The influence of various types of small defects on the fatigue limit of precipitation-hardened 17-4PH stainless steel

Accepted Manuscript The Influence of various types of small defects on the threshold behaviour of precipitation-hardened 17-4PH stainless steel Bernd M. Schönbauer, Keiji Yanase, Masahiro Endo PII: DOI: Reference:

S0167-8442(16)30222-1 http://dx.doi.org/10.1016/j.tafmec.2016.10.003 TAFMEC 1777

To appear in:

Theoretical and Applied Fracture Mechanics

Received Date: Revised Date: Accepted Date:

2 August 2016 30 September 2016 11 October 2016

Please cite this article as: B.M. Schönbauer, K. Yanase, M. Endo, The Influence of various types of small defects on the threshold behaviour of precipitation-hardened 17-4PH stainless steel, Theoretical and Applied Fracture Mechanics (2016), doi: http://dx.doi.org/10.1016/j.tafmec.2016.10.003

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THE INFLUENCE OF VARIOUS TYPES OF SMALL DEFECTS ON THE THRESHOLD BEHAVIOUR OF PRECIPITATION-HARDENED 17-4PH STAINLESS STEEL Bernd M. Schönbauer1*, Keiji Yanase2,3 and Masahiro Endo2,3 1

Institute of Physics and Materials Science, University of Natural Resources and Life Sciences (BOKU), Peter-Jordan-Str. 82, 1190 Vienna, Austria 2

3

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 *Corresponding author: [email protected]

Keywords: 17-4PH stainless steel; fatigue limit; small defects; corrosion pits; model

parameter

ABSTRACT Fatigue tests were performed on 17-4PH stainless steel specimens containing small artificial defects, with ranging from 30-900 m at stress ratios, R, of -1, 0.05 and 0.4. An investigation was thus conducted to examine the influence of various types of small artificial defects on fatigue strength, including circumferential notches, corrosion pits, drilled holes and pre-cracked holes. The fatigue limit was determined by the threshold condition for the propagation of a crack emanating from the defects. The threshold stress intensity factor range, Kth, exhibited a defect size dependency for 80 m, and it became a constant value for 80 m independent of R. Based on the parameter model and a material constant of Kth for long cracks, the fatigue limit could be predicted as a function of R, with the exception of drilled holes with relatively large diameters of 100 and 300 m, for which the fatigue limit was determined by the critical condition for crack initiation. When artificial defects were absent or non-detrimental, intrinsic defects, such as non-metallic inclusions, were found to control the fatigue strength and, in addition, were responsible for the scatter in the fatigue limit. The proposed method enables the quantitative evaluation of the lower bound of the scatter as a function of the number of test specimens, or the overall control volume of fatigue-loaded components.

1

INTRODUCTION

High-strength metallic materials are usually very sensitive to small defects that locally give rise to stress concentration. Under fatigue loading, flaws or non-metallic inclusions of only a few microns can cause crack initiation, often leading to the onset of a fatal fracture. In practice, the size of inherent defects in modern steels (e.g., precipitates and non-metallic inclusions) is highly controlled during the manufacturing process. Therefore, the risk of fatigue failure due to small surface defects such as scratches, machined flaws, insufficient surface finishes, punch marks and environmentallyinduced surface flaws (e.g., corrosion pits) is a matter of concern. The precipitation-hardening chromium-nickel-copper stainless steel 17-4PH possesses high strength, high toughness and good fabrication characteristics. Furthermore, its resistance to corrosion is comparable to that of AISI 304 austenitic stainless steel in most environments. Thus, it is an excellent material for applications where both high strength and good corrosion resistance are required, such as in the aerospace, chemical, food processing, paper and power industries.

A previous study examined the very high cycle fatigue (VHCF) properties of 17-4PH stainless steel as associated with failure from inherent defects [1]. It was demonstrated that the fatigue limit was determined by the maximum size of non-metallic inclusions and could be predicted using the parameter model proposed by Murakami and Endo [2]. Schönbauer et al. conducted a detailed investigation into the influence of corrosion pits on the fatigue strength of 17-4PH stainless steel, proposing a method for fatigue limit prediction in the presence of corrosion pits [3]. This predictive method can be applied to different environments and stress ratios, as well as to a wide range of pit sizes. However, on the downside, the method requires an extensive number of fatigue tests in order to determine all of the material parameters for prediction. Further recent studies have reported on the fatigue properties of 17-4PH stainless steel with respect to various influences: Lin and Lin [4] (a corrosive environment), Wu and Lin [5, 6] (frequency), as well as Hsu and Lin [7]. Nie and Mutoh proposed a model for fatigue limit prediction in defect-free 17-4PH stainless steel [8], while Yadollahi et al. investigated the fatigue behaviour of the material produced by an additive manufacturing process [9]. Results obtained from the fatigue testing of specimens containing diverse artificial defects with a wide range of sizes are reported in this study, with an accompanying discussion on the factors which govern the fatigue limits. The influences of circumferential shallow and sharp notches, corrosion pits and drilled holes are examined. Comparable geometries (i.e., aspect ratios and sizes) are employed for pits and holes, in order to explore the similarities and possible disparities between those two different types of defects. Detailed microscopic observations of the specimen surfaces during fatigue loading and of the fracture surfaces were conducted to investigate the process of crack initiation and propagation. The experimentally determined fatigue limits were quantitatively evaluated using the parameter model and threshold stress intensity factor (SIF) range, Kth, with respect to the effects of defect geometry and stress ratio, R.

