Fatigue Life for Different Stress Concentration Factors for Stainless

materials

Article Fatigue Life for Diﬀerent Stress Concentration Factors for Stainless Steel 1.4301

Przemysław Strzelecki 1,* , Adam Mazurkiewicz 1, Janusz Musiał 1, Tomasz Tomaszewski 1 and Małgorzata Słomion 2

1 Mechanical Engineering Department, University of Science and Technology, Kaliskiego 7 Street, 85-789 Bydgoszcz, Poland; [email protected] (A.M.); [email protected] (J.M.); [email protected] (T.T.) 2 Faculty of Management, University of Science and Technology, Kaliskiego 7 Street, 85-789 Bydgoszcz, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-52-340-86-72

Received: 26 September 2019; Accepted: 5 November 2019; Published: 8 November 2019

Abstract: This paper presents the results of the static tensile and fatigue life tests under rotating bending of round 1.4301 (AISI 304) steel samples. The fatigue tests were carried out on smooth and notched samples with three diﬀerent rounding angles with a shape factor of 1.4, 2 and 2.6. A fatigue life was determined for samples with diﬀerent shape factors subject to identical loads. The results showed that the scatter of fatigue test results decreases with an increase in shape factor. To evaluate the cracking properties (cracking mode and mechanism), microstructure and fractographic tests of the fractured samples were carried out.

Keywords: fatigue design; S–N curve; high-cycle fatigue; stainless steel

1. Introduction The use of stainless steel in engineering has grown significantly in recent years. In 2018, the use of stainless steel in the industry has grown over 60% compared to 2010 [1], estimated at 50.7 Mt [2]. Due to the common use of this material in engineering, tests to evaluate its structure and properties are crucial. As a result, several articles on its properties have been published [3–7]. Since the material is often used in mechanical engineering, evaluation of its basic mechanical properties, including tensile strength and fatigue life, is crucial. To determine the fatigue life of a material, an S–N curve (stress vs. number of cycles) is often determined for the smooth samples and a stress concentration factor is calculated to correct the results for a specific structural component [8]. S–N curves can be determined by different models, the comparison of which is presented in [9–11]. The last square method is the most simple and commonly used method to estimate model parameters and it is presented in standard [12] and [13]. Other methods, such as the maximum likelihood method [14–16] and bootstrap method [17], are also used. Recently, a new method to calculate the fatigue strength for different geometries was presented by Ai et al. [9]. Some of the authors also conducted tests with stepwise increasing amplitude [18]. To increase the reliability of the estimated fatigue life, a reliability factor is also determined depending on the required probability of failure [8,12,19]. The procedure assumes a constant scatter of results for each geometry of the tested component; however, no such relation was shown by the researchers. A study [20] (pp. 377–380) by Schijve presents the tests carried out on two structural components in which the fatigue life at 50% failure probability was 8.5 times higher for two different components. For the same components, at the failure probability of 1%, the difference in fatigue life was 2.3 times.

Materials 2019, 12, 3677; doi:10.3390/ma12223677 www.mdpi.com/journal/materials Materials 2019, 12, 3677 2 of 9

The study aimed to verify whether the scatter of fatigue test results varies depending on the stress concentration factor. The 1.4301 stainless steel samples, a material commonly used in mechanical engineering, were used as a test material. The test results showed that the scatter of fatigue life depends on the geometry of the components.

2. Materials and Methods Austenitic 1.4301 (AISI 304) stainless steel was used in the tests [2]. The chemical composition of steel was measured by using a spectrometer, the Oxford Instrument Foundry-Master UV (Oxford Materials 2019, 12, x FOR PEER REVIEW 2 of 9 Instrument, Abingdon, UK), which fulﬁls the standard requirements [21] and is shown in Table1. The samples were made from a 10 mm drawn bar in a raw state, with the dimensions consistent with mechanical engineering, were used as a test material. The test results showed that the scatter of the standard requirements [22]. The drawing was made at room temperature. The smooth samples for fatigue life depends on the geometry of the components. fatigue tests were prepared in accordance with Figure1a, and the notched samples were prepared in 2.accordance Materials withand Methods Figure1b with the dimensions speciﬁed in Table2.

