fatigue life and damage of a turbine blade steel in the VHCF-regime. Int J Fatigue 2013;49:90–9. [15] Schönbauer BM, Perlega A, Stanzl-Tschegg SE. Influence of stress ratio and environmental surface degradation on the VHCF behaviour of steam turbine blade steels. In: Proceedings of VHCF-6, Chengdu; 2014. [16] Matsunaga H, Sun C, Hong Y, Murakami Y. Dominant factors for very-highcycle fatigue of high-strength steels and a new design method for components. Fatigue Fract Eng M 2015;38:1274–84. [17] Abe T, Furuya Y, Matsuoka S. Gigacycle fatigue properties of 1800 MPa class spring steels. Fatigue Fract Eng M 2004;27:159–67. [18] Schönbauer B, Perlega A, Karr UP, Gandy D, Stanzl-Tschegg S. Pit-to-crack transition under cyclic loading in 12% Cr steam turbine blade steel. Int J Fatigue 2015;76:19–32. [19] Murakami Y, Nomoto T, Ueda T, Murakami Y. On the mechanism of fatigue failure in the superlong life regime (N>107 cycles). Part 1: influence of hydrogen trapped by inclusions. Fatigue Fract Eng M 2000;23:893–902. [20] 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. Int J Fatigue 2006;28:1521–32. [21] Sakai T. Review and Prospects for Current Studies on Very High Cycle Fatigue of Metallic Materials for Machine Structural Use. JSME Int J A – Solid M 2009;3:425–39. [22] Murakami Y, Nomoto T, Ueda T. Factors influencing the mechanism of superlong fatigue failure in steels. Fatigue Fract Eng M 1999;22:581–90. [23] Shiozawa K, Lu L, Ishihara S. S–N curve characteristics and subsurface crack initiation behaviour in ultra-long life fatigue of a high carbon-chromium bearing steel. Fatigue Fract Eng M 2001;24:781–90. [24] Sakai T, Takeda M, Tanaka N, Kanemitsu M, Oguma N, Shiozawa K. Characteristic S–N property of high carbon chromium bearing steel in ultrawide life region under rotating bending. Mater Sci Res Int 2001;STP1:41–6. [25] Mayer H, Fitzka M, Schuller R. Constant and variable amplitude ultrasonic fatigue of 2024-T351 aluminium alloy at different load ratios. Ultrasonics 2013;53:1425–32. [26] Stanzl S. A new experimental method for measuring life time and crack growth of materials under multi-stage and random loadings. Ultrasonics 1981;19:269–72. [27] Mayer H. Fatigue crack growth and threshold measurements at very high frequencies. Int Mater Rev 1999;44(1):1–34. [28] Zhao P, Xuan F-Z. Ratcheting behavior of advanced 9–12% chromium ferrite steel under creep–fatigue loadings: Fracture modes and dislocation patterns. Mater Sci Eng 2012;A539:301–7. [29] Karadag M, Stephens RI. The influence of high R ratio on unnotched fatigue behavior of 1045 steel with three different heat treatments. Int J Fatigue 2003;25:191–200.
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[30] Zhuang WZ, Halford GR. Investigation of residual stress relaxation under cyclic load. Int J Fatigue 2001;23(Suppl. 1):31–7. [31] ISO 18265:2004(E). Metallic materials – conversion of hardness values; 2003. [32] Ochi Y, Matsumura T, Masaki K, Yoshida S. High-cycle rotating bending fatigue property in very long-life regime of high-strength steels. Fatigue Fract Eng M 2002;25:823–30. [33] Murakami Y, Uemura Y, Natsume Y, Miyakawa S. Effect of mean stress on the fatigue strength of high-strength steels containing small defects or nonmetallic inclusions. Trans Jpn Soc Mech Eng A 1990;56:1074–81.
