Calcul Fatigue Resistance Materiaux

- -- ---- - I, ANALYTICALSTRENGTH ASSESSMENT 5t h Edition VDMA Verlag I I Forschungskuratorium II Maschinenbau FKM-Guideline ANALYTICAL STRENGTH ASSESSMENT OF COMPONENTS IN MECHANICAL ENGINEERING 5 th , revisededition,2003, English Version Translation by E. Haibach Title of the originalGerman Version: RECHNERISCHERFESTIGKEITSNACHWEIS FURMASCHINENBAUTEILE 5., iiberarbeitete Ausgabe, 2003 Editor: Forschungskuratorium Maschinenbau(FKM) Postfach71 0864, D - 60498 Frankfurt / Main Phone *49 - 69 - 6603 - 1345 (c) 2003 byVDMA VerlagGmbH Lyoner StraBe 18 60528 Frankfurt am Main www.vdma-verlag.de All rights reserved AIle Rechte, insbesondere das Recht der Vervielfaltigung und Verbreitung sowie der Ubersetzung vorbehalten. Kein Teil des Werkes darfin irgend- einer Form (Druck, Fotokopie, Mikrofilm oder anderesVerfahren) ohne schriftliche Genehmigung des Verlages reproduziert oder unter Verwendung elektronischer Systeme gespeichert, verarbeitet, vervielfaltigt oder verbreitet werden. ISBN 3-8163-0425-7 3 This FKM-Guideline was elaborated under contract between Forschungskuratorium Maschinenbau e. V. (FKM), Frankfurt / Main, and IMAMaterialforschung und Anwendungstechnik Gmhfl, Dresden, as contractor in charge, by Dr.-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 fur Maschinelle Anlagentechnik undBetriebsfestigkeit, and it was discussed among experts from industry and research institutes in the FKM expert group"Strength of components" . Financial grants wereobtainedfromthe"Bundesministerium fUrWirtschaft (BMWi, Bonn)"through the "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 experts involved. Terms of liability The FKM-Guideline is intended toconform with the state of the art. It has been preparedwiththenecessarycare. The user isexpectedtodecide, whetherthe guidelinemeetshisparticular requirements, and toobserve appropriate care in itsapplication. Neither the publisher nor the editor, the involved experts, or the translator shall be liable tothe purchaser or any other personor entitywith respect toany liability, loss, or damagecausedor allegedtohavebeencaused directly or indirectly by this guideline. Preface to the English Version of the 5 th Edition. For engineers concerned with construction and calculation in mechanicalengineering or in related fields ofindustrytheFKM-Guidelineforanalytical strength assessment isavailablesince1994. Thisguidelinewas elaborated by an expert group "Strength of components" of the "ForschungskuratoriumMaschinenbau (FKM), Frankfurt/Main," with financial support by the Bundesministerium fur Wirtschaft (BMWi), by the "Arbeitsgemeinschaft industrieller Forschungsvereini- gungen 'OttovonGuericke" andby the"Forschungs- kuratorium Maschinenbau. Based onformer TGL standards and on the former guideline VDI 2226, and referring to more recent sources it was developed to the current state of knowledge. The FKM-Guideline - is applicableinmechanical engineering and in related fields 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 relevant influences, -describestheassessment of thestaticstrengthandof the fatigue strength, the latter according to an assessment ofthefatigue limit, of theconstant amplitudefatigue strength, or of thevariable amplitudefatiguestrength according to the service stress conditions, - isvalidforcomponentsfromsteel, cast steel, orcast ironmaterialsat temperatures from -40°C to 500 °C, as wellas forcomponentsfromaluminumalloys andcast aluminum alloys at temperatures from -40°C to 200 °C, - is applicable for components produced with or without machining, or by welding, - allows an assessment in considering nominal stresses as well as local elastic stresses derived from finite element or boundary element analyses, from theoretical mechanics solutions, or from measurements. A uniformlystructuredcalculationprocedure applies to all of these cases of application. The calculation procedure is almost completely predetermined. The user has to make some decisions only. The FKM-Guideline is a commented algorithm, consistingof statements, formulae, andtables. Mostof the included figures have an explanatory function only. 4 Textual declarations are given where appropriate to ensure a reliable application. Itscontent complieswiththestateof knowledgeto an extend that maybe presented in a guideline and it enables quite comprehensive possibilities of calculation. The employed symbols are adapted to the extended requirements of notation. The presented calculation procedure is complemented by explanatory examples. Practically the described procedure of strength assessment shouldberealizedbymeans of asuitable computer program. Presently available are the PC computer programs "RIFESTPLUS" (applicable for a calculation usingelastically determined local stresses, in particular with shell-shaped(2D) or block-shaped(3D) components) and "WELLE" (applicable for a calculation using nominal stresses as it is appropriate in the frequently arising case of axles or shafts with gears etc). The preceding editions of the FKM-Guideline observed a remarkably great interest from which the need of an up to date guideline for analytical strength analyses becomesapparent. Moreover theinterest ofuserswas confirmed bythe well attended VDI conferences on "Computational Strength Analysis of Metallic Components", that wereorganizedfor presentationof the FKM-Guideline at Fulda in 1995, 1998 and 2002. Thecontents-relatedchangesintroducedwiththethird edition from 1998 were mainly concerned with the consideration of stainless steel and of forgingsteel, with thetechnologicalsize factor, withthe section factor for assessingthestaticstrength, withthefatigue limit of grey cast iron and of malleable cast iron, with additional fatigueclasses of welded structural detailsandwiththe local stressanalysisfor weldedcomponents, withthe specification of anestimateddamagesumsmaller than one for the assessment of the variable amplitudefatigue strength, with the assessment of multiaxialstresses, and with the experimental determination of component strength values. Anessentialformal changeinthethirdeditionwasa new textual structure providing four main chapters,that describe theassessment of thestaticstrengthorof the fatigue strength with either nominal stresses or local stresses, respectively. For easeof application each of these chapters gives a complete description of the particularcalculation procedure, although thisresults in repetitions of the same or almost the same parts of text in the corresponding sections. Themajorchangein the forthedition from 2002 is the possibilityof consideringstructural components made from aluminum alloys or cast aluminum alloys by applying the same calculation procedure that was developed for components from steel, cast steel and cast iron materialsso far. Thedecisionsnecessary toinclude aluminummaterials werederivedfromliteratureevaluations. It hadtobe recognized, however, that some of the relevant factors of influence were not yet examined with the desirable clearness or thatavailable results could not be evaluated objectively due to large scatter. In these cases the decision was based on a careful consideration of substantial relations. Concerning an analytical strength assessment of components from aluminum alloys or from cast aluminumalloys this guideline is delivered to the technical communitybysupposingthatforthetime being it will be applied withappropriate cautionand with particular reference toexistingexperience so far. The involvedresearch institutes andthe"Forschungs- kuratoriumMaschinenbau(FKM)" will appreciateany reportson practical experienceas well as any proposals for improvement. Further improvements may also be expected from ongoingresearchprojectsconcerningtheprocedureof static strength assessment using local elasticstresses, Chapter 3, and the fatigue assessment of extremely sharp notches. Last not least the fifth edition of the FKM-Guideline is a revision of the forth edition with several necessary, mainly formal amendments being introduced. It is presented in both a German version and anEnglish version with the expectation that it might observesimilar attention as the preceding editions on a broadened international basis of application. 5 Notes of the translator ThisEnglishtranslationis intendedto keep as close as possible to theoriginal Germanversion,but by usinga common vocabulary andsimplesentences. If thegiven translationisdifferent fromaliteral one, thetechnical meaning of the sentence and/or of the paragraph is maintained, however. The translation observes an almost identical structure of theheadlines,of the chapters, of theparagraphs andof the sentences, and even of the numbering of the pages. Also the tables and the figures as well as their numbering andheadlines areadaptedastheyare, whileonlythe verbal terms have been translated. In particular the original German notation ofthe mathematicalsymbols, indicesandformulas, as well as their numbering, has not been modified in order to insure identity with the German original in this respect. The applier of this guideline is kindlyaskedto accept the moreor lessunusual kind ofnotationwhichis duetothe needofclearlydistinguishingbetweena great number of variables. Inparticular theapplier is pointedto thespeciality, that a comma ( , ) is used with numerical values instead of a decimalpoint ( . ), hence 1,5 equals1.5 for example. . Forupdates and amendments see www.fkm-guideline.de 6 References /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 Working GroupXIII-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 Proceedings Festigkeitsberechnung 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 2 nd Edition ofthe FKM-Guideline 7 Contents Page 5 Appendices Page 0 General survey 5.1 Material tables. 131 0.1 Scope 9 5.2 Stress concentration factors 178 0.2 Technical background 5.3 Fatigue notch factors 187 0.3 Structure andelements 5.4 Fatigue classes (FAT) for welded components of structural steel andof 1 Assessment of the static strength aluminum alloys 195 using nominal stresses 5.5 Comments about the fatiguestrength 1.0 General 19 of welded components 209 1.1 Characteristic stress values 5.6 Adjusting the stress ratio of a stress 1.2 Material properties 22 spectrum to agree with that of theS-N curve 1.3 Design parameters 30 and deriving a steppedspectrum 216 1.4 Component strength 33 5.7 Assessment using classes of utilization 218 1.5 Safety factors 34 5.8 Particular strength characteristics of 1.6 Assessment 36 surface hardened components 222 5.9 An improvedmethod for computing the 2 Assessment of the fatigue strength component fatiguelimit in the case of using nominal stresses synchronous multiaxial stresses 223 2.0 General 41 5.10 Approximate assessment of the fatigue 2.1 Parameters of the stress spectrum strength in the case of non-proportional 2.2 Material properties 47 multiaxial stresses 226 2.3 Design Parameters 50 5.11 Experimental determination of 2.4 Component strength 57 component strength values 227 2.5 Safety factors 68 5.12 Stress concentration factor for a substitute 2.6 Assessment 70 structure 230 3 Assessment of the static strength 6 Examples using local stresses 6.1 Shaft with shoulder 231 3.0 General 73 6.2 Shaft with V-belt drive 236 3.1 Characteristic stress values 6.3 Compressor flangemade of grey 3.2 Material properties 76 cast iron 241 3.3 Design parameters 85 6.4 Welded notched component 245 3.4 Component strength 89 6.5 Cantilever subjectto two independent loads 250 3.5 Safety factors 90 6.6 Component made of a wrought 3.6 Assessment 93 aluminum alloy 256 4 Assessment of the fatigue strength 7 Symbols and basic formulas using local stresses 7.1 Abbreviations 259 4.0 General 97 7.2 Indices 4.1 Parameters of the stress spectrum 7.3 Lower case characters 4.2 Material properties 103 7.4 Upper case characters 260 4.3 Design parameters 106 7.5 Greek alphabetic characters 261 4.4 Component strength 113 7.6 Basic formulas 262 4.5 Safety factors 125 4.6 Assessment 127 8 Subject index 263 8 9 oGeneral survey 1Subject of Chapter 5.11"Experimental determinationofcomponent strengthvalues"is nottherealizationofanexperimental assessment of strength, but the question how specific and sufficiently reliable component strength valuessuitable for the general procedure of strength assessment may be derived experimentally. 2Inparticular, what critical pointsof theconsidered cross-sections or component. If anapplication of theguideline is intended outside the mentionedfieldofapplicationadditional specifications are to be agreed upon. Theguideline is not valid if an assessment of strength is required according to other standards, rules or guidelines, or if more specific design codes are applicable, as for example for bolted joints. Theguideline is valid forcomponents producedwithor withoutmachiningorby weldingof steel, of ironor of aluminummaterials that are intendedfor use under normal or elevated temperature conditions, and in detail - for components withgeometrical notches, for components with welded joints, for staticloading, - for fatigue loading withmore than about 10 4 constant or variable amplitude cycles, - for milled or forgedsteel, also stainless steel, cast iron materials as well as aluminum alloys or cast aluminum alloys, - for component temperatures from- 40°Cto 500°C for steel, from- 25°C to 500°C for cast iron materials and from- 25°C to 200°C for aluminum materials, - for a non-corrosive environment. This guideline is validfor components inmechanical engineering and in related fields of industry. Its application has to be agreedbetween the contracting parties. For components subjected to mechanical loadings it allows an analytical assessment of the static strength andof the fatiguestrength, the latter as an assessmentof the fatigue limit, of the constant amplitude fatigue strengthor of the variableamplitudefatigue strength, according to the servicestress conditions. Other analytical assessments, for example of safety against brittlefracture, of stability, or of deformation under load, as well as an experimental assessment of strength * 1 , are not subject of thisguideline. It is presupposed, that the components are professionally produced with regard to construction, material and workmanship, andthattheyarefaultless inatechnical sense. 