FKM_Guidelines-Calcul-Fatigue-Resistance-Materiaux (1).pdf

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I,

ANALYTICAL STRENGTH ASSESSMENT 5t h Edition

II I

VDMA Verlag

Forschungskuratorium Maschinenbau

I

FKM-Guideline

ANALYTICAL STRENGTH ASSESSMENT OF COMPONENTS IN MECHANICAL ENGINEERING 5 th , revised edition, 2003, English Version

Translation by E. Haibach

Title of the original German Version:

RECHNERISCHER FESTIGKEITSNACHWEIS FUR MASCHINENBAUTEILE 5., iiberarbeitete Ausgabe, 2003

Editor: Forschungskuratorium Maschinenbau (FKM) Postfach 71 0864, D - 60498 Frankfurt / Main Phone *49 - 69 - 6603 - 1345

(c) 2003 byVDMA Verlag GmbH 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 irgendeiner Form (Druck, Fotokopie, Mikrofilm oder anderes Verfahren) 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 IMA Materialforschung und Anwendungstechnik Gmhfl, Dresden, as contractor in charge, by

Dr.-Ing. Bernd Hanel, IMA Materialforschung und Anwendungstechnik 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 und Betriebsfestigkeit,

and it was discussed among experts from industry and research institutes in the FKM expert group "Strength of components" .

Financial grants were obtained from the "Bundesministerium fUr Wirtschaft (BMWi, Bonn)" through the "Arbeitsgemeinschaft industrieller Forschungsvereinigungen 'Otto von Guericke ' e.V. (AiF, K6ln)" under contract AiF-No. D-156 and 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 to conform with the state of the art. It has been prepared with the necessary care. The user is expected to decide, whether the guideline meets his particular requirements, and to observe appropriate care in its application. Neither the publisher nor the editor, the involved experts, or the translator shall be liable to the purchaser or any other person or entity with respect to any liability, loss, or damage caused or alleged to have been caused directly or indirectly by this guideline.

4

Preface to the English Version of the 5th Edition. For engineers concerned with construction and calculation in mechanical engineering or in related fields of industry the FKM-Guideline for analytical strength assessment is available since 1994. This guideline was elaborated by an expert group "Strength of components" of the "Forschungskuratorium Maschinenbau (FKM), Frankfurt/Main," with financial support by the Bundesministerium fur Wirtschaft (BMWi), by the "Arbeitsgemeinschaft industrieller Forschungsvereinigungen 'Otto von Guericke" and by the "Forschungskuratorium Maschinenbau. Based on former 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 applicable in mechanical engineering and in related fields of industry, - allows the analytical strength assessment for rodshaped (lD), for shell-shaped (2D) and for block-shaped (3D) components under consideration of all relevant influences, - describes the assessment of the static strength and of the fatigue strength, the latter according to an assessment of the fatigue limit, of the constant amplitude fatigue strength, or of the variable amplitude fatigue strength according to the service stress conditions, - is valid for components from steel, cast steel, or cast iron materials at temperatures from -40°C to 500 °C, as well as for components from aluminum alloys and cast 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 uniformly structured calculation procedure 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, consisting of statements, formulae, and tables. Most of the included figures have an explanatory function only.

Textual declarations are given where appropriate to ensure a reliable application. Its content complies with the state of knowledge to an extend that may be 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 should be realized by means of a suitable computer program. Presently available are the PC computer programs "RIFESTPLUS" (applicable for a calculation using elastically 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 becomes apparent. Moreover the interest of users was confirmed by the well attended VDI conferences on "Computational Strength Analysis of Metallic Components", that were organized for presentation of the FKM-Guideline at Fulda in 1995, 1998 and 2002. The contents-related changes introduced with the third edition from 1998 were mainly concerned with the consideration of stainless steel and of forging steel, with the technological size factor, with the section factor for assessing the static strength, with the fatigue limit of grey cast iron and of malleable cast iron, with additional fatigue classes of welded structural details and with the local stress analysis for welded components, with the specification of an estimated damage sum smaller than one for the assessment of the variable amplitude fatigue strength, with the assessment of multiaxial stresses, and with the experimental determination of component strength values. An essential formal change in the third edition was a new textual structure providing four main chapters, that describe the assessment of the static strength or of the fatigue strength with either nominal stresses or local stresses, respectively. For ease of application each of these chapters gives a complete description of the particular calculation procedure, although this results in repetitions of the same or almost the same parts of text in the corresponding sections.

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The major change in the forth edition from 2002 is the possibility of considering structural 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 materials so far. The decisions necessary to include aluminum materials were derived from literature evaluations. It had to be recognized, however, that some of the relevant factors of influence were not yet examined with the desirable clearness or that available 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 aluminum alloys this guideline is delivered to the technical community by supposing that for the time being it will be applied with appropriate caution and with particular reference to existing experience so far. The involved research institutes and the "Forschungskuratorium Maschinenbau (FKM)" will appreciate any reports on practical experience as well as any proposals for improvement. Further improvements may also be expected from ongoing research projects concerning the procedure of static strength assessment using local elastic stresses, 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 an English version with the expectation that it might observe similar attention as the preceding editions on a broadened international basis of application.

Notes of the translator This English translation is intended to keep as close as possible to the original German version, but by using a common vocabulary and simple sentences. If the given translation is different from a literal one, the technical meaning of the sentence and/or of the paragraph is maintained, however. The translation observes an almost identical structure of the headlines, of the chapters, of the paragraphs and of the sentences, and even of the numbering of the pages. Also the tables and the figures as well as their numbering and headlines are adapted as they are, while only the verbal terms have been translated.

In particular the original German notation of the mathematical symbols, indices and formulas, 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 kindly asked to accept the more or less unusual kind of notation which is due to the need of clearly distinguishing between a great number of variables. In particular the applier is pointed to the speciality, that a comma ( , ) is used with numerical values instead of a decimal point ( . ), hence 1,5 equals 1.5 . for example.

For updates and amendments see www.fkm-guideline.de

6

References /1/

TGL 19 340 (1983). Ermiidungsfestigkeit, Dauerfestigkeit der Maschinenbauteile.

/2/

TGL 19 341 (1988). Festigkeitsnachweis fiir Bauteile aus Eisengusswerkstoffen.

/3/

TGL 19 333 (1979). Schwingfestigkeit, Zeitfestigkeit von Achsen und Wellen.

/4/

TGL 19 350 (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/

DIN 18 800 Teil 1 (1990). Stahlbauten, Bemessung und Konstruktion.

/8/

DIN ENV 1993 (1993). Bemessung und Konstruktion von Stahlbauten, Teil1-1: Allgemeine Bemessungsregeln, ... (Eurocode 3).

/9/

Hobbacher, A.: Fatigue design of welded joints and components. Recommendations of the Joint Working Group XIII-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 Festigkeitsnachweis fiir Maschinenbauteile, Kommentare.

/19/

FKM-Forschungsheft 180 (1994). Schweillverbindungen II.

/20/

FKM-Forschungsheft 143 (1989). Schweillverbindungen I.

/21/

FKM-Richtlinie Rechnerischer Festigkeitsnachweis fiir 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

0

General survey

0.1 0.2 0.3

Scope Technical background Structure and elements

1

Assessment of the static strength using nominal stresses

1.0 1.1 1.2

General Characteristic stress values Material properties Design parameters Component strength Safety factors Assessment

1.3

1.4 1.5

1.6

2

9

19 22 30 33 34 36

Assessment of the fatigue strength using nominal stresses

2.0 2.1 2.2 2.3 2.4 2.5 2.6

General Parameters of the stress spectrum Material properties Design Parameters Component strength Safety factors Assessment

3

Assessment of the static strength using local stresses

3.0 3.1 3.2 3.3 3.4 3.5 3.6

General Characteristic stress values Material properties Design parameters Component strength Safety factors Assessment

4

Assessment of the fatigue strength using local stresses

4.0 4.1 4.2 4.3 4.4 4.5 4.6

General Parameters of the stress spectrum Material properties Design parameters Component strength Safety factors Assessment

41 47 50 57 68 70

5

Appendices

Page

5.1 5.2 5.3 5.4

Material tables. Stress concentration factors Fatigue notch factors Fatigue classes (FAT) for welded components of structural steel and of aluminum alloys 5.5 Comments about the fatigue strength of welded components 5.6 Adjusting the stress ratio of a stress spectrum to agree with that of the S-N curve and deriving a stepped spectrum 5.7 Assessment using classes of utilization 5.8 Particular strength characteristics of surface hardened components 5.9 An improved method for computing the component fatigue limit in the case of synchronous multiaxial stresses 5.10 Approximate assessment of the fatigue strength in the case of non-proportional multiaxial stresses 5.11 Experimental determination of component strength values 5.12 Stress concentration factor for a substitute structure

6

Examples

73

6.1 6.2 6.3

76 85 89 90 93

6.4 6.5 6.6

Shaft with shoulder Shaft with V-belt drive Compressor flange made of grey cast iron Welded notched component Cantilever subject to two independent loads Component made of a wrought aluminum alloy

97 103 106 113 125 127

131 178 187

195 209

216 218 222

223

226 227 230

231 236 241 245 250 256

7

Symbols and basic formulas

7.1 7.2 7.3 7.4 7.5 7.6

Abbreviations Indices Lower case characters Upper case characters Greek alphabetic characters Basic formulas

260 261 262

8

Subject index

263

259

8

9

o General survey

lRo2 EN.dog

0.1 Scope This guideline is valid for components in mechanical engineering and in related fields of industry. Its application has to be agreed between the contracting parties. For components subjected to mechanical loadings it allows an analytical assessment of the static strength and of the fatigue strength, the latter as an assessment of the fatigue limit, of the constant amplitude fatigue strength or of the variable amplitude fatigue strength, according to the service stress conditions. Other analytical assessments, for example of safety against brittle fracture, of stability, or of deformation under load, as well as an experimental assessment of strength *1, are not subject of this guideline. It is presupposed, that the components are professionally produced with regard to construction, material and workmanship, and that they are faultless in a technical sense. The guideline is valid for components produced with or without machining or by welding of steel, of iron or of aluminum materials that are intended for use under normal or elevated temperature conditions, and in detail - for components with geometrical notches, for components with welded joints, for static loading, - for fatigue loading with more than about 104 constant or variable amplitude cycles, - for milled or forged steel, also stainless steel, cast iron materials as well as aluminum alloys or cast aluminum alloys, - for component temperatures from- 40°C to 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. If an application of the guideline is intended outside the mentioned field of application additional specifications are to be agreed upon.

The guideline 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.

1 Subject of Chapter 5.11 "Experimental determination of component strength values" is not the realization of an experimental assessment of strength, but the question how specific and sufficiently reliable component strength values suitable for the general procedure of strength assessment may be derived experimentally. 2 In particular, what critical points of the considered cross-sections or component.

o General survey 0.2 Technical Background Basis of the guideline are the references listed on page 7, in particular the former TGL-Standards, the former Vlrl-Guideline 2226, as well as the- regulations of DIN 18 800, the IIW-Recommendations and Eurocode 3. Moreover the guideline was developed to the current state of knowledge by taking into account the results of more recent investigations.

0.3 Structure and elements Page

Contents 0.3.0

General

0.3.1

Procedure of calculation

0.3.2

Service stresses

0.3.3 0.3.3.0 0.3.3.1

Methods of strength assessment General Assessment of the static strength using nominal stresses, Chapter 1 Assessment of the fatigue strength using nominal stresses, Chapter 2 Assessment of the static strength using local stresses, Chapter 3 Assessment of the fatigue strength using local stresses, Chapter 4

0.3.3.2 0.3.3.3 0.3.3.4

9

10

11

12

13

0.3.4 0.3.4.0 0.3.4.1 0.3.4.2 0.3.4.3

Kinds of components General Rod-shaped (lD) components Shell-shaped (2D) components Block-shaped (3D) components

13

0.3.5

Uniaxial and multiaxial stresses

16

14 15

0.3.0 General An assessment of the static strength is required prior to an assessment of the fatigue strength. Before applying the guideline it has to be decided -

what cross-sections or structural detail of the 2 component shall be assessed * and what service loadings are to be considered.

The service loadings are to be determined on the safe side, that is, with a sufficient probability they should be higher than most of the normally occurring loadings *3. The strength values are supposed to correspond to an anticipated probability of 97,5 % (average probability of survival Po = 97,5 %).

3 Usually this probability can hardly be quantified, however.

10

0.3.1 Procedure of calculation The procedure of calculation for an assessment of the static strength is presented in Figure 0.0.1, the almost identical procedure for an assessment of the fatigue strength in Figure 0.0.2 *4. Sequential procedure of calculation

Safety factors

o General survey At the assessment stage (box at bottom of either Figure) the characteristic values of service stress occurring in the component (box at top on the left) and the component strength values derived from the mechanical material properties and the design parameters (middle column) are compared by including the required safety factors (box at bottom on the right). In specifying component fatigue strength values the mean stress and the variable amplitude effects are regarded as essential factors of influence. The assessment of strength is successful if the degree of utilization is less or equal 1,00, where the degree of utilization is defined by 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 Figure 0.0.1 Procedure of calculation for an assessment of the static strength.

--

Characteristic service S~resses

Sequential procedure of caJc.ulation

For an application of the guideline the stresses resulting from the service loadings have to be determined for the so-called reference point of the component, that is the potential point of fatigue crack initiation at the crosssection or at the component under consideration. In case of doubt several reference points are to be considered, for example in the case of welded joints the toe and the root of the weld. There is a need to distinguish the names and subscripts 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.

Component fati;~~l;it~~~~~~~l forzeromean stress

.,

:

Component fatigiielimlt for-the actualmean stress

Component fatigue strength i I

.~~--

JI Safety factors

Figure 0.0.2 Procedure of calculation for an assessment of the fatigue strength.

4 A survey on the analytical procedures of assessment based on the equations of the guideline may be found in Chapter 7.6. 5 Nominal stresses can be computed for a well defmed cross-section only.

The stresses are to be determined according to known principles and techniques: analytically according to elementary or advanced methods of theoretical mechanics, numerically after the finite element or the 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 kind of stress determination for the reference 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).

6 The elastic stress at the root of a notch exceeds the nominal stress by a stress concentration factor. In the case of welded joints effective notch stresses are applied to the assessment of the fatigue strength only. Structural stresses, also termed geometrical or hot spot stresses, are normally in use with welded joints only. For further information see Chapter 5.5.

11

Correspondingly the component strength values are to be determined as nominal strength values or as local strength values of the elastic local stress, of the effective notch stress or of the structural stress. With the procedures of calculation structured uniformly for both types of stress determination it is intended that more or less identical results will be obtained from comparable strength assessments based on either nominal stresses or local stresses.

0.3.3 Methods of strength assessment 0.3.3.0 General In order to present the guideline clearly arranged and user-friendly, it is organized in four chapters, Figure 0.0.3: - Assessment of the static strength using nominal stresses, Chapter I, Assessment of the fatigue strength using nominal stresses, Chapter 2, Assessment of the static strength using local stresses, Chapter 3, Assessment of the fatigue strength using local stresses, Chapter 4.

.~. Static strength

LNoml?al

Nominalstresses ) ;/ Static

strength

aSseSSlllent

~~. .r" Chapter 3: " 1.

15 The relevant temperature factors will be applied in combination with the safety factors at the assessment stage.

According to the temperature T the temperature factors apply as follows:

28

1.2 Material properties

1 Assessment of the static strength

using nominal stresses for fme grain structural steel, T > 60°C = KT,p = 1 - 1,2 . 10 -3 • T / DC,

KT,m

(1.2.28)

for other kinds of steel *17, T > 100°C, Figure 1.2.2: (1.2.29) 3 KT,m = KT,p = 1-1,7' 10- • (T / °C-100), for GS, T> 100°C: 1 - 1,5 . 10 -3 . (T /

°c -

(1.2.30) 100),

T / "C) 2.

(1.2.31)

Kr,m = Kr,p =

-

for GGG, T > 100°C: 1 - 2,4 . (10

K r. m = Kr,p =

-3 .

Kr,m = 1 - 4,5 . 10 -3 . (T / °C - 50) ~ 0,1, - 4, 5 . 10 -3 . (T / °C - 50) > KT=,1p - 0"1

*16.

- 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, 3 Kr,p = 1- 4,5' 10- . (T / °C - 100) ~ 0,1, Eq. (1.2.32) and (1.2.33) are valid from the indicated temperature T up to 200°C, and in general only, if the relevant characteristic stress does not act on long terms.

o,s

High temperature Rm,T strength

Eq. (1.2.28) to (1.2.31) are valid from the indicated temperature T up to 500°C. For a temperature above 350°C they are valid only, if the relevant characteristic stress does not act on long terms.

Rm;T

1

R. 'jm. Cre.ep.Strength I~TI Rm.Tl.

.1

If,;"' i.I

I 0/0 creep Iimit' Rp."f'

0,3 t--e-~+--'----+-~*+~'-Th-iL.".j

Rp,TiR p

I

I

.High temperature

Rp'Rm'}pt

fatigueslrength

O,l

CreepStreiiglh RmiTt O,21----,--+---+-~-+.......,,..-.;.1~~

·c:sw,zdiT-,....,...+~-------i'\----f'\-,--....-+\~-1

104 cycles approximately. Relevant are the stress spectra of the individual stress components. They are specified by a number of steps, i = 1 to j , giving the amplitudes Sa,zd,i. ... and the related mean values Sm,zd,i , ... of stress cycles, Figure 2.1.1, as well as the related numbers of cycles n, according to the required fatigue life *1.

2.1.1.1 Rod-shaped (ID) components Rod-shaped (ID) non-welded components For rod-shaped (lD) non-welded components an axial stress Szd , a bending stress Sb , a shear stress T s- and a torsional stress Tt are to be considered *3 . The respective amplitudes and mean values are Sa,zd,i , Sa,b,i , Ta,s,i , Ta,t,i , Sm,zd,i, Sm,b,i, Tm.s.i s Tm,t,i .

(2.1.1)

S.,zd,i

Figure 2.1.1 Sm,zd,f - -- -

Stress cycle Example: stress cycle (axial stress), stress ratio: . = Sm,zd,i -Sa,zd,i Zd,1 Sm,Z,1 d . + Sa,Z,1 d··

S.,zd,1

R

t

1 As a rule a stress spectrum is to be determined for normal service conditions, see footnote 3 on page 19. The largest amplitude Sa zd 1 ofa service stress spectrum with its related mean stress value Sm,zd,1' defme the step i = 1 and serve as the characteristic stress values. 2 Stress components acting opposingly can cancel each other inpart or completely.

