materials

Article Mechanical Properties, Short Time Creep, and Fatigue of an Austenitic Steel

Josip Brnic 1,*, Goran Turkalj 1, Marko Canadija 1, Domagoj Lanc 1, Sanjin Krscanski 1, Marino Brcic 1, Qiang Li 2 and Jitai Niu 2,3

1 Department of Engineering Mechanics, Faculty of Engineering, University of Rijeka, Rijeka 51000, Croatia; [email protected] (G.T.); [email protected] (M.C.); [email protected] (D.L.); [email protected] (S.K.); [email protected] (M.B.) 2 School of Material Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, China; [email protected] (Q.L.); [email protected] (J.N.) 3 School of Material Science and Engineering, Harbin Institute of Technology, Harbin 150001, China * Correspondence: [email protected]; Tel.: +385-51-651-491; Fax: +385-51-651-490

Academic Editor: Richard Thackray Received: 26 February 2016; Accepted: 15 April 2016; Published: 20 April 2016

Abstract: The correct choice of a material in the process of structural design is the most important task. This study deals with determining and analyzing the mechanical properties of the material, and the material resistance to short-time creep and fatigue. The material under consideration in this investigation is austenitic stainless steel X6CrNiTi18-10. The results presenting ultimate tensile strength and 0.2 offset yield strength at room and elevated temperatures are displayed in the form of engineering stress-strain diagrams. Besides, the creep behavior of the steel is presented in the form of creep curves. The material is consequently considered to be creep resistant at temperatures of 400 ˝C and 500 ˝C when subjected to a stress which is less than 0.9 of the yield strength at the mentioned temperatures. Even when the applied stress at a temperature of 600 ˝C is less than 0.5 of the yield strength, the steel may be considered as resistant to creep. Cyclic tensile fatigue tests were carried out at stress ratio R = 0.25 using a servo-pulser machine and the results were recorded. The analysis shows that the stress level of 434.33 MPa can be adopted as a fatigue limit. The impact energy was also determined and the fracture toughness assessed.

Keywords: mechanical properties; creep test; fatigue; austenitic stainless steel

1. Introduction The structure is usually designed both in accordance with the purpose for the use intended and with favorable material selection. Service life conditions are determined by the purpose of the structure and accordingly the properties of the material have to comply with these conditions. It is known that material properties are tied in with the material chemical composition, the processing path, and the resulting microstructure. The properties depending on the microstructure are called structure–sensitive properties, for example, yield strength, hardness, etc.,[1]. A material selection process for structural design includes issues such as strength, stiffness, weight, etc., as mentioned in Ref. [2]. The designing process has to include an efficient selection of materials and it is conducted under the assumption that the engineering material does not contain any failures. Furthermore, the proper use of the structure ensures that no failure will occur in it during its service life [3]. Any engineering structure (or structural element) needs to be shaped. This means that the material is subjected to processes (called manufacture) that include forming (i.e., forging, casting), joining (i.e., welding), material removal (i.e., machining) and the finishing process [4]. In all the applied processes mentioned, i.e., in designing, manufacturing, service life conditions and maintenance, various failure

Materials 2016, 9, 298; doi:10.3390/ma9040298 www.mdpi.com/journal/materials Materials 2016, 9, 298 2 of 19 modes may occur. In engineering practice, many failures can occur and any failure has a cause of its origin and the mode of its representation. The analysis of failure provides an answer to how and why an engineering component has failed, and in this sense such a discipline becomes a very powerful tool in modern structural design [5]. Common causes of failures are usually mentioned such as pre-existing defects (for example pre-existing cracks), defects initiating from imperfections, but also categories such as design errors, misuse, inadequate maintenance, assembly error, etc. In engineering practice a lot of failure modes have been observed, for example, force induced elastic deformation, creep, yielding, buckling, fatigue, fracture, corrosion, thermal shock, etc.,[6]. Creep is mentioned as one of the possible failure modes and in this investigation the short-time creep resistance of the considered material will be examined. Creep as a thermally activated phenomenon is usually defined as time dependent behavior of the material where at constant stress (load) the strain continuously increases [7]. Its occurrence is appreciable at temperatures above 0.4 Tm, where Tm is the melting temperature [8]. This behavior of the metallic material is usually displayed in the form of a curve consisting of three stages (I-transient creep, II-steady–state creep, III-accelerating creep). Material properties, the features of its machinability as well as numerical analysis of the structure made of the considered material belong to the most important information about both material and structure. In this sense, it is also recommended to get an insight into some investigations not only made by the authors of this work but also by other authors [9–23]. The possibility of the use of the finite element method in the shear stress analysis of the structure made of any of the mentioned materials is presented in [24]. The main task of the research presented in this paper is to determine the properties of the materials so as to provide the relevant information about the structure and behavior of the material under certain conditions of exploitation. In addition, a brief overview of recently published papers relating to steel X6CrNiTi18-10 is presented. The material damage and the microhardness variations of X6CrNiTi18-10 were analyzed in order to determine the incubation period, performing the tests at different cavitation conditions in a cavitation chamber [25]. Since the low-cycle fatigue damage evolution in the metastable austenitic steel causes a deformation induced phase transformation from austenite to martensite, the microstructure changes in the pre-crack stage were investigated [26]. In Ref. [27] the surface integrity of some materials, including X6CrNiTi18-10, was quantified by means of 2D and 3D surface roughness parameters, strain-hardening effects and associated residual stresses. Furthermore, the phase formation and annealing behavior are described after nitrogen PIII (Plasma immersion ion implantation) in two austenitic stainless steels, 1.4541 (X6CrNiTi18-10) and 1.4571 (X6CrNiMoTi17–12–2), differing only in the Mo content, [28]. In Ref. [29] a viscoplastic constitutive model is developed based on the results of uniaxial tensile tests on some austenitic stainless steels, also including AISI 321. In Ref. [30] the hot workability of AISI 304 and 321 austenitic stainless steels were compared through single-hit Gleeble simulated thermomechanical processing between 800 ˝C and 1200 ˝C (the strain rate varies between 0.001 s´1 and 5 s´1). An optimizing deep drilling parameter based on the Taguchi method for minimizing surface roughness was considered in Ref. [31], while the influence of nitriding time on the microstructure and microhardness of AISI 321 austenite stainless steel was investigated in Ref. [32]. The microstructural character of dissimilar welds between Incoloy 800H and 321 Stainless Steel was discussed in Ref. [33]. In Ref. [34] the effect of low temperature nitriding on the fatigue behavior of a titanium stabilized AISI 321 grade austenitic stainless steel is presented.

2. Information Concerning the Material, Equipment, Specimens, Test Procedures, and Standards The material considered in this research is X6CrNiTi18-10 steel, delivered as 18 mm soft annealed round bar. The added titanium content helps in preventing chromium carbide precipitation when exposed to high temperatures, which may occur on account of wrong applications or may be generated from the welding process. The material retains good strength and is treated as very resistant to oxidation and intergranular corrosion in dry service conditions up to 850 ˝C. Its maximum service temperature can be significantly reduced in a hot atmosphere due to corrosive compounds such as Materials 2016, 9, 298 3 of 19 water and sulfur compounds. However, the grade 321 possesses good creep strength. This steel is known as heat resistant steel and austenitic corrosion resistant steel. In accordance with the commonly used definition of steel as an alloy of iron and carbon (<2%) with or without the addition of other alloying elements, Table1 presents the chemical composition of the considered steel.

Table 1. Material chemical composition: X6CrNiTi18-10 steel.

Material: X6CrNiTi18-10 Designation Steel name Steel number (Mat. No; W. Nr; Mat. Code) EN 10088-3-2014/DIN 17440: X6CrNiTi18-10; AISI 321; ASTM „ A249 1.4541 (321) UNS S32100; BS: 321S51. Chemical composition of considered material Mass (%) C Si Mn P S Cr Ni V 0.0176 0.436 1.44 0.0209 0.0174 16.95 9.263 0.204 Mo Cu Al Ti Pb Sn Co W Rest 0.241 0.548 0.0208 0.266 0.006 0.0443 0.1 0.107 70.318

The basic properties of steel depend on the chemical composition, resulting microstructure, the state, form, and dimensions of the finished product. This means that processing as a means to development and control of the microstructure as well as heat treatment are of significance for achieving the required material properties. The properties (for example: yield strength, hardness) that depend on the microstructure are called structure-sensitive properties. The general properties of this material are: good corrosion resistance, medium values of mechanical properties, average forgeability, poor machinability, excellent weldability (TIG, MAG, Arc, laser beam, and submerged arc welding, except gas welding). Core X6CrNiTi18-10 steel is titanium-stabilized steel with improved intergranular corrosion resistance and may be used in an extended temperature range. With respect to well-balanced material properties, it is suitable for many applications and can be used at elevated temperatures. As regards processing, it can be said that it is suitable for machining (but not automated), hammer and die forging, cold forming, but it is not suitable for polishing, etc. However, due to formation of titanium carbo-nitrides, its machinability differs from other low carbon stainless steels with titanium free variants. Its main applications are in: the automotive industry, the chemical industry (chemical processing equipment), building and construction industries, food and beverage industries, and aviation and aerospace industries (used for aircraft parts, such as exhaust systems), jet engine parts, weld equipment, power station constructions, furnace heat treated parts, oil refiners, as well as general use in mechanical engineering. Due to its vibration fatigue resistance, application is quite extensive in the aircraft industry, where operating temperatures are higher than 400 ˝C and where corrosive conditions are not too severe. Concerning its special property, it is usually stated to be suitable for continuous exposure to high temperatures up to 850 ˝C in an oxidizing atmosphere (750 ˝C containing sulfur). Its optimal fabrication and mechanical properties are achieved after solution annealing (temperature range: from 1075 ˝C to 1125 ˝C) followed by rapid cooling (air or water). Equipment used in these investigations can be divided into equipment used to perform uniaxial tests at room and high temperatures and equipment used to determine impact energy. The former was the (Zwick/Roell) 400 kN capacity materials testing machine for uniaxial tests, while the latter was the Charpy impact machine. Also, if the uniaxial test was performed at room temperature then the macro extensometer was used whereas for high temperature tests high temperature extensometer and furnace (900 ˝C/Mytech) were used. Specimens used in uniaxial tests to determine engineering stress-strain diagrams and in creep testing were machined from 18 mm steel rod. The diameter of the specimen in its central part is 5 mm. Materials 2016, 9, 298 4 of 19

