- -- ---- -I,ANALYTICALSTRENGTHASSESSMENT5t h EditionVDMA VerlagI IForschungskuratorium IIMaschinenbauFKM-GuidelineANALYTICAL STRENGTH ASSESSMENTOF COMPONENTSIN MECHANICAL ENGINEERING5th, revisededition,2003, English VersionTranslation by E. HaibachTitle of the originalGerman Version:RECHNERISCHERFESTIGKEITSNACHWEISFURMASCHINENBAUTEILE5., iiberarbeitete Ausgabe, 2003Editor:Forschungskuratorium Maschinenbau(FKM)Postfach71 0864, D - 60498 Frankfurt / MainPhone *49 - 69 - 6603 - 1345(c) 2003byVDMA VerlagGmbHLyoner StraBe 1860528 Frankfurt am Mainwww.vdma-verlag.deAll rights reservedAIle Rechte, insbesondere das Rechtder Vervielfaltigung und Verbreitungsowie der Ubersetzung vorbehalten.Kein Teil des Werkes darfin irgend-einer Form (Druck, Fotokopie,Mikrofilm oder anderesVerfahren) ohneschriftliche Genehmigung des Verlagesreproduziert oder unter Verwendungelektronischer Systeme gespeichert,verarbeitet, vervielfaltigt oderverbreitet werden.ISBN 3-8163-0425-73This FKM-Guideline was elaborated under contract betweenForschungskuratorium Maschinenbau e. V. (FKM), Frankfurt / Main, andIMAMaterialforschung und Anwendungstechnik Gmhfl, Dresden,as contractor in charge,byDr.-Ing.Bernd Hanel,IMA Materialforschung undAnwendungstechnik GmbH, Dresden,Prof. Dr.-Ing.Erwin Haibach,Wiesbaden,Prof. Dr.-Ing.TimID Seeger,Technische Hochschule Darmstadt, Fachgebiet Werkstoffmechanik,Dipl.-Ing. Gert Wlrthgen,IMA Materialforschung und Anwendungstechnik GmbH, Dresden,Prof. Dr.-Ing. Harald Zenner,Technische Universitat Clausthal, Institut furMaschinelle Anlagentechnik undBetriebsfestigkeit,and it was discussed among experts from industry and research institutesin the FKM expert group"Strength of components" .Financial grants wereobtainedfromthe"Bundesministerium fUrWirtschaft (BMWi, Bonn)"throughthe "Arbeitsgemeinschaft industrieller Forschungsvereinigungen 'Otto von Guericke ' e. V. (AiF,K6ln)" under contract AiF-No. D-156and B-9434. The"Forschungskuratorium Maschinenbau e.V."gratefully acknowledges the financial support from BMWi and AiF and the contributions by the expertsinvolved.Terms of liabilityThe FKM-Guideline is intended toconform with the state of the art. It has beenpreparedwiththenecessarycare. The user isexpectedtodecide, whethertheguidelinemeetshisparticular requirements, and toobserve appropriate care initsapplication. Neither the publisher nor the editor, the involved experts, or thetranslator shall be liable tothe purchaser or any other personor entitywithrespect toany liability, loss, or damagecausedor allegedtohavebeencauseddirectly or indirectly by this guideline.Preface to the English Version ofthe 5thEdition.For engineers concerned with construction andcalculation in mechanicalengineering or in related fieldsofindustrytheFKM-Guidelineforanalytical strengthassessment isavailablesince1994. Thisguidelinewaselaborated by an expert group "Strength of components"of the "ForschungskuratoriumMaschinenbau (FKM),Frankfurt/Main," with financial support by theBundesministerium fur Wirtschaft (BMWi), by the"Arbeitsgemeinschaft industrieller Forschungsvereini-gungen 'OttovonGuericke" andby the"Forschungs-kuratorium Maschinenbau.Based onformer TGL standards and on the formerguideline VDI 2226, and referring to more recentsources it was developed to the current state ofknowledge.The FKM-Guideline- is applicableinmechanical engineering and in relatedfields of industry,- allows the analytical strength assessment for rod-shaped (lD), for shell-shaped (2D) and for block-shaped(3D) components under consideration of all relevantinfluences,-describestheassessment of thestaticstrengthandofthe fatigue strength, the latter according to an assessmentofthefatigue limit, of theconstant amplitudefatiguestrength, or of thevariable amplitudefatiguestrengthaccording to the service stress conditions,- isvalidforcomponentsfromsteel, cast steel, orcastironmaterialsat temperatures from -40C to 500 C, aswellas forcomponentsfromaluminumalloys andcastaluminum alloys at temperatures from -40C to 200 C,- is applicable for components produced with or withoutmachining, or by welding,- allows an assessment in considering nominal stresses aswell as local elastic stresses derived from finite elementor boundary element analyses, from theoreticalmechanics solutions, or from measurements.A uniformlystructuredcalculationprocedure applies toall of these cases of application. The calculationprocedure is almost completely predetermined. The userhas to make some decisions only.The FKM-Guideline is a commented algorithm,consistingof statements, formulae, andtables. Mostofthe included figures have an explanatory function only.4Textual declarations are given where appropriate toensure a reliable application.Itscontent complieswiththestateof knowledgeto anextend that maybe presented in a guideline and itenables quite comprehensive possibilities of calculation.The employed symbols are adapted to the extendedrequirements of notation. The presented calculationprocedure is complemented by explanatory examples.Practically the described procedure of strengthassessment shouldberealizedbymeans of asuitablecomputer program. Presently available are the PCcomputer programs "RIFESTPLUS" (applicable for acalculation usingelastically determined local stresses, inparticular with shell-shaped(2D) or block-shaped(3D)components) and "WELLE" (applicable for a calculationusing nominal stresses as it is appropriate in thefrequently arising case of axles or shafts with gears etc).The preceding editions of the FKM-Guideline observeda remarkably great interest from which the need of an upto date guideline for analytical strength analysesbecomesapparent. Moreover theinterest ofuserswasconfirmed bythe well attended VDI conferences on"Computational Strength Analysis of MetallicComponents", that wereorganizedfor presentationofthe FKM-Guideline at Fulda in 1995, 1998 and 2002.Thecontents-relatedchangesintroducedwiththethirdedition from 1998 were mainly concerned with theconsideration of stainless steel and of forgingsteel, withthetechnologicalsize factor, withthe section factor forassessingthestaticstrength, withthefatigue limit ofgrey cast iron and of malleable cast iron, with additionalfatigueclasses of welded structural detailsandwiththelocal stressanalysisfor weldedcomponents, withthespecification of anestimateddamagesumsmaller thanone for the assessment of the variable amplitudefatiguestrength, with the assessment of multiaxialstresses, andwith the experimental determination of componentstrength values.Anessentialformal changeinthethirdeditionwasanew textual structure providing four main chapters,thatdescribe theassessment of thestaticstrengthorof thefatigue strength with either nominal stresses or localstresses, respectively. For easeof application each ofthese chapters gives a complete description of theparticularcalculation procedure, although thisresults inrepetitions of the same or almost the same parts of text inthe corresponding sections.Themajorchangein the forthedition from 2002 is thepossibilityof consideringstructural components madefrom aluminum alloys or cast aluminum alloys byapplying the same calculation procedure that wasdeveloped for components from steel, cast steel and castiron materialsso far.Thedecisionsnecessary toinclude aluminummaterialswerederivedfromliteratureevaluations. It hadtoberecognized, however, that some of the relevant factors ofinfluence were not yet examined with the desirableclearness or thatavailable results could not be evaluatedobjectively due to large scatter. In these cases thedecision was based on a careful consideration ofsubstantial relations.Concerning an analytical strength assessment ofcomponents from aluminum alloys or from castaluminumalloys this guideline is delivered to thetechnical communitybysupposingthatforthetimebeing it will be applied withappropriate cautionandwith particular reference toexistingexperience sofar.The involvedresearch institutes andthe"Forschungs-kuratoriumMaschinenbau(FKM)" will appreciateanyreportson practical experienceas well as any proposalsfor improvement.Further improvements may also be expected fromongoingresearchprojectsconcerningtheprocedureofstatic strength assessment using local elasticstresses,Chapter 3, and the fatigue assessment of extremely sharpnotches.Last not least the fifth edition of the FKM-Guideline is arevision of the forth edition with several necessary,mainly formal amendments being introduced. It ispresented in both a German version and anEnglishversion with the expectation that it might observesimilarattention as the preceding editions on a broadenedinternational basis of application.5Notes of the translatorThisEnglishtranslationis intendedto keep as close aspossible to theoriginal Germanversion,but by usingacommon vocabulary andsimplesentences. If thegiventranslationisdifferent fromaliteral one, thetechnicalmeaning of the sentence and/or of the paragraph ismaintained, however.The translation observes an almost identical structure oftheheadlines,of the chapters, of theparagraphs andofthe sentences, and even of the numbering of the pages.Also the tables and the figures as well as their numberingandheadlines areadaptedastheyare, whileonlytheverbal terms have been translated.In particular the original German notation ofthemathematicalsymbols, indicesandformulas, as wellas their numbering, has not been modified in order toinsure identity with the German original in thisrespect.The applier of this guideline is kindlyaskedto acceptthe moreor lessunusual kind ofnotationwhichisduetothe needofclearlydistinguishingbetweenagreat number of variables.Inparticular theapplier is pointedto thespeciality,that a comma ( , ) is used with numerical valuesinstead of a decimalpoint ( . ), hence 1,5 equals1.5for example. .Forupdates and amendments seewww.fkm-guideline.de6References/1/ TGL19 340 (1983). Ermiidungsfestigkeit, Dauerfestigkeit der Maschinenbauteile./2/ TGL19 341 (1988). Festigkeitsnachweis fiir Bauteile aus Eisengusswerkstoffen./3/ TGL19 333 (1979). Schwingfestigkeit, Zeitfestigkeit von Achsen und Wellen./4/ TGL19 350 (1986). Ermiidungsfestigkeit, Betriebsfestigkeit der Maschinenbauteile./5/ TGL 19 352 (Entwurf 1988). Aufstellung und Uberlagerung von Beanspruchungskollektiven./6/ Richtlinie VDI 2226 (1965). Empfehlung fiir die Festigkeitsberechnung metallischer Bauteile./7/ DIN18 800 Teil 1 (1990). Stahlbauten, Bemessung und Konstruktion./8/ DINENV1993 (1993). Bemessung und Konstruktion von Stahlbauten, Teil1-1:Allgemeine Bemessungsregeln, ... (Eurocode 3)./9/ Hobbacher, A.: Fatiguedesign of welded joints and components. Recommendations of the Joint WorkingGroupXIII-XV, XIII-1539-96/ XV-845-96. Abbington Publishing, Abbington Hall, Abbington,Cambridge CB1 6AH, England, 19996/10/ Haibach, E.: Betriebsfestigkeits - Verfahren und Daten zur Bauteilberechnung, 2.Aufl.Berlin und Heidelberg,Springer-Verlag, 2002, ISBN 3-540-43142-X./11/ Radaj, D.: Ermiidungsfestigkeit.Grundlage fur Leichtbau, Maschinenbau und Stahlbau.Berlin und Heidelberg: Springer-Verlag, 2003, ISBN 3-540-44063-1./12/ FKM-Forschungsheft 241 (1999). Rechnerischer Festigkeitsnachweis fiir Bauteile aus Alumininiumwerkstoff./13/ FKM-Forschungsheft 230 (1998). Randschichthartung./14/ FKM-Forschungsheft 227 (1997). Lebensdauervorhersage II./15/ FKM-Forschungsheft 221-2 (1997). Mehrachsige und zusammengesetzte Beanspruchungen./16/ FKM-Forschungsheft 221 (1996). Wechselfestigkeit von Flachproben aus Grauguss./17/ FKM-Forschungsheft 183-2 (1994). Rechnerischer Festigkeitsnachweis fur Maschinenbauteile, Richtlinie. *1/18/ FKM-Forschungsheft 183-1 (1994). Rechnerischer Festigkeitsnachweisfiir Maschinenbauteile, Kommentare./19/ FKM-Forschungsheft 180 (1994). Schweillverbindungen II./20/ FKM-Forschungsheft 143 (1989). Schweillverbindungen I./21/ FKM-Richtlinie Rechnerischer Festigkeitsnachweisfiir Maschinenbauteile,3.,vollstandig iiberarbeitete und erweiterte Ausgabe (1998)./22/ FKM-Richtlinie Rechnerischer Festigkeitsnachweis fur Maschinenbauteile,4., erweiterte Ausgabe (2002).Related Conference ProceedingsFestigkeitsberechnung metallischer Bauteile, Empfehlungen fur Konstrukteure und Entwicklungsingenieure.VDI Berichte 1227, Diisseldorf, VDI-Verlag, 1995.Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Entwicklungsingenieure und Konstrukteure.VDI Berichte 1442, Diisseldorf, VDI-Verlag, 1998.Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Entwicklungsingenieure und Konstrukteure.VDI Berichte 1698, Dusseldorf,VDI-Verlag, 2002.Bauteillebensdauer Nachweiskonzepte. DVM-Bericht 800, Deutscher Verband fur Materialsforschung und-prufung,Berlin 1997.Betriebsfestigkeit - Neue Entwicklungen bei der Lebensdauerberechnung von Bauteilen.DVM-Bericht 802,Deutscher Verband fur Materialsforschung und -prufung, Berlin 2003.1 1'"and 2ndEdition ofthe FKM-Guideline7ContentsPage5 Appendices Page0 General survey5.1 Material tables. 1310.1 Scope 95.2 Stress concentration factors 1780.2 Technical background5.3 Fatigue notch factors 1870.3 Structure andelements5.4 Fatigue classes (FAT) for weldedcomponents of structural steel andof1 Assessment of the static strengthaluminum alloys 195using nominal stresses5.5 Comments about the fatiguestrength1.0 General 19of welded components 2091.1 Characteristic stress values5.6 Adjusting the stress ratio of a stress1.2 Material properties 22spectrum to agree with that of theS-N curve1.3 Design parameters 30and deriving a steppedspectrum 2161.4 Component strength 335.7 Assessment using classes of utilization 2181.5 Safety factors 345.8 Particular strength characteristics of1.6 Assessment 36surface hardened components 2225.9 An improvedmethod for computing the2 Assessment of the fatigue strengthcomponent fatiguelimit in the case ofusing nominal stressessynchronous multiaxial stresses 2232.0 General 415.10 Approximate assessment of the fatigue2.1 Parameters of the stress spectrumstrength in the case of non-proportional2.2 Material properties 47multiaxial stresses 2262.3 Design Parameters 505.11 Experimental determination of2.4 Component strength 57component strength values 2272.5 Safety factors 685.12 Stress concentration factor for a substitute2.6 Assessment 70structure 2303 Assessment of the static strength6 Examplesusing local stresses6.1 Shaft with shoulder 2313.0 General 736.2 Shaft with V-belt drive 2363.1 Characteristic stress values6.3 Compressor flangemade of grey3.2 Material properties 76cast iron 2413.3 Design parameters 856.4 Welded notched component 2453.4 Component strength 896.5 Cantilever subjectto two independent loads 2503.5 Safety factors 906.6 Component made of a wrought3.6 Assessment 93aluminum alloy 2564 Assessment of the fatigue strength7 Symbols and basic formulasusing local stresses7.1 Abbreviations 2594.0 General 977.2 Indices4.1 Parameters of the stress spectrum7.3 Lower case characters4.2 Material properties 1037.4 Upper case characters 2604.3 Design parameters 1067.5 Greek alphabetic characters 2614.4 Component strength 1137.6 Basic formulas 2624.5 Safety factors 1254.6 Assessment 1278 Subject index 26389oGeneral survey1Subject of Chapter 5.11"Experimental determinationofcomponentstrengthvalues"is nottherealizationofanexperimental assessment ofstrength, but the question how specific and sufficiently reliablecomponent strength valuessuitable for the general procedure of strengthassessment may be derived experimentally.2Inparticular, what critical pointsof theconsidered cross-sections orcomponent.If anapplication of theguideline is intended outside thementionedfieldofapplicationadditional specificationsare to be agreed upon.Theguideline is not valid if an assessment of strength isrequired according to other standards, rules orguidelines, or if more specific design codes areapplicable, as for example for bolted joints.Theguideline is valid forcomponents producedwithorwithoutmachiningorby weldingof steel, of ironor ofaluminummaterials that are intendedfor use undernormal or elevated temperature conditions, and in detail- for components withgeometrical notches,for components with welded joints,for staticloading,- for fatigue loading withmore than about 104constant or variable amplitude cycles,- for milled or forgedsteel, also stainless steel, castiron materials as well as aluminum alloys or castaluminum alloys,- for component temperaturesfrom- 40Cto 500C for steel,from- 25C to 500C for cast iron materials andfrom- 25C to 200C for aluminum materials,- for a non-corrosive environment.This guideline is validfor components inmechanicalengineering and in related fields of industry. Itsapplication has to be agreedbetween the contractingparties.For components subjected to mechanical loadings itallows an analytical assessment of the static strengthandof the fatiguestrength, the latter as an assessmentofthe fatigue limit, of the constant amplitude fatiguestrengthor of the variableamplitudefatigue strength,according to the servicestress conditions.Other analytical assessments, for example of safetyagainst brittlefracture, of stability, or of deformationunder load, as well as an experimental assessment ofstrength *1, are not subject of thisguideline.It is presupposed, that the components are professionallyproduced with regard to construction, material andworkmanship, andthattheyarefaultless inatechnicalsense.12111314151613Page910Contents0.3.0 General0.3.1 Procedure of calculation0.3.2 Service stresses0.3.3 Methods of strength assessment0.3.3.0 General0.3.3.1 Assessment of the staticstrengthusingnominal stresses, Chapter 10.3.3.2 Assessment of the fatigue strengthusingnominal stresses, Chapter 20.3.3.3 Assessment of the staticstrengthusing local stresses, Chapter 30.3.3.4 Assessment of the fatiguestrengthusing local stresses, Chapter 40.3.4 Kindsof components0.3.4.0 General0.3.4.1 Rod-shaped (lD) components0.3.4.2 Shell-shaped (2D) components0.3.4.3 Block-shaped (3D) components0.3.5 Uniaxial and multiaxial stresses0.3.0 General0.2 Technical Background3 Usually this probability can hardly be quantified, however.Basis of theguideline arethereferenceslisted onpage7, inparticulartheformer TGL-Standards, theformerVlrl-Guideline2226, aswell asthe- regulationsof DIN18 800, the IIW-Recommendations and Eurocode 3.Moreover the guideline was developed to the currentstateof knowledgeby taking intoaccount theresults ofmore recent investigations.0.3 Structure and elementsAn assessment of the static strength is required prior toan assessment of the fatiguestrength.Before applying the guideline it has to be decided- what cross-sections or structural detailof the2component shall be assessed * andwhat service loadings are to be considered.The serviceloadingsare tobedeterminedonthesafeside,that is, witha sufficient probability theyshould behigher than most of the normally occurring loadings *3.Thestrengthvalues are supposed tocorrespondtoananticipated probability of 97,5% (average probability ofsurvival Po =97,5 %).lRo2 EN.dog oGeneral survey0.1 Scope10oGeneral survey0.3.1 Procedure of calculationFigure 0.0.2 Procedure of calculation for an assessmentof the fatigue strength.At the assessment stage (box at bottom of either Figure)thecharacteristicvaluesofservicestressoccurringinthe component (box at top on the left) and thecomponent strength values derived from the mechanicalmaterial propertiesandthedesignparameters (middlecolumn) arecompared by includingtherequiredsafetyfactors (box at bottomon the right). In specifyingcomponent fatiguestrengthvaluesthemeanstress andthevariableamplitudeeffects areregardedasessentialfactors of influence. The assessment of strength issuccessful if the degreeof utilization is lessor equal1,00, wherethedegree of utilizationisdefinedby theratio of the characteristic service stress to the componentstrength value that has been reduced by the safety factor,Chapter 1.6.In Figure 0.0.1 and Figure 0.0.2 the arrangements of theindividual boxes from top to bottom illustrate thesequential procedure of calculation.0.3.2 Service stressesFor an application of the guideline the stresses resultingfrom the service loadings have to be determined for theso-called reference point of thecomponent, that isthepotential point of fatiguecrackinitiationat thecross-section or at the component under consideration. In caseofdoubtseveral referencepointsareto beconsidered,for example in the case of welded jointsthe toe and theroot of the weld.There is a need to distinguishthenames andsubscriptsof the different components or types of stress, that mayact in rod-shaped (lD), in shell-shaped (2D) or inblock-shaped (3D) components, respectively, Chapter0.3.4.Thestresses aretobe determinedaccordingtoknownprinciples and techniques: analytically according toelementary or advanced methods of theoreticalmechanics, numericallyafter thefiniteelement ortheboundary element method, or experimentally bymeasurement.All stresses, except the stress amplitudes, are combinedwith a sign, in particular compressive stresses arenegative.To perform an assessment it is necessary to decide aboutthe kindof stress determinationforthereference pointconsidered: The stresses can be determinedas nominal stresses*5 (notation S and T),as elastically determined local stresses, effective6notch stresses or structural (hot spot) stresses *(notation o and r).SafetyfactorsSafetyfactors--Sequentialprocedure ofcaJc.ulationSequentialprocedure ofcalculationComponent forzeromean stress :.,ComponentfatiguestrengthiII JComponent fatigiielimltfor-the actualmean stressCharacteristicservice Theprocedureofcalculationforanassessmentof thestaticstrengthis presentedinFigure0.0.1, thealmostidentical procedure for an assessment of the fatiguestrength in Figure 0.0.2*4.Figure 0.0.1 Procedure of calculation for an assessmentof the static strength.4Asurveyonthe analytical proceduresof assessment basedontheequations of the guideline may be found inChapter 7.6.5 Nominal stresses can be computedfor a well defmedcross-section only.6 The elastic stress at the root of a notch exceeds the nominal stress by astress concentration factor. In thecase ofwelded jointseffective notchstressesare appliedto the assessment of the fatigue strengthonly.Structural stresses, alsotermedgeometrical or hot spot stresses, arenormallyinusewithwelded joints only. Forfurther information seeChapter 5.5.11oGeneral surveyFigure 0.0.3 Organization of the guideline.7 Accordingto rod-, shell- or block-shaped components, Chapter 