42

2 Assessment of the fatigue strength using nominal stresses

2.1 Characteristic service stresses

(2.1.9)

Rod-shaped (ID) welded components

Parameters of the stress spectrum are:

For rod-shaped (lD) welded components the (nominal) stress values are in general to be determined separately for the toe section and for the throat section *4. Respective amplitudes and mean values see Eq. (2.1.1).

Sa,zd 1 characteristic (largest) stress amplitude of the , stress spectrum, equal to the amplitude in step 1 Sa,zd,i amplitude in step i, Sa,zd,i > 0, Sa,zd,i+ 1 / Sa,zd,i :s: 1, Sm,zd,i mean value in step i, N total number of cycles corresponding to the required fatigue life (required total number of cycles), N = Lni (summed up for 1 to j), n.1 related number of cycles in step i, N, = Lni (summed up for 1 to i), H total number of cycles of a given spectrum, 8 H = Hj = Lhi (summed up for 1 to j) * , h·1 related number of cycles in step i, Hi = Lhi (summed up for 1 to i), step, i = 1 to j, total number of steps, step for the smallest j amplitudes damage potential. Yzd

2.1.1.2 Shell-shaped (2D) components Shell-shaped (2D) non-welded components For shell-shaped (2D) non-welded components the (nominal) axial stresses in x- and y-direction, Szdx = Sx and Szdy = Sy, as well as a shear stress T, = T are to be considered. The respective amplitudes and related mean values are Sa,x,i, , Sa,y,i , Ta,i , Sm,x,i, , Sm,y,i, Tm,i .

(2.1.4)

Shell-shaped (2D) welded components For shell-shaped (2D) welded components, Figure 0.0.6, stress values are in general to be determined separately for the toe section and for the throat section *4. Respective amplitudes and mean values see Eq. (2.1.4).

2.1.2 Parameters of the stress spectrum 2.1.2.0 General A stress spectrum describes the stress cycles contained in the stress history of concern *5 • If the stress cycles show variable amplitudes a stress

spectrum is to be determined for every stress component *6. The constant amplitude stress spectrum may be regarded in the following as a special case '7 , for which i = I and Sa,zd = Sa,zd,i

=

Sa,zd,l ,

Yzd =

ke

j hi

Sa zd,i

kO"

L-=""' --'-

i=l H [ Sa,zd,l )

(2.1.10)

where 1 -1 is the field of alternating tension stress.

In case of a possible overload in service the stress ratio Rzd remains the same. Normal stress:

Field I:

KAK,zd =

Field III: 0 < Rzd < 0,5, field of fluctuating tension stress, where Rzd = 0 is the zero tension stress. Field IV: stress.

Rzd ~

Rzd

> 1: 1/ ( 1-

Ma) ,

0,5, field of high fluctuating tension KAK,zd-

For bending b the index zd is to be replaced by the index b, "tension stress" by "tension bending stress", and "compression stress" by "compression bending stress".

KAK,zd =

(not existing), (lower boundary changed), (unchanged), (unchanged).

(2.4.10)

1+ _cr_ . m,zd

'

(2.4.12)

Sa,zd

Field IV, Rzd~ 0,5:

AK,zd-

For torsion the index s is to be replaced by the index 1.

The mean stress factor KAK,zd ... is dependent on the mean stress and on the mean stress sensitivity.

, / Sa,zd

1+ M cr /3 I+M cr M S 3

K

2.4.2.1 Mean stress factor

1

1+M cr . Sm,zd

Field III, 0< Rzd < 0,5:

Shear stress: *3:

Field I: Field II: - 1 ~ Rs~ 0 Field III: 0 < n, < 0,5 Field IV: Rs~ 0,5

(2.4.9)

Rzd

Ma Sm,zd Sa,zd

3+M cr 3.(I+M ) 2 cr

'

(2.4.13)

stress ratio *6, Chapter 2.4.2.2, mean stress sensitivity, Chapter 2.4.2.4, mean stress *6, Chapter 2.4.2.2, stress amplitude.

For bending the index zd is to be replaced by b.

3 The fatigue limit diagram (Haigh diagram) for normal stress shows . increasing amplitudes for Rzd < -1 (negative mean stress). For negative mean stress the fatigue limit diagram (Haigh diagram) for shear stress is the same as for positive mean stress and symmetrical to Tm,s = O. Practically it is restricted to the fields of positive mean stress or a stress ratio Rs ~ -1 , as the mean stress in shear is always regarded to be positive, Tm,s ~ O.

Using the term Sm zd I Sa zd instead of (1 + Rzd ) I (1 - Rzd ) avoids numerical probl~, when the stress ratio becomes Rzd =- 00.

4 The type of overloading F2 is described first because it is of primary practical importance .

6 Or equivalent mean stress, equivalent minimum stress, equivalent maximum stress, Chapter 2.4.2.2.

5 Sm,zd / Sa,zd=(l+Rzd)/(l-Rzd)'

(2.4.11)

2.4 Component strength 2.4.2 Component fatigue limit according to mean stress Shear stress:

60

2 Assessment of the fatigue strength using nominal stresses For positive mean stresses, tm,s ~ 0, the same equations are valid if Sm,zd is replaced by tm,s and M, is replaced by M,

For KAK,s Field I is not existing and Field II is restricted to positive mean stresses R, ~ -1 . For positive mean stress, or R, ~ -1 , the same equations are valid if M cr is replaced by M.

For torsion the index s is to be replaced by t.

For torsion the index s is to be replaced by t.

Calculation for the type of overloading F3 In case of a possible overload in service the minimum stress Smin,zd remains the same.

Calculation for the type of overloading Fl In case of a possible overload in service the mean stress Sm,zd remains the same.

Normal stress:

Normal stress:

Smin,zd

For Smin,zd =

<

KE,cr ,SWK,zd -1

Smzd

For Sm,zd =

< - - - there is

'

KE,oo ,SWK,zd

I-M cr

KAK,zd = 1 1 (1 -

*7

KAK,zd = 11 (1 - M cr),

Ma) s

KAK,zd = 1 -

*7

I-Moo

Ma ),

(2.4.18)

Smin,zd

~

0 there is

1-M cr .Smin,zd I+M oo

(2.4.19)

(2.4.15)

Field III

(2.4.16)

2. 3+M oo for 0 < Smin,zd < there is 3 (1 + M cr )2 1+M cr 13 M cr 1+ M - -3-' Smin,zd KAK, d - _ _----"'cr _ z I+Moo 13

Field III

1 3 +M cr for - - < Sm,zd < ( )2 I+M oo I+M cr

Ma)~

for - 2 1(1 -

Sm,zd s 1 1 (1 + Ma) there is

Ma . Sm,zd,

there is

Field II (2.4.14)

Field II for -1 1 (1 -

-2

there is

(2.4.20)

Field IV Field IV for Smin,zd;?:

_2 . 3 + Moo 3

K

AK,zd -

(2.4.17) Sm,zd KE,cr SWK,zd

M,

mean stress *6, Chapter 2.4.2.2, residual stress factor, Chapter 2.4.2.3, component fatigue limit for completely reversed stress, Chapter 2.4.1, mean stress sensitivity, Chapter 2.4.2.4.

For bending the index zd is to be replaced by b.

M,

(I+M oo

Y

there is

3+Moo ( )2' 3· I+M oo

(2.4.21)

minimum stress *6, Chapter 2.4.2.2, residual stress factor, Chapter 2.4.2.3, component fatigue limit for completely reversed stress, Chapter 2.4.1, mean stress sensitivity, Chapter 2.4.2.4.

For bending the index zd is to be replaced by b.

Shear stress: Shear stress: For KAK,s Field I is not existing and Field II is restricted to positive mean stresses tm,s ~ 0 or o ~tm,s = Tm,s I(KE,< ' TWK,s) ~ 1/(1 + M"t).

7 The abbreviation Srn,zd = Sm,zd / (KE,cr' SWK,zd) applies inthe following to Smin,zd, Smax,zd , tm,s , ..., accordingly.

For KAK,s Field I is not existing and Field II is restricted to positive mean stresses Tm,s ~ 0 or - 1 s tmin,s = Tmin,s 1 (KE,< . TWK,s) s 0 . For positive mean stresses, tm,s ~ 0 , the same equations are valid if Smin,zd is replaced by tmin,s and M, is replaced by M r . For torsion the index s is to be replaced by t.

2.4 Component strength 2.4.2 Component fatigue limit according to mean stress

61

2 Assessment of the fatigue strength using nominal stresses

Calculation for the type of overloading F4

Individual mean stress

In case of a possible overload in service the maximum stress Smax,zd remains the same.

As a rule the individual mean stress Sm,zd is used to determine Smin,zd , Smax,zd and Rzd . For normal stress the respective equations are Smin,zd = Sm,zd - Sa,zd , (2.4.26) Smax,zd = Sm,zd + Sa,zd , Rzd= Smin,zd 1 Smax,zd ,

Normal stress:

Smax,zd

For Smax,zd =

KE,cr ,SWK,zd

KAK,zd = 1 1 (l -

< 0 there is

*7

110- ),

(2.4.22)

KAK,zd

s

2 1 (l + 110-) there is

I-M cr 'smax I-M cr

(2.4.23)

Field III 2 4 . 3 +M cr there is for - - - < Smax,zd No,cr.

KBK,zd = [(

1 cr -I).D + 1] k~ . ( N~cr ) :0 , N

(v zd)

M

where the damage potential is *6 *7

(2.4.48)

Component constant amplitude S-N curve model II: slopingfor N > ND,cr (non-welded aluminum alloys)

k

)kcr

'"j h i (S a,zd,i Vzd-_ k cr L.=-' -. i=l H Sa,zd,l

l

(2.4.54)

,

Assessment ofthe fatigue strength for finite life: KBK,zd = (N O,cr / N) l/k cr

for N'< No,cr.

(2.4.49)

KBK,zd = (N O,cr / N) l/kO,cr for No,cr SAK,zd , until a..!alue N equal to the required total number of cycles N is obtained. From the respective value of Sa,zd,1 the variable amplitude fatigue strength factor is obtained as

66

2 Assessment of the fatigue strength using nominal stresses Calculation using a class of utilization The variable amplitude fatigue strength factor KBK,zd is to be determined according to the appropriate class of utilization "12 , Chapter 5.7.

Calculation amplitude

using

a

damage-equivalent

When using a damage-equivalent stress amplitude the variable amplitude fatigue strength factor for both constant amplitude S-N curves model I and model II is KBK,zd = 1.

If a value KBK,zd < I is obtained from Eq. (2.4.63), then the value to be applied is

= 1.

(2.4.64)

Component constant amplitude S-N curve model II: slopingfor N > N D, 0' (non-welded aluminum alloys) *11

In case of a component constant amplitude S-N curve model II (sloping for N > ND,O' or slope kD,a < kD,a < (0) the number of cycles N is first to be computed for a . ' 1/3 smgle value Sa,zd,1 = SAK,zd / (fn,O' ) as follows O

N={[A

kon

-1]'D +1}.[SAK'Zd)k M S a.zd.l

with

Akon fn,O'

f

ND,a

( II a

)kal3

(2.4.65) after Eq. (2.4.58) to (2.4.62) and the explanations as before, factor by which the endurance limit is lower than the fatigue limit, Table 2.4.4.

If a value N = N* > N is obtained then the calculation of N, Eq. (2.4.65), is to be continued for differing values Sa,zd,1 > SAK,zd / ( fn,O' )1/3 until a value N equal to the required total number of cycles N is obtained. From the respective value of Sa,zd,1 the variable amplitude fatigue strength factor is obtained as KBK,zd

(2.4.69)

(2.4.63)

KBI ND cr II, kD e II = co or for N > ND:"t.it" ' kD:"t:II= co.

ND'7 8 =10

N (lg)

Figure 2.4.6 Component constant amplitude S-N curve for welded components *13 Top: Bottom:

Normal stress S. Shear stress T.

Steel, cast iron materials and aluminum alloys, welded (Model I): horizontal for N > ND,cr, kD,cr = co or for N>ND,"t, kD,"t=co NC is the referencenumber of cycles correspondingto the characteristic strength values SAC and TAC. SAK,zd/ SAC = (Nc / ND,cr) 11ko = 0,736 and TAK,s / TAC = (Nc / ND,"t ) 11 kr = 0,457.

68

2.5 Safety factors

2.5 Safety factors

*1

!R25 EN .docl

Contents

Page

2.5.0

General

2.5.1

Steel

2.5.2 2.5.2.0 2.5.2.1 2.5.2.2

Cast iron materials General Ductile cast iron materials Non-ductile cast iron materials

2.5.3 2.5.3.0 2.5.3.1 2.5.3.2

Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys

2.5.4

Cast aluminum alloys

2.5.5

Total safety factor

68

2 Assessment of the fatigue strength using nominal stresses

2.5.2 Cast iron materials 2.5.2.0 General Ductile and non-ductile cast tron materials are to be distinguished.

2.5.2.1 Ductile cast iron materials 69

Cast iron material with an elongation As :2: 12,5 % are considered as ductile cast iron materials, in particular all types of GS and some types of GGG. Values of elongation see Table 5.1.12. Safety factors for ductile cast iron materials are given in Table 2.5.2. Compared to Table 2.5.1 they are higher because of an additional partial safety factor jF that accounts for inevitable but allowable defects in castings *4. The factor is different for severe or moderate consequences of failure and moreover for castings that have been subject to non-destructive testing or have not.

2.5.0 General According to this chapter the safety factors are to be determined.

Table 2.5.2 Safety factors for ductile cast iron materials GS; GGG) (A,:2: 12,5%\

The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average probability of survival of Po = 97,5 % *2.

JD

Consequences of failure severe moderatev!

I

castings not subject to non-destructive testing ~2 regular no 2,1 I 1,8 yes ~3 Inspection 1,9 I 1,7

The safety factors apply both to non-welded and welded components.

castings subject to non-destructive testing ~4 regular no 1,9 I 1,65 yes ~3 Inspection 1,7 I 1,5

2.5.1 Steel The basic safety factor concerning the fatigue strength

~1

See footnote

~1

of Table 2.5.1.

'IS

(2.5.1)

~2 Compared to Table 2.5.1 an additional partial safety factor jF = 1,4 is introduced to account for inevitable but allowable defects in castings.

This value may be reduced under favorable conditions, that is depending on the possibilities of inspection and on the consequences of failure, Table 2.5.1.

~3 Regular inspection in the sense of damage monitoring. Reduction by about 10 %.

.in = 1,5.

Compared to Table 2.5.1 an additional partial safety factor 1,25 is introduced, for which it is assumed that a higher quality of the castings is obviously guaranteed when testing. ~4

jF Table 2.5.1 Safety factors for steel *3 (not for GS) and for ductile wrought aluminum alloys (A:2: 12,5 %). Consequences of failure moderate ~1 severe

jD regular inspections

=

no

1,5

yes~2

1,35

1,3 1,2

~1

Moderate consequences of failure of a less important component in the sense of "non catastrophic" effects of a failure; for example because of a load redistribution towards other members of a statical indeterminate system. Reduction by about 15 %. ~2 Regular inspection in the sense of damage monitoring. Reduction by about 10 %.

1 Chapters 2.5 and 4.5 are identical.

2 Statistical confidenceS ; 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 safety factor to jF = 1,0 does not seem possible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components have to meet special demands on qualification and checks of the production process, as well as on the extent of quality and product testing in order to guarantee little scatter of their mechanical properties.

69

2.5 Safety factors

2 Assessment of the fatigue strength using nominal stresses

2.5.2.2 Non-ductile cast iron materials

2.5.3.2 Non-ductile wrought aluminum alloy

Cast iron materials with an elongation AS < 12,5 % (for GT A3 < 12,5 %) are considered as non-ductile materials, in particular some types of GGG as well as all types of GT and GG. Values of elongation for GGG and GT see Table 5.1.12 or 5.1.13. The value for GG is AS = O.

Wrought aluminum alloys with an elongation A < 12,5 % are considered as non-ductile materials. Values of elongation see Table 5.1.22 to 5.1.30.

For non-ductile cast iron materials the safety factors from Table 2.5.2 are to be increased by adding a value Llj, Figure 2.5.1 *s: Llj

= 0,5

-JAs /50%,

(2.5.2)

AS Elongation, to be replaced by A3 for GT.

For non-ductile wrought aluminum alloys all safety factors from Table 2.5.1 are to be increased by adding a value Llj , Eq. (2.5.2).

2.5.4 Cast aluminum alloys Cast aluminum alloys are always considered as nonductile materials. All safety factors from Table 2.5.2 are to be increased by adding a value Llj , Eq. (2.5.2). Values of elongation see Table 5.1. 31 to 5.1. 38.

GG 0,5

2.5.5 Total safety factor

Llj

o

1U 12,5

Similar to an assessment of the component static strength, Chapter 1.5.5, a "total safety factor" jges is to be derived: 20 As ,A3 in %

jges =

Figure 2.5.1 Value Llj to be added to the safety factor In , defined as a function of the elongation As or A3 , respectively.

2.5.3 Wrought aluminum alloys 2.5.3.0 (;eneral Ductile and non-ductile wrought aluminum alloys are to be distinguished.

2.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloys with an elongation A"C. 12,5 % are considered as ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. Safety factors for ductile wrought aluminum alloys are the same as for steel according to Table 2.5.1.

S For example the safety factor for GG is at least

in Gn

= I,S

+ O,S

= 2,0

(2.S.3)

= 1,5 from Table 2.5.2, j = O,S after Eq. (2.S.2) for AS = 0).

Jn Kt,D

i

D

,

(2.5.4)

T,D

safety factor, Table 2.5.1 or 2.5.2, temperature factor, Chapter 2.2.3.

70

2.6 Assessment

2.6 Assessment Contents

2 Assessment of the fatigue strength using nominal stresses

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EN.dog Page

2.6.0

General

70

2.6.1 2.6.1.1 2.6.1.2

Rod-shaped (lD) components Individual types of stress Combined types of stress

71

2.6.2 2.6.2.1 2.6.2.2

Shell-shaped (2D) components Individual types of stress Combined types of stress

An assessment of the variable amplitude fatigue strength and an assessment of the fatigue limit or of the endurance limit are to be distinguished. In each case the calculation is the same when using the appropriate variable amplitude fatigue strength factor KBK,zd , ... , Chapter 2.4.3, and when taking

(2.6.1)

Sa,zd, I = Sa,zd , ... , in case of a constant amplitude spectrum, or 72

2.6.0 General According to this chapter the assessment of the fatigue strength using nominal stresses is to be carried out. In general the assessments for the individual types of stress and for the combined types of stress are to be carried out separately *1. The procedure of assessment applies to both non-welded and welded components. For welded components assessments are generally to be carried out separately for the toe section and for the throat section. They are to be carried out in the same way, but using the respective cross-section values, nominal stresses and fatigue classes FAT as these are in general different for the toe and throat section.