2 2.1

MATERIAL AND EXPERIMENTAL PROCEDURE Material

The testing material was a chromium-nickel-copper stainless steel 17-4PH precipitation-hardened at 621 °C for 4 hours (condition H1150). The chemical composition and the mechanical properties at room temperature are summarised in Tables 1 and 2, respectively. The average grain size was 11 m, independent of orientation. Further information about the test material is provided in [1]. 2.2

Test setups and specimen shapes

Fatigue tests were performed using a rotating bending testing machine, a servo-hydraulic, tensioncompression testing machine and an ultrasonic fatigue testing equipment. The specimen shapes are presented in Fig. 1. Rotating bending and tension-compression/tension-tension tests were conducted at frequencies of 40-67 Hz. The minimum specimen diameter was 6-10 mm, depending on the capacity of the respective machine for the maximum stress applied during testing. An asymmetrical specimen design was used in servo-hydraulic testing. In the area with a diameter of 10 mm (which is slightly larger than the test section), four stain gauges were attached to ensure a proper alignment of the specimen after fixation to the load train. Tests at approximately 20 kHz were carried out using the ultrasonic fatigue testing equipment developed at BOKU, Vienna [10, 11]. The equipment ensures an accuracy of ±1% of the nominal displacement amplitude by using a closedloop control with a vibration gauge at one end of the specimen that serves as the feedback in a test

generator. During ultrasonic fatigue testing, a specimen is stimulated to resonance vibration and, for tests at fully-reversed loading (R = -1), only one end of a specimen is fixed to the resonance system, while the other end is able to vibrate freely (the specimen geometry for tests at R = -1 is identical to that shown in Fig. 1a, but with a threaded rod on one side only). Tests at R > -1 were executed by mounting the ultrasonic fatigue-testing equipment into the load train of an electromechanical load frame and by superimposing a force at one end of the specimen. Compressed air cooling as well as pulsed loading was employed to prevent self-heating of the specimen during fatigue loading at 20 kHz. The lengths of pulses and pauses were chosen according to the applied load amplitude to keep the specimen temperature below 30 °C. More details about the principles of ultrasonic fatigue testing and related recent developments are provided in [12] and [13], respectively. All tests were performed in laboratory air at room temperature. Artificial defects (circumferential notches, corrosion pits and drilled holes) were introduced into the gauge lengths of all specimens (i.e., on the surface with uniform diameters across their 10 mmlengths). The geometries of the defects are shown schematically in Fig. 2. The depths, d, of the circumferential notches which were manually machined using a lathe, were 10, 30 and 80 m, and the notch root radii, , were prepared to an extremely small size of 6-9 m. Furthermore, specimens with single corrosion pits with diameters, 2c, ranging from 50-250 m were used. The pre-pitting procedure was developed and arranged at the National Physical Laboratory in the United Kingdom [14]. After fatigue failure, the pits were measured on the fracture surfaces using a scanning electron microscope (SEM), to determine their maximum surface widths, 2c, and depths, a. For run-out specimens, fatigue tests were again conducted at higher stress ranges to obtain the fracture surfaces which originated from pits. The ratios of depth to half the surface width, a/c, as measured for all specimens tested in this study, were between 1.0 and 1.5. For the purpose of comparison with the corrosion pits, specimens with drilled holes were prepared. The drilled holes were introduced into the surface of specimens by using a precision-drilling machine. The diameters, 2c, were 50, 100 and 300 m, respectively, with identical aspect ratios of a/c = 1.25. Calculation of the geometrical parameter values of various defects, , was made according to the rules proposed in [2], cf. Fig. 2. With respect to corrosion pits of irregular shape, the smooth, enclosing contour lines were used to estimate the effective values of , cf. [15]. Specimen surfaces were ground and electro-polished. After the introduction of circumferential notches or drilled holes, stress-relief annealing was conducted in a vacuum at 600°C for one hour, to minimise any residual stresses that could possibly have been generated during either lathing or drilling. As discussed in [3], there was no evidence of any significant influence of annealing on the specimens’ mechanical properties. Those specimens were again electro-polished slightly, prior to carrying out the fatigue tests. Specimens with corrosion pits were ground with only abrasive papers of up to #4000 grade and subsequently stress-relief annealed. The electro-polishing process was omitted for those particular specimens, since corrosion pits preferentially grow out of surface inclusions which would have been eliminated during this procedure, and residual stresses were expected to be absent in the vicinity of the pits.

3 3.1

RESULTS S-N data

Fig. 3 illustrates the S-N diagrams (stress range, , vs. the number of cycles to failure, Nf), in which the results of the fatigue testing of three types of small defects (circumferential notches, corrosion pits and drilled holes) are plotted for three different R-ratios of -1, 0.05 and 0.4,

respectively. In this figure, the S-N data previously obtained for smooth specimens [1, 3] are also presented for the purpose of comparison. It is observed that fatigue strength decreases significantly with an increase in defect size where all R-ratios are concerned. Fatigue test results for corrosion pits at R-ratios of 0.05 and 0.4 have already been reported [3]. In this study, additional tests at R = -1 were performed in order to investigate the S-N characteristics in greater detail. The fatigue limit for circumferential notches with

= 95 m (d = 30 m) was comparable to that

of specimens containing corrosion pits with the same size of drilled holes with

= 90-110 m. The results for

= 35 m (2c = 50 m) at R = -1 are also provided, which are almost the

same as that obtained for circumferential notches with a comparable value of m). However, the fatigue limit for drilled holes with the size of

= 32 m (d = 10

= 69 m (2c = 100 m) was

significantly higher than that for circumferential notches and corrosion pits with a range of = 90-110 m, although their size differed only slightly. Furthermore, also specimens with 300 µm diameter drilled holes (

= 208 m) exhibited a higher fatigue limit than those with notches and

pits with significantly smaller size (

= 90-110 m).