[34] Gumbel EJ. Statistics of extremes. Columbia University Press; 1958. [35] Beretta S, Murakami Y. Statistical analysis of defects for fatigue strength prediction and quality control of materials. Fatigue Fract Eng M 1998;21:1049–65. [36] Beretta S, Murakami Y. Largest-extreme-value distribution analysis of multiple inclusion types in determining steel cleanliness. Metall Trans B 2001;32B:517–23.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
VHCF properties and fatigue limit prediction of precipitation hardened 17-4PH stainless steel Bernd M. Schönbauer a,b,c,⇑, Keiji Yanase a,b, Masahiro Endo a,b a
Department of Mechanical Engineering, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan Institute of Materials Science and Technology, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan c Institute of Physics and Materials Science, University of Natural Resources and Life Sciences (BOKU), Peter-Jordan-Str. 82, 1190 Vienna, Austria b
a r t i c l e
i n f o
Article history: Received 2 December 2015 Received in revised form 24 March 2016 Accepted 31 March 2016 Available online 1 April 2016 Keywords: 17-4PH stainless steel Fatigue limit Very high cycle fatigue pffiffiffiffiffiffiffiffiffiffi area parameter model Non-metallic inclusions
a b s t r a c t In this work, the very high cycle fatigue properties of precipitation-hardened chromium–nickel–copper stainless steel 17-4PH are investigated, and the factors determining the fatigue strength are discussed. In addition, fatigue test results on comparable materials reported in the literature are evaluated, and the influence of material hardness on the fatigue life and the endurance strength is quantified. Fractographic investigations show that fatigue fracture initiates predominantly from non-metallic inclusions at the surface and in the interior of specimens. It is found that the endurance limit at more than 1010 pffiffiffiffiffiffiffiffiffiffi loading cycles can be predicted by the area parameter model. The stress ratio dependency on the fatigue strength is determined with good accuracy using a simple method. Furthermore, the lower bound of the fatigue limit is predicted by the inclusion rating and use of the extreme value theory. In addition, the role of the optically dark areas observed around internal inclusions is discussed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Precipitation hardened stainless steel 17-4PH possesses excellent properties in terms of static and fatigue strengths, toughness, fabrication characteristics and heat treatment distortion. In particular, its resistance to corrosion is comparable to that of AISI 304 austenitic stainless steel in most environments. Therefore, it is widely used in applications where high strength as well as good corrosion resistance is required, e.g., in the aerospace, chemical, food-processing, paper and power industries. Some investigations on the fatigue properties of 17-4PH are reported in the literature. For instance, Wu and Lin [1,2] investigated the influence of temperature and cyclic loading frequency on the fatigue life for different heat treatments. Hsu and Lin [3] performed fatigue crack growth rate measurements at high temperatures with different frequencies. The corrosion fatigue behaviour was investigated by Viswanathan et al. [4], Lin and Lin [5] and Schönbauer et al. [6]. Nie and Mutoh [7] proposed a method to predict the fatigue strength of 17-4PH stainless steel by assuming that material failure initiates from the matrix based on the small crack model proposed by El Haddad et al. [8]. A similar approach was used by Schönbauer ⇑ Corresponding author at: Institute of Physics and Materials Science, University of Natural Resources and Life Sciences (BOKU), Peter-Jordan-Str. 82, 1190 Vienna, Austria. E-mail address: [email protected] (B.M. Schönbauer). http://dx.doi.org/10.1016/j.ijfatigue.2016.03.034 0142-1123/Ó 2016 Elsevier Ltd. All rights reserved.
et al. [6] for fatigue limit prediction in the presence of corrosion pits, which is applicable to different environments, stress ratios and a wide range of defect sizes. However, an extensive number of fatigue tests are required to determine all the material parameters necessary for the prediction. In laboratory tests, fatigue crack initiation in 17-4PH stainless steel is mainly observed at slip bands or non-metallic inclusions [1,6,7]. In actual components, surface discontinuities (e.g., scratches, pits, surface roughness, etc.) existing at critical locations can cause fatigue crack initiation. In the presence of compressive residual stresses at the surface of the material, fatigue failure from internal defects, such as non-metallic inclusions, becomes more dominant, especially in the very high cycle fatigue (VHCF) regime. Therefore, a simple model that can estimate the fatigue limit by taking the effect of small defects into account is essential for practical applications. pffiffiffiffiffiffiffiffiffiffi Murakami and Endo [9] proposed the area parameter model that can predict the fatigue limit using only two parameters: the square root of the projection area of a small defect or a crack perpffiffiffiffiffiffiffiffiffiffi pendicular to the loading direction ( area) and the Vickers hardness (HV). This model is based on the phenomenological fact that the fatigue limit is not a critical condition for crack initiation, but that it corresponds to the non-propagation of a small crack [10]. From this perspective, the fatigue limit in the presence of a small defect (e.g., a non-metallic inclusion) is determined by the
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Nomenclature b FGA Fj GBF HRC HV n N Nf ODA R RT S0 SEM SIF T V
factor for fatigue limit prediction dependent on location of defect fine granular area cumulative distribution function granular bright facet Rockwell hardness (C scale) Vickers hardness number of specimens number of cycles number of cycles to failure optically dark area stress ratio room temperature control surface area of specimens subjected to maximum stresses scanning electron microscope stress intensity factor return period prediction volume in which the maximum inclusion size is rated