The geometry of each specimen used in the uniaxial test (room and high temperature) was defined according to that specified in ASTM: E 8M-15a, and its ends were threaded to match the holders of the testingMaterialsMaterials machine,2016 2016, 9, ,9 298, 298 Figure 1. 4 4of of 19 19

FigureFigure 1. 1. Specimen’s Specimen’s geometry–tensile geometry–tensile test. test. Figure 1. Specimen’s geometry–tensile test. TestTest procedure procedure and and standards standards in in accordance accordance with with which which uniaxial uniaxial tests tests were were carried carried out out are are as as Test procedure and standards in accordance with which uniaxial tests were carried out are follows.follows. TensileTensile teststests relatedrelated toto determinationdetermination ofof engineeringengineering stress-strainstress-strain diagramsdiagrams atat roomroom as follows. Tensile tests related to determination of engineering stress-strain diagrams at room temperaturetemperature were were performed performed according according to to ASTM: ASTM: E E 8M 8M-15a,-15a, while while those those related related to to high high temperatures temperatures temperature were performed according to ASTM: E 8M-15a, while those related to high temperatures werewere performed performed in in accordance accordance with with ASTM: ASTM: E21-09 E21-09 standard standard [35]. [35]. Creep Creep testing testing was was carried carried out out were performed in accordance with ASTM: E21-09 standard [35]. Creep testing was carried out accordingaccording to to the the ASTM: ASTM: E E 139-11 139-11 standard standard [35]. [35]. Ch Charpyarpy tests tests were were carried carried out out according according to to ASTM: ASTM: according to the ASTM: E 139-11 standard [35]. Charpy tests were carried out according to ASTM: E23-12cE23-12c standard standard and and specimens specimens used used in in these these tests tests were were also also manufactured manufactured in in accordance accordance with with the the E23-12c standard and specimens used in these tests were also manufactured in accordance with the samesame standards. standards. All All of of the the mentioned mentioned standards standards ca cann also also be be found found in in the the Annual Annual Book, Book, Ref. Ref. [35]. [35]. same standards. All of the mentioned standards can also be found in the Annual Book, Ref. [35]. 3.3. Test Test Results Results and and Discussion Discussion 3. Test Results and Discussion

3.1.3.1. Mechanical Mechanical Properties-Engineering Properties-Engineering Stress-Strain Stress-Strain Diagrams Diagrams EngineeringEngineering stress-strain stress-strain diagrams diagrams werewere were obtainedobtained obtained byby by performing performing uniaxial uniaxial tests tests at at room room and and high high temperatures.temperatures. A A minimum minimum of of fivefive five tests tests waswas was performedperformed performed forfor for eacheach each testtest test temperature.temperature. temperature. SinceSince Since engineeringengineering engineering stress-strainstress-strain diagramsdiagrams diagrams carriedcarried carried out out out at at at the the the considered considered considered temperature temperature temperature do do do not not not differ differ differ from from from each each each other other other at all,at at all, orall, aoror very aa veryvery little, little,little, only only oneonly diagram oneone diagramdiagram is shown isis shown forshown each forfor of the eacheach considered ofof thethe consideredconsidered temperatures temperaturestemperatures (the first conducted (the(the firstfirst test),conductedconducted Figure test), 2test),. On Figure Figure the basis 2. 2. On On of the experimentalthe basis basis of of experime experime investigations,ntalntal investigations, investigations, the ultimate the the tensile ultimate ultimate strength tensile tensile and strength strength yield strengthandand yield yield are strength strength said to are decrease are said said to withto decrease decrease an increase with with inan an temperature, in increasecrease in in temperature, excepttemperature, at a temperature except except at at a a oftemperature temperature 250 ˝C where of of these250250 °C °C properties where where these these increase properties properties a little. increase increase a a little. little.

(a(a) ) (b(b))

FigureFigure 2. 2. Engineering Engineering stress-strain stress-strain diagrams diagrams at at room room and and high high temperatures: temperatures: X6CrNiTi18-10 X6CrNiTi18-10 steel. steel. Figure 2. Engineering stress-strain diagrams at room and high temperatures: X6CrNiTi18-10 steel. (a()a )Stress-strain Stress-strain diagrams: diagrams: 20 20 °C °C to to 800 800 °C; °C; ( b(b) )Stress-strain Stress-strain diagrams: diagrams: 150 150 °C °C to to 550 550 °C. °C. (a) Stress-strain diagrams: 20 ˝C to 800 ˝C; (b) Stress-strain diagrams: 150 ˝C to 550 ˝C. TheThe modulus modulus of of elasticity elasticity continuously continuously decreases decreases with with an an increase increase in in temperature. temperature. Also, Also, from from thethe engineering Theengineering modulus stress-strain stress-strain of elasticity diagram, continuouslydiagram, it it is is decreases visible visible that that with strains strains an increase at at 300 300 in °C, temperature.°C, 400 400 °C, °C, and and Also, 500 500 from °C °C theareare ˝ ˝ ˝ engineeringsomewhatsomewhat reduced reduced stress-strain in in comparison comparison diagram, itwith with is visible the the ones ones that at at strains higher higher at temperatures. temperatures. 300 C, 400 C, On On and the the 500 basis basisC of areof engineering engineering somewhat stress-strainstress-strain diagrams diagrams it it is is visible visible that that strains strains at at 300 300 °C, °C, 400 400 °C °C and and 500 500 °C °C are are somewhat somewhat reduced reduced in in comparisoncomparison with with those those at at higher higher temperatures. temperatures. As As a a consequence consequence of of dynamic dynamic strain strain aging, aging, which which is is treatedtreated as as hardening hardening phenomenon, phenomenon, in in the the stress-strain stress-strain curves curves some some effects effects can can arise. arise. Serrations Serrations in in the the stress-strainstress-strain curves curves are are the the most most visible visible effects effects of of dy dynamicnamic strain strain aging. aging. When When this this effect effect is is not not seen seen otherother effects effects can can be be present. present. Usually, Usually, if if serration serrations sare are not not seen, seen, dynamic dynamic strain strain aging aging can can be be marked marked Materials 2016, 9, 298 5 of 19 reduced in comparison with the ones at higher temperatures. On the basis of engineering stress-strain diagrams it is visible that strains at 300 ˝C, 400 ˝C and 500 ˝C are somewhat reduced in comparison with those at higher temperatures. As a consequence of dynamic strain aging, which is treated as hardening phenomenon, in the stress-strain curves some effects can arise. Serrations in the stress-strain curves are the most visible effects of dynamic strain aging. When this effect is not seen other effects can be present. Usually, if serrations are not seen, dynamic strain aging can be marked by lower strain rateMaterials sensitivity. 2016, 9, Also,298 dynamic strain aging causes a minimum variation of ductility with temperature,5 of 19 a plateauby lower in strain strength rate assensitivity. well as a Also, peak dynamic in work strain hardening. aging causes a minimum variation of ductility with temperature, a plateau in strength as well as a peak in work hardening. 3.1.1. Graphical Representation of the Temperature Dependency of Mechanical Properties 3.1.1.Experimentally Graphical Representation determined of mechanical the Temper propertiesature Dependency such as of ultimate Mechanical tensile Properties strength, yield strength (0.2 offsetExperimentally yield strength), determined modulus mechanical of elasticity, properties and elongationsuch as ultimate are displayed tensile strength, in Figure yield3 using specialstrength characters (0.2 offset (‚, yield). Approximation strength), modulus curves of elasticity, related and to theelongation same properties are displayed are in presented Figure 3 using solidusing or dashedspecial characters lines. These (▪, ♦). approximation Approximation curvescurves related relating to tothe the same mentioned properties propertiesare presented describe theirusing experimentally solid or dashed obtained lines. valuesThese approximation with greater orcurves lower relating accuracy. to the To mentioned determine properties the accuracy of approximation,describe their theexperimentally coefficient obtained of determination values with (R 2greater) is used or lower as a measureaccuracy. ofTo accordance determine the between accuracy of approximation, the coefficient of determination (R2) is used as a measure of accordance experimentally obtained results and polynomial approximation and serves as a statistic that gives between experimentally obtained results and polynomial approximation and serves as a statistic that informationgives information on the fiton of the a fit model of a model [36]. [36].