AusteniticTable 1. Chemical 1.4301 (AISI composition 304) stainless of austenitic steel was steel used 1.4301 in the (X5CrNi18-10) tests [2]. The accordingchemical composition to [21] and of steel wasmeasured measured value. by using a spectrometer, the Oxford Instrument Foundry-Master UV (Oxford Instrument, Abingdon, UK), which fulfils the standard requirements [21] and is shown in Table 1. % by Mass The samples were made from a 10 mm drawn bar in a raw state, with the dimensions consistent with the standard requirementsItem [22]. The drawing C was Si made Mn at room P temperature. S Cr The smooth Ni samples for fatigueStandard tests were requirements prepared [in21 accordance] 0.07 with1.00 Figure2.00 1a, and0.045 the notched0.015 17.5–19.5 samples 8.0–10.5were prepared ≤ ≤ ≤ ≤ ≤ in accordance withMeasured Figure value 1b with the dimensions 0.05 0.75 specified 1.56 in 0.043 Table 0.0102. 18.1 9.7

(a) (b)

FigureFigure 1. 1. GeometryGeometry of of the the specimen specimen for for fatigue fatigue testing testing ( (aa)) Smooth; Smooth; ( (bb)) Notched. Notched.

Table 2. Dimensions of the notched specimens. Table 1. Chemical composition of austenitic steel 1.4301 (X5CrNi18-10) according to [21] and

measured value. No. r [mm] Kt [-] 1% by 1.5 Mass 1.4 Item C 2Si 0.5Mn P 2 S Cr Ni Standard requirements [21] ≤0.073 ≤1.00 0.25≤2.00 ≤0.045 2.6 ≤0.015 17.5–19.5 8.0–10.5 Measured value 0.05 0.75 1.56 0.043 0.010 18.1 9.7 A static tension test was carried out on an Instron 8874 testing machine in accordance with the standard requirements [23]. TheTable strain 2. Dimensions rate was 0.0198of the notched mm/s, whichspecimens. is similar to that presented in [24].

A rotating bending machine described inNo. [25 ]r was[mm] used Kt in[-] the fatigue tests. Figure2 shows the test stand diagram. On one side, the sample was1 attached1.5 to the1.4 test stand shaft via a clamp and on the other 1 side a bearing with a load m was mounted.2 The shaft0.5 speed 2 Mo was 3000 min− at a loading frequency of 50 Hz. The bending moment Mg was equal3 to0.25 the load2.6m suspended on the bearing multiplied by the distance between the bearing center and the point of minimum cross-section l, which was 46 mm. A loadA static weighing tension between test was 5 kgcarried and 13.8out kgon wasan Inst applied.ron 8874 A rotatingtesting machine bending in test accordance was carried with out the in standardaccordance requirements with the standard [23]. The procedure strain rate [26 ].was The 0.0198 measuring mm/s, accuracy which is was similar 1.15% to withthat presented a permissible in [24].accuracy A rotating of 1.3% bending [26]. machine described in [25] was used in the fatigue tests. Figure 2 shows the test stand diagram. On one side, the sample was attached to the test stand shaft via a clamp and on the other side a bearing with a load m was mounted. The shaft speed Mo was 3000 min−1 at a loading frequency of 50 Hz. The bending moment Mg was equal to the load m suspended on the bearing multiplied by the distance between the bearing center and the point of minimum cross-section l, which was 46 mm. A load weighing between 5 kg and 13.8 kg was applied. A rotating bending test was carried out in accordance with the standard procedure [26]. The measuring accuracy was 1.15% with a permissible accuracy of 1.3% [26].