Sa,zd,l

~

Sa,zd,eff

and

N

=

ND,cr

(2.6.2)

in case of a damage-equivalent stress amplitude. Sa,zd, ... ,

constant stress amplitude for which the required number of cycles is N, Sa,zd,eff, ... , damage-equivalent stress amplitude, ND,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 2.4.3.2.

Superposition For proportional or synchronous stress components of same type of stress the superposition is to be carried out according to Chapter 2.1. If different types of stress like axial stress,· bending stress, ... *4 act simultaneously and if the resulting stress

is multiaxial, Chapter 0.3.5 and Figure 0.0.9, both the individual types of stress and the combined types of stress are to be considered as described below *5.

Degree of utilization The assessment is to be carried out by determining the degree of utilization of the component fatigue strength. In the general context of the present Chapter the degree of utilization is the quotient of the (nominal) characteristic stress amplitude Sa,zd,l , ..., divided by the allowable (nominal) stress amplitude of the component fatigue strength at the reference point *2. The allowable stress amplitude is the quotient of the component variable amplitude fatigue strength after Chapter 2.4.3, SBI 16 mm,

7 Usually stress concentraction factors do nor exist in combinationwith local stresses. 8 The stress concentration factors Kt.o and Kt., given in Chapter 5.12 for a substitute structure are intended to be used in Chapter 4.3.1.1 only and should not be used in the present context.

9 For the toe of a weld the calculation is to be carried out as for nonwelded components.

88

3.3 Design parameters

3.3.5 Constant K NL The Constant KNL allows for the non-linear elastic stress strain characteristic of GG in tension and compression or in bending. For all kinds of material except for GG there is K NL = 1.

(3.3.16)

For GG the values (3.3.17)

K NL = KNL,Zug

apply to the tension side of the cross section (tension or tension from bending). The reciprocal values KNL,Druck

= 1/ KNL,Zug

(3.3.18)

apply to the compression side of the cross section (compression or compression in bending). Values of the KNL,Zug and KNL,Druck from Table 3.3.4.

Table 3.3.4 Constant KNL -c- 1. Type of material

GG

GG

GG

GG

GG

GG

-10

-15

-20

-25

-30

-35

KNL,Zug

1,15

1,15

1,10

1,10

1,05

1,05

KNL,Druck

0,87

0,87

0,91

0,91

0,95

0,95

~ 1 For unnotched and slightly notched components at tension or compression there is KNL = 1.

3 Assessment of the static strength using local stresses

89

3.4 Component strength

3.4 Component strength Contents

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EN.dog

Page

3.4.0 General 3.4.1 Non-welded components 3.4.2 Welded components

89

3 Assessment of the static strength using local stresses

3.4.2 Welded components For welded components the strength values are generally to be determined separately for the toe and for the root of the weld. For the toe of the weld the calculation is to be carried out as for non-welded components. For the root of the weld of rod-shaped (lD) welded components the local values of the component static strength for normal stress (tension or compression) as well as for shear stress are

3.4.0 General According this chapter the local values of the component static strength are to be determined. Non-welded and welded components are to be distinguished. They can be both rod-shaped (10), shellshaped (2D), or block-shaped (3D).

csx = fa . Rm I KSK,a , 'tSK = f~' Rml KsK,~.

(3.4.4)

For the root of the weld of shell-shaped (2D) welded components the local values of the component static strength for normal stresses (tension or compression) in the directions x and y as well as for shear stress are

3.4.1 Non-welded components crSK,x = fa . Rm I KSK,ax , crSK,y = fa . Rm I KsK,cry , TSK = f~' Rml KSK,~,

The local values of the component static strength of rodshaped (lD) components for normal stress (tension or compression) and for shear stress are *1 *2 O'sK=fa'Rm/KSK,a,

(3.4.1)

'tSK = f~ . Rm I KSK,~ . The local values of the component static strength of shell-shaped (2D) components for normal stresses (tension or compression) in the directions x and y as well as for shear stress are O'SK,x = fa . Rm I KSK,ax , O'SK,y = fa . Rm I KsK,cry , 'tSK = f~' Rml KsK,~ .

(3.4.2)

compression strength factor, Chapter 3.2.4, shear strength factor, Chapter 3.2.4, tensile strength, Chapter 3.2.1, design factor, Chapter 3.3.1. The local values of the component static strength of block-shaped (3D) components for the principal stresses (tension or compression) in the directions 1, 2 and 3 are O'l,SK = fa . Rm I KSK,a1 , 0'2,SK = fa . Rm I KSK,a2 , 0'3,SK = fa . Rm I K SK,a3 ,

(3.4.3)

compression strength factor, Chapter 3.2.4, tensile strength, Chapter 3.2.1, Rm KSK,al ... design factor, chapter 3.3.1.

fa

1 The component static strength values are different for normal stress and for shear stress, and moreover they are different due to different section factors according to the type of stress. 2 Basically the tensile strength Rm is the reference value of static strength, even if in the case of a low Rp / Rm ratio the yield strength is to be used for the assessment of the static strength, a fact that is accounted for in Chapter 1.5.5.

(3.4.5)

compression strength factor, Chapter 3.2.4, shear strength factor, Chapter 3.2.4. f~ tensile strength, Chapter 3.2.1, Rm design factor, Chapter 3.3.1. KsK, a, ... fa

For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the calculation is to be carried out as for shell-shaped (2D) welded components, if the stresses at the surface crx , cry and r are of interest only.

90

3.5 Safety factors

3.5 Safety factors

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Contents 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

General Steel 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 Global safety factor

EN .docl

Page 90

3 Assessment of the static strength using local stresses Table 3.5.1 Safety factors jm and jp for steel (not for GS) and for ductile wrought aluminum alloys As> 12,5 %). Consequences of failure jm ->1 ->2 severe moderate jp ->3 jmt ->S jpt ->4 high

91

92

3.5.0 General According to this chapter the safety factors are to be determined *1. The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average probability of survival of Po = 97,5 % *2.

Probability of occurrence of the characteristic service stress values

low ->6

2,0 1,5 1,5

1,75 1,3 1,3

1,0

1,0

1,8 1,35 1,35

1,6 1,2 1,2

1,0

1,0

->1 referring tothe tensile strength Rm ortothe strength atelevated temperature RmT, ->2 referring tothe yield strength Rp ortothe hot yield strength Rp,T , ->3 referring tothe creep strength Rm,Tt, ->4 referring tothe creep limit Rp,Tt . ->S moderate consequences of failure of a less important component in the sense of "no catastrophic effects" being associated with a failure; for example because of a load redistribution towards other members of a statically undeterminate system. Reduction byapproximately IS %.

The safety factors may be reduced under favorable conditions, that is depending on the probability of occurrence of the characteristic stress values in question and depending on the consequences offailure.

->6 or only infrequent occurrences of the characteristic service stress values, for example due to anapplication ofproof loads or due to loads during anassembling operation. Reduction byapproximately 10 %.

The safety factors are valid both for non-welded and welded components.

3.5.2 Cast iron materials

The safety factors given in the following are valid for ductile and for non-ductile materials. In this respect any types of steel are ductile materials, as well as cast iron materials and wrought aluminum alloys with an elongation As~ 12,5 %, while GT, GG and cast aluminum alloys are always considered as non-ductile materials here. *3

3.5.2.0 General Ductile and non-ductile cast iron materials are to be distinguished.

3.5.2.1 Ductile cast iron materials Cast

iron

materials with an elongation % are considered as ductile, in particular all types of GS and some types of GGG (not GT and not GG). Values of elongation see Table 5.1.12. A5~12,5

3.5.1 Steel Safety factors applicable to the tensile strength and to the yield strength, to the creep strength and to the creep limit are given in Table 3.5.1.

1 The 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 as well. 2 Statistical confidence S = SO %. 3 All types of GT, GG and cast aluminum alloys have elongations As < 12,S % and are considered as non-ductile materials here. Wrought aluminum alloys with elongations As < 12,S % are considered asnonductile materials, too. For non-ductile materials the assessment of the static strength is to be carried outwith local stresses.

Safety factors for ductile cast iron materials are given by Table 3.5.2. Compared to Table 3.5.1 they are higher because of an additional partial safety factor jF that accounts for inevitable but allowable defects in castings. The factor is different for castings that have been subject to non-destructive testing or have not *4 .

4 In mechanical engineering. cast components areof standard quality for which a further reduction of the partial safety factor to jr = 1,0 does not seem possible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components have to meet special demands and (cont'dpage 91)

91

3.5 Safety factors

Table 3.5.2 Safety factors jm and jp for ductile cast iron materials (GS; GGG with A5~ 12,5 %) -}1 Consequences of failure severe moderate

jm

jp jmt

castings not subject to non-destructive testing-}2 high 2,8 2,45

low

2,1

1,8

2,1 1,4 2,55

1,8 1,4 2,2

1,9

1,65

1,9 1,4

1,65 1,4

castings subject to non-destructive testing -}3 high 2,5 2,2 Probability of occurrence of the characteristic service stress values

GG 0,5 Aj

o

Jpt

Probability of occurrence of the characteristic service stress values

3 Assessment of the static strength using local stresses

low

1,9

1,65

1,9 1,25 2,25

1,65 1,25 2,0

1,7

1,5

1,7 1,25

1,5 1,25

-}1 Explanatory notes for the safety factors see Table

1U 12,5

20 As ,A3 in %

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.

3.5.3 Wrought aluminum alloys 3.5.3.0 General Ductile and non-ductile wrought aluminum alloys are to be distinguished.

3.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloy with an elongation A ~ 12,5 % are considered as ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. The safety factors for ductile wrought aluminum alloys are the same as for steel, Table 3.5.1.

3.5.1.

-}2

Compared to Table 3.5.1 an additional partial safety factor jF = 1,4 is introduced to account for inevitable but allowable defects in castings.

-}3

Compared to Table 3.5.1 an additional partial safety factor jF = 1,25 is introduced, for which it is assumed that a higher quality of the castings is obviously guaranteed when testing.

3.5.2.2 Non-ductile cast iron materials Cast iron materials with an elongation As < 12,5 % (A3 < 12,5 % for GT) are considered as non-ductile materials, in particular some types of GGG as well as all types of GT and GG. Values of elongation for GGG and GT see Table 5.1.12 or 5.1.13. The value for GG is As = 0 *5. For non-ductile cast iron materials the safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1 *6: L\j

=

0,5 -~A5 /50%.

(3.5.2)

3.5.3.1 Non-ductile wrought aluminum alloys Wrought aluminum alloy with an elongation A < 12,5 % are considered as non-ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. For non-ductile wrought aluminum alloys all safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1 and Eq. (3.5.2).

3.5.4 Cast aluminum alloys Cast aluminum alloys are always considered as nonductile materials. Values of elongation see Table 5.1.31 to 5.1.38. For cast aluminum alloys all safety factors from Table 3.5.2 are to be increased by adding a value L\j, Figure 3.5.1 and Eq. (3.5.2).

AS Elongation, to be replaced by A3 for GT.

checks' on qualification of the production process, as well as on the quality and extent of product testing in order to guarantee little scatter of their mechanical properties. 5 For GG the values Jp and Jpt are not relevant since the yield strength and the creep limit of GO are not specified.

6 For example the safety factor Jm for GG is at least

jm

(3.S.3)

= 2,0 + O,S = 2,S .

( jm = 2,0 from Table 3.5.2, moderate consequences, nondestructively tested, low probability, ~j O,S for AS = 0 from Eq.

=

(3.S.2) ).

92

3.5 Safety factors

3.5.5 Total safety factor From the individual safety factors the total safety factor is to be derived *7:

jges

(3.5.4)

jges =

MAX(~ ~.Rm ~ ~.Rm] KT,m ' KT,p

.lm ... Kt,m ...

R p ' KTt,m ' KTt,p

n, ,

safety factors, Table 3.5.1 and 3.5.2, temperature factors, Chapter 3.2.5 *8.

Simplifications The following simplifications apply to Eq. (3.5.4): In the case of normal temperature the third and fourth term have no relevance *9, and moreover there is 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 fourth term have no relevance *11.

7 MAX means that the maximum value of the four terms in the parenthetical expression is valid. 8 Applicable to the tensile strength Rm or to the yield strength Rp to allow for the tensile strength at elevated temperature ~ T ' the hot yield strength ~,T' the creep strength Rm,Tt , or the creep limit 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 there is a ratio of the safety factorsjp I jm = 0,75. 11 Since a yield strength and a creep limit are not specified.

3 Assessment of the static strength using local stresses

93

3.6 Assessment

3.6 Assessment Contents

3 Assessment of the static strength using nominal stresses !R36 EN.dog

strength, O"SK , ..., divided by the total safety factor jges. The degree of utilization is always a positive value.

Page

3.6.0

General

3.6.1 3.6.1.1 3.6.1.2

Rod-shaped (ID) components Individual types of stress Combined types of stress

3.6.2 3.6.2.1 3.6.2.2

Shell-shaped (2D) components Individual types of stress Combined types of stress

3.6.2 3.6.2.1 3.6.2.2

Block-shaped (3D) components Individual types of stress Combined types of stress

93

94

95

Superposition For stress components of the same type of stress the superposition is to be carried out according to Chapter 3.1. If different types of stress like normal stress and shear stress act simultaneously and if the resulting state of stress is multiaxial, see Figure 0.0.9 *5, the particular

extreme maximum stresses and the extreme minimum stresses are to be overlaid as indicated in the following. 96

Kinds of component

3.6.0 General According to this chapter the assessment of the component static strength using local stresses is to be carried out. In general the assessments for the individual types of stress and for the combined stress are to be carried out separately * I *2. In general the assessments for the extreme maximum and minimum stresses (normal stresses in tension and compression and/or shear stress) are to be carried out separately. For steel or wrought aluminum alloys the highest absolute value of stress is relevant *3.

Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. They can 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-welded components The degrees of utilization of rod-shaped non-welded components for the different types of stress like normal stress or shear stress are

The calculation applies to both non-welded and welded components. For welded components assessments are generally to be carried out separately for the toe and for the root of the weld as indicated in the following.

aSK,O' =

aSK,~

Degree of utilization The assessments are to be carried out by determining the degrees of utilization of the component static strength. In the context of the present Chapter the degree of utilization is the quotient of the characteristic stress (extreme stress O"max,ex, , ...) divided by the allowable static stress at the reference point *4. The allowable static stress is the quotient of the component static

I It is a general principle for an assessment of the static strength to suppose that all types of stress observe their maximum (or minimum) values atthe same time. 2 This is in order toexamine the degrees ofutilization ofthe individual types ofstress in general, and in particular if they may occur separately.

Different in the case ofcast iron materials or cast aluminium alloys with different static tension and compression strength values.

3

4 The reference point isthe critical point ofthe cross section that observes the highest degree ofutilization.

=

Cimax,ex

~

1,

(3.6.1)

CiSK / jges 'tmax,ex 'tSK / jges

s

1,

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 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. 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 points W are to be considered. As a rule bending will be more important. Moreover see Footnote 1.

94

3 Assessment of the static strength using nominal stresses

3.6 Assessment

Rod-shaped (ID) welded components For the toe of the weld of rod-shaped (lD) welded components the calculation is to be carried out as for rod-shaped (lD) non-welded components. For the root of the weld of rod-shaped (lD) welded components the degrees of utilization for normal stress and/or shear stress follow from the equivalent nominal stresses, Chapter 3.1.1.1: . O"max,ex wv aSK, wv,e = / .'.$; 1, O"SK Jges

(3.6.2)

q

f,

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,

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.

Rod-shaped (ID) welded components For the toe of the weld of rod-shaped (lD) welded components the calculation is to be carried out as for rod-shaped (lD) non-welded components.

(3.6.8) aSK,wv,cr, ... degree of utilization , Eq. (3.6.2).

3.6.2 Shell-shaped (2D) components

The degrees of utilization of shell-shaped (20) nonwelded components for the types of stress like normal stress in the directions x and y as well as shear stress are

3.6.1.2 Combined types of stress

asK,crx =

O"max,ex,x ..$; 1, O"SK,x / Jges

asK,cry =

O"max,ex,y ..$; 1, O"SK,y / Jges

Rod-shaped (ID) non-welded components

(3.6.4)

where

s = aSK,cr ,

(3.6.5)

(3.6.9)

't max, ex I----I.$; 1, 'tSK / jges

For rod-shaped (lD) non-welded components the degree of utilization for combined types of stress is *6

2)'

(3.6.7)

./3-1 shear strength factor, Table 3.2.5.

Shell-shaped (2D) non-welded components

total safety factor, Chapter 3.5.5.

aNH=±{lsl +~s2 +4.t

7

*'

3.6.2.1 Individual types of stress

related component static strength values, Chapter 3.4.2,

aSK,crv = q . aNH + (l - q) . llGH.$; 1,

./3-(l/f't)

For the root of the. weld of rod-shaped (ID) welded components the degree of utilization for combined types of stress (or loadings) is *8

'tmax, ex,wv aSK,wv,'t = ..$; 1, 'tSK / Jges

O"SK, ...

For non-ductile wrought aluminum alloys (elongation A < 12,5 %) there is q = 0,5 , otherwise

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,

(3.6.6)

t = aSK,cr ,

7Table 1.6.1 Constant q(f

t ) .

aSK,cr, .., degree of utilization, Eq. (3.6.1).

r, q

6 The applied strength hypothesis for combined types of stress is a combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Depending on the ductility of the material the combination is controlled by a parameter q as a function off, according to Eq. (1.6.7) and Table 1.6.1. For steel isq = 0 so 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.

Steel, Wrought AI-alloys 0,577 0,00

GOO

GT, Cast

GG

Al-alloys

0,65 0,264

0,75 0,544

0,85 0,759

Caution: For non-ductile wrought aluminium alloys (elongation A < 12,5 %) there is q = 0,5. 8 Eq. (3.6.8) does not agree with the structure ofEq. (3.1.2) on page 74. is an approximation which has to be regarded as provisional and therefore itis tobe applied with caution. It

95

3.6 Assessment

3 Assessment of the static strength using nominal stresses

J

related static component strength, Chapter 3.4.1,

crSK,x , ...