0.3.4.8Theextreme maximumor minimumstresses for theassessment of thestatic strength may be different from the maximum and minimum stressesfor theassessment of thefatiguestrength, that aredeterminedfrom thelargest amplitude and the related mean value of a stress spectrum.0.3.3.1 Assessment of the static strength usingnominal stresses, Chapter 1Relevant nominal characteristicservicestressesare theextreme maximum andextrememinimum values of theindividual types of stress or stress components, e.g.nominal values of the axial (or tension-compression)stress, Szd, of the bendingstress, Sb, and so forth*7*8,Chapter 1.1.Relevant material properties are the tensile strength andtheyieldstrength (yieldstress or 0.2proof stress) aswell as the strength values for shear derived from these.Atechnological size effect is taken into account ifappropriate. The influenceofanelevatedtemperatureon the material properties - strength at elevatedtemperature and creep strength, yield strength atelevated temperature andI% creep limit - is allowed forby means of temperature factors, Chapter1.2.Designparametersarethesection factors, by whichanexperienced partial plasticity of the component isallowed .accordingtoyieldstrength, type of loading,shapeofcross-section, andstress concentration factor.Fromthe section factor and from further parametersanoverall design factor is derived, Chapter1.3.The nominal values of the static component strength arederived from the tensile strength, divided by therespective overall design factor, Chapter1.4.As commonin practice the safetyfactor against thetensile strength is 2,0. For materials with a yieldstrength lessthan 0,75times the tensile strengththesafety factoris1,5 against the yieldstrength, however.Underfavorableconditionsthesesafety factors may bereduced, Chapter 1.5.The assessment is carried out by proving that the degreeof utilization is less or equal 1,00 . The degree ofutilization for an individualstress component or type ofstressistheratioofits nominal characteristicservicestress value, divided bythe allowable nominal staticcomponent strength value, which follows from thenominal static component strengthdivided by the safetyfactor.If there areseveral stress componentsor types of stresstheir individual degreesofutilizationarecombinedtoobtainanentire degreeofutilization. The interactionformula to be applied to that combinationallows for theductility of the material in question, Chapter1.6.For welded components the assessment of the staticstrengthhasto be carriedout forthetoe section as fornon-welded components, and for the throat section withIFatiguestrength'assessment~Fatii:ue strengthNominal stresses. ~ .Staticstrength LNoml?alNominalstresses ) stresses;/StaticstrengthaSseSSlllent~ ~ ..r"Chapter 3: " 100C: (1.2.30)Kr,m =Kr,p =1 - 1,5 . 10 -3. (T / c -100),- for GGG, T > 100C:K r. m =Kr,p =1 - 2,4 . (10-3 . T / "C)2. (1.2.31)Kr,m =1 -4,5 . 10-3.(T / C - 50)0,1,K =1 - 4 5 . 10 -3. (T / C - 50) >01T,p, - "- for not age-hardening aluminum alloys:T> 100C, Figure 1.2.3 (1.2.33)Kr,m =1 - 4,5 . 10 -3.(T / C - 100)0,1,Kr,p = 1- 4,5' 10-3. (T / C - 100)0,1,Eq. (1.2.32) and(1.2.33) arevalidfromtheindicatedtemperature T up to 200C, andingeneral only, if therelevant characteristic stress does not act on long terms.2S0 300TIT.20.0High temperaturestrength Rm,TRm;T 1R. 'jm.Cre.ep.Strength Rm.Tl. .1If,;"' i.IISO () 5&lliQQI.High temperaturefatigueslrengthO,l 50C,Figure1.2.3 (1.2.32)16 There is an insignificant discontinuity at T = 60C.17 For stainless steel novalues areknown uptonow.Long-tenn valuesLong term values of the static strength areR""Tt = KTt,m R", ,=KTt,p R, ,KTt,m, KTt,p temperature factors,Figure1.2.2 and 1.2.3, Eq. (1.2.35),R"" R, tensile strength and yield strength,Eq. (1.2.1) to (1.2.3).1.2 Material properties291 Assessment of the static strengthusing nominal stressesThe values Tl and arenot explicitlyneededforan assessment of the static strength, as only thetemperature factorsKTl,m andKTt,p are needed.Aluminum alloysFor aluminum alloys andt =105hours Krt,m is given byFigure 1.2.4 *20.Figure 1.2.4Temperaturefactor Krt,m Rm,Tt I R.nforaluminum alloys andt =105hours.Thegivencurveis thesame as in Figure1.2.3, except that the factor(1 / jm ) isdifferent.Eq.(1.2.35) apply to temperatures from approximately350C upto 500C,but only forstresses acting on longterms. Ingeneral theydonot apply to temperaturesbelow about 350C *19.1 Approximate values, applicable from about 350Cto500C.2 Not valid for stainless steel.Cast ironGS6 GGG7materialsCreep strengthaTt.m-7,524 2,50bTLm9,894 - 1,83CTtm -3,417 0em19,57 201% Creep limitaTtn- 10,582 0,12bTt.D8,127 1,52cTt.n- 1,607 - 1,28Co35,76 183 Initially for St38,Rm= 360MPa, similar toSt37.4 Initially for H 52, Rm= 490MPa, similar to StE 355; theabsolutevalues Rill,Tt are thesame asfor St38.5Initially for C45N(normalized) with Rm=620 MPa. For C35N,with Rm= 550 MPa the constants -3,001and -3,252aretobereplacedby-2,949and -3,198. The absolute valuesRill,Tt arethe same asforC45N.Table 1.2.7 Constants aTt,m, ..., Cp Steel Non- Fine grain Heat-alloyed structural treatable-structural steel steelsteel Creep strengthaTLm- 0,994 -1,127 - 3,001bTLm 2,485 2,485 3,987cTt.m-1,260 -1,260 - 1,423em20 20 24,271% Creep limitaTt.n - 5,019 - 6,352 - 3,252bTLn 7,227 9,305 5,942Cn n - 2,636 - 3,456 - 2,728Cn 20 20 17,71200 300 400TrC1\\\\:I \..t-RT 100oconstants, Table 1.2.7,operation time in hours h atthetemperature T.aTt,m, ..., Cpt0,61,0R""TI I R",0,80,4Steel and cast iron materialsDependingonthetemperatureTandonthe operationtime t at that temperature the temperature factorsKrt,mand KTt,p apply, Figure 1.2.2*182K=10(aTt,m+ bTt,m . Pm+ CTt,m . Pm)Tt,m , (1.2.35)2K=lO(aTt,p+ bTt,p . Pp+ CTt,p . Pp)np ,Pm =10 -4. (T / C + 273)'(Cm+ 19(t/h)),Pp=10 - 4.(T / C + 273). (Cm+19(t/ h)),0,218 Larsen-Miller-parameter P andLarsen-Miller-constant C.19 Because the values would be unrealistic for temperaturesT < 350C, where thevalues KT,m and KT,p arerelevant instead.20Thetemperaturefactor Kt,pis not defmed up to now. It maybeassumed, however, as itis essential for the assessment of the staticstrength, thattheterm Rp,Tt/ jpt ismore or less equal toRill,Tt / Jmt ,see Figure 1.2.2 (required safety factorsjpt =1,0 andjmt = 1,5).ALarsen-Miller equation similar toEq. (1.2.32) or(1.2.33) applicable toderive the values of KTt,mandKTt,paccording to temperature T andoperation time Thas notbeen specified for aluminum alloys uptonow.6 Initially for GS-C 25 with Rm= 440 MPa.-c-7 Initially for GGG-40 with Rm=423 MPa.1.3 Design parameters301 Assessment of the static strengthusingnominal stressesAccordingtothischapter thedesignparameters aretobe determined.1.3.0 General1.3 Design parametersContents1.3.0 GeneralKSK,zd = 1/ a.w, . (1.3.4)KSK,b =I / (npl,b . a.w ),KsK,s = 1/ a.w ,KSK,t =I / (npl,t . a.w ).For the throat section of shell-shaped (2D) weldedcomponents the design factors for normal stresses in thedirections x and y as well as for shear stress are1.3.1.2 Welded componentsFor welded componentsthe design factorsaregenerallytobedeterminedseparatelyfor thetoesectionandforthe throat section.For the toe section the calculationis to be carried out asfor non-welded components.For the throat section of rod-shaped (lD) weldedcomponents the design factors for axial (tension orcompression), for bending, for shear andfor torsionalstress arePage303111mEN.dogDesign factorsGeneralNon-welded componentsWelded componentsSection factorsWeld factor a.w1.3.11.3.1.01.3.1.11.3.1.21.3.21.3.3(1.3.5)1.3.1 Design factors1.3.1.0 GeneralNon-welded and welded components are to bedistinguished. They can be both rod-shaped (lD) orshell-shaped (2D).KsK,x= 1/ a.w,KsK,y= 1/ a.w,KsK,s =I / a.w ,npl,b ... section factor, Chapter 1.3.2,a.w weld factor, Chapter 1.3.3.Weld factorsa.waregiven for tension, forcompressionand for shear stress.1.3.1.1 Non-welded componentsThe design factors of rod-shaped (lD) non-weldedcomponents for axial (tension or compression), forbending, for shear,and for torsional stress areFor tensionandtensioninbendinga.wfor tensionis tobe applied. For compression and compression inbendinga.wforcompressionis to be applied. Forshearand for torsion aw for shear is to be applied.KSK,zd=l, (1.3.1)KSK,b =I / npl,b ,KSK,s =I,KSK,t =I / npl,t ,npl,b ... section factor*1, Chapter 1.3.2.The design factors of shell-shaped (2D) non-weldedcomponents for normal stresses in the directions x and yas well as for shear stress areKSK,x=I,KsK,y =I,KsK,s = 1.(1.3.2)1.3.2 Section factorsThesection factorsnpl,b andnpl,t allow for the influenceof the stress gradient in bending and/or torsion inconnectionwiththe shape ofthe crosssectiononthestaticstrength of components, Figure 1.3.1. Theyserveto make best use of the load carryingcapacity of acomponent byaccepting someyielding as the outsidefiber stress exceeds the yield strength.An essential condition is the existence of a stressgradient normalto the surface of the component, Figure1.3.1.It hasto beobserved, however,that thederivedsectionfactors only apply to thenotched section considered andnot to the component as a whole. Therefore othersections may have tobe considered in addition, seeChapter1.0 and Figure1.0.1.1 KsK,zd = =1 means,that the value ofthe related section factorisnpl,zd = =1.1.3 Design parameters1-SSK,b (npl,b)1--Rp 311 Assessment of the static strengthusing nominal stressesFor other types ofsteel, GSandGGG*4 the sectionfactors for tension or compression, for bending, forshear, and for torsion are*5 *6npl,zd =1,npl,b = MIN (JRp,max / R p ; Kp,b ),npl,s=1,npl,t = MIN (JRp,max/ R p ; Kp,t),tRp,maxn,Kp,b,Kp,tconstant, Table 1.3.1,yield strength, Chapter 1.2,plastic notch factors, Table 1.3.2.(1.3.9)Figure 1.3.1 Definitionofthe sectionfactor npl,b forbending of anotched bar, for instance.Bendingmoment Mb, yieldstrengthRp, staticcomponent strengthfor bending SSK,b, section factor npl,b= SSK,b I Rp.Light straight line: fictitious distribution of the stress calculatedelastically. Solid angular line: real stress distribution when providingelastic ideal-plastic material behavior.Surface hardened ComponentsThesection factorsarenot applicable if thecomponenthasbeensurfaceorcasehardened, seeTable 2.3.5*2npl,b, ... = I (1.3.6)Steel and cast iron materialFor austenitic steel in the solution annealed condition *3the section factors for tension or compression, forbending, for shear, and for torsion areTable 1.3.1 Constant Rp,max1.Kind of material Steel, GS GGG Aluminumalloys.Rp,max'/ MFa 1050 320 250-c- 1 Constant defining an upper bound value of the sectionfactordependingon the kind of material.Table 1.3.2 Plastic notch factors Kp,band Kp,t .Cross-section Bending TorsionKp,b Kp,trectangle11,5 -circle1,701,33 circular ring 1,27 1 I-section or box -(1.3.15)npl,zd = I,npl,b =Kp,b ,npl,s =1,np1,t=Kp,t .