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Figure 2. Scheme of test equipment for rotating bending. Figure 2. Scheme of test equipment for rotating bending. 3. Results 3. Results Table3 shows the mechanical properties calculated based on an axial tensile test at a constant Table 3 shows the mechanical properties calculated based on an axial tensile test at a constant loading rate. The table showsFigure the 2. Scheme average of valuestest equipment calculated for rotating for 20 tests. bending. Figure 3 shows an example loadingstress–strain rate. The diagram table forshows the the test. average The values values for ca yieldlculated strength for 20 andtests. ultimate Figure 3 strength shows an are example higher stress–strain diagram for the test. The values for yield strength and ultimate strength are higher than than3. Results the minimum requirements in [27] which should be least 350 MPa and 700 MPa for Sy and Su, therespectively. minimum Itrequirements should be mentioned in [27] which that theshould requirements be least 350 for plateMPa and steel 700 according MPa for to S [28y and] are S ofu, Table 3 shows the mechanical properties calculated based on an axial tensile test at a constant respectively.a lower value, It withshould a minimumbe mentioned of 230 that MPa the andrequir 540ements MPa forfor yieldplate strengthsteel according and ultimate to [28] strength,are of a loading rate. The table shows the average values calculated for 20 tests. Figure 3 shows an example lowerrespectively. value, with Mechanical a minimum properties of 230 are MPa diﬀ anderent 540 for MPa drawn for and yield plane strength bars becauseand ultimate a bar strength, has high stress–strain diagram for the test. The values for yield strength and ultimate strength are higher than respectively.plastic strain Mechanical after drawing. properties are different for drawn and plane bars because a bar has high plasticthe minimum strain after requirements drawing. in [27] which should be least 350 MPa and 700 MPa for Sy and Su, respectively. It should be mentionedTable 3. Mechanical that the propertiesrequirements for the for 1.4301 plate steel. steel according to [28] are of a lower value, with a minimum of 230 MPa and 540 MPa for yield strength and ultimate strength, respectively. MechanicalE [MPa] propertiesSu [MPa] are differentSy [MPa] for drawn andA [%] plane barsZ [%]because a bar has high plastic strain after drawing.206 553 803 561 78.3 43.8

Figure 3. Stress–strain curve for static load for exemplary specimen.

The microstructure was tested in a cross section perpendicular to the axis of the sample without a load using a scanning digital microscope, the OLYMPUS LEXT OLS4100 Laser Confocal Microscope Figure 3. Stress–strain curve for static load for exemplary specimen. (Olympus, Tokyo, Japan).Figure 3.Figure Stress–strain 4 shows curve the forexampl static eload image. for exemplary Austenite specimen. grains are dominant in the visibleThe structure microstructure and have was sizes tested between in a cross 20 μ sectionm and 50 perpendicular μm. The mean to the size axis of the of the grains sample was without 38.3 μm a andload theThe using standard microstructure a scanning deviation digital was wastested microscope, equal in a crossto the8.5 section OLYMPUS μm. The perpendicular calculation LEXT OLS4100 towas the Laser maaxisde of Confocalby the ImageJ sample Microscope software without version(Olympus,a load using 1.52a Tokyo, a on scanning four Japan). images, digital Figure taken microscope,4 showsfrom the the the sca example OLYMPUSnning digital image. LEXT microscope Austenite OLS4100 OLYMPUS grainsLaser Confocal are dominant LEXT Microscope OLS4100, in the accordingvisible(Olympus, structure to Tokyo, standard and Japan). have [29]. sizes Figure A betweensmall 4 shows number 20 µ them and examplof 50martensiteµem. image. The meangrains Austenite size (approximate of grains the grains are 6%) wasdominant can 38.3 µalso min andthebe observed.thevisible standard structure deviation and have was sizes equal between to 8.5 µm. 20 The μm calculation and 50 μm. was The made mean by size ImageJ of the software grains versionwas 38.3 1.52a μm onand four the images,standard taken deviation from the was scanning equal to digital 8.5 μ microscopem. The calculation OLYMPUS was LEXT made OLS4100, by ImageJ according software to standardversion 1.52a [29]. on A four small images, number taken of martensite from the sca grainsnning (approximate digital microscope 6%) can OLYMPUS also be observed. LEXT OLS4100, according to standard [29]. A small number of martensite grains (approximate 6%) can also be observed.

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Figure 4. MicrostructureMicrostructure of the 1.4301 stainless steel, transverse section in etched.

A fractography of fatigue fractures was carried out for each sample geometry. Figure 55 showsshows the example fracture images. The The tests tests were were carried carried out on on a a JEOL JEOL JSM-6610 JSM-6610 Series Series Scanning Scanning Electron Electron Microscope (JEOL, Tokyo, Japan). The study aimed to compare the propagation of the fatigue cracks for different different sample geometries. Figure 55aa showsshows thethe fracturefracture ofof aa smoothsmooth sample.sample. ItIt didiffersffers from the fractures in thethe notchednotched samples,samples, whichwhich areare oftenoften usedused inin fatiguefatigue tests.tests. In smooth samples, the crack propagates from several points around the entire sample perimeter, as seen in FigureFigure5 5a.a. InIn notchednotched samples, the crack is initiated in one or two points, as seen in FigureFigure5 5b–d.b–d. TheThe resultsresults areare consistentconsistent with the results presented in in [30] [30] (p. (p. 39). 39). Figure6 6 shows shows thethe relationshiprelationship betweenbetween fatiguefatigue liveslives andand appliedapplied nominalnominal stresses.stresses. TheThe numbernumber of samples and the load range were determined in accordance with [[13].13]. A minimum of 30 tests at fivefive different different load levels, i.e., six samples for a a single single load, load, were were carried carried out out for for each each sample sample geometry. geometry. The load levels were selected to obtain thethe fatiguefatigue lifelife betweenbetween 22 × 104 andand 10 1066 cycles.cycles. × A 3-parameter Weibull distributiondistribution [[31]31] waswas usedused toto plotplot thethe regressionregression line:line:

( ) ( )( ) ! " !αv # 𝑓(𝑁)αv = Ni∙ξ(Si) exp −( Ni) ξ(Si) , (1) f (N) = () − () exp −() , (1) β(S ) · β(S ) − β(S ) where: i i i where:αv the shape parameter, β (Si) the scale parameter 10m log(S)+b, α the shape parameter, ξ(Sv i) the location parameter 10n log(S)+d, m log(S)+b bβ (Si) theconstant scale parameterterm in an 10S–N· curve ,equation, n log(S)+d dξ (Si) theconstant location term parameter in an S–N 10 curve· equation, in the location parameter, mb constant scale coefficient term in in an an S–N S–N curve curve equation, equation, nd constant scale coefficient term in in an an S–N S–N curve curve equation equation in in the the location location parameter, parameter. m Tablescale 4 coe showsﬃcient the in values an S–N of curvethe coefficients equation, estimated using Equation (1). A maximum likelihood methodn scale was coe usedﬃcient to determine in an S–N curvethe Equation equation (1) in parameters. the location A parameter. method used to determine the S–N curve was discussed in [15,16,32–34]. The calculations were carried out using R software version 3.5.1 [35]. Figure 7 shows the S–N curves for 5% and 95% failure probability to highlight the different ranges of

Materials 2019, 12, x FOR PEER REVIEW 5 of 9 scatterMaterials of 2019 test, 12 results, x FOR PEERfor different REVIEW sample geometries. A solid line shows the S–N curve at 50% failure5 of 9 probability. scatter of test results for different sample geometries. A solid line shows the S–N curve at 50% failure Materials 2019 12 probability. , , 3677 5 of 9

(a) (b)

Figure 5. Fatigue fracture of specimen (a) smooth; (b) notched r = 1.5; (c) notched r = 0.5; (d) notched r = 0.25.

Figure 5. 5. FatigueFatigue fracture fracture ofE of specimen [MPa] specimen (Sau) ( asmooth;[MPa]) smooth; (bS)y ( notchedb[MPa]) notched r A= 1.5;[%]r = ( 1.5;c) Znotched ( c[%]) notched r = 0.5;r = (d0.5;) notched (d) notched r = 0.25. 206 553 803 561 78.3 43.8 r = 0.25. Table 3. Mechanical properties for the 1.4301 steel.

E [MPa] Su [MPa] Sy [MPa] A [%] Z [%] 206 553 803 561 78.3 43.8 Stress amplitude [MPa] amplitude Stress

Smooth specmens Notched specimens r=1.5 Notched specimens r=0.5 Notched specimens r=0.25 Stress amplitude [MPa] amplitude Stress 100 200 300 400 500

104 Smooth specmens 105 106 Notched specimens r=1.5 Notched specimens r=0.5 Number of cycles N Notched specimens r=0.25

100 200 300Figure 400 500 6. S–NS–N curves curves for 1.4301 steel. 104 105 106 Table4 shows the values of the coe fficients estimated using Equation (1). A maximum likelihood Number of cycles N method was used to determine the Equation (1) parameters. A method used to determine the S–N curve was discussed in [15,16,32–Figure34]. The6. S–N calculations curves for 1.4301 were steel. carried out using R software version 3.5.1 [35]. Figure7 shows the S–N curves for 5% and 95% failure probability to highlight the di fferent Materials 2019, 12, 3677 6 of 9 ranges of scatter of test results for different sample geometries. A solid line shows the S–N curve at 50% failure probability.

Table 4. Value of linear regression parameters for the 1.4301 steel.