12 11 13 14 15 16 13 Page 9 10 Contents 0.3.0 General 0.3.1 Procedure of calculation 0.3.2 Service stresses 0.3.3 Methods of strength assessment 0.3.3.0 General 0.3.3.1 Assessment of the staticstrength usingnominal stresses, Chapter 1 0.3.3.2 Assessment of the fatigue strength usingnominal stresses, Chapter 2 0.3.3.3 Assessment of the staticstrength using local stresses, Chapter 3 0.3.3.4 Assessment of the fatiguestrength using local stresses, Chapter 4 0.3.4 Kindsof components 0.3.4.0 General 0.3.4.1 Rod-shaped (lD) components 0.3.4.2 Shell-shaped (2D) components 0.3.4.3 Block-shaped (3D) components 0.3.5 Uniaxial and multiaxial stresses 0.3.0 General 0.2 Technical Background 3 Usually this probability can hardly be quantified, however. Basis of theguideline arethereferenceslisted onpage 7, inparticulartheformer TGL-Standards, theformer Vlrl-Guideline2226, aswell asthe- regulationsof DIN 18 800, the IIW-Recommendations and Eurocode 3. Moreover the guideline was developed to the current stateof knowledgeby taking intoaccount theresults of more recent investigations. 0.3 Structure and elements An assessment of the static strength is required prior to an assessment of the fatiguestrength. Before applying the guideline it has to be decided - what cross-sections or structural detailof the 2 component shall be assessed * and what service loadings are to be considered. The serviceloadingsare tobedeterminedonthesafe side,that is, witha sufficient probability theyshould be higher than most of the normally occurring loadings *3. Thestrengthvalues are supposed tocorrespondtoan anticipated probability of 97,5% (average probability of survival Po =97,5 %). lRo2 EN.dog oGeneral survey 0.1 Scope 10 oGeneral survey 0.3.1 Procedure of calculation Figure 0.0.2 Procedure of calculation for an assessment of the fatigue strength. At the assessment stage (box at bottom of either Figure) thecharacteristicvaluesofservicestressoccurringin the component (box at top on the left) and the component strength values derived from the mechanical material propertiesandthedesignparameters (middle column) arecompared by includingtherequiredsafety factors (box at bottomon the right). In specifying component fatiguestrengthvaluesthemeanstress and thevariableamplitudeeffects areregardedasessential factors of influence. The assessment of strength is successful if the degreeof utilization is lessor equal 1,00, wherethedegree of utilizationisdefinedby the ratio of the characteristic service stress to the component strength 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 the individual boxes from top to bottom illustrate the sequential procedure of calculation. 0.3.2 Service stresses For an application of the guideline the stresses resulting from the service loadings have to be determined for the so-called reference point of thecomponent, that isthe potential point of fatiguecrackinitiationat thecross- section or at the component under consideration. In case ofdoubtseveral referencepointsareto beconsidered, for example in the case of welded jointsthe toe and the root of the weld. There is a need to distinguishthenames andsubscripts of the different components or types of stress, that may act in rod-shaped (lD), in shell-shaped (2D) or in block-shaped (3D) components, respectively, Chapter 0.3.4. Thestresses aretobe determinedaccordingtoknown principles and techniques: analytically according to elementary or advanced methods of theoretical mechanics, numericallyafter thefiniteelement orthe boundary element method, or experimentally by measurement. All stresses, except the stress amplitudes, are combined with a sign, in particular compressive stresses are negative. To perform an assessment it is necessary to decide about the kindof stress determinationforthereference point considered: The stresses can be determined as nominal stresses*5 (notation S and T), as elastically determined local stresses, effective 6 notch stresses or structural (hot spot) stresses * (notation o and r). Safety factors Safety factors -- Sequential procedure of caJc.ulation Sequential procedure of calculation Component forzeromean stress : ., Component fatigue strength i I I J Component fatigiielimlt for-the actualmean stress Characteristic service Theprocedureofcalculationforanassessmentof the staticstrengthis presentedinFigure0.0.1, thealmost identical procedure for an assessment of the fatigue strength in Figure 0.0.2*4. Figure 0.0.1 Procedure of calculation for an assessment of the static strength. 4Asurveyonthe analytical proceduresof assessment basedonthe equations 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 a stress concentration factor. In thecase ofwelded jointseffective notch stressesare appliedto the assessment of the fatigue strengthonly. Structural stresses, alsotermedgeometrical or hot spot stresses, are normallyinusewithwelded joints only. Forfurther information see Chapter 5.5. 11 oGeneral survey Figure 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 the static strength may be different from the maximum and minimum stresses for theassessment of thefatiguestrength, that aredeterminedfrom the largest amplitude and the related mean value of a stress spectrum. 0.3.3.1 Assessment of the static strength using nominal stresses, Chapter 1 Relevant nominal characteristicservicestressesare the extreme maximum andextrememinimum values of the individual 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 and theyieldstrength (yieldstress or 0.2proof stress) as well as the strength values for shear derived from these. Atechnological size effect is taken into account if appropriate. The influenceofanelevatedtemperature on the material properties - strength at elevated temperature and creep strength, yield strength at elevated temperature andI% creep limit - is allowed for by means of temperature factors, Chapter1.2. Designparametersarethesection factors, by whichan experienced partial plasticity of the component is allowed .accordingtoyieldstrength, type of loading, shapeofcross-section, andstress concentration factor. Fromthe section factor and from further parametersan overall design factor is derived, Chapter1.3. The nominal values of the static component strength are derived from the tensile strength, divided by the respective overall design factor, Chapter1.4. As commonin practice the safetyfactor against the tensile strength is 2,0. For materials with a yield strength lessthan 0,75times the tensile strengththe safety factoris1,5 against the yieldstrength, however. Underfavorableconditionsthesesafety factors may be reduced, Chapter 1.5. The assessment is carried out by proving that the degree of utilization is less or equal 1,00 . The degree of utilization for an individualstress component or type of stressistheratioofits nominal characteristicservice stress value, divided bythe allowable nominal static component strength value, which follows from the nominal static component strengthdivided by the safety factor. If there areseveral stress componentsor types of stress their individual degreesofutilizationarecombinedto obtainanentire degreeofutilization. The interaction formula to be applied to that combinationallows for the ductility of the material in question, Chapter1.6. For welded components the assessment of the static strengthhasto be carriedout forthetoe section as for non-welded components, and for the throat section with I Fatigue strength' assessment ~ Fatii:ue strength Nominal stresses . ~ . Staticstrength LNoml?al Nominalstresses ) stresses ;/ Static strength aSseSSlllent ~ ~ . .r"Chapter 3: " 100°C: (1.2.30) Kr,m =Kr,p =1 - 1,5 . 10 -3. (T / °c -100), - for GGG, T > 100°C: 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) >01 T,p, - " - for not age-hardening aluminum alloys: T> 100°C, 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) arevalidfromtheindicated temperature T up to 200°C, andingeneral only, if the relevant characteristic stress does not act on long terms. 2S0 300 TIT. 20.0 High temperature strength Rm,T Rm;T 1 R. 'jm. Cre.ep.Strength Rm.Tl. .1 If,;"' i.I ISO () 5&lliQ Q I .High temperature fatigueslrength O,l 50°C, Figure1.2.3 (1.2.32) 16 There is an insignificant discontinuity at T = 60°C. 17 For stainless steel novalues areknown uptonow. Long-tenn values Long term values of the static strength are R""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 properties 29 1 Assessment of the static strength using nominal stresses The values Tl and arenot explicitlyneededfor an assessment of the static strength, as only the temperature factorsKTl,m andKTt,p are needed. Aluminum alloys For aluminum alloys andt =10 5 hours Krt,m is given by Figure 1.2.4 *20. Figure 1.2.4Temperaturefactor Krt,m Rm,Tt I R.nfor aluminum alloys andt =10 5 hours. Thegivencurveis thesame as in Figure1.2.3, except that the factor (1 / jm ) isdifferent. Eq.(1.2.35) apply to temperatures from approximately 350°C upto 500°C,but only forstresses acting on long terms. Ingeneral theydonot apply to temperatures below about 350°C *19. 1 Approximate values, applicable from about 350°Cto500°C. 2 Not valid for stainless steel. Cast iron GS6 GGG7 materials Creep strength aTt.m -7,524 2,50 bTLm 9,894 - 1,83 CTtm -3,417 0 em 19,57 20 1% Creep limit aTtn - 10,582 0,12 bTt.D 8,127 1,52 cTt.n - 1,607 - 1,28 Co 35,76 18 3 Initially for St38,R m = 360MPa, similar toSt37. 4 Initially for H 52, R m = 490MPa, similar to StE 355; theabsolute values Rill,Tt are thesame asfor St38. 5Initially for C45N(normalized) with R m =620 MPa. For C35N, with R m = 550 MPa the constants -3,001and -3,252aretobereplaced by-2,949and -3,198. The absolute valuesRill,Tt arethe same asfor C45N. Table 1.2.7 Constants aTt,m, ..., Cp Steel Non- Fine grain Heat- alloyed structural treatable- structural steel steel steel Creep strength aTLm - 0,994 -1,127 - 3,001 bTLm 2,485 2,485 3,987 cTt.m -1,260 -1,260 - 1,423 em 20 20 24,27 1% Creep limit aTt.n - 5,019 - 6,352 - 3,252 bTLn 7,227 9,305 5,942 Cn n - 2,636 - 3,456 - 2,728 Cn 20 20 17,71 200 300 400 TrC 1\ \ \ \ : I \..t- RT 100 o constants, Table 1.2.7, operation time in hours h atthe temperature T. aTt,m, ..., Cp t 0,6 1,0 R""TI I R", 0,8 0,4 Steel and cast iron materials DependingonthetemperatureTandonthe operation time t at that temperature the temperature factorsKrt,m and KTt,p apply, Figure 1.2.2*18 2 K =10(aTt,m+ bTt,m . Pm+ CTt,m . Pm) Tt,m , (1.2.35) 2 K =lO(aTt,p+ bTt,p . Pp+ CTt,p . Pp) np , Pm =10 -4. (T / C + 273)'(C m + 19(t/h)), P p =10 - 4.(T / C + 273). (C m +19(t/ h)), 0,2 18 Larsen-Miller-parameter P andLarsen-Miller-constant C. 19 Because the values would be unrealistic for temperatures T < 350°C, where thevalues KT,m and KT,p arerelevant instead. 20Thetemperaturefactor Kt,pis not defmed up to now. It maybe assumed, however, as itis essential for the assessment of the static strength, thattheterm R p, 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 to derive the values of KTt,mandKTt,paccording to temperature T and operation time Thas notbeen specified for aluminum alloys uptonow. 6 Initially for GS-C 25 with R m = 440 MPa. -c-7 Initially for GGG-40 with R m =423 MPa. 1.3 Design parameters 30 1 Assessment of the static strength usingnominal stresses Accordingtothischapter thedesignparameters areto be determined. 1.3.0 General 1.3 Design parameters Contents 1.3.0 General KSK,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) welded components the design factors for normal stresses in the directions x and y as well as for shear stress are 1.3.1.2 Welded components For welded componentsthe design factorsaregenerally tobedeterminedseparatelyfor thetoesectionandfor the throat section. For the toe section the calculationis to be carried out as for non-welded components. For the throat section of rod-shaped (lD) welded components the design factors for axial (tension or compression), for bending, for shear andfor torsional stress are Page 30 31 11mEN.dog Design factors General Non-welded components Welded components Section factors Weld factor a.w 1.3.1 1.3.1.0 1.3.1.1 1.3.1.2 1.3.2 1.3.3 (1.3.5) 1.3.1 Design factors 1.3.1.0 General Non-welded and welded components are to be distinguished. They can be both rod-shaped (lD) or shell-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, forcompression and for shear stress. 1.3.1.1 Non-welded components The design factors of rod-shaped (lD) non-welded components for axial (tension or compression), for bending, for shear,and for torsional stress are For tensionandtensioninbendinga.wfor tensionis to be applied. For compression and compression in bendinga.wforcompressionis to be applied. Forshear and for torsion a w 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-welded components for normal stresses in the directions x and y as well as for shear stress are KSK,x=I, KsK,y =I, KsK,s = 1. (1.3.2) 1.3.2 Section factors Thesection factorsnpl,b andnpl,t allow for the influence of the stress gradient in bending and/or torsion in connectionwiththe shape ofthe crosssectiononthe staticstrength of components, Figure 1.3.1. Theyserve to make best use of the load carryingcapacity of a component byaccepting someyielding as the outside fiber stress exceeds the yield strength. An essential condition is the existence of a stress gradient normalto the surface of the component, Figure 1.3.1. It hasto beobserved, however,that thederivedsection factors only apply to thenotched section considered and not to the component as a whole. Therefore other sections may have tobe considered in addition, see Chapter1.0 and Figure1.0.1. 1 KsK,zd = =1 means,that the value ofthe related section factor isnpl,zd = =1. 