94 63 32 σ m (TTTTT ) 3.34066 10 8.38792 10 6.09445 10 1.88466 642.468

10 4 7 3 4 2 1 εt (TT ) 5.2065 10  5.15185  10 T 4.95939  10 T 2.74578  10 T 76.1836 94 73 32 1 σ0.2 (TTTTT ) 1.05807  10  5.06733  10  1.37419  10  6.13642  10  402.068

(a)

ET( ) 5.45165  1073 T  5.066  10 42 T  2.49019  10  1 T  229.624

(b)

Figure 3. Cont. Materials 2016, 9, 298 6 of 19

Materials 2016, 9, 298 6 of 19 Materials 2016, 9, 298 6 of 19

ψ(TTTTT ) 5.98894 1010 4 1.08478 10 6 3 8.0243 10 4 2 2.63097 10 1 92.6016

10 4 7 3 4 2 1 ε (TT ) 5.2065 1010  4 5.15185  10 6 T 3 4.95939  4 10 2 T 2.74578 1  10 T 76.1836 t ψ(TTTTT ) 5.98894 10 1.08478 10 8.0243 10 2.63097 10 92.6016 10 4 7 3 4 2 1 εt (TT ) 5.2065 10  5.15185  10 T(c 4.95939)  10 T 2.74578  10 T 76.1836

Figure 3. Dependence of mechanical properties(c )on temperature: X6CrNiTi18-10 steel. (a) Ultimate

tensile strength (σm) and 0.2 offset yield strength (σ0.2) versus temperature; (b) The modulus of FigureFigure 3. Dependence3. Dependence of of mechanical mechanical properties on on temperature: temperature: X6CrNiTi18-10 X6CrNiTi18-10 steel. steel.(a) Ultimate (a) Ultimate elasticity (E) versus temperature; (c) Total elongation (εt) and reduction in the area (ψ) versus tensiletensile strength strength (σ ()σ andm) and 0.2 0.2 offset offset yield yield strength strength (σ (σ) 0.2versus) versustemperature; temperature; (b )(b The) The modulus modulus of elasticityof temperature. m 0.2 elasticity (E) versus temperature; (c) Total elongation (εt) and reduction in the area (ψ) versus (E) versus temperature; (c) Total elongation (εt) and reduction in the area (ψ) versus temperature. temperature. 3.1.2. Descriptive Error Bars-Mechanical Properties 3.1.2.3.1.2. Descriptive Descriptive Error Error Bars-Mechanical Bars-Mechanical Properties Properties The structure operating under certain environmental conditions is to be subjected to certain loads.The ItThe is structure also structure necessary operating operating to choose underunder acertain material environmental environmental whose properties conditions conditions will is meetto is be to thesubjected be structure subjected to certain service to certain life requirements,loads.loads. It isIt alsois also i.e. necessary, necessarythe onesto basedto choosechoose on a known material material material wh whoseose propertiesproperti propertieses will so will meetthat meet thethe behaviorstructure the structure service of the service lifestructure life i.e. canrequirements, requirements,be predicted. i.e. ,Besides, the, the ones ones very based based important onon known aspects, material material e.g., properti properties the esaccuracy so that so that theof thebehavior the experimental behavior of the of structure the results structure and can be predicted. Besides, very important aspects, e.g., the accuracy of the experimental results and theircan be interpretation, predicted. Besides, arise from very the important experimental aspects, data e.g.,. In theaccordance accuracy with of the this, experimental several uniaxial results tensile and their interpretation, arise from the experimental data. In accordance with this, several uniaxial tensile teststheir regarding interpretation, determination arise from of the ultimate experimental tensile data.strength In accordancewere performed. with this, In the several so called uniaxial descriptive tensile teststests regarding regarding determination determination of of ultimateultimate tensile tensile stre strengthngth were were performed. performed. In the In so the called so called descriptive descriptive errorerror bars, bars, Figure Figure 4, 4,an an analysis analysis ofof ultimaultimatete tensiletensile strength strength is shownis shown where where range range (R) and (R )standard and standard error bars, Figure4, an analysis of ultimate tensile strength is shown where range ( R) and standard deviationdeviation (SD (SD) are) are used. used. The The standard standard deviation was was calculated calculated as givenas given in Ref. in Ref.[37]. [37]. deviation (SD) are used. The standard deviation was calculated as given in Ref. [37].

Figure 4. Cont. Materials 2016, 9, 298 7 of 19 Materials 2016, 9, 298 7 of 19

Figure 4. Descriptive error bars: Ultimate tensile strength of steel X6CrNiTi18-10. (The small triangles Figure 4. Descriptive error bars: Ultimate tensile strength of steel X6CrNiTi18-10. (The small triangles are experimental data points (test results), while R = range; SD = standard deviation; i = a number of are experimental data points (test results), while R = range; SD = standard deviation; i = a number of the test, n = the total number of tests). the test, n = the total number of tests).

2 xi  x 2 (1) SD  i pxi ´ xq SD “ g i n 1 (1) fř n ´ f 1 e InIn Equation (1), (1), xxii is is the the individualindividual datadata of the co considerednsidered property property at at each each test, test, xx is is thethe meanmean valuevalue ofof thethe consideredconsidered property,property, calculatedcalculated as:as: x x “ xi (2) x n i  i (2) ÿi n In Equation (2), n is the total number of the tests/experiments (at each test one data of the In Equation (2), n is the total number of the tests/experiments (at each test one data of the considered property is obtained). In this consideration there are: x = (σ ; σ ); x “(σ ; σ ); x i m,i 0.2,i σ m σ0.2 iconsidered“ 1...n. property is obtained). In this consideration there are: i = ( σ m,i ; σ0.2,i ); x  ( m; 0.2 ); in 1 ... . 3.2. Determining the Resistance of Material to Creep 3.2. Determining the Resistance of Material to Creep 3.2.1. Short-Time Creep Tests 3.2.1.To Short-Time assess the Creep short-time Tests creep behavior of the considered material or to predict its creep resistance, several uniaxial short-time creep tests were carried out. Data defining creep tests as well as material To assess the short-time creep behavior of the considered material or to predict its creep creep responses are shown in Figures5–8. In these investigations short-time creep behavior was resistance, several uniaxial short-time creep tests were carried out. Data defining creep tests as well considered since most materials can be subjected to such temperature conditions (occurrence of high as material creep responses are shown in Figures 5–8. In these investigations short-time creep behavior was considered since most materials can be subjected to such temperature conditions (occurrence of high temperature due to error in cooling, hazard, fire, etc.). Only some of the special Materials 2016, 9, 298 8 of 19

MaterialsMaterials 2016 2016, ,9 9, ,298 298 88 of of 19 19 temperatureMaterials 2016, 9 due, 298 to error in cooling, hazard, fire, etc.). Only some of the special materials are intended8 of 19 materialsto be used are in intended structures to designedbe used in for structures long term desi operationgned for long at high term temperatures. operation at high In long temperatures. term creep materialsmaterials are are intended intended to to be be used used in in structures structures desi designedgned for for long long term term operation operation at at high high temperatures. temperatures. Inprocesses, long term however, creep processes, special equipmenthowever, special for creep equi processpment for monitoring creep process is to moni be used.toring In is theseto be used. tests, InIn long long term term creep creep processes, processes, however, however, special special equi equipmentpment for for creep creep process process moni monitoringtoring is is to to be be used. used. Instress these levels tests, are stress selected levels in are accordance selected within accord the 0.2ance offset with yield the 0.2 strength offset previouslyyield strength determined previously at InIn thesethese tests,tests, stressstress levelslevels areare selectedselected inin accordaccordanceance withwith thethe 0.20.2 offsetoffset yieldyield strengthstrength previouslypreviously determinedthe considered at the temperature considered (for temperature example: 253.6 (for exampl MPa ise: equivalent 253.6 MPa to is 0.2 equivalent offset yield to strength 0.2 offset for yield this determineddetermined atat thethe consideredconsidered temperaturetemperature (for(for examplexample:e: 253.6253.6 MPaMPa isis equivalentequivalent toto 0.20.2 offsetoffset yieldyield strengthmaterial for at 400 this˝ C).material at 400 °C). strengthstrength for for this this material material at at 400 400 °C). °C).

Figure 5. Creep behavior of steel X6CrNiTi18-10 at the temperature of 400 ˝°C. FigureFigure 5.5. Creep Creep behavior behavior ofof steelsteel X6CrNiTi18-10 X6CrNiTi18-10 at at the the temperature temperature ofof of 400400 400 °C. °C.C.

Figure 6. Creep behavior of steel X6CrNiTi18-10 at a temperature of 500 °C. FigureFigure 6.6. Creep Creep behavior behavior ofof steelsteel X6CrNiTi18-10 X6CrNiTi18-10 at at a a temperature temperature ofof of 500500 500 ˝°C. °C.C.

FigureFigure 7. 7. Creep Creep behavior behavior of of steel steel X6CrNiTi18-10 X6CrNiTi18-10 at at a a temperature temperature of of 600 600 °C. °C. Figure 7. Creep behavior of steel X6CrNiTi18-10 at a temperature ofof 600600 ˝°C.C. Materials 2016, 9, 298 9 of 19 Materials 2016, 9, 298 9 of 19

Figure 8. Creep behavior of steel X6CrNiTi18-10 at a temperature ofof 700700 ˝°C.C.