2 2· 2, 0, O"a,i+1/ O"a,i s 1,

8 In the following all variables and equations are presented for the local stress o only, but written with the appropriate indices they are valid for all other types ofstress as well. normal

9 In this case anassessment ofthe variable amplitude fatigue strength is tobe carried out. lOin this case an assess~nt ofthe fatigue limit isto be carried out for type I SoN curves if N= N ;:: ND,cr.,.2r an assessment ofthe endurance limit for type II SoN curves if N = N ;:: NDcr II , respectively, oran assessment for finite life based on the constant amplitude SoN curve (formally similar.20 an assessment ~ the variable amplitude fatigue 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.

2.1.2.2 Stress ratio spectrum

A constant stress ratio applies to all steps of a stress ratio spectrum:

Res,i = Res ,

(4.1.12)

11 The values N -total number ofcycles required -and II -total num~ ofcycles ofa given spectrum - are different ingeneral. The terms ni IN and hi I H are equivalent. 12 The damage potential is a characteristic for the shape of a stress spectrum. The values kcr = 5for normal stress and k't = 8for shear stress are valid for non-welded components. The values kcr = 3 and ~ = 8 are valid for welded components. The term hi IH may be replaced by ni IN . 13 A mean stress spectrum, for example, results from a static load with dynamic loads superimposed, a fluctuating stress spectrum, for example, results for a crane hook when lifting variable loads.

100

4.1 Characteristic service stresses

4 Assessment of the fatigue strength

using local stresses

4.1.3 Adjusting a stress spectrum to match the component constant amplitude S-Ncurve This chapter mainly applies to stress spectra the steps of which do not have the same stress ratio.

A mean stress spectrum, for example, has different amplitudes Ga,i ' and constant mean stress values Gm,i = Gm ' and consequently the individual steps have different stress ratios Ra,i . On the other hand the component constant amplitude S-N curve, Chapter 4.4.3.2, is derived for a constant stress ratio Ra . To allow the proper application of Miner's rule, Chapter 4.4.3.1, all steps of a spectrum, however, must have or must be converted to that stress ratio Ra,i = Ra, Chapter 5.6.1.

4.1.4 Determination of the parameters of a stress spectrum 5/6) there is

°

[

Step i P

1 2 3 4 5 6 7 8

Ga

°

1 0,875 0,750 0,625 0,500 0,375 0,250 0,125

i/

hi

Gal

1/3

2/3

1 0,917 0,833 0,750 0,667 0,583 0,500 0,417

1 0,958 0,917 0,875 0,833 0,792 0,750 0,708

a.l

p

(4.1.17)

a,l p=o

H·1

2 2 10 12 64 76 340 416 2000 2400 11000 13400 61600 75000 924984 1000000

Figure 4.1.3 Standard stress spectra Top: Binomial distribution. Bottom: Exponential distribution (straight line distribution). Spectrum parameter p, total number of cycles H = Hj = ~ hi = 106, number of steps j = 8 , damage potential Vcr for an exponent k cr = 5 of the component constant amplitude S-N curve.

= p + (1- p) .[:a,i)

: a,i )

Application: In case of existing experiences about the shape of the stress spectrum a suitable standard stress spectrum may be applied to assess the variable amplitude fatigue strength in two ways: -

Application of the damage potential v.,; Eq. (4.1.10) for an assessment of the variable amplitude fatigue strength according to the elementary version of Miner's rule, Chapter 4.4.3.1.

-

Application of the data on Ga,i / Ga,1 and hi of the steps i = 1 to j from Figure 4.1.3 for assessing the variable amplitude fatigue strength according to the consistent version of Miner's rule, Chapter 4.4.3.1.

The appropriate standard stress spectrum has to be specified separate from this guideline.

102

4.1 Characteristic service stresses

4.1.4.2 Class of utilization *15

A class of utilization is an approximately damageequivalent combination of different shapes of stress spectra and of specific figures of the required total numbers of cycles, Figure 4.1.4, see also Chapter 5.7.

4 Assessment of the fatigue strength using local stresses

question. In particular it is defined by the shape of the stress

cra.

WL

cra,1 Cl'a,cJt ~~......,-,...----i

....--~~--

ND,Q' N

Iii'

Figure 4.1.5 Damage-equivalent stress amplitude

Figure 4.1.4 Spectra corresponding to the same class of utilization

Component constant amplitude S-N. curve WL, number of cycles at the knee point ND cr, component variable amplitude fatigue life curve LL. Characteristic stress amplitude 0"a,1, required total number ofcycles. The damage-equivalent stress amplitude O"a,eff is. assigned to ND,O" and hence itallows an assessment ofthe variable amplitude fatigue strength to be performed asan assessment ofthe fatigue limit.

Example: Welded component, stress spectra with binomial distribution, stress. All three stress spectra are approximately damageequivalent and correspond to the same class of utilization B5, Table 5.7.4.

spectrum, the required total number of cycles and the characteristic (largest) stress amplitude, Figure 4.1.5.

N

normal

Parameters of the so derived stress spectrum Parameters of a so derived stress spectrum 0"a,1 B

O"m

characteristic (largest) stress amplitude equal to the amplitude in step 1 of the stress spectrum, class of utilization (a combination of the shape of the stress spectrum and the required total number of cycles), mean stress *16.

Analytical relationship: See Chapter 5.7. Application: In case of existing experiences about the shape of stress spectrum and the required total number of cycles a FEM-class of loading may be applied to the assessment of the variable amplitude fatigue strength, Chapter 2.4.3.1. The appropriate class of utilization has to be specified separate from this guideline.

4.1.4.3 Damage-equivalent stress amplitude

The damage-equivalent stress amplitude is a constant stress amplitude with an assigned number of cycles equal to the number of cycles at the knee point of the component constant amplitude S-N curve, ND CJ • It is damage-equivalent to the stress spectrum in

O"a,eff

damage-equivalent stress amplitude

O"m

related mean value.

Analytical relationship: Based on the elementary version of Miner's rule the damage-equivalent stress amplitude is obtained as d7 1 j 0"a.eff "" k n' ·crak 60 DC: (4.2.7)

for other kinds of steel *7, T> 100°C, Figure 4.2.1: (4.2.8) KT,D = 1-1,4' 10- 3. (T / °C-100), for GS, T> 100°C: KT,D = 1- 1,2 . 10 -3. (T / °C- 100),

4.2.3 Temperature factor 4.2.3.0 General

(4.2.6)

-

The temperature factor considers that the material fatigue strength for completely reversed stress decreases with increasing temperature.

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 3.2.3 in the Chapter 3.2,

Normal temperature, low temperature and elevated temperature are to be distinguished.

aT,D Constant, Table 4.2.2.

4.2.3.1 Normal temperature Normal temperatures are as follows: for fine grain structural steel from -40°C to 60°C, - for other kinds of steel from -40°C to + 100°C, for cast iron materials from -25°C to + 100°C, - for age-hardening aluminum alloys from -25°C to 50°C, - for non-age-hardening aluminum alloys from -25°C to 100°e.

Table 4.2.2 Constant aT,D *8. Kind of material aT,D

8

(4.2.9)

GGG 1,6

GT 1,3

GG 1,0

Forstainless steel novalues are known up to now.

(4.2.11)

105

4.2 Material parameters

4 Assessment of the fatigue strength

with local stresses Rm,T R m 'jm

High temperature strength Rm,T

I

I Rp I Rp'R m ' jp

o4 I~-+--''r-~:-- Rp,T ,

High temperature yieldstreilgth Rp,T 1 % creep limit Rp;Tt . Rp,Tt It p '1

0,3t----K:--+---",;:t-''':--tt--r---,.-J

R p . Rm ' jpt

Creep Strength R,.,Tt

0,2 m ........."'f-...,...,..,..,.,..,~=--+~-fu~-1

Rm,T~

1

R';;"""' jmt 0;1

o

o

100

ZOO

2.2.1.

300 400 Tin "C

500

Creep$trengthR,.;Tt Rm,Tt I Rm 'jmt

0,1 t====J=::='=b--L....,,=-1-..+1

o

o

100

Z,2.1b

200

300 400 Till 'c

500

Figure 4.2.1 Temperature dependent values of the static strength and of the fatigue strength plotted for comparison. Safety factorsj according to Chapter 3.5 or 4.5, respectively. Rm,TI Rm = KT,m,

Rm,Tt l Rm = KTt,m,

Rp,T I Rp = KT,p, Rp,Tt l Rp = KTt,p'

Rm,T, Rp,T as well as Rm, Tt, Rp,Tt

5

for t = 10 h.

Fatigue strength value at elevated temperature : crW,zd,T I crW,zd = KT,D· Top: Non-alloyed structural steel, as in the Figure 3.2.2, Rp I Rm = n, I R m = 0,65 , crW,zd I Rm = 0,45, Jm = 2,0, Jp = jmt = 1,5, Jpt = 1,0, in = 1,5 . Bottom: GG, as in Figure 3.2.2, crW,zd I Rm = 0,30, Jm = 3,0, Jrnt = in

= 2,4 .

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 alloys up to 200°C. The values CYW,zd,T and 1:W,s,T are not explicitly needed for an assessment of the fatigue strength, as only the temperature factor KT,D is used. For elevated temperature, and in particular when the mean stress Sm, i:- 0 , the fatigue strength in terms of the maximum stress may be higher than the static strength so that the assessment is governed by the static strength.

106

4.3 Design parameters

4 Assessment of the fatigue strength using local stresses KwK,crx =

4.3 Design parameters

(4.3.2)

1R43 EN.dog

Content

=_1_'(1+_1_.(_1_ _ 1)) ncr,x Kf KR,cr

Page

4.3.0

General

4.3.1 4.3.1.0 4.3.1.1 4.3.1.2

Design factors General Non-welded components Welded components

4.3.2 4.3.2.0 4.3.2.1 4.3.2.2

Kt-K f ratios General Computation of Kj-K, ratios Kj-K, ratio for superimposed notches

4.3.3 4.3.4 4.3.5 4.3.6 4.3.7

Roughness factor Surface treatment and coating factor Constant KNL,E Fatigue classes (FAT) Thickness factor

106

w K

: ,O"Y1= ncr,y

107 108

'(1+~.(_1 Kf

KR,cr

1 K y .K s .KNL,E '

-1)1 )

K y .K s .KNL,E

KwK,~ =

~ n1, {1+ ~f K~, -I)J Ky l Ks -(

>

109 110

III 112

The design factors of block-shaped non-welded components for the principle stresses in the directions 1, 2 and 3 (normal to the surface) are *2 KWK,crl =

(4.3.3)

~ n:,1 {1+ ~f -(K~,o -I)) >KYKS\N~E K WK,cr2 =

4.3.0 General According to this chapter the design parameters are to be determined in terms of design factors.

1

=_1 .(1+-2-.(_1 -1)] n cr,2 Kf K R,« KWK,cr3 =

++ ~f

4.3.1 Design factors 4.3.1.0 General Non-welded and distinguished.

welded

components

are

to

be

4.3.1.1 Non-welded components Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) non-welded components are to be distinguished. The design factors of rod-shaped (lD) non-welded components for normal stress and for shear stress are ·1 KWK,cr =

(4.3.1)

~ n1 {I+ ~f K~,o -I)) >K y >KS\N~E 0

-(

-(

K~o -I)) KYKS\N~E >

Kt-K f ratio, Chapter 4.3.2, constant, Table 4.3.1, if no better estimate is available, KR,cr, ... roughness factor, Chapter 4.3.3, Ky surface treatment factor, Chapter 4.3.4, Ks coating factor, Chapter 4.3.4, constant for GG, Chapter 4.3.5. KNL,E ncr, .., Kf

Table 4.3.1 Constant K,

.

Kind of material

Steel wrought Al-alloys

GS

GGG

GT cast Al-alloys

GG

Kf

2,0

2,0

1,5

1,2

1,0

'

KWK,~ =

=_1

n,

'(1+~.(_1 -1))' 1 x, Ky.K s KR,~

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

A better estimate of K f may be obtained from stress concentration factors Kt,cr and Kt,~ of a substitute structure, Chapter 5.12, and the Kt-K f ratios, Chapter 4.3.2.1: Kf~Kt:cr=Kt,cr/ncr or Kf~Kf,~=Kt,~/n~.

1 About the

purpose ofthe constant Kf see Footnote 1 inChapter 2.3.

2 The Kt-Kf ratio in direction 3 normal to the surface, ",,3. , is not contained in Eq. (4.3.3) since a stress gradient normal tothe surface isnot considered.

107

4.3 Design parameters

4,3.1.2 Welded components For the base material of welded components the design factors are to be computed as for non-welded components.

4 Assessment of the fatigue strength using local stresses FAT ft Kv Kg KNL,E

fatigue class, Chapter 4.3.6, thickness factor, Chapter 4.3.7, surface treatment factor, Chapter 4.3.4 *5, coating factor, Chapter 4.3.4; constant for GG, Chapter 4.3.5.

The design factors for the toe and for the root of a weld are in general to be determined separately, since the local stresses and the fatigue classes (FAT) may be different.

The fatigue classes FAT are in general different for normal stresses in the directions x and y as well as for shear stress.

Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) welded components are to be distinguished. The calculation can be carried out with structural stresses or with effective notch stresses.

For certain 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.

Calculation with structural stresses

Calculation with effective notch stresses

Steel and cast iron material

Steel and cast iron material as well as aluminum alloys

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), KWK,~ = 145/ (FAT' ft' Ko ),

(4.3.4)

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 KWK,crx = 225 / (FAT' ft' Ky' KNL,E), KwK,cry = 225 / (FAT' ft' Kv KNL,E), KwK,~ = 145/ (FAT' ft' Ko ).

(4.3.5)

The design factors of rod-shaped (lD) welded components made of ~ steel, of cast iron materials l'' , and of a1uminum alloys for normal stress and for shear stress are *6, KWK,crK = 1/ (Kv Kg' KNL,E), KWK,~K = 1/ !Ky' Kg).

For shell-shaped (2D) welded components, as a rule, only the effective notch stress in direction of the maximum effective notch stress and the corresponding shear stress are to be considered. The design factors are as before KWK,crK = 1 / (Ko . Kg . KNL,E ), KWK,~K = 1/ (Ky' Kg),

Aluminum alloys The design factors of rod-shaped (lD) welded components from aluminum alloys *4 for normal stress and for shear stress are, KWK,cr = 81 / (FAT' ft' Ky' Kg), 52 / (FAT' ft' Ky' Ks).

(4.3.6)

KwK,~ =

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 KWK,sx = 81 / (FAT' ft' Ky' Kg), KwK,sy = 81 / (FAT' ft' Ky' Kg), KwK,~ = 52/ (FAT' fi' Ky' Kg),

(4.3.8)

Kv Ks KNL,E

(4.3.9)

surface treatment factor, Chapter 4.3.4 *5, coating factor, Chapter 4.3.4, constant for GG, Chapter 4.3.5

For certain 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.

(4.3.7)

To some part the FAT values where derived with reference to the IIW recommendations and Eurocode 3 (Ref. /9/, /81). Moreover the design factors are supposed tobe valid, however, not only for weldable structural ste~1 but also for other kinds of steel (conditionally weldable steel, stainless steel) and weldable cast iron materials). 3

To some part the FAT values where derived with reference tothe IIW reco~endations (Ref. /91). Moreover the design factors are supposed to be v.ahd, however, for all weldable aluminum alloys, except the aluminum alloys 5000, 6000 and 7000. Numerical values see Footnote 7 on page 103.

4

5 As a rule

Ky is not relevant for welded components, that is Ky = I.

principle for steel: KWK,crK = 225 / (FAT ... ) where FAT = 225, 145 / (FAT ... ) where FAT = 145; aluminum alloys 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.

6 On

and

K~K,~K =

108

4.3 Design parameters

4 Assessment of the fatigue strength

using local stresses 3

4.3.2 Kt-Kr ratios

GG~V

400

//'~~it//

800

4.3.2.0 General

The Kj-K, ratios nO", ... allow for an influence on the fatigue strength resulting from the design (contour and size) of a non-welded component. Condition for the application of a Kj-K; ratio is a stress gradient normal to the direction of stress as shown in Figure 3.3.1 *7.

/ /

Kt-Kr ratios for normal stress 1,1

The Kt-Kr ratio for normal stress, Ocr, Figure 4.3.1, is to be computed from the related stress gradient GO" after Eq. (4.3.13) to (4.3.15). ;;;;

0,1 rnm"

1

there is

n 0" = 1 +G 0" . mm Itl

(4.3.13)

-(a o -0,5+

r

for 0,1 mm" 1 25 mrn the thickness factor is a function of the sheet metal thickness t (in mrn):

it = (25 mm / t)

n.

(4.3.34)

n after Table 4.3.7.

17 All fatigue classes for structural stresses given in the IIWRecommendations are considered except those for the base material. Considered are for steel FAT::; 140 for normal stress and FAT:::;; 100 for shear stress, or for aluminum alloys FAT::; 50 for normal stress and FAr::; 36 for shear stress. The calculation for the base material of welded components is to be carried out as for non-welded components. 18 The generally applicable fatigue strength values do not depend on the design of a component nor on the shape of the weld, because all these influences on the fatigue strength are considered when computing effective notch stresses. Chapter 5.5 (This is different from computing nominal stresses or structural stresses, see Chapter 5.5). 19 'Thethickness factor is supposed to be valid for steel, but also for aluminum alloys

4 Assessment of the fatigue strength using local stresses Table 4.3.7 Exponent n for the thickness factor. Type of the welded joint cruciform joints, transverse T-joints, plates with transverse attachments - as welded - toe ground transverse butt welds, - as welded butt welds ground flush, base material, longitudinal welds or attachments, - as welded or ground

n

0,3 0,2 0,2 0,1

113

4.4 Component strength, 4.4.1 Fatigue limit for completely reversed stress

4.4 Component strength

1R44 EN.dog

Content

Page

4 Assessment of the fatigue strength using local stresses aWK

= aW,zd I KwK,cr ,

aW,zd,1:W,s

4.4.0

General

4.4.1

Component fatigue limit for completely reversed stress

4.4.2 4.4.2.0 4.4.2.1

4.4.2.2 4.4.2.3 4.4.2.4

Component fatigue limit according to mean stress General Mean stress factor Calculation for type of overloading F2 Calculation for type of overloading FI Calculation for type of overloading F3 Calculation for type of overloading F4 Individual or equivalent mean stress Residual stress factor Mean stress sensitivity

113 KWK,cr ...

114

115 116 117 118

4.4.3

Component variable amplitude fatigue 119 strength 4.4.3.0 General 4.4.3.1 Variable amplitude fatigue strength factor 120 Calculation for a constant amplitude spectrum Calculation for a variable amplitude spectrum Elementary version of Miner's rule based on the damage potential Calculation according to the consistent version of Miner's rule 121 Calculation using a class of utilisation 123 4.4.3.2 Component constant amplitude S-N curve

4.4.0 General According to this chapter the component fatigue strength is to be calculated as follows: - Step 1: component fatigue limit for completely reversed stress in considering the design factor, Chapter 4.4.1, - Step 2: component fatigue limit in considering the mean stress factor, Chapter 4.4.2, - Step 3: component variable amplitude fatigue strength in considering the variable amplitude fatigue strength factor, Chapter4.4.3.