1.3 Design parameters 1-SSK,b (npl,b) 1--R p 31 1 Assessment of the static strength using nominal stresses For other types ofsteel, GSandGGG*4 the section factors for tension or compression, for bending, for shear, and for torsion are*5 *6 npl,zd =1, npl,b = MIN (JRp,max / R p ; Kp,b ), npl,s=1, npl,t = MIN (JRp,max/ R p ; Kp,t), t Rp,max n, Kp,b,Kp,t constant, 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 for bending of anotched bar, for instance. Bendingmoment Mb, yieldstrengthR p , staticcomponent strength for bending SSK,b, section factor npl,b= SSK,b I R p . Light straight line: fictitious distribution of the stress calculated elastically. Solid angular line: real stress distribution when providing elastic ideal-plastic material behavior. Surface hardened Components Thesection factorsarenot applicable if thecomponent hasbeensurfaceorcasehardened, seeTable 2.3.5*2 npl,b, ... = I (1.3.6) Steel and cast iron material For austenitic steel in the solution annealed condition *3 the section factors for tension or compression, for bending, for shear, and for torsion are Table 1.3.1 Constant Rp,max1. Kind of material Steel, GS GGG Aluminum alloys. Rp,max'/ MFa 1050 320 250 -c- 1 Constant defining an upper bound value of the sectionfactor dependingon the kind of material. Table 1.3.2 Plastic notch factors Kp,band Kp,t . Cross-section Bending Torsion Kp,b Kp,t rectangle 1 1,5 - circle 1,701,33 circular ring 1,27 1 I-section or box - (1.3.15) npl,zd = I, npl,b =Kp,b , npl,s =1, n p1,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 is 3 K p t = 1,33' 1- (dID) , (1.3.14) , 1-(dID)4 d, D inner and outer diameters. 1- (b I B) . (h I H)2 K p b = 1,5· --'-----'---'---'-:- , 1- (b I B)· (h IH)3 b, B inner and outer width, h, H inner and outer hight. 2Becausetheplasticityof ahardsurfacelayer-forexample asa result of case hardening - islimited, it mayobservecrackswhen yielding occurs, particularly at notches where the calculationof nominal stress neglects the stress and strain concentration. Possibly this rule is too far on the safe side, as npl =1,1 is allowedfor casehardenedshafts accordingto the recent DIN743 (launchedin 2000). 3 Because of the high ductility of austeniticsteel in the solutionannealed conditionthe plastic notch factors Kp,b and Kp,t are relevant and not the givenmaterial dependentsectionfactors. 4 GT and GO are not consideredhere becausethe assessmentof the static strengthhas to be carriedout usinglocal stressesfor these materials. 5 MIN means that the smaller value fromthe right side of the equationis valid. 6 Upper and lower bound values of the section factors are the plastic notch factor and 1,00 1.3 Design parameters Aluminum alloys Forductilewroughtaluminum alloys(A2 12,5 %)the section factorsare to be determined from Eq (1.3.9)*7. 1.3.3 Weld factorU w Theweld factor Ci.waccountsfortheeffect of a weld. It appliesto the throat sectionof welded componentsonly, Tab. 1.3.3 *8. Table 1.3.3 Weld factor Ci.w~ 1 . 32 1 Assessment of the static strength using nominal stresses Joint Weld quality Typeof RmS R m > stress 360 MPa 360Mua full all Compression penetration ~ 2 weld verified 1,0 1,0 or with Tension 10 back weld not verified partial all Compression 0,95 0,80 penetration or 0,80 or fillet Tension weld all all Shear welds butt weld Tension 0,55 - ~ 3 055 ~ 1 Accordingto DIN 18 800 part 1, Table 21 and Eq. (75). ~ 2 For aluminumalloys(independent of Rm ) thevalues typedin in boldface should be applied for the time being. ~ 3 Butt weldsofsectionalsteelfromSt 37-2or USt37-2with a product thickness t> 16 mm. 7Less ductile aluminum alloys (A 12,5%). For non-ductile wrought aluminium alloys (as well asfor cast aluminium alloys, and for GT or GG) the assessment of the static strength istobe carried out according toChapter 3. 10For example a tension stress fromaxialloading and a tension stress frombending acting at thereferencepoint, wherebothresult fromthe same single extemalload affecting the component 11 Forexample a tension stress fromaxial loadingand a compression stress from bending acting at the reference point, where both result from the same single external load affecting the component. 12 Stress components acting opposingly may cancel each other inpart or completely. 38 1.6 Assessment 1 Assessment of the static strength using nominal stresses aSK,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 with Smin,ex,zd , Smin,ex,b, Tmin.ex,s and Tmin.ex.t areto beincluded in this comparative evaluation. In the general case - without knowing whether the stresses act unidirectionally or opposingly *13 - the degreesof utilizationaretobeinserted intoEq. (1.6.6) bothwithequal or withdifferent signs; thenthe least favorable case is relevant. (1.6.9) Smax,ex,y aSK,y = ::;; 1, SSK,y / jges Smax,ex,x aSK,x = s1, SSK,x / jges Tmax,ex s 1· aSK,s = , T SK / jges Smax,ex,x ... extreme maximum stresses according to type of stress; the extreme minimum stresses, Smin,ex,x ... , are to be considered inthe same way as the extreme maximum stresses,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 (or zero). Ingeneral tension and compression stresses are to be considered separately. For shear stress the highest absolute value is relevant. Shell-shaped (2D) welded components For the toe section of shell-shaped (2D) welded components the calculationis tobe carriedout asfor shell-shaped (2D)non-welded components. For the throat section of shell-shaped (2D) welded components the degrees of utilization for normal stresses inthe directions xandyas well as for shear stress follow from the equivalent nominal stresses, Chapter 1.1.1.2: 1.6,2 Shell-shaped (2D) components 1.6.2.1 Individual types of stress Shell-shaped (2D) non-welded components The degrees of utilization of shell-shaped (2D) non- weldedcomponentsfor the types of stress like normal stress in thedirections x and y as wellas shear stress are (1.6.8) aSK,Swv = Rod-shaped (1D) welded components For the toe section of rod-shaped (10) welded components the calculationis tobecarriedout asfor rod-shaped (lD) non-welded components. For the throat section of rod-shaped (10) welded components thedegree of utilization for combined types of stresses (or loadings) is *14 Rulesof sign: If theindividual typesof stress (tension or compression and bending, or shear and torsion, respectively)always act unidirectionally at thereference point*10, thedegrees of utilization aSK,wv,zd and aSK,wv,b and/or aSK,wv,s andaSK,wv,t are tobe insertedintoEq. (1.6.8) with equal (positive) signs (summation); then the result will be on the safe side. If they act always opposingly, however, *11, theyareto be inserted into Eq. (1.6.8) with different signs (subtraction)*12. In the general case - without knowing whether the stresses act unidirectionally or opposingly '13 - the degrees of utilizationaretobeinserted intoEq. (1.6.8) bothwithequal or withdifferent signs; thenthe least favorable caseis relevant. Moreover the degrees of utilization calculated with Smin,ex,wv,zd, Smin,ex,wv,b, Tmin,ex,wv,s andTmin,ex,wv,t areto be included inthis comparative evaluation. S a - max,ex,wv,x O. Theequationsarevalid forroundmembers, approximately they 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,zd SWK,b fatigue strength value for completely reversed axial stress of the unnotched test specimen of the diameter do , fatigue strength value for completely reversed bending stress of the notched component of the diameter or width d. Kfb in bending is dependent on the notch radius r and on the diameter or width dof the notch net section. Kf,t for torsion in analogy. The .defmitionof the fatigue notchfactor for bending derivedfrom experimental data - under the provisionthat the unnotchedandthe notched 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 G cr (r) applies to axial stressandto bending stress; nevertheless thereis adifference forbending because of the Kt-KfTatio ncr(d)additionally contained in Eq. (2.3.10) and (2.3.18). The relatedstress gradientapplies to shearstress andto torsion stress; nevertheless there is a difference for torsion because of the Kt-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, for bending, for shear andfor torsional stressof therod- shaped(lD) non-weldedstructural detailspresented in Chapter 5.3are to be computed from the experimentally derived fatigue notch factors of test specimens given there, and from the respective Kf -K, ratios. In particular *II K - K (d) ncr (rp ) f,zd - f,zd p' --(-)- , ncr r Kf,b (dp) = SW,b,P / SWK,b,P, (2.3.21) SW,b,P fatigue limit for completely reversed bending stress of the unnotched test specimen of diameter dp, SWK,b,P Fatigue limit for completelyreversed bending stress of the notched test specimen of diameter dp. Kf,b is dependent on the notch radius rp and on the diameter or width of the notch net section d. Kf,t for torsion in analogy. 13The fatigue notchfactors giveninChapter 5.3 are applicableto components from steel without surface treatment. Additionally, however, a procedure for components being surface hardened and for components made 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 specified in Chapter 5.3.A possible incorrectness thatmay occur will be reduced by the division of ncr(rp ) / ncr(r). 2.3 Design parameters 54 2 Assessment of the fatigue strength using nominal stresses Caution: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 of alternating compression stress, Rzd = -1 is the completely reversed stress, Rzd >-1 is the field of alternating tension stress. Field III: 0 ND,u (Steel and cast iron material) Incaseofacomponent constant amplitude S-Ncurve model I ( horizontal for N > ND,cr or slope kD,o =(0) the number of cycles N to be computed foran valueSa,zd,l is (2.4.57) [ s )kcr N= {[ A kon - 1 ] . D M + I}' SAK,zd . ND,cr , a,zd,l where A _ [Sa,zd,l )k cr-1 [ZI j Z2] k - -- . -+ L- on SAK,zd Nl v=m N2 [ ) kcr - 1 [S )k cr-1 Zl = _ Sa,zd,m , a,zd,l a.zd.l Z2 =)k cr-1 _ [S;,Zd,V+1 )k cr-1 a,zd,l a,zd,l m-1 h. [S d.i )k cr Nl=L -.: i=l H Sa,zd,l For the summation of the term Z2, Eq. (2.4.60), it is to be observed that Sa,zd,j+l =O. N number of cycles of the component constant amplitude S-N curve, Chapter 2.4.3.2, ND,cr number of cycles at knee point of the component constant 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-N curve 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 became known as the modified version orthe Haibach method ofMiner's rule. 9Theconsistent version of Miner'sruleallowsfor thefact, thatthe component fatigue limit will decrease as the damage sum increases. The decrease applies tocomponent constant amplitude S-N curvesmodel I as well as tomodel II for ND,s 10 6 . Using the consistent version of Miner's rule the variable amplitude fatigue strength factor is to be computes! iteratively for differing values ofSa,zd,l , untila valueN equal to the required total number of cycles N is obtained. The respective value of Sa,zd,l is used to derive the variable amplitude fatigue strength factor. non-welded welded components components Steel, GS, 0,3 0,5 Aluminum alloys GGG, GT, GG 1,0 1,0 Stress spectrum 2:U N(lg) Figure 2.4.4 Elementary version of Miner's rule, com- ponent constant amplitude S-N curve model I, D M =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 , recommended value. Characteristics ofthe stress spectrum according toChapter 2.1, component constant amplitude SoNcurve according toChapter 2.4.3.2. s a (lg) v,Sa.l KBK,zd =1. (2.4.56) If for a component constant amplitude S-N curve model II (slopingfor N>ND,cr )avalueKBK,zdisobtained from Eq. (2.4.53) that is smaller than the value obtained fromEq. (2.4.50) or (2.4.52), thenthe higher value from Eq. (2.4.50) or (2.4.52) is to be used. slope of the component constant amplitude S-N curve 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 component constant 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 model I (horizontal for N> ND,cr ) a value KBK,zd < 1is obtained from Eq. (2.4.53), then the value to be used is 2.4 Component fatigue strength 2.4.3 Component variable amplitude fatigue strength 66 2 Assessment of the fatigue strength using nominal stresses i 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 for differingvalues Sa,zd,1 >SAK,zd, until a..!alue Nequal tothe requiredtotal number of cycles N isobtained. From the respective value of Sa,zd,1 the variable amplitude fatigue strength factor is obtained as Calculation using a classof utilization The variable amplitude fatiguestrength factorKBK,zd is tobedeterminedaccordingtothe appropriateclass of utilization"12, Chapter 5.7. Calculation using a damage-equivalent stress amplitude Whenusinga damage-equivalent stress amplitudethe variable amplitude fatigue strength factor for both constant amplitude S-N curves modelI and model II is KBI100°C, Figure 1.2.2: (3.2.29) KT,m =KT,p = 1-1,7' 10,3. (T/ °C-100), for GS, T> 100 D C: (3.2.30) -3 0 KT,m =KT,p = 1- 1,5 . 10 . (T / C- 100), for GGG, GT and GG, T >100 D C, Figure 3.2.2: K T.m =Kr,p = 1- aT,m. (10 -3. T /DC) 2. (3.2.31) aT,m Constant Figure 3.2.2 Temperature dependent values of the staticstrength of non-alloyed structural steel and of GG plotted forcomparison. Safety factors after Chapter 3.5. Rm,T/R m= KT,m, Rp,T/Rp=KT,p, Rm,Tt / R m = KTt,m, Rp,Tt / Rp = KTt,p' Top: Non-alloyed structural steel with R p / R m =R e / R m =0,65, Rm,T, Rp,T aswell asRm,T1> Rp,Tt fort = 10 5 h, Jm=2,0, jp =Jmt= 1,5 , Jpt= 1,0. Bottom: 00, Rm,T aswell as Rm,Tt fort = 10 5 h, Jm=3,0, jmt =2,4. Eq. (3.2.28) to (3.2.31) are validfromthe indicated temperature T up to 500 DC. For a temperature above 350° Ctheyare valid only, if therelevant characteristic stress does not act onlong terms. Table 3.2.6Constant aT,m. Kind of material GGG GT GG aT,m 2,4 2,0 1,6 o 3.2.2b 100 200300 400 500 Tin ·C 15There isaninsignificant discontinuity at T =60°C. 16For stainless steel no values are known upto now. 3.2 Material properties 83 3 Assessment of the static strength using nominal stresses (3.2.34) Thevalues R""Tt and arenotneededexplicitlyfor an assessment of the static strength, as only the temperature factorsKTt,m andKTt,p areneeded. Steel and cast iron material For GG a yield strength value is not defined and therefore the value Rp,Tt doesnot exist. DependingonthetemperatureTandontheoperation time tat that temperature the temperature factorsKTt,m and KTt,p apply, Figure 3.2.2*17 2 K =10(aTt,m+bTt,m . Pm+ cTt,m . Pm) Tt,m , (3.2.35) 2 K =lO(aTt,p+bTt,p ·Pp+cTt,p .pp) np , Pm = 10 -4. (T / C + 273)' (C m + 19(t/ hj), P p =10 - 4. (T / C + 273). (C m + 19(t / hj), aTt,m, ..., Cp constants, Table 3.2.7, t operation time inhours h at the temperature T. Eq. (3.2.35) applies to temperatures from approximately 350°C upto 500°C, butonlyforstresses actingonlong terms. In general they do not apply to temperatures below about 350°C*18. Long-term values Long term values of the static strength are R""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 temperaturc strengthRm,T Ri'D;'l'l R. 