In accordance with the short-time creep tests, steel X6CrNiTi18-10 is considered to be creep resistantIn accordance at temperatures with theof 400 short-time °C and 500 creep °C tests,when steelthe stress X6CrNiTi18-10 level does not is considered exceed 0.9 toof the be creepyield ˝ ˝ resistantstrength at temperaturesthe mentioned of temperatures. 400 C and 500 Also,C this when steel the may stress be level treated does as not creep exceed resistant 0.9 of at the a yieldtemperature strength of at 600 the mentioned°C if the applied temperatures. stress does Also, not this exceed steel may 0.5 beof treatedthe yield as creepstrength resistant at this at ˝ atemperature. temperature In of 600addition,C if the even applied at temperatures stress does not of exceed 700 °C 0.5 this of the material yield strength may be at treated this temperature. as creep ˝ Inresistant addition, when even the at applied temperatures stress does of 700 not Cexceed this material 30% of the may yield be treated strength. as creep resistant when the applied stress does not exceed 30% of the yield strength. 3.2.2. Creep Test Modeling 3.2.2. Creep Test Modeling To perform a creep test, appropriate but usually expensive equipment is indispensable. To perform a creep test, appropriate but usually expensive equipment is indispensable. Although Although the creep test shows deformation behavior of the material realistically, sometimes it is the creep test shows deformation behavior of the material realistically, sometimes it is possible, based possible, based on known data of the behavior from similar conditions, to predict the creep behavior on known data of the behavior from similar conditions, to predict the creep behavior for the prescribed for the prescribed conditions. This prediction can be done using similar analytical methods or conditions. This prediction can be done using similar analytical methods or rheological models that are rheological models that are used to model/simulate real creep processes. In the following part there used to model/simulate real creep processes. In the following part there are two rheological models are two rheological models and one analytical method (formula) proposed to be used in creep and one analytical method (formula) proposed to be used in creep modeling. All of the proposed modeling. All of the proposed tools can be used for modeling the first and second creep stages. Well tools can be used for modeling the first and second creep stages. Well known rheological models are known rheological models are the Burgers model and the Standard linear solid model (SLS). The the Burgers model and the Standard linear solid model (SLS). The Burgers model is represented in Burgers model is represented in Refs. [20,38]: Refs. [20,38]: 1 1 t  p´E2{η1qt  ε ptq “ σ 11` 1 ´ e  Et21η ` t (3) εσteE1 E2 1 η2 (3) „ EE´¯ η   12 2 In Equation (3) there are: ε(t)-strain, σ-stress, E1-modulus of elasticity, t-time, all related to consideredIn Equation creep curve,(3) there while are:E 2,εη(t)1,-strain, and η2 areσ-stress, parameters E1-modulus whose of values elasticity, are determined t-time, all on related the basis to ofconsidered equality ofcreep the discussedcurve, while creep , curveη, and and η Equation are parameters (3). The whose Standard values linear are solid determined model (SLS) on the is representedbasis of equality Refs. of [22 the,39 discussed]: creep curve and Equation (3). The Standard linear solid model (SLS) is represented Refs. [22,39]: E1E2t σ 1 1 ´ η ε ptq “ ` σ ´ e pE1EEt`E2q (4) E E ` E E  12 1 1 112 1 EE12 teˆ ˙ (4) EEEE In Equation (4) there are: ε(t)-strain,1121σ-stress,t-time, E1, E2, and η are parameters whose values are determined on the basis of equality of the discussed creep curve and Equation (4). In Equation (4) there are: ε(t)-strain, σ-stress, t-time, E1, E2, and η are parameters whose values An analytical formula to model/simulate creep behavior is proposed in Refs. [11,12,22]: are determined on the basis of equality of the discussed creep curve and Equation (4). An analytical formula to model/simulate creep behavior is proposed in Refs. [11,12,22]: ε ptq “ D´Tσptr (5) Tpr tD  t (5) In Equation (5) there are: T-temperature, σ-stress, t-time and D, p and r are parameters which are toIn be Equation determined. (5) there All ofare: the T- mentionedtemperature, Equations σ-stress, (3)–(5) t-time can and be D used, p and for r three are parameters different types which of modelling,are to be determined. namely, for: All of the mentioned Equations (3)–(5) can be used for three different types of modelling, namely, for: Materials 2016, 9, 298 10 of 19

ε() =ε(), σ = , = (6a) ε() =ε(σ, ), = (6b)

tTt ,,  (6c)

The first type of modeling, Equation (6a), denotes the modeling of one exactly defined creep curve that is described by the defined creep temperature and the defined stress level at this temperature. The last type of modeling, Equation (6c), is the most useful and applicable one. Namely, this modeling covers an entire range of stress levels and temperature levels for the considered time range. In Table 2, data relating to creep modelling are presented, while creep modelling curves are presented in Figure 9.

Table 2. Creep modeling data: X6CrNiTi18-10 steel.

Material: X6CrNiTi18-10 steel TpTrT() () Application of Equation (6c) ε = (,Tt ,)  DT ()   t Constant temperature T 400 500 600 700 (°C) Constant stress level x ≤ 0.9 x = 0.7–0.9 x ≤ 0.5 x ≤ 0.3 Materials 2016, 9, 298 10 of 19 σ(MPa) = x × σ. 376 214–275 150 63 Time (min) 1200 Parameters DT( ) 6.150138 1083 T 1.1354401 10 42 T 6.7433968 10  2 T 11.784261 Analytical Equation (5) ε ptq “ ε ptq, σ “ const73, T “ const 32 (6a) pT( ) 7.7811369 10 T 1.6357754 10 T 1.0613631 T 213.60664 83 42 2 rT( )εpt 7.751213q “ ε p σ 10, tq T, T 1.3200375“ const  10 T  7.1958106  10  T  12.690118 (6b)

ε ptq “ ε pσ, T, tq (6c) In general, all of the above mentioned models for simulating creep behavior are considered to Thebe satisfactory. first type of However, modeling, an Equation analytical (6a), formula denotes is proposed the modeling as the ofbest one model. exactly When defined rheological creep curve that ismodels described are considered, by the defined then creepthe Burgers temperature model seems and the to definedbe more stresssuitable level for atthe this creep temperature. processes The where the dominated creep phase is the steady-state phase, while for creep process with dominated last type of modeling, Equation (6c), is the most useful and applicable one. Namely, this modeling transient phase (more expressed parabolic shape), the SLS model is considered to be more suitable. covers an entire range of stress levels and temperature levels for the considered time range. In Table2, Also, it needs to be said that any of the used models are more suitable when only a particular curve data relatingis selected to to creep be modeled. modelling are presented, while creep modelling curves are presented in Figure9.

Figure 9. Experimental and modeled creep curves: steel X6CrNiTi18-10. Modeling was performed Figure 9. Experimental and modeled creep curves: steel X6CrNiTi18-10. Modeling was performed using Equation (5) by applying the principle 6c. using Equation (5) by applying the principle 6c.

Table 2. Creep modeling data: X6CrNiTi18-10 steel.

Material: X6CrNiTi18-10 steel Application of Equation (6c) ε = εpσ, T, tq “ DpTq´T ¨ σppTq ¨ trpTq Constant 400 500 600 700 temperature T (˝C) Constant stress level x ď 0.9 x = 0.7–0.9 x ď 0.5 x ď 0.3 σ pMPaq = x ˆ σ0.2 376 214–275 150 63 Time (min) 1200 Analytical Equation Parameters (5) DpTq “ 6.150138 ˆ 10´8T3 ´ 1.1354401 ˆ 10´4T2 ` 6.7433968 ˆ 10´2T ´ 11.784261 ppTq “ 7.7811369 ˆ 10´7T3 ´ 1.6357754 ˆ 10´3T2 ` 1.0613631 ˆ T ´ 213.60664 rpTq “ ´7.751213 ˆ 10´8T3 ` 1.3200375 ˆ 10´4T2 ´ 7.1958106 ˆ 10´2T ` 12.690118

In general, all of the above mentioned models for simulating creep behavior are considered to be satisfactory. However, an analytical formula is proposed as the best model. When rheological models are considered, then the Burgers model seems to be more suitable for the creep processes where the dominated creep phase is the steady-state phase, while for creep process with dominated transient phase (more expressed parabolic shape), the SLS model is considered to be more suitable. Also, it needs to be said that any of the used models are more suitable when only a particular curve is selected to be modeled. Materials 2016, 9, 298 11 of 19

3.3. Correlation between Charpy V-Notch Impact Energy and Fracture Toughness Materials 2016, 9, 298 11 of 19 Undoubtedly fracture toughness is one of the most important material properties used to design structure3.3. Correlation against between fracture. Charpy Fracture V-Notch toughness Impact Energy is a parameter and Fracture that Toughness defines material resistance to crack extensionUndoubtedly [40], and itfracture represents toughness a critical is one value of the of most the stressimportant intensity material factor properties (SIF or usedK), designatedto design as structureKIc. Designation against fracture.KIc indicates Fracture that toughness this is a minimumis a parameter value that of defines fracture material toughness resistance determined to crack by usingextension a specimen [40], and that it meetsrepresents the planea critical strain value conditions of the stress and intensity besides, factor is tensile (SIF or loaded K), designated (first mode). as