4.4.1 Component fatigue limit for completely reversed stress According to this chapter the component fatigue limit for completely reversed stress is to be calculated in considering the design factor.

(4.4.1)

1:WK = 1:w,s I KWK;t ,

material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1 design factor, Chapter 4.3.1

Eq. (4.4.1) is based on the fatigue limit for completely reversed stress, Eq. (4.2.1), (4.2.3) or (4.2.4), and on the design factor, Eq. (4.3.1), (4.3.4), (4.3.6) or (4.3.8). It applies to non-welded components for calculations with local stresses and to welded components both for calculations with structural stresses or with effective notch stresses *2. The component fatigue limits of shell-shaped (2D) components for completely reversed normal stresses in the directions x and y as well as for shear stress are aWK,x = aW,zd I KWK,crx ,

(4.4.2)

awK,y = aW,zd I KWK,cry ,

1:WK = 1:w,s I KwK,s , aW,zd, 'tw,s KwK,crx,...

material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1 design factor, Chapter 4.3.1

Eq. (4.4.2) is based on the fatigue limit for completely reversed stress, Eq. (4.2.1), (4.2.3) or (4.2.4), and on the design factor, Eq. (4.3.2), (4.3.5), (4.3.7) or (4.3.9). It applies to non-welded components for calculations with local stresses and to welded components both for calculations with structural stresses or with effective notch stresses. The component fatigue limits of block-shaped (3D) components for completely reversed principal stresses in the directions 1, 2, and 3 are al,WK = aW,zd l KWK,crl ,

(4.4.3)

a2,WK = aW,zd l KWK,cr2, a3,WK = aW,zd l KWK,cr3,

aW,zd,1:W,s K WK, I ...

material or weld specific fatigue limit for completely reversed stress, Chapter 2.2.1 design factor, chapter 4.3.1

Eq. (4.4.3) is based on the fatigue limit for completely reversed stress, Eq. (4.2.1), and on the design factor, Eq. (4.3.3). It applies to non-welded components. For certain applications block-shaped (3D) components may be welded at the surface, for example through surfacing welds. Then the calculation is to be carried out as for shell-shaped (2D) welded components.

Caution: See the comment in the second paragraph of Chapter 4.4.2. Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. The component fatigue limits of rod-shaped (lD) components for completely reversed normal stress and shear stress are *I

1 The component fatigue limits for completely reversed stress are different for normal stress and for shear stress, and moreover because of different stress gradients or different weld characteristics depending on the type of stress. 2 Structural stresses crWK, ... or effective notch stresses crWK,K . The index K is to be added where appropriate.

--r I

114 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress

4.4.2 Component fatigue limit according to mean stress 1R442 EN.dog 4.4.2.0 General According to this chapter the amplitude of the component fatigue limit is to be determined according to a given mean stress and, where appropriate, in considering a multiaxial state of stress. Comment: For non-welded components of austenitic steel, or of wrought or cast aluminum alloys the component fatigue limit is different from the component endurance limit for N = 00 , Chapter 4.4.3.2. Observing the specific input values the calculation applies to non-welded components (with local stresses) and to welded components (with structural stresses or effective notch stresses) *1. An improved procedure for non-welded components of steel to compute the component fatigue limit in the case of synchronous multiaxial stresses is given in Chapter 5.9. In combination with a stress spectrum the indicated stress ratio R, , ... commonly refers to step I of the stress spectrum (maximum amplitude), Ra,I, ... *2 *3. The mean stress factor, Figure 4.4.1, allows for the influence of the mean stress on the fatigue strength. Without mean stress the mean stress factor is KAK,cr

= KAK;t = 1.

(4.4.4)

The residual stress factor accounts for the influence of the residual stress on the fatigue strength. For nonwelded components the residual stress factor for normal stress and for shear stress is K E,cr = KE;r

= 1.

(4.4.5)

Rod-shaped (10), shell-shaped (2D) and block-shaped (3D) components are to be distinguished.

4 assessment of the fatigue strength with nominal stresses Rod-shaped (ID) components The mean stress dependent amplitudes of the component fatigue limit of rod-shaped (10) components for normal stress and for shear stress are 0'AK = KAK,cr . KE,cr . O'WK , 1:AK

=

KAK,cr, .. , KE,cr,

.

O'WK,

.

(4.4.6)

KAK;t . KE,~ . 1:WK ,

mean stress factor, Chapter 4.4.2.1, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1.

Eq. (4.4.6) applies' to non-welded and to welded components. Shell-shaped (2D) components The mean stress dependent amplitudes of the component fatigue limit of shell-shaped (2D) components for normal stress in the directions x and y as well as for shear stress are 0'AK,x = KAK.,x . KE,cr . O'WK,x ,

= KAK.,y . KE,cr = KAK.,~ . KE,~

0'AK,y 1:AK KAK.,x, ... KE,cr, '"

O'WK,x' .. ,

(4.4.7)

. O'WK,y , . 1:WK ,

mean stress factor, Chapter 4.4.2.1, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1.

Eq. (4.4.7) applies to non-welded and to welded components. Block-shaped (3D) components The mean stress dependent amplitudes of the component fatigue limit of block-shaped (3D) components *4 for principal stresses in the directions I, 2 and 3 are O'I,AK = KAK.,crl . KE,cr . O'I,WK , O'2,AK

= KAK.,cr2

(4.4.7)

. KE,cr . 0'2, WK ,

O'3,AK = KAK.,cr3 . KE,cr . O'3,WK , KAK.,crl , ... KE,cr,

.

O'I,WK, ..

mean stress factor, Chapter 4.4.2.1, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1.

1 Struktural stresses crWK' ... or effective notch stresses crWK.,K . In the following the missing index K is to be added where appropriate. 2 This definition is necessary only for mean stress spectra, not for stress ratio spectra or for fluctuating stress spectra, for which the stress ratios of all steps are identical. 3 For more details see Chapter 5.6.

4 For certain applications block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then the calculation may be carried out as for shell-shaped (2D) components.

i I

115 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress

Figure 4.4.1 Amplitude of the component fatigue strength as a function of mean stress or stress ratio (Haigh diagram), described in four fields of mean stress Example: Normal stress, types of overloading FI and F2. Given:

Component fatigue strength for completely reversed

4 assessment of the fatigue strength with nominal stresses

R :-= "

Q

@

(M~=O)

CD

stress crwK ' service stress amplitude cra , stress ratio Derived:

(M~=MQ/3)

Ra ,

(M~=O)

®

Amplitudes of the component fatigue limit oAK for the types of overloading FI and F2.

Type of overloading The mean stress factor, KAK,cr or KAK,~, depends on the type of overloading, Fl to F4. It distinguishes the way how the stress may increase in the case of a possible overload in service (not by crash). Therefore it is to be determined in the sense of a safety of operation in service, that is for normal stress as follows: - Type Fl: the mean stress am remains the same, - Type F2: the stress ratio Rcr remains the same, - Type F3: the minimum stress amin remains the same, - Type F4: the maximum stress a max remains the same. For shear stress a is to be replaced by L. Intermediate types of overloading are possible. Dependent on the type of overloading the amplitude of the component fatigue limit is different, Figure 4.4.1.

Shear stress: *5: Field I: Field II: - 1S; R~S; 0 Field III: 0 < R~ < 0,5 Field IV: R~~ 0,5

(not existing), (lower boundary changed), (unchanged), (unchanged).

4.4.2.1 Mean stress factor The mean stress factor for normal stress, KAK,cr , or shear stress, KAK,1: , depends on the mean stress and on the mean stress sensitivity.

Calculation for the type of overloading F2

*6

In case of a possible overload in service the stress ratio

Rcr remains the same. Normal stress:

Fields of mean stress In determining the mean stress factor, KAK,cr , ... , four fields of mean stress are to be distinguished. These depend on the stress ratio Rcr or on the mean stress am respectively, see Chapter 4.4.2.2.

Field I:

n, > 1:

KAK,cr=

1/ (1 - Ma),

(4.4.9)

(4.4.10)

Normal stress: Field I: Rcr > I, field of fluctuating compression stress, where Rcr = + or - 00 is the zero compression stress. Field II: -00 S; Rcr S; 0, where R, < -1 is the field of 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, stress.

~

0,5, field of high fluctuating tension

5 The fatigue limit diagram (Haigh diagram) for normal stress shows increasing amplitudes for R < -1 (compression mean stress). For negative mean stress the fatigue limit diagram (Haigh diagram) for shear stress is the same as for positive mean stress and symmetrical to ~m = O. Practically it is restricted to the fields of positive mean stress or a stress ratio R~ 2:- 1 , as the mean stress in shear is always regarded to be positive, ~m 2: 0 . 6 The type of overloading F2 is described first because it is of primary practical importance. (4.4.11)

Using the term crm / cra instead of (1 + Rcr ) / (1 - Rcr ) avoids numerical problems, when the stress ratio becomes Ra = - 00.

116

4 assessment of the fatigue strength with nominal stresses

4.4 Component strength 4.4.2 Component fatigue limit according to mean stress

Field III, Q< n, < 0,5:

Field IV

I+M cr /3 K

AK,cr -

Field IV, K

I+M cr M ' I+~. crm 3 ca

n,

AK,cr -

n, M;

am aa

~

(4.4.12) (4.4.17)

0,5:

3+M cr ( \2 3· 1 + Mcrl

(4.4.13)

'

am KE,cr aWK

M,

stress ratio *8, Chapter 4.4.2.2, mean stress sensitivity, Chapter 4.4.2.4, mean stress *8, Chapter 4.4.2.2, stress amplitude.

mean stress *8, Chapter 4.4.2.2, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4. I, mean stress sensitivity, Chapter 4.4.2.4.

Shear stress:

For KAK,'[ Field I is not existing and Field II is restricted to positive mean stresses ~ tm = Om / (KE,' . 0WK) ~ 1 / (1 + M'[) . For positive mean stresses the same equations are valid if Sm is replaced by t m and M, is replaced by M'[ .

°

Shear stress:

For KAK,'[ Field I is not existing and Field II is restricted to positive mean stresses R'[ ~ -I . For positive mean stresses, or R'[ ~ -I , the same equations are valid if M, is replaced by M'[

Calculation for the type of overloading F3

In case of a possible overload in service the minimum stress amin remains the same. Calculation for the type of overloading Fl

Normal stress:

In case of a possible overload in service the mean stress am remains the same.

-2

For smin = crmin / (KE,a . crWK) < - - - there is *9 I-M cr

Normal stress:

Field I

(4.4.18)

For sm= crm / (KE,a . crWK) < -1 / (l -M cr ) there is *9 (4.4.14)

Field II for - 2 /(1 -

Field II for -I / (l - M cr )

~

sm

s

1 / (l

Mcr)~

Smin

~

° there is

1-M cr .Smin.,zd I+M cr

+ M cr ) there is

(4.4.19)

(4.4.15)

Field III Field III for

°< Smin < -

2

3

(4.4.16)

KAK, cr =

Field IV Or equivalent mean stress, equivalent minimum stress, equivalent maximum stress, Chapter 4.4.2.2.

8

9 In the following the abbreviation sm= crm I accordingly tosmin , smax , tm , ... .

(KE.cr . 0"Wl()

applies

.

3+M

cr there is (I+M cr ) 2

1+ M cr /3 M cr ---·s· I+M cr 3 mm

--~~-----

I+M cr /3

(4.4.20)

117 4.4 Component strength 4.4.2 Component fatigue limit according to mean stress K

-

3+M cr

AKa - (1 + M cr)2 O"min

(4.4.21)

'

minimum stress *8, Chapter 4.4.2.2, residual stress factor, Chapter 4.4.2.3, component fatigue limit for completely reversed stress, Chapter 4.4.1, mean stress sensitivity, Chapter 4.4.2.4.

KE,a

O"WK

M,

Shear stress: For KAK" Field I is not existing and Field II is restricted to positive mean stresses, that is - 1 :::; tmin = 'tmin I (KE,t . 'tWK ) :::; O. For positive mean stresses, 'tm 2: 0 , the same equations are valid if Smin is replaced by tmin and Mcr is replaced by M,

Calculation for the type of overloading F4 In case of a possible overload in service the maximum stress O"max remains the same.

Normal stress:

For Smax= CY max I (KE,a . CYWK) < 0 there is *9 KAK,a =

1 I (1 - M, ),

4 assessment of the fatigue strength with nominal stresses

Shear stress: For shear stress the type of overloading F4 ('tmax remaining constant) can practically not being realized.

4.4.2.2 Individual or equivalent mean stress In each case Ra , O"min , and O"max are determined by mean stress and stress amplitude. The mean stress may be taken either as the individual mean stress according to type of stress or as an equivalent mean stress from the individual mean stresses of all types of stress. Individual mean stress As a rule the individual mean stress O"m is used to determine O"min , O"max and Ra . For normal stress the respective equations are (4.4.26) O"min = O"m - O"a , O"max = O"m + O"a , Ra = O"min I O"max , O"a O"min O"max Ra

stress amplitude, minimum stress, maximum stress, stress ratio.

For shear stress

0"

is to be replaced by t

.

(4.4.22) Equivalent mean stress *10,

for 0:::; smax :::; 2 I (I + M a ) there is KAK.

.o

I-M cr ,smax = ---.,;;---:,:;:::;.:. 1- M cr '

(4.4.23)

Field III

2 4 . 3 +M cr for - - - < Smax 1

GS

GGG

GT

GG

0,35 - 0,1

0,35 0,05

0,35 0,08

0,35 0,13

0 0,5

Kind of material

Wrought aluminum alloys 1,0 - 0,04

aM bM

Cast aluminum alloys 1,0 0,2

1> 1 also stainless steel.

11 Not applicable to components being cold rolled or shot-peened.

4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength

4.4.3 Component variable amplitude fatigue strength 1R443 EN.dog

119

4 Assessment of the fatigue strength using local stresses Except for GG, the following restrictions apply, Figure 4.4.3: crSK ~

4.4.3.0 General

'tBK

According to this chapter the amplitude of the component variable amplitude fatigue strength is to be derived from the stress spectrum and the component constant amplitude S-N curve, Chapter 4.4.3.2. The variable amplitude fatigue strength factor KBK•a , ... , to be calculated depends on the stress spectrum, that is on the required total number of cycles *1 and on the shape of the stress spectrum, as well as on the component constant amplitude S-N curve, and in addition it depends on the type of stress (normal stress or shear stress).

Rp

Observing the specific input values the calculation applies to both non-welded components (component constant amplitude S-N curve model I or model II) and to welded components (component constant amplitude S-N curve model I only). Rod-shaped (lD), shell-shaped (2D) and block-shaped (3D) components are to be distinguished.

(4.4.42)

, ,

yield strength, Chapter 1.2.1.1, plastic notch factors, Table 1.3.2, shear strength factor, Table 1.2.5.

Kp,o , K p,.

f. 4

N,

'!Ii.

Component fatigue life curve

N Component s-N curve

2

It has to be distinguished, whether - in case of a constant amplitude spectrum - an assessment of the fatigue limit (or endurance limit) or of the fatigue strength for finite life is intended, or whether - in case of a variable amplitude spectrum - an assessment of the variable amplitude fatigue strength is intended *2. The calculation for a constant amplitude stress spectrum is a special case of the more general case of calculation for a variable amplitude stress spectrum. In any case the way of calculation is the same, but the variable amplitude fatigue strength factors are different.

0,75 Rp . Kp,o

s 0,75 f.' Rp' Kp,.

lOB 2.••2

N,

'!Ii

Figure 4.4.2 Component constant amplitude S-N curve, component fatigue life curve derived by the consistent version of Miner's rule, and influence of the critical damage sum DM . Highest amplitude in stress spectrum GSK, component fatigue limit GAJ(, number of cycles N after the component constant amplitude S-N curve, number of cyclesN after the component fatigue life curve for DM < 1 or N' for DM = 1. It isN = N + (N' - N) DM. This formula implies that a number of cycles N -7 N is obtaine~ for spectra of increasing damage potential and a nu~er of cycles N = N for the constant amplitude stress spectrum as N' - N -7 O. In German the fatigue life curve is usually termed 'Gassner curve' and the constant amplitude S-N curve is usually termed' Woehler curve'.

Rod-shaped (ID) components The amplitudes of the component variable amplitude fatigue strength (highest amplitude in stress spectrum) of rod-shaped (lD) components for normal stress and for shear stress are, Figure 4.4.2, crSK 'tSK

= KsK,o . c AK , = KsK,•. 'tAK,

KSK,o , ... crAK,...

(4.4.41)

variable amplitude fatigue strength factor, Chapter 4.4.3.1, component fatigue limit, Chapter 4.4.2.

1 Required total number of cy~les and required component fatigue life are corresponding denotations. 2 In a simplified manner the variable amplitude fatigue strength can be derived on the basis of a damage-equivalent stress amplitude. Then the assessment ofthe variable amplitude fatigue strength turns out to be an assessment of the fatigue limit.

Figure 4.4.3 Restriction of the amplitudes of the variable amplitude fatigue strength, or of the maximum value crrn,1 + crBK,1 and the minimum value crrn,1 - crBK,1 respectively, in relation to the yield strength, displayed in terms of the Haigh-diagram.

4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength Shell-shaped (2D) components The amplitudes of the component variable fatigue strength (highest amplitude in stress of shell-shaped (2D) components for normal the directions x and y as well as for shear Figure 4.4.2,

O"AK,x, ...

4 Assessment of the fatigue strength using local stresses Calculation for a constant amplitude spectrum

amplitude spectrum) stresses in stress are,

O"BK,x = KBK,crx· O"AK,x, O"BK,y = KBK,cry . 0"AK,y , 'tBK = KBK,'t . 'tAK, KBK,crx , ...