'Jm CrecpStrellgth . IR..Tt Rm,Tt 1 }fn7'jlllt 0,5 I Higll temperature fatigueslrength 0,1 .__ 6W;.d.T.00W••d 1 crw.>.d . R.,.jo Aluminum alloys According tothetemperature Tthetemperature factors KT,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> 100°C, 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 indicated temperatureTupto200°C, andingeneral only, if the relevant characteristic stress doesnotact onlongterms. o 1.2.3 o so 100 150 200 250 100 T/'C Figure 3.2.3 Temperature dependent values of thestatic strength of aluminum alloysplotted for comparison. Static strength values: Rm,T/Rm=KT,m =Rp,T/Rp=KT,p' Rm,Tt/ R m =KTt,m =Rp,Tt / Rp=KTt,p . Rm,Tt,Rp,Tt for t = 10 5 h. Fatigue limit for completely reversed stress (N= 10 6 cycles): 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 temperatures T < 350°C, where thevalues KT,m andKT,p are relevant instead. 3.2 Material properties 84 3 Assessment of the static strength using nominal stresses Aluminum alloys For aluminum alloys andt = 10 5 hoursKTt,m is given by Figure1.2.4*19. Figure 3.2.4Temperature factor KTl,m R.n.Tt/ R.n for aluminum alloys and t =10 5 hours. The given curve is the same as in Figure 3.2.3, except that the factor (1 / jm) is different. \ \ \ \ i i Table 3.2.7 Constants aTt,m, ... , C p Steel Non- Fine grain Heat- alloyed structural treatable- structural steel steel steel Creep strength aTt.m - 0,994 -1,127 - 3,001 b Tlm 2,485 2,485 3,987 CTtm - 1,260 - 1,260 - 1,423 C m 20 20 24,27 1%Creep limit aTt.n - 5,019 - 6,352 - 3,252 bTt.n 7,227 9,305 5,942 cTt.n - 2,636 - 3,456 - 2,728 Co 20 20 17,71 Cast iron GS GGG,GT GG material Creep strength aTtm -7,524 2,50 -1,46 bTtm 9,894 - 1,83 2,36 CTtm - 3,417 ° -0,90 C m 19,57 20 25 1% Creep limit aTtn - 10,582 0,12 - b Tln 8,127 1,52 - CTt.n - 1,607 - 1,28 - C n 35,76 18 - 12,5 %). jm ->1 Consequences of failure jp ->2 severe moderate jmt ->3 ->S jpt ->4 high 2,0 1,75 1,5 1,3 Probability of 1,5 1,3 occurrence of 1,0 1,0 the characteristic low 1,8 1,6 service stress ->6 1,35 1,2 values 1,35 1,2 1,0 1,0 Table 3.5.1 Safety factors jm and jp for steel (not for GS) and for ductile wrought aluminumalloys 91 92 1R35 EN.docl Page 90 General Steel Castironmaterials General Ductile cast iron materials Non-ductile cast iron materials Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys Cast aluminum alloys Global safety factor 3.5.0 3.5.1 3.5.2 3.5.2.0 3.5.2.1 3.5.2.2 3.5.3 3.5.3.0 3.5.3.1 3.5.3.2 3.5.4 3.5.5 3.5 Safety factors 3.5.0 General Accordingto this chapter the safetyfactors are tobe determined *1. Thesafety factorsarevalid under thecondition that the designloadsare reliably determined on the safe side and that the material properties correspondtoan average probability of survival of Po =97,5 % *2. The safety factors may be reduced under favorable conditions, that is depending on the probability of occurrence of thecharacteristic stress valuesin question anddepending on the consequences offailure. The safetyfactors are validbothfor non-welded and welded components. The safetyfactors given inthefollowingarevalidfor ductileandfornon-ductile materials.In thisrespect any typesofsteel areductilematerials, aswell ascast iron materials and wrought aluminum alloys with an elongation A s ~ 12,5 %, while GT, GG and cast aluminumalloys are always consideredas non-ductile materials here. *3 3.5.1 Steel Safety factors applicabletothe tensilestrengthandto the yieldstrength, to the creepstrength andto the creep limitare givenin Table 3.5.1. 1The safety factors in Chapter 1.5 are the same, but with the difference, that non-ductile cast iron materials and non-ductile aluminum alloys are considered here aswell. 2Statistical confidence S=SO %. 3All types of GT, GGandcast aluminumalloys haveelongations As < 12,S% and are considered asnon-ductile materialshere. Wrought aluminumalloyswithelongationsAs< 12,S% are considered asnon- ductilematerials, too. For non-ductilematerialstheassessment of the static strength istobecarried outwith local stresses. ->1referring tothe tensile strength R m ortothe strength at elevated temperature RmT, ->2 referring tothe yield strength R p ortothe hot yield strength R p, T, ->3 referring tothe creep strength Rm,Tt , ->4 referring tothe creep limit R p, Tt . ->Smoderateconsequences of failure of a lessimportant component in the sense of "no catastrophic effects" being associated with a failure;for examplebecause of aloadredistributiontowards othermembersof a statically undeterminate system. Reduction byapproximately IS%. ->6 or onlyinfrequent occurrences of thecharacteristicservicestress values, for example due toanapplication ofproof loads or due to loads during anassembling operation. Reduction byapproximately 10 %. 3.5.2 Cast iron materials 3.5.2.0General Ductile and non-ductile cast iron materials are to be distinguished. 3.5.2.1Ductile cast iron materials Cast iron materials with an elongation A 5 ~ 1 2 , 5 % areconsideredasductile, inparticular all typesof GSandsometypesof GGG(not GTandnot GG). Values of elongation see Table 5.1.12. Safetyfactors for ductilecast iron materials are given by Table 3.5.2. Compared to Table 3.5.1 they are higher because of anadditional partial safety factorjF that accounts for inevitable but allowable defects in castings. The factor isdifferent for castingsthat have been subject to non-destructive testing or have not*4. 4 Inmechanical engineering. cast components areof standard quality forwhich a furtherreduction of thepartialsafetyfactor tojr = 1,0 does not seem possible up tonow. Asafety factor jF = 1,0may beapplied tohigh quality cast components inthe aircraft industry however. Those high quality cast componentshaveto meet special demandsand (cont'dpage91) 3.5 Safety factors 91 3 Assessment of the static strength using localstresses Ductile and non-ductilewrought aluminum alloys are to be distinguished. 3.5.3 Wrought aluminum alloys 3.5.3.0General 20 As ,A3in% 1U12,5 GG 0,5 Aj o 3.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloy with an elongation A~ 12,5 % areconsideredasductilematerials. Values of elongation see Table 5.1.22 to 5.1.30. Thesafety factors forductilewroughtaluminum alloys are the same as for steel, Table 3.5.1. Figure 3.5.1 Value L\j to be added to the safety factors jm and jp, defmed as a function of the elongation As or A3 respectively. Table 3.5.2 Safety factors jm and jp for ductile cast iron materials (GS; GGG withA 5 ~ 12,5 %) -}1 jm Consequences of failure jp severe moderate jmt Jpt castings not subject to non-destructive testing-}2 high 2,8 2,45 2,1 1,8 Probability of 2,1 1,8 occurrence of 1,4 1,4 the characteristic low 2,55 2,2 service stress 1,9 1,65 values 1,9 1,65 1,4 1,4 castings subject to non-destructive testing-}3 high 2,5 2,2 1,9 1,65 Probability of 1,9 1,65 occurrence of 1,25 1,25 the characteristic low 2,25 2,0 service stress 1,7 1,5 values 1,7 1,5 1,25 1,25 3.5.2.2 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=1,4 is introduced to account for inevitable but allowabledefects in castings. -}3 Compared to Table 3.5.1an additional partial safety factor jF=1,25 is introduced, forwhichit is assumedthata higherqualityof the castings is obviously guaranteed when testing. Cast iron materials with anelongation As < 12,5 % (A3 < 12,5 %for GT) are considered as non-ductile materials, inparticularsometypesofGGGas well as alltypes of GT and GG. Values of elongation for GGG andGTsee Table5.1.12or5.1.13. Thevaluefor GG is As = 0 *5. For non-ductile cast iron materials the safety factors fromTable3.5.2 areto be increasedby adding a value L\j, Figure 3.5.1*6: L\j= 0,5 - ~ A 5 /50%. (3.5.2) 3.5.3.1Non-ductile wrought aluminum alloys Wrought aluminum alloy with an elongation A< 12,5 % areconsideredasnon-ductilematerials. Values of elongation see Table 5.1.22 to 5.1.30. For non-ductile wrought aluminumalloys all safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1and Eq. (3.5.2). 3.5.4 Cast aluminum alloys Cast aluminumalloys are always consideredas non- ductile materials. Values of elongationsee Table 5.1.31 to 5.1.38. Forcastaluminumalloysall safetyfactorsfromTable 3.5.2aretobeincreasedbyaddinga valueL\j, Figure 3.5.1and 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 asonthe quality and extent of product testing in order to guarantee little scatter of their mechanical properties. 5ForGGthevaluesJpand Jpt arenotrelevant since theyieldstrength and the creep limit ofGO are not specified. 6 For example thesafety factor JmforGGis atleast jm = 2,0 +O,S = 2,S . (3.S.3) 3.5 Safety factors 3.5.5 Total safety factor From theindividual safetyfactorsthe total safety factor jges is to be derived*7: jges = (3.5.4) KT,m' KT,p R p ' KTt,m' KTt,p n, , 92 3 Assessment of the static strength using local stresses .lm... Kt,m... safety factors, Table 3.5.1 and 3.5.2, temperature factors, Chapter 3.2.5*8. Simplifications Thefollowing simplificationsapplyto Eq. (3.5.4): In the case of normal temperature the thirdand fourthtermhave no relevance*9, and moreover thereis KT,m = K T.p =1 , for Rp / Rms 0,75 the first term has no relevance, for Rp / Rm > 0,75 the second term has no relevance *10, for GG the second and fourthterm have no relevance*11. 7 MAXmeans that the maximumvalue of the four terms inthe parenthetical expression is valid. 8ApplicabletothetensilestrengthR m ortotheyieldstrengthR p to allow for the tensile strength at elevated temperatureT ' the hot yield strength the creepstrength Rm,Tt , or the creeplimit Rp,Tt, respectively' 9 The terms containing the factors KTt,m and KTt,p must not be applied in 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 Assessment 93 3 Assessment of the static strength using nominal stresses 3.6 Assessment Contents 3.6.0 3.6.1 3.6.1.1 3.6.1.2 3.6.2 3.6.2.1 3.6.2.2 3.6.2 3.6.2.1 3.6.2.2 General Rod-shaped (ID) components Individual types of stress Combined types of stress Shell-shaped (2D) components Individual types of stress Combined types of stress Block-shaped (3D) components Individual types of stress Combined types of stress !R36 EN.dog Page 93 94 95 96 strength, O"SK ,..., divided by the total safety factor jges. The degree of utilization is always a positive value. Superposition For stresscomponentsof the sametypeofstressthe superposition is to be carriedout according to Chapter 3.1. If different types of stress likenormalstress andshear stressact simultaneously and if theresulting stateof stress ismultiaxial, see Figure0.0.9 *5, theparticular extrememaximumstresses andtheextrememinimum stresses are to be overlaid as indicated in the following. 3.6.0 General According to this chapter the assessment of the component staticstrengthusinglocal stresses isto be carried out. Ingeneral theassessmentsfor theindividualtypes of stress andfor thecombined stress are to be carried out separately * I *2. Ingeneral theassessmentsfor theextrememaximum andminimumstresses(normal stresses intension and compressionand/or shear stress)aretobecarriedout separately. For steel or wrought aluminumalloys the highest absolute value of stress is relevant *3. The calculation applies to both non-welded and welded components. For welded components assessmentsare generally to be carried out separately for the toe and for the root of the weld as indicated in the following. Degreeof utilization The assessments are to be carried out by determining the degrees of utilizationof thecomponent static strength. In the context of the present Chapter the degreeof utilization is the quotient of the characteristicstress (extremestress O"max,ex, , ...) divided by theallowable static stress at the referencepoint *4. Theallowable static stress is the quotient of the component static I It is a general principlefor anassessment of thestaticstrength to supposethat all types of stressobservetheir maximum(orminimum) values atthe same time. 2Thisisin order toexamine the degrees ofutilization ofthe individual types ofstress in general, and in particular ifthey mayoccur separately. 3 Different in the case ofcast iron materials or cast aluminium alloys with different static tension and compression strengthvalues. 4 The reference point isthe critical point ofthe cross section that observes the highest degree ofutilization. Kindsof component Rod-shaped (lD), shell-shaped(2D)andblock-shaped (3D) components areto be distinguished. Theycan be both non-welded or welded 3.6.1 Rod-shaped (ID) components 3.6.1.1 Individual types of stress Rod-shaped (ID)non-weldedcomponents The degrees of utilization of rod-shaped non-welded components for the different types of stress like normal stress or shear stress are aSK,O' = Ci max, ex ~ 1, (3.6.1) CiSK/ jges a S K , ~ = 'tmax,ex s 1, 'tSK/ jges O"max,ex, , ... extreme maximum stresses according to type of stress; the extreme minimum stresses, O"min,ex, , ..., are to be considered in 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). In generalnormal stresses intension orcompression are to be considered separately. For shear the highest absolutevalue 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 empirical interaction formula only. For example the extreme stresses from bending and shear will -as arule - occur atdifferent points ofthe cross-section, so that different reference pointsWare tobe considered. As a rule bending will be more important. Moreover see Footnote 1. 94 3.6 Assessment 3 Assessment of thestatic strength using nominal stresses Rod-shaped (ID) welded components For the toe of the weld of rod-shaped(lD) welded components thecalculationisto becarriedoutasfor rod-shaped (lD) non-welded components. For the root of the weldof rod-shaped(lD) welded components the degrees of utilization for normal stress and/orshearstress follow fromtheequivalent nominal stresses, Chapter 3.1.1.1: (3.6.7) . O"max,exwv aSK, = '.$;1, wv,e / . O"SK Jges 't max, ex,wv aSK,wv,'t = ..