FractureKIc. Designation toughness is statedindicates to bethat a subjectthis is a concerned minimum withvalue predicting of fracture failure toughness mode, determined especially by one containingusing a specimen crack-like that defects meets [ 41the]. Inplane engineering strain conditions practice, and fracture besides, toughness is tensile canloaded be experimentally(first mode). determinedFracture toughness by a number is stated of standard to be a testssubject [42 concer]. However,ned with experiments predicting relatedfailure mode, to the measurementespecially one of fracturecontaining toughness crack-like are defects not intended [41]. In for engineering materials practice, that behave fracture plastically. toughness In can this be case, experimentally the J-integral (or,determined for example, by a CTOD) number as of a standard fracture tests parameter [42]. Ho iswever, fairly experiments appropriate. related On the to the other measurement hand, to avoid of problemsfracture such toughness as complicated are not intended manufacturing for material of thes that specimen, behave differences plastically. between In this case, the crackthe J-integral in the real structure,(or, for andexample, the manufactured CTOD) as a fracture crack on parameter the specimen, is fairly other appropriate. methods existingOn the other for fracture hand, to toughness avoid assessmentproblems aresuch used. as complicated One of these manufacturing such methods of th ise the specimen, determination differences of thebetween Charpy the impact crack in energy. the Correlationreal structure, between and thethe Charpymanufactured impact crack energy on and the fracturespecimen, toughness other methods was reviewed existing in for Refs. fracture [43,44 ]. toughness assessment are used. One of these such methods is the determination of the Charpy impact In these investigations the Charpy test was used to assess the fracture toughness. The specimens were energy. Correlation between the Charpy impact energy and fracture toughness was reviewed in Refs. machined from the material rod (longitudinal direction). The formula used to assess fracture toughness [43,44]. In these investigations the Charpy test was used to assess the fracture toughness. The is based on the measured Charpy V-notch impact energy, i.e., it is a well-known Roberts-Newton specimens were machined from the material rod (longitudinal direction). The formula used to assess formula that is independent of the temperature: fracture toughness is based on the measured Charpy V-notch impact energy, i.e., it is a well-known Roberts-Newton formula that is independent of the temperature:0.63 KIc “ 8.47 pCVNq (7) KIc = 8.47 (CVN)0.63 (7) However, although this formula can be applied independently of the temperature, the CVN However, although this formula can be applied independently of the temperature, the CVN impact energy is inserted in it in accordance with the obtained result at the considered temperature. impact energy is inserted in it in accordance with the obtained result at the considered temperature. TheThe geometry geometry of of the the specimens specimens used used in in thesethese investigationsinvestigations is is shown shown in in Figure Figure 10a. 10a. Experimentally Experimentally obtainedobtained results results of of the the Charpy Charpy V-notch V-notch impact impact energyenergy and the the calculated calculated values values of of fracture fracture toughness toughness 3 areare presented presented in in Figure Figure 10 10b.b. Note: Note: Specimen Specimen (10(10ˆ × 10 ׈ 5555 mm mm3) )is is manufactured manufactured from from a rod a rod in insuch such wayway that that its its largest largest dimension dimension (55 (55 mm) mm) coincides coincides withwith thethe length of of the the rod. rod.

(a)

Figure 10. Cont. Materials 2016, 9, 298 12 of 19 Materials 2016, 9, 298 12 of 19

CVN(T) 8.2587104T2 2.63111101T 210.123 3 2 1 KIc (T)  1.0233910 T 3.2897910 T 163.636

CVN = Charpy V-notch impact energy (measured, presented as an average value based on three tests), KIc = fracture toughness (calculated). (b)

Figure 10. Charpy V-notch specimen and impact energy determination. (a) Specimen’s geometry- Figure 10. Charpy V-notch specimen and impact energy determination. (a) Specimen’s geometry- Charpy V-notch impact energy determination; (b) Charpy V-notch energy (CVN); and calculated Charpy V-notch impact energy determination; (b) Charpy V-notch energy (CVN); and calculated fracture toughness (KIc) versus temperature. fracture toughness (KIc) versus temperature. 3.4. Fatigue Testing of Tensile Stressed Specimens 3.4. Fatigue Testing of Tensile Stressed Specimens 3.4.1. General Consideration 3.4.1. General Consideration As engineering structures are frequently subjected to different loadings, it is surely of interest to investigateAs engineering the resistance structures of the are material frequently to failure subjected at the mentioned to different loadings. loadings, It is it known is surely that of when interest toa investigate material is thesubjected resistance to a ofrepeated the material load (cyclic to failure load), at fatigue the mentioned failure may loadings. result in Itfracture is known of the that whenconsidered a material engineering is subjected element to a repeated at a stress load level (cyclic that load), is much fatigue lower failure than may the result fracture in fracture stress of thecorresponding considered engineering to a monotonic element tensile at aload. stress Fati levelgue may that isbe muchdefined lower as the than process the fracture of damage stress correspondingaccumulation todue a to monotonic cyclic loading tensile [45]. load. The main Fatigue task may for the be defineddesigner asdealing the process with a structure of damage accumulationdesign subjected due toto cyclicrepeated loading load is [45 to]. ensure The main the required task for thestructure designer service dealing life. Fatigue with a structuredesign designcriteria subjected are based to on repeated known loadfatigue is tolifeensure models the in accordance required structure with the servicerequired life. durability Fatigue of design the criteriastructure. are basedThese onmodels known are: fatigue stress-life life model, models deformation-life in accordance model with the and required crack-propagation durability rate of the structure.model. In These this modelspaper a are:stress-life stress-life model model, is app deformation-lifelied. In these investigations model and crack-propagationthe specimens were rate model.subjected In this to papertensile astresses stress-life at the model prescribed is applied. stress In ratio these and investigations the cyclic loading the specimens processes were carried subjected toout tensile in accordance stresses at with the the prescribed sinusoidal stress law. ratioThe abscissa and the (the cyclic number loading of cycles processes (N) to werefailure) carried is usually out in accordanceplotted on with a logarithmic the sinusoidal scale, while law. Thethe ordinate abscissa (cyclic (the number maximum of stress, cycles or (N cyclic) to failure) mean stress is usually or plottedstress onamplitude) a logarithmic is plotted scale, on whilea linear the scale ordinate or on (cyclica logarithmic maximum scale.stress, Fatigue or can cyclic be considered mean stress in or stressthe cases amplitude) of tensile is plottedloading on(or aanother linear scaletype of or lo onad) a logarithmicfor unnotched scale. (smooth) Fatigue or notched can beconsidered specimens. in However, attention should be paid to ensure that the test specimen is compatible with the testing the cases of tensile loading (or another type of load) for unnotched (smooth) or notched specimens. structure generating test data. The geometry (including dimensions) of the specimen as well as the However, attention should be paid to ensure that the test specimen is compatible with the testing testing procedure are recommended by standard (ASME standard, ISO standard). Each fatigue test structure generating test data. The geometry (including dimensions) of the specimen as well as the performed at the prescribed fatigue stress and at the prescribed stress ratio generates one point in the testing procedure are recommended by standard (ASME standard, ISO standard). Each fatigue test S-N system. Usually several fatigue tests are performed for the same fatigue stress level since a scatter performedrelated to at the the number prescribed of cycles fatigue to failure stress exists. and at On the the prescribed basis of the stress recorded ratio test generates data the one S-N point system, in the S-Norsystem. S-N diagram Usually (also several called fatigue S-N curve, tests ӧℎ are performed curve or for fatigue the same life) fatigueis created stress and level it represents since a scatter the related to the number of cycles to failure exists. On the basis of the recorded test data the S-N system, Materials 2016, 9, 298 13 of 19 or S-N diagram (also called S-N curve, Wohler curve or fatigue life) is created and it represents the applied fatigue stresses versus the number of cycles to failure for the considered material and for the prescribed stress ratio. A. Wohler, a German scientist [46] carried out numerous tests using smooth and notchedMaterials 2016 specimens, 9, 298 taken from railway axles. When regardless of the number of cycles13 of the19 test specimen remains unbroken (i.e., without the occurrence of failure) at the prescribed conditions of the applied fatigue stresses versus the number of cycles to failure for the considered material and for the test, the fatigue limit has been reached, and the stress associated with this limit is called the fatigue limit prescribed stress ratio. A. ӧℎ, a German scientist [46] carried out numerous tests using smooth (endurance limit) [3,47,48]. This in fact means that there is a theoretical level of stress for the prescribed and notched specimens taken from railway axles. When regardless of the number of cycles the test stressspecimen ratio below remains which unbroken the material (i.e., without will not the fail occurrence for any numberof failure) of at cycles. the prescribed The S-N conditionsdiagram consistsof of twothe parts test, the (areas) fatigue of whichlimit has the been first reached, area belongs and the to stre thess finiteassociated fatigue with region this limit (finite is called fatigue the life)fatigue and the secondlimit one (endurance that belongs limit) to [3,47,48]. the infinite This fatigue in fact means regime that (life). there If bothis a theoretical parts are level presented of stress in linearfor the form, thenprescribed the diagram stress contains ratio below the inclined which andthe material the horizontal will not line. fail Namely,for any number in this caseof cycles. the infinite The S-N part of the S-Ndiagramcurve consists (infinite of fatiguetwo parts region) (areas) becomesof which the practically first areahorizontal. belongs to the This finite is validfatigue for region a material (finite with clearlyfatigue expresses life) and fatigue the second limit. one By contrast,that belongs the toS-N thecurve infinite may fatigue have regime a shape (life). that If correspondsboth parts are to the materialpresented without in linear clear form, fatigue then limit. the diagram In the standards contains the as inclined well as and in literature the horizontal in general, line. Namely, a proposition in this case the infinite part of the S-N curve (infinite fatigue region) becomes practically horizontal. This related to the performing of the fatigue test and also for fatigue limit determination can be found. is valid for a material with clearly expresses fatigue limit. By contrast, the S-N curve may have a shape For steel alloys, as fatigue limit, the number of the cycles at which the specimen remains unbroken, that corresponds to the material without clear fatigue limit. In the standards as well as in literature 7 is usuallyin general, adopted a proposition in an amount related of to 10 thecycles. performing Some of engineering the fatigue componentstest and also arefor fatigue subjected limit to low stressesdetermination relative to can the be material found. For ultimate steel alloys, tensile as fatigue strength limit, but the at number a very of large the cycles number at which of cycles the and that duespecimen to long remains service unbroken, life and/or is usually high frequencyadopted in load. an amount So, high of cycle107 cycles. fatigue Some (HCF) engineering is treated as crackcomponents growth phenomenon are subjected related to low tostresses the previously relative to mentionedthe material stressed ultimate components.tensile strength In but any at case, a in engineeringvery large practice number the of influencecycles and ofthat HCF due exerted to long onservice the lifelife ofand/or the componenthigh frequency is to load. be eliminatedSo, high or reducedcycle to fatigue a minimum. (HCF) is If treated testing as procedures crack growth require phenomenon 109 cycles, related it may to bethe said previously that these mentioned cases belong to thestressed so called components. ultra-high In cycleany case, fatigue in engineering regime (UHCF). practice Somethe influence factors of such HCF as exerted surface on finish, the life applied of the component is to be eliminated or reduced to a minimum. If testing procedures require 109 cycles, loading conditions, deviations in specimen alignment, etc., cause scatter in fatigue data. A group of it may be said that these cases belong to the so called ultra-high cycle fatigue regime (UHCF). Some methods also exists that provides a means to deal with the scatter fatigue data and in this sense provide factors such as surface finish, applied loading conditions, deviations in specimen alignment, etc., an estimatecause scatter for median in fatigue fatigue data. strengthA group atof themethods considered also exists number that pr ofovides cycles. a Tomeans the to mentioned deal with groupthe of methodsscatter (tools) fatigue there data may and be in counted: this sense conventional provide an S-Nestimatetests, for advanced median statisticalfatigue strength methods, at the quantal responseconsidered tests, andnumber accelerated of cycles. stressTo the tests mentioned [45]. Within group theseof methods groups (tools) there there are severalmay be methods:counted: for example,conventional methods S-N such tests, as advanced the Staircase statistical method, methods, Two-point quantal method, responseetc. tests,which and belongaccelerated to the stress quantal responsetests [45]. tests Within (regarded these asgroups a group there of are methods). several me Conversely,thods: for example, fatigue methods limit is such often as consideredthe Staircase to be a materialmethod, property. Two-point method, etc. which belong to the quantal response tests (regarded as a group of methods). Conversely, fatigue limit is often considered to be a material property. 3.4.2. Fatigue Testing 3.4.2. Fatigue Testing In the case presented in this paper, fatigue tests of cyclic tensile stressed specimens were carried In the case presented in this paper, fatigue tests of cyclic tensile stressed specimens were carried out in accordance with the standard ISO 12107:2012 (2012) [49], at the prescribed stress ratio of R = 0.25 out in accordance with the standard ISO 12107:2012 (2012) [49], at the prescribed stress ratio of and atR room= 0.25 temperature.and at room temperature. The geometry The ofgeometry the specimen of the specimen is shown is in shown Figure in 11 Figure while 11 test while results test data as wellresults as fatigue data as limitwell as are fatigue presented limit are in Figurepresented 12 .in Figure 12.