(1.3.8) 1or plate, 1,70 = 16/ (3 . It), d 1,33 =4/3.thin-walled, 1,27 =4 / It. 5 thin-walled, otherwisethere is3Kp t = 1,33' 1- (dID) , (1.3.14), 1-(dID)4d, D inner and outer diameters.1- (b I B) . (h I H)2Kp b = 1,5 --'-----'---'---'-:-, 1- (b I B) (h IH)3b, B inner and outer width, h, H inner and outer hight.2Becausetheplasticityof ahardsurfacelayer-forexample asaresult of case hardening - islimited, it mayobservecrackswhenyielding occurs, particularly at notches where the calculationofnominal stress neglects the stress and strain concentration.Possibly this rule is too far on the safe side, as npl =1,1 is allowedforcasehardenedshafts accordingto the recent DIN743 (launchedin 2000).3 Because of the high ductility of austeniticsteel in the solutionannealedconditionthe plastic notch factors Kp,b and Kp,t are relevant and not thegivenmaterial dependentsectionfactors.4 GT and GO are not consideredhere becausethe assessmentof the staticstrengthhas to be carriedout usinglocal stressesfor these materials.5 MIN means that the smaller value fromthe right side of the equationisvalid.6 Upper and lower bound values of the section factors are the plasticnotch factor and 1,001.3 Design parametersAluminum alloysForductilewroughtaluminum alloys(A2 12,5 %)thesection factorsare to be determined from Eq (1.3.9)*7.1.3.3 Weld factorUwTheweld factor Ci.waccountsfortheeffect of a weld. Itappliesto the throat sectionof welded componentsonly,Tab. 1.3.3 *8.Table 1.3.3 Weld factor Ci.w~ 1 .321 Assessment of the static strengthusing nominal stressesJoint Weld qualityTypeof RmS Rm>stress 360 MPa 360Muafull all Compressionpenetration~ 2weld verified 1,0 1,0or with Tension 10back weld notverifiedpartial all Compression 0,95 0,80penetration or 0,80or fillet Tensionweldall all Shearweldsbutt weld Tension 0,55 -~ 3055~ 1 Accordingto DIN 18 800 part 1, Table 21 and Eq. (75).~ 2 For aluminumalloys(independent of Rm ) thevalues typedinin boldface should be applied for the time being.~ 3 Butt weldsofsectionalsteelfromSt 37-2or USt37-2with aproduct thickness t> 16 mm.7Less ductile aluminum alloys (A 12,5%). For non-ductile wrought aluminium alloys (aswell asfor cast aluminium alloys, and for GT or GG) the assessment ofthe static strength istobe carried out according toChapter 3.10For example a tension stress fromaxialloading and a tension stressfrombending acting at thereferencepoint, wherebothresult fromthesame single extemalload affecting the component11 Forexample a tension stress fromaxial loadingand a compressionstress from bending acting at the reference point, where both result fromthe same single external load affecting the component.12 Stress components acting opposingly may cancel each other inpart orcompletely.381.6 Assessment 1 Assessment of the static strengthusing nominal stressesaSK,wv,zd, ... degree of utilization, Eq. (1.6.2).J(aSK,WV,Zd+aSK,wv,b)2+(aSK,wv,s +aSK, wv.t )2 ,Moreover the degrees of utilization calculated withSmin,ex,zd , Smin,ex,b, Tmin.ex,s and Tmin.ex.t areto beincludedin this comparative evaluation.In the general case - without knowing whether thestresses act unidirectionally or opposingly *13 - thedegreesof utilizationaretobeinserted intoEq. (1.6.6)bothwithequal or withdifferent signs; thenthe leastfavorable case is relevant.(1.6.9)Smax,ex,yaSK,y = ::;; 1,SSK,y / jgesSmax,ex,xaSK,x = s1,SSK,x / jgesTmax,ex s 1aSK,s = ,TSK / jgesSmax,ex,x ... extreme maximum stresses according totype of stress; the extreme minimumstresses, Smin,ex,x ... , are to be consideredinthe same way as the extreme maximumstresses,Chapter 1.1.1.2,SSK,x ... related component static strength,Chapter 1.4.1,Jges total safety factor, Chapter 1.5.5.All extreme stresses may be positive or negative (orzero). Ingeneral tension and compression stresses are tobe considered separately. For shear stress the highestabsolute value is relevant.Shell-shaped (2D) welded componentsFor the toe section of shell-shaped (2D) weldedcomponents the calculationis tobe carriedout asforshell-shaped (2D)non-welded components.For the throat section of shell-shaped (2D) weldedcomponents the degrees of utilization for normalstresses inthe directions xandyas well as for shearstress follow from the equivalent nominal stresses,Chapter 1.1.1.2:1.6,2 Shell-shaped (2D) components1.6.2.1 Individual types of stressShell-shaped (2D) non-welded componentsThe degrees of utilization of shell-shaped (2D) non-weldedcomponentsfor the types of stress like normalstress in thedirections x and y as wellas shear stress are(1.6.8) aSK,Swv =Rod-shaped (1D) welded componentsFor the toe section of rod-shaped (10) weldedcomponents the calculationis tobecarriedout asforrod-shaped (lD) non-welded components.For the throat section of rod-shaped (10) weldedcomponents thedegree of utilization for combined typesof stresses (or loadings) is *14Rulesof sign: If theindividual typesof stress (tensionor compression and bending, or shear and torsion,respectively)always act unidirectionally at thereferencepoint*10, thedegrees of utilization aSK,wv,zd and aSK,wv,band/or aSK,wv,s andaSK,wv,t are tobe insertedintoEq.(1.6.8) with equal (positive) signs (summation); then theresult will be on the safe side. If they act alwaysopposingly, however, *11, theyareto be inserted into Eq.(1.6.8) with different signs (subtraction)*12.In the general case - without knowing whether thestresses act unidirectionally or opposingly '13 - thedegrees of utilizationaretobeinserted intoEq. (1.6.8)bothwithequal or withdifferent signs; thenthe leastfavorable caseis relevant.Moreover the degrees of utilization calculated withSmin,ex,wv,zd, Smin,ex,wv,b, Tmin,ex,wv,s andTmin,ex,wv,t areto beincluded inthis comparative evaluation.Sa - max,ex,wv,x O. Theequationsarevalid forroundmembers, approximatelythey apply to roundmembers with a central borehole too.12The basic definitionof the fatigue notch factor Kf,b for bending is:(2.3.20)Kf,b = crW,zd/ SWK,b 'crW,zdSWK,bfatigue strength value for completely reversed axial stressof the unnotched test specimen of the diameter do ,fatigue strength value for completely reversed bending stressof the notched component of the diameter or width d.Kfb in bending is dependent on the notch radius r and on the diameter orwidth dof the notch net section. Kf,t for torsion in analogy.The .defmitionof the fatigue notchfactor for bending derivedfromexperimental data - under the provisionthat the unnotchedandthenotched specimen have the same diameter dp- is:rp = 0 for t! d > 0,25 ort! b > 0,25,q>= 1I(4.M+2) for 0,25 or 0,25. 3The relatedstressgradient Gcr(r) applies to axial stressandtobending stress; nevertheless thereis adifference forbending because ofthe Kt-KfTatio ncr(d)additionally contained in Eq. (2.3.10) and (2.3.18).The relatedstress gradientapplies to shearstress andtotorsion stress; nevertheless there is a difference for torsion because of theKt-KfTatio additionally contained in Eq. (2.3.10)and (2.3.18).flat member of thickness s.(2.3.18)The fatigue notch factors, Kf,zd , ... , for axial, forbending, for shear andfor torsional stressof therod-shaped(lD) non-weldedstructural detailspresented inChapter 5.3are to be computed from the experimentallyderived fatigue notch factors of test specimens giventhere, and from the respective Kf -K, ratios. Inparticular *IIK - K (d) ncr (rp )f,zd - f,zd p' --(-)- ,ncr rKf,b (dp) = SW,b,P / SWK,b,P, (2.3.21)SW,b,P fatigue limit for completely reversed bending stress of theunnotched test specimen of diameter dp,SWK,b,P Fatigue limit for completelyreversed bending stress of thenotched test specimen of diameter dp.Kf,b is dependent on the notch radius rp and on the diameter or width ofthe notch net section d. Kf,t for torsion in analogy.13The fatigue notchfactors giveninChapter 5.3 are applicabletocomponents from steel without surface treatment. Additionally, however,a procedure for components being surface hardened and for componentsmade of cast iron materials and aluminum alloys is describedthere.14Forcomputing Kt-Kfratiosthenotchradii, r or rp, arerequired.Particularly for cases that may produce some doubt the radii are specifiedin Chapter 5.3.A possible incorrectness thatmay occur will be reducedby the division of ncr(rp ) / ncr(r).2.3 Design parameters542 Assessment of the fatigue strengthusing nominal stressesCaution:If afatigue notchfactors Kf,zd, ... 1, fieldof fluctuatingcompression stress,where Rzd = +or - ex) is the zero compression stress.FieldII:- ex)0, whereRzd < -1is the field ofalternating compression stress, Rzd = -1 is thecompletely reversed stress, Rzd >-1 is the field ofalternating tension stress.Field III: 0 ND,u (Steel and cast iron material)Incaseofacomponent constant amplitude S-Ncurvemodel I ( horizontal for N > ND,cr or slope kD,o =(0) thenumber of cycles N to be computed foran valueSa,zd,lis (2.4.57)[s )kcrN= {[ Akon- 1 ] . DM + I}' SAK,zd . ND,cr ,a,zd,lwhereA_ [Sa,zd,l )kcr-1[ZI j Z2]k - -- . -+ L-on SAK,zd Nl v=m N2[ )kcr - 1 [S )kcr-1Zl = _ Sa,zd,m ,a,zd,l a.zd.lZ2 =)kcr-1_ [S;,Zd,V+1 )kcr-1a,zd,l a,zd,lm-1 h. [S d.i )kcrNl=L -.: i=l H Sa,zd,lFor the summation of the term Z2, Eq. (2.4.60), it is tobe observed that Sa,zd,j+l =O.N number of cycles of the component constantamplitude S-N curve, Chapter 2.4.3.2,ND,cr number of cycles at knee point of the componentconstant amplitude S-N curve, Chapter 2.4.3.2,DM critical damage sum, Table 2.4.3,Sa,zd,i stress amplitude in step i of the spectrum,Sa,zd,l stress amplitude in step i =1 of the spectrum,SAK,zd amplitude of the component fatigue limit,ka slope of the component constant amplitude S-Ncurve for N < ND,cr , Chapter 2.4.3.2,j total number of steps in the spectrum,10 The consistent version ofMiner's rule was first developed by Haibach.Asimplifiedversion allowing for the decrease ofthe fatigue limit becameknown as the modified version orthe Haibach method ofMiner's rule.9Theconsistent version of Miner'sruleallowsfor thefact, thatthecomponent fatigue limit will decrease as the damage sum increases.The decrease applies tocomponent constant amplitude S-N curvesmodelI as well as tomodel II for ND,s 106.Using the consistent version of Miner's rule the variableamplitude fatigue strength factor is to be computes!iteratively for differing values ofSa,zd,l , untila valueNequal to the required total number of cycles N isobtained. The respective value of Sa,zd,l is used to derivethe variable amplitude fatigue strength factor.non-welded weldedcomponents componentsSteel, GS, 0,3 0,5Aluminum alloysGGG, GT, GG 1,0 1,0Stress spectrum2:U N(lg)Figure 2.4.4 Elementary version of Miner's rule, com-ponent constant amplitude S-N curve model I, DM=1.8 hi / H maybe replaced by n, / N ,N Required total number ofcycles according to the required fatigue life,N= ni (summed up for 1toj),nj number ofcycles instep iaccording tothe required fatigue life.Table 2.4.3 Critical damage sum DM , recommendedvalue.Characteristics ofthe stress spectrum according toChapter 2.1,component constant amplitude SoNcurve according toChapter 2.4.3.2.sa(lg)v,Sa.lKBK,zd =1. (2.4.56)If for a component constant amplitude S-N curve modelII (slopingfor N>ND,cr )avalueKBK,zdisobtainedfrom Eq. (2.4.53) that is smaller than the value obtainedfromEq. (2.4.50) or (2.4.52), thenthe higher valuefrom Eq. (2.4.50) or (2.4.52) is to be used.slope of the component constant amplitude S-Ncurve for N < ND,cr , Chapter 2.4.3.2,DM critical damage sum, Table 2.4.3,ND,cr number of cycles at knee point of the componentconstant amplitude S-N curve, Chapter 2.4.3.2,total number of cycles of the given spectrum,H= H, =L hi (summed up for i =1 toj),related number of cycles in step i,Hi = L hi (summed up for i = 1 to i) *8,total number of steps in the spectrum,number of the step in the spectrum,Sa,zd,i stress amplitude in step i of the spectrum,Sa,zd,l stress amplitude in step i =1 of the spectrum.If for a component constant amplitude S-N curve modelI (horizontal for N> ND,cr ) a value KBK,zd < 1isobtained from Eq. (2.4.53), then the value to be used is2.4 Component fatigue strength2.4.3 Component variable amplitude fatigue strength662 Assessment of the fatigue strengthusing nominal stressesi number of thestep in thespectrum,m number i =m of the first step belowSAK,zd,H total number of cycles in the given spectrum,H=Hj =L hi (summed up for Ito j),hi number of cyclesin step i,Hi =L hi (summed up for I to i)"8.The computation is to be repeated iteratively fordifferingvalues Sa,zd,1 >SAK,zd, until a..!alue Nequaltothe requiredtotal number of cycles N isobtained.From the respective value of Sa,zd,1 the variableamplitude fatigue strength factor is obtained asCalculation using a classof utilizationThe variable amplitude fatiguestrength factorKBK,zd istobedeterminedaccordingtothe appropriateclass ofutilization"12, Chapter 5.7.Calculation using a damage-equivalent stressamplitudeWhenusinga damage-equivalent stress amplitudethevariable amplitude fatigue strength factor for bothconstant amplitude S-N curves modelI and model II isKBI100C, Figure1.2.2: (3.2.29)KT,m =KT,p = 1-1,7' 10,3. (T/ C-100),for GS, T> 100DC: (3.2.30)-3 0KT,m =KT,p = 1- 1,5 . 