$;1, 'tSK/ Jges (3.6.2) For non-ductilewrought aluminumalloys (elongation A < 12,5 %) there is q = 0,5 , otherwise ./3-(l/f't) 7 q * ./3-1 ' f, shear strength factor, Table 3.2.5. Rod-shaped (ID) weldedcomponents For the toe of the weld of rod-shaped (lD) welded componentsthecalculationistobecarriedout asfor rod-shaped (lD) non-welded components. For the root of the. weldof rod-shaped (ID) welded components the degree of utilization for combined types of stress (or loadings) is *8 O"SK, ... aSK,wv,cr, ... degree of utilization , Eq. (3.6.2). 3.6.2 Shell-shaped (2D) components 3.6.2.1 Individual types of stress Shell-shaped (2D) non-welded components The degrees of utilization of shell-shaped (20) non- welded components forthetypes of stresslikenormal stress in the directions x and y as well as shear stress are (3.6.8) (3.6.9) O"max,ex,x asK,crx = ..$; 1, O"SK,x / Jges O"max,ex,wv , ... Extreme maximum equivalent structural stresses; the extreme minimum stresses, Smin,ex,wv,zd .. , , are to be considered in the same way as the maximum stresses, Chapter 3.1.1.1, related component static strength values, Chapter 3.4.2, total safety factor, Chapter 3.5.5. All extreme stresses are positive or negative (or zero). In general normal stresses in tension or compression are to be considered separately. For shear the highest absolute value of shear stress is relevant. 3.6.1.2 Combined types of stress Rod-shaped (ID) non-welded components For rod-shaped (lD) non-welded components the degree of utilization for combined types of stress is *6 O"max,ex,y asK,cry = ..$;1, O"SK,y / Jges 'tmax, ex I----I.$; 1, 'tSK/ jges aSK,crv = q . aNH + (l- q) . llGH.$; 1, where aNH=±{lsl+ ~ s 2 +4.t 2)' (3.6.4) (3.6.5) O"max,ex,x, ... Extreme maximum stresses according to type of stress, Chapter 3.1.1.1; the extreme minimum stresses,O"min,ex,x , ..., are to be considered in the same way as the maximum stresses, Chapter 3.1.1.2, 6The applied strengthhypothesis for combinedtypes of stress is a combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Dependingonthe ductilityof thematerial thecombinationis controlled 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 isof effect. For GG isq=0,759 so that both the normal stress hypothesis and the 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(f t ) . Steel, GOO GT, GG Wrought Cast AI-alloys Al-alloys r, 0,577 0,65 0,75 0,85 q 0,00 0,264 0,544 0,759 Caution: For non-ductile wrought aluminium alloys (elongation A < 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 and therefore itis tobe applied with caution. 95 3.6 Assessment 3 Assessment of the static strength using nominal stresses crSK,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"m· Res,i =Res , (4.1.11) (4.1.12) 8 In the following allvariables and equations are presented for the local normal stress oonly, butwritten with theappropriateindices theyare valid for all other types ofstress as well. 9 In this case anassessment ofthe variable amplitude fatigue strength is tobe carried out. lOinthis case ana s s e s s ~ n t ofthe fatigue limit istobe carried out for type I SoN curves if N= N;:: ND,cr.,.2r an assessment ofthe endurance limit for typeII SoNcurves ifN=N;:: NDcr II , respectively, oran assessment for finite lifebasedonthe constant amplitude SoNcurve (formally similar.20 an assessment ~ the variableamplitudefatigue strength) if N= N < ND,cr or N= N;:: ND,cr, II for Typ I orTyp II SoN curves, respectively. ND,cr orND,cr, II isthe number ofcycles at the fatigue limit ofthe component constant amplitude SoN curve, Chapter 2.4.3.2. 11 The valuesN-total number ofcycles required -and II -totaln u m ~ ofcycles ofagiven spectrum - are different ingeneral. The terms ni IN andhi IHare equivalent. 12Thedamagepotential isacharacteristicfor theshapeof a stress spectrum. The values kcr = 5for normalstress and k't = 8for shear stress are valid for non-welded components. The values kcr=3and ~ =8are valid for welded components. The term hi IH may be replaced by ni IN . 13Amean stress spectrum, for example, results from a static load with dynamic loads superimposed, a fluctuating stress spectrum, for example, results for acrane hook when lifting variable loads. 4.1 Characteristic service stresses 100 4 Assessment of the fatigue strength using local stresses 100°C: KT,D = 1-1,2. 10 -3.(T/ °C-100), (4.2.9) - for GGG, GT and GG, T >100°C, Figure 4.2.1: KT,D'" 1- aT,D'(10 - 3. T / 0C)2, (4.2.10) for aluminum alloys, T > 50°C: KT,D = 1- 1,2' 10 -3.(T / °C - 50)2, Figure 3.2.3in theChapter 3.2, 't:W,s Kindof material fw,O" Case hardening steel 0,400,577 Stainless steel 0,40 0,577 Forging steel 0,40 0,577 Steelother thanthese 0,45 0,577 GS 0,34 0,577 GGG 0,34 0,65 GT 0,30 0,75 GG 0,30 0,85 Wrought aluminum alloys 0,30 0,577 Cast aluminum alloys 0,30 0,75 4.2.3 Temperature factor 4.2.3.0 General Table 4.2.1 Fatigue strength factorsforcompletely reversed normal stress, fw,O" , and shear stress, 1 fw0" and fw arevalid fora number of cyclesN= 10 6 • fw'is equal 'to, Table 3.2.5. Bla'nk-hardened. The influence of the carburization on the component fatigue strength is tobe considered by the surface treatment factor, Kv, Chapter 4.3.4. 0,577 = 1//3, according tothev. Mises criterion. Also valid for welded components. Preliminary values. fW,O" does not correspond tothe endurance limit for N =co here! The temperature factor considers that the material fatigue strength forcompletelyreversedstressdecreases withincreasing temperature. Normal temperature, low temperature and elevated temperature areto be distinguished. aT,DConstant, Table 4.2.2. 4.2.3.1Normal temperature Normal temperatures areas follows: for finegrain structural steel from-40°C to 60°C, - for other kinds of steel from-40°C to + 100°C, for cast ironmaterials from-25°C to + 100°C, - for age-hardening aluminum alloys from-25°C to 50°C, - fornon-age-hardening aluminum alloys from-25°C to100°e. Table 4.2.2 Constant aT,D*8. Kind of material GGG GT GG aT,D 1,6 1,3 1,0 8 Forstainless steel novalues areknown upto now. 4.2 Material parameters 105 4 Assessment of the fatigue strength with local stresses Eq. (4.2.7) to (4.2.10) apply to steel and cast iron materials from the indicated temperature T up to 500°C. Eq. (4.2.11) applies to aluminum alloysup to 200°C. ThevaluesCYW,zd,T and1:W,s,T are notexplicitly needed for anassessment of thefatigue strength, as only the temperaturefactorKT,D is used. For elevated temperature, and in particular when the meanstress Sm, i:- 0, thefatigue strengthintermsof the maximum stress may be higher than the static strengthso thatthe assessment is governed by the static strength. High temperature strength Rm,T High temperature yieldstreilgth Rp,T Rm,T R m 'jm I I o4Rp,T Rp I , Rp'R m ' jp o 0;1 1% creeplimit Rp;Tt 0,3t----K:--+---",;:t-''':--tt--r---,.-J .Rp,Tt It p '1 R p . R m ' jpt Creep Strength R,.,Tt 0,2 m.........1 R';;"""' jmt o 100 ZOO 300 400 500 2.2.1. Tin"C Creep$trengthR,.;Tt Rm,Tt I Rm 'jmt 100 200 300 400 500 Till 'c o Z,2.1b o 0,1 t====J=::='=b--L....,,=-1-..+1 Figure 4.2.1 Temperature dependent values of the static strengthand of the fatigue strength plotted for comparison. Safetyfactorsj according toChapter 3.5or4.5, respectively. Rm,TI R m =KT,m, Rm,Tt l Rm=KTt,m, Rm,T, Rp,T as well as Rp,T I Rp =KT,p, Rp,Tt l Rp =KTt,p' R m, Tt, R p, Tt for t=10 5 h. Fatiguestrength value atelevated temperature: crW,zd,T I crW,zd= KT,D· Top: Non-alloyedstructuralsteel, asin theFigure 3.2.2, R p I R m = n, I R m =0,65, crW,zdI R m =0,45, Jm =2,0, Jp =jmt = 1,5, Jpt = 1,0, in = 1,5 . Bottom: GG, asin Figure 3.2.2, crW,zdI R m =0,30, Jm =3,0, Jrnt =in =2,4 . Table 4.3.1 Constant K, . 4 Assessment of the fatigue strength using local stresses 1 Kt-K f ratio, 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)] n cr ,2 K f K R,« KWK,cr3= ++-(-I))> ncr, .., Kf The design factors of block-shaped non-welded components forthe principle stresses in the directions 1, 2 and 3 (normal to the surface) are*2 KwK,crx = (4.3.2) =_1_'(1+_1_.(_1__1)) 1 ncr,x K f KR,cr K y .K s .KNL,E' K w : ,O"Y 1= -1)1 ncr,y K f KR,cr ) K y .K s .KNL,E = n 1, {1+ -(-I)J Ky l Ks > KR,cr, ... K y K s KNL,E 106 4.3Design parameters 4.3.0 General Accordingtothis chapter thedesignparametersareto be determined interms of design factors. 4.3 Design parameters 1R43 EN. dog Content Page 4.3.0 General 106 4.3.1 Design factors 4.3.1.0 General 4.3.1.1 Non-welded components 4.3.1.2 Welded components 107 4.3.2 Kt-K f ratios 108 4.3.2.0 General 4.3.2.1 Computation of Kj-K, ratios 4.3.2.2 Kj-K, ratio forsuperimposed notches 109 4.3.3 Roughness factor 4.3.4 Surface treatment and coating factor 110 4.3.5 Constant KNL,E III 4.3.6 Fatigue classes (FAT) 112 4.3.7 Thickness factor 4.3.1 Designfactors 4.3.1.0 General Non-welded and welded components are to be distinguished. 4.3.1.1 Non-welded components Rod-shaped(lD), shell-shaped(2D) andblock-shaped (3D)non-welded components areto be distinguished. The design factors of rod-shaped (lD) non-welded components fornormal stress and forshear stressare·1 KWK,cr = (4.3.1) n 1 0 {I+-( -I))>K y ' = =_1-1))' 1 n, x, Ky.K s The design factors of shell-shaped (2D) non-welded components for normal stresses inthedirections x andy as wellas forshear stress are Kind of Steel GS GGG GT GG material wrought cast Al-alloys Al-alloys Kf 2,0 2,0 1,5 1,2 1,0 Abetter estimate of Kf maybe obtainedfromstress concentration factors Kt,cr and of a substitute structure, Chapter5.12, andthe Kt-K f ratios, Chapter 4.3.2.1: or 1 About the purpose ofthe constant Kf see Footnote1 inChapter 2.3. 2The Kt-Kf ratioin direction3 normal to thesurface, ",,3. , is not contained inEq. (4.3.3) since a stress gradient normal tothe surface isnot considered. 4.3 Design parameters 4,3.1.2 Welded components For the basematerial of welded components the design factors are to be computed as for non-welded components. The design factors for the toe and for the root of a weld are ingeneral tobedetermined separately, sincethe local stresses and thefatigue classes (FAT) maybe different. Rod-shaped(lD), shell-shaped(2D)andblock-shaped (3D)weldedcomponents aretobedistinguished. The calculationcan be carried out with structural stresses or with effective notch stresses. 107 4 Assessment of the fatigue strength using local stresses FAT fatigue class, Chapter 4.3.6, f t thickness 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 for normalstresses in the directionsx and y as well as for shear stress. For certainapplications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the design factors are to be calculated as for shell-shaped (2D) welded components. Calculation with structural stresses Steel andcast iron material The design factors of rod-shaped (lD) welded components made of steel or of cast iron materials *3 for normal 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) welded components for normal stresses in the directions x and y as well as for shear stress are The design factors of shell-shaped (2D) welded components for normal stresses in the directions x and y as well as for shear stress are Aluminum alloys The design factors of rod-shaped (lD) welded components fromaluminumalloys*4for normal stress and 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' K s). 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 stresses Steel and cast iron material as well as aluminum alloys The design factors of rod-shaped (lD) welded components made of steel, of cast iron materials l'' and f 1 , o a uminumalloys for normal stressandforshear stress 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 the maximumeffective notchstressandthecorresponding shear stress are to be considered. The design factors are as before KWK,crK = 1 / (Ko . Kg . KNL,E ), (4.3.9) = 1/ (Ky' Kg), Kv surface treatment factor, Chapter 4.3.4*5, K s coating factor, Chapter 4.3.4, KNL,E constant for GG, Chapter 4.3.5 Forcertain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the design factors are to be calculated as for shell-shaped (2D) welded components. 3 To some part theFAT values where derived with reference to the IIW recommendations andEurocode3 (Ref. /9/, /81). Moreover thedesign factors 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 to be v.ahd, however, for all weldable aluminumalloys, except the aluminum alloys 5000, 6000 and 7000. Numerical values see Footnote 7 on 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; aluminumalloys accordingly, Weld quality conforming tonormal production standard. In combination with effective notch stresses the thickness factor ft is not applied, since the thickness effect isaccounted for by the stress analysis. 4.3Designparameters 108 4 Assessment of the fatigue strength using localstresses 4.3.2 Kt-Kr ratios 4.3.2.0 General The Kj-K, ratios nO", ... allowfor aninfluenceonthe fatiguestrengthresulting fromthedesign(contour and size) of a non-welded component. Condition for theapplicationof a Kj-K; ratio is a stress gradient normal tothedirectionofstressasshownin Figure 3.3.1*7. 4.3.2.1 Computation of Kt-Kr ratios Kt-Kr ratios for normal stress The Kt-K r ratio for normal stress,Ocr, Figure 4.3.1, is to becomputedfromtherelatedstressgradient GO" after Eq.(4.3.13) to (4.3.15). ForG0" ;;;; 0,1rnm"1 there is (4.3.13) -(a o -0,5+ R m ) n = 1 +G . mmrItl bo ·MPa 0" 0" , 800 400 800 1200 100 350 400 900 800 400 10 5 0,5 2 inMP;---:: / V [GGG , "/ -: / 1/0.65' V / v .,',.I / 1 10,70 7'"" i GS V/ . -: / 1 10,75 :/ II /V 1/ -: //' / V / -: / 1/0,85 V ./J V ,,-/ j /I/;;/ I /// il / / 110,95 / II {III ill /v / Iff; 1/ 1 // /II til (f; , 2/ do = r 0,267- ! \ I I 2 3 1,4 1,1 1,2 1,04 1,01 .0,010,020,050,10,2 1,02 (4.3.14) ( R) - ao+ m n =1 G . mm. 10 bo . MPa 0" 0" , for 0,1 mm" 1 I, fieldof fluctuatingcompressionstress, where Rcr = + or - 00is the zero compression stress. FieldII: -00 S; Rcr S; 0, whereR,< -1isthefieldof alternating compression stress, R,= -1 is the completely reversed stress, R; > -1 is the field of alternating 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 tension stress. 