Fatigue failure of smooth specimens occurred mainly from non-metallic inclusions in a wide range of Nf, from approximately 105 to more than 1010 cycles, and the existence of a fatigue limit is unclear, as evidenced in Fig. 3, cf. [1]. In contrast, fatigue failure from artificial defects was observed only at Nf < 2×107 cycles and the fatigue limit could be clearly defined. These results suggest a distinct difference between the fatigue fracture mechanisms originating from intrinsic inherent non-metallic inclusions and that from artificial defects. Based upon observation of the circumferential notches and drilled holes during testing above the fatigue limit, it was found that the crack initiation process was mostly completed before N = 107 cycles, and thereafter the initiated cracks continued to propagate, ultimately leading to specimen failure. The failure of smooth specimens which occurred at more than N = 107 cycles was caused primarily by internal, non-metallic inclusions, and accordingly the direct observation of the fatigue processes of internal crack initiation and propagation was impossible. It is noted that a few specimens failed from non-metallic inclusions located at the specimens surface and they showed similar in fatigue life compared to failure caused by internal inclusions [1, 3]. In a previous study [1], the surface of a smooth specimen tested at R = -1 was directly observed at N = 1.00×107 cycles and after specimen failure (Nf = 1.03×107 cycles). Although the crack initiation site where final failure occurred was unfortunately not observed at 1.00×107 cycles, there was clear evidence of the evolution of slip bands as well as of initiation and growth of a new crack from an inclusion at other locations. During this period of 3×105 cycles the average crack growth rate was very small (< 5×10-11 m/cycle), which indicates that even after N = 107 cycles, irreversible fatigue damage continued to progress steadily. If similar phenomena are assumed to occur inside smooth specimens, then the observed disappearance of a fatigue limit and the large scatter as appeared in S-N data (cf. Fig. 3) are indeed comprehensible. 3.2

Fractographic investigations of the behaviour of cracks emanating from artificial small defects

In this section, the behaviour of cracks emanating from different types of small artificial defects is microscopically investigated, in order to understand fatigue limit mechanisms. In this regard, the circumferential notch is rather convenient for the systematic investigation of the mechanical effects of geometries. Its depth and sharpness can be easily adjusted for convenience, while the influence of statistical microstructural factors is less pronounced, owing to the fact that the notch intersects numerous grains. Furthermore, from its initial stages, the fatigue process can be observed directly at

the surface of the notch root. In contrast, the use of artificial corrosion pits and drilled holes is suitable for the simulation of the effects of actual surface defects, such as corrosion pits, nonmetallic inclusions, precipitates and other types of intrinsic micro-discontinuities and inhomogeneities with irregular shapes. Moreover, the growth behaviour of small cracks on the surface of specimens can be easily investigated by using these pit-like surface defects. Circumferential notches Fig. 4 presents the non-propagating cracks observed at notch roots, either at or just below the fatigue limit. The cracks were present throughout almost the entire length of the notch root, probably due to the existence of high stresses near the sharp notch root (the stress concentration factor ranges approximately from 3 to 7). These cracks initiated in the early stages of load cycling prior to N = 107 cycles, and endured a number of load cycles up to more than N = 109 cycles without causing fatigue failure. Above the fatigue limit, almost all specimens failed at N < 107 cycles, in conjunction with the continuous propagation of cracks which originated from the notches. This result indicates that the fatigue limit was determined by the threshold condition for the propagation of cracks which had initiated at the notches. It is also interesting to note the presence of considerable brownish-red debris along the crack, which are considered to be oxidation products emanating from the interior of the cracks, as seen in Fig. 4. This phenomenon suggests that the oxide- or roughness-induced crack closure could perhaps contribute to the non-propagation of a surface crack. Corrosion pits Observation of non-propagating cracks at corrosion pits was possible only for a few specimens, because the surface area around the pits was often heavily corroded. Fig. 5 presents examples of non-propagating cracks which emanated from the corrosion pits, observed in specimens tested under the stress range, , below the fatigue limit. As in the case of circumferential notches, the fatigue limit of all specimens with corrosion pits was determined by the threshold condition of whether a crack which had originated from pits would continue or stop its propagation. The images at the bottom show the internal shapes and dimensions of the respective pits, used for the estimation of . For all run-out specimens after fatigue tests, the fracture surfaces, including pit sections, were obtained by breaking specimens under stresses slightly above each threshold level. Further observations of non-propagating fatigue cracks at corrosion pits in 17-PH stainless steel have been documented in a previous study [3]. Drilled holes Fatigue tests were conducted with three sizes of drilled holes of 50, 100 and 300 m in diameter. A constant aspect ratio between depth and half diameter, a/c = 1.25, was used for all holes which is comparable to that of corrosion pits. The stress concentration factor of those holes is 2.2 at the hole edge [16]. At the fatigue limit, non-propagating cracks were observed only at holes with diameters of 50 m. Examples of non-propagating cracks emanating from two 50 m diameter holes that were both introduced in one specimen are shown in Fig. 6. Short cracks were observed at the edge of both holes at 8.60×106 cycles. Thereafter, the crack that emanated from one of the two holes (bottom right in Fig. 6) did not propagate at all. In contrast, the crack from the other hole (bottom left) exhibited propagation, albeit only slightly, during the period up to N = 2.02×108 cycles but it finally stopped propagation at least for an additional load cycling of N = 2.10×108 cycles. In this case, therefore, the fatigue limit is considered to be a critical stress that distinguishes between the propagation and non-propagation of a small crack emanating from the defect.