120

Component constant amplitude S-N curve model I: horizontal for N > No,cr (steel and cast iron material) Assessment ofthe fatigue strength for finite Life: -)lIk KBK,cr= (No,cr/N cr forN: No,cr.

Block-shaped (3D) components

Assessment ofthe endurance Limit:

The amplitudes of the component variable amplitude fatigue strength (highest amplitude in stress spectrum) of block-shaped (3D) components for the principal stresses in the directions I, 2 and 3 are, Figure 4.4.2,

KBK,cr = f n,e

KBK,crl , ... O"l,AK, ...

(4.4.45)

variable amplitude fatigue strength factor, Chapter 4.4.3.1, component fatigue limit, Chapter 4.4.2.

Except for GG, the following restrictions apply, Figure 4.4.3: O"l,BK O"Z,BK

s 0,75 Rp . Kp,crl , s 0,75 Rp . Kp,crz,

(4.4.48)

Component constant amplitude S-N curve model II: sloping for N > Nn,cr (non-welded aluminum alloys)

Rp

O"l,BK = KBK,crl . O"l,AK, O"Z,BK = KBK,crZ . O"z,AK , 0"3,BK = KBK,cr3 . 0"3,AK,

*4

(4.4.46)

(4.4.51)

forN > NO,cr,ll. (4.4.52)

N

number of cycles of the component constant amplitudeS-N curve, Chapter 4.4.3.2, N required number of cycles, No,cr number of cycles at knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, ka slope of the component constant amplitude S-N curve for N < No,cr, Chapter 4.4.3.2. No.e.n number of cycles at second knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, ko,cr slope of the component constant amplitude S-N curve for N > No,cr , Chapter 4.4.3.2, f n.e factor by which the endurance limit is lower than the fatigue limit, Chapter 4.4.3.2, Table 4.4.4.

0"3,BK : No,a ) a value KBl NO,a ) a value KBK,cr is obtained from Eq. (4.4.53) that is smaller than the value obtained from Eq. (4.4.50) or (4.4.52), then the higher value from Eq. (4.4.50) or (4.4.52) is to be used.

5 Direct calculation without iteration. The results from the elementary version ofMiner's rule approach the results from the consistent version of Miner's rule on the safe side. 6 When computing the d~ge potential (and also in the following equations) the values ni and N according toth.:..;equired total number of cycles can be replaced by the values hi and H according to the total number ofcycles inthe given standard type spectrum, see Chapter 4.1. 7 Instead ofAJcon after Eq. (4:4.57) and (4.4.63) ishere A ele = I / (va) ke .

N

(4.4.55)

8 hi / H may also be replaced by n, / N , N Required total number ofcycles according tothe required fatigue life, N = Eni(summed up for I toj), ni number ofcycles instep i according tothe required fatigue life.

Characteristics ofthe stress spectrum according toChapter 4.1, component constant amplitude S-N curve according toChapter 4.4.3.2. Table 4.4.3 Critical damage sum DM, recommended values.

Steel, GS, Aluminum alloys GGG,GT,GG

non-welded components 0,3

welded components 0,5

1,0

1,0

Calculation according to the consistent version of Miner's rule *9 *10 Using the consistent version of Miner's rule the variable amplitude fatigue strength factor is to be computed iteratively for differing values of Ga,l , until a value N equal to the required total number of cycles N is obtained. The respective value of Ga,1 is used to derive the variable amplitude fatigue strength factor. Component constant amplitude S-N curve model I: horizontal for N > ND,a (Steel and cast iron material) In case of a component constant amplitude S-N curve model I ( horizontal for N > No,a or slope kD,o = (0) the number of cycles N to be computed for a value Sa,1 is (4.4.57) a N = {[ Akon -1] . DM + I}' [G AI< . NO,a,

)k

G a.l

where

9 The consistent version of Miner's rule allows for the fact, that the component fatigue limit will decrease asthe damage sum increases. The decrease applies tocomponent constant amplitude S-N curves model Ias well astomodel IIfor N D,s 2': 10 6 . 10 The consistent version ofMiner's rule was first developed byHaibach. simplified version allowing for the decrease ofthe fatigue limit became known as the modified version orthe Haibach method ofMiner's rule. A

4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength

Akon

= (

aaI a~

ka - I )

[

ZI J. Z2 ] . NI + v~m N2 '

k-I ( )k -I ( ) k-I ( )k -I ( )

ZI = a AK

a

a a,m

_

a a.l

Z2 =

a a,v

m-J

a

a a,v+!

_

a

(4.4.60)

a a,1

hi (aa,i

L -=-' -

)k

a a,1

i=1 H

N2 = v hi (aa,i

L-=-' -

i=1 H

(4.4.59)

a a.I

a a.l

Nl =

a

(4.4.58)

a

)k a

In case of a component constant amplitude S-N curve model II (sloping for N > No,a or slope kD,a < kD,a < (0) the number of cycles N is first to be computed for a single value aa,1 = a AK / (fn,a )1/3 as follows {[

Akon - I ] , DM + I}'

(aa

a

AK ) k a.l

N D:" / 3 ([n,,,)

with

(4.4.65)

Akon

after Eq. (4.4.58) to (4.4.62) and the explanations as before, factor by which the endurance limit is lower than the fatigue limit, Table 4.4.4.

(4.4.62)

aa,1

fn,a

N

number of cycles of the component constant amplitude S-N curve, Chapter 4.4.3.2, N D,« number of cycles at knee point of the component constant amplitude S-N curve, Chapter 4.4.3.2, DM critical damage sum, Table 4.4.3, stress amplitude in step i of the spectrum, stress amplitude in step 1 of the spectrum, component fatigue limit, slope of the component constant amplitude S-N curve for N < No, a , Chapter 4.4.3.2, j total number of steps in the spectrum, i number of the step in the spectrum, m number i = m of the first step below a AK , H total number of cycles in the given spectrum, H = Hj = L: hi (summed up for 1 to j), h·I number of cycles in step i, Hi = L: hi (summed up for I to i) '8. The computation is to be repeated iteratively for differing values a a,I > a AK , until a value N equal to the required total number of cycles N is obtained. From the respective value of aa,1 the variable amplitude fatigue strength factor is obtained as

(4.4.63)

If a value KSK,a < I is obtained from Eq. (4.4.63), then the value to be applied is KSK,a = 1.

Component constant amplitude S-N curve model II: sloping for N > ND,a (non-welded aluminum alloys) *11

(4.4.61)

,

= aa,1 / aAK·

4 Assessment of the fatigue strength using local stresses

N=

For the summation of the term Z2, Eq. (4.4.60), it is to be observed that aaj+! = O.

KSK,a

122

(4.4.64)

If a value N = N* > N is obtained then the calculation of N, Eq. (4.4.65), is to be continued fqr differing values aa,1 > a AK / ( fn,a )1/3 until a value N equal to the required total number of cycles N is obtained. From the respective value of aa,1 the variable amplitude fatigue strength factor is obtained as KSK,a = aa,1 . (fn,a

)1/3/ aAK

(4.4.66)

If a value N = N *:s N is obtained then the variable amplitude fatigue strength factor is

(4.4.67) If a value KSK,a < fn,a is obtained from Eq. (4.4.67) then the value to be applied is KSK,a = fn,a .

(4.4.68)

Calculation using a class of utilization The variable amplitude fatigue strength factor KSK,a is to be determined according to the appropriate class of utilization *12 , Chapter 5.7.

Calculation using a damage-equivalent stress amplitude When using a damage-equivalent stress amplitude the variable amplitude fatigue strength factor for both constant amplitude S-N curves model I and model II is KSK,a = 1.

(4.4.69)

12Class ofutilization asa characteristic ofthestress spectrum. It isan approximately damage equivalent combination oftherequired total number ofcycles N with theshape ofa particular standard stress spectrum thefrequency distribution ofwhich is ofbinomial orexponential type modified bya spectrum parameter p. It provides a result that corresponds toa calculation based ontheelementary version ofMiner's II Simplified and approximate calculation.

rule

4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength 4.4.3.2 Component constant amplitude S-N curve Component constant amplitude S-N curves for nonwelded components (without surface hardening) and for welded components *13 are shown for normal stress and for shear stress in Figure 4.4.5 and 4.4.6. The particular number of cycles at the knee point No,cr , ... and the values of slope kcr, ... are given in Table 4.4.4. The component fatigue limit crAK , ... is the reference fatigue strength value for calculation. It follows from Chapter 4.4.2. For S-N curves Model I the fatigue limit crAK and the endurance limit o AK,II for N = 00 are identical, while for S-N curves Model II (valid for nonwelded components of austenitic steel or of aluminum alloys) they are different by a factor fII,cr , Table 4.4.4 and Figure 4.4.5. A lower boundary of the numbers of cycles is implicitly defined by the maximum stress being limited according to the static strength requirements, Chapter 1. For surface hardened components "14 the slope of the component constant amplitude S-N curves is more shallow. Instead of the values of slope kcr = 5 and k, = 8 for not surface hardened components, Table 4.4.4, the values that apply to surface hardened components are kcr = 15 and k, = 25 , while the number of cycles at the knee point No,cr and No,~ remain unchanged, see also Chapter 5.8. The component constant amplitude S-N curves for welded components are valid for the toe section and for the throat section.

13 With reference to IIW-Recommendations and Eurocode 3.

14 Not applicable to cold rolled or shot-peened components.

123

4 Assessment of the fatigue strength using local stresses

4.4 Component fatigue strength 4.4.3 Component variable amplitude fatigue strength

124

4 Assessment of the fatigue strength using local stresses

Table 4.4.4 Number of cycles at the knee point, slope of the component constant amplitude S-N curves, and values of flI,cr and flI, NO,a, kO,a = co or for N > NO,~, k O,~ = co

horizontal for N > NO,a,lI, kO,a,1I = co or for N > N0, ~,II ' kO, ~,II = co.

N (lg)

etra bild,,14

Normal stress a. Shear stress t.

Aluminum alloys and austenitic steel (Model II): sloping for N > NO a, kO a, or for N > NO:~, kO:~'

Nn,T =10 8

N (lg)

Figure 4.4.5 Component constant amplitude S-N curve for non-welded components *14 Top: Bottom:

I----------+--~~---

Nc = 6

ND,T =10 6 Bifa bildwl7

TAK

Figure 4.4.6 Component constant amplitude S-N curve for welded components *13 Top: Bottom:

Normal stress a. Shear stress t;

Steel, cast iron materials and aluminum alloys, welded (Model I): horizontal for N > NO a, kO a = co or for N > NO' ~, k ~ = co NC is the reference number of cycles

D

corresponding to the characteristic strength values a AC and ~ AC. aAK / aAC = (Nc / NO,a ) 11ko = 0,736 and

~AK / ~AC

=

(Nc / NO,~) 11kr = 0,457.

125

4.5 Safety factors

4.5 Safety factors

*1

IR25 EN .docl

Contents

Page

4.5.0

General

4.5.1

Steel

4.5.2 4.5.2.0 4.5.2.1 4.5.2.2

Cast iron materials General Ductile cast iron materials Non-ductile cast iron materials

4.5.3 4.5.3.0 4.5.3.1 4.5.3.2

Wrought aluminum alloys General Ductile wrought aluminum alloys Non-ductile wrought aluminum alloys

4.5.4

Cast aluminum alloys

4.5.5

Total safety factor

68

4 Assessment of the fatigue strength using local stresses

4.5.2 Cast iron materials 4.5.2.0 General Ductile and non-ductile cast iron materials are to be distinguished.

4.5.2.1 Ductile cast iron materials 69

Cast iron materials with an elongation A5 ~ 12,5 % are considered as ductile cast iron materials, in particular all types of GS and some types of GGG. Values of elongation see Table 5.1.12. Safety factors for ductile cast iron materials are given in Table 4.5.2. Compared to Table 4.5.1 they are higher because of an additional partial safety factor jp that accounts for inevitable but allowable defects in castings *4. The factor is different for severe or moderate consequences of failure and moreover for castings that have been subject to non-destructive testing or have not.

4.5.0 General According to this chapter the safety factors are to be determined. The safety factors are valid under the condition that the design loads are reliably determined on the safe side and that the material properties correspond to an average

Table 4.5.2 Safety factors for ductile cast iron materials (GS; GGG) (A5~ 12,5 %).

I

Jo

probability of survival of Po = 97,5 % *2.

Consequences of failure Severe moderate? 1

I

castings not subject to non-destructive testing ?2

The safety factors apply both to non-welded and welded components.

regular inspection

no yes?3

I I

2,1 1,9

I I

1,8 1,7

castings subject to non-destructive testing ?4

4.5.1 Steel The basic safety factor concerning the fatigue strength is

Jo =

(4.5.1)

1,5.

regular inspection

I I

1,9 1,7

I

I

1,65 1,5

? 1 See footnote? I of Table4.5.1. ?2 Compared to Table 4.5.1 an additional partial safety factor = 1,4 is introduced to account for inevitable but allowable defects in castings.

This value may be reduced under favorable conditions, that is depending on the possibilities of inspection and on the consequences of failure, Table 4.5.1.

jF

Table 4.5.1 Safety factors for steel *3 (not for GS) and for ductile wrought aluminum alloys (A~ 12,5 %).

jp

?3 Regular inspection in the senseof damage monitoring. Reduction by about10 %. ?4 Compared to Table 4.5.1 an additional partial safety factor = 1,25 is introduced, for which it is assumed that a higher quality ofthecastings isobviously guaranteed when testing.

Consequences of failure moderate ?1 severe

jo regular inspections

no yes ?3

I I

no yes?2

1,5 1,35

1,3 1,2

? 1 Moderate consequences of failure of a less important component in the sense of "non catastrophic" effects of a failure; for example because of a load redistribution towards other members of a statical indeterminate system. Reduction by about 15 %. ? 2 Regular inspection in the sense of damage monitoring. Reduction by about 10 %.

1 Chapters 4.5 and2.5 are identical.

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 safety factor to jF = 1,0 does not seempossible up to now. A safety factor jF = 1,0 may be applied to high quality cast components in the aircraft industry however. Those high quality cast components, have to meet special demands on qualification and checks of the production process, as well as on the extent of quality and product testing in order to guarantee little scatter of their mechanical properties.

126

4.5 Safety factors

4 Assessment of the fatigue strength using local stresses

4.5.2.2 Non-ductile cast iron materials

4.5.3.2 Non-ductile wrought aluminum alloy

Cast iron materials with an elongation As < 12,5 % (for GT A3 < 12,5 %) are considered as non-ductile materials, in particular some types of GGG as well as all types of GT and GG. Values of elongation for GGG and GT see Table 5.1.12 or 5.1.13. The value for GG is As = O.

Wrought aluminum alloys with an elongation A < 12,5 % are considered as non-ductile materials. Values of elongation see Table 5.1.22 to 5.1.30.

For non-ductile cast iron materials the safety factors from Table 4.5.2 are to be increased by adding a value ~j, Figure 4.5.1 *s:

~j

=

0,5 -~ As /50%,

(4.5.2)

AS Elongation, to be replaced by A3 for GT.

For non-ductile wrought aluminum alloys all safety factors from Table 4.5.1 are to be increased by adding a value Aj , Eq. (4.5.2).

4.5.4 Cast aluminum alloys Cast aluminum alloys are always considered as nonductile materials. All safety factors from Table 4.5.2 are to be increased by adding a value 4i , Eq. (4.5.2). Values of elongation see Table 5.1. 31 to 5. 1.38.

GG

0,5

~.---GGG-,----r~1

4.5.5 Total safety factor

GT

~j

Similar to an assessment of the component static strength, Chapter 3.5.5, a "total safety factor" .lges is to be derived:

o

10 12,5

20 As, A3 in %

.

_ In

Jges-~ ,

T,O

Figure 4.5.1 Value ~j to be added to the safety factor Jn , defined as a function of the elongation As or A3 , respectively.

4.5.3 Wrought aluminum alloys 4.5.3.0 General Ductile and non-ductile wrought aluminum alloys are to be distinguished.

4.5.3.1 Ductile wrought aluminum alloys Wrought aluminum alloys with an elongation A~ 12,5 % are considered as ductile materials. Values of elongation see Table 5.1.22 to 5.1.30. Safety factors for ductile wrought aluminum alloys are the same as for steel according to Table 4.5.1.

S For example the safety factor for GG is at least

Jn = (Jn

1,5

+ 0,5

= 2,0

(4.5.3)

= 1,5 from Table 4.5.2, j = 0,5 after Eq. (4.5.2) for AS = 0).

safety factor, Table 4.5.1 or 4.5.2, temperature factor, Chapter 4.2.3.

(4.5.4)

1 I

127 4.6 Assessment

4.6 Assessment Contents

4 Assessment of the fatigue strength using local stresses 1R46 EN.doq

Page

4.6.0

General

127

4.6.1 4.6.1.1 4.6.1.2

Rod-shaped (lD) components Individual types of stress Combined types of stress

128

4.6.2 4.6.2.1 4.6.2.2

Shell-shaped (2D) components Individual types of stress Combined types of stress

4.6.3 4.6.3.1 4.6.3.2

Block-shaped (3D) components Individual types of stress Combined types of stress

129

fatigue strength after Chapter 4.4.3, GBK , ... , divided by the total safety factor jges. The degree of utilization is always a positive value *4. An assessment of the variable amplitude fatigue strength, an assessment of the constant amplitude fatigue strength for finite life, or an assessment of the fatigue limit or of the endurance limit are to be distinguished. In each case the calculation is the same when using the appropriate variable amplitude fatigue strength factors KBK,o , ... , Chapter 2.4.3, and when taking G a,l

=

G a , ... ,

in case of a constant amplitude spectrum, or Ga , l = Ga,eff

4.6.0 General According to this chapter the assessment of the fatigue strength using local stresses is to be carried out. In general the assessments for the individual types of stress and for the combined types of stress are to be carried out separately *1. The procedure of assessment applies to both non-welded and welded components. For welded components the assessment is to be carried out with structural stresses or effective notch stresses *2. Assessments are generally to be carried out separately for the toe and for the root of a weld. They are to be carried out in the same way, but using the respective local stresses and fatigue classes FAT as these are in general different for the toe and the root of a weld.

Degree of utilization The assessment is to be carried out by determining the degree of utilization of the component fatigue strength. In the general context of the present Chapter the degree of utilization is the quotient of the (local) characteristic stress amplitude Ga,l> ... , divided by the allowable (local) stress amplitude of the component fatigue strength at the reference point *3. The allowable stress amplitude is the quotient of the component variable amplitude

1 It is essential to examine the degree of utilization not only of the combined types of stress but also of the individual types of stress in general, and in particular if these may occur separately. 2 The additional index K marking effective notch stresses is to be added to the stress symbols where appropriate. 3 The reference point is the critical point of the considered component that observes the highest degree of utilization.