5Thefatiguelimit diagram(Haighdiagram) for normal stress shows increasing amplitudes for R ND,a (Steel and cast iron material) Incaseof acomponent constant amplitude S-Ncurve model I ( horizontal for N > No,a or slopekD,o=(0) the numberof cycles Nto be computed foravalueSa,1is (4.4.57) N= {[ A kon -1] . D M + I}' [GAI< )k a . NO,a, Ga.l where 8 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) ishere A ele = I / (va)ke . (4.4.55) 9Theconsistent versionof Miner'sruleallowsfor thefact, thatthe component fatigue limit will decrease asthe damage sum increases. The decrease applies tocomponent constant amplitude S-N curves model Ias well astomodel IIfor ND,s 2':10 6 . 10 The consistent version ofMiner's rule was first developed byHaibach. A simplified version allowing for the decrease ofthe fatigue limit became known as the modified version orthe Haibach method ofMiner's rule. 4.4 Component fatigue strength 4.4.3Component variable amplitude fatigue strength 122 4 Assessment of the fatigue strength using local stresses (4.4.67) (4.4.68) KSK,a= fn,a . Incase of a component constant amplitude S-Ncurve model II(sloping for N > No,aorslopekD,a NO a, kO a= co or for N > NO' k D = co NC is the reference number of cycles correspondingto the characteristic strength values aAC and AC. aAK / aAC= (Nc / NO,a ) 11ko= 0,736 and /= (Nc /11kr = 0,457. 4.5 Safety factors 125 4 Assessment of the fatigue strength using local stresses 4.5 Safety factors *1 Contents 4.5.0 General 4.5.1 Steel IR25 EN.docl Page 68 4.5.2 Cast iron materials 4.5.2.0 General Ductile and non-ductile cast iron materials are to be distinguished. 4.5.0 General 4.5.2 4.5.2.0 4.5.2.1 4.5.2.2 4.5.3 4.5.3.0 4.5.3.1 4.5.3.2 4.5.4 4.5.5 Cast iron materials General Ductile cast iron materials Non-ductile cast iron materials Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys Cast aluminum alloys Totalsafetyfactor 69 4.5.2.1 Ductile cast iron materials Cast ironmaterials with an elongationA5 ~ 12,5 %are consideredas ductile cast ironmaterials, in particular all types of GS and some types of GGG. Values of elongation see Table 5.1.12. Safety factorsfor ductile cast iron materials are given in Table4.5.2. ComparedtoTable4.5.1 theyarehigher because of an additional partial safety factor jp that accountsforinevitable but allowabledefectsincastings *4. The factor is different for severe or moderate consequencesoffailureand moreover for castingsthat have been subject tonon-destructive testing or have not. 4.5.1Steel Thebasic safetyfactor concerningthefatiguestrength is According to this chapter the safety factors areto be determined. Thisvaluemaybe reducedunderfavorableconditions, that is dependingonthepossibilitiesof inspectionand ontheconsequences 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.Reduction by about 10 %. ? 1 See footnote? I of Table4.5.1. Jo I Consequences of failure Severe I moderate? 1 castings not subject tonon-destructive testing?2 regular no I 2,1 I 1,8 inspection yes?3 I 1,9 I 1,7 castings subject tonon-destructive testing?4 regular no I 1,9 I 1,65 inspection yes?3 I 1,7 I 1,5 ?2 Compared toTable4.5.1anadditional partial safety factor jF= 1,4 is introduced to account for inevitable but allowable defects in castings. (4.5.1) Jo =1,5. Thesafety factorsare valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to anaverage probability of survival of Po =97,5 % *2. Thesafetyfactorsapplybothtonon-welded and welded components. Table4.5.1 Safety factors forsteel *3 (not for GS) and for ductile wrought aluminum alloys ( A ~ 12,5 %). jo Consequences of failure severe moderate ?1 regular I no 1,5 1,3 inspections I yes?2 1,35 1,2 ? 1 Moderateconsequences of failureof a less important component in the sense of"non catastrophic"effectsof afailure; for example becauseof a load redistributiontowardsother members of a statical indeterminate system. Reduction by about 15 %. ?4 Compared toTable4.5.1 anadditional partial safety factor jp = 1,25 is introduced, for which it is assumed that a higher quality ofthecastings 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 quality for which a further reduction of the partial safetyfactor to jF= 1,0 does not seempossible up to now. ?2 Regular inspection in the senseof damage monitoring.Reduction by about 10 %. 1 Chapters 4.5and2.5areidentical. A safety factor jF = 1,0may be applied tohighquality cast components in the aircraft industry however. Those high quality cast components, havetomeet special demands onqualification and checks of the production process,as well as on the extent of quality andproduct testing inordertoguarantee littlescatterof their mechanical properties. 4.5 Safety factors 126 4 Assessment of the fatigue strength using local stresses 1 I 4.5.2.2 Non-ductile cast iron materials Cast iron materials with an elongation As -:>3 No. 4 5 ad,p -:> -:> ClOE 1.1121 500 310 200 185 220 115 130 0,56 C15E 1.1141 800 545 320 270 345 185 205 0,68 C16E 1.1148 800 545 320 270 345 185 205 0,68 17Cr3 1.7016 800 545 320 270 345 185 205 0,37 28Cr4 * 1.7030 900 620 360 295 385 210 230 0,33 16MnCr5 * 1.7131 1000 695 400 320 430 230 255 0,44 20MnCr5 * 1.7147 1200 850 480 365 510 280 305 0,48 18CrMo4 * 1.7243 1100 775 440 340 470 255 280 0,52 18CrMoS4 * 1.7244 1100 775 440 340 470 255 280 0,52 22CrMoS3-5 * 1.7333 1100 775 440 340 470 255 280 0,28 20MoCr3 1.7320 900 620 360 295 385 210 230 0,33 20MoCr4 1.7321 900 620 360 295 385 210 230 0,33 16NiCr4 1.5714 1000 695 400 320 430 230 255 0,30 10NiCr5-4 * 1.5805 900 620 360 295 385 210 230 0,61 18NiCr5-4 * 1.5810 1200 850 480 365 510 280 305 0,37 l7CrNi6-6 * 1.5918 1200 850 480 365 510 280 305 0,37 l5NiCr13 * 1.5752 1000 695 400 320 430 230 255 0,30- 20NiCrMo2-2 * 1.6523 1100 775 440 340 470 255 280 0,52 l7NiCrMo6-4 * 1.6566 1200 850 480 365 510 280 305 0,37 20NiCrMoS6-4 * 1.6571 1200 850 480 365 510 280 305 0,37 * 1.6587 1200 850 480 365 510 280 305 0,37 14NiCrMo13-4 * 1.6657 1200 850 480 365 510 280 305 0,37 -:> 1Values afterDINEN 10084AppendixF ("tensile strength values after quenching and tempering at 200°C") 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 Material Rm,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,p No. -:>2 -:>3 -:>3 24CrMo13-6 1.8516 1000 800 450 360 480 260 285 0,22 0,26 31CrMo12 1.8515 1030 835 465 370 495 270 295 0,21 0,27 32CrAIMo7-1O 1.8505 1030 835 465 370 495 270 295 0,21 0,27 3lCrMoV5 1.8519 1100 900 495 385 525 285 315 0,31 0,36 33CrMoV12-9 1.8522 1150 950 520 395 550 300 330 0,30 0,35 34CrAINi7-1O 1.8550 900 680 405 335 435 235 260 0,17 0,17 41CrAlMo7-1O 1.8509 950 750 430 345 460 250 275 0,23 0,24 40CrMoV13-9 1.8523 950 750 430 345 460 250 275 0,23 0,24 34CrAIMo5-1O 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. 137 5.1 Material tables 5 Appendices Table 5.1.8Mechanical properties in MFa for stainlesssteels, after DIN EN10 088-2(1995-08-00) (selected types of material only) vI v 2 Type of material Type of material, Mate- Kindof Rm,N R,N after DIN / SEW rial product CJW,zd,N CJSch,zd,N CJW,b,N '"CW,.,N '"CW,t,N No. v3 d d ali al d di. 1. tl Femtic stee s ill ie anne e con ition,stan ar qu HIes, X2CrNi12 - 1.4003P(25) 450 250 180 170 205 105 120 X6CrAl13 X6CrAI13 1.4002P(25) 400 210 160 155 180 90 110 X6Crl7 X6Cr17 1.4016P(25) 430 240 170 165 195 100 115 X6CrMo17-1 X6CrMo17 1 1.4113H(12) 450 260 180 170 205 105 120 d 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 650 450 260 230 290 150 170 QT750 750 550 300 260 330 175 195 X4CrNiMo16-5-1 - 1.4418P(75) QT840 840 680 335 280 410 195 220 d I . 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 430 335 460 245 275 P950 950 800 380 310 410 220 245 P850 850 600 340 285 370 195 220 d d oualiti Id 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) 600 250 240 215 270 140 160 X2CrNiNI8-1O X2CrNi 18 10 1.4311 P(75) 550 270 220 200 245 125 145 X5CrNil8-10 X5CrNi 18 10 1.4301 P(75) 520 220 210 190 235 120 140 X6CrNiTi18-1O X6CrNi 18 10 1.4541 P(75) 500 200 200 185 225 115 135 X6CrNiMoTil7-12-2 X6CrNiMoTi 1722 1.4571 P(75) 520 220 210 190 235 120 140 X2CrNiMoN17-13-5 X2CrNiMoN17135 1.4439P(75) 580 270 230 210 260 135 155 vI 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 to 6 mm thickness, QT650 heat treatedto a tensile strength of650 MPa, PI070 hot rolled plate with a tensile strength of 1070 MPa. 5.1 Material tables 138 5 Appendices Table 5.1.9Mechanical properties in MFa of steels for bigger forgings, afterSEW 550 (1976-08-00) 0,75; Tablebelow: R pO,2,N / Rm,N < 0,75throughout. ~ 3 Elongation in %.For non-ductile materials, A 5 < 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 tables Table 5.1.21. Survey of the Aluminum materials. 142 I 5 Appendices Table 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) 5.1.23 Aluminum alloys Strips, 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) 5.1.32 Aluminum alloys Permanent 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) 5.1.38 Alloys for high pressure die castings DIN1725 T. 2 (02/86) Tables 5.1.22 to 5.1.38 give the respective values of elongation: For non-ductile materials, A < 12,5%,the assessment of the component static strength is to be carried of using local stresses, Chapter 1.0, andall safety factorsareto be increasedby addinga value , see Eq. (2.5.2), ... inChapter 2.5, 3.5or 4.5, respectively. Attention: The fatiguelimitvalues GW,zd, ... given in the Table 5.1.22to 5.1.38refer to the knee point of the S-N curve at N =ND,O' =N D,< =10 6 cycles. The endurance limit valuesGW,Il,zd , ... refer to a number of N =ND,O'.II =N D.< ,II = 10 8 cycles, and are lower than the fatiguelimit by a factorfIl,O' or fIl, < (see also page 131): - fIl,O' =(10 8 / 10 6 ) 1/15 =0,74 (kD,O' = 15 for normal stress), - fIl,< = (10 8 / 10 6 ) 1/25 = 0,83 (k D,< =25 for shear stress). 5.1 Material tables 143 5 Appendices strips, s eets, pJates, er DIN EN 485-2 (03/95) (selected types0 maten oly), Material Condition Nom, thickness R m Re crW,zd crSch,zd crW,b ~ W , s ~ W , t A{>1 Hardness inmm number from to % HB ENAW-2014 T3 No,cr andN>No,'t , andthe S-N curve model I (horizontal forN>No,cr andN>No,'t) the variable amplitude fatigue strength factorsforbending andfortorsion is KE,cr =KE,'t =1. Amplitude of the component fatiguelimit The amplitude of thecomponent fatiguelimitresults fromthemeanstress factor, theresidual stressfactor andthe component fatigue limit for completely reversed bending andtorsionalstress: SBKb =1· 233MPa =233 MPa, =1 . 179 MPa =179 MPa . (2.4.41) 5SAFETY FACTORS In generalthereis In =1,5. (2.5.1) For moderate consequence of failureandregular inspection, however, thereis jo= 1,2. Tab. 2.5.1 For normal temperature thereis KT,o =1, andtherefore jges =1,2. (2.2.4) (2.5.4) 6 ASSESSMENT Largest stress amplitudes forbending andfortorsion, see above, Sa,b,1 =Sa,b =150 MPa , Ta.t, I =Ta.t =100 MPa. 6.1 Shaft with shoulder 235 6 Examples KAK,v=1+0,213.0,235/0,778= 0,940. (2.4.13) Residual stress factorfornormal stress andforshear stress Because of - 00< -0,267 ~ 0 fieldII applies: M cr =0,213, 1 Related equivalent meanstress forbending andtorsion 1 8·0,573·0,526 B3 =-' = 1028 J3 3.0,573 2 +(4/3).0,526 2 ' 7.0,573 2 +12.0,526 2 A4 =7,224 Tab. 5.9.1 0,573 2 +0,526 2 (2.6.5) (2.6.4) Tab 5.7.1 Tab. 2.2.1 (2.6.7) (2.6.6) KBK,b =1,26, KBK,1 =1,15. Combined types of stress fw,'t = 1 /.J3, q= 0, sa =aBK,b=0,732 , t a = aBK,1= 0,715, aGH=JO,732 2 +0,715 2 =1,023, aBK,Sv= 1,023. Complementary assessment 2: Assessment applying a class of utilization Differing fromthe constant amplitude loading condi- tionsandthe assessment of thefatigue limit considered above an assessment of a variable amplitude loading according totheclassof utilization B5 iscarried out here. Inthiscasetheclass of utilization B5 may, for example, stand forbinominally distributed amplitudes of thestress spectrum, a spectrum parameter p=1/3 anda required total number of cyclesN= 10 7 , Table 5.7.2. aBK b= 150 = 0,732, (2.6.1) , 246/1,2 a = 100 = °715. BK,1 168/1,2 ' Degrees of utilization Individual types of stress, bending andtorsion, The amplitudes of the component variable amplitude fatigue strength forbending andfor torsion for bending andfortorsion are (2.4.41) SBK,b= KBK,b. SAK,b = 1,26' 246MPa= = 310MPa, TBK,1= KBK,I'TAK,1= 1,15' 168 MPa= =193MPa. The variable amplitude fatigue strength factorfor the class of utilization B5 forbending andfor torsion is With thesevalues instead of thevalues 246 MPa and 168 MPa thedegrees of utilization arelower than those fromabove. (5.9.3) (5.9.2) (5.9.18) - 0,536 Sa,b =150 MPa, SWK,b=262MPa, Sa = 150 / 262 = 0,573, Ta,l =100 MPa, TWK,1 =190 MPa, t a =100 / 190=0,526, sa,v =JO,573 2 +0,526 2 =0,778. Common meanstress factor smin,v= 0,235 - 0,778 = - 0,543, smax,v=0,235 + 0,778=1,013, Rcr,v - 0,543 / 1,013 The constants B I , Al andAS arenot needed asSm=0. Tm,l =50 MPa, TWK,1 =190 MPa, t m =50/190=0,263, (5.9.6) Sm = 0, Sms=(3/7). 1,028' 0,263 =0,116, t ml =(1 /E).J7,224.0,263 2 =0,154, sm,v= 0,87. (0,116+ 0,154) = 0,235. (5.9.5) Complementary assessment 1: Amplitude of the component fatigue limit for the given mean stress - improved method of calculation according to Chapter 5.9 Related equivalent stress amplitude forbending and torsion KE,cr =KE;t =1. (2.4.5) The amplitude of thecomponent fatigue limit results fromthemeanstress factor, theresidual stress factor andthe component fatigue limit forcompletely reversed bending andtorsional stress: SAK,b = KAK,v. KE,cr. SWK,b = (2.4.6) = 0,940' I. 262MPa= 246 MPa, TAK,1= KAK,v. KE,'t . SWK,b = =0,940. 1 . 190 MPa =168 MPa. Using these values instead of thevalues 233MPa and 179 MPa somewhat different degrees of utilization are obtained. 