On the other hand, for larger holes of 100 and 300 m in diameter, no crack initiation was observed at the fatigue limit. For investigation on statistical effects, 12 holes of 300 m in diameter were introduced in a specimen, but yet none demonstrated any crack initiation after load cycling of N = 1.50×107 cycles slightly below the fatigue limit. At a stress only 3 % larger than the fatigue limit, however, a crack initiated at a hole before N = 1.5×105 cycles and continued to propagate until final failure. This suggests that for such relatively large holes, the fatigue limit could be a limiting stress to determine whether or not the mechanical conditions for crack initiation are satisfied at the hole edges. The essential difference between the effect of holes of 100 and 300 m in diameter and that of 50 m diameter holes and corrosion pits would be the dissimilarity in local geometric sharpness at the crack initiation sites. In order to ascertain the reasons for this difference, additional tests were carried out with specimens containing pre-cracked holes as follows: (1) One specimen with a 100 m diameter drilled hole, along with three specimens with a 300 m diameter drilled hole, were all fatigue-loaded at stress ranges higher than the respective fatigue limit, until small cracks were visible at the hole edges (i.e., the introduction of pre-cracks). (2) The specimens were annealed for stress relief (one hour at 600°C in a high vacuum), later tested again at stress ranges comparatively lower than those applied for pre-cracking in step (1). (3) Fatigue testing was periodically interrupted and the crack length at surface was measured using a light microscope. When crack propagation was observed, fatigue testing was continued until the length of new propagation attained at least of 20 m. The specimen was first annealed, then retested by decreasing the stress range. Conversely, when no crack propagation was observed at least over an additional 108 cycles, the specimen was annealed and then re-tested at a higher stress range. (4) Step (3) was continued in a stepwise manner, to identify the threshold level defined by the maximum stress range under which a pre-crack exhibits no propagation during load cycling of at least 108 cycles. Throughout the above-mentioned tests, it was found that the propagation of pre-cracks occurred at stress ranges much lower than the fatigue limit of specimens containing holes without pre-cracks. Furthermore, it was determined that the threshold levels for crack propagation were identical to those obtained for circumferential notches and corrosion pits with a similar . Fig. 7 presents examples of short cracks at drilled holes, detected shortly after step (1) of the aforementioned procedure. The bottom pictures show SEM images of the fracture surfaces observed after breaking the specimens, with the internal shapes of the pre-cracks outlined with dashed lines. The shapes of the pre-cracks could be distinguished by the beach marks. After the final test at step (4), some of the pre-cracked specimens were heat-tinted (400°C for 2 hours in air), then broken to facilitate the determination of the crack geometry, as shown in Fig. 8. According to Fig. 8, it is reasonable to assume that the crack shape is semi-elliptical, with a 0.8 ratio of depth to half the surface width, a/c. Based on this assumption, the value was estimated for the pre-cracked holes of the specimens tested during step (3). At R = 0.05, a specimen containing a drilled hole of 100 m in diameter was not failed from the hole after N = 1.20×108 cycles (star symbol in Fig. 3). In this case, the fatigue failure originated from a non-metallic inclusion in the interior of the specimen (cf. Fig. 9) and, after the test, no crack was observed at the edge of the drilled hole. This result suggests that, from crack initiation to final failure of the specimen, fatigue damage can progress inside the specimen, with no notable signs on the surface (see also Section 3.1).

4

DISCUSSION

4.1

S-N data for R = -1

In a previous study on the fatigue properties of 17-4PH stainless steel [1], it was shown that the fatigue limit of smooth specimens was mainly determined by non-metallic inclusions and could be evaluated using the parameter model proposed by Murakami and Endo [2]. Based on this model, the fatigue limit in the presence of small defects or cracks can be predicted using only two parameters: the square root of the projection area of a small defect/crack perpendicular to the loading direction ( ), as well as the Vickers hardness (HV). For surface defects and for R = -1, the stress range at the fatigue limit, w, can be calculated by the following equation: (1)

.

where w is in MPa, is in m and HV is in kgf/mm2. This equation is quite useful in the practical engineering context, since the fatigue limit can be predicted within an error margin of about 10%, without the need for fatigue testing. Originally, the parameter model was proposed on the basis of the phenomenological fact that the fatigue limit is not a critical condition for crack initiation, but rather for the non-propagation of a small crack [17]. In this regard, the fatigue limit problem in the presence of small defects is reduced to a small crack problem where SIF is applicable. The translation between the fatigue limit stress range, w, and the threshold SIF range, Kth, can be made by using the following formula, which is based on the linear-elastic fracture mechanics analysis [15, 17]: (2)

,

where KImax is the maximum SIF value along the front of a three-dimensional surface crack with an arbitrary shape in a semi-infinite body, with a Poisson’s ratio of 0.3, under remote tensile stress,  In Eq. 2, if the unit of KImax is expressed by MPa m,  is in MPa and is in m. The following failure criterion expressed by Kth [15] is given based on Eqs. 1 and 2, by setting KImax = Kth/2 and  = w/2 as follows: (3)

,

where Kth is in MPa m, is in m and HV is in kgf/mm2. The use of Eq. 3 is restricted to small-sized defects or cracks which have the nature of size-dependency on the threshold level, i.e., t

. For larger cracks, the value of Kth becomes a material constant that is equal to

the threshold SIF range of a long crack, Kth,lc. The transition size in m,

trans ,

can be

estimated as follows, by equating Kth in Eq. 3 to Kth,lc: .

(4)

The value of Kth,lc = 6.7 MPa m at R = -1 has already been determined for the same 17-4PH stainless steel in a previous study [3]. With this value and HV = 352, a transition size of

trans

=

80 m can be calculated from Eq. 4. This value is in the order of several grains (the average grain size is 11 m), and it is a peculiarly small value when compared with many other ferrous and nonferrous metals with trans ≥ 1000 m [15].

Using Eq. 2 and the threshold condition, Kth = Kth,lc, the fatigue limit in the presence of a crack emanating from a large surface defect or a long surface crack with estimated by the following equation:

≥

trans

, where w is in MPa, Kth,lc is in MPa m and

can be

(5)

is in m. Fig. 10 depicts the relationship

between stress range, , and defect size, , in which the experimental results are plotted at an R of -1 for specimens containing artificial defects (cf. Fig. 3). Furthermore, the predicted fatigue limit according to Eqs. 1 and 5 is illustrated in this figure by two straight lines intersecting at trans

= 80 m. The same experimental results are shown in Fig. 11 in the form of a relationship

between the SIF range, K, and defect size, . In this figure, two straight lines also represent the threshold condition for crack propagation, i.e., Kth, as predicted by Eq. 3 and a constant value of Kth,lc = 6.7 MPa m. Figs. 10 and 11 include the data derived from the tests performed with the repeated use of a specimen containing a pre-cracked hole, as defined by the procedure described in Section 3.2. The downward-facing long arrows in those figures indicate the re-use of specimens after pre-cracking. The numbers (0, 1, 2, … and ⓪, ①, ②, …) adjacent to the symbols denote the sequence of the tests performed when a specimen was used repeatedly. Other unnumbered symbols indicate the experimental results obtained by a one-time use of specimens under respective loading conditions. As evidenced in Figs. 10 and 11, neither failure data (solid symbols) nor crack propagation data (half solid symbols) are present below these prediction lines.

