Fatigue Testing and Analysis of Results

7~ ,4/l ~

FATIGUE TESTING

AND

ANALYSIS OF RESULTS

by

W. WEIBULL

BOCKAMOLLANBRöSARPS STATION

SWEDEN

PublishedJhr and on behalfof

ADVISORY GROUPFORAERONAUTICAL RESEARCHAND DEVELOPMENT

N( )RTH ATLANTIC TREATY ORGANIZATION

by

PERGAMON PRESSOXFORD• LONDON• NEW YORK~PARIS

1961

PERGAMON PRESS LTD.HeadingtonHill Hall, Oxford

4 & 5 FitzroySquare,London W.1

PERGAMON PRESSINC.122 East 55thStreet,New York 22, N.Y.StatlerCenter 640, 900 Wilshire Boulevard

Los Angeles17, Caljfornia

PERGAMON PRESS S.A.R.L.24 RuedesEcoles,ParisFe / 77/

PERGAMONPRESSG.m.b.H.Koiserstrasse75, Frankfurt am Main

ADVISORY GROUP FOR

AERONAUTICAL RESEARCH AND DEVELOPMENT

NORTH ATLANTIC TREATY OROMQSZATIDN

Library ofCongressCard No.59—14498

Setin Baskervilte10 on 11 Pt. andprinted in NorthernIreland at

TEE UNIVERSITIES PRESS, BELFAST

TO

DERYCK C. SMITH

1916— 1959

Executive — Structures and MaterialsPanel

Advisory Group for AeronauticalResearchand DevelopmentNorth Atlantic Treaty Organization

T4

Copyright

©1961

CONTENTSPAGE

FOREWORD .. . . xiii

CHAPTER I. SYMBoLS AND NOMENCLATURE

10. General .. .. . .

11. Applied stresscycles.. .. .. 312. StrengthsEnd fatigue limits .. 413. Fatiguelife and numbersofcycles .. 414. Statisticalquantitiesand mathematicalsigns .. .. .. 515. Typesofappliedload cycle .. .. .. 516. Variable-stresslevel tests . . . . . . 6

CHAPTER II. FATIGUE TESTING METHOG5

20. General .. .. 721. Routinetests .. 10

21.1. All-failed tests . . . . . . . . . . 1121.2. Fraction-failedtests .. .. .. 12

22. Short-life tests .. .. .. 1322.1. Constant-stressamplitude tests .. 1422.2. Constant-strainamplitude tests .. .. .. 15

23. Long-life tests .. .. .. 1523.1. Responsetests . . . . 15

23.11. The probitmethod .. .. .. .. 1523.12. Thestaircasemethod .. .. 16

23.2. Increasing-amplitudetests .. .. 1723.21. Steptests .. .. .. 1723.22. The Prot tests .. .. .. .. 18

24. Cumulative-damagetests .. .. .. 1824.1. Preloadingtests .. 1924.2. Prestressingtests . . . . . . .. 19

25. Service-simulatingtests .. 2025.1. Prograsametests .. .. .. 2025.2. Speclrtlm tests . . . . 21

26. Abbreviatednod acceleratedtests . . . . . . 2127. Methodsfor detenniaingcrack initiation and etaekpropagation 22

27.1. Non-,Irstroetivetests . . . . . . . . 2327.2. Destructivetests . . . . . . . . 24

CHAPTER III. FATIGUE lEtTING MACITIrsE5 AND EQUIPMENTs

30. General .. .. .. .. 2531. Machinesfor generalpurposes .. .. 26

31.1. Axial loading .. .. .. 2631.11. Load produced by mechanicaldeflexion and variable springs

and/ormasses .. .. .. .. 2631.12. Load producedby deadWeightsand/orconstantspringforces .. 2831.13. Load producedby centrifugal forces .. .. 2831.14. Load producedby electro-magnetieforces .. .. 2931.15. Load producedby hydraulicforces .. .. .. 2931.16. Load producedby pneumaticforces .. .. 3031.17. Load producedby thermaldilatation .. .. 30

vst

CONTENTS

31.2. Repeatedbending . ..

31.21. Loadproducedby mechanicaldeflexion31.22. Load producedby deadWeights ..

31.23. Load producedby centrifugalforces31.24. Load producedby eleetro-magsseticforces31.25. Load producedby hydraulicforces ..

31.26. Load producedby pneumaticforces31.3. Rotatingbending ..

31.31. Load producedby mechanicaldeflexion31.32. Load producedby deadWeightsand/orconstantspringforces

31.4. Torsion.. .. .. ..

31.41. Load producedby mechanicaldeflexionsand inertiaforces

41.2. Electrical instrumentsand devices basedon measurementof resistance,inductance,orcapacitance .. .. .. .. .. .. 68

CONTENTS

41.3. Photo-electricinstrumentsand devices .. .. .. 6941.4. Optical instrumentsand devices .. .. 6941.5. Pneumaticinstrumentsand devices .. .. .. 69

42. Strain-measuringinstrumentsand devices .. .. .. 6942.0. General .. .. .. 6942.1. Meelsanicalinstrumentsand devices .. 7042.2. Electrical instrumentsanddevicesbasedon measurementofresistance.. 7042.3. Opticalinstrumentsand devices .. .. .. .. 71

43. Load-measuringinstrumentsand devices .. .. .. 7243.0. General .. .. .. 7243.1. Mechanicalinstrumentsanddevices .. .. .. 7243.2. Electricalinstrumentsaud devices .. .. .. .. .. .. 72

43.21. Basedon measurementof resistance 7243.22. Basedon measurementofinductanceor capacitance 73

43.3. Piezo-electricinstrumentsanddevices .. .. 7343.4. Optical instrumentsand devices .. .. .. .. 74

44. Stress-measuringinstrumentsand devices.. .. .. 7444.0. General .. .. .. 7444.1. Optical instrumentsand devices .. .. .. 7444.2. X-ray instrumentsand devices .. .. .. .. 75

45. Instrumentsand devicesfor determiningsurfaceconditions 7545.0. General .. .. .. 7545.1. Stylusmethods .. 7645.2. Tapersectioningmethods 7645.3. Optical interferencemethods .. 7645.4. Optical reflectionmethods .. .. 7745.5. Reflectionelectron microscopy 77

46. Instrumentsanddevicesfor detectingcracks,flaws and inbomogeneities .. 7746.0. General .. 7746.1. Microscopicmethodt .. 7846.2. Electrical-resistancemethods . . .. 7846.3. Eddy-currentmethods 7846.4. Magnafluxmethods .. 7946.5. Ultrasonic methods .. .. 79

47. Instrumentsand devicesfor countingnumbersofstresscycles .. 8047.0. General 8047.1. Counters .. .. 8047.2. Frequency-measuringinstrumentsand devices .. 81

CssAerERV. TEST PIFCEt: DESIGN. PREPARATION, MEASUREMENT ANn PROTECTION

313132323334343434353636

31.42. Load producedby deadweights31.43. Load producedby centrifugal forces31.44. Load producedby electro-magneticforces31.45. Load producedby pneumaticforces

31.5. Combinedbendingandtorsion31.51. Load producedby mechanicaldeflexion31.52. Load producedby centrifugal forces31.53. Load producedby electro-magneticforces

31.6. Biaxial andtriaxial loading ..

32. Machinesfor specialpurposes ..

32.1. High frequencies32.2. Elevatedor low temperaturesand cyclic thermalstresses32.3. Corrodingenvironmentsand fretting corrosion32.4. Multi-stressleveltests . . . .

32.5. Contactstresses .. .. ..

32.6. Repeatedimpact .. ..

32.7. Combinedcreepand fatigue tests33. Equipmentsfor testingpartsandastemblies

33.0. General ..

33.1. Wires, tyresandropes ..

33.2. Coil and leafsprings .. ..

33.3. Turbine andpropellerblades33.4. Largespecimens,structures,beams,rails

33.5. Aircraft structures .. .. ..

34. Componentsoffatigue testingmachines34.0. General .. .. ..

34.1. Load-producingmechanisms34.2. Load-transmittingmembers ..

34.3. Measuringdevices34.4. Control devicesand shut-offapparatuses34.5. Counters .. .. ..

34.6. Frameworks .. .. ..

35. Calibrationand checkingof testingmachines35.0. General ..

35.1. Staticcalibrationandchecking ..

35.2. Dynamiccalibrationand checking ..

36. Accuraciesof actual testingmachinesand equipments

CHAPTER IV. INtTRUMRNTS AND MEAsUR5NG DEYIGES

40. General ..

41. Displacement-measuringinstrumentsand devices..41.0. General .. ..

41.1. Mechanicalinstrumentsand devices

37373738383838.383940404142434546474747

48495050

51535353555758606060606163

64

666666

67

50. General .. . .

SI. Unnutehedspecinlens . . . . . . .