6.2Shaft with V-belt drive 236 6 Examples Given Loading:Maximum torque (ratedtorque), idealizedas a fluctuatingloading (loadratioR M =0), figure6.2.1: 6.2 Shaft with V-belt drive*1 lR62 EN.docl Keywords: Shaft, V-belt drive, rolled steel, assessment of the staticstrength, assessment of the fatiguelimit, type of overloading F1, combined types of stress. M, =M max = 1 kNm. Material: St 60after DINEN10 025. Dimensions: (6.2.1) Surface:average roughness of the shaft: R z =25J..Lm. Type of overloading:whenoverloaded in service the tensionof the beltremainsconstant and with thatthe mean stressremainsapproximately constant as well (Type of overloading Fl). Safety requirements:according to the statements "severe consequences of failure; noregular inspections" . Task: Assessment of the component staticstrength and assessment of the component fatigue limit. Methodof calculation: Rod-shaped (ID)componerit. Assessment usingnominal stresses, Chapter 1 and2. Length of shaft1 =400mm, diameter of shaft d=56mm. Pulley in center position, bearing on the left horizontally fixed, torque input at the right end. ASSESSMENT OF THECOMPONENT STATIC STRENGTH 1 LOADINGS (6.2.2) Data ofthe drive Diameter of pulleyNo.1: d1W =200mm, Diameter of pulleyNo 2: d2W= 100 mm, Center distance: e =200mm, Wedge angle: Ys =35°, Friction coefficient between belt andpulley: J..L=0,1. Specifying the loadings is notsubject of the guideline. Therefore the loadings areoutlined here in brief *2. M, is the torqueinput to the shaft. The torque input resultsin a maximum of six loads F x , ... , M, at the pulley. The initial tension of the belt results in a maximum of two lateral forces F y , F z . The sense of rotation anddirection of input andoutput arenot important for the loads. The torqueis transmitted by the initial tension and frictional contact of the belt. Therefore the loadings "torque"and"initial tension" are to be distinguished. The axial load of the shaft andthe lateral moments at the pulley are zero: Z Figure 6.2.1 Shaft andloads duetothetorqueM n at theV-belt drive. F I - F 2 =F, *2 Calculation equations Loading"torque" Circumferential force transmitting the torque Ft=M n ' 2/d 1w , = 1000 kNmm . 2 I 200mm = 10 kN. (6.2.3) Inclination of the belt 1 Results of computation obtained by the PC-program "Welle" 2 Full presentation ofthe example s given in the manual ofthe PC-program "Welle". sina, = (d 1w - d 2w ) 12e, (6.2.4) = (200 - 100) mm I (2 . 200 mm) = 0,25, a, =14,48°. 6.2 Shaft withV-belt drive 237 6 Examples M z - 2,349kNm ..;.,:: o lI:l C>J B« 0 and < 180°. Auxiliary variable ASSESSMENT OF THE COMPONENT STATIC STRENGTH 1CHARACTERISTIC STRESSES Maximum torsion moment Figure 6.2.2 Resulting moments atmid shaft. Thereference point fortheassessment of thestatic strength is inthemiddle of the shaft (totheright of the pulley). Maximum bending moment (point B in Figure 6.2.2) Mb=Myz+M; (6.2.12) + 2, 349kNm 2 = 2,362 kNm. (6.2.6) Valueof thegroove angle Ys =350. Effective coefficient of friction J.lth =/ sin(ys/ 2) = 0,1 / sin(35012) =0,3326. _3 Arc of belt contact at the smaller pulley (No.2) (6.2.7) = 180°- 2·1a.1 = 180°- 2· 14,48= 151,0°. 2MATERIAL PROPERTIES Smax ex b = 32 Mb / pd 3 (1.1.1) ='32'2,362 kNm / (n. (56mm)3 ) =137 MPa, T max ext = 16 M t / pd 3 ='t6'· 1 kNm / (rt . (56mm)3 ) =29,0 MPa. Extreme maximum stresses*5 Tensile strength andyieldstrength forthestandard dimension Rm,N =590 MPa, Rp,N = 335 MPa. Tab. 5.1.1 Technological sizefactor (6.2.10) (6.2.9) I I 2 m+l Fs p = M, ·-·--·cosa. d 1w m->I 2 2,403+1 =1000 kNmm' 200mm 2,403-1. cosine 14,47° = 23,49 kN. Resulting loads F x = 0, F y = + F sp = 23,49 kN, F z =0, M x= M y= M z= O. 2RESULTING MOMENTS AT MID SHAFT Tensile strength andyield strength of thecomponent 4 Practically anincreasedinitial tension value needs tobeconsidered. 5Fromhereon the numbers of equations, tablesandfiguresare those of the guideline. From theloadings "maximum torque" (M; =1 kNm and F z = 2,5 kN) and from theloading "initial tension" (Fy = 23,486 kN) themoments in the middle of theshaft (to theright of the pulley) are M, = - 1 kNm, (6.2.11) My= +F, . I / 4=2,5 kN. 400mm/ 4 = +0,250 kNm, . M z = - F y . I /4=23,49 kN. 400mm / 4 = - 2,349 kNm . The bending moments My and M, arepresented in Figure 6.2.2. The loading without torque (only initial tension) corresponds to the point A. The loading under maximum M, torque (including initial tension) corresponds to thepoint B. ad,m =0,15, ad,p = 0,3 , deff,N=40mm, deff =d=56mm, =0,982, Kd,p =0,960. Anisotropy factor K A = 1. R m =0,982. 1 ·590 MPa=579 MPa, R p =0,960 . 1 . 335MPa=321 MPa. Tab. 1.2.1 Tab. 1.2.3 (1.2.9) (1.2.17) (1.2.1) 3 Torque and the pre-tension aretobedetermined for the smaller pulley 6.2 Shaft withV-belt drive 238 6 Examples 3DESIGN PARAMETERS 6 ASSESSMENT Designfactorfor bending Sectionfactor Rp,max= 1050 MPa, Tab. 1.3.1 R p =321 MPa, Kp,b= 1,70, Tab. 1.3.2 npl,b=MIN(J1050/321 ; 1,70)=1,70, 1.3.9) Designfactor Maximumstresses for bendingand for torsion, see above, Smax,ex,b= 137,0 MPa, Tmax,ex,t'= 29,0 MPa. Component static strengthfor bendingand for torsion, see above, SSK,b=985 MPa, TSK,t =447 MPa. KSK,b= 1 /1,70=0,588. (1.3.1) Degrees of utilization Individual types of stress, bendingand torsion, Component staticstrength for bendingand torsion Component staticstrength for bendingresultingfrom the tensile strength and designfactor: Rp,max= 1050 MPa, Tab. 1.3.1 R p =321 MPa, Kp,t = 1,33, Tab. 1.3.2 npI,t =MIN(J1050/321 ; 1,33) =1,33. 1.3.9) Designfactor (1.6.1) (1.6.5) (1.6.4) Tab. 1.2.5 (1.6.7) (1.6.6) 137 =0376 aSK,b=985I 2,70 ' , a = 29,0 =0176. SK,t 447 I 2,70 ' Combined types of stress f't =0,577, q=0, s =aSK,b=0,376, t=a SKt =0,176, a GH =~ 0 , 3 7 6 2 +0,176 2 =0,415, aSK,Sv=0,415. The degree of utilization of the component static strength is 42%. The assessment of the static strength is achieved. (1.3.1) Tab. 1.2.5 (1.4.1) KSK,t = 1 /1,33=0,752. fa = 1 , SSK,b=579 MPa/ 0,588=985 MPa. 4 COMPONENT STATIC STRENGTH Designfactorfor torsion Section factor 5SAFETY FACTORS For severe consequences of failureand high probability of the occurrence of the characteristic stress there is Component static strength for torsionresultingfrom the shear strength factorf't , the tensile strengthand the design factor: f't =0,577, Tab. 1.2.5 TSK,t =0,577. 579 MPa/ 0,752 =445 MPa. (1.4.1) Mm,b= ° The maximum amplitudeof the bendingmomentfor the rotatingshaft is, as for the assessment of the static strength, Ma,b =2,362 kNm. Again the reference point for the assessment of the fatigue strengthis in the middle of the shaft (to the right of the pulley). Cyclic bending moment The mean value and amplitude of the maximum cyclic bending moment is to be determined. The mean value of the bendingmomentfor the rotating shaft is ASSESSMENT OF THE COMPONENT FATIGUE STRENGTH 1 CHARACTERISTIC STRESSES (1.5.4) Tab. 1.5.1 jm=2,0, jp=1,5. For normaltemperature there is KT,m=KT,p= 1, (1.2.26) and in Eq. (1.5.4) the terms 3 and 4 have no relevance: R p =321 MPa, R m =579 MPa, jges =MAX (2,0; 1,5. 579) 321 =MAX(2,0;2,70) =2,70. The yield strength R p (the second term) is determining. 6.2Shaft with V-belt drive 239 6 Examples The cyclic stresses resultingfrom thebending moment and thetorsion moment are Materialfatiguelimits for completely reversed normal stress, crW,zd ,and shearstress, 'tw,s, : It is valid for the non-rotating shaft too. Characteristic stresses Smb = 0, (2.1.1) , 3 Sa,b = 32 Ma,b/ pd = 32. 2,362 kNm /(n. (56 mmr' ) = 137 MPa Tm,t = 16 Mt,m /pd 3 = 16 . 0,5 kNm / (n. (56mm)3) = 14,5 MPa, Ta,t = Tm,t ==14,5 MPa. 2MATERIAL PARAMETERS (2.3.1) (2.3.17) (2.3.13) (2.3.10) Tab. 2.2.1 Tab. 2.3.4 (2.3.26) KWK,b = 0,979+1/0,858 - 1= 1,144 G, (r) = 0, n, (r) =1 , d =56 mm, G, (d) = 2/ d =0,0357mm-1 , n, (d)=1,027. Fatigue notch factor Kf,t =1 / (1. 1,027) =0,974. Roughness factor R m = 579MPa , R z = 25 um , fw"= 0,58, aR,cr =0,22, Rm,N,min = 400MPa, KR" =0,918. For nosurface treatment is Ky= 1. For steel and cast iron materials isKs = 1. For materials except GGis KNL,E = 1. Therefore: Design factor Designfactor for torsion Fatigue notch factor Stress concentration factor for the cylindrical shaft *6 Kt,t = 1. K,-K r ratios, nonotchradius, For nosurface treatment is Ky= 1. For steel and cast iron materials isKs = 1. For materials except GGis KNL,E = 1. Therefore: Design factor Tab. 2.2.1 (2.2.1) Tab. 2.2.1 (2.2.1) R m = 579MPa, fw,cr = 0,45, crW,zd= 0,45. 579MPa=261 MPa, fw" =0,577, 'tw,s= 0,577.261MPa= 151MPa. The amplitude of thebending moment isvarying within the limits defined bynotorque input or maximum torque input, points A and B inFigure 6.2.2. The assumption of a continuous action of themaximum bending moment isanapproach onthesafeside. Fluctuating torsion moment The mean value and amplitude of thetorsion moment fluctuating between zero and maximum is Mm,t = Ma,t =IMxl /2=0,5 kNm. 3 DESIGN PARAMETERS KWK,t = 0,974 +1/0,918 - 1= 1,063 (2.3.1) Design factorfor bending Fatigue notch factor Stress concentration factorfor thecylindrical shaft*6 Kt,b= 1. K,-K r ratios, nonotch radius, Component fatigue limit for completely reversed torsionalstress resulting from the material fatigue limit for shear stress and the design factor for torsion, Component fatigue limit for completely reversed bending and torsional stress Component fatigue limit for completely reversed bending stress resulting from thematerial fatigue limit for normal stress and thedesign factor for bending, G cr (r) = 0, ncr (r) = 1 , d =56mm, Gcr(d) =2/ d= 0,0357mm-1 , ncr (d) = 1,022 . Fatigue strength reduction factor (2.3.17) (2.3.13) 4COMPONENT FATIGUE STRENGTH SWK,b= 261MPa /1,144=228 MPa. (2.4.1) 6 Assuming an unnotched cylindrical shaft is an unrealistic simplifica- tion for the presentexample. Actually a keyway or a press-fit between pulley andshaft, Chapter 5.3.3.4, would have tobeconsidered. Kf,b =1 / (1. 1,022)=0,979. Roughness factor R m = 579MPa, R z = 25um, aR,cr =0,22, Rm,N,min = 400 MPa, KR,cr = 0,858. (2.3.10) Tab. 2.3.4 (2.3.26) TWK,t = 151 MPa / 1,063= 142MPa. (2.4.1) 6.2 Shaft withV-belt drive 240 6 Examples Amplitude of the component fatigue limit forthe given mean stressforbending and torsion Meanstresssensitivity R m =579 MPa, aM =0,00035, bM =-0,1, Me; = 0,103, fW;t =0,577 , M't= 0,577. 0,103 = 0,059. Tab. 2.4.2 (2.4.34) Tab. 2.2.1 (2.4.34) model I (horizontal for N>ND,e; and N>ND,'t ) the variable amplitude fatiguestrength factorsforbending and for torsion is KBK,b = KBK,t = 1. (2.4.48) The amplitude of the component variable amplitude fatigue strength resultsfrom the variable amplitude fatigue strength factor and fromthe amplitude of the component fatigue limit for bending and fortorsion, Largest stress amplitudes for bending and fortorsion, see above, For severe consequence of failureand no regular inspectionsthere is 5 SAFETY FACTORS SBK b =1 . 225 MPa=225MPa, t =1 . 141 MPa=141 MPa. , (2.2.5) (2.5.4) (2.4.41) (2.5.1),Tab. 2.5.1 KT,D =1, Jges = 1,5 . .io= 1,5. For normal temperature there is 6 ASSESSMENT Sm =Sm,b= °, (2.4.31) T m =Tm,t =14,5MPa, fw,'t =0,577, Tab. 2.2.1 q = °, (2.4.29) Sm,v= Sm,v,GH =J3 . 14,5MPa = 25,1MPa, (2.4.29)(2.4.28) Tm,v =0,577·25,1MPa=14,5MPa. (2.4.30) Calculation forthe type of overloading F1. Meanstressfactorforbending Sm,b,v=Sm,v / SWK,b=25,1/228=0,110, Me; =0,103, - 1 / (1 - Me;) =- 1 / (1 - 0,103) = - 1,115, 1 / (1+Me;) = 1 / (1 +0,103) = 0,907. Because of - 1,115:::;; 0,110:::;; 0,907 field II applies: Equivalent mean stress For normal stressandfor shear stressthere is SAK,b = 0,989. 1 . 228MPa = 225 MPa, (2.4.6) TAK,t = 0,994. 1 . 142 MPa = 141 MPa. KE,e; =KE,'t =1. (2.4.5) Amplitude of the component fatigue limit The amplitude of the component fatigue limit results fromthe mean stressfactor, the residual stressfactor and the component fatiguelimit for completelyreversed bendingstressandtorsional stress, tm,t,v=Tm,v/ TWK,t=14,5/142 =0,102 M, =0,059, 1 / (1+M't) =1 / (1 + 0,059)=0,944 . Because of 0:::;; 0,102:::;; 0,944 field II applies: KAK,'t = 1 - 0,059'0,102= 0,994. (2.4.15) Residual stressfactor (2.6.5) (2.6.4) Tab. 2.2.1 (2.6.7) (2.6.6) Combinedtypes of stress fw,'t = 0,577, q= 0, Sa = aBK,b= 0,913 , t a =aBK,t =0,155. a GH =+0,155 2 = 0,926, aBK,Sv= 0,926. Sa b l = Sa b = 137 MPa, Ta',t:! =T a:t =14,5MPa. Amplitude of the component variable amplitude fatigue strengthfor bendingand for torsion, see above, SBK,b = 225 MPa, TBK,t = 141 MPa. Degreesof utilization Individual types of stress, bending and torsion, a = 137 = °(261) BK,b 225/15 ' • • , a BK t = 14,5 = 0,155. , 141/ 1,5 (2.4.15) KAK,e; = 1 - 0,103. 0,110= 0,989. Meanstressfactorfortorsion Component variable amplitude fatiguestrengthfor bending and torsion Variableamplitude fatiguestrength factor Considering the component constant amplitudefatigue limit, N>ND,e; andN>ND,'t , and the S-N curve The degree of utilizationof the component fatigue limit is 93%. The assessment of the fatigue limit is achieved. * 7 7See the objections in footnote4 and 6, however. 241 6.3 Compressor flange made of grey cast iron 6 Examples 6.3Compressorflangemade of grey cast iron "'I 1R63 EN.docl ASSESSMENT OF THE COMPONENT STATIC STRENGTH 1 CHARACTERISTIC STRESSES 2MATERIAL PROPERIES GI max ex = 33,6 MPa, G 2 max ex = 11,2MPa . , , , , Maximumstresses Key words: Greycast ironGG-30, assessment of the static strength, assessment of the fatigue limit, local elastic stresses, type of overloading F2, elevated temperature, combined types of stresses GI andG2 . Given Stresses:Proportional, constant amplitude loading, locally elasticstressesin the directions1 (longitudinal) and 2 (circumferential) at the reference point(node 99) of a block-shaped (3D) component, Figure 6.3.1, GI =GI,m±GI,a =15,0 MPa ± 18,6 MPa, G2 = G2,m ±G2,a = 5,0 MPa ±6,2MPa, G3 =0. Stress amplitudes at the neighbouring point(node 98) in a distance s =7,7mm belowthe surface Tensile strength for the standarddimension Rm,N= 300 MPa. Technological size factor deff =2s =2 . 32 mm =64 mm , Kd,m=0,800 . Anisotropyfactor K A = 1. Tensilestrength of the component *2 (3.1.6) Tab. 5.1.14 Tab. 3.2.3 (3.2.5) (3.2.18) GI,a= ± 10,0MPa, G2,a= ± 5,3MPa. Flange Section factor for GG 3 DESIGN PARAMETERS (3.2.1) R m =0,800' 1 . 300 MPa=240 MPa: Temperature factors aT,m =1,6, Tab. 3.2.6 K T m =0,769, (3.2.31) Crr: =25, Tab. 3.2.7 aTt,m = - 1,46, bn,m=2,36, CTt,m= - 0,90 , Pm =10 - 4. (380+ 273). (25 + 19 100.000) = =1,959, (3.2.35) _ (-1,46+2,36.1,959-0,90.1,959 2 ) KTt,m -10 =0,511. 91. 87 92 6 . ~ . 1 111 npl,O'I =npl,O'2 =1. (3.3.7) Constant KNL for the consideration of the non-linear elastic strain characteristic of GG for tension Figure 6.3.1 Compressor flange made of grey cast iron. Material: GG-30according to DIN1691 or DIN EN i,:,61. KNL =1,05. Tab. 3.3.4 Temperature and time: T= 380°C, t = 100.000 h. Dimensions:Effective wall thickness at the reference point(node 99)s ;::: 32 mm. Surface: Skin Type of overloading:: When overloaded in service the stress ratiosremain constant (Type of overloadingF2). Safety requirement: accordingto the statements: "severe consequences of failure; no regularinspection", casting tested non-destructively. Task: Assessment of the static strength and assessment of the fatiguelimit. Method of calculation: Block-shaped(3D) component. Assessment usinglocal elastic stresses, Chapter 3 and 4 Design factor for directions1 and 2 KSK,O'I =KSK,O'2= 1/ (1'1,05) =0,952. (3.3.3) 4COMPONENT STRENGTH Component strength resulting fromthe tensile strength and the design factor. For directions1 and 2 there is f O' =1 , Tab. 3.2. GI,SK =G2,SK =240 MFa/ 0,952=252MPa. (3.4.3) I Results of computation obtained by the PC-program "RIFESTPLUS" 2 Numbers of Equations, tables and figures arethose of the guideline. 