Figure 11. Specimen’s geometry-fatigue test. Figure 11. Specimen’s geometry-fatigue test. Materials 2016, 9, 298 14 of 19 Materials 2016, 9, 298 14 of 19

Figure 12. Fatigue tests (at room temperature and stress ratio R = 0.25) for X6CrNiTi18-10 steel: Figure 12. Fatigue tests (at room temperature and stress ratio R = 0.25) for X6CrNiTi18-10 steel: maximum stress versus number of cycles to failure (○ = no failure, ♦ = failure), approximated “S-N” maximum stress versus number of cycles to failure ( = no failure,  = failure), approximated “S-N” curve (line) in fatigue limit region (\) and fatigue limit (endurance limit) in fatigue infinite region (–). curve (line) in fatigue limit region (z) and fatigue limit# (endurance limit) in fatigue infinite region (–).

Fatigue testing started in such a way that the first tests were at the stress level (600 MPa) near the tensileFatigue strength testing (608 started MPa) in suchof the a waytested that mate therial. first Afterwards tests were atthese the stressspecimens level (600wereMPa) tested near by decreasingthe tensile stress strength regime. (608 MPa)A number of the of tested10 million material. cycles Afterwardswas selected these as the specimens desired number were testedof cycles by atdecreasing which the stress specimen regime. remains A number unbroken. of 10 million In genera cyclesl, at wasthe considered selected as thestress desired level numbersome specimens of cycles mayat which be expected the specimen to be broken remains (failed) unbroken. while In some general, others at the may considered not. Namely, stress in levelsome some cases specimens there is a runoutmay be where expected the totime be to broken failure (failed) exceeds while that someavailabl otherse for maythe test not. (censoring). Namely, in As some is visible, cases there in this is stress-lifea runoutwhere model, the the time entire to failureprocedure exceeds of fatigue that available testing included for the test 21 tests (censoring). of which As seven is visible, tests belong in this tostress-life the staircase model, method the entire (modified procedure staircase of fatigue method) testing used included for fatigue 21 tests limit of which determination. seven tests In belong finite fatigueto the staircase life the approximated method (modified curve staircase (line) is de method)termined used without for fatigue taking limit into account determination. runouts. In finite fatigue life the approximated curve (line) is determined without taking into account runouts. 3.4.3. Fatigue Limit Calculation 3.4.3. Fatigue Limit Calculation The fatigue limit (endurance limit) or so called fatigue strength in the infinite fatigue life range The fatigue limit (endurance limit) or so called fatigue strength in the infinite fatigue life range can be estimated in accordance with the modified staircase method and in Figure 12 it is presented can be estimated in accordance with the modified staircase method and in Figure 12 it is presented by by the horizontal line. Specimens were tested under decreasing stress regime. In Table 3 data related the horizontal line. Specimens were tested under decreasing stress regime. In Table3 data related to to failed and not-failed specimens for analysis in the modified Staircase method are presented. failed and not-failed specimens for analysis in the modified Staircase method are presented. Fatigue Fatigue data used in the modified Staircase method analysis are completed from fatigue testing. Data data used in the modified Staircase method analysis are completed from fatigue testing. Data are are presented using the following designations: specimens failed (♦) or not-failed (○) for the presented using the following designations: specimens failed ( ) or not-failed ( ) for the appropriate appropriate stress levels at a certain number of cycles. In this sense, fatigue stress levels applied are: stress levels at a certain number of cycles. In this sense, fatigue stress levels applied# are: 450 MPa (as 450 MPa (as σ, the last stress level from the finite fatigue life, hence it is visible that all of the σ2, the last stress level from the finite fatigue life, hence it is visible that all of the specimens failed), specimens failed), 440 MPa (as σ, first stress level at which the first and last specimens occur that 440 MPa (as σ1, first stress level at which the first and last specimens occur that are not-failed among are not-failed among one that failed), 430 MPa (as σ, stress level at which specimen not-failed). It is one that failed), 430 MPa (as σ0, stress level at which specimen not-failed). It is worth pointing out worth pointing out that the highest level of the stress was σ and it coincides with the lowest stress that the highest level of the stress was σ2 and it coincides with the lowest stress measured in the finite measured in the finite fatigue regime. Let, in general, the magnitude of stress be designated as “σ” fatigue regime. Let, in general, the magnitude of stress be designated as “σi” (MPa) related to the (MPa) related to the specific “i-th” level of testing, and the number of failure events as “fi” related to specific “i-th” level of testing, and the number of failure events as “f ” related to the same specific the same specific (considered) stress level. As observed, each stress leveli (430, 440, 450) increases to (considered) stress level. As observed, each stress level (430, 440, 450) increases to the previous one in the previous one in stress intensity which is equal to the stress step, d = 10 MPa. Table 4 presents an stress intensity which is equal to the stress step, d = 10 MPa. Table4 presents an analysis of the staircase analysis of the staircase data needed for the derivation of constants. Furthermore, the mentioned data needed for the derivation of constants. Furthermore, the mentioned constants are needed for the constants are needed for the fatigue limit calculation, Table 5. fatigue limit calculation, Table5.

Materials 2016, 9, 298 15 of 19

Table 3. Data for modified staircase method related to failed () and not-failed ( ) specimens. # Number of Specimen Stress œi MPa 1 2 3 4 5 6 7 450 – – – – 440 – – – – 430 #––––––# # Table 4. Data analysis for modified staircase method.

2 Stress œi (MPa) Level of Stress i f i if i i f i 450 2 3 6 12 440 1 1 1 1 430 0 0 0 0 – 4 7 13 ř Table 5. Calculation of the constants A, B, C, D in accordance with ISO standard.