In Figs. 10 and 11, regarding specimens with circumferential notches and corrosion pits, the fatigue limit stress ranges, w, and the threshold SIF ranges, Kth, are approximately 10% higher than the prediction lines, all within the typical accuracy limits of the parameter model [2]. Moreover, the experimentally determined values of w and Kth for specimens with 50 m diameter drilled holes (

= 35 m) show good correlation with the predictions based on Eqs. 1 and 3, and are similar

to those for 10 m deep circumferential notches ( = 32 m). Non-propagating cracks were clearly visible for both of these defects, either at or just below the fatigue limit, as previously shown in Figs. 4-6. However, prediction becomes highly conservative for drilled holes with larger diameters of 100 and 300m. Non-propagating small cracks were not observed for these holes, even after load cycling of about N = 109 cycles. The absence of non-propagating cracks suggests that the fracture mechanics approach is not applicable for such defects. However, once a hole has a small pre-crack, fracture mechanics becomes effective and accordingly, w and Kth can be reasonably estimated by Eq. 5 and Kth,lc = 6.7 MPa m, respectively, as presented in Figs. 10 and 11. 4.2

S-N data for R > -1

In the parameter model [15], the R-ratio dependency of the fatigue limit can be taken into account by the introduction of a correction factor of {(1-R)/2}, thereby extending Eqs. 1 and 3 as follows: (6) (7)

where w is in MPa, Kth is in MPa m, is in m and HV is in kgf/mm2. A convenient equation in the form of  = 0.226+HV∙10-4 is also proposed for the determination of the exponent, , and has worked successfully for a variety of steels [15]. However, it has been found that this equation was not applicable for several materials [1, 18-21]. Schönbauer et al. [3] presented a novel method by which the value can be determined, based on appropriate fractographic investigations of smooth specimens which had failed as a result of non-metallic inclusions in the VHCF regime. An  -value of 0.421 was obtained for the present material using this method. This value is comparatively larger than that calculated by the conventional equation as  = 0.226+HV∙10-4 = 0.226+352∙10-4 = 0.261. Determination of the value has usually been achieved via a series of fatigue tests on specimens containing artificial defects of specific sizes [15]. Consequently, in this study, the fatigue test results were duly evaluated, as obtained at the R-ratios of -1, 0.05 and 0.4, by using specimens with circumferential sharp notches of 10 and 30 m in depth, for the purposes of comparison with the value obtained by Schönbauer et al. [1]. Fig. 12 demonstrates the values of 1/6 w /{b(HV+120)} as a function of (1-R)/2 on a double-logarithmic graph, where the factor b is 1.43 for surface defects, 1.56 for internal defects and 1.41 for sub-surface defects just in contact with the surface. On the left, the results for the smooth specimens failed from non-metallic inclusions [1] are plotted, and on the right, the experimental results for specimens with circumferential notches are plotted. For smooth specimens, according to the method by Schönbauer et al. [1], a straight line was drawn through the lowest levels recorded for specimens which had failed at about N = 1010 cycles. The slope indicates a value of  = 0.421. For specimens with circumferential notches, a straight line was drawn through the fatigue limit for the respective R-ratio. A value of  = 0.434 was determined from the slope of this particular line. The coefficient of determination, r² = 1.000, reveals that the regression line perfectly fits the data. It is interesting to note that this value ( = 0.434) is only 3% higher than that for non-metallic inclusions ( = 0.421), demonstrating that the method by Schönbauer et al. [1] can be effectively employed for the determination of the -value. If the fatigue strength is controlled by inherent defects, then this method proves to be particularly useful, since the -value can be determined solely by using smooth specimens. A value of  = 0.434 is used hereafter in this report.

The relationships between stress range, ,and defect size, , plotted with the experimental results for specimens containing artificial defects at R = 0.05 and 0.4 are shown in Figs. 13 and 14, respectively. In these figures, additional experimental data for pre-pitted specimens have also been plotted, as previously obtained by using the same material but at the slightly higher temperature of 90 °C [3]. There is a very good correlation with the experimental results obtained at room temperature in the current research. As observed in the case of R = -1 (see discussion in Section 4.1), only the data for drilled holes with diameters of 100 and 300 m demonstrated a significantly higher fatigue limit, when compared to that for other defects. In the case of R = 0.05, in order to investigate the difference between a round hole and a cracked hole, a specimen with a 300 m diameter hole with a pre-crack was tested by repeated stress-relief annealing in a sequential manner, as indicated by the downward-facing arrow in Fig. 13 (i.e., 0→1→2). Although the pre-crack was merely 50 m in length, due to the existence of this very short crack, the threshold level substantially decreased to nearly the same degree as for corrosion pits with an identical about 250 m.

of

The fatigue limit predicted according to Eq. 6 has been represented by a straight line with a slope of -1/6 in Figs. 13 and 14, in good accordance with the experimental data for circumferential notches

and corrosion pits up to a defect size of approximately

= 100 m. The transition size from a

small to large defect, trans , appears to be the same value of 80 m as obtained for R = -1 and, furthermore, may be independent of the R-ratio. This suggests that the following extended version of Eq. 5 would be promising for

≥ 80 m: (8)

wherew is in MPa, Kth,lc|R = -1, defined as Kth of a long crack under fully reversed loading (R = -1), is in MPa m and is in m. As seen in Figs. 13 and 14, the experimental data of w for ≥ 80 m is in good agreement with the prediction line, with a slope of -1/2 according to Eq. 8. Similarly, for

≥ 80 m,it is expected that Kth,lc be expressed as: (9)

Conversely, for

< 80 m, Eq. 7 can be used to predict the threshold SIF range, Kth. The

relationships between the SIF range, K, and defect size, in Figs. 15 and 16, respectively.