threshold condition for propagation of a crack emanating from a defect. For this type of problem, fracture mechanics can be used and the stress intensity factor (SIF) can be calculated. Finally, a generalised expression of the fatigue limit rw is given as [11]:
b ðHV þ 120Þ
rw ¼ pffiffiffiffiffiffiffiffiffiffi1=6 area
a 1R ; 2
ð1Þ
V0
control volume of specimens subjected to maximum stresses VHCF very high cycle fatigue y reduced variates j pffiffiffiffiffiffiffiffiffiffi area the square root of the projection area of a small defect or a crack perpendicular to the ffiloading direction pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi parea ffiffiffiffiffiffiffiffiffiffiInc inclusion size in terms of area pffiffiffiffiffiffiffiffiffiffi in terms of area parea ffiffiffiffiffiffiffiffiffiffimax maximum inclusion size pffiffiffiffiffiffiffiffiffi ffi areaODA ODA size in terms of area DK stress intensity factor range DKODA stress intensity factor range of an optically dark area DKth threshold stress intensity factor range DKth,lc threshold stress intensity factor range of a long cracks a exponent in the correction factor for the stress-ratio dependency of the fatigue limit Dr stress range (for fully reversed loading, also the compression part is taken into account) r nominal stress rw fatigue limit rwl lower bound of the scatter in the fatigue limit
pffiffiffiffiffiffiffiffiffiffi bending testing. The results are evaluated using the area parameter model to predict the fatigue strength of 17-4PH stainless steel for different stress ratios with a focus on addressing failure from non-metallic inclusions. Furthermore, the lower bound of the scatter in the fatigue limit is determined using statistics of extremes by analysing the defect size at crack initiation sites. 2. Material and experimental procedure
where the factor b is 1.43 for a surface defect/crack, 1.56 for an internal defect/crack and 1.41 for a subsurface defect just in contact pffiffiffiffiffiffiffiffiffiffi with the surface. Here, rw is in MPa, area is in lm and HV is in 2 kgf/mm . The influence of the stress ratio R can be taken into account by the correction factor {(1 R)/2}a, where a is given by:
a ¼ 0:226 þ HV 104 :
ð2Þ
This equation was initially derived based on the experimental results for two steels, and thereafter, it has successively been applied to a variety of steels [11]. However, it has been reported that the values of a determined experimentally for ductile cast iron [12], high strength steels [13] and turbine blade steels [14,15] were significantly different from those calculated using Eq. (2). The origin of fatigue fracture in the VHCF regime is often found in the interior of specimens. Non-metallic inclusions are regularly observed at the crack initiation sites [16], but failure can also originate from the matrix [17,18]. In the centre of a so-called ‘‘fish-eye” fracture, a fine grained area is often observed and appears dark when observed with an optical microscope and bright with a scanning electron microscope (SEM). Different explanations are provided to describe the formation of this area [19–21], which was named an ‘‘optically dark area” (ODA) by Murakami et al. [19,22], a ‘‘granular bright facet” (GBF) by Shiozawa et al. [23] and a ‘‘fine granular area” (FGA) by Sakai et al. [24]. Hereafter, the first expression (ODA) will be used in this work. For some high-strength steels in the VHCF regime, it is reported that the governing parameter for pffiffiffiffiffiffiffiffiffiffi the fatigue strength prediction according to Eq. (1) is the area of the ODA [19]. The use of the size of internal inclusions may lead to non-conservative results. In this investigation, the fatigue test results in the VHCF regime up to 1010 cycles to failure are reported. Tests were performed at three different R-ratios with ultrasonic fatigue testing and rotating
2.1. Material The material tested was precipitation-hardened chromium–nic kel–copper stainless steel 17-4PH that was hardened at 913 °C and age-hardened at 621 °C for 4 h (condition H1150). The chemical composition and the mechanical properties are given in Tables 1 and 2, respectively. The microstructure of the material is shown in Fig. 1. Equiaxed martensite laths are visible within the austenite grains. An average grain size of 11 lm was measured, independent of orientation. The number of inclusions per area was determined to be 23.1 per mm2 in the inspection area of 32 mm2. 2.2. Test setups Most tests were performed using an ultrasonic fatigue testing technique developed at BOKU [25,26], which stimulates specimens to resonance vibration at a frequency of approximately 20 kHz. This closed-loop controlled ultrasonic fatigue testing equipment ensures an accuracy of ±1% of the nominal displacement amplitude by using a vibration gauge at one end of the specimen that serves as the feed-back in a test generator. For tests performed under fully reversed loading (R = 1), only one end of a specimen is fixed to the resonance system and the other end vibrates freely. By superimposing a static force at this end of the specimen, tests at R – 1 can be performed. More details on the design of ultrasonic
Table 1 Chemical composition of the 17-4PH in weight %. C
Si
Mn
Cr
Cu
Ni
Nb + Ta
P
S
0.033
0.40
0.49
15.57
3.31
4.37
0.23
0.027
0.001
B.M. Schönbauer et al. / International Journal of Fatigue 88 (2016) 205–216 Table 2 Mechanical properties of the 17-4PH at room temperature. Tensile strength (MPa)
Yield strength (MPa)
Elongation (%)
Reduction of area (%)
Vickers hardness (kgf/mm2)
1030
983
21
61
352
207
measured at the surface using X-ray diffraction. To investigate the influence of annealing on the mechanical properties, tensile and hardness tests were performed both before and after heat treatment. After stress-relief annealing, the tensile strength and Vickers hardness were reduced by 3% and 1%, respectively, which was considered acceptable. The geometry for the rotating bending test specimens is shown in Fig. 2c. The control volume in which the maximum cyclic stress is higher than 95% of the nominal bending stress is 49 mm3 and the control surface area is 251 mm2. The surface of the specimens was ground and electropolished after machining. The residual stress measured on the surface after electropolishing was 6 ± 15 MPa. 3. Results 3.1. S–N data
Fig. 1. Microstructure of 17-4PH.