Geometry of Specimen r, [mm] αv m b n d Smooth 25 1.21 10.2 32.1 1.08 7.52 − − Notched 1.5 2.32 9.2 28.9 2.72 2.24 − − 0.5 1.27 7.2 22.6 3.54 13.57 − − Materials 2019, 12, x FOR PEER REVIEW 0.25 2.16 4.9 16.7 2.83 2.89 6 of 9 − −

Smooth specimens

Notched specimens r=1.5

Notched specimens r=0.5 Stress amplitude [MPa] Notched specimens r=0.25

Curves with probability 50% Curves with probability 5% Curves with probability 95% 100 200 300 400 500

104 105 106 Number of cycles N Figure 7. S–N curves for 1.4301 steel with 5% and 95% probability of failure. Figure 7. S–N curves for 1.4301 steel with 5% and 95% probability of failure. To verify the scatter of fatigue life, the coeﬃcient of variation was calculated and expressed Table 4. Value of linear regression parameters for the 1.4301 steel. following [15]: σx Geometry of Specimen r,V [mm]= 100%,αv m b n d (2) Smooth 25 µx ·1.21 −10.2 32.1 −1.08 7.52 Notched s 1.5 2.32 −9.2 28.9 −2.72 2.24 " 2# 20.5 1.272 −7.2 22.61 −3.54 13.57 σx = β(Si) Γ 1 + Γ 1 + , (3) 0.25· 2.16αv −−4.9 16.7αv 2.83 −2.89 where: To verify the scatter of fatigue life, the coefficient of variation was calculated and expressed followingV the coe [15]:ﬃ cient of variation Γ gamma function 𝑉= ∙ 100%, (2) σx standard deviation of the 3-parameter Weibull distribution for 105 cycles µx expected value of the 3-parameter Weibull distribution for 105 cycles. 2 1 Figure8 shows the calculation𝜎 = results.𝛽 (𝑆) The∙𝛤1+ graph also−𝛤1+ includes a regression , line plotted using the(3) 𝛼 𝛼 following equation: 2 where: V = 22.9 K 90.9 Kt + 129. (4) t − V the coefficient of variation Γ gamma function σx standard deviation of the 3-parameter Weibull distribution for 105 cycles μx expected value of the 3-parameter Weibull distribution for 105 cycles. Figure 8 shows the calculation results. The graph also includes a regression line plotted using the following equation:

𝑉=22.9 𝐾 −90.9 𝐾 + 129. (4)

Materials 2019, 12, 3677 7 of 9 Materials 2019, 12, x FOR PEER REVIEW 7 of 9 [%] V Coefficient of variation variation of Coefficient 40 45 50 55 60