, for R = 0.05 and 0.4 are featured

The threshold phenomena for all types of artificial defects, except drilled holes, are wellcharacterised by Eqs. 7 and 9, where Kth exhibits a defect-size-dependency for 80 m and becomes a constant value above this size. In the context of the material studied, the transition size, trans = 80 m, is almost independent of the R-ratio and may be regarded as an intrinsic material parameter representing a boundary between small and large cracks. 4.3

Peculiar fatigue characteristics observed in the investigated 17-4PH stainless steel

The contributions of intrinsic and artificial defects to the determination of fatigue limits Specimens with artificial surface defects displayed a definite fatigue limit and in most cases, the knee point appeared before N = 107 cycles in the S-N data, while the knee point was unclear for smooth specimens for which the inherent non-metallic inclusions would control the fatigue strength. For the latter, the S-N data reflecting a trend of monotonic decrease up to N = 1010 cycles, cf. Section 3.1. Millar and O’Donnell [22], as well as Murakami et al. [23], provided a thorough overview of the disappearance of the conventional fatigue limit in smooth specimens and the possible reasons for this. In addition, Murakami and Nagata [24] conducted tension-compression fatigue tests at R = -1 for sub-zero-treated martensitic stainless steel smooth specimens, as well as for specimens with small drilled holes, at a frequency of 20-300 Hz. They reported results similar to those in the present study, concluding that the disappearance of the conventional fatigue limit as a result of a fatigue crack originating at non-metallic inclusions is caused by a synergetic effect between cyclic stress and hydrogen trapped by the non-metallic inclusions. Kuroshima and Harada [25] gave a different explanation for the further decrease of the fatigue strength when crack initiation site is shifted from the surface to the interior. They pointed out that the propagation of surface cracks can be stopped due to the effect of oxide-induced crack closure, while oxidation processes are not expected in the interior where the environmental condition is similar to vacuum. Furthermore, different experiments in vacuum showed [26, 27] that the fracture surfaces generated at low stress intensities feature a morphology similar to the so-called “optically-dark area” [28] or “fine-granular area” [29] often observed around the origin of internal fatigue cracks. However, the environmental influences do not solely explain the disappearance of the conventional fatigue limit for the investigated 17-4PH stainless steel, since several smooth specimens that were tested in the VHCF

regime also failed from surface defects [1, 3]. At this point in time, it remains unclear whether the fatigue strength of the material in the present study is influenced not only by mechanical factors, but also substantially by environmental factors. Nonetheless, a method for the quantitative evaluation of the fatigue strength of smooth specimens, focusing on the size of non-metallic inclusions, was presented in a previous study [1] and the experimental results could be reasonably accounted for based on this method. Differences and similarities of various types of artificial defects The observations outlined in Sections 4.1 and 4.2 give rise to the question about the essential difference between the effect of drilled holes and corrosion pits on the fatigue limit. What must be clarified is why there exists a much less severe influence on the fatigue limit by drilled holes of 100 and 300 m in diameter, compared with that by corrosion pits with approximately the same sizes and aspect ratios. An evident shape difference between a hole and a pit is the surface roughness of the interior walls, cf. Figs. 5-8. In other words, the wall of a corrosion pit contains many small notches with the root radius, , much smaller than the representative radius of c. The notch root radius, , is less than 10 m for all the circumferential notches investigated, 25 m for a 50 m diameter hole and virtually zero for pre-cracked holes. They are comparable with the local notch root radii of corrosion pits. As for corrosion pits, it has been demonstrated that the fatigue limit of specimens which possess such sharp defects is determined by the threshold condition for propagation of a crack. Accordingly, w and Kth for such sharp defects were reasonably predicted by Eqs. 6-9, independently of the type of defects and the R-ratio. On the other hand, with respect to specimens with drilled holes of 100 and 300 m in diameter, the fatigue limit was determined by the critical condition for crack initiation at the hole edges and as a result, the experimental results for w and Kth were comparatively higher than the values estimated by Eqs. 6-9. This scenario confirms that for blunt, round holes, the critical condition for crack initiation is higher than that for the non-propagation of a crack. For this reason, at a stress slightly higher than the fatigue limit, those cracks initiated at holes with 100 and 300 m diameters (i.e., with radii of 50 and 150 m) will never stop propagation. The critical root radius that satisfies the non-propagation conditions seems to lie between 25 and 50 m, if estimated from the experimental results for the investigated 17-4PH stainless steel. This value is an important parameter for the prediction of w and Kth. In the context of mild steel specimens with deep notches, it is already known that non-propagating macro cracks are observed only when the notch root radius, , is smaller than a specific value designated by 0, and the fatigue limit becomes almost constant for  < 0 for the same notch depth [30]. Nisitani demonstrated that the value of 0 is a material constant, independent of notch depth, based on an elastic calculation [31]. In essence, the notch root radius, , dominates the relative stress distribution near the notch root in the absence of a crack. This concept has provided a physical rationale for 0 being a material constant. When the notch becomes extremely shallow, however, relative stress distribution is not determined solely by , so that 0 no longer remains a material constant - e.g., when the notch depth is smaller than 0.5 mm for annealed medium carbon steel [32]. The investigated small artificial defects in this study may well fall into the category of the above-mentioned, very shallow notches. It is therefore uncertain whether the critical value corresponding to 0 is a material constant. However, it should be noted that the critical value of  = 25-50m for the present material is extremely small, compared with many other metallic materials for which the parameter model is usually applicable to holes with diameters of at least up to 500 m ( = 250 m).