components can be found in [27]. The test environment was laboratory air at 90 °C by placing the specimen in a test chamber and blowing air around the specimen that was heated using a coil. A thermo-couple was attached to the specimen and temperature adjustment was provided by closed-loop control which ensured a constant temperature with an accuracy of ±1 °C. Furthermore, rotating bending tests were performed at room temperature with a test frequency of 67 Hz at Fukuoka University. 2.3. Test specimens The specimen geometries for ultrasonic fatigue testing at R = –1 and R – –1 are shown in Fig. 2a and b, respectively. The control volume and control surface area in the gauge length (which was 10 mm in length), i.e., the volume and surface area subjected to a constant stress during fatigue testing, are 126 mm3 and 126 mm2, respectively. The surface of specimens was ground over the gauge length with abrasive paper up to a grade of #4000, and stressrelief annealing was conducted in a vacuum at 600 °C for one hour afterwards. A compressive residual stress of 65 ± 29 MPa was
Fatigue tests were performed at R = 1, 0.05 and 0.4. The S–N data are shown in Fig. 3, in which the stress on the ordinate is expressed by the range, Dr. Most tests were performed at approximately 20 kHz using an ultrasonic fatigue technique, and six rotating bending tests (R = 1) were conducted. Additionally, one specimen was tested at 5 Hz using an ultrasonic fatigue test specimen, as shown in Fig. 2b, at R = 0.4 using a servohydraulic testing machine. No significant influence associated with the testing method and specimen geometry on the fatigue life was found. The fatigue strength decreases as the stress ratio R increases. A fatigue limit was not determined since fatigue failure occurred after more than 1010 loading cycles. 3.2. Fractography The fracture surfaces of the failed specimens were analysed using a SEM. For most ultrasonic fatigue test specimens, a nonmetallic inclusion was found at the crack initiation site, see Fig. 4a–c. At R = 1, all the specimens failed as a result of internal inclusions. Two of them were located slightly below the surface of the specimen, see Fig. 4b (labelled as ‘‘Subsurface” in Fig. 3). At R = 0.05, all the specimens failed from interior inclusions, except one in which failure resulted from a surface inclusion. At R = 0.4, crack initiation from surface and interior inclusions was observed. At one of these crack initiation sites, a structural inhomogeneity was found, see Fig. 4d. This inhomogeneity was analysed using energy dispersive X-ray spectroscopy and a high amount of chromium and niobium was detected. Furthermore, cup-and-cone like
Fig. 2. Specimen geometries for ultrasonic fatigue testing at (a) R = 1 and (b) R – 1 and (c) rotating bending testing (dimensions in mm).
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Fig. 3. S–N test results for different R-ratios. Run-out specimens are marked with arrows.
fractures occurred in two specimens, which exhibited large degrees of plastic deformation during failure (see Fig. 5). These appeared similar to fracture surfaces observed in tensile tests. Although fatigue failure took place after more than 107 cycles, no distinct fatigue features were observable on the fracture surfaces. The cup-and-cone like fracture is often observed during fatigue testing of ductile steels at high stress ratios (cf. [14,18,28,29]) and is associated with cyclic creep/ratcheting. For more details, we refer to Schönbauer et al. [6]. To investigate any influence of test frequency and temperature on the fracture mode, an additional test was performed at 5 Hz at room temperature (RT). Again, a cup-and-cone like fracture occurred, and the fatigue life was consistent with the ultrasonic fatigue test results (see the x-marked
diamond symbol in Fig. 3). Although only one specimen was tested under these conditions, the result clearly shows that the aforementioned fracture mode is independent of the test procedure and the temperature for the investigated range (5 Hz–20 kHz and RT–90 °C). Thirteen inclusions at the crack initiation site of the specimens which failed during ultrasonic fatigue testing were analysed using energy dispersive X-ray spectroscopy. The chemical composition of these inclusions was determined to be calcium aluminate x(CaO) Al2O3, mostly containing MgO or, less often, MnO. Examples of the respective non-metallic inclusions are shown in Fig. 6. The relationship between the size and location for all the inclusions, which was measured at the fracture surfaces of ultrasonic fatigue test specimens, is shown in Fig. 7. The crack initiation sites are almost uniformly distributed. However, it is clear that crack initiation at the surface is preferred at R = 0.4. As mentioned in Section 2.3, residual stresses of 65 ± 29 MPa were measured on the surface of the ultrasonic fatigue specimens. These compressive residual stresses resulted in crack initiation at internal inclusions, as observed for tests at low stress ratios. However, it is known that high R-ratios cause the relaxation of residual stresses [30] because the maximum stress experienced during cyclic loading approaches the yield strength of the material. This fact may explain the frequent observation of surface crack initiation at R = 0.4. As shown in Fig. 3, the rotating bending fatigue test results are comparable to those obtained using the ultrasonic fatigue testing technique. However, exclusive surface failure is apparent because of the presence of the maximum bending stress at the surface of specimen. In Fig. 8, the fracture surface of a rotating bending specimen is shown. The location of the crack initiation in the highmagnification image is marked by an arrow. No inclusion was observed, but a small shallow pit is visible in the area believed to be the fracture origin. Fig. 9 shows images taken at the different surface areas of specimens where the fatigue cracks and slip bands initiated. The pictures at the top were selectively taken at N = 1.00 107 cycles, in
Fig. 4. Crack initiation sites for tests conducted at f = 20 kHz: (a) surface inclusion (Dr = 610 MPa, R = 0.4, Nf = 4.03 105 cycles), (b) subsurface inclusion (Dr = 1200 MPa, R = 1, Nf = 2.51 107 cycles), (c) fish-eye fracture (Dr = 1120 MPa, R = 1, Nf = 1.78 108 cycles) and (d) surface inhomogeneity (Dr = 600 MPa, R = 0.4, Nf = 4.34 106 cycles).