1.0 1.5 2.0 2.5 Stress concentration factor K t Figure 8. Relationship of variation to stress concentration factor. Figure 8. Relationship of variation to stress concentration factor. 4. Discussion 4. Discussion The test results show that the scatter of results depends on the sample geometry, as seen in FiguresThe7 andtest8 .results The test show results that for the 1.4301 scatter stainless of result steels aredepends similar on to the resultssample obtained geometry, for as AW seen 6063 in T6Figures aluminium 7 and alloy,8. The presented test results in [for36]. 1.4301 The linear stainles regressions steel are Equation similar (4)to showsthe results that theobtained lowest for scatter AW of6063 results T6 aluminium is observed alloy, for thepresented shape factorin [36]. of The 2. Alinear similar regression value was Equation obtained (4) shows for AW that 6063, the as lowest seen inscatter [36]. of The results notch is radius observed of the for specimens the shape was factor made of with2. A similar an accuracy value of was 0.01 obtained mm. The for precision AW 6063, of the as notchseen in radius, [36]. The with notch this radius accuracy of the of production, specimens was is insignificant made with an for accuracy smoothspecimens of 0.01 mm. and The those precision with aof notch the notch radius radius, equal with to 1.5 this mm accuracy and 0.5 of mm.production, However, is insignificant for the specimen for smooth with aspecimens radius of and 0.25 those mm, thiswith accuracy a notch ofradius production equal to influences 1.5 mm and the 0.5 stress mm. concentration However, for factor, the specimen which can with be 2.61 a radius or 2.59 of for0.25 a radiusmm, this equal accuracy to 0.26 of mm production or 0.24 mm, influences respectively. the stress The di concentrationfference can be factor,2 MPa which for theoreticalcan be 2.61 stress or 2.59 in ± thefor roota radius of the equal notch to for0.26 nominal mm or stress0.24 mm, equal respec to 200tively. MPa. The difference can be ±2 MPa for theoretical stressThe in the test root results of the are notch crucial for innominal the design stress of equal new to machine 200 MPa. components. The required failure probabilityThe test of theresults bogie are frame crucial of a railwayin the design vehicle of must new not machine exceed 5%components. in accordance The with required [37]. A failure lower reliabilityprobability coe offfi thecient bogie can beframe calculated of a railway using Equationvehicle must [8] (pp. not 179–180) exceed 5% and in a varianceaccordance calculated with [37]. from A Equationlower reliability (4), to reduce coefficient the amount can be of calculated material required. using Equation [8] (pp. 179–180) and a variance calculatedThe scatter from ofEquation fatigue life(4), isto lowerreduce for the notched amount specimens of material because required. smooth specimens have a larger, highlyThe stressed scatter volume. of fatigue This life phenomenon is lower for can notc behed explained specimens by the because weakest smooth link theory specimens presented have by a Weibulllarger, highly [38]. stressed volume. This phenomenon can be explained by the weakest link theory presentedThe change by Weibull in fatigue [38]. life scatter was also observed when using a salt solution. The test results showingThe change the effects in fatigue of a corrosive life scatter agent was on also fatigue observ lifeed and when scatter using of a resultssalt solution. for low-carbon The test results 0.26% Cshowing steel are the presented effects of ina corrosive [39]. For agent smooth on samplesfatigue life in theand airscatter at room of results temperature, for low-carbon the fatigue 0.26% life C determinationsteel are presented error wasin [39]. 4%, For whereas, smooth for samples the samples in the in 3.5%air at KCI room and temperat 5.5% KCIure, solution, the fatigue the error life wasdetermination 1% and 1.5%, error respectively. was 4%, whereas, It clearly for shows the sample that eachs in factor 3.5% a KCIffecting and the 5.5% fatigue KCI solution, life also a fftheects error the scatterwas 1% of and results—a 1.5%, respectively. fact verified inIt clearly the studies, shows in whichthat each the factor authors affecting attempted the tofatigue explain life the also scatter affects of fatiguethe scatter life resultsof results—a by the fact presence verified of materialin the studies, defects, in e.g., which [40 –the44]. authors The studies attempted correlate to explain the fatigue the lifescatter scatter of fatigue with a life random results size by andthe presence distribution of mate of materialrial defects, defects. e.g., [40–44]. The studies correlate the fatigue life scatter with a random size and distribution of material defects. 5. Conclusions 5. Conclusions The following conclusions can be drawn based on the results: The following conclusions can be drawn based on the results: notched samples feature lower fatigue life scatter than smooth samples, • • increasenotched insamples the stress feature concentration lower fatigue factor life decreases scatter than the smooth scatter of samples, results, • anincrease increase in the in the stress scatter concentration of fatiguelife factor was decreases observed the for scatter samples of withresults,Kt = 2.6, explained by the • higheran increase sensitivity in the ofscatter notched of fatigue samples life to was the observed accuracy offor sample samples preparation with Kt = 2.6, techniques, explained by the whichhigher can sensitivity be further of explainednotched samples by a diff erentto the load accuracy gradient of sample for a specific preparation sample techniques, geometry, which in • turnwhich should can be be further verified explained in further studies.by a different load gradient for a specific sample geometry, which in turn should be verified in further studies.