(4.6.1)

(4.6.2)

in case of a damage-equivalent stress amplitude. Ga ,

characteristic constant amplitude stress for which the required number of cycles is N, ... , damage-equivalent stress amplitude.

... ,

Ga"eff,

Superposition For proportional or synchronous stress components of same type of stress the superposition is to be carried out according to Chapter 4.1. If different types of stress like normal stress and shear stress act simultaneously and if the resulting stress is multiaxial, Chapter 0.3.5 and Figure 0.0.9, both the individual types of stress and the combined types of stress are to be considered as described below *5.

Kinds of component Rod-shaped (10), shell-shaped (2D) and block-shaped (3D) components are to be distinguished. They can be both non-welded or welded.

4 As the degree of utilization is the quotient of two amplitude which always are positive. 5 Proportional, synchronous and non-proportional multiaxial stresses are to be distinguished. , Chapter 0.3.5. Only under special conditions of proportional stresses the character of Eq. (4.6.4), (4.6.9) and (4.6.14) is that of a strength hypothesis from a material-mechanics point of view. For example the extreme stresses from bending and shear will - as a rule - occur at different points of the crosssection, so that different reference points W are to be considered. As a rule bending will be more important. More general the Eq. (4.6.4), (4.6.9) and (4.6.14) have the character of an empirical interaction formula. They are applicable for proportional stresses and approximately applicable for synchronous stresses; an improved procedure for non-welded components is given in Chapter 5.9. For non-proportional stresses the Eq. (4.6.4), (4.6.9) and (4.6.14) are not suitable; an approximate procedure applicable for non-proportional stresses is proposed in Chapter 5.10.

128

4 Assessment of the fatigue strength using local stresses

4.6 Assessment

Table 4.6.1 Values of q as dependent on f w ,< ~1

4.6.1 Rod-shaped (ID) components 4.6.1.1 Individual types of stress The degrees of utilization of rod-shaped (ID) components for variable amplitude types of stress like normal stress and shear stress are ~

I,

(4.6.3)

f w< q ~1

A

GT, cast Al alloys 0,75 0,544

Steel, GGG wrought Al alloys 0,577 0,65 0 0,264

GG

0,85 0,759

Exceptions: For non-ductile wrought aluminum alloys (elongation < 12,5 %) q = 0,5 , for surface hardened or welded components

q = I.

4.6.2 Shell-shaped (2D) components O"a,1 , ... characteristic stress amplitude (largest stress amplitude in the spectrum) according to type of stress, Chapter 4.1.1.1 and Eq. (4.6.1) or (4.6.2), O"SK, ... related amplitude of the component variable amplitude fatigue strength, Chapter 4.4.3, jges total safety factor, Chapter 4.5.5.

4.6.2.1 Individual types of stress The degrees of utilization of shell-shaped (2D) components for variable amplitude types of stress like normal stress in the directions x and y as well as shear are aSK,crx

0'., x, I

=

0' BK,x

4.6.1.2 Combined types of stress The degree of utilization of rod-shaped components for combined types of stress is *6 aSK,Sv = q' aNH + (l - q) . aoH

s

1,

(ID)

/

O'.,y,]

aSK,cry = 0' BK,y

/

~

1,

~

1,

(4.6.8)

j erf j erf

(4.6.4)

where aNH =1 {Isal + aoH

~s; + 4· t; ).

(4.6.5)

=Js; +t; , (4.6.6)

Sa= aSK,cr ,

aSK,cr, ... degrees

of utilization after Eq.

(4.6.3).

For non-ductile wrought aluminum alloys (elongation A < 12,5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to be applied. Otherwise there is, Table 4.6.1,

q fw,'t

J3 -(l/fw"t) J3 -1

(4.6.7)

shear fatigue strength factor, Table 4.2.1 or 4.6.1.

0"a,x,1,... characteristic stress amplitude (largest stress amplitude in the spectrum) according to type of stress, Chapter 4.1.1.2 and Eq. (4.6.1) or (4.6.2), O"SK,x, ... related amplitude of the component variable amplitude fatigue strength, Chapter 4.4.3, jges total safety factor, Chapter 4.5.5.

4.6.1.2 Combined types of stress The degree of utilization of shell-shaped components for combined types of stresses is *6 aSK,crv = q . aNH + (l - q) . aoH~ 1, where

(2D)

(4.6.9) (4.6.10)

aNH =1{lsa,x

J

2

+Sa,yl+~(Sa,x -Sa,y)2 +4.t;), 2

2

aoH = sa,x + sa,y - sa,x . sa,y + t a ' sa,x = aSK,crx , 6 Eq. (4.6.4), (4.6.9) and (4.6.14) is a combination ofthe normal stress criterion (NH) and the v. Mises criterion (GH). Depending on the ductility ofthematerial thecombination is controlled bya parameter q as a function of fw,< according to Eq. (4.6.7), (4.6.12) or (4.6.17) and Table 4.6.1. For instance q = 0 forsteel sothat only thev. Mises criterion is of effect, while q = 0,264 for GGG so that both the normal stress criterion and thev.Mises criterion areof partial influence.

(4.6.11)

sa,y= aSK,cry , ta = aSK,"t , aSK,crx, ... degrees of utilization after Eq. (4.6.8) .

129 4 Assessment of the fatigue strength using local stresses

4.6 Assessment

For non-ductile wrought aluminum alloys (elongation A < 12.5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to' be applied. Otherwise there is, Table 4.6.1, q f w"

(4.6.12)

J3 -1

shear fatigue strength factor, Table 4.2.1 or 4.6.1

Rules of signs: If the normal stresses ax and a y always act proportional or synchronous in phase the degrees of utilization aSK,ax and aSK,cry are to be inserted in Eq. (4.6.11) with the same (positive) signs. If they act always proportional or synchronous 1800 out of phase, however, the degrees of utilization aSK,ax and aSK,cry are to be inserted in Eq. (4.6.11) with opposite signs *7 . If the individual types of stress act non-proportional, that is neither proportional nor synchronous, the Eq. (4.6.9) to (4.6.11) are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.

4.6.3 Block-shaped (3D) components

~

1,

~

1,

~

1,

(4.6.13)

(J I BK / j erf

aSK,a2 =

(J 2,0,1 (J 2,BK / j erf (J 3,0,1

aSK,a3 = (J3 BK / jerf

(4.6.14)

,I ,I

aoH = 1/ 2 "2\(Sa,1 -Sa,2) +(Sa,2

(4.6.15)

2

-Sa,3) +(Sa,3 -Sa,l)

2) ,

(4.6.16)

Sa,I = aSK,al , Sa,2 = aSK,a2 , Sa,3 = aSK,a3 , aSK,al ... degrees of utilization after Eq.

(4.6.13).

For non-ductile wrought aluminum alloys (elongation A < 12,5 %) q = 0,5 is to be applied. For surface hardened or for welded components q = 1 is to be applied. Otherwise there is, Table 4.6.1, q fw"

The degrees of utilization of block-shaped (3D) components for the principle stresses in the directions 1, 2 and 3 are

= q . aNH + (1 - q) . aGH~ 1,

aNH = MAX (Isa,d Sa,21 Sa,31) ,

*8

4.6.3.1 Individual types of stress

(J l,a,1

The degree of utilization of block-shaped (3D) components for combined types of stresses is *6 *9 aSK,sv

J3-(l/fw,)

aSK,al =

4.6.3.2 Combined types of stresses

J3-(l/fw,)

(4.6.17)

J3 -1 shear

fatigue

strength

factor,

Tab.

4.2.1.

Rules of signs: If the principle stresses al , a2 and a3 always act proportional or synchronous in phase the degrees of utilization aSK,al , aSK,a2 and aSK,a3 are to be inserted in Eq. (4.6.16) with the same (positive) signs. If they act always proportional or synchronous 1800 out of phase, however, the respective degrees of utilization aSK,aI , aSK,a2 and aSK,a3 are to be inserted in Eq. (4.6.16) with opposite signs *12. If the individual principle stresses act non-proportional (that is in a nonconstant direction), the Eq. (4.6.14) to (4.6.16) are not applicable and the procedure proposed in Chapter 5.10 is to be applied instead.

al,a,l , ... characteristic stress amplitude (largest stress amplitude in the spectrum) ofthe particular principle stress, Chapter 4.1.1.3 and Eq. (4.6.1) or (4.6.2), al,SK, ... related amplitude of the component variable amplitude fatigue strength, Chapter 4.4.3, jges total safety factor, Chapter 4.5.5.

7 For example normal stresses iii thedirections x and ythatresult from the same single external load affecting the component. 8 Sometimes block-shaped (3D) components may be welded at the surface, for example by surfacing welds. Then assessment can becarried out as for shell-shaped (2D) welded components, if the stresses ax, ay and, areofinterest only.

9 MAX means themaximum ofthevalues

inparenthesis to bevalid.

130

4.6 Assessment

4 Assessment of the fatigue strength using local stresses

131

5.1 Material tables

5 Appendices

IRT51

EN. dog

5.1 Material tables Contents 5.1.0 5.1.1 5.1.2

Page General Material tables for steel and cast iron materials Material tables for for aluminum alloys

131 132 132/ 142

5 Appendices

fw,o-

Fatigue strength factor for completely reversed normal stress, Table 2.2.1.

Material fatigue strength for completely reversed shear stress -Cw,s = fW,t' crW,zd, (2.2.1) (5.2) fW,t Shear fatigue strength factor, Tab. 2.2.1. Material fatigue strength for completely reversed bending stress c W,b = ncr(do) . crW,zd, no-(do) Kj-Kj ratio, Eq.(2.3.14)

5.1.0 General No responsibility can be taken for the mechanical material properties indicated in the material tables below, see page 3 "Terms of liability". The newest versions of the standards are decisive. The data given are not to be used for selecting the material in design since this would require additional material properties to be considered that are not contained in the tables below.

*5,

(5.3) with do = 7,5 mm.

Material fatigue strength for completely reversed torsional stress -CW,t = nldo)' -cw,s, (5.4) nldo) Kt-Kfratio, Eq.(2.3.14) *5, with do = 7,5 mm. Material fatigue strength for zero-tension axial stress (amplitude) crSch,zd = crW,zd / (1 + Mo- ), Mean stress sensitivity, Eq. (2.4.34)

(5.5)

The tables *I contain mechanical properties according to standards Rm,N , ... . They apply in the case of steel to the smallest dimension of a semi-finished product *2, in the case of cast iron materials and cast aluminum alloys for the test piece. In the case of wrought aluminum alloys the tables give component values Rm= Rm.N, ... , of the semi-finished product indicated. Properties according to standards, component values and component properties according standards are to be distinguished, as explained in the Chapters 1.2,2.2, 3.2 or 4.2.

M,

Rm,N or Rm are the minimum value, the guaranteed value or the lower boundary of the specified range of the tensile strength. The minimum value or the guaranteed value ofthe yield strength are Rp,N or R, *3 *4.

For aluminum alloys (constant amplitude S-N curve model II, Figure 2.4.4 and Table 2.4.4) crW,zd, ..., is the fatigue limit, while the endurance limit crW,II,zd, ..., is achieved at a number of cycles N = ND, II,o- = ND,II;, = 108 . It is lower than crW,zd or -cw,s by a factor fII, or fn,t :

The material fatigue strength values in the tables for completely reversed loading, crW,zd,N , or for zerotension loading, crSch zd N ' ..., are intended for information only, because they can be computed as described below and are not necessary for the assessment therefore. All following equations are supposed to be valid for a material test specimen of the diameter do = 7,5 mm independent of the real dimension of the semi-finished product or of the raw casting (index N left out, e.g. crW,zd instead of crW,zd,N , etc.)

*6.

Comment: The values crw, zd , ... , Eq. (5.1)6to (5.5), apply to a number of cycles N = ND,s = ND,t = 10 .

For steel and cast iron materials (constant amplitude S-N curve modell, Figure 2.4.4 and Table 2.4.4) crW,zd, ..., is the fatigue limit = endurance limit. Example: Quenched and tempered steel, - fw,o- = 0,45 (Tab. 2.2.1), - fatigue limit crW,zd = fw,o- . Rm = 0,45 Rm .

0-

_ fILo- = (108/106 ) 1/15 = 0,74 (kD,o-= 15 for normal stress) and _ fILt = (108/106 ) 1/25 = 0,83 (kD,t = 25 for shear stress). Example: -

fw,o- = 0,30 (Tab. 2.2.1), fILo- = 0,74, Endurance limit crW,II,zd = fILo- . fw,o- . Rm= = 0,74 . 0,30 . Rm = 0,22 . Rm .

Material fatigue strength for completely reversed normal stress crW.zd = fw,o- . Rm ,

(2.2.1) (5.1)

I Kinds of material (e.g. non-alloyed structural steel) and types of material within the kind ofmaterial (e.g. St37-2) are distinguished.

2

Ifdifferent dimensions ofa semi-finished product are given.

3 For the values Rm,N ' Rp,N, Rm ' Rp , an average probability of survival PO = 97,5 % is supposed that should also apply to the further values crW,zd,N ' "" crW,zd , "', derived therefrom.

4 Rp stands both for the yield stress R,

orthe 0.2 proofstress RpO,2 .

5 Eq. (5.3) for bending (and Eq. (5.4) for torsion in analogy) results from a combination ofthe following equations: - Eq. (2.4. I) (crW,b in the meaning ofa component value SWK,b ) - Eq. (2.3.1) (KWK,b = K(b), - Eq. (2.3. 10) (Kt,b = I ; ncr(r) = I ; K(b = 11 ncr(d) ), - Eq. (2.3.14) (ncr(d) with d = do = 7,5 mrn for the material in question, - Eq. (2.3.17) (Ocr (do) = 2/ do = 0,267 mrn -I ).

Eq. (5.5) follows from Eq. (2.4.10) with Rzrl = 0 orSm,zd / Sa,zd = I, respectively.

6

132 5.1 Material tables

5 Appendices

5.1.1 Material tables for steel and cast iron materials

5.1.2 Material tables for aluminum alloys

The tables 5.1.1 to 5.1.14, from page 132 on, contain mechanical properties according to standards, Rm.N, ... , for the following kinds of material: for rolled steel (nonalloyed structural steel, weldable fine grain structural steel, quenched and tempered steel, case hardening steel, nitriding steel and stainless steel), for forging steel and for cast iron materials (cast steel, heat treatable steel castings, nodular cast iron (GGG), malleable cast iron (GT) and cast iron with lamellar graphite (GG)). From these and according to Chapter 1.2.1 or 3.2.1 the component properties according to standards Rrn are to be computed under observation of the technological size factor according to the diameter or width of the semifinished product or of the raw casting, respectively. The fatigue limit values endurance limit as well.

O"W.zd.N. ..,

correspond to the

Table 5.1.21 on page 142 gives a survey of the aluminum materials. The tables 5.1.22 to 5.1.30, from page 143 on, contain component properties according to standards, R.ll , ..., for wrought aluminum alloys according to the type of material and its condition. They are valid for the indicated dimensions. The tables 5.1.31 to 5.1.38, from page 172 on, contain material properties according to standards, Rrn•N , ... , for cast aluminum alloys according to the type of material and its condition, from which - and according to Chapter 1.2.1 or 3.2.1 - the component properties according to standards, Rm , ... , are to be computed under observation of the technological size factor according to the width of the raw casting. The fatigue limit values O"W.zd , O"W.zd.N , ... , are different from those of the endurance limit, however, see page 131.

Table 5.1.1 Mechanical properties in MPa for non-alloy structural steels, after DIN EN 10 025 (1994-03-00) Type of material

Type of material, after DIN 17 100

S185 S235JR S235JRGI S235JRGlC S235JRG2 S235JRG2C S235JO S235JOC S235J2G3 S235J2G4 S235J2G3C S275JR S275JRC S275JO S275JOC S275J2G3 S275J2G4 S275J2G3C S355JR S355JO S355JOC S355J2G3 S355J2G4 S355J2G3C S355K2G3 S355K2G4 E295 E335 E360

St 33 St 37-2 USt 37-2 UQSt 37-2 RSt 37-2 RQSt 37-2 St 37-3 U QSt 37-3 U St 37-3 N QSt 37-3N St 44-2 QSt 44-2 St 44-3 U QSt 44-3 U St 44-3 N QSt 44-3N St 52-3 U QSt 52-3 U St 52-3 N QSt 52-3 N

St 50-2 St 60-2 St 70-2

Material No. 1.0035 1.0037 1.0036 1.0121 1.0038 1.0122 1.0114 1.0115 1.0116 1.0117 1.0118 1.0044 1.0128 1.0143 1.0140 1.0144 1.0145 1.0141 1.0045 1.0553 1.0554 1.0570 1.0577 1.0569 1.0595 1.0596 1.0050 1.0060 1.0070

c- 1.

Rm.N

s,.N 2

O"W,zd,N

O"Sch,zd,N

O"W,b,N

310 360

185 235

140 160

138 158

155 180

80 95

90 105

430

275

195

185

215

110

125

510

355

230

215

255

130

150

490 590 690

295 335 360

220 265 310

205 240 270

245 290 340

125 155 180

145 170 200

1 Effective Diameter del(N = 40 mm. c- 2 Re.N / Rrn,N < 0,75 for all types ofmatenal hsted.

'tW.s.N

'tW.I,N

133

5.1 Material tables

5 Appendices

Table 5.1.2 Mechanical properties in MFa for weldable fine grain structural steels in the normalized condition, after DIN 17102 (1983-10-00) ~1. Type of material

Material No.

Rm,N

Re,N

()W,zd,N

()Sch,zd,N

()W,b,N

1:W,s,N

1:W,t,N

~2

ad,rn

ad,p

~3

~3

StE StE StE StE

255 285 315 355

1.0461 1.0486 1.0505 1.0562

360 390 440 490

255 285 315 355

160 175 200 220

160 170 190 205

180 195 220 245

95 100 115 125

105 115 130 145

0,33 0,31 0,28 0,26

0,41 0,38 0,35 0,30

StE StE StE StE

380 420 460 500

1.8900 1.8902 1.8905 1.8907

500 530 560 610

380 420 460 500

225 240 250 275

210 220 230 245

250 265 280 300

130 140 145 160

145 155 165 180

0,26 0,24 0,23 0,22

0,34 0,31 0,30 0,31

~ 1 Effective Diameter for the tensile strength deff,N ~ 2 Re,N / ~N ~

= 70 mm, for the yield strength deff,N = 40 mm.