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Fig. 5. Cup-and-cone like fatigue fracture (Dr = 610 MPa, R = 0.4, Nf = 1.89 107 cycles): (a) fractured specimen with high plastic deformation and (b) fracture surface.
which 97% of the total fatigue life was already consumed. The pictures at the bottom show the same areas after fatigue failure at Nf = 1.03 107 cycles. The crack initiation site where final failure occurred was unfortunately not observed at N = 1.00 107 cycles. In Fig. 9a, the crack initiation and propagation from a small pit is visible. Such pits probably originate from inclusions during electropolishing of specimens. A small pit is also shown in Fig. 9b with slip bands in its vicinity. No cracking was observed after N = 1.00 107 cycles, but a small crack initiated prior to specimen failure. The evolution of the slip bands is also visible in Fig. 9c, but no distinct cracking is observed. These observations suggest that crack initiation mainly took place at shallow pits that formed during electropolishing. It is important to note that even after N = 107 cycles, there is steady progress of fatigue damage, such as crack propagation and slip bands evolution. Thus, it should be recognised that for the investigated 17-4PH stainless steel, the true fatigue limit to determine infinite life cannot be calibrated with the 107 load cycles that is conventionally employed in laboratory tests for steels. The defect size on the fracture surface for the rotating bending test specimens was not clearly measureable for most of the specimens because the crack initiation area was deformed during fracture. However, it was apparent that the fracture origin sites were located at the surface. Optically dark areas (ODAs) were observable around inclusions when the failure originated in the interior of ultrasonic fatigue specimens at all stress ratios. Their size was not easily measureable
209
Fig. 7. Size and location of non-metallic inclusions on the fracture surfaces.
because the border between the ODA and the neighbouring ‘‘fish-eye” region is blurred. Therefore, SEM micrographs, as well as light microscopic images were used to measure the size of the ODAs, as shown in Fig. 10. pffiffiffiffiffiffiffiffiffiffi The area of the ODAs and inclusions measured at the fracture surfaces are plotted versus the number of cycles to failure in Fig. 11. Although the ODA size increases with number of cycles to failure (shown by a dashed line), the mean value of the inclusion size is constant (shown by a solid line).
4. Discussion 4.1. Comparison with literature In the following, the fatigue test results are compared with the data reported in the literature. The material properties and specimen sizes are summarised in Table 3. For investigations in which the Rockwell hardness (HRC) was quoted, the values were converted into Vickers hardnesses (HV) according to the international standard ISO 18265 [31]. In Fig. 12, the S–N data at R = 1 measured in the present investigation are compared with those reported by Viswanathan et al. [4] and Nie and Mutoh [7]. Viswanathan et al. performed deflection controlled reversed bending tests on material with the same heat treatment condition as used in the present investigation. The
Fig. 6. Non-metallic inclusions: (a) CaOAl2O3, (b) CaO–MgO–Al2O3 and (c) CaO–MnO–Al2O3.
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This can suppress crack initiation at the surface, which is usually the preferred crack initiation site for failure up to 107 cycles. Consequently, failure occurs from internal inclusions, which consume a much higher number of load cycles for crack initiation and small crack growth. Similar observations were made by Ochi et al. [32], who systematically investigated the influence of residual stresses on the fatigue behaviour of high-strength steels. In the present investigation, it is assumed that the determined fatigue strength in the VHCF regime is not significantly affected by residual stresses because the data at R = 0.4 (where the relaxation of residual stresses is expected due to high maximum stresses) show good correlation for failure from the surface and the interior (see Fig. 3). 4.2. Influence of stress ratio R
Fig. 8. Fracture surface from the rotating bending specimen at Dr = 1100 MPa for Nf = 3.69 107 cycles (arrow marks crack initiation site).
results by Nie and Mutoh were obtained using an electrodynamic vibration fatigue testing machine at 100 Hz. Their heat treatment was slightly different (H1025), and consequently, the material hardness was higher. As is seen in Fig. 12, the endurance strengths at 108 cycles are comparable for all three investigations. The fatigue life determined by Nie and Mutoh is considerably longer than those reported by Viswanathan et al., and the data obtained in the present study lies in between. Wu and Lin [1] performed fatigue testing on 17-4PH stainless steel with different heat treatments. A commercial closed-loop servohydraulic test machine was used for experiments at R = 0.1. In Fig. 13, their results obtained with materials in heat treat conditions of H900 and H1150 are compared with the present investigation at R = 0.05. Significantly different S–N data were obtained for the different heat treatments. The data point of the specimen that failed from the surface at approximately 105 cycles in the present study lies in between those data. No investigations in the VHCF regime are reported by Wu and Lin [1]. To investigate the influence of material hardness on the fatigue life, the data are plotted in a modified S–N diagram in Fig. 14 where the stress range Dr is normalised by (HV + 120) in accordance with Eq. (1). With this approach, much better data consistency is achieved. In the approach by Murakami and Endo [9], the material hardness is used only to predict the fatigue limit. However, the current findings suggest that the material hardness can also be used for comparison of the fatigue life time for similar materials and loading conditions. When the influence of the hardness is taken into account, the fatigue strength for the data reported by Nie and Mutoh agree well with the other researchers’ data, although their data are slightly lower at N > 107. Normalising the stress range by (HV + 120) leads to good congruency for the results tested under different heat treatment conditions by Wu and Lin at R = 0.1. Furthermore, the surface failure at R = 0.05 obtained in the present investigation correlates very well with their data. However, there is still a significant gap in the fatigue life between surface and interior crack initiation. As already discussed in Section 3.2, compressive residual stresses were measured in the ultrasonic fatigue test specimens.