Formula Material: X6CrNiTi18-10

A “ i ˆ fi 7 B “ i2 ˆ f 13 ř i C “ fi 4 ř 2 D “ BˆC´A 0.1875 řC2

The lower limit of fatigue strength in infinite fatigue life (i.e., fatigue limit, endurance limit) is defined as (in accordance with ISO standard):

σ f pP, 1´αq “ µy ´ kpP,1´α,do f q ˆ σy (8)

In this Equation there are: The mean fatigue strength

A 1 µ “ σ ` d ´ (9) y 0 C 2 ˆ ˙ where d is stress step-The coefficient for the one sided tolerance limit for a normal distribution kpP,1´α,νq. The estimated standard deviation of the fatigue strength

σy “ 1.62 ˆ d pD ` 0.029q . (10)

In accordance with the standard recommendation of ν “ n ´ 1 “ 6 where n is the number of items in a considered group. Consecutively, for a desired probability of P “ 10% and a confidence level p1 ´ αq = 90%, in accordance with the table B1 (ISO), it follows: kpP,1´α,νq = kp0.1;0.9;6q “ 2.333. In accordance with Equations (9) and (10), it is:

A 1 7 1 µ “ σ ` dp ´ q “ 430 ` 10p ˆ q “ 442.5 MPa (11) y 0 C 2 4 2 or this can be obtained as: 430 ` 440 ` 450 ` 440 ` 450 ` 440 ` 450 µ “ “ 442.8 (12) y 7

σy “ 1.62 ˆ d pD ` 0.029q “ 1.62 ˆ 10 p0.1875 ` 0.029q “ 3.5 MPa (13) Materials 2016, 9, 298 16 of 19

Finally, the fatigue limit is:

σ f p0.1;0.9;6q “ µy ´ kpP,1´α,νq ˆ σy “ 442.5 ´ 2.333 ˆ 3.5 “ 434.33 MPa (14)

Similar investigations related to fatigue of X6CrNiTi18-10 steel have not been found in the literatureMaterials so far. 2016,However, 9, 298 many materials have been tested for fatigue as well as phenomena16 of 19 that occur with fatigue such as those considered in [50]. Similar investigations related to fatigue of X6CrNiTi18-10 steel have not been found in the 3.5. Basicliterature Analysis so offar. the However, Microstructure many materials have been tested for fatigue as well as phenomena that occur with fatigue such as those considered in [50]. As is well known, material properties depend on the chemical composition, processing path, and microstructure.3.5. Basic Analysis For of the the Microstructure considered steel and its composition, some of properties depend on the microstructure.As is well Theknown, properties material pr thatoperties depend depend on theon the microstructure chemical composition, are called processing structure path, sensitive propertiesand (formicrostructure. example, For yield the strength,considered hardness). steel and its Coldcomposition, or hot some rolling, of properties for example, depend is on the the means to microstructure. The properties that depend on the microstructure are called structure sensitive develop and control the microstructure. Since the microstructure can be changed when the material properties (for example, yield strength, hardness). Cold or hot rolling, for example, is the means to is exposeddevelop to high and control temperature, the microstructure. three specimens Since the exposedmicrostructure to different can be chan temperatureged when the conditions material were examined.is exposed The firstto high specimen temperature, is referredthree specimens to as deliveredexposed to different material, temperature and the otherconditions two were specimens with referenceexamined. to The creep first conditionsspecimen is referred carried to out as del ativered different material, temperatures and the other and twodifferent specimensstress with levels. The formerreference creep to test creep was conditions carried outcarried at 500out ˝atC, diffe 153rent MPa, temperatures 1200 min andand thedifferent latter stress one atlevels. 700 ˝TheC, 63 MPa, 1200 min.former Optical creepmicrographs test was carried of out the at examined500 °C, 153 specimensMPa, 1200 min are and shown the latter in Figure one at 70013. °C, 63 MPa, 1200 min. Optical micrographs of the examined specimens are shown in Figure 13.

(a) (b)

(c) (d)

(e) (f)

Figure 13. X6CrNiTi18-10 steel: optical micrographs, aqua regia. (a) As-received material (austenitic Figure 13.stainlessX6CrNiTi18-10 steel, annealed steel: bar), optical the cross-section micrographs, of the aquaspecimen, regia. 500×; (a )(b As-received) As received materialmaterial, the (austenitic stainlesslongitudinal-section steel, annealed of bar), the specimen, the cross-section 500×; (c) After of the performing specimen, the 500creepˆ ;(processb) As at received500 °C/153 material, the longitudinal-sectionMPa/1200 min, the cross-section of the specimen, of the specimen, 500ˆ;( 500×;c) After (d) After performing performing the the creepcreep process process at 500 at 500 ˝C/ 153 MPa/1200°C/153 MPa/1200 min, the min, cross-section the longitudinal of the-section specimen, of the specimen, 500ˆ;(d 500×;) After (e) performingAfter performing the creepthe creep process at 500 ˝C/153process MPa/1200 at 700 °C/63 min, MPa/1200 the longitudinal-section min, the cross-section ofof the the specimen, specimen, 1000×; 500 (f) ˆAfter;(e )the After creep performing process the performed at 700 °C/63 MPa/1200 min, the longitudinal-section of the specimen, 1000×. creep process at 700 ˝C/63 MPa/1200 min, the cross-section of the specimen, 1000ˆ;(f) After the creep process performed at 700 ˝C/63 MPa/1200 min, the longitudinal-section of the specimen, 1000ˆ. Materials 2016, 9, 298 17 of 19

On the basis of the given micrographs, it can be said as follows. The basic microstructure (main phase/main structure) of as-received material is austenite characterized by polygonal austenite grains, Figure 13a,b. Also, there is a mixture of austenite and ferrite. A lot of impurity exists in the material and this is distributed in the form of non-uniform black particles. In between there are twin grains. Considering the longitudinal section, it can be concluded that the slip line and twin crystals are included in the austenite. The ferrite has been stretched and that suggests that the material has suffered some plastic deformation in the longitudinal direction. In the case of the specimen that was previously subjected to creep (500 ˝C/153 MPa/1200 min), Figure 13c,d, the temperature of the creep process was not so high but the stress level was high and the austenite grains were increased. It is shown that not only slip lines increase after creep deformation, but the ferrite content increases as well. Some ferrite precipitated from the austenite which indicated that the stability of the austenite of this material was not good enough. At the same time a higher number of twin grains occurs which have better polygonal shapes. Also, the formation of holes due to the diffusion of failures in the crystal lattice is noticed. As regards the case presented in Figure 13e,f; that is, when the specimen was previously subjected to creep (700 ˝C/63 MPa/1200 min), since the temperature increases, although the stress level was low the temperature increased, the grains are increased and the number of twin grains also increases. In this case, the influence of high temperature on the deformation process is apparent. Some recrystallized grains can be found, which indicates that this material starts to recrystallize at a temperature of 700 ˝C.

4. Conclusions The results of this research present very good information for designers involved in design of structures made of steel X6CrNiTi18-10. The obtained results relating to tensile strength and yield strength show that this material has good ultimate tensile strength and yield strength not only at room temperature but also at high temperatures as is apparent from Table2. Furthermore, the steel is creep resistant over a wide range of temperatures and stress levels, as can be seen from Figures5–8. Also, after carrying out the tests, the fatigue limit of the cyclic tensile stressed steel at a stress ratio of R = 0.25 can be adopted in an amount of 434.33 MPa. Finally, the steel is characterized by an impact energy obtained with the Charpy impact machine in an amount of 176 J/20 ˝C from which a fracture ? toughness of 220 MPa m was calculated.

Acknowledgments: This work was supported by the Croatian Science Foundation under the project 6876 and it is also partially supported by the University of Rijeka within a project 13.09.1.1.01. Microstructure analysis was made by Jitai Niu and Qiang Li from School of Materials Science, Henan Polytechnic University, Jiaozuo, China, while some additional explanations in this field were done by Roman Sturm from the Faculty of Mechanical Engineering, University of Ljubljana. Author Contributions: Josip Brnic performed the experiments, analyzed the data, and wrote the paper; Goran Turkalj analyzed the fatigue data; Marko Canadija analyzed the creep and tensile data; Domagoj Lanc performed the fatigue test; Sanjin Krš´canskianalyzed the creep; Marino Brcic analyzed the tensile test data; Qiang Li and Jitai Niu peformed the microstructure tests and analysis. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Bramfit, B.L. Effect of Composition, Processing and Structure on Properties of Irons and Steels. Mater. Park ASM Int. 1997, 1997, 357–382. 2. Callister, W.D.; Rethwisch, D.G. Fundamentals of Materials Science and Engineering: An Integrated Approach; John Wiley & Sons: New York, NY, USA, 2012. 3. Dowling, N.E. Mechanical Behaviour of Material; Pearson: New York, NY, USA, 2013. 4. Ashby, F. Materials Selection in Mechanical Design; Butterworth-Heinemann: New York, NY, USA, 2011. 5. Brooks, C.R.; Choundry, A. Failure Analysis of Engineering Materials; McGraw-Hill: New York, NY, USA, 2002. 6. Collins, J.A. Failure of Materials in Mechanical Design; John Wiley & Sons: New York, NY, USA, 1993. 7. Solecki, R.; Conant, P.R. Advanced Mechanics of Materials; Oxford University Press: New York, NY, USA, 2003. Materials 2016, 9, 298 18 of 19