10 . (T / C- 100),for GGG, GT and GG, T >100DC, Figure 3.2.2:KT.m=Kr,p = 1- aT,m. (10 -3. T /DC) 2. (3.2.31)aT,m ConstantFigure 3.2.2 Temperature dependent values of thestaticstrength of non-alloyed structural steel and of GGplotted forcomparison.Safety factors after Chapter 3.5.Rm,T/Rm= KT,m, Rp,T/Rp=KT,p,Rm,Tt / Rm= KTt,m, Rp,Tt / Rp = KTt,p'Top: Non-alloyed structural steel with Rp/ Rm=Re/ Rm=0,65,Rm,T, Rp,T aswell asRm,T1> Rp,Tt fort = 105h,Jm=2,0, jp =Jmt= 1,5 , Jpt= 1,0.Bottom: 00,Rm,T aswell as Rm,Tt fort = 105h,Jm=3,0, jmt =2,4.Eq. (3.2.28) to (3.2.31) are validfromthe indicatedtemperature T up to 500DC.For a temperature above350 Ctheyare valid only, if therelevant characteristicstress does not act onlong terms.Table 3.2.6Constant aT,m.Kind of material GGG GT GGaT,m2,4 2,0 1,6o3.2.2b100 200300 400 500Tin C15There isaninsignificant discontinuity at T =60C.16For stainless steel no values are known upto now.3.2 Material properties833 Assessment of the static strengthusing nominal stresses(3.2.34)Thevalues R""Tt and arenotneededexplicitlyforan assessment of the static strength, as only thetemperature factorsKTt,m andKTt,p areneeded.Steel and cast iron materialFor GG a yield strength value is not defined andtherefore the value Rp,Tt doesnot exist.DependingonthetemperatureTandontheoperationtime tat that temperature the temperature factorsKTt,mand KTt,p apply, Figure 3.2.2*172K=10(aTt,m+bTt,m . Pm+ cTt,m . Pm)Tt,m , (3.2.35)2K =lO(aTt,p+bTt,p Pp+cTt,p .pp)np ,Pm = 10 -4. (T / C + 273)' (Cm+ 19(t/ hj),Pp=10 - 4. (T / C + 273). (Cm+ 19(t / hj),aTt,m, ..., Cp constants, Table 3.2.7,t operation time inhours h at thetemperature T.Eq. (3.2.35) applies to temperatures from approximately350C upto 500C, butonlyforstresses actingonlongterms. In general they do not apply to temperaturesbelow about 350C*18.Long-term valuesLong term values of the static strength areR""Tt =KTt,m. R; ,=KTt,p .KTt,m, KTt,p temperature factors,Figure 3.2.2 and3.2.3, Eq. (3;2.35),Rm, R, tensile strength and yield strength;Eq. (3.2.1) to(3.2.3).High temperaturcstrengthRm,TRi'D;'l'lR. 'JmCrecpStrellgth. IR..TtRm,Tt 1}fn7'jlllt0,5IHigll temperaturefatigueslrength0,1 .__ 6W;.d.T.00Wd 1crw.>.d . R.,.joAluminum alloysAccording tothetemperature Tthetemperature factorsKT,mand KT,p foraluminum alloysapplyas follows:- forage-hardening aluminum alloys:T > 50DC,Figure 3.2.3 (3.2.32)Kr,m =1 - 4,5. 10 -3. (T /DC - 50) ;:: 0,1,Kr,p =1 - 4,5. 10 -3. (T /DC - 50) ;:: 0,1,- fornon-age-hardening aluminum alloys:T> 100C, Figure 3.2.3 (3.2.33)Kr,m=1 - 4,5. 10 -3. (T / C - 100)0,1,Kr,p =1 - 4,5. 10 -3. (T / C - 100)0,1,Eq. (3.2.32) and(3.2.33) arevalidfromthe indicatedtemperatureTupto200C, andingeneral only, if therelevant characteristic stress doesnotact onlongterms.o1.2.3o so 100 150 200250 100T/'CFigure 3.2.3 Temperature dependent values of thestaticstrength of aluminum alloysplotted for comparison.Static strength values:Rm,T/Rm=KT,m =Rp,T/Rp=KT,p'Rm,Tt/ Rm=KTt,m =Rp,Tt / Rp=KTt,p .Rm,Tt,Rp,Tt for t = 105h.Fatigue limit for completely reversed stress (N= 106cycles):crW,zd/ Rm = 0,30 ; crW,zd,T/ crW,zd = KT,D .Safety factors according to Chapter 3.5and4.5:17 Larsen-Miller-parameter P andLarsen-Miller-constant C.18 Because the values would be unrealistic for temperaturesT < 350C, where thevalues KT,m andKT,p are relevant instead.3.2 Material properties843 Assessment of the static strengthusing nominal stressesAluminum alloysFor aluminum alloys andt = 105hoursKTt,m is given byFigure1.2.4*19.Figure 3.2.4Temperature factor KTl,m R.n.Tt/ R.n foraluminum alloys and t =105hours.The given curve is the same as in Figure 3.2.3, except that the factor(1 / jm) is different.\\\\ ii Table 3.2.7 Constants aTt,m, ... , Cp Steel Non- Fine grain Heat-alloyed structural treatable-structural steel steelsteel Creep strengthaTt.m- 0,994 -1,127 - 3,001bTlm2,485 2,485 3,987CTtm- 1,260 - 1,260 - 1,423Cm20 20 24,271%Creep limitaTt.n- 5,019 - 6,352 - 3,252bTt.n7,227 9,305 5,942cTt.n- 2,636 - 3,456 - 2,728Co20 20 17,71Cast iron GS GGG,GT GGmaterial Creep strengthaTtm-7,524 2,50 -1,46bTtm9,894 - 1,83 2,36CTtm- 3,417-0,90Cm19,57 20 251% Creep limitaTtn- 10,582 0,12 -bTln8,127 1,52 -CTt.n- 1,607 - 1,28 -Cn35,76 18 - 12,5 %).jm->1Consequences of failurejp->2severe moderatejmt->3->Sjpt->4high 2,0 1,751,5 1,3Probability of 1,5 1,3occurrence of 1,0 1,0the characteristiclow 1,8 1,6service stress->61,35 1,2values1,35 1,21,0 1,0Table 3.5.1 Safety factors jm and jp for steel(not for GS) and for ductile wrought aluminumalloys91921R35 EN.doclPage90 GeneralSteelCastironmaterialsGeneralDuctile cast iron materialsNon-ductile cast iron materialsWrought aluminum alloysGeneralDuctile wrought aluminum alloysNon-ductile wrought aluminum alloysCast aluminum alloysGlobal safety factor3.5.03.5.13.5.23.5.2.03.5.2.13.5.2.23.5.33.5.3.03.5.3.13.5.3.23.5.43.5.53.5 Safety factors3.5.0 GeneralAccordingto this chapter the safetyfactors are tobedetermined *1.Thesafety factorsarevalid under thecondition that thedesignloadsare reliably determined on the safe side andthat the material properties correspondtoan averageprobability of survival of Po =97,5 % *2.The safety factors may be reduced under favorableconditions, that is depending on the probability ofoccurrence of thecharacteristic stress valuesin questionanddepending on the consequences offailure.The safetyfactors are validbothfor non-welded andwelded components.The safetyfactors given inthefollowingarevalidforductileandfornon-ductile materials.In thisrespect anytypesofsteel areductilematerials, aswell ascast ironmaterials and wrought aluminum alloys with anelongation A s ~ 12,5 %, while GT, GG and castaluminumalloys are always consideredas non-ductilematerials here. *33.5.1 SteelSafety factors applicabletothe tensilestrengthandtothe yieldstrength, to the creepstrength andto the creeplimitare givenin Table 3.5.1.1The safety factors in Chapter 1.5 are the same, but with thedifference, that non-ductile cast iron materials and non-ductilealuminum alloys are considered here aswell.2Statistical confidence S=SO %.3All types of GT, GGandcast aluminumalloys haveelongationsAs < 12,S% and are considered asnon-ductile materialshere. WroughtaluminumalloyswithelongationsAs< 12,S% are considered asnon-ductilematerials, too. For non-ductilematerialstheassessment of thestatic strength istobecarried outwith local stresses.->1referring tothe tensile strength Rmortothe strength at elevatedtemperature RmT,->2 referring tothe yield strength Rportothe hot yield strength Rp,T,->3 referring tothe creep strength Rm,Tt ,->4 referring tothe creep limit Rp,Tt .->Smoderateconsequences of failure of a lessimportant component inthe sense of "no catastrophic effects" being associated with a failure;forexamplebecause of aloadredistributiontowards othermembersof astatically undeterminate system. Reduction byapproximately IS%.->6 or onlyinfrequent occurrences of thecharacteristicservicestressvalues, for example due toanapplication ofproof loads or due to loadsduring anassembling operation. Reduction byapproximately 10 %.3.5.2 Cast iron materials3.5.2.0GeneralDuctile and non-ductile cast iron materials are to bedistinguished.3.5.2.1Ductile cast iron materialsCast iron materials with an elongationA 5 ~ 1 2 , 5 % areconsideredasductile, inparticular alltypesof GSandsometypesof GGG(not GTandnotGG). Values of elongation see Table 5.1.12.Safetyfactors for ductilecast iron materials are givenby Table 3.5.2. Compared to Table 3.5.1 they arehigher because of anadditional partial safety factorjFthat accounts for inevitable but allowable defects incastings. The factor isdifferent for castingsthat havebeen subject to non-destructive testing or have not*4.4 Inmechanical engineering. cast components areof standard qualityforwhich a furtherreduction of thepartialsafetyfactor tojr = 1,0does not seem possible up tonow.Asafety factor jF = 1,0may beapplied tohigh quality castcomponents inthe aircraft industry however. Those high quality castcomponentshaveto meet special demandsand (cont'dpage91)3.5 Safety factors913 Assessment of the static strengthusing localstressesDuctile and non-ductilewrought aluminum alloys are tobe distinguished.3.5.3 Wrought aluminum alloys3.5.3.0General20As ,A3in%1U12,5GG0,5Ajo3.5.3.1 Ductile wrought aluminum alloysWrought aluminum alloy with an elongationA~ 12,5 % areconsideredasductilematerials. Valuesof elongation see Table 5.1.22 to 5.1.30.Thesafety factors forductilewroughtaluminum alloysare the same as for steel, Table 3.5.1.Figure 3.5.1 Value L\j to be added to the safety factorsjm and jp, defmed as a function of the elongation As orA3 respectively.Table 3.5.2 Safety factors jm and jp for ductile cast ironmaterials (GS; GGG withA 5 ~ 12,5 %) -}1jmConsequences of failurejpsevere moderatejmtJptcastings not subject to non-destructive testing-}2high 2,8 2,452,1 1,8Probability of 2,1 1,8occurrence of 1,4 1,4the characteristic low 2,55 2,2service stress 1,9 1,65values 1,9 1,651,4 1,4castings subject to non-destructive testing-}3high 2,5 2,21,9 1,65Probability of 1,9 1,65occurrence of 1,25 1,25the characteristic low 2,25 2,0service stress 1,7 1,5values 1,7 1,51,25 1,253.5.2.2 Non-ductile cast iron materials-}1 Explanatory notes for the safety factorssee Table 3.5.1.-}2 Compared toTable 3.5.1an additionalpartial safety factor jF=1,4is introduced to account for inevitable but allowabledefects in castings.-}3 Compared to Table 3.5.1an additional partial safety factor jF=1,25is introduced, forwhichit is assumedthata higherqualityof the castingsis obviously guaranteed when testing.Cast iron materials with anelongation As < 12,5 %(A3 < 12,5 %for GT) are considered as non-ductilematerials, inparticularsometypesofGGGas well asalltypes of GT and GG. Values of elongation for GGGandGTsee Table5.1.12or5.1.13. Thevaluefor GGis As = 0 *5.For non-ductile cast iron materials the safety factorsfromTable3.5.2 areto be increasedby adding a valueL\j, Figure 3.5.1*6:L\j= 0,5 - ~ A 5 /50%. (3.5.2)3.5.3.1Non-ductile wrought aluminum alloysWrought aluminum alloy with an elongationA< 12,5 % areconsideredasnon-ductilematerials.Values of elongation see Table 5.1.22 to 5.1.30.For non-ductile wrought aluminumalloys all safetyfactors from Table 3.5.2 are to be increased by adding avalue L\j, Figure 3.5.1and Eq. (3.5.2).3.5.4 Cast aluminum alloysCast aluminumalloys are always consideredas non-ductile materials. Values of elongationsee Table 5.1.31to 5.1.38.Forcastaluminumalloysall safetyfactorsfromTable3.5.2aretobeincreasedbyaddinga valueL\j, Figure3.5.1and Eq. (3.5.2).AS Elongation, to be replaced by A3 for GT.( jm = 2,0from Table 3.5.2, moderate consequences, non-destructivelytested, lowprobability, ~ j = O,Sfor AS = 0 fromEq.(3.S.2) ).checks' on qualification of the productionprocess, aswell asonthequality and extent of product testing in order to guarantee littlescatter of their mechanical properties.5ForGGthevaluesJpand Jpt arenotrelevant since theyieldstrengthand the creep limit ofGO are not specified.6 For example thesafety factor JmforGGis atleastjm = 2,0 +O,S = 2,S . (3.S.3)3.5 Safety factors3.5.5 Total safety factorFrom theindividual safetyfactorsthe total safety factorjges is to be derived*7:jges = (3.5.4)