The R-ratio dependency in Eq. (1) is expressed by the term {(1 R)/2}a, in which the exponent a was originally determined using specimens containing artificial defects [33]. In this investigation, the determination of the value of a using fractographic information on non-metallic inclusions is studied. Fig. 15 shows the pffiffiffiffiffiffiffiffiffiffi1=6 value of rw area =fb ðHV þ 120Þg as a function of (1 R)/2 on a double-logarithmic graph, where b is 1.43 for surface defects, 1.56 for internal defects and 1.41 for subsurface defects just in contact with the surface (cf. Eq. (1)). In the figure, the data for inclusions observed on the fracture surfaces are plotted using solid symbols. The data for unbroken specimens are also plotted using pffiffiffiffiffiffiffiffiffiffi open symbols, for which the value of area of the inclusions was determined by breaking specimens in the subsequent fatigue tests at higher stress levels. In Fig. 15, a straight solid line is drawn through the lowest solid symbols. It is noted that these data points represent failure at approximately 1010 cycles, and therefore, should be representative for the endurance limit in the VHCF regime. A value of a = 0.421 is determined from the slope of the line. The coefficient of determination is r2 = 0.991, which shows that the regression line adequately fits the data. In addition, a horizontal dashed line at the ordinate value of 1 is plotted, which represents the predicted fatigue limit at R = –1 according to Eq. (1). It is noted that at R = 1 (i.e., (1 R)/2 = 1), all the data points lie above this line. As will be reported in a forthcoming paper, additional fatigue tests with specimens containing small circumferential notches with depths of 10 lm and 30 lm were performed at the same three R-ratios of 1, 0.05 and 0.4. The values of a = 0.434 determined in those tests is only 3% higher than that obtained from non-metallic inclusions. Therefore, we may conclude that the appropriate fractographic investigation of specimens which failed from nonmetallic inclusions in the VHCF regime is suitable for the determination of the exponent a. The determined value of a = 0.421 is significantly higher than the values of a = 0.261 according to Eq. (2) with HV = 352. This equation has successfully been used for estimating the value of a in a number of steels since it was initially derived based on experimental data for only two steels. However, some investigations have reported that the value of a differed significantly from those calculated by Eq. (2). For example, Furuya and Abe [13] reported a value of a = 0.5 for several steels and Kovacs et al. [14] found a = 0.546 for a martensitic 12% Cr steel. Although these investigations do not consider the defect size for determination of a (i.e., only the fatigue limit is plotted versus (1 R)/2), their results are in better agreement with the present findings than those from Eq. (2). Nevertheless, it would be very helpful to develop a simple formula similar to Eq. (2) that is based on many experimental results obtained using different materials in the future.
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Fig. 9. Surface areas of a rotating bending specimen after cyclic loading at Dr = 1200 MPa. Images show cracks and slip bands at N = 1.00 107 cycles (top) and after failure at Nf = 1.03 107 (bottom).
Fig. 10. SEM and optical micrographs of a fish-eye fracture with ODA around a non-metallic inclusion (Dr = 1060 MPa, R = 1, Nf = 7.54 108 cycles).
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Fig. 11. Size of the ODAs and non-metallic inclusions at the crack initiation sites.
Fig. 12. Comparison of the S–N test results at R = -1 with the data reported by Viswanathan et al. [4] and Nie and Mutoh [7].
4.3. Prediction of fatigue strength In the following sections, the fatigue data are evaluated using pffiffiffiffiffiffiffiffiffiffi Eq. (1) with the inclusion size, areaInc , a Vickers hardness of HV = 352 and a = 0.421 for the present steel, which yields:
b ð352 þ 120Þ
rw ¼ pffiffiffiffiffiffiffiffiffiffi 1=6 areaInc
0:421 1R : 2
ð3Þ
The results are plotted using a modified S–N diagram, as shown in Fig. 16, in which the nominal stress r is divided by the predicted fatigue limit rw (note that either the stress range or amplitude must be used for both r and rw). As seen, no failures are observed below r/rw = 1. The prediction according to Eq. (3) is conservative even for the data obtained at more than Nf = 1010 cycles to failure and works well for all three R-ratios. The solid and dashed lines show the trends for fatigue failure from the surface and the interior, respectively. In calculations of rw for the rotating bending specimens, the size of the crack initiation sites is estimated to be the mean size of the non-metallic pffiffiffiffiffiffiffiffiffiffi inclusions (in terms of areaÞ because the fracture origins were the small pits that formed from inclusions during electropolishing (see Section 3.2). It is reported by Murakami et al. [19] that the fatigue limit prediction for high-strength steels according to Eq. (3) can be pffiffiffiffiffiffiffiffiffiffi non-conservative when the inclusion size, areaInc , is used. In this pffiffiffiffiffiffiffiffiffiffi case, the use of the ODA size, areaODA , which is the size of the ODA including the inclusion, leads to reasonable results. Based on this
Fig. 13. Comparison of the S–N test results at R = 0.05 with data reported by Wu and Lin at R = 0.1 [1]. The run-out specimens are marked with arrows.