8. Raghavan, V. Materials Science and Engineering; Prentice-Hall of India: New Delhi, India, 2004. 9. Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D. AISI 316Ti (1.4571) steel-Mechanical, creep and fracture properties versus temperature. J. Constr. Steel Res. 2011, 67, 1948–1952. [CrossRef] 10. Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D.; Krscanski, S.B. Martensitic Stainless Steel AISI 420-Mechanical Properties, Creep and Fracture Toughness. Mech. Time-Depend. Mater. 2011, 15, 341–352. [CrossRef] 11. Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D.; Canadija, M.; Brcic, M. Information relevant for the design of structure: Ferritic-heat resistant high chromium steel X10CrAlSi25. Mater. Des. 2014, 63, 508–518. [CrossRef] 12. Brnic, J.; Turkalj, G.; Lanc, D.; Canadija, M.; Brcic, M.; Vukelic, G. Comparison of material properties: Steel 20MnCr5 and similar steels. J. Constr. Steel Res. 2014, 95, 81–89. [CrossRef] 13. Milutinovic, M.; Movrin, D.; Pepelnjak, T. Theoretical and experimental investigation of cold hobbling processes in cases of cone-like punch manufacturing. Int. J. Adv. Manuf. Technol. 2012, 58, 895–906. [CrossRef] 14. Tušek, J. Mathematical modelling of melting rate in twin-wire welding. J. Mater. Process Technol. 2000, 100, 250–256. [CrossRef] 15. Pepelnjak, T.; Petek, A.; Kuzman, K. Analysis of the forming limit diagram in digital environment. Adv. Mater. Res. 2005, 6, 697–704. [CrossRef] 16. Klobˇcar, D.; Kosec, L.; Kosec, B. Thermo fatigue cracking of die casting dies. Eng. Fail. Anal. 2012, 20, 43–53. [CrossRef] 17. Brnic, J.; Turkalj, G.; Canadija, M.; Niu, J. Experimental determination and prediction of the mechanical properties of steel 1.7225. Mater. Sci. Eng. A 2014, 600, 47–52. [CrossRef] 18. Brnic, J.; Canadija, M.; Turkalj, G.; Lanc, D.; Pepelnjak, T.; Barisic, B.; Vukelic, G.; Brcic, M. Tool material behaviour at elevated temperatures. Mater. Manuf. Process. 2009, 24, 758–762. [CrossRef] 19. Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D.; Krscanski, S. Responses of Austenitic Stainless Steel American Iron and Steel Institute (AISI) 303 (1.4305) Subjected to Different Environmental Conditions. J. Test. Eval. 2012, 40, 319–328. [CrossRef] 20. Brnic, J.; Canadija, M.; Turkalj, G.; Lanc, D. 50CrMo4 steel-determination of mechanical properties at lowered and elevated temperatures, creep behavior, and fracture toughness calculation. J. Eng. Mater. Techn. Trans. ASME 2010, 132, 0210041–0210046. [CrossRef] 21. Brnic, J.; Niu, J.; Canadija, M.; Turkalj, G.; Lanc, D. Behavior of AISI 316L steel subjected to uniaxial state of stress at elevated temperatures. J. Mater. Sci. Technol. 2009, 25, 175–180. 22. Brnic, J.; Turkal, G.; Niu, J.; Canadija, M.; Lanc, D. Analysis of experimental data on the behavior of steel S275JR-Reliability of modern design. Mater. Des. 2013, 47, 497–504. [CrossRef] 23. Brnic, J.; Turkalj, G.; Canadija, M.; Krscanski, S.; Brcic, M.; Lanc, D. Deformation Behavior and Material Properties of Austenitic Heat-Resistant Steel X15CrNiSi25–20 Subjected to High Temperatures and Creep. Mater. Des. 2015, 69, 219–229. [CrossRef] 24. Brnic, J.; Turkalj, G.; Canadija, M. Shear stress analysis in engineering beams using deplanation field of special 2-D finite elements. Meccanica 2010, 45, 227–235. [CrossRef] 25. Krella, A. Influence of cavitation intensity on X6CrNiTi18-10 stainless steel performance in the incubation period. Wear 2005, 258, 1723–1731. [CrossRef] 26. Grosse, M.; Niffenegger, M.; Kalkhof, D. Monitoring of low-cycle fatigue degradation in X6CrNiTi18-10 austenitic steel. J. Nucl. Mater. 2001, 296, 305–311. [CrossRef] 27. Grzesik, W.; Zak,˙ K. Surface integrity generated by oblique machining of steel and iron parts. J. Mater. Proc. Technol. 2012, 12, 2586–2596. [CrossRef] 28. Mändl, S.; Günzel, R.; Richter, E.; Möller, W.; Rauschenbach, B. Annealing behaviour of nitrogen implanted stainless steel. Surf. Coat. Technol. 2000, 128, 423–428. [CrossRef] 29. Kim, J.H.; Kim, S.K.; Lee, C.S.; Kim, M.H.; Lee, J.M. A constitutive equation for predicting the material nonlinear behavior of AISI 316L, 321, and 347 stainless steel under low-temperature conditions. Int. J. Mech. Sci. 2014, 87, 218–225. [CrossRef] 30. Richard, K.C.; Nkhoma, C.W.; Siyasiya, W.E. Hot workability of AISI 321 and AISI 304 austenitic stainless steels. J. Alloy. Compd. 2014, 595, 103–112. 31. Siddiquee, A.N.; Khan, Z.A.; Kumar, P.G.M.; Agarwal, G.; Khan, N.Z. Optimization of Deep Drilling Process Parameters of AISI 321 Steel Using Taguchi Method. Procedia Mater. Sci. 2014, 6, 1217–1225. [CrossRef] Materials 2016, 9, 298 19 of 19

32. Wang, J.; Lin, Y.; Yan, J.; Zen, D.; Zhang, Q.; Huang, R.; Fan, H. Influence of time on the microstructure of AISI 321 austenitic stainless steel in salt bath nitriding. Surf. Coat. Technol. 2012, 206, 3399–3404. [CrossRef] 33. Sayiram, G.; Arivazhagan, N. Microstructural characterization of dissimilar welds between Incoloy 800H and 321 Austenitic Stainless Steel. Mater. Charact. 2015, 102, 180–188. [CrossRef] 34. Celik, O.; Baydogan, M.; Atar, E.; Kayali, S.; Cimenoglu, H. Fatigue performance of low temperature nitrided AISI 321 grade austenitic stainless steel. Mater. Sci. Eng. A 2013, 565, 38–43. [CrossRef] 35. Metals-Mechanical Testing; Elevated and Low-Temperature Tests; Metallography. In Annual Book of ASTM Standards; ASTM International: Baltimore, MD, USA, 2015. 36. Draper, N.R.; Smith, H. Applied Regression Analysis; Wiley-Interscience Publications: Los Angeles, CA, USA, 1998. 37. Bevington, P.R.; Robinson, D.K. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, NY, USA, 2003. 38. Findley, W.N.; Lai, J.S.; Onaran, K. Creep and Relaxation if Nonlinear Viscoelastic Materials; Dover Publications: New York, NY, USA, 1989. 39. Almagableh, A.; Mantena, P.R.; Alostaz, A. Creep and stress relaxation modeling of vinyl ester nanocomposites reinforced by nanoclay and graphite platelets. J. Appl. Polym. Sci. 2009, 15, 1635–1641. [CrossRef] 40. Blinn, M.P.; Williams, R.A. Design for Fracture Toughness. Mater. Sel. Des. ASM Int. 1997, 20, 533–544. 41. Zhang, L. Failure Assessment of Thin-Walled Structures with Particular Reference to Pipelines; WIT Press: Southampton, UK, 2010. 42. Anderson, T.L. Fracture Mechanics; CRC Press: Boca Raton, FL, USA, 2005. 43. Roberts, R.; Newton, C. Interpretive report on small scale test correlation with KIc data. Weld Res. Counc. Bull. 1981, 265, 1–16. 44. Shekhter, A.; Kim, S.; Carr, D.G.; Crocker, A.B.L.; Ringer, S.P. Assessment of temper embrittlement in an ex-service 1Cr-1Mo-0.25V power generating rotor by Charpy V-notch testing; KIc fracture toughness and small punch test. Int. J. Press. Vessels Pip. 2002, 79, 611–615. [CrossRef] 45. Pollak, R.D. Analysis of Methods for Determining High Cycle Fatigue Strength of a Material with Investigation of Ti-6Al-4V Gigacycle Fatigue Behavior. Ph.D. Disertation, Air Force Inst of Tech Wright-Patterson AFB OH School of Engineering and Management, Dayton, OH, USA, 2005. 46. Wöhler, A. Über die Festigkeits-Versuche mit Eisen und Stahl (engl. On Strength Tests of Iron and Steel). Z. Bauwes. 1870, 20, 73–106. 47. Schivije, J. Fatigue of Structures and Materials; Springer: Delft, The Netherlands, 2009. 48. Suresh, S. Fatigue of Materials; Cambridge University Press: Cambridge, UK, 2003. 49. 12107:2012-Metallic Materials-Fatigue Testing-Statistical Planning and Analysis of Data; International Organization for Standardization: Geneva, Switzerland, 2012. 50. Baumert, E.K.; Tohidi, F.S.; Hosseini, E.; Pierron, O.N. Fatigue-induced thick oxide formation and its role on fatigue crack initiation in Ni thin films at low temperatures. Acta Mater. 2014, 67, 156–167. [CrossRef]

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