KT,m' KT,p Rp' KTt,m' KTt,p n, ,923 Assessment of the static strengthusing local stresses.lm...Kt,m...safety factors, Table 3.5.1 and 3.5.2,temperature factors, Chapter 3.2.5*8.SimplificationsThefollowing simplificationsapplyto Eq. (3.5.4):In the case of normal temperature the thirdandfourthtermhave no relevance*9, and moreoverthereis KT,m = KT.p =1 ,for Rp / Rms 0,75 the first term has no relevance,for Rp / Rm > 0,75 the second term has norelevance *10,for GG the second and fourthterm have norelevance*11.7 MAXmeans that the maximumvalue of the four terms intheparenthetical expression is valid.8ApplicabletothetensilestrengthRmortotheyieldstrengthRp toallow for the tensile strength at elevated temperatureT ' the hot yieldstrength the creepstrength Rm,Tt , or the creeplimit Rp,Tt,respectively'9 The terms containing the factors KTt,m and KTt,p must not be appliedin the case of normal temperature, as they will produce misleading results.10 If thereis a ratio of the safetyfactorsjpI jm= 0,75.11 Since a yield strength and a creep limit are not specified.3.6 Assessment933 Assessment of the static strengthusing nominal stresses3.6 AssessmentContents3.6.03.6.13.6.1.13.6.1.23.6.23.6.2.13.6.2.23.6.23.6.2.13.6.2.2GeneralRod-shaped (ID) componentsIndividual types of stressCombined types of stressShell-shaped (2D) componentsIndividual types of stressCombined types of stressBlock-shaped (3D) componentsIndividual types of stressCombined types of stress!R36 EN.dogPage93949596strength, O"SK ,..., divided by the total safety factor jges.The degree of utilization is always a positive value.SuperpositionFor stresscomponentsof the sametypeofstressthesuperposition is to be carriedout according to Chapter3.1.If different types of stress likenormalstress andshearstressact simultaneously and if theresulting stateofstress ismultiaxial, see Figure0.0.9 *5, theparticularextrememaximumstresses andtheextrememinimumstresses are to be overlaid as indicated in the following.3.6.0 GeneralAccording to this chapter the assessment of thecomponent staticstrengthusinglocal stresses isto becarried out.Ingeneral theassessmentsfor theindividualtypes ofstress andfor thecombined stress are to be carried outseparately * I *2.Ingeneral theassessmentsfor theextrememaximumandminimumstresses(normal stresses intension andcompressionand/or shear stress)aretobecarriedoutseparately. For steel or wrought aluminumalloys thehighest absolute value of stress is relevant *3.The calculation applies to both non-welded and weldedcomponents. For welded components assessmentsaregenerally to be carried out separately for the toe and forthe root of the weld as indicated in the following.Degreeof utilizationThe assessments are to be carried out by determining thedegrees of utilizationof thecomponent static strength.In the context of the present Chapter the degreeofutilization is the quotient of the characteristicstress(extremestress O"max,ex, , ...) divided by theallowablestatic stress at the referencepoint *4. Theallowablestatic stress is the quotient of the component staticI It is a general principlefor anassessment of thestaticstrength tosupposethat all types of stressobservetheir maximum(orminimum)values atthe same time.2Thisisin order toexamine the degrees ofutilization ofthe individualtypes ofstress in general, and in particular ifthey mayoccur separately.3 Different in the case ofcast iron materials or cast aluminium alloys withdifferent static tension and compression strengthvalues.4 The reference point isthe critical point ofthe cross section that observesthe highest degree ofutilization.Kindsof componentRod-shaped (lD), shell-shaped(2D)andblock-shaped(3D) components areto be distinguished. Theycan beboth non-welded or welded3.6.1 Rod-shaped (ID) components3.6.1.1 Individual types of stressRod-shaped (ID)non-weldedcomponentsThe degrees of utilization of rod-shaped non-weldedcomponents for the different types of stress like normalstress or shear stress areaSK,O' =Ci max, ex~ 1, (3.6.1)CiSK/ jgesa S K , ~ ='tmax,exs 1,'tSK/ jgesO"max,ex, , ... extreme maximum stresses according totype of stress; the extreme minimumstresses, O"min,ex, , ..., are to be consideredin the same way as the maximum stresses,Chapter 3.1.1.1,O"SK, ... related component static strength,Chapter 3.4.1,jges total safetyfactor, Chapter 3.5.5.All extreme stresses are positive or negative (or zero). Ingeneralnormal stresses intension orcompression areto be considered separately. For shear the highestabsolutevalue of shear stress is relevant.5 Only in the case ofstresses acting simultaneously the character ofEq.(1.6.4) and (1.6.12) isthat ofa strength hypothesis. If Eq. (1.6.4) and(1.6.12) are applied in other cases, they have the character ofan empiricalinteraction formula only. For example the extreme stresses from bendingand shear will -as arule - occur atdifferent points ofthe cross-section, sothat different reference pointsWare tobe considered. As a rule bendingwill be more important. Moreover see Footnote 1.943.6 Assessment3 Assessment of thestatic strengthusing nominal stressesRod-shaped (ID) welded componentsFor the toe of the weld of rod-shaped(lD) weldedcomponents thecalculationisto becarriedoutasforrod-shaped (lD) non-welded components.For the root of the weldof rod-shaped(lD) weldedcomponents the degrees of utilization for normal stressand/orshearstress follow fromtheequivalent nominalstresses, Chapter 3.1.1.1:(3.6.7). O"max,exwvaSK, = '.$;1,wv,e / .O"SK Jges't max, ex,wvaSK,wv,'t = ..$;1,'tSK/ Jges(3.6.2)For non-ductilewrought aluminumalloys (elongationA < 12,5 %) there is q = 0,5 , otherwise./3-(l/f't) 7q *./3-1 'f, shear strength factor, Table 3.2.5.Rod-shaped (ID) weldedcomponentsFor the toe of the weld of rod-shaped (lD) weldedcomponentsthecalculationistobecarriedout asforrod-shaped (lD) non-welded components.For the root of the. weldof rod-shaped (ID) weldedcomponents the degree of utilization for combined typesof stress (or loadings) is *8O"SK, ...aSK,wv,cr, ... degree of utilization , Eq. (3.6.2).3.6.2 Shell-shaped (2D) components3.6.2.1 Individual types of stressShell-shaped (2D) non-welded componentsThe degrees of utilization of shell-shaped (20) non-welded components forthetypes of stresslikenormalstress in the directions x and y as well as shear stress are(3.6.8)(3.6.9)O"max,ex,xasK,crx = ..$; 1,O"SK,x / JgesO"max,ex,wv , ... Extreme maximum equivalent structuralstresses; the extreme minimum stresses,Smin,ex,wv,zd .. , , are to be considered inthe same way as the maximum stresses,Chapter 3.1.1.1,related component static strengthvalues, Chapter 3.4.2,total safety factor, Chapter 3.5.5.All extreme stresses are positive or negative (or zero). Ingeneral normal stresses in tension or compression are tobe considered separately. For shear the highest absolutevalue of shear stress is relevant.3.6.1.2 Combined types of stressRod-shaped (ID) non-welded componentsFor rod-shaped (lD) non-welded components the degreeof utilization for combined types of stress is *6O"max,ex,yasK,cry = ..$;1,O"SK,y / Jges'tmax, exI----I.$; 1,'tSK/ jgesaSK,crv = q . aNH + (l- q) . llGH.$; 1,whereaNH={lsl+ ~ s 2 +4.t2)'(3.6.4)(3.6.5)O"max,ex,x, ... Extreme maximum stresses according totype of stress, Chapter 3.1.1.1; theextreme minimum stresses,O"min,ex,x , ...,are to be considered in the same way asthe maximum stresses, Chapter 3.1.1.2,6The applied strengthhypothesis for combinedtypes of stress is acombination ofthe normal stress criterion (NH) and the v. Mises criterion(GH). Dependingonthe ductilityof thematerial thecombinationiscontrolled by a parameter q as a function off, according toEq.(1.6.7)and Table1.6.1. For steel isq= 0so that only the v. Mises criterion isofeffect. For GG isq=0,759 so that both the normal stress hypothesis andthe v. Mises criterion are of partial influence.s = aSK,cr ,t = aSK,cr ,aSK,cr, .., degree of utilization, Eq. (3.6.1).(3.6.6)7Table 1.6.1Constant q(ft) .Steel, GOO GT,GGWrought CastAI-alloys Al-alloysr, 0,577 0,65 0,75 0,85q 0,00 0,264 0,544 0,759Caution: For non-ductile wrought aluminium alloys (elongationA < 12,5 %) there is q= 0,5.8Eq. (3.6.8) does not agree with the structure ofEq. (3.1.2) on page 74.It is anapproximationwhichhas to be regardedas provisional andtherefore itis tobe applied with caution.953.6 Assessment 3 Assessment of the static strengthusing nominal stressescrSK,x, ... related static component strength,Chapter 3.4.1,Total safety factor, Chapter 3.5.5.J2 2 2 0, O"a,i+1/O"a,i s 1,O"m,i =O"mRes,i =Res ,(4.1.11)(4.1.12)8 In the following allvariables and equations are presented for the localnormal stress oonly, butwritten with theappropriateindices theyarevalid for all other types ofstress as well.9 In this case anassessment ofthe variable amplitude fatigue strength istobe carried out.lOinthis case ana s s e s s ~ n t ofthe fatigue limit istobe carried out fortype I SoN curves if N= N;:: ND,cr.,.2r an assessment ofthe endurancelimit for typeII SoNcurves ifN=N;:: NDcr II , respectively, oranassessment for finite lifebasedonthe constant amplitude SoNcurve(formally similar.20 an assessment ~ the variableamplitudefatiguestrength) if N= N < ND,cr or N= N;:: ND,cr, II for Typ I orTyp IISoN curves, respectively. ND,cr orND,cr, II isthe number ofcycles atthe fatigue limit ofthe component constant amplitude SoN curve, Chapter2.4.3.2.11 The valuesN-total number ofcycles required -and II -totaln u m ~ofcycles ofagiven spectrum - are different ingeneral. The terms ni INandhi IHare equivalent.12Thedamagepotential isacharacteristicfor theshapeof a stressspectrum. The values kcr = 5for normalstress and k't = 8for shear stressare valid for non-welded components. The values kcr=3and ~ =8arevalid for welded components.The term hi IH may be replaced by ni IN .13Amean stress spectrum, for example, results from a static load withdynamic loads superimposed, a fluctuating stress spectrum, for example,results for acrane hook when lifting variable loads.4.1 Characteristic service stresses1004 Assessment of the fatigue strengthusing local stresses100C:KT,D = 1-1,2. 