51.0. General51.1. Tension-compressionspecimens . .

51.2. Repeated-bendingspecinsens51.3. Rutating-bendingspecimens .

51.4. Torsionspecimens52. Notclsedspecimens .. .. .

52.0. General52.1. Circularspecimens .

52.2. Flat specimens53. Simulatedcomponentsand scaledmodels54. Actual components

54.0. General54.1. Bolted andriveted joints54.2. Welded and bondedjoints54.3. Screwconnexions,aircraft joints, attachangles

8283

8384

858586

8686878788

8888

898989

Vt” ix

61.8. Anisotropy61.9. Origin ..

62. Typeof stresSing ..

62.0. General ..

62.1. Tension-compression62.2. Repeatedbending62.3. Rotating bending62.4. Torsion ..

62.5. Combinedbendingand torsion62.6. Biaxial and eriaxialstresses62.7. Surface-contactstresses62.8. Failurecriteria for multi-axial stresses

63. Test piece . . ..

63.0. General ..

63.1. Size .. .. ..

63.2. Shape .. ..

63.3. Stressconcentrations . .

63.4. Surfacecondition63.5. ResidualStresses ..

64. Testing machine ..

64.0. General ..

64.1. Type of loading64.2. Designoftesting machine64.3. Speed .. ..

64.4. Accuracyofindividual machines64.5. Variationsof similarmachines

65. Environment65.0. General ..

65.1. Temperature ..

8989898989899090919191919292929393

9494949596979899

100100

102102

102103

105106

106108

108109

110Ill111111113114

. . . 117118

120120120121

. . . . .. 122123

124124

124125

CONTENTS

65.2. Vacuumand air65 3. Non-corrodingenvironment65.4. Corrodingenvironment65.5. Frettingcorrosion65.6. Sunlightand Iseatradiation65.7. Nuclear radiation

66. Testing technique66.1. Definition offatigue life66.2. Runoutnumberofcycles66.3. Restinterval

CHAPTER VII. PLANNING OF TEST PROGRAMMES

70. General .. ..

71. Designof testseries ..

72. Specificationand samplingof testpieces73. Choiceof testpiece74. Choiceof testingmachine

CHAPTER VIII. PRESENTATION OF RESULTS

126127127128129129129130

131132

133134137140141

143145145146146146147147147147151159167174174178181

CONTENTS

54.4. Loadedholes,lugs .. .. ..

54.5. Structural components,beams,sandwichconstructions54.6. Aircraft wings, tail planes .. ..

54.7. Fuselages .. .. ..

55. Preparationoftestpieces .. ..

55.0. General .. .. .. ..

55.1. Mechanicaltreatment .. ..

55.2. Heat treatment ..

56. Measurementsoftestpieces .. .. ..

56.0. General .. .. .. ..

56.1. Measurementofdimensions .. ..

56.2. Measurementofsurfacegeometry ..

56.3. Measurementofttressdistributions ..

57. Protectionof testpieces .. .. .. . .

57.0. General .. ..

57.1. Protectionagainstmechanicaldamage57.2. Protectionagainstchemicalaggression

CHAPTER VI. FACTORS AFPEGTINO TEST RESULTS

60. General .. .. .. .. .. ..

61. Material .. .. .. ..

61.1. Compositionandheattreatment ..

61.2. Structurein general—Grainsize .. .. . .

61.3. Inclusionsand inhomogeneities ..

61.4. Structuralsurfaceconditionsproducedby heattreatment61.5. Structuralsurfaceconditionsproducedby mechanicaltreatment61.6. Structuralchangesrelating to sizeof testpiece61.7. Structuralchangescausedby preloadingandprestressing

80. General .. ..

81. Specificationof test couditions .. . . . . ..

81.1. Material . .

81.2. Type of appliedload81.3. Test piece81.4. Testing machine .. ..

81.5. Environment ..

81.6. Testing technique82. S—NandS—Sdiagrams ..

82.1. TheS—Ndiagrams ..

82.2. The S—Sdiagrams ..

83. Graphical and analytical representationof strengthand life distributions84. P—S—Ndiagrams85. Analytical representationof load and life relations ..

85.1. Relationsbetweenload and life (S—Nequations) ..

85.2. Relationsbetweentwo load components(S~—S~equations)86. Analytical representationof probability, load andlife relations

CHAPTER IX. ANALYSIs OP RESULTS

90. Generalstatistical conceptsand methods .. . . . . . . .. .. 18490.0. General .. .. .. .. 18490.1. Random variables, probability, distribution and frequency functions.

Franslbrsnationof random variables . . . . . . . . .. 184111.2. General propertiesof meaiss,variancesandcovariances . . . . . . 188111.3. Order statistics. Principle of lril)al)ility papers. Plotting pusitinns.

Randi,Iis sansplingnunsliers . . . . . . . . . . . 192911.4. Fitting of curves to observations... . . . . . . . . .. 20190.5. Estimatesofvarious statistics .. . . .. . . .. .. 20890.6. Significance tests .. .. .. .. .. 21090.7. Confidenceand toleranceintervals .. .. .. .. .. .. 213

91. Determination of averageload-life relations . . . . . . . . .. 21591.1. Graphical methods .. .. .. .. .. 21691.2. Analytical methods .. .. .. .. .. 218

92. Determinationof fatigue-life distributions .. .. . . .. .. 22392.0. General .. .. .. .. 22392.1. Graphical methods .. .. .. 22492.2. Analytical methods .. .. .. .. .. .. 225

x xi

CONTENTS

93. Determinationof fatigue-strengthdistributions .. ..

93.0. General ..

93.1. Graphicalmethods .. ..

93.2. Analytical methods94. Determinationofprobability-load-liferelations

94.0. General94.1. Combination ofaverageS—Ncurveand deviationsfrom it94.2. Fitting P—S--Ndiagrams to observations,shapeofdistribution unknown94.3. Fitting P—S—Ndiagrams to observations,shapeof distribution assumed

95. Evaluation ofdata from responsetests .. .. ..

95.0. General .. .. .. ..

95.1. Probitmethods .. .. ..

95.2. Staircasemethods ..

96. Evaluationofdata from increasing-amplitudetests ..

96.0. General .. ..

96.1. Step tests .. .. .. ..

96.2. Prot tests .. ..

BHSLIOGsSAPHv ..

FOREWORD

In dedicatingthis volume to Deryck C. Smith, the Advisory Groupfor AeronauticalResearchand Developmentwishes to commemorate

the servicesof an outstandingmemberof its staff.

Mr. Smithwascalledto theorganizationto formulatea new sectionwithin the frameworkof AGARD. By his original ideas,his forcefulpersonality,andhis untiring devotion,he broughttogethera dynamicgroup of membersfor his Panel, and imbued them with his own

enthusiasmfor the work to beaccomplished.

This volumeis butoneof theseveralpublicationswhich indicatetheimportanceandscopeof the work which was undertakenby the Panelunderhis guidance.

Officially AGARD has suffered a severeloss in the death of anexecutivewho had the vision andthe ability to seeand to carryoutan ever expandingprogramto increasethe value of AGARD to theNATO nations.

Personally,the staff will long remembera congenialassociate,ahelpful andstimulatingco-worker,a cherishedfriend.

THEonoi~voN KAEMAN

Chairman—AGARD

226226228229237237238241243245245246247247247248248250

xis xsit

CHAPTER I

SYMBOLS AND NOMENCLATURE

SECTION 10. GENERAL

There is a wide variety of symbols and nomenclatureused in differentcountries, not to say within each country, and with few exceptionsnointernationallyacceptedstandardsexist. The choiceof symbolsto be usedin the presentbook was not, therefore, easily taken and a definite andunobjectionablelist cannot,for the time being,be established.

Under thesecircumstances, it was decidedto follow mainly the nomen-clature and symbols—someof them tentative—proposedby the ASTMCommitteeE—9 on Fatigue, although somemodifications, chosenfrom thereferenceslisted below or obtainedas a resultof personal discussionswithseveral experts,havebeenintroduced.

Thereis onequestionwhichseemsto deserveparticularmention, andthatis the ambiguoussignificanceof the symbol for “stress”,5, and its varioussubscripts. In fact, thereare two quite different conceptsof “stress” whichareboth denotedby S and which have to be keptstrictly apart in ordertoavoid confusion. One of them is “the stress applied to the test piece”,resulting from the givenload; theother is “the stressat which somethinghappensto an individual test piece”, i.e. a strengthvalue.

Into the first categoryfall the quantitiesmentionedin Section 11 suchas5

max,5

as‘5

’nv K5

, etc.whicharefactorsdefining thetestconditionsandhavinga magnitudewhich canbe specifiedby a definite number, for example,anapplied stressamplitudeSa = 10 kg/mm

2. Into thesecondcategoryfall the

quantities mentionedin Section 12 suchasS~5

N’ 5,,, K,., etc.which indicatesome property of the material and accordingly take a valuevarying fromspecimento specimen; in otherwnrds thesequantitiesarerandomvariableswith a magnitude which cannot be specified by a definite number butrequire fi)r their definition a distribution function or, less completely,oneormore statistics; for example, the lhtigue strength

5N at a given fatiguelife,

say N = 10~,wlsich may be specifiedby its arithmetic mean or medianS~and its lower bound

1Ns or variance Gg

2as a substitutefor the distri-

bution function.Strictly speaking,quantitiesof tlse first categoryare non-randomvariables

only in so far as the nominal stressapplied—i.e.the stressaimed at—isconcerned,whichdiffers from thestressactuallyappliedbecauseofsystematicor accidentalerrorsin thecalibrationof the testingmachineor variationsinthe dimensionsand shapeof thetest piece.

The stressactually applied is evidently a random variable and thus of acharacterquite different from the nominal stress. Its scatteradds to the

PATIGUE TESTING AND ANALYSIS OP RESULTS

scatterdue to thematerial. In most casesthe actualstressesare unknownandonly thenominalstressesaregiven. Consequently,no distinction betweenthe two sourcesof scattercan be madeand the total scatter is frequentlyattributed to the test piecealone. It is obvious that in caseswhere suchadistinction is required,differentsymbolsfor nominal andactualstressesmustbe introduced.