242 6.3Compressor flange made of grey cast iron 6 Examples 5SAFETY FACTORS Because of thelowelongation of GGthesafety factor is tobeincreased by : For severe consequences of failure andhigh probability of theoccurrence of themaximum stress andfornon- destructivelytested castings there is Tab. 3.5.2 Material fatiguelimit forcompletelyreversednormal stress, CfW,zd, (4.1.1 ) Constant amplitude cyclic stresses crl.a= 18,6 MPa, 01,m= 15,0 MPa. cr2,a=6,2 MPa, 02.m=5,0MPa, cr3,a=0, 03.m= °. 2MATERIAL PROPERTIES ASSESSMENT OFTHEFATIGUE STRENGTH 1CHARACTERISTIC STRESSES Note: For the assessment of thecomponent static strength thepresented computation for thecombined typesof stress applies toboth proportionalstresses and non-proportio-nal stresses o l andcr2, seefootnote1 in Chapter 3.6. (3.5.4) (3.5.2) Jm= 2,5, jmt = 1,9. KT,m = 0,769, KTt,m = 0,511. For GGtheterms2 and4 of Eq. (3.5.4) arenot relevant. Therefore . = Jges 0,769'0,511 = MAX(3,90; 4,70) = 4,70. = 0,5, jm=3,0, jmt =2,4. Temperature factors, seeabove, The creep strength Rm,Tt is is determining, Figure 3.2.2. 6 ASSESSMENT Maximum stresses, seeabove, R m = 240MPa, fw,cr = 0,30, crW,zd = 0,30. 240MPa =72,0 MPa. Temperature factor aT,D= 1,0, KT,D= 0,856. Tab. 4.2.1 (4.2.1 ) Tab. 4.2.2 (4.2.8) crLmax.ex =33,6 MPa, cr2,max,ex= 11,2 MPa. Component strength values, seeabove, 3DESIGN PARAMETERS 33,6 crl,SK = cr2,SK, = 252 MPa. aSK,cr2= 252/4,70 =0,209. Degrees of utilizaion Individual types of stress, directions1 and2 (4.3.28) (4.3.29) Tab. 4.3.2 (4.3.10) Tah. 4.3 ( (4.3.16) 0,0600 Ch.4.3.3 100 MPa, Tab. 4.3.4 (4.3.26) K v = 1. Kt-Kf ratios Gal __I_.(I_IO,OJ 7,7mm 18,6 G? - I (I 5.3J = 0,0189mm- l , o : - 7,7mm' - 6,2 aa= - 0,05, b G = 3200, nal =1,179, n cr2 =1,056. Coatingfactor KKS = 1. ConstantKNL.E KNL,E= 1,025. 3 Even though the present assessment ofthe creep strengthmayhetar on the safe side, see Chapter 3.1.0 on.Elevated temperature' Roughness factor R m = 240MPa, R z = 200um , aR,cr =0,06, Rm,N.min= KR,cr = 0,906, Surface treatment factor, Tab. 3.2.5 (3.6.23) (3.6.22) f, = 0,85, q= 0,759, 81 = aSK,crl = 0,627, S2 = a SK.cr2 = 0,209, Combined types of stress a GH = ((0,627 -0,209)2+0,209 2 +0,627 2 ) = 0,553, (3.6.21) a NH =MAX(0,627; 0,209) =0,627, aSK.sY=0,759. 0,626+(I - 0,759). 0,553 = = 0,608. (3.6.20) The degree of utilization of the component static strength is61%. The assessment of the static strength is achieved. *3 6.3Compressor flange made of grey cast iron 243 6 Examples Design factors Kf =1, KWK,al =1,1\9 -(1+i-( 0,:06 -1)) =0,913, KWK,a2= 1,;56 -( 1 + i -( 0,:06 -1)) =1,019. Tab. 4.3.1 1 1·1·1,025 (4.3.3) 1 1·1·1,025 crl,AK =0,713. 1 . 79 MPa=56 MPa , (4.4.8) cr2,AK =0,713. 1 ·71MPa=50 MPa . Component variable amplitude fatiguestrength for bendingand torsion Considering the component constant amplitude fatigue limit, N>No,a andN>NO;t , and the S-Ncurve model I(horizontal forN>NO,a andN>No,'t)the variable amplitude fatiguestrength factorsfor normal stressis KBK,al = KBK,a2= 1. (4.4.47) The amplitude of the component variable amplitude fatigue strength resultsfromthe variable amplitude fatigue strength factorand fromthe amplitude of the component fatiguelimit for normal stress 4COMPONENT FATIGUE STRENGTH Component fatiguelimit for completely reversed normal stresses Component fatiguelimit for completely reversed normal stressresulting fromthe materialfatigue limit for normal stressand the designfactors: crl,BK =1·56 MPa=56 MPa, cr2,BK= 1 . 50 MPa = 50 MPa. (4.4.45) crl,WK =72,0 MPa/ 0,913=79 MPa, (4.4.3) cr2,WK= 72,0 MPa/ 1,019 = 71 MPa. Amplitude of the component fatiguelimit for thegiven mean stress 5SAFETY FACTORS For severe consequence of failure, for noregular inspection and for castingstested non-destructively Because of the low elongation of GGthe safetyfactoris to be increasedby: According to Chapter 4.4.2.2 the individual mean stressesare to be appliedinsteadof an equivalent mean stress. Calculation forthe type of overloading F2. crl,min= 15 MPa- 18,6MPa = - 3,6MPa, crl,max=15 MPaMPa + 18,6=33,6MPa, Ral =- 3,6/33,6 =- 0,107. Because of - CX) < -0,107°field II applies: Meanstresssensitivity aM = 0, b M =0,5, M a =0,5. Mean stressfactorfor direction1 Tab. 4.4.2 (4.4.34) (4.4.26) .io =1,9. = 0,5, .in = 2,4. Temperature factor, see above, KT,O =0,856. Total safety factor jges= 2,4/0,856= 2,80. Tab. 4.5.2 (4.5.2) (4.5.4) M a =0,5, 1 KAK,al = 1+0,5.15/18,6 =0,713. Mean stressfactorfor direction 2 The stressratiosof bothdirections agree: R a 2 =Ral =- 0,107, KAK,a2 = 0,713. Residual stress factor (4.4.10) 6 ASSESSMENT Stress amplitudes, see above cra,l = 18,6MPa, cr a,2 = 6,2 MPa. Amplitudes of the component variable amplitude fatigue strength, see above, crl,BK= 56 MPa, cr2,BK= 50 MPa. For normal stress there is KE,a =1. (4.4.5) Amplitude of the component fatigue limit The amplitude of the component fatiguelimit results from the mean stressfactor, the residual stressfactor and the component fatiguelimit for completelyreversed normal stress: Degreesof utilization Individual types of stress, direction1 and 2 aBK,al = =0,929 , , aBK,a2 = 50 80 = 0,346. , (4.6.17) . Tab. 4.2.1 (4.6.23) (4.6.22) 6.3Compressor flange made of grey cast iron Combined typesof stress fw,'t =0,85, q=0,759, Sl,a =aBK,crl =0,929, S2,a=a BK,cr2 =0,346, a GH = ±.((0,929-0,346)2+0,346 2 +0,929 2) = 0,813, (4.6.21) a NH =MAX(0,929; 0,346)=0,929, aBK,sv= 0,759. 0,929+(1 - 0,759). 0,813 = = 0,901. (4.6.20) The degree of utilizationof thecomponent fatigue strengthis90 %. The assessment of the fatigue limit is achieved. Note:Different from an assessment of the static strength the presented calculation for combined types of stress applies inthe case of proportional stresses only. For non-proportional stresses o l andcr2 the rules of superposition in Chapter 4.6 arenotapplicable andthe procedure proposed inChapter 5.10 is to be applied instead. 244 ........ 6 Examples 245 6.4 Welded notched component 6 Examples 6.4 Welded notched component Key words: Milledsteel, weldednotchedcomponent, assessment of the static strength, assessment of the variable amplitude fatiguestrength, type of overloading F2, class of utilization, nominal stress, structural stress, effective notch stress. Given: Stresses: Cyclic variable amplitude axialstresses, Figure 6.4.1. Characteristic nominal stresses, determined elementary: Safetyrequirement: Accordingtothestatements "with moderate consequences of failure; regular inspections". Task: Assessmentof thestaticstrength andassessment of the variable amplitude fatigue strength. Methodofcalculation: Rod-shaped(ID) component. Theassessment of thestaticstrength isto be carried out using nominal stresses and structural stresses (an assessment ofthe static strengthusing effectivenotch stresses isnot possible). The assessment of thevariable amplitude fatigue strengthis tobe carriedout using nominal stresses, structural stressesandeffective notch stresses. 2MATERIAL PROPERTIES Smax exzd =150 MPa + 75MPa =225MPa . , , Smax,ex,wv,zd =Sl.,zd =Smax,ex,zd = 225 MPa . (1.1.2) *1(1.1.1) Maximum equivalent nominal stress Maximum nominal stress The degrees of utilization obtained with nominal stresses, with structural stresses and with effective notchstressesshould agree. For welded components the assessment of the component staticstrength is ingeneral to be carried out separately for the toesection(toeof theweld) and for thethroat section (root of theweld). Inthepresent case theassessment of thethroat section (rootof theweld)is sufficient. An equivalent stressis to be computed for the throat section. Calculation using nominal stresses 1CHARACTERISTIC STRESSES ASSESSMENT OF THECOMPONENT STATIC STRENGTH Tensile strength andyield strength of theplate material R m =610 MPa,R p =500 MPa. Tab. 5.1.2 The values apply tothecomponent. Thetechnological size factoris notrelevant, Eq. (1.2.15). Szd =Sm,zd ± Sa,zd =150 MPa ± 75 MPa. Characteristicstructuralstresses at theedge of the weld seam, determined by finite element analysis without observing the weld seam, (stress concentration factor Kt,cr = O'max / Szd= 2,5), Figure 6.4.1 Welded notched component F F 6.4..1 0'=O'm ±O'a=375MPa ± 187,5MPa. Characteristiceffectivenotchstresses attheedge of the weld determined by finite element analysis in considering the weld seam with an effective notch radius r = 1 mm, (stress concentration factor Kt,crK= O'K,max / Szd= 5,6), O'K =O'K,m ±O'K,a=840 MPa ±420 MPa. Therespectivecharacteristicstress amplitudes refer to the largest amplitude of the stress spectrumwhich co-responds to the class of utilization B2. S1:d 3 DESIGN PARAMETERS Material: StE 500, DIN17 102. Dimensions: Width of plate B =375mm Thickness of plate s =20 mm, Radius of cut-out r=100 mm. Weldseam: Full penetrationbuttweld, aswelded, toe angle S; 30 0, tested non-destructively, low residual stresses. Sectionfactor npl,zd=1 . Weldfactor Ow Ow =1,0. (1.3.9) Tab. 1.3.3 Typeof overloading: When overloadedinservice the stressratios remain constant (type of overloading F2). 1 Numbers of equations, tables and figures arethose of the guideline. 246 6.4 Welded notched component 6 Examples Design factor KSK,zd=1 /(1 . 1 ) =1 . (1.3.4) Maximum equivalent structural stress O'max,ex,wv= O'-L= 562,5 MPa. (3.1.2) 2MATERIAL PROPERTIES 4COMPONENT STATIC STRENGTH Tensilestrength and yieldstress of the platematerial Nominal value ofthe component static strength resul- tingfromthe tensilestrength and the designfactor: The values applytothecomponent. The technological size factoris notrelevant, Eq. (3.2.15). fer = 1 , SSK,zd=1 ·610 MPa/ I =610 MPa. Tab. 1.2.5 (1.4.1) R m = 610 MPa, R, = 500 MPa. Tab. 5.1.2 3 DESIGN PARAMETERS 5SAFETY FACTORS Plasticnotchfactor Tab. 1.5.1 For moderate consequences of failure, however, there is Kp,er =Kt,a =2,5. Section factor (3.3.13) Dueto a highyield stress, R p / R m >0,75, the tensile strength is deciding. (3.3.16) Tab. 3.3.3 KNL = I. Weld factorOw Ow =1,0. E= 2,1. 10 5 MPa, Tab. 3.3.1 8 ert r = 5% = 0,05, R p = 500 MPa, npl." = MIN(Jr- 2 -,1-. 1-0- 5 .-0-,0-5-/5-0-0; 2,5) = 2,5 . (3.3.9) The sectionfactor is limited by the plasticnotchfactor . Constant KNL (1.5.4) Tab. 1.5.1 Jm =1,75 , jp=1,3 . For normal temperature thereis KT,m =KT,p=I , (1.2.26) and in Eq. (1.5.4)the terms3 and 4 have no relevance: R m =610 MPa, R p =500MPa . jges =MAX (1,75; 1,3· : ~ ~ ) =MAX(1,75; 1,59) =1,75. 6 ASSESSMENT Designfactor KSK,er = 1 / (2,5. 1 . 1,0) = 0,400 . (3.3.4) Maximum nominal stress, see above, Smax,ex,wv,zd=225 MPa. Component staticstrength,nominal value, see above, SSK,zd = 610MPa. Degree of utilization 4 COMPONENT STATIC STRENGTH Local valueofthecomponent static strengthresulting from the tensile strength and the designfactor: fa= 1 , Tab. 3.2.5 O'SK= 1 ·610 MPa/ 0,400= 1525 MPa. (3.4.4) (1.6.1) 225 aSK d = = 0,646 . .z 610/1,75 The degreeof utilization of the component static strengthis65%. The assessment of the static strength is achieved. 5 SAFETY FACTORS Safety factors according to Chapter 3, as before: jges =1,75. (3.5.4) 6 ASSESSMENT .Calculation using structural stresses 1 CHARACTERISTIC STRESSES Maximum structural stressat the inside edge of the weld (3.1.1) O'max,ex =375 MPa+187,5MPa=562,5 MPa. Maximum structural stress, see above, O'max,ex,wv= 562,5 MPa. Component structural staticstrength, see above, O'SK =1525 MPa. 247 6.4 Weldednotched component 6 Examples Degree of utilization Fatigue class 562,5 aSK,cr =1525/1,75 =0,646. (3.6.1) FAT 40. Thickness factor Component fatigue limit for completelyreversedstress Component fatigue limit for completely reversed nominal stressresultingfromtheweldspecific fatigue limit for normal stress and the design factor: The degree of utilization of the component static strength is 65 %(as with nominal stresses). The assessmentof the static strength is achieved. ASSESSMENT OF THE COMPONENT FATIGUE STRENGTH For weldedcomponents the assessment ofthefatigue strength is in general to be carried out separately for the toesection(toeoftheweld) andforthethroat section (root of the weld). Furthermoretheassessment ofthefatiguestrengthfor welded components is in general to be carried out separatelyfor thebasematerial (withrollingskin)and for the weld. *2. The lessfavorable caseisdeciding. Becauseofthecomparativelylow fatiguepropertiesof welded componentsthe weld is normally deciding. In this present case an assessment of the fatigue strength for the root of the weld is sufficient. Surface treatment factor Kv=1. Constant KNL,E KNL,E= 1. Design factor KWK,zd=225 / (40 . 1 . 1 . 1) =5,63. 4COMPONENT FATIGUE STRENGTH SWK,zd=92 MPa / 5,63=16,3 MPa. (2.3.33) (2.3.28) (2.3.32) (2.3.4) (2.4.1) Mean stress sensitivity, low residualstresses, Amplitudeofthe component fatiguelimit forthegiven mean stress Calculation usingnominal stresses 1 CHARACTERISTIC STRESSES For the weld section the (largest) amplitude and the mean value of the characteristic nominal stress is M cr =0,3. Calculation for the type of overloading F2. '. Tab. 2.4.1 2Because ofdifferent slopes the SoN curves ofnon-welded and ofwelded components may overlap for amplitudes exceeding the fatigue limits Independent of the type of steel the weld specific fatigue limit for completelyreversed nominal stress is Thefatigue class(FAT) is requiredto derive the design factor after Eq. (2.3.4). However theweldednotched component consideredisnot containedinTable5.4.1 andtherefore anassessment usingnominal stresses is not possible, on principle. Nevertheless in order to demonstrate the respective way of calculation, a (re-calculated) fatigueclassissupposedtobeapproxi- mately valid for the calculation below: Smin,zd =150 MPa - 75 MPa=75 MPa, (2.4.26) Smax,zd =150 MPa +75 MPa=225 MPa, Rzd=75 /225=+ 0,333. Because of 0