consideration, the fatigue limit is re-estimated for the present material using the following equation:
rw ¼
0:421 1:56 ð352 þ 120Þ 1 R : pffiffiffiffiffiffiffiffiffiffi 1=6 2 areaODA
ð4Þ
Table 3 Comparison of material properties and specimen sizes of different investigations.
a
Investigation
Condition for heat treatment
Tensile strength (MPa)
Yield strength (MPa)
Vickers hardness HV (kgf/mm2)
Control volume V0 (mm3)
Control surface area S0 (mm2)
Test frequency (Hz)
Present investigation
H1150
1030
983
352
126 49a
126 251
20000 67
Viswanathan et al. [4]
H1150
–
–
328 (34 HRC)
–
1500
12
Nie and Mutoh [7]
H1025
1073
1056
390
6a
26a
100
Wu and Lin [1]
H900 H1150
1414 966
1387 880
448 (45.5 HRC) 315 (32.5 HRC)
509
339
20
Volume/surface in which the stress is higher than 95% of the nominal stress.
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Fig. 14. Modified S–N data from the present investigation and the literature [1,4,7]. The run-out specimens are marked with arrows.
Fig. 16. Modified S–N diagram. Fig. 15. Influence of the stress ratio R on the fatigue limit.
As shown by the dot-dashed line in Fig. 16, the fatigue strength is underestimated by approximately 40% if the ODA is considered. It is mentioned in Section 3.2 that the border between the ODA and the subsequent fracture surface of the fish-eye features was not clearly distinguishable (see Fig. 10). Therefore, the measured size of the ODAs may be too large. However, even if the ODA sizes are overestimated from the micrographs and corrected smaller sizes are used instead, the prediction would still be highly conservative. This raises a question about the difference between the mechanical effects of the ODAs observed in 17-4PH stainless steel and in other materials. Shiozawa et al. [20,23] first noted that the SIF of the inclusions usually decreases with the number of cycles to failure, whereas the SIF is nearly constant for ODAs. Furthermore, they mentioned that the value of the SIF range DK at the border of the ODA is almost equal to the threshold SIF range of a long crack DKth,lc. This means that ODA formation takes place until DK reaches the threshold for a long crack and conventional crack propagation starts afterwards.
It was shown in Fig. 11 that the size of the inclusions that pffiffiffiffiffiffiffiffiffiffi caused failure, areaInc , is independent of the number of cycles pffiffiffiffiffiffiffiffiffiffi to failure, Nf, but the size of the ODAs, areaODA , increases with Nf. However, it is obvious from Fig. 16 that Nf is depending on the size of inclusions or ODAs and the nominal stress according to Eqs. (3) and (4). In order to calculate the SIF ranges for inclusions and ODAs, following formulae [11] were used:
DK ¼ 0:65 Dr
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi p area;
ð5Þ
for surface inclusions and:
DK ¼ 0:5 Dr
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi p area;
ð6Þ
for internal inclusions and ODAs. The DK values were normalised by the experimentally determined R-ratio dependency {(1 R)/2}0.421 and plotted against the number of cycles to failure, Nf, in Fig. 17. Although the normalised DK values for inclusions decrease with Nf, the values for the ODAs are nearly constant, with a mean value
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As seen from Fig. 18, as well as Fig. 16, the inclusion size is the determining parameter for the threshold conditions. Nevertheless, it is obvious in Fig. 18 that the SIF range of ODAs, DKODA, is not a constant value, but in fact depends on the size. It is interesting that the size-dependency of DKODA follows the same slope of 1/3 that is characterised by Eq. (7), although the values of DKODA are approximately 40% higher than DKth (as shown by the dot-dashed line in Fig. 18). The reason for this behaviour is unclear at present, and further investigations are necessary to gain more insight on the role of ODAs for threshold conditions. 4.4. Extreme value distribution of inclusion size and estimation of the lower bound of the fatigue limit
Fig. 17. SIF range normalised by {(1 R)/2}0.421 vs. number of cycles to failure, Nf.