In their early paper on the parameter model, Murakami and Endo reported that the experimentally obtained fatigue limits of SUS603 (similar to 17-4PH stainless steel) and YUS170 (an austenitic stainless steel) containing drilled holes were approximately 20% higher than the predictions by Eqs. 1 and 3 [2]. According to their interpretation, the reason for such exceptional data was that non-propagating cracks were unlikely to be detected in stainless steels, even in the presence of sharp notches [33-35]. Currently, however, it may be difficult to ascertain the mechanics and mechanisms of crack initiation at small defects in 17-4PH stainless steel. Therefore, in order to quantitatively evaluate the fatigue strength of specimens with round pits and notches, it is essential to undertake a systematic investigation of the notch effect for a variety of notch radii and depths. Critical defect size for transition from small to large cracks Another interesting, yet peculiar, result obtained for this study, concerns the very small value of the transition defect size ( trans = 80 m), above which the threshold SIF of a sharp defect or crack becomes a material constant. As documented in existing literature [2], this characteristics is in strong contrast with many other metallic materials for which Eqs. 1 and 3 can still be effective beyond a size of approximately one millimetre (i.e., trans ≥ 1000m). Based on Eq. 4, it is evident that transition size is an intrinsic parameter, determined by two material constants, i.e., Kth,lc and HV. Consequently, owing to the material’s high static strength (HV) and low Kth lc, its results in a small value. Such a material is literally the 17-4 PH stainless steel investigated in this study. trans

4.4

Estimation of the lower bound of the fatigue limit

As reported in a previous study [15], the influence of non-metallic inclusions on the fatigue limit of 17-4PH stainless steel smooth specimens can be evaluated by using the following generalised equation of Eq. 6: (10) where the factor b is 1.43 for a surface inclusion, 1.56 for an internal inclusion and 1.41 for a subsurface inclusion just in contact with the surface [15]. In essence, fatigue strength is dependent on the size and location of the most detrimental inclusion. Therefore, when inherent non-metallic inclusions control the fatigue strength of smooth specimens, the scatter in fatigue strength is inevitable. From the engineering perspective, it is important to predict the lower bound of scatter. The lower bound of fatigue limit range, wl, is predicted by assuming the worst-case scenario that the largest inclusion with a size of ma is located at the most detrimental position, i.e., just below the surface [15]. Based upon this assumption, the lower bound is calculated for the present material by substituting ma , b = 1.41 and other material constants into Eq. 10, as follows: (11) In this equation, the anticipated maximum inclusion size, ma , increases with the control volume, i.e., the number of test specimens, or the critical volume of machine parts and structural components. As previously demonstrated [1], the distribution of inclusion size in the investigated 17-4PH stainless steel can be analysed, based on the extreme value theory [15, 36], with which the expected maximum inclusion size,

ma

, can be estimated.

In Fig. 17, the -values of the maximum inclusions found at the crack initiation sites of the smooth specimens, broken in ultrasonic fatigue tests, are plotted in an extreme value distribution diagram [1]. These specimens have a standard inspection volume, V0, of 126 mm³, cf. Fig. 1a. The expected size of the maximum inclusion, ma , can be calculated as a function of the return period T = 1/(1-F), i.e., the number of fatigue specimens with a standard inspection volume of V0, or the prediction volume, V (i.e., the total control volume of target structural components). Further details about the application of this method are readily available [15]. As an example,

ma

of

21.3 and 32.0 m are determined for V = 10 and 10 mm³, respectively, as illustrated by dotted and 4

dashed lines in Fig. 17. With these values of

6

ma

and Eq. 11, the lower bound of fatigue limit at

R = -1 are correspondingly calculated as wl = 799 and 747 MPa. Fig. 18 illustrates the relationship between the fatigue limit stress range, w, and defect size, . In this figure, the experimental results of fatigue limits for specimens with artificial defects (i.e., only the data for run-out specimens and specimens where no crack growth was observed were plotted) for R = -1 are plotted together with the predictive lines of Eqs. 1 and 5 and, additionally, the wl levels predicted above are denoted by horizontal lines. As discovered, the lower bound of the fatigue limit is not a fixed material constant, but a value dependent on the number of specimens or the overall control volume of structural components. Therefore, it is important to note that the actual fatigue limit of a great number of mechanical parts, or of a massive structural component, may eventually be lower than the reference strength determined by laboratory fatigue tests conducted on a limited number of small-sized specimens. When of an artificial defect is comparable to the ma of inherent defects, fatigue strength is determined by the competition between artificial and inherent defects. In particular, in cases where it is smaller than ma , such defects can be regarded as being non-detrimental, in that they will not reduce the fatigue limit below the lower bound level. However, this method for evaluating the non-detrimental defects with the use of ma is not necessarily applicable to the blunt, round defects, for which the fatigue limit is determined by the crack initiation condition. For example, as previously mentioned in Section 3.2, one specimen containing a drilled hole with a diameter of 100 m ( = 69 m) was tested at 720 MPa and R = 0.05 and the fracture occurred after N = 1.20×108 cycles, due to a much smaller non-metallic inclusion with = 13 m present in the interior of the specimen (see Fig. 9 and the star symbol in Fig. 3). In that case, the predicted fatigue limit according to Eq. 10 with = 13 m, R = 0.05 and b = 1.56 is 700 MPa that is lower than the applied stress range of 720 MPa. Given a significantly minor effect on the fatigue limit by 100 m diameter drilled holes ( = 69 m) that will not be a crack initiation site at this stress level, fatigue failure from the internal inclusion (

5

= 13 m) is comprehensible.