< 0,75 up to and including StE 355, Re,N / ~N > 0,75 from StE 380 on.

3 More specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.

Table 5.1.3 Mechanical properties in MFa for weldable fine grain structural steels in the normalized condition, after DIN EN 10 113 (1993-04-00) -c- 1. Type of material S 275 N S 275 NL S 355 N S 355 NL S 420N S 420 NL S460N S 460 NL S275M S 275 ML S 355M S 355 ML S420M S 420 ML S460M S 460 ML ~

Rrn,N

1.0490 1.0491 1.0545 1.0546 1.8902 1.8912 1.8901 1.8903 1.8818 1.8819 1.8823 1.8834 1.8825 1.8836 1.8827 1.8838

370

275

165

160

185

95

470

355

210

200

235

520

420

235

215

550

460

245

360

275

450

ad,rn

ad,p

~3

~3

110

0,30

0,30

120

140

0,25

0,28

260

135

150

0,23

0,30

225

275

140

160

0,00

0,22

160

158

180

95

105

0,30

0,30

355

205

190

225

115

130

0,25

0,28

500

420

225

210

250

130

145

0,23

0,30

530

460

240

220

265

140

155

0,00

0,22

Re,N

()W,zd,N

()Sch,zd,N

()W,b,N

1:W,s,N

1:W,t,N

~2

I Effective Diameter for the tensile strength deff,N

~ 2 Re,N / ~N ~

Material No.

= 100 mm, for the yield strength deff,N = 30 mm.

< 0,75 up to and including S 275 NL, Re,N / ~N > 0,75 from S 355 Non.

3 More specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.

134 5 Appendices

5.1 Material tables

Table 5.1.4 Mechanical properties in MFa for quenched and tempered steels in the quenched and tempered condition, after DIN EN 10 083-1 (1996-10-00) -¢-1. Notes? 1 to -¢-4 see next page. Type of material, after DIN EN 10 027-1 C22E C22R C22 C25E C25R C25 C30E C30R C30 C35E C35R C35 C40E C40R C40 C45E C45R C45 C50E C50R C50 C55E C55R C55 C60E C60R C60 28Mn6 38Cr2 38CrS2 46Cr2 46CrS2 34Cr4 34CrS4 37Cr4 37CrS4 41Cr4 41CrS4 25CrMo4 25CrMoS4 34CrMo4 34CrMoS4 42CrMo4 42CrMoS4 50CrMo4 36CrNiMo4 34CrNiM06 30CrNiMo8 -¢- 1 36NiCrMo16?1 51CrV4

Type of material, after DIN 17200 Ck 22 Cm22 C 22 Ck 25 Cm25 C25 Ck 30 Cm30 C 30 Ck 35 Cm35 C 35 Ck40 Cm40 C40 Ck45 Cm45 C45 Ck 50 Cm50 C 50 Ck 55 Cm55 C 55 Ck60 Cm60 C60 28Mn6 38 Cr 2 38 CrS 2 46 Cr 2 46 CrS 2 34 Cr4 34 CrS 4 37 Cr4 37 CrS 4 41 Cr 4 41 CrS 4 25 CrMo4 25 CrMoS 4 34 CrMo 4 34 CrMoS 4 42 CrMo 4 42 CrMoS 4 50 CrMo4 36 CrNiMo 4 34 CrNoMo6 30 CrNiMo 8 50 CrY 4

Material No.

1.1151 1.1149 1.0402 1.1158 1.1163 1.0406 1.1178 1.1179 1.0528 1.1181 1.1180 1.0501 1.1186 1.1189 1.0511 1.1191 1.1201 1.0503 1.1206 1.1241 1.0540 1.1203 1.1209 1.0535 1.1221 1.1223 1.0601 1.1170 1.7003 1.7023 1.7006 1.7025 1.7033 1.7037 1.7034 1.7038 1.7035 1.7039 1.7218 1.7213 1.7220 1.7226 1.7225 1.7227 1.7228 1.6511 1.6582 1.6580 1.6773 1.8159

R,N

crW,zd,N

crSch,zd,N

crW,b,N

LW,s,N

LW,t,N

ad,rn

llci,p

?2

-¢-3

-¢-3

?3

?3

?3

?4

?4

340 225

210

250

130

145

0,19

0,43

370 250

225

275

145

160

0,29

0,40

600

400 270

245

295·

155

175

0,26

0,37

630

430 285

255

310

165

185

0,20

0,39

650

460 295

260

320

170

190

0,12

0,36

700

490 315

275

345

180

205

0,16

0,36

750

520 340

290

365

195

215

0,21

0,35

800

550 360

305

390

210

230

0,19

0,35

850

580 385

320

415

220

245

0,18

0,34

800 800

590 360 550 360

305 305

390 390

210 210

230 230

0,30 0,37

0,38 0,52

900

650 405

335

435

235

260

0,41

0,54

900

700 405

335

435

235

260

0,33

0,49

950

750 430

345

460

245

270

0,32

0,46

1000

800 450

360

480

260

285

0,30

0,44

900

700 405

335

435

235

260

0,33

0,49

1000

800 450

360

480

260

285

0,30

0,44

1100

900 495

385

525

285

315

0,32

0,43

1100 900 495 1100 900 495 1200 1000 540 1250 1050 565 1250 1050 565 1100 900 495

385 385 410 420 420 385

525 525 570 595 595 525

285 285 310 325 325 285

315 315 340 355 355 315

0,28 0,32 0,33 0,36 0,28 0,28

0,38 0,38 0,39 0,42 0,32 0,33

Rm,N

500 550

135 5 Appendices

5.1 Material tables

Table 5.1.5 Mechanical properties in MPa for quenched and tempered steels in the normalized condition, after DIN EN 10 083-1 (1996-10-00) -9-1. Type of material, after DIN EN 10 027-1 C22E C22R C22 C25E C25R C25 C30E C30R C30 C35E C35R C35 C40E C40R C40 C45E C45R C45 CSOE C50R C50 C55E C55R C55 C60E C60R C60 28Mn6

Type of material, after DIN 17200

Material No.

Ck22 Cm22 C 22 Ck 25 Cm25 C 25 Ck 30 Cm30 C 30 Ck 35 Cm35 C 35 Ck40 Cm40 C40 Ck45 Cm45 C45 Ck50 Cm50 C 50 Ck 55 Cm55 C 55 Ck60 Cm60 C60 28Mn6

1.1151 1.1149 1.0402 1.1158 1.1163 1.0406 1.1178 1.1179 1.0528 1.1181 1.1180 1.0501 1.1186 1.1189 1.0511 1.1191 1.1201 1.0503 1.1206 1.1241 1.0540 1.1203 1.1209 1.0535 1.1221 1.1223 1.0601 1.1170

Rn,N

Re,N

crW,zd,N

CJSch,zd,N

CJW,b,N

't W,s,N

'tW,I,N

-9-2

~m

ad,p

-9-3

-9-3

430

240

195

185

215

110

125

0,08

0,19

470

260

210

200

235

120

140

0,10

0,18

510

280

230

215

255

135

150

0,10

0,19

550

300

250

225

275

145

160

0,10

0,19

580

320

260

235

285

150

170

0,09

0,19

620

340

280

250

305

160

180

0,10

0,20

650

355

295

260

320

170

190

0,10

0,19

680

370

305

270

335

175

195

0,09

0,20

710

380

320

280

350

185

205

0,09

0,19

630

345

285

250

310

165

185

0,07

0,17

-9- 1 Effective diameter deff,N = 16 rom. -9- 2 Re,N / Rm,N < 0,75 for all types of material listed. -9- 3 More specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.

Notes referring to Table 5.1.4: -9- 1 Effective diameter deff,N;= 40 rom for 30 CrNiMo 8 and 36 NiCrMo 16, deff,N = 16 rom for all other types of material listed. -9- 2 Re,N / Rm,N < 0,75 up to and including 46 Cr 2, 46 CrS 2; Re,N / Rm,N > 0,75 from 34 Cr 4, 34 CrS 4 on. -9- 3 The fatigue strength values of the sulphur bearing steels 38 CrS 2 to 42CrMoS 4 are lower than the values listed for 28 Cr 2 to 42 CrMo 4. -9- 4 M ore specific values for the individual types of material compared to the average values given in Table 1.2.1 and 3.2.1.

136

5 Appendices

5.1 Material tables

Table 5.1.6 Mechanical properties in MPa for case hardening steels in the blank hardened condition -:> 1, after DIN EN 10 084 (1998-06-00) (selected types of material only) -:>2. Type of material -:>3 ClOE C15E C16E 17Cr3 28Cr4 * 16MnCr5 * 20MnCr5 * 18CrMo4 * 18CrMoS4 * 22CrMoS3-5 * 20MoCr3 20MoCr4 16NiCr4 10NiCr5-4 * 18NiCr5-4 * l7CrNi6-6 * l5NiCr13 * 20NiCrMo2-2 * l7NiCrMo6-4 * 20NiCrMoS6-4 * 18CrNiMo7~6

* *

14NiCrMo13-4 -:> 1 Values after

DIN EN

Material No.

Rm,N

Re,N -:> 4 -:> 5

O'W,zd,N

O'Sch,zd,N

O'W,b,N

1: W,s,N

1:W,t,N

1.1121 1.1141 1.1148 1.7016 1.7030 1.7131 1.7147 1.7243 1.7244 1.7333 1.7320 1.7321 1.5714 1.5805 1.5810 1.5918 1.5752 1.6523 1.6566 1.6571 1.6587 1.6657

500 800 800 800 900 1000 1200 1100 1100 1100 900 900 1000 900 1200 1200 1000 1100 1200 1200 1200 1200

310 545 545 545 620 695 850 775 775 775 620 620 695 620 850 850 695 775 850 850 850 850

200 320 320 320 360 400 480 440 440 440 360 360 400 360 480 480 400 440 480 480 480 480

185 270 270 270 295 320 365 340 340 340 295 295 320 295 365 365 320 340 365 365 365 365

220 345 345 345 385 430 510 470 470 470 385 385 430 385 510 510 430 470 510 510 510 510

115 185 185 185 210 230 280 255 255 255 210 210 230 210 280 280 230 255 280 280 280 280

130 205 205 205 230 255 305 280 280 280 230 230 255 230 305 305 255 280 305 305 305 305

10084 Appendix

F ("tensile strength values after quenching and tempering at

ad,rn -:> ad,p

6

0,56 0,68 0,68 0,37 0,33 0,44 0,48 0,52 0,52 0,28 0,33 0,33 0,30 0,61 0,37 0,37 0,300,52 0,37 0,37 0,37 0,37

200°C") given for information only.

-c- 2 Effective diameter deff,N = 16 mm, -c- 3 Only up to 40 mm diameter, types of material marked by * up to 100 mm diameter, however. -:> 4 Re,N after DIN 17210 (Draft 1984-10-00), fitted. -:> 5 Re,N / ~,N < 0,75 for all types of material listed. -:> 6 More specific values for the individual types of material compared to the average values given in Table 1.2.1

and

3.2.1.

Table 5.1. 7 Mechanical properties in l\1Pa for nidriding steels in the quenched and tempered condition, after DIN EN 10 085 (2001-07-00) -:>1. Type of material

24CrMo13-6 31CrMo12 32CrAIMo7-1O 3lCrMoV5 33CrMoV12-9 34CrAINi7-1O 41CrAlMo7-1O 40CrMoV13-9 34CrAIMo5-1O

Material No.

Rm,N

Re,N -:>2

O'W,zd,N

O'Sch,zd,N

O'W,b,N

1: W,s,N

1:W,t,N

ad,rn -:>3

ad,p -:>3

1.8516 1.8515 1.8505 1.8519 1.8522 1.8550 1.8509 1.8523 1.8507-:>4

1000 1030 1030 1100 1150 900 950 950 800

800 835 835 900 950 680 750 750 600

450 465 465 495 520 405 430 430 360

360 370 370 385 395 335 345 345 305

480 495 495 525 550 435 460 460 390

260 270 270 285 300 235 250 250 210

285 295 295 315 330 260 275 275 230

0,22 0,21 0,21 0,31 0,30 0,17 0,23 0,23 0,00

0,26 0,27 0,27 0,36 0,35 0,17 0,24 0,24 0,00

-:> 1 Effective diameter deff,N = 40 mm. -:> 2 Re,N / ~N > 0,75 for all types of material listed. -:> 3 More specific values for the individual types of materiaI compared to the average values for the kind of material given in Table 1.2.1 and 3.2.1. -:> 4 Only up to 100 mm diameter.

137 5 Appendices

5.1 Material tables

Table 5.1.8 Mechanical properties in MFa for stainless steels, after DIN EN 10 088-2 (1995-08-00) (selected types of material only) v I v 2 Type of material

Type of material, after DIN / SEW

Mate- Kind of rial product v3 No.

Rm,N

R,N

CJW,zd,N

CJSch,zd,N

CJW,b,N

'"CW,.,N

'"CW,t,N

450 400 430 450

250 210 240 260

180 160 170 180

170 155 165 170

205 180 195 205

105 90 100 105

120 110 115 120

Martensitic steeIs 'ill th e h eat treate d con d" inon, stan dar d oualiti qua ities. X20Cr13 X20Cr 13 1.4021 P(75) QT650 650 QT750 750 X4CrNiMo16-5-1 P(75) 1.4418 QT840 840

450 550

260 300

230 260

290 330

150 175

170 195

680

335

280

410

195

220

430 380 340

335 310 285

460 410 370

245 220 195

275 245 220

240 220 210 200 210 230

215 200 190 185 190 210

270 245 235 225 235 260

140 125 120 115 120 135

160 145 140 135 140 155

. tl ie annealed con diition, . F emtic stee 1s ill stan dar d qualiHIes,

X2CrNi12 X6CrAl13 X6Crl7 X6CrMo17-1

X6CrAI13 X6Cr17 X6CrMo 17 1

1.4003 1.4002 1.4016 1.4113

P(25) P(25) P(25) H(12)

P ecipitation .. h ar demng . martensitic steeIs ill . tll e heat treate d condition, special X5CrNiCuNb16-4 1.4542 P(50) P1070 1070 1000 P950 950 800 P850 850 600

qualities.

-

, ' anneaIed condiition, Austemtic steeIs 'ill t h e soiution oualiti stan dar d qua ities. C(6) X10CrNi18-8 X12CrNi 177 1.4310 600 250 X2CrNiNI8-1O X2CrNi 18 10 P(75) 550 270 1.4311 X5CrNil8-10 X5CrNi 18 10 P(75) 520 220 1.4301 X6CrNiTi18-1O X6CrNi 18 10 P(75) 500 200 1.4541 X6CrNiMoTil7-12-2 X6CrNiMoTi 1722 1.4571 P(75) 520 220 X2CrNiMoN17-13-5 X2CrNiMoN17135 1.4439 P(75) 580 270

v I The fatigue strength values are provisional values. v 2 An effective diameter deff,N is not required, as there is no technological size effect within the dimensions covered by the standard. v 3 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) cold r~l1ed strip up to 6 mm thickness, QT650 heat treated to a tensile strength of650 MPa, PI070 hot rolled plate with a tensile strength of 1070 MPa.

138

5 Appendices

5.1 Material tables

Table 5.1.9 Mechanical properties in MFa of steels for bigger forgings, after SEW 550 (1976-08-00) 0,75; Table below: R pO,2,N / Rm,N < 0,75 throughout.

3 Elongation in %. For non-ductile materials, A5 < 12,5%, the assessment of the static strength is to be carried out by using local stresses, Chapter 1.0, and all safety factors are to be increased by 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.

142

5.1 Material tables Table 5.1.21. Survey of the Aluminum materials. Table

Kind of material

5.1.22

Wrought Strips, sheets, plates Aluminum alloys Strips, sheets

5.1.23

Semi-finished product / Type of casting

5 Appendices

IRT51Al-a.do~ Material standard (Edition) DIN EN 485-2

(03/95)

DIN 1745 T. 1

(02/83)

5.1.24

Cold drawn rods / bars and tubes

DIN EN 754-2

(08/97)

5.1.25

Rods / bars

DIN 1747 T. 1

(02/83)

5.1.26

Extruded rods / bars, tubes and profiles

DIN EN 755-2

(08/97)

5.1.27

Extruded profiles

DIN 1748 T. 1

(02/83)

5.1.28

Forgings

DIN EN 586-2

(U/94)

5.1.29

Die forgings

DIN 1749 T. 1

(12/76)

5.1.30

Hand forgings

DIN 17606

(12/76)

DIN EN 1706

(06/98)

DIN EN 1706

(06/98)

5.1.31 5.1.32

Cast Sand castings Aluminum alloys Permanent mould castings

5.1.33

Investment castings

DIN EN 1706

(06/98)

5. 1.34

High pressure die castings

DIN EN 1706

(06/98)

5.1.35

Casting alloys for general applications

DIN 1725 T. 2

(02/86)

5. 1.36

Alloys with special mechanical properties

DIN 1725 T. 2

(02/86)

5. 1.37

Alloys for special applications

DIN 1725 T. 2

(02/86)

5.1.38

Alloys for high pressure die castings

DIN 1725 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, and all safety factors are to be increased by adding a value ~j , see Eq. (2.5.2), ... in Chapter 2.5, 3.5 or 4.5, respectively.

Attention: The fatigue limit values GW,zd, ... given in the Table 5.1.22 to 5.1.38 refer to the knee point of the S-N curve at N = ND,O' = ND,< = 106 cycles. The endurance limit values GW,Il,zd , ... refer to a number of N = ND,O'.II = ND.< ,II = 108 cycles, and are lower than the fatigue limit by a factor fIl,O' or fIl,< (see also page 131): -

fIl,O' = (108 / 106 ) fIl,< = (108 / 106 )

1/15 1/25

= 0,74 (kD,O' = 15 for normal stress), = 0,83 (kD,< = 25 for shear stress).

143

5.1 Material tables

5 Appendices

Table 5.1.22 Mechanical properties in MPa for wrought aluminum alloys, strips, s h eets, pJates, I aft er DIN EN 485-2 (03/95) (selected types 0 f matenial onlly), Material

Condition

EN AW-2014

T3

AlCu4SiMg

T4 T451 T451 T42

T6 T651 T651

T62 EN AW-2017A

T4 T451

AICu4MgSi(A) T451

T42

EN AW-2024

T4

AICu4Mgl

T3 T351

T351

T42

T8 T851 T851 T62 -c-

Nom, thickness inmm from to 1,5