p of approximately 8 MPa m. However, the threshold SIF range for pffiffiffiffiffi long cracks for the present material is DK th;lc ¼ 6:7 MPa m at R = 1, which has previously been determined by Schönbauer et al. [6] (shown by the dashed line in Fig. 17). Consequently, the assumption that ODAs tend to grow until their SIF ranges reach a value comparable to the threshold for a long crack is not convincing for the present results. It is well known that the threshold SIF range, DKth, is dependent on the crack length or defect size when their sizes are small compared to long cracks. Therefore, the relationship between the SIF ranges normalised by the R-ratio dependency {(1 R)/2}0.421 and the size of the internal inclusions and ODAs are plotted in Fig. 18. The solid straight line shows the threshold SIF ranges for small internal cracks or defects, which pffiffiffiffiffiffiffiffiffiffi was calculated according to the area parameter model [11] as:
pffiffiffiffiffiffiffiffiffiffi1=3 1 R 0:421 area : 2
Non-metallic inclusions are found to be the most critical intrinsic defects and determine the fatigue failure in the investigated 17-4PH stainless steel. Therefore, the distribution of inclusion size is analysed based on the extreme value theory [34]. Using this method, the lower bound of the fatigue limit can be predicted according to the expected maximum inclusion size as proposed by Murakami [11]. Details on the theory and procedure exercised in what follows are well described in the literature [11,34–36]. It can be assumed that the fatigue failure of a specimen pffiffiffiffiffiffiffiffiffiffi originates at the largest inclusion with a size of areamax in a conpffiffiffiffiffiffiffiffiffiffi trol volume V0. The values of areamax measured for inclusions found at the fracture origins for n specimens during fatigue testing pffiffiffiffiffiffiffiffiffiffi can be classified in ascending order as areamax;1 . . . pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi areamax;j . . . areamax;n . With this, the cumulative distribution function Fj (%) and the reduced variates yj can be calculated from:
Fj ¼
j 100ð%Þ; nþ1
yj ¼ ln ln
j : nþ1
ð8Þ ð9Þ
Eq. (7) is a corresponding expression to Eq. (4). Additionally, the pffiffiffiffiffi threshold SIF range for long cracks, DK th;lc ¼ 6:7 MPa m, is plotted as a dotted line.
In Fig. 19, the data are plotted in an extreme value distribution diagram. Additionally, the return period T = 1/(1 F) = V/V0 and the prediction volume V, i.e., the volume in which the maximum inclusion size is rated, are indicated. The straight line in Fig. 19 can be expressed by the following equation:
Fig. 18. Stress intensity factor range normalised by {(1 R)/2}0.421 vs. internal pffiffiffiffiffiffiffiffiffiffi inclusion/ODA size, area.
Fig. 19. Extreme value distribution of the inclusion size.
DK th ¼ 2:77 103 ð352 þ 120Þ
ð7Þ
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pffiffiffiffiffiffiffiffiffiffi areamax ¼ l y þ m;
ð10Þ
where:
T 1 ffi lnðTÞ ðwhen V 0 VÞ; y ¼ ln ln T
0:421 1:41 ð352 þ 120Þ 1 R : pffiffiffiffiffiffiffiffiffiffi 1=6 2 areamax
5. The lower bound of the fatigue limit can be predicted using the inclusion rating and the extreme value theory.
ð11Þ References
where l and m are the material parameters, which are measured to be l = 2.33 and m = 11.14, respectively. By substituting T = V/V0 into pffiffiffiffiffiffiffiffiffiffi Eq. (11), the maximum inclusion size for areamax of an arbitrary prediction volume V can be calculated using Eq. (10). This type of material shows a scatter in the fatigue strength because of inclusions. If the extreme case is assumed that an inclupffiffiffiffiffiffiffiffiffiffi sion with the predicted maximum value of areamax is located just below the surface (i.e., the most harmful position), the lower bound of the scatter in the fatigue limit, rwl, can be calculated as [11]:
rwl ¼
215
ð12Þ
The endurance limit at R = 1 for 1010 cycles is found to be approximately 1000 MPa in the present investigation (see Fig. 12). The maximum size of the non-metallic inclusions found pffiffiffiffiffiffiffiffiffiffi at 26 fracture surfaces in this study was areamax ¼ 18:5 lm, as shown in Fig. 19. This inclusion has a potential to reduce the fatigue limit to rwl = 818 MPa at R = 1 if it is located just below the surface. For large volumes, for instance V = 100 V0 (T = 100) and pffiffiffiffiffiffiffiffiffiffi V = 1000 V0 (T = 1000), the expected value of areamax is calculated to be 21.8 lm and 27.2 lm according to Eq. (10); and the lower bound rwl could result in 796 MPa and 767 MPa, respectively, which is considerably smaller than the aforementioned value of 1000 MPa. Therefore, it is important to recognise that the lower bound is not a fixed material constant, but a value that is dependent on the number of specimens or the overall control volume of the machine parts or structural components.
5. Conclusions In this work, the fatigue properties of precipitation hardened c hromium–nickel–copper stainless steel 17-4PH were investigated. Experiments were performed at three different stress ratios in the VHCF regime up to more than 1010 cycles to failure. Fractographic investigations were conducted to identify the crack initiation sites. The data obtained were compared with data from the literature pffiffiffiffiffiffiffiffiffiffi and evaluated using the area parameter model. The following results were found: 1. Ultrasonic fatigue failure preferably originates from nonmetallic inclusions at the surface and in the interior of specimens. For rotating bending fatigue specimens with electropolished surfaces, crack initiation occurs from small pits that are probably formed from surface inclusions during electropolishing. pffiffiffiffiffiffiffiffiffiffi 2. The fatigue strength can be estimated according to the area parameter model by using the Vickers hardness, HV, and the square root of the projection area of non-metallic inclusions pffiffiffiffiffiffiffiffiffiffi perpendicular to the loading direction, area. 3. The stress ratio dependency of the fatigue limit can be a described by the term 1R . The exponent of a can be deter2 mined appropriately from the fractographic investigations on the specimens failed from non-metallic inclusions. 4. Optically dark areas (ODAs) are formed during failure from internal inclusions. The stress intensity factor range at the border of ODA, DKODA, is correlated to the size-dependent threshold value for propagation of small cracks, DKth. However, the values of DKODA are approximately 40% higher than the calculated value of DKth.
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