CONCLUSIONS

In this study, the influence of small artificial defects on the fatigue properties of precipitationhardened, chromium-nickel-copper stainless steel 17-4PH was investigated. Experiments were performed at three different stress ratios, with specimens containing circumferential notches, artificially-generated corrosion pits and drilled holes. The data obtained were evaluated using the parameter model and a conventional fracture mechanics approach. The following results were obtained:

1. When the fatigue limit of specimens with artificial defects is determined by the threshold condition for the propagation of a crack, the shape and dimension of defects can be evaluated by the square root of the projection area, perpendicular to the loading direction, , irrespective of defect types and sizes. 2. Fatigue strength, in the presence of defects with sizes up to approximately 80 m, can be estimated according to the parameter model. For larger defects, the fatigue limit is determined by the threshold stress intensity range of a long crack, Kth,lc. 3. As an exception, drilled holes with diameters larger than 100 m display higher fatigue limits, especially when compared to other defects with the same . This is due to the fact that the fatigue limit is determined by the crack initiation condition, rather than by the nonpropagation condition. Therefore, in the presence of small cracks at the edge of drilled holes, the fatigue limit becomes comparable to that of other defects. The notch root radius at the crack initiation site of defects is intimately associated with this behaviour. 4. The dependency of stress ratio, R, on the fatigue limit can be described by a single term of 1 2

, independent of defect size. The coefficient of  is 0.434 for the current material,

which can be experimentally determined using smooth specimens, as well as specimens containing small artificial defects. 5. When artificial defects are very small, the reduction of the fatigue limit by non-metallic inclusions, or other intrinsic material defects, becomes more pronounced. Due to such defects, as inherently existed in the structure of the material, the fatigue limit is dependent on the number of test specimens, or the overall control volume of machine parts or structural components. The lower bound of scatter in the fatigue limit can be reasonably estimated, using inclusion ratings and the extreme value theory.

ACKNOWLEDGMENT The authors wish to thank Dr. Shengqi Zhou of the National Physical Laboratory (UK) for the supply of pre-pitted test specimens.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Table 1. Chemical composition of the 17-4PH stainless steel 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

Table 2. Mechanical properties of the 17-4PH stainless steel at room temperature Tensile strength (MPa)

Yield strength (MPa)

Elongation (%)

Reduction of area (%)

Vickers hardness (kgf/mm²)

1030

983

21

61

352

Fig. 1. Specimen geometries for (a) ultrasonic fatigue-testing at R > -1, (b) servo-hydraulic, axial-load-testing and (c) rotating-bending testing (dimensions in mm). Fig. 2. Geometries of artificial defects.

Fig. 3. S-N data for specimens with circumferential notches (left column), corrosion pits (middle column) and drilled holes (right column) at R = -1 (top row), R = 0.05 (middle row) and R = 0.4 (bottom row).

Fig. 4. Non-propagating cracks observed at the root of circumferential notches. Fig. 5. (a) Non-propagating cracks emanating from corrosion pits that were observed on the surface of specimens. Arrows indicate crack tips. (b) Internal geometry of pit. The fracture surfaces were obtained in subsequent tests above the fatigue limit.

Fig. 6. Non-propagating cracks at drilled holes with a diameter of 50 m.  = 820 MPa at R = -1 (N = 4.34×108 cycles). Fig. 7. Drilled holes with pre-cracks; optical micrographs of crack initiation sites on the surface after pre-cracking at given stress ratio, R, stress range, , and number of cycles, N, (top) and SEM micrographs of their corresponding internal geometries on the fracture surface after fracture (bottom). The front of initial pre-cracks is indicated by dashed lines. Fig. 8. Fracture surface observed by breaking the specimen with a pre-cracked hole, used for determination of the threshold conditions (marked with sequential numbers ⓪,①,②,… in Figs. 10 and 11). Crack geometry was highlighted by heat-tinting after final testing. Fig. 9. Fatigue failure from internal inclusion after fatigue testing at  = 720 MPa (R = 0.05, N = 1.20×108 cycles).

Fig. 10. Stress range, , vs. defect size, , at R = -1. Solid symbols represent failed specimens and open symbols designate run-out specimens. Downward-facing long arrows designate specimens for which drilled holes were pre-cracked above the fatigue limit, then tested at lower stress ranges. The sequential numbers (0, 1, 2, … and ⓪ ① ② ) denote the sequence in which tests were performed using a repeatedly-annealed specimen.

Fig. 11. SIF range, K, vs. defect size, , at R = -1. Solid symbols represent failed specimens and open symbols represent run-out specimens. Downward-facing long arrows designate specimens for which drilled holes were pre-cracked above the fatigue limit, then tested at lower stress ranges. The sequential numbers (0, 1, 2, … and ⓪ ① ② ) denote the sequence in which tests were performed using a repeatedly-annealed specimen.

Fig. 12. Influence of stress ratio, R, on the fatigue limit; solid and open symbols represent failed and run-out specimens, respectively. Fig. 13. Stress range, , vs. defect size, , at R = 0.05. Solid symbols represent failed specimens and open symbols represent run-out specimens. Downward-facing long arrows indicate specimens for which drilled holes were pre-cracked above the fatigue limit, then tested at lower stress ranges. The sequential numbers (0, 1, 2, …) denote the sequence in which tests were performed by using a repeatedly-annealed specimen. Fig. 14. Stress range, , vs. defect size, symbols represent run-out specimens.

, at R = 0.4. Solid symbols represent failed specimens and open

Fig. 15. SIF range, K, vs. defect size, , at R = 0.05. Solid symbols represent failed specimens and open symbols represent run-out specimens. Downward-facing long arrows indicate specimens for which drilled holes were pre-cracked above the fatigue limit, then tested at lower stress ranges. The numerical numbers (0, 1, 2, …) denote the sequence in which tests were performed by using a repeatedly-annealed specimen.

Fig. 16. The SIF range, K, vs. defect size, symbols represent run-out specimens.

, at R = 0.4. Solid symbols represent failed specimens and open

Fig. 17. Extreme value distribution of the inclusion size.

Fig. 18. Relationship between fatigue limit stress range, w, and defect size, fatigue limit for intrinsic defects (horizontal lines)

, with predicted lower bounds of

Highlights 1. The influence of artificial defects on the fatigue limit is investigated. 2. The fatigue limit can be estimated using t e √area parameter model. 3. For defects larger than √area=80 µm, the fatigue limit is determined by Kth,lc. 4. The stress ratio dependency is determined. 5. Drilled holes with diameters >50 µm cannot be compared with corrosion pits.