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Author Contributions: Conceptualization, P.S. and A.M.; methodology, P.S.; A.M. and T.T.; software, P.S. and J.M.; validation, P.S.; formal analysis, P.S.; J.M. and T.T.; writing—original draft preparation, P.S.; M.S. and T.T.; writing—review and editing, P.S.; M.S. and A.M.; visualization, P.S. and M.S.; supervision, J.M. and A.M. Funding: The research for this article was financially supported by the National Science Centre, project no. DEC-2017/01/X/ST8/00562. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Forum, I.S.S. Global Consolidation Stainless Steel Cold All Products Consumption Index. International Stainless Steel. Available online: http://www.worldstainless.org/Files/issf/non-image-files/PDF/statistics/190527_SCF_ Public.pdf (accessed on 27 May 2019). 2. International Stainless Steel Forum Stainless Steel in Figures 2019; International Stainless Steel. Available online: http://www.worldstainless.org/Files/issf/non-image-files/PDF/ISSF_Stainless_Steel_in_ Figures_2019_English_public_version.pdf (accessed on 27 May 2019). 3. Mohd, S.; Bhuiyan, M.S.; Nie, D.; Otsuka, Y.; Mutoh, Y. Fatigue strength scatter characteristics of JIS SUS630 stainless steel with duplex S-N curve. Int. J. Fatigue 2015, 82, 371–378. [CrossRef] 4. Akita, M.; Nakajima, M.; Uematsu, Y.; Tokaji, K.; Jung, J.-W. Some factors exerting an influence on the coaxing effect of austenitic stainless steels. Fatigue Fract. Eng. Mater. Struct. 2012, 35, 1095–1104. [CrossRef] 5. Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D.; Krscanski, S.; Brcic, M.; Li, Q.; Niu, J. Mechanical properties, short time creep, and fatigue of an austenitic steel. Materials 2016, 9, 298. [CrossRef][PubMed] 6. Jiang, H.; Han, K.; Li, D.; Cao, Z. Microstructure and Mechanical Properties Investigation of the CoCrFeNiNbx High Entropy Alloy Coatings. Crystals 2018, 8, 409. [CrossRef] 7. Tomaszewski, T. Analysis of the statistical size effect model with a critical volume in the range of high-cycle fatigue. Proced. Struct. Integr. 2018, 13, 1756–1761. [CrossRef] 8. Lee, Y.L.; Paw, J.; Hathaway, R.B.; Barkey, M.E. Fatigue Testing and Analysis—Theory and Practice; Elsevier Butterworth–Heinemann: Oxford, UK, 2005; ISBN 978-0-7506-7719-6. 9. Ai, Y.; Zhu, S.P.; Liao, D.; Correia, J.A.F.O.; De Jesus, A.M.P.; Keshtegar, B. Probabilistic modelling of notch fatigue and size effect of components using highly stressed volume approach. Int. J. Fatigue 2019, 127, 110–119. [CrossRef] 10. Strzelecki, P.; Sempruch, J.; Nowicki, K. Comparing guidelines concerning construction of the S-N curve within limited fatigue life range. Polish Marit. Res. 2015, 22, 67–74. [CrossRef] 11. Kurek, M.; Lagoda, T.; Katzy, D. Comparison of Fatigue Characteristics of some Selected Materials. Mater. Test. 2014, 56, 92–95. [CrossRef] 12. ASTM E-739-91. Standard Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε-N) Fatigue Data; ASTM International: West Conshohocken, PA, USA, 2015. 13. ISO-12107. Metallic Materials—Fatigue Testing—Statistical Planning and Analysis of Data; ISO: Geneva, Switzerland, 2012. 14. Loren, S. Fatigue limit estimated using finite lives. Fatigue Fract. Eng. Mater. Struct. 2003, 26, 757–766. [CrossRef] 15. Rinne, H. The Weibull Distribution; Chapman and Hall/CRC: Boca Raton, FL, USA, 2008; ISBN 9780429142574. 16. Strzelecki, P.; Tomaszewski, T. Application of Weibull distribution to describe S-N curve with using small number specimens. AIP Conf. Proc. 2016, 1780, 020007. 17. Klemenc, J.; Fajdiga, M. Estimating S-N curves and their scatter using a differential ant-stigmergy algorithm. Int. J. Fatigue 2012, 43, 90–97. [CrossRef] 18. Topoliński,T.; Cichański,A.; Mazurkiewicz, A.; Nowicki, K. Fatigue Energy Dissipation in Trabecular Bone Samples with Stepwise-Increasing Amplitude Loading*. Mater. Test. 2011, 53, 344–350. [CrossRef] 19. Strzelecki, P.; Sempruch, J. Verification of analytical models of the S-N curve within limited fatigue life. J. Theor. Appl. Mech. 2016, 54, 63. [CrossRef] 20. Schijve, J. Fatigue of Structures and Materials, 2nd ed.; Springer Science+Business Media: Berlin, Germany, 2009; ISBN 978-1-4020-6807-2. 21. EN 10088-1. Stainless Steels—Part 1: List of Stainless Steels Aciers; CEN: Brussels, Belgium, 2014. Materials 2019, 12, 3677 9 of 9