10 -3.(T/ C-100), (4.2.9)- for GGG, GT and GG, T >100C, Figure 4.2.1:KT,D'" 1- aT,D'(10 - 3. T / 0C)2, (4.2.10)for aluminum alloys, T > 50C:KT,D = 1- 1,2' 10 -3.(T / C - 50)2,Figure 3.2.3in theChapter 3.2,'t:W,sKindof materialfw,O"Case hardening steel0,400,577Stainless steel 0,400,577Forging steel 0,400,577Steelother thanthese 0,45 0,577GS 0,34 0,577GGG 0,34 0,65GT 0,30 0,75GG 0,30 0,85Wrought aluminum alloys 0,300,577Cast aluminum alloys 0,300,754.2.3 Temperature factor4.2.3.0 GeneralTable 4.2.1 Fatigue strength factorsforcompletelyreversed normal stress, fw,O" , and shear stress, 1 fw0" and fw arevalid fora number of cyclesN= 106fw'is equal 'to, Table 3.2.5.Bla'nk-hardened. The influence of the carburization on thecomponent fatigue strength is tobe considered by the surfacetreatment factor, Kv, Chapter 4.3.4.0,577 = 1//3, according tothev. Mises criterion. Also valid forwelded components.Preliminary values.fW,O" does not correspond tothe endurance limit for N =co here!The temperature factor considers that the materialfatigue strength forcompletelyreversedstressdecreaseswithincreasing temperature.Normal temperature, low temperature and elevatedtemperature areto be distinguished.aT,DConstant, Table 4.2.2.4.2.3.1Normal temperatureNormal temperatures areas follows:for finegrain structural steel from-40C to 60C,- for other kinds of steel from-40C to + 100C,for cast ironmaterials from-25C to + 100C,- for age-hardening aluminum alloysfrom-25C to 50C,- fornon-age-hardening aluminum alloysfrom-25C to100e.Table 4.2.2 Constant aT,D*8.Kind of material GGG GT GGaT,D1,6 1,3 1,08 Forstainless steel novalues areknown upto now.4.2 Material parameters1054 Assessment of the fatigue strengthwith local stressesEq. (4.2.7) to (4.2.10) apply to steel and cast ironmaterials from the indicated temperature T up to 500C.Eq. (4.2.11) applies to aluminum alloysup to 200C.ThevaluesCYW,zd,T and1:W,s,T are notexplicitly neededfor anassessment of thefatigue strength, as only thetemperaturefactorKT,D is used.For elevated temperature, and in particular when themeanstress Sm, i:- 0, thefatigue strengthintermsofthe maximum stress may be higher than the staticstrengthso thatthe assessment is governed by the staticstrength.High temperaturestrength Rm,THigh temperatureyieldstreilgth Rp,TRm,TRm'jmI Io4Rp,T Rp I, Rp'Rm ' jpo0;11% creeplimit Rp;Tt0,3t----K:--+---",;:t-''':--tt--r---,.-J .Rp,Tt Itp'1Rp. Rm ' jptCreep Strength R,.,Tt0,2 m.........1R';;"""' jmto 100 ZOO 300 400 5002.2.1. Tin"CCreep$trengthR,.;TtRm,Tt IRm 'jmt100 200 300 400 500Till 'coZ,2.1bo0,1 t====J=::='=b--L....,,=-1-..+1Figure 4.2.1 Temperature dependent values of thestatic strengthand of the fatigue strength plotted forcomparison.Safetyfactorsj according toChapter 3.5or4.5, respectively.Rm,TI Rm =KT,m,Rm,Tt l Rm=KTt,m,Rm,T, Rp,T as well asRp,T I Rp =KT,p,Rp,Tt l Rp =KTt,p'Rm,Tt, Rp,Tt for t=105h.Fatiguestrength value atelevated temperature:crW,zd,T I crW,zd= KT,DTop: Non-alloyedstructuralsteel, asin theFigure 3.2.2,Rp I Rm = n, I Rm =0,65, crW,zdI Rm =0,45,Jm =2,0, Jp =jmt = 1,5, Jpt = 1,0, in = 1,5 .Bottom: GG, asin Figure 3.2.2,crW,zdI Rm =0,30, Jm =3,0, Jrnt =in =2,4 .Table 4.3.1 Constant K, .4 Assessment of the fatigue strengthusing local stresses1Kt-Kfratio, Chapter 4.3.2,constant, Table 4.3.1,if no better estimate is available,roughness factor, Chapter 4.3.3,surface treatment factor, Chapter 4.3.4,coating factor, Chapter 4.3.4,constant forGG, Chapter 4.3.5.KWK,crl = (4.3.3) n:,1 {1+-I))> KWK,cr2 ==_1.(1+-2-.(_1-1)]ncr,2 K fK R,KWK,cr3=++-(-I))> ncr, ..,KfThe design factors of block-shaped non-weldedcomponents forthe principle stresses in the directions 1,2 and 3 (normal to the surface) are*2KwK,crx = (4.3.2)=_1_'(1+_1_.(_1__1)) 1ncr,x KfKR,cr K y .Ks .KNL,E'Kw: ,O"Y1= -1)1ncr,y KfKR,cr ) Ky.Ks .KNL,E = n1,{1+ -(-I)J Ky lKs>KR,cr, ...K yKsKNL,E1064.3Design parameters4.3.0 GeneralAccordingtothis chapter thedesignparametersaretobe determined interms of design factors.4.3 Design parameters 1R43 EN. dogContent Page4.3.0 General 1064.3.1 Design factors4.3.1.0 General4.3.1.1 Non-welded components4.3.1.2 Welded components 1074.3.2 Kt-Kfratios 1084.3.2.0 General4.3.2.1 Computation of Kj-K, ratios4.3.2.2 Kj-K, ratio forsuperimposed notches 1094.3.3 Roughness factor4.3.4 Surface treatment and coating factor 1104.3.5 Constant KNL,E III4.3.6 Fatigue classes (FAT) 1124.3.7 Thickness factor4.3.1 Designfactors4.3.1.0 GeneralNon-welded and welded components are to bedistinguished.4.3.1.1 Non-welded componentsRod-shaped(lD), shell-shaped(2D) andblock-shaped(3D)non-welded components areto be distinguished.The design factors of rod-shaped (lD) non-weldedcomponents fornormal stress and forshear stressare1KWK,cr = (4.3.1) n10 {I+-( -I))>Ky ' ==_1-1))' 1n, x, Ky.KsThe design factors of shell-shaped (2D) non-weldedcomponents for normal stresses inthedirections x andyas wellas forshear stress areKind of Steel GS GGG GT GGmaterial wrought castAl-alloys Al-alloysKf2,0 2,0 1,5 1,2 1,0Abetter estimate of Kf maybe obtainedfromstressconcentration factors Kt,cr and of a substitutestructure, Chapter5.12, andthe Kt-Kf ratios, Chapter4.3.2.1: or1 About the purpose ofthe constant Kf see Footnote1 inChapter 2.3.2The Kt-Kf ratioin direction3 normal to thesurface, ",,3. , is notcontained inEq. (4.3.3) since a stress gradient normal tothe surface isnotconsidered.4.3 Design parameters4,3.1.2 Welded componentsFor the basematerial of welded components the designfactors are to be computed as for non-weldedcomponents.The design factors for the toe and for the root of a weldare ingeneral tobedetermined separately, sincethelocal stresses and thefatigue classes (FAT) maybedifferent.Rod-shaped(lD), shell-shaped(2D)andblock-shaped(3D)weldedcomponents aretobedistinguished. Thecalculationcan be carried out with structural stresses orwith effective notch stresses.1074 Assessment of the fatigue strengthusing local stressesFAT fatigue class, Chapter 4.3.6,ftthickness factor, Chapter 4.3.7,Kv surface treatment factor, Chapter 4.3.4*5,Kg coating factor, Chapter 4.3.4;KNL,E constant for GG, Chapter 4.3.5.The fatigue classesFATare in general different fornormalstresses in the directionsx and y as well as forshear stress.For certainapplications block-shaped (3D) componentsmay be welded at the surface, for example by surfacingwelds. Then the design factors are to be calculated as forshell-shaped (2D) welded components.Calculation with structural stressesSteel andcast iron materialThe design factors of rod-shaped (lD) weldedcomponents made of steel or of cast iron materials *3 fornormal stress and for shear stress are,KWK,cr =225 / (FAT' ft' Kv KNL,E), (4.3.4) =145/ (FAT' ft'Ko ),The design factors of shell-shaped (2D) weldedcomponents for normal stresses in the directions x and yas well as for shear stress areThe design factors of shell-shaped (2D) weldedcomponents for normal stresses in the directions x and yas well as for shear stress areAluminum alloysThe design factors of rod-shaped (lD) weldedcomponents fromaluminumalloys*4for normal stressand for shear stress are,KWK,crx =225 / (FAT' ft' Ky' KNL,E),KwK,cry =225 / (FAT' ft' Kv KNL,E), =145/ (FAT' ft'Ko ).KWK,cr = 81 / (FAT' ft' Ky' Kg), =52 / (FAT' ft' Ky' Ks).KWK,sx = 81 / (FAT' ft' Ky' Kg),KwK,sy =81 / (FAT' ft' Ky' Kg), = 52/ (FAT' fi' Ky' Kg),(4.3.5)(4.3.6)(4.3.7)Calculation with effective notch stressesSteel and cast iron material as well as aluminumalloysThe design factors of rod-shaped (lD) weldedcomponents made of steel, of cast iron materials l'' andf 1 ,o a uminumalloys for normal stressandforshearstress are *6,KWK,crK = 1/ (Kv Kg' KNL,E), (4.3.8)= 1/ !Ky' Kg).For shell-shaped(2D) weldedcomponents, as a rule,only the effective notch stress in direction of themaximumeffective notchstressandthecorrespondingshear stress are to be considered. The design factors areas beforeKWK,crK = 1 / (Ko . Kg . KNL,E ), (4.3.9)= 1/ (Ky' Kg),Kv surface treatment factor, Chapter 4.3.4*5,Kscoating factor, Chapter 4.3.4,KNL,E constant for GG, Chapter 4.3.5Forcertain applications block-shaped (3D) componentsmay be welded at the surface, for example by surfacingwelds. Then the design factors are to be calculated as forshell-shaped (2D) welded components.3 To some part theFAT values where derived with reference to the IIWrecommendations andEurocode3 (Ref. /9/, /81). Moreover thedesignfactors are supposed tobe valid, however, not only for weldable structural but also for other kinds of steel (conditionallyweldable steel,stainless steel) and weldable cast iron materials).4 To some part theFAT values where derived with reference tothe IIW(Ref. /91). Moreover the design factors are supposed tobe v.ahd, however, for all weldable aluminumalloys, except thealuminum alloys 5000, 6000 and 7000. Numerical values see Footnote 7on page 103.5 As arule Kyis not relevant for welded components, that is Ky= I.6 On principle for steel: KWK,crK = 225/ (FAT ... ) where FAT = 225,and = 145/ (FAT...) whereFAT= 145; aluminumalloysaccordingly, Weld quality conforming tonormal production standard.In combination with effective notch stresses the thickness factor ft is notapplied, since the thickness effect isaccounted for by the stress analysis.4.3Designparameters1084 Assessment of the fatigue strengthusing localstresses4.3.2 Kt-Kr ratios4.3.2.0 GeneralThe Kj-K, ratios nO", ... allowfor aninfluenceonthefatiguestrengthresulting fromthedesign(contour andsize) of a non-welded component.Condition for theapplicationof a Kj-K; ratio is a stressgradient normal tothedirectionofstressasshowninFigure 3.3.1*7.4.3.2.1 Computation of Kt-Kr ratiosKt-Kr ratios for normal stressThe Kt-Kr ratio for normal stress,Ocr, Figure 4.3.1, is tobecomputedfromtherelatedstressgradient GO" afterEq.(4.3.13) to (4.3.15).ForG0" ;;;; 0,1rnm"1 there is (4.3.13)-(ao-0,5+ Rm)n = 1 +G . mmrItl bo MPa0" 0" ,800400800120010035040090080040010 5 0,5 2inMP;---::

/ V[GGG,"/-:/ 1/0.65'V/v .,',.I/ 1 10,707'""iGSV/.-:/ 1 10,75 :/II

/V 1/-://'/

V/-:

/ 1/0,85V./JV

,,-/j /I/;;/ I/// il //110,95 /II {IIIill/v/Iff;1/ 1 // /IItil