REFERENCESInternational Unions:(I) InternationalUnion of PureandApplied Physics(1955),“SymbolsandUnits”,

DocumentU.I.P.6,Reportpublishedwith thefinancialsupportoftheUNESCO.

France:(I) Socidtd Francaisede Metallurgic (1957), “Terminologie proposdepour Ia

designationdesexperimentationssur Ia fatigue et des phCnomeneslies is Iafatigue”, GroupeIV—Guidc dela Fatigue,DocumentGF 3.

Germany:(1) DeutseherNormenausschuss(1953), “Dauerschwingversuch:Begriffe—Zeichen

.—DurchfUrung—--Auswertung”,DeutscheNormen, DIN 50 100.(2) (1954), “Dauerschwingversuch: Stichwortverzeichnis zu DIN 50 100

in 4 Sprachen”,DeutscheNormen,DIN 50 100, Beiblatt (Vornorm).

italy:(1) Unificazione Italiana (1957), “Prove dci materiali metallici. Provedi faticaa

temperaturaambiente: Generalita—Simboli-—Definizioni”, UNI 3964.(2) Locati, L. (1942), “Terminologia nella scienzadella “fatica” dci metalli”,

MetallssrgoItala, June 1942, pp. 237-241.

Netherlands:(I) Nationaal Luchtvaartlaboratorium, Asnsterdam (1954), “A proposal for

fatiguesymbolsandnomenclatureto beusedin reportsin the Englishlanguage”.

Sweden:(1) Tekniska Nomenklaturcentralen(1946), “Benamningar och beteckningar

inosnhallfasthetslaran”.PubI. TNC 8.(2) StatistiskaForeningen, Stockholm (1954), “Nordisk Statistisk Nomenklatur”.

Engelsk-NordiskochSvensk-EngclskOrdlista.

UnitedKingdom:(1) Royal AeronauticalSociety(1958), “Termsand Notation ~r Aircraft Structural

Fatigue”. FatigueData SheetG. 00.02.

UnitedStates:(1) American StandardsAssociation (1942), “The American Standard Letter

Symbolsfor Conceptsin Mechanicsof Solid Bodies”, ASA No. Z 10.(2) American Society for Testing Materials (1937), “Nomcnclature for various

ranges of stressin fatigue”. Proc. Amer. Soc. Test. Mat. \ ol. 37, pp. 159-163.(3) (1948), “Symbols and Nomenclature for fatigue testing”. Bull. No.

153, pp. 36-37.(4) (1949), “Symbols and Nomenclaturesfor fatigue testing”. Section II

of “Manual on fatigue testing”. Amer. Soc. Test. Mat. STP No. 91, pp. 3-5.(5) (1955), “ASTM Standardson Plastics. Specifications—Methodsof

testing—Nomenclature-—Definitions”.

StressCycle.

StressLevel.

S = Nominal Stress.

Snssx = MaximumStress.

sygnoLs AND NOMENCLATURE

SECTION 11. APPLIED STRESS CYCLES

A stresscycle is thesmallestsectionof thestress-timefunctionwhichis repeatedperiodically and identically as shown in Figs. 11.1,11.2 and 11.3. The stresscycle is definedby: (a) the stresscom-ponents,(b) the shapeand (c) the frequency,i.e. the number ofcyclesperminuteor per second. The simplestshapeof the cycleis the harmonicwavein which the profile is a sine or cosinecurve(Fig. 11.1). The varying stress of this cycle has one maximumandone minimum value. Its damagingeffect is definedby onepairof stresscomponents. This appearsto be the casealso when

5mmOne stress cycis

Fig. 11.2.

One st,ess cycle

Fig. 11.3.

the waveis non-harmonicwith one maximum and oneminimumvalue asdemonstratedin Fig. 11.2. A stressvarying accordingtoFig. 11.3 requirestwo pairsof stresscomponentsfor its definition.The pair—or pairs—of stressor strain componentsnecessarytodefinethe apphedcycle.Theappliedstresscalculatedon the areaof the net sectionof thetest pieceby simple sheoryignoring stressraisersand disregardingplastic flow. tn most of the definitions given below the word“stress”may bereplacedby “load”.The highestalgebraicvalue of the stressin the stresscycle, tensilestress being considered positive and compressivestressnegative.

Fig. 11.1.

__________________— ~max

2 23

FATIGUE TESTING AND ANALYSIS OF RESULTS SYMBOLS AND NOMENCLATURE

The lowestalgebraicvalue of thestress in the stresscycle, tensilestresS being consideredpositive and compressiveStress negative.The algebraicdifferencebetweenthemaximumandtheminimumstressin one cycle: 5, =

5msx — SmSn.

Onehalf therangeofstress: 5,, =

The algebraicmean of the maximum and the minimum stressinonecycle: 5,,, = I(Sinax + Ssstn).The algebraicratio of the minimum stressto the maximum stressin one cycle: R = SmSn/S,ssx.The ratio of thestressamplitude to the mean stress:A = S,,/S,,.This ratio is particularlyusedin high-temperaturework.The ratio of the greateststressin the region of a notchor otherstress raiser as determinedby advancedtheory, pbotnelasticity,or direct measurementof elastic strain, to the correspondingnominalStress.

SECTION 12. STRENGTHS AND FATIGUE LIMITS

St = StaticTensileStrength.

S,, = StaticCom-pressiveStrength.

= FatigueStrength. The stresswhich producesfatigue failure at a number of stresscyclesequal to N. Thestresshasto be expressedin termsof a pairof stresscomponents,such as the stressamplitude and the meanstress,oras the maximum and tlse minimum stresses.One of thecomponentsis keptconstantduring thetest, for examplethemeanstress,wbicb is thenacharacteristicof thetest conditions,while theother component,for example the stressamplitude, is a propertyof the material and accordingly a random variable defined byastatisticaldistributionfunction.Thefatiguestrengthfor N—÷ ccx.Thefatiguestrengthfor N—÷ 0. Thisvalue is not necessarilyequaltoS~or5,.Theratio of thefatiguestrengthofa memberorspecimenwith nostressconcentrationto thefatiguestrengthof a specimenwith stressconcentration.

q = Notch Sensitivity. A measureof the degreeof agreementbetweenK,. and K~for aparticular specimenor member of given size and shape. Thusq = (K, — l)/(K, — I). Notch sensitivity varies between zero

(whenK, = 1) and unity (when K1

= K,).

SECTION 13. FATIGUE LIFE AND NUMBERS OF CYCLES

N = FatigueLife.

N, = Run-outNumber (of cycles).

n = StressCycles The numberof eyelet which has been imposed on a specimenImposed. without failure at anystageofa fatigue test.

C = Cycle Ratio. The ratioof the stresscyclesactually appliedat a given stresslevelto the expectedfatigue life at that stresslevel, basedon the S—Ndiagram: C = n/N.

X = log N. In somecasesan unspecifiedrandomvariable.D = FatigueDamage.Changeof fatigue propertiesof a test piece subjectedtn cycling

stresses.

SECTION 14. STATISTICAL QUANTITIES ANDMATHEMATICAL SIGNS

P = Probability ofFailure.

Q Probability ofSurvival.

F(x) = Distribution A non-decreasingpoint function wlsieb correspondsto the pro-Functionofx. bability function in such a way that F(x) = P(~~ x) = the

probability that the randomvariable E takes a value equal to orless thanx.

G(n) = InverseFunctionof F(x), i.e. G~F(x)] = x.f(x) = Frequencyor DensityFunctionofx, i.e. dF(x)/dx = f(x).E(x) = MathematicalExpectationorMeanValue of a randomvariableE.

= D’(x) = var (x) = Varianceof x.cm,, = StandardDeviationofx.6 = Estimateof cx froma sample.coy (x,y) = Covarianceofx andy.n andj = SampleSize = Numberofvaluesin asample.us andi = OrderNumbersin a randomsampleorderedfrom leastto greatest.a,b and B = Parametersof an S—Nequations.E andfi = Parametersofa distributionfunction.& and fi = Estimatesof a and fi from a sample.

I = Arithmetic Meanof observedvaluesXm.

X = Median ofobservedvaluesXm.= Summationsign.

e = SubscriptcorrespondingtoN =

o = Subscriptcorrespondingto lower boundofa randomvariable, i.e. to P = 0.

a = S — S~DeviationofS from mean.

u = U — U = Deviationof U from mean.

Axial Loads

SECTION 15. TYPES OF APPLIED LOAD CYCLE

FluctuatingTensile Minimum loadand maximumload both tensile.Load.

RepeatedTensile Minimum loadzero, maximumload tensile. (B = 0)Load.

AlternatingAxial Unspecifiedaxial load cycle.Load.

ReversedAxial Load. Alternatingloadwith maximumloadnumericallyequalto minimumload. (5,,, 0).

Repeated CotopressivcMaxim,,,,, l,,ad zero,osinimumload compressive.Load.

FluctuatingCom— Minimum load and maxidsumload both compressive.pressiveLoad.

Plain BendingLoads

Fluctuating, repeated,alternatingand reversedbending loads definedanalogicallywithdefinitionsfor axial loads.

Rotating BendingLoads

A rotatingspecimenis subjectedto a constantnon-rotatingbendingmoment, or a non-rotating specimenis subjectedto a rotatingconstantbendingmoment.

Srntn= MinimumStress.

5, = Rangeof Stress.