22. PN-EN 10278. Dimensions and Tolerances of Bright Steel Products; Polish Committee for Standardization: Warsaw, Poland, 2003. 23. PN-EN ISO 6892-1:2016. Metallic Materials—Tensile Testing—Part. 1: Method of Test at Room Temperature; Polish Committee for Standardization: Warsaw, Poland, 2016. 24. Boroński,D.; Kotyk, M.; Maćkowiak, P.; Snie˙zek,´ L. Mechanical properties of explosively welded AA2519-AA1050-Ti6Al4V layered material at ambient and cryogenic conditions. Mater. Des. 2017, 133, 390–403. [CrossRef] 25. Strzelecki, P.; Sempruch, J. Experimental Verification of the Analytical Method for Estimated S-N Curve in Limited Fatigue Life. Mater. Sci. Forum 2012, 726, 11–16. [CrossRef] 26. ISO-1143. Metallic Materials—Rotating Bar Bending Fatigue Testing; ISO: Geneva, Switzerland, 2010. 27. EN 10088-3. Stainless Steels—Part 3: Technical Delivery Conditions for Semi-Finished Products, Bars, Rods, Wire, Sections and Bright Products of Corrosion Resisting Steels for General Purposes; DIN: Berlin, Germany, 2005. 28. EN 10088-4. Stainless Steels—Part 4: Technical Delivery Conditions for Sheet/Plate and Strip of Corrosion Resisting Steels for Construction Purposes; BSI: London, UK, 2010. 29. ASTM E-112-12. Standard Test. Methods for Determining Average Grain Size; ASTM International: West Conshohocken, PA, USA, 2012. 30. Kocańda,S.; Szala, J. Basis of Calculation of Fatigue; Wydawnictwo Naukowe PWN: Warsaw, Poland, 1997. (In Polish) 31. Weibull, W. A Statistical Representation of Fatigue Failures in Solids; Elanders boktr.: Stockholm, Sweden, 1949. 32. Ling, J.; Pan, J. A maximum likelihood method for estimating P_S_N curves. Int. J. Fatigue 1997, 19, 415–419. [CrossRef] 33. Strzelecki, P.; Tomaszewski, T.; Sempruch, J. A method for determining a complete S-N curve using maximum likelihood. In Proceedings of the 22nd International Conference on Engineering Mechanics, Svratka, Czech Republic, 9–12 May 2016; Zolotarev, I., Radolf, V., Eds.; Institute of Thermomechanics of the Czech Academy of Sciences: Svratka, Czech Republic, 2016; pp. 530–533. 34. Pollak, R.D.; Palazotto, A.N. A comparison of maximum likelihood models for fatigue strength characterization in materials exhibiting a fatigue limit. Probab. Eng. Mech. 2009, 24, 236–241. [CrossRef] 35. R Core Team R: A Language and Environment for Statistical Computing; R Core Team R: Vienna, Austria, 2015. 36. Strzelecki, P. Scatter of fatigue life regarding stress concentration factor. Proced. Struct. Integr. 2018, 13, 631–635. [CrossRef] 37. PN-EN 13749 Railway Applications—Wheelsets and Bogies—Method of Specifying the Structural Requirements of Bogie Frames; CEN: Brussels, Belgium, 2011. 38. Weibull, W. A Statistical Theory of the Strength of Materials; Generalstabens litografiska anstalts förlag: Stockholm, Sweden, 1939; p. 151. 39. Gope, P.C. Scatter analysis of fatigue life and prediction of S-N curve. J. Fail. Anal. Prev. 2012, 12, 507–517. [CrossRef] 40. Zheng, X.; Engler-Pinto, C.; Su, X.; Cui, H.; Wen, W. Correlation between Scatter in Fatigue Life and Fatigue Crack Initiation Sites in Cast Aluminum Alloys. SAE Int. J. Mater. Manuf. 2012, 5, 270–276. [CrossRef] 41. Mohd, S.; Mutoh, Y.; Otsuka, Y.; Miyashita, Y.; Koike, T.; Suzuki, T. Scatter analysis of fatigue life and pore size data of die-cast AM60B magnesium alloy. Eng. Fail. Anal. 2012, 22, 64–72. [CrossRef] 42. Siqueira, A.F.; Baptista, C.A.R.P.; Molent, L. On the determination of a scatter factor for fatigue lives based on the lead crack concept. J. Aerosp. Technol. Manag. 2013, 5, 223–230. [CrossRef] 43. Ai, Y.; Zhu, S.P.; Liao, D.; Correia, J.A.F.O.; Souto, C.; De Jesus, A.M.P.; Keshtegar, B. Probabilistic modeling of fatigue life distribution and size effect of components with random defects. Int. J. Fatigue 2019, 126, 165–173. [CrossRef] 44. Murakami, Y. Material defects as the basis of fatigue design. Int. J. Fatigue 2012, 41, 2–10. [CrossRef]

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