(f;,2/ do = r0,267-! \ I I231,41,11,21,041,01.0,010,020,050,10,21,02(4.3.14)(R) - ao+ mn =1 G . mm. 10 bo . MPa0" 0" ,for 0,1 mm" 1 I, fieldof fluctuatingcompressionstress,where Rcr = + or - 00is the zero compression stress.FieldII: -00 S; Rcr S; 0, whereR,< -1isthefieldofalternating compression stress, R,= -1 is thecompletely reversed stress, R; > -1 is the field ofalternating tension stress.Field III: 0 < Rcr < 0,5, field of fluctuating tension stress,where R, =0 is the zero tension stress.Field IV: R,0,5, field of high fluctuating tensionstress.5Thefatiguelimit diagram(Haighdiagram) for normal stress showsincreasing amplitudes for R ND,a (Steel and cast iron material)Incaseof acomponent constant amplitude S-Ncurvemodel I ( horizontal for N > No,a or slopekD,o=(0) thenumberof cycles Nto be computed foravalueSa,1is(4.4.57)N= {[ Akon-1] . DM + I}' [GAI< )ka. NO,a,Ga.lwhere8 hi / H may also be replaced by n, / N ,NRequired total number ofcycles according tothe required fatigue life,N= Eni(summed up for I toj),ni number ofcycles instep iaccording tothe required fatigue life.7 Instead ofAJcon after Eq. (4:4.57) and (4.4.63) ishereAele= I / (va)ke . (4.4.55)9Theconsistent versionof Miner'sruleallowsfor thefact, thatthecomponent fatigue limit will decrease asthe damage sum increases.The decrease applies tocomponent constant amplitude S-N curves modelIas well astomodel IIfor ND,s 2':106.10 The consistent version ofMiner's rule was first developed byHaibach.A simplified version allowing for the decrease ofthe fatigue limit becameknown as the modified version orthe Haibach method ofMiner's rule.4.4 Component fatigue strength4.4.3Component variable amplitude fatigue strength1224 Assessment of the fatigue strengthusing local stresses(4.4.67)(4.4.68) KSK,a= fn,a .Incase of a component constant amplitude S-Ncurvemodel II(sloping for N > No,aorslopekD,a NO a, kO a= coor for N > NO' k D = coNC is the reference number of cyclescorrespondingto the characteristic strength values aAC and AC.aAK / aAC= (Nc / NO,a ) 11ko= 0,736 and /= (Nc /11kr = 0,457.4.5 Safety factors1254 Assessment of the fatigue strengthusing local stresses4.5 Safety factors *1Contents4.5.0 General4.5.1 SteelIR25 EN.doclPage684.5.2 Cast iron materials4.5.2.0 GeneralDuctile and non-ductile cast iron materials are to bedistinguished.4.5.0 General4.5.24.5.2.04.5.2.14.5.2.24.5.34.5.3.04.5.3.14.5.3.24.5.44.5.5Cast iron materialsGeneralDuctile cast iron materialsNon-ductile cast iron materialsWrought aluminum alloysGeneralDuctile wrought aluminum alloysNon-ductile wrought aluminum alloysCast aluminum alloysTotalsafetyfactor694.5.2.1 Ductile cast iron materialsCast ironmaterials with an elongationA5 ~ 12,5 %areconsideredas ductile cast ironmaterials, in particularall types of GS and some types of GGG. Values ofelongation see Table 5.1.12.Safety factorsfor ductile cast iron materials are given inTable4.5.2. ComparedtoTable4.5.1 theyarehigherbecause of an additional partial safety factor jp thataccountsforinevitable but allowabledefectsincastings*4. The factor is different for severe or moderateconsequencesoffailureand moreover for castingsthathave been subject tonon-destructive testing or have not.4.5.1SteelThebasic safetyfactor concerningthefatiguestrengthisAccording to this chapter the safety factors areto bedetermined.Thisvaluemaybe reducedunderfavorableconditions,that is dependingonthepossibilitiesof inspectionandontheconsequences of failure, Table 4.5.1.Table 4.5.2 Safety factors for ductile cast iron materials(GS; GGG) ( A 5 ~ 12,5 %).?3 Regular inspection in the senseof damage monitoring.Reductionby about 10 %.? 1 See footnote? I of Table4.5.1.JoIConsequences of failureSevere I moderate?1castings not subject tonon-destructive testing?2regular noI2,1I1,8inspection yes?3 I 1,9I1,7castings subject tonon-destructive testing?4regular noI1,9I1,65inspection yes?3 I 1,7I1,5?2 Compared toTable4.5.1anadditional partial safety factorjF= 1,4 is introduced to account for inevitable but allowable defectsin castings.(4.5.1) Jo =1,5.Thesafety factorsare valid under the condition that thedesign loads are reliably determined on the safe side andthat the material properties correspond to anaverageprobability of survival of Po =97,5 % *2.Thesafetyfactorsapplybothtonon-welded and weldedcomponents.Table4.5.1 Safety factors forsteel *3 (not for GS) andfor ductile wrought aluminum alloys ( A ~ 12,5 %).jo Consequences of failuresevere moderate ?1regularIno 1,5 1,3inspections I yes?2 1,35 1,2? 1 Moderateconsequences of failureof a less important componentin the sense of"non catastrophic"effectsof afailure; for examplebecauseof a load redistributiontowardsother members of a staticalindeterminate system. Reduction by about 15 %.?4 Compared toTable4.5.1 anadditional partial safety factorjp = 1,25 is introduced, for which it is assumed that a higher qualityofthecastings isobviously guaranteed when testing.2 Statistical confidence S= 50% .3 Steel is always considered as a ductile material.4 In mechanical engineering cast components are of standard qualityfor which a further reduction of the partial safetyfactor to jF= 1,0does not seempossible up to now.?2 Regular inspection in the senseof damage monitoring.Reductionby about 10 %.1 Chapters 4.5and2.5areidentical.A safety factor jF = 1,0may be applied tohighquality castcomponents in the aircraft industry however. Those high quality castcomponents, havetomeet special demands onqualification andchecks of the production process,as well as on the extent of qualityandproduct testing inordertoguarantee littlescatterof theirmechanical properties.4.5 Safety factors1264 Assessment of the fatigue strengthusing local stresses1I4.5.2.2 Non-ductile cast iron materialsCast iron materials with an elongation As-:>3No.4 5ad,p-:> -:>ClOE 1.1121 500 310 200 185 220 115 130 0,56C15E 1.1141 800 545 320 270 345 185 205 0,68C16E 1.1148 800 545 320 270 345 185 205 0,6817Cr3 1.7016 800 545 320 270 345 185 205 0,3728Cr4 * 1.7030 900 620 360 295 385 210 230 0,3316MnCr5 * 1.7131 1000 695 400 320 430 230 255 0,4420MnCr5 * 1.7147 1200 850 480 365 510 280 305 0,4818CrMo4 * 1.7243 1100 775 440 340 470 255 280 0,5218CrMoS4 * 1.7244 1100 775 440 340 470 255 280 0,5222CrMoS3-5 * 1.7333 1100 775 440 340 470 255 280 0,2820MoCr3 1.7320 900 620 360 295 385 210 230 0,3320MoCr4 1.7321 900 620 360 295 385 210 230 0,3316NiCr4 1.5714 1000 695 400 320 430 230 255 0,3010NiCr5-4 * 1.5805 900 620 360 295 385 210 230 0,6118NiCr5-4 * 1.5810 1200 850 480 365 510 280 305 0,37l7CrNi6-6 * 1.5918 1200 850 480 365 510 280 305 0,37l5NiCr13 * 1.5752 1000 695 400 320 430 230 255 0,30-20NiCrMo2-2 * 1.6523 1100 775 440 340 470 255 280 0,52l7NiCrMo6-4 * 1.6566 1200 850 480 365 510 280 305 0,3720NiCrMoS6-4 * 1.6571 1200 850 480 365 510 280 305 0,37 * 1.6587 1200 850 480 365 510 280 305 0,3714NiCrMo13-4 * 1.6657 1200 850 480 365 510 280 305 0,37-:> 1Values afterDINEN 10084AppendixF ("tensile strength values after quenching and tempering at 200C") given for information only.-c- 2 Effective diameter deff,N=16 mm,-c- 3Onlyup to 40mm diameter, typesof material marked by * up to100 mm diameter, however.-:> 4 Re,N afterDIN 17210(Draft 1984-10-00), fitted.-:> 5Re,N /< 0,75 for all types of material listed.-:> 6 More specificvaluesfor the individual typesof material comparedto the averagevalues given in Table 1.2.1and 3.2.1.Table 5.1. 7 Mechanical properties in l\1Pa for nidriding steelsin thequenched and tempered condition,after DIN EN 10 085(2001-07-00) -:>1.Type of material MaterialRm,N Re,N O'W,zd,N O'Sch,zd,N O'W,b,N 1: W,s,N 1:W,t,N ad,rn ad,pNo. -:>2 -:>3 -:>324CrMo13-6 1.8516 1000 800 450 360 480 260 285 0,22 0,2631CrMo12 1.8515 1030 835 465 370 495 270 295 0,21 0,2732CrAIMo7-1O 1.8505 1030 835 465 370 495 270 295 0,21 0,273lCrMoV5 1.8519 1100 900 495 385 525 285 315 0,31 0,3633CrMoV12-9 1.8522 1150 950 520 395 550 300 330 0,30 0,3534CrAINi7-1O 1.8550 900 680 405 335 435 235 260 0,17 0,1741CrAlMo7-1O 1.8509 950 750 430 345 460 250 275 0,23 0,2440CrMoV13-9 1.8523 950 750 430 345 460 250 275 0,23 0,2434CrAIMo5-1O 1.8507-:>4 800 600 360 305 390 210 230 0,00 0,00-:> 1Effectivediameter deff,N= 40mm.-:> 2 Re,N / > 0,75 for all typesof material listed.-:> 3 More specific valuesfor the individual types of materiaI comparedto the average values for the kind of material given in Table 1.2.1 and 3.2.1.-:> 4 Onlyup to 100 mm diameter.1375.1 Material tables 5 AppendicesTable 5.1.8Mechanical properties in MFa for stainlesssteels, after DIN EN10 088-2(1995-08-00) (selected types ofmaterial only) vI v 2Type of material Type of material, Mate- KindofRm,N R,Nafter DIN / SEW rial productCJW,zd,N CJSch,zd,N CJW,b,N '"CW,.,N '"CW,t,NNo.v3d d alial d di.1. tlFemtic stee s ill ie anne e con ition,stan ar qu HIes,X2CrNi12 - 1.4003P(25) 450 250 180 170 205 105 120X6CrAl13 X6CrAI13 1.4002P(25) 400 210 160 155 180 90 110X6Crl7 X6Cr17 1.4016P(25) 430 240 170 165 195 100 115X6CrMo17-1 X6CrMo17 1 1.4113H(12) 450 260 180 170 205 105 120d d oualiti d d" I' h h Martensitic stee s ill t e eat treate con inon, stan ar quaities.X20Cr13 X20Cr 13 1.4021P(75)QT650 650 450 260 230 290 150 170QT750 750 550 300 260 330 175 195X4CrNiMo16-5-1- 1.4418P(75)QT840 840 680 335 280 410 195 220dI . tll h d .P ..ecipitation ar emng martensitic stee s ill e heat treate condition, special qualities.X5CrNiCuNb16-4-1.4542 P(50)P1070 1070 1000 430 335 460 245 275P950 950 800 380 310 410 220 245P850 850 600 340 285 370 195 220d d oualitiId di , I'hi' Austemtic stee s ill t e so ution annea e con ition, stan ar qua ities.X10CrNi18-8 X12CrNi177 1.4310 C(6) 600 250 240 215 270 140 160X2CrNiNI8-1O X2CrNi 18 10 1.4311 P(75) 550 270 220 200 245 125 145X5CrNil8-10 X5CrNi 18 10 1.4301 P(75) 520 220 210 190 235 120 140X6CrNiTi18-1O X6CrNi 18 10 1.4541 P(75) 500 200 200 185 225 115 135X6CrNiMoTil7-12-2 X6CrNiMoTi 1722 1.4571 P(75) 520 220 210 190 235 120 140X2CrNiMoN17-13-5 X2CrNiMoN17135 1.4439P(75) 580 270 230 210 260 135 155vI The fatiguestrength valuesare provisionalvalues.v2 An effective diameterdeff,N is not required, as there is no technologicalsize effect within the dimensions covered by the standard.v3 Kind of product: P(2S) hot rolled plates up to 25 mm thickness,H(12) hot rolled strip up to 12 mm thickness, C(6)coldr ~ l 1 e d strip up to6 mm thickness, QT650 heat treatedto a tensile strength of650 MPa, PI070 hot rolled plate with a tensile strength of 1070 MPa.5.1 Material tables1385 AppendicesTable 5.1.9Mechanical properties in MFa of steels for bigger forgings, afterSEW 550 (1976-08-00) 0,75; Tablebelow: RpO,2,N/ Rm,N < 0,75throughout.~ 3 Elongation in %.For non-ductile materials, A5 < 12,5%, the assessmentof the static strengthis to be carriedout by using local stresses, Chapter 1.0,and all safety factorsare to be increasedby adding a value t.j , Eq. (2.5.2), ... , see Chapters 2.5,3.5 or 4.5, respectively.Table 5.1.14 Mechanical properties for grey cast irions see previous page.5.1 Material tablesTable 5.1.21. Survey of the Aluminum materials.142I 5 AppendicesTable Kind of material Semi-finished product / Type of casting Material standard (Edition)5.1.22 Wrought Strips, sheets, plates DIN EN 485-2 (03/95)5.1.23Aluminum alloysStrips, sheets DIN1745 T. 1 (02/83)5.1.24 Cold drawn rods / bars and tubes DIN EN 754-2 (08/97)5.1.25 Rods / bars DIN1747 T. 1 (02/83)5.1.26 Extruded rods / bars, tubes and profiles DIN EN 755-2 (08/97)5.1.27 Extruded profiles DIN1748 T.1 (02/83)5.1.28 Forgings DIN EN 586-2 (U/94)5.1.29 Die forgings DIN1749 T. 1 (12/76)5.1.30 Hand forgings DIN 17606 (12/76)5.1.31 Cast Sand castings DIN EN1706 (06/98)5.1.32Aluminum alloysPermanent mould castings DIN EN1706 (06/98)5.1.33 Investment castings DIN EN1706 (06/98)5. 1.34 High pressure die castings DIN EN1706 (06/98)5.1.35 Casting alloys for general applications DIN1725 T. 2 (02/86)5. 1.36 Alloys with special mechanical properties DIN1725 T. 2 (02/86)5. 1.37 Alloys for special applications DIN1725 T. 2 (02/86)5.1