5,, = StressAmplitude.5,,, = MeanStress.

B = StressRatio.

A = StressAmplitudeRatio.= StressConcen-

trationFactnr.

TIse ratioof the numberofspecimenswhich havefailedto thetotalnumberof specimenstested.It follows that P + Q = I.

= FatigueLimit.= UltimateFatigue

Strength.K, = FatigueNotch

Factor.

The numberof stresscyclesat whicb fatigue failure occurs for agiven testcondition.Numberof cyclesat which test is discontinued.

4 5

FATIGUE TESTING AND ANALYSIS OF RESULTS

TorsionalLoadsFluctuating, repeated,alternatingand reversedtorsional loads definedanalogically with

definitionsfor axial loads.

CombinedLoadsTo be specified for eachcondition, including any relative phasedifferencesbetweenthe

components.

SECTION 16. VARIABLE-STRESS LEVEL TESTSTestduringwhicha specimenis subjectedto stresscyclesdifferingin stressamplitudeand/ormeanstress.Fixed number of stress cycles of constant amplitude and meanstress.An aggregateofsteps.The pattern in which the steps are arrangedwithin the block.Total numberof cyclesorvalueof En/Nof the block orestimatednmnberofblocksto failure.Fixed number of stresscycles of magnitudevarying cnntinuouslyaccordingto a givenpattern.A fatigue testwhich isprecededby a numberofhigh loads.A step precedingthe last stress level which is continueduntilfailureoccurs.Load is composedof a limited numberof steps,usually groupedinto blockswhich arerepeateduntil failure occurs.Thesequenceof thestepsis random.

Consecutivestresscyclesareof differentmagnitude.

CHAPTER II

FATIGUE TESTING METHODS

SECTION 20. GENERAL

The objectiveof afatigue test is, generallyspeaking,to determinethefatiguelife and/or thedangerpoint, i.e. thelocationoffailure,ofa testpiecesubjectedto a prescribedsequenceof stressamplitudes. In somespecific casesthismay be the solepurposeof the test; e.g. if the test pieceis a complicatedmachine part or an assemblyof componentsand the applied load is asequenceof varyingstressamplitudesintendedto simulate thestresshistoryencounteredin actualservice.

In most cases,however,it is requiredthat the test be designedin suchaway that it doesnot only answerthe specific questionwhich has beenput,but will alsoallow a generalizationof theresultobtainedandcontribute tothe discovery of laws or rules relating fatigue life with various influentialfactors. For this purpose it is indispensablethat the test conditions besimplified, he it with regard to thesequenceof stressamplitudesor to thetest pieceor to both of thesefactors. By simplifying and idealizing the testconditionsit will bepossibleto varyoneora fewofthefactorswhich influencethefatigue life and to statetheir effects.

Evenif theseconditionsarefulfilled, therewill alwaysremaina numberofunknownanduncontrollablefactorswhich producea largescatterin fatiguelife evenof test pieceswhichareconsideredto be identical. In thepast,thisscatterin fatigue life wasnot regardedasaproblemandonly afewspecimenswere usedto determinethe fatigue limit or the relation betweenload andlife. It is now generallyacceptedthat thescatter is an inherentpart of thefatigue properties,and that a largenumber of specimensis requiredevenifaveragevaluesonly areconcerned.This requirementhassomeinfluenceonthechoiceof thetestingprocedure.

The two above-mentionedfactors: (i) the sequenceof stressamplitudesand (ii) the test piece,will stow be used asa basisfor a classificationof thedifferent methodsof fatiguc testing.

Thesimplestsequenceof amplitudesis obtainedby applying reversalsofstressof a constantamplitudc to thetest pieceuntil failure occurs. Different

specimensof the testseriessnaybe subjectedto different stressamplitudes,but for eachindividual item the amplitudewill neverbe varied. This typeof fatigue testing is called a con.staot-amplitudetest.

Dependingupon the choiceof stresslevels,constant-amplitudetestsmaybeclassified into threecategories:

(i) theroutine test, whereappliedstressesarechosetsin sucha way that allspecimensare expectedto fail aftera moderatenumberof cycles,saylO~to l0~. A few run-outs, although not intended,maybeallowed;

Variable-stressLevelTest.

Step.

Block.ShapeofBlock.SizeofBlock.

Period.

PrcloadTest.Prestress.

ProgranimeTest.

RandomizedPro-grammeTest.

SpectrumTest.

6 7

FATIGUE TESTING AND ANALYSIS OF RESULTS

(ii) theshort-ijfe test, where stresslevels are situatedabovetheyield Stressandsomeof thespecimensareexpectedto fail staticallyat the appli-cationof theload; and

(iii) the long-ijfe test,wherestresslevelsaresituatedbelowor justabovethefatigue limit and a fraction of the specimensdoes not fail after apreassignednumber of cycles(usuallybetween106 and 1 0~).

Obviously, thereis no abrupttransitionfromonetypeto another. Supposefor examplethat five samplesof equalsizen aredrawn at randomfrom arealor hypotheticalpopulationandtestedatfive differentstresslevelsasindicatedin Fig. 20.1; then it may be postulatedthat all specimenshavingthe same

Fig. 20.1. P—S—Ndiagramincludingstaticallyfracturedspecimensand run-outs.

order number, from least to greatestfatigue life, will have approximatelyidentical static and fatigue properties—thelarger the sample,the smallerthe individual deviationsfrom average—whicharerepresentedby a familyof S—Ncurves, of which three, themedianandthe two extremecurves,areindicatedin the Fig. Theestimatedrangeof the tensilestrengthS,~for thegiven samplesize is marked by a—b, and that of the fatigue strength5

N (N = 10~,say) is markedby c—d. If now thestresslevel S = .~, fifty percentof thespecimenstestedareexpectedto fail within thefirst cycle (N = 0)whereasthe remaining half areexpectedto have a fatigue life N � 1. Inthesameway, if S =

5N~fifty per cent of thespccimenstestedare expected

to endurempre than l0~stressreversals.A short-life test thus includesstresslevels above the lower boundof the

tensilestrength (point b) and a long-life test includesstresslevels below theupper bound of thefatigue strength(point c).

In somecasesit will be requiredto substitutemorecomplicatedsequencesof stresssamplitudes than constantones. The sequenceobtained by sub-jecting each test piece to reversalsof monotonic increasingamplitude iscalled the increasing-amplitudetest. It is atypical long-life test,exclusivelyusedfor thesamepurposeasthe responsetest (seeSection 23, paragraph1), and

FATIGUE TE5T5NG METHODS

it is, therefore,in spiteof not being a constant-amplitudetest,presentedinthe samesection as the responsetest. The increasein amplitude may beeither by stepsor continuous as demonstratedin Section 23, paragraph2.

More complicated sequencesof amplitude are required in order tosimulate the stressesto which a specimenis subjectedin actual service. Arealistic simulationis verycomplicated. In orderto discoverlaws in relationto the accumulation of fatigue damagein a specimensubjected to stressreversals of different amplitudes, the sequenceof stressamplitudes, alsocalled the programme or the spectrum of loading, may be simplified.Independent of the pattern used such tests will be designatedvariable-

amplitude tests,theonly exceptionbeingthemonotonicincreasing-amplitudetest which is regardedas a category by itself. Two alternativeswill beconsidered. If the objective of the test is to investigatecumulativedamagetheory, in which easethe sequenceis frequently simplified, composedofperhapstwo or threestresslevelsonly, the testwill be called the cumulative-

damage test, discussedin Section 24, whereastests using a more elaboratepattern for simulating purposeswill be called the service-simulatingtests,discussedin Section 25.

Having thusclassifiedthevariousfatiguetestson thebasisof thesequenceof stressamplitudes,subclassesmay be obtainedby consideringthedifferenttypesof testpieceavailable. It will suffice to divide the testpiecesinto twocategories,which will be designatedspecimensand components.

Theterm specimenis hereusedin the senseof a test pieceof simpleshape,frequentlystandardized,ofsmall size, andpreparedcarefully andwith goodsurfacefinish. The purposeof the simplification is not only to make it lessexpensivebut more to reduce the variability of the product and to keepdifferent influential factors under control. Test piecesof this type wereoriginally intendedfor testing the material and for statingits fatigue pro-perties. They arenow alsousedextensivelyfor researchpurposes.

Even if the simplified specimenmay simulate many of the propertiesofactual machine parts, there are two factors pertaining to the componentwhich are not representedin thespecimen,i.e. designand fabrication. Forthis reasonit is indispensableto carry out actual testswith componentsinexactly thesamecondition as usedin actual service.

‘Else tcrm component is here used to signify any machine part, actualstructure, maclsinc and assembly, including elements simulating actualcomponents.

Ilse dilferent types of test mentioned above may be applied either tospecimens or to components. Of the different combinations possible,TEMPLIN (1949) haspaid particularattention to threeof thesecombinations,viz, the routine test applied to specimensand componentsand theservice-simtslating test applied to components. They have beendesignatedby himas the material test, thestructural test and the actual-servicetest.

It may be appropriate to mention someof the purposesfor which datafrom such testsare intended.

Testsof thematerial type areusefulfor a comparisonof thebehaviourofdifferent materialssubjectedto repeatedstresses,of the effects of various

Sm,,.

10

8 9

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING METHODS

manufacturingprocesses,of thebehaviourof materialsin variousenviron-ments,ofvarioussimplegeometricalfactorssuchasdifferentsizesandshapesof flotches,and differentsurfacefinishes. They mayalsobeusedto establishcorrelationswith other mechanicalproperties, different typesof stressing,chemicalcompositionsand for evaluating the effects of surfacetreatmentssuchascase-hardening,decarburization,nitriding, shot-peeningand platingon the fatigue propertiesof different materials.

Testsof thestructural type may be useful for a comparisonof componentsmadefromdifferent materials,ofdifferent designandofstructuresfabricatedby different procedures. They mayalsobeusedfor revealingstressconcen-trations and fabricationfaults, for developingbetter designsor fabricationproceduresand for establishingdesigncriteria. In somecases,the locationof this failure point is theonly information required (DE LEIRES, 1956).

All fatigue testsarevery time-absorbing,particularly when a number oftestssufficiently large to allow statisticaltreatment is required. This diffi-culty has beenapparentto researchworkersalmostfrom the beginning offatigue testing, and several methodshave beensuggestedin an attempt todiscoversomerapid methodwhichcouldbesubstitutedfor thenormalfatiguetesting methods. Such abbreviatedand acceleratedtestsare discussedinSection26.

Fatiguetestscompletelydifferent in typefrom the above-mentionedtestsarethosewhichhaveasobjectivea studyofthe initiation andpropagationoffatigue cracks. In the routine teststhe mostcommonpracticeis to run thetestuntil completefractureof thespecimenoccurs. Froma theoreticalpointof view, it would bemuchbetterto split up thetestinto two parts. The pre-crack stage and the post-crack stage, owing to the fact that the fatiguedamageis of a quite different characterin thesetwo stages. Simplelawsarethereforenot to be expectedwithout such a separation. This is perhapsparticularly true when size effects and similar problems are concerned.Somecommentson testsintendedfor thedeterminationof thecrackinitiationandfor a studyof thecrack propagationareto be found in Section 27.

The above-mentionedmethodsmustbe modified for certainspecialpurposes.Someparticular casesare indicatedand referencesare given in Section28.

References: BELYAEV (1951), BERG (1941), CAZAUD (1934), CHRtSTOL(1937), DE LEIRE5 (1956), FRANKE (1929), GILLETT, GROVERandJACKSON

(1946), GOUGH and CLEN5HAW (1935), JOHN5TONE (1947), MOORE (1925),MOORE,SPARGEN and CLAU55EN (1938), PETERsON (1945), SIEBEL (1938),SIEBEL and LUDWIG (1953—1957),SIGwART andPETERSEN (1953), TEMPLIN

(1948).—ASTM STP91 (1949), ASTM STP91—A (1958), DIN 50100(1953).

SECTION21. ROUTINE TESTS

The purposeof theroutine test is to estimatetherelation betweenload andlife; in the past,with the chiefaim of determining the fatigue limit by anextrapolation of thecurve fitted by eyeto the data points.

Later it has becomeapparentthat not too much confidenceshould beplacedon resultsobtainedfrom an extrapolationof empirical curvescarried

out without using propercaution,and sincemore powerful testsfor statinglong-life fatigue propertieshave been available, the use of a routine testshould be restricted to the range of stress levels actually studied. (Theproblemofextrapolatingcurvesto rangesoutsidetheobservationsis discussedin Sections71 and 91.)

This type of test is usually designedwith the intention of having all thespecimensfail. There is, however, in some casesand for some purposesreasonto discontinuethetestwhen a certainfraction at eachstresslevel hasfailed, and the routinetestsmaythenbe classified into all-failed andfraction-failed tests.

21.1 All-failed Tests

The purposeof the all-failed test is usually to determinethe relationbetweenthefatigue life andthe amplitude of the applied stressfor the testpieceused,keepingthe meanstressSm or thestressratio Rconstant. Theresult and its usefulnessdepend upou the total number of specimens,thechoiceof stresslevels, and the allocation of specimensto the stresslevels.

If the total numberof specimensis small, theonly informationobtainableis an estimateof the averageS—Ncurve correspondingto a probability offailure (or of survival) of aboutfifty per cent. In the past,before designingfor limited life wasactuallyneeded,this wasall that wasrequiredofthetest.It was consideredneither necessarynor desirableto usemanyspecimensforeachtestseries. The normalprocedurewasto run a single testat eachstresslevel, reducing the range of stresswith each succeedingspecimen. Thepretensionswerevery moderateindeed. It wasstatedthat thedeterminationof the limiting stressof a metal could be determinedwith “a number ofspecimenswhich cannotbe safely reducedbelow four, even under the bestcircumstances”.

FINDLEY (1949) suggeststhat at least tenspecimensbe testedfor anS—Ndiagram, but that a larger number of specimenswould be desirable forestablishingthe S—Ndiagram accuratelyand indicating the variability ofthematerial. He proposesthat for this purposeat least20 (preferably 50)specimensshouldbe preparedandtested.

It has beenexperimentallyverified (WE5BULL, 1958a) that, even if thernswsberof specimenstestedhas a self-evidentinfluence on the accuracyofthe parameterscomputed from the observations,other factors may be ofequalimportance. In sometases,small testseriescould givejust asgoodorevenbetteraccttracythanseriesthreeor four timesaslarge. The efficiencyofa test seriesin tlsis respectdependsalsoupon the choiceof thestresslevels,the inherent scatterof the specimensusedand of the testing machineandpossiblyof someotherfactors; so, in away, a small numberofspecimenscanto someextentbe compensatedby a more efficient designof the test condi-tions. This problemwill, however,hemorethoroughlydiscussedinSection71.

It is believedthat sometwenty to thirty specimenswill give afair estimateofthevarianceofthefatiguestrengthandthat fifty to one-hundredspecimenswill be required for establishingan acceptableP—S—Ndiagram, providedefficient statisticalmethodsare usedfor theevaluationof theobserveddata.

10 11

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTINO METHODS

The choiceofstresslevels dependsupon thepurposefor which thedata arerequired. If themain interestis in the long-life rangeof the S—Ncurve, lowstresslevels will be chosen. If the completeS—Ndiagram or the P—S—Ndiagramis wanted, the stresslevelsmay bemore evenly distributed. It isstrongly recommendedthat somestatic tests should also he included, ifpossibleusing specimensidentical to thoseused in the fatigue tests. It isdesirableto introducethe experimentallydeterminedvalue of the statictensilestrengthsS~as a unit and to userelativestresses,i.e. to expressthestressesaspercentageof S~,becauseparametersreferring to relative stresseshave a more general validity than if the stressesare given in absolutedimensions.

The influenceof themagnitudeof thestresslevelson the efficiencyof thetest serieswith regard to the accuracyof computedparametersmay brieflybestatedby sayingthat the greaterthedifferencebetweenthehighest andthe lowest stresslevels, the greaterthe accuracy. Also from this point ofview it is advantageousif the staticstrengthS,~canbe usedas anintegratingpart for theevaluationof the test data.

Theallocationofteststo thestresslevels is not very crucial on condition that aproper transformationof thequantities (5, N) hasbeenperformed,resultingin a homogeneousvarianceofthevariables,as demonstratedin Section91.All theobservationscan thenbe pooledandused to determinethe distri-bution of the deviations from the averagecurve. Frequently, the bestmethod appearsto be to allocatean equal number of tests to the stresslevels; the fitting of P—S—Ndiagramscan thenbe performedmore easilyasdemonstratedin Section94.

Sincethe numbersof specimensat eachstresslevel have beendecided,attentionmustbepaid to anunbiaseddistributionoftheitems. The problemofdesigningthetestseriesproperly is discussedmorethoroughlyin Section71.

References:FINDLEY (1949), FINDLEY, CENTURY andHENDRIcKSON (1952),MULLER (1937), WEeK (1950),WEIBULL (l958a), WELLINGER (1955), TON

ZEERLEDER (1935)—DIN 50142 (1941), DIN 50113 (1952), DVM Specifi-cations (1933), French Air Ministry (1938).

21.2 Fraction-failed Tests

For practical designpurposesit is of little interest to know thefatigue lireof the betterspecimensof a fatigue testedgroup, as thedesignerhasto basehis calculationson theworst part of the group. It would be quite stifticientfor him to have a safeknowledgeof the lower part of the life or strengthdistribution.

Sincethetotal time requiredfor a testseriesis largely determinedby thelong-life items, it is obvious that a considerablesaving in time may beobtained by stopping the tests when a certain fraction of the group hasfailed. For example, a seriesof 120 specimensallocatedto five stresslevels(WEIBULL, l956c, Table 1) requireda total machine time of l44~2millioncycles, the 12 smallestvalues of eachstresslevel taking l7~3million or 12per centand the 12 largest taking I 26~8million or 88 per centof thetotaltime. If the latter had beenstoppedat the medianvaluesof life, a savingof

9l~8million cycleswould haveresulted. The total time of the 50 per centfraction-failedseriesis thus36~3per centof thatof theall-failed series.

Still morereductionin testing timewill resultaccordingto a “least-of-fourmethod”, proposedby ScHUETTE (1954). Four specimensaretestedsimul-taneouslyandthe test is discontinuedassoon as oneof them hasfailed. Bymeansof thesedataan S—Ncurve for approximately 80 per centsurvival isobtained.

If theobservationsareevaluatedby efficientstatisticalmethodsnot verymuchdesigninformationis lost by testinga fraction only. Such methodsarediscussedin Sections9 1—94. A reductionof thetime requiredfor theexperi-ment can be important when the resultsareneededas soon as possibleorwhen thecostassociatedwith a failed item is muchlargerthan thecostof alife-testeditem which did not fail.

Thereis no fundamentaldifferencein testing techniquebetweenthis typeandtheall-failed test. If a sufficientnumber oftestingmachinesis availablefor simultaneous testing, the test can be stopped at exactly the desiredfraction. Otherwiseasafevalue of themedianlife for eachstresslevel mustbeestimatedandan approximatefraction of failureswill result.

This type of test may be regardedas a modification of the all-failed testand it is run for the samepurpose,i.e. to establishtheS—Ndiagram or partof the P—S—Ndiagram. The alternativefraction-failure test, the responsetest, wherethetestsarestoppedat a preassignedcyclelife, equalfor all stresslevels, is different in characterand hasanotherobjective. It will thereforebe discussedin aseparateSection.

Refcrences: SeHUETTE (1954), WEIBULL (l955a, 1956c).

SECTION 22. SHORT-LIFE TESTS

By far the greaterpart of conventionalfatigue testing hasbeenconcernedwith establishingfatiguelives at stresseswell below the yield stressof thematerial. In somecases,however,optimumdesignrequiresknowledgeofthebehaviourof the material under stressesleading to fatigue failure after asmall number of stress—orstrain—reversals.

One of the difficulties associatedwith testing at stressesproducinglargeplastic deformationsis the accurate control of applied loads,in particularofthemeanstress. For this reason,it appearseasierto basethe testing equip-ment on thestrainamplitude,ratherthan on thestressamplitude. It mustbe emphasized,however, that there is a basic difference betweencurvesrelating stressand fatigue life and curvesrelating strain and fatigue life,and at preserttit is impossibleto transformoneto theother.

It is obviousthat thesetwo modesof stressingareequivalentaslong asthetest pieceis acting asa perfectelastic body, i.e. aslong as thereis a uniquerelation betweendisplacementand applied load. This condition may, atlow stresses,beftslfilled during thefirst stageof thefatigue life, but it will beinvalidated assoonascracksappear. At highstresses,it may beinvalidatedevenduring the first stressreversals. As an examplereferenceis madeto apaperby LIU et al. (1948). Unnotched specimensof aluminium alloy24S—T were subjected to completely reversed axial strains of such a

12 13

FATIGUE TESTING AND ANALYSIS OF RE5ULT5 FATIGUE TESTING METHODS

magnitudethat failure occurredin somesevencycles. The maximumtruestressin eachsucceedingcycleincreaseduntil it hadreachedavalueof 12 percenthigherthan the initial value.

Another exampleis reportedby Low (1956). A presetangularmovementwasappliedto theendsof aflat rectangulartestpiece. Thecurvatureat thetestsection,andthereforethemaximum fibre strain,amountingto a valueofup to 5 per cent, was determinedby a spherometer. Preliminary testsshowed that the spherometerreadings remainedthe same throughout thegreaterpart of a test, but oncelocalizedyielding or crackingof the testpieceoccurred,the angularmovement,required to give thesamereading,alteredconsiderably. It is obviousthat thefatigue life observedwill dependconsiderably on whether the preset angular movement of the testingmachineis changedor not. A properinterpretationof theresult of a short-life test thusrequiresa moredetaileddescriptionof thetest conditions.

Usually different testing machineshave to be usedto cover thecompleterangeof theS—Ncurves. Testsin which failureoccursin lessthan 10 kc areimpracticableto performwith mostof theconventionaltesting machine’s.Testsin which failure is expectedto occurin 0’S to 10 ke are frequentlycarried out with hydraulically operatedtesting machines,whereasfailuresexpectedto appearin lessthan500cyclesareusuallyperformedby theuseofmanually operatedmachines. For this purpose,conventionalstatic testingmachinesmaybeused. Thespeedis, of course,very low. A few cyclesperminute may be obtainedin this way. A reduction of the speedis requirednot only becauseof the machinebut in order to keep theheatingof thetestpiece,due to large plastic deformations,within reasonablelimits.

For all specimenstestedat stresslevels higher than theyield strength ofthematerial, it is advisableto applythe first reversalof load manuallyinorder to producethe plastic deformation. This proceduresimplifies themaintenanceof the desiredmean load.

From the preceding,it is apparentthat short-life testshave to bedividedinto eonstant-sfressamplitude andconstant-strainamplitudetests.

Methodsof analysingdata from fatigue testsincluding staticfracturesarediscussedin Section 91.

22.1 Constant-stressAmplitude Tests

Available data on fatigue testing ofsteel specimensat stressesproducingfailure in less than 30 Icc are summarizedby WEI5MAN andKAPLAN (1950).Only a few of the data are for tests resulting in failure in less than I kc.They wereperformedon unnotchedspecimenssubjectedto bendingandtoaxial loadat a stressratio R = 0.

Tests with notched specimensof steel and of 61 S—T6, 24S—T3 and755—T6 aluminium alloys havebeenconductedby HARDRATH and ILLG(1954). A most remarkableresultwasthat theminimum life to failure atstressesnear the ultimate strengthwas drastically reducedwith increasingstress-concentrationfactor. Failure wasfound to occurin approximately10kc for unnotchedspecimens,1 ke for specimenswith K

1= 2, andin 04 he

for specimenswith K1

= 4. Further,in testswith R = —1 andK1

= 4, the

S against log N curveswere found to be concaveupwards for almost thecompleterange, a reversalin curvature occurring at about 10 cycles ofreversals.

References:HARDRATH, LANDERS and UTLEY (1953),HARDRATH andILLG(1954),WEI5MAN andKAPLAN (1950).

22.2 Constant-strainAmplitude Tests

Testsof this type were already in useby KOMMER5 (1912) who appliedmaximumfibre strainsin therangeof2~5to 0~7percent to specimensofsteel.A bending fatigue test including five widely differing materials,steelsandaluminium alloys, is reportedby Low (1956). The fatigue life in reversedbendingwasfound to. dependsolely on thedegreeof strain, and is indepen-dent of the material for maximum fibre strainsbetween+5 and +4 percent. In testsusinglowerstrains,thefatigue dependedalsoon the material.Curves of deflexion againstcycle life were found to be smoothover thewholerange,from which it follows that the curvesof stressagainstcyclelifeall showan abruptchangeof slopeat the yield stressof thematerial. It isa remarkableresult that all the curvesplotted on log—log scalesare,withina reasonable,non-systematicscatter, identical. The slope d log N/d log S= —24 (5 denoting thestrain). This result agreesvery closely with thatobtainedby KoMrssEns (1912).

Testsof this type are describedalso by Lsu etal. (1948) as mentionedaboveand by PARDUE et al. (1950). The latter investigation examinesspecimensof sevendifferentmaterialssubjectedto strainreversalsresultingin failure in less than 10 kc.

References: KOMMERS (1912), Lsu, LYNCH, RIPLING and SACHS (1948),Low (1956), PARnUE, MELeHOR andGooD (1950).

SECTION 23. LONG-LIFE TESTS

The objectof thelong-life test is to determinea numberof percentagepointsof thedistribution ofthefatiguestrengthata preassignedcyclelife. It differsfrom the routinetest in that the observedvaluesof fatigue life arenutuseddirectly, only the fraction that failed at different stress levels being used.This procedureobviuuslymeansa loss of someof theinformation which isprovidedby the test. It is thcrefnrerecommendedtbat theobservedcycles-to-failure shouldbe regardedaspartof aroutinetest, andusedaccordingly.

Tbe lung-life testsmay be classifiedinto aconstant-amplitudetest,whichis called the responsetest, and the increasing-amplitudetest.

23.1 ResponseTests

Theresponsetest is conductedaccordingto two different methods. Thefirst, using theprobit method,is designedwith predeterminedStresslevelsandnumbersof specimensat each stresslevel; the second,using the stair-casemethod, is a sequentialtest, the choiceof stresslevel is determinedby theprecedingresult.

23.11 The probit method.—Theobject of the probit method is todeterminethe completedistribution functionof the fatiguestrengthor part

14 15


of it. The examinationmaybe concentratedto different parts of thedistri-bution, but the number of tests required for a safe estimate of extremepercentagepointswould be prohibitive.

The common procedureis to divide the specimensavailable into severalgroups and to test one group at a chosenstresslevel, the next group at asecondlevel, andso on. The datawhich areusedfor theevaluationconsistofthenumbersof failures andnon-failuresat eachstresslevel.

The stresslevels arechosenin such a way that one of them will give afractionof failuresprior to thepreassignedfatiguelife estimatedto be equalto thepercentageof main interest,be it 50 percentorsomeothervalue. It isrecommendedthatthereshouldbe twostresslevelsaboveandtwobelowthemeanlevel. If the region of themedianis of main interest thestresslevelscould be located close together,and sometimesthreelevelswould be suffi-cient. If moregeneral information is desired, the levels ought to be morewidely spread.

Theanalysisof thedatamaybe madegraphicallyor analytically. In anycase,if equal groupshavebeenuseda weighting procedureis required.This complicationcan be eliminatedby allocatingmore tests to percentagepoints correspondingto large variance of theobservations. If the distri-bution is assumedto be normal, the following table indicatesappropriatesizes of thegroups. This table may also apply to distributions other thannormal.

An acceptableaccuracyof the response curve, including confidencelimits, will requirea total number of somefifty specimens.

Methods for analysingthedataarediscussedin Section95, paragraph1.

ExpectedPercentageSurvival

Relative GrvupSize

25to75 1tSto2O 1580to85 1~5tOto9O 25to95 32to98 5

(Front theASTM STP91-A)

References: BLas (l935a,b, 1937), FINNEY (1952), FISHER and YATES

(1943), GOLUB and GRUBBS (1956), MOORE andWISHART (1933).23.12 The staircase ,nethod.—Ifthemain interest is limited to the

medianvalueof the fatiguestrengththe stair-casemethodwill reducethenumberof specimensrequired. On theotherhand,it is not agoodmethodfor estimatingsmall or largepercentagepoints unless thedistribution isassuredlynormal.

The procedureof the staircasemethod is as follows. The first test isstartedat a stresslevel which is equalto an estimatedmeanvalueof thefatiguestrength. If a failure occursprior to thepreassignedcyclelife, thenextspecimenis testedat a lower level; if thespecimendoesnot fail within

thepreassignednumberofcycles,the next test is run ata higher level. Theintervals betweenthe stresslevels should be approximatelyequal to thestandarddeviation,butthis is not astrict condition. Theintervalshouldnot,however,be largerthantwice thestandarddeviation.

Thetestcontinuesin this way, the stresslevelof eachsucceedingtestbeingraisedor lowereddependingon theprecedingresult.

This procedureresultsin the testing beingconcentratedmainly on threestresslevels, centredon the meanlevel. For this reason,this methodis moreefficient than the probit method with regard to the determinationof themeanvalue, resulting in a reduction in numberof specimensof aboutfortyper cent.

A disadvantageof this—as of all—sequentialmethodsis that only onespecimencan betestedat a time. If morethan30 specimensarerequired,the time requiredfor thetest will be ratherlong. A modificationmaythenbe introduced,wherebythetotal numberof specimensis split into subgroupsof equal size. Eachgroupmay then be testedsimultaneouslyandindepen-dentlyof eachother. This methodis called the modjfied stair-casetest.

Methodsfor analysingthedataarediscussedin Section95, paragraph2.References: BROWNLEE, HODGER and R0SENBLATT (1953), DIXON and

MOOD (1948), DIXON and MASSEY (1957), FRIEDMAN (1947), ROBBIN5 andMONRO (1951).

23.2 Increasing-amplitude Tests

It appearsvery temptingfor the purposeof savingtilne andspecimenstousefor further testsa specimenwhichhassurviveda preassignednumberofcycles. In view of the fact that the fatigue propertiesof thespecimen,inparticularits fatigue limit, may havechangedconsiderablyas a resultoftheprestressing,cautionis stronglyrecommendedbeforethis typeoftestbe used.Theeffectofprestressingdependsuponthematerialandstressconcentrationswithin thespecimen.

If this effecthasnot beenprovento be negligible, theresultsof increasing-amplitudetestsmay bequite misleading,but for somematerialsthis type oftestappearsto be quite satisfactory.

A convincing examplewhere excellent agreementof the distribution ofthefatiguelimit obtainedby a probit methodandby asteptest (seebelow)is presentedby STULEN (1951). ThematerialwasSAE 4330heattreatedtoa Rockwell C hardnessof 30.

This type of test can be conductedin two different ways. In the firstalternative,the stresslevel is raisedby steps; this methodis called the stepmethod. In the secondalternative, the stresslevel is raisedcontinuously;this methodis called,after its inventor,the Prot method.

Theobjectof both of themis to determinethe fatiguelimit.23.21 Steptests.—Thesteptestshouldbe startedat a stresslevel which.

is estimatedto correspondto a fraction failed of approximately 30 per centafter a preassignednumberof cycles, being usually l0~. If the specimensurvives,thestresslevel is raisedto avalue estimatedto give 5 percentmorefailures. This procedureis repeatedwith the samespecimenuntil failure

16 17


occurs. The fatiguelimit is supposedto be themeanbetweenthe last andthenextto laststresslevel. This methodrequiresat least10, andpreferably20, specimensfor a determinationof thefatigue limit.

Methods of analysingthe dataare discussedin Section 96, paragraph1.References: HEMPEL (1952), KöRBER (1939a,b),KöRBER and HEMPEL

(1940), MOORE and JASPER (1924), SINCLAIR (1952), STULEN (1951),KOMMER5 (1934),JENKIN (1923). -

23.22 The Prot tests.—Ifthefatigue limit be determinedby increasingtheamplitudeuntil failure occurs,it appearsto bemore rationalto raisetheStresslevel continuously. This methodhasbeenproposedby PROT (1945),who useda rotatingbendingmachine.This typeof fatiguetesting machineis veryeasilyadaptedfor this purpose.

Thetestis startedatastresslevel estimatedto be 60 to 70 per centof thefatiguelimit of thespecimen,andtheStresslevelis raisedat aconstantrate.This procedureis repeatedwith agroupofspecimens.Twoothergroupsaretestedin thesamemannerbut with different rates. The lowestrate shouldbe as small as possible, the highestrateshould not exceedtherate causingyielding of thespecimen.

This type of test requires10, andpreferably20, tests for eachrate, i.e.aboutthreetimesas manytestsas thesteptest.

Methodsof analysingthedataarediscussedin Section96, paragraph2.References:B0RE5IandDoLAsc (1953),CORTEN, DIMOFF andDOLAN (1954),

HENRY (1951), JoHNssoN (1949), PROT (1947, 1948a,b, 1951), VIT0vEcandLAZAN (1955),WARD, SCHWARTZandSCHWARTZ (1952).

SECTION 24. CUMULATIVE-DAMAGE TESTS

The cumulative-damagetest differs from theprecedingtypes (except theincreasing-amplitudetest) in that eachindividual specimenis subjectedtomore than onestresslevel. The purposeof the test is to discover laws orrulesrelating thefatigue life of thespecimenor ofthecomponentto differentpatternsof appliedsequencesof stresslevels in orderto makeit possibletopredict a safelife of a machinepart or an assemblyfrom the stresshistoryencounteredin actualservice.

The normal procedurefor a cumulative-damagetest is to subject thespecimento a well-definedfatigue treatment,preferablyof a simplepattern,composedof singleloadsor a fixed numberof Stresscyclesof two or moreamplitudes, after which the fatigue damagesuffered by the test piece ismeasured.

Variousmethodshave beenproposedfor measuringthis damage. One ofthem, frequently used, consistsof subjecting the damagedtest piece to afixed stresslevel, called the test stress,until failure occurs. The remaininglife is takenasameasureofthedamage.It hasbeenfound that this measuredependsentirely upon themagnitudeof the teststresschosen,and one andthesamefatiguetreatmentmayproduceareducedlife at onestresslevel andan increasedlife at another.

The only rational andsafemethodof designinga damagetest thereforeappearsto beto establishthecompleteS—Ncurve, orstill better theP—S—N

diagram, of the damagedtest piece. For this purpose,a large éroup ofidentical testpiecesis subjectedto a specifiedfatigue treatment. Afterwardsthey may be regardedas new test pieceswith different fatigue propertieswhich haveto be comparedwith thoseofthevirgin testpieces. For specialpurposes,this rather elaborateproceduremay be replaced by a simpledeterminationof thefatiguelimit, theultimatetensilestrength,or someotherstatisticof immediateinterest. In any ease,the failure of thetest piecewillalwaysoccurata predeterminedstresslevel, this beingthedefinition of thedamagetest in contrastto the service-simulatingtest discussedbelow.

Thefatigue-damagetestsmay be divided into two classeswith regardtothenatureof thefatiguetreatment. The first, thepreloadingtest is definedbya pretreatmentconsistingof a single or a few preloads; the secondis theprestressingtest, wherethepretreatmentconsistsof one or more steps,eachstepbeinga fixed numberof stresscyclesof constantstressamplitudeandmeanstress.

24.1 PreloadiagTestsThetestpieceis subjectedto oneor moreprior loads,tensionor compres-

sion, by which the fatigue propertieswill beaffected.This type of test is of particular interest in connexion with notched

specimensor componentssuchasriveted or boltedjoints, wherethepreloadmay frequentlyhave a beneficial effect resulting from the smoothingout ofinitial stressconcentrations.Thepreloadmaybe repeateda fixed numberof timesafter theapplicationof theteststresslevel.

References: BENNETT and BAKER (1950), BOLLENRATH (1938), DOUGLAS

and TAYLOR (1938), FISHER (1938), FISHER, CRoss and Noams (1952),HALL and PARKER (1948), HEYWOOD (1955, l956a,b),HONNEGGER (1926),JENKINS and STEVENS (1956a,b),KERRY, NICHOLS and VINCENT (1952),Un (1949, 1951), ROSENTHAL, SINES and ZIZICA5 (1949), SCHIJvE andJACOBS (l956a), THUM (1931), THUM and ERKER (1942), VITOvEC andLAZAN (1955).

24.2 PFestressingTests

In this type of test, thetest pieceis subjectedto one or more stepsof aprogrammeor to somepatternof continuouslyvariedstressamplitude.

Thesetestsareextensivelyused to examinr thedamagingeffect of simpli-fied combinations of stepsor spectrawith re~ardto thenumberof prestresscycles, differencesbetweenascendingand deseendingsequencesof stresslevels, etc.

References: BENNETT (1945, 1946), BENNETT andBAKER (1950), BOLLEN-RATH andCORNELIUS (1942/1943),BRUEGGEMAN, MAYER andSMITH (1945),CHOQUET (1954), CORTEN andDOLAN (1956), DIETER, HORN and MEHL(1954), DOLAN and BROWN (1952), DROZD, GEROLD and SCHULZ (1950),EPREMIAN andMEHL (1952), FRENCH (1933), GILBERT and PALMER (1955),GROVER, BIsHoP and JACKSON (1951), GUNN (1955), HARTMAN (1953),HEYER (1943), HOTTENROTT (1953), HOWELL et al. (1948),JASPER (1930),KERRY, NICKOL5 and VINCENT (1952), KOMMERS (1930, 1932, 1935, 1937,

I

183 19

r

FATIGUE TESTING AND ANALYSIS OF RE5ULT5

1938, 1943, 1945), MAcGREGOR and CRosssaN (1952), MINER (1945),MULLERS-sTOcK l938a,b), PLANTEMA (1956), RICHART and NEwMARK(1948a,b),RUS5EL andWELGEER (1936), SGHIJYE and JAcOBS (1955, 1 956a),ScHwINNING and STROBEL (1930), SEREN5EN (1956), SHA5HIN (l95la,b),STICKLEY (1942), WARNOCK and POPE (1947), WILKINs (1956).

SECTION 25. SERVICE-SIMULATING TESTS

A componentin actualservice is subjectedto an extremelycomplicatedpatternofstresscyclesof varying amplitudeandmeanstress. Theseappearin arandomorder,andmustthereforebedescribedinstatisticalterms. Whenthesestressesaresimulatedin a fatiguetesting machine,theonly workablemethodis to introduceconsiderablesimplifications. Two waysof doingthismaybe distinguished.Thefirst alternativeis calledprogrammetesting,whereablock—i.e.an aggregrateof steps,eachstepconsistingof afixed numberofstresscyclesof constantamplitude—isappliedto the testpieceandrepeateduntil failureoccurs. This mayhappenwithin anyoneofthesteps,andconse~quentlythestresslevel at which failure occurscannotbe anticipated. Thesecondalternativeis called spectrnmtesting andis definedby theconditionthatconsecutivestresscyclesbe of different magnitude,arrangedaccordingto somepattern.

25.1 ProgrammeTests

The relativefrequencyof a stresscycleof a certainamplitudehasbeendeterminedby a countinginstrument. A limited numberof amplitudesisselectedandto eachof themis assigneda fixed numberwhichconstitutesastep.

Thefewer thecycleswithin eachstep,naturally themorerealistic will bethe simulation. A limit is imposed, however, by the condition that thelargestamplitudemusthaveat leastoneor preferablya few cycles in thestep. In addition,conventionaltestingmachinesmakeit preferableto haveas few changesof stressamplitude asmay be acceptablefrom a simulationpoint of view.

The stepsaregroupedtogether in blocks which arerepeateduntil failureoccurswithout changingtheshapeof theblock, i.e. the patternin which thestepsare arrangedwithin the block. In recentyearsan improvement hasbeenintroduced,by changingtheshapeof consecutiveblocks in a randoln

manner. This type of testis called a randomizedprogrammetest.Anothermodificationof theprogrammetestis the retnrn periodtest, where

eachloadappearsat theendofits return periodas determinedfrom theloadspectrumrecordedin actualservice.

References:CARL and WEGENG (1954),Cox, KREPPSand BANKARD (1955),DEGENHARDT (1942), ENsLowandPIPER (1952), FKAN550N (1956), FAIRMAN

(1955), FREUDENTHAL (1953, l956b), FREUDENTHAL and HELLER (1956),FREUDENTHAL, HELLER and O’LEARY (1955), GASSNER (I 939a,b, 1941,l954b), PIERPONT (1947), SMITH (l955a), TENCATE (1949), VALLAT (1956),VOUTE (1948), WHALEY (1957), WALLGREN (1949).

25.2 SpectrumTestsThe spectrumtest representsa more realisticsimulation, but it requires

new designsof testingmachinesor at leasta modificationof theconventionalones. The easiestway of realizing this condition is accomplishedby anamplitude modulation of rotating bending machines, or by the super-position of two vibrations of different frequencies,but the requirementofsimulatingthe relativefrequenciesof eachstressamplitudeis not as easilysatisfiedas by meansof programmetesting.

The completelyrandomizedspectrumload is obtainedby randomizingtheindividual stresscycles. This hasbeenperformedby monitoringelectro-mechanicaltesting machinesaccordingto experimentallyrecordedstresshistories. This device is particularly useful for a study of the effectson the fatigue life of jet noise, wing flutter, and vibrations of a similarnature.

In general,actual componentsareusedin theservice-simulatingtests,but it may in somecasesbe convenientandalsoacceptableto simulate,notonly thestresshistory, but also the test piece. Referencemay be madetoan investigation(HYLER et al., 1958)wherethecorrelationbetweencompo-site structures (aluminium—alloy box beams and I-beams) and simplesimulationelementshasbeenstatedon the condition that thefailure modeandthesecondarystressesareduplicated.

References:HARDRATFI and UTLEY (1952), HEAD andHO0KE (1956), HESS,FRALIGH and HABBARD (1957),L0cATI (1952, 1956), MILES (1954), POWELL(1955), SERENSEN (1956), STARKEY and MARCO (1956).

SECTION 26. ABBREVIATED AND ACCELERATED TESTS

The possibility of substitutingsomeshort-cutmethodfor thetime-absorbingfatigue test is an old dream. Sinceit has becomeapparentthat the largescatterin fatiguelife requiresthe testing of a considerablenumberof testpieces,and that no reliable resultscanbe expectedfrom an extrapolationoutside therangecoveredby observations,a solution of this problemhasbecomeevenmore urgent.

It seemssafeto saythat almost any physical property of the materialwhichcan reasonablyhe expectedto be correlatedto its fatiguebehaviourhas beeninvestigatedfor this purpose. Among such propertiescan bementioned: static proportional limit and yield limit, apparentand truetensilestrength,dynamicproportionallimit, damping,modulusof elasticity,luaglietic pioperties,electricalresistaitee,surfaceactivity ofstressedmaterial,coellicient of thermalexpansion. I\4ethodshavebeenbasedon progressiveloads, effect of prior fatigue stresson thestatic tensilestrength, and theapplieatiooof X-ray diffractioo.

An extensiveinventoryof thepossibilitiesof predictingfatiguepropertiesby meansof the propertieslisted abovehas beenpresentedin a WADCReport by VIT0vEG andLAZAN (1953), but no method, evenif useful forcomparative purpose,has beenfound capableof substituting the regularlong-time fatigue test.

FATIGUE TESTING METHODS

20 21


Instead of describing the efforts bestowedon this problem withoutdefinitesuccess,it seemsbetterto quotepart of thesummaryof theabove-mentionedreportwhich still givesagood pictureof theactualstatus:

Sincefatiguecracksare, in general,brittle tensilecrack,,proportionalitybetweenfatiguestrengthandtensilestrengthwas assumedin earlywork. However,no generalrelationshipof this typecouldbe foundfor all typesof materialsandall condilions. The relationshipbetweenfatigueandotherstaticpropertiessuchasproportionallimit, yield strength,andtrue tensilestrengthhavebeenconsideredagainwithout success.This approachhasbeenelaboratedupon by developingformulas,particularlyfor steel,whichgive the fatiguelimitas afunction ofseveralstaticpropertiessuchasyield strength,apparenttensilestrength,elongation,andreductionof area,etc. Theseformulasseemapplicableonly underspecialandhighly limited conditions.

Basedon thefactthatfatigueiscausedbyreversedslipping, thefatigue limit wasproposedto be identicalto thatstressatwhichslip lines beginto formor atwhich slip lines do notappearagainafterprestressing.No proportionalitybetweenthis so determinedstressandthefatiguestrengthcouldbeobservedsinceothersecondaryeffectssuchasstrainhardening,aging,etc., influencethefatigueproperties.

Attemptshavealsobeenmadeto associatefatiguepropertieswith thestress-straincharacter-istics under reversedstress. A large number of fatigue tests showedthat the dynamicproportionallimit givesa goodindicationofthefatiguestrengthfor manymetalsandalloydand appearsto have fewer ezceptions(for example,Duralumin) than do othermethods.

In severalothermethodstheclsangeof otherphysicalpropertiescausedby alternatingstresshave been investigatedfor possibleassociationwith fatigueproperties. Propertiesstudiedin this way includedamping,magneticproperties,electricalresistance,coefficientof thermalexpansion,mosaicsizedetectedby X-rays,surfacestressesdetectedby X-rays,surfaceactivity, and ultimatetensilestrength. In generalthechangeof theproperty asafunction ofreversedstressonly hasbeeninvestigated,and only recentlyhavestresshistoryeffects beenstudied. All of thesephysicalpropertieshavebeen found to be affectedbyfatiguestress,but in mosteasesthe magnitudeof changeis relatively small and thereforedifficult to detennineaccurately. To date,insufficient basic work has been completedtoclarify thesignificanceofsuchassociations.

In other groupsof short-timetests fatigue rupture propertiesare determinedunderconditionsof uniformly increasingstressorothertypesof constantloadcondition. Specialattentionmay be directedto Prot’s methodin which thestressis uniformly increaseduntilfailure. For reasonsdiscussedpreviously the progressiveload increasemethod doesnotappearto beapplicablefor all materials.

Reference:VITOYEG andLAZAN (1953).

SECTION 27. METHODS FOR DETERMINING CRACKINITIATION AND CRACK PROPAGATION

The initiation of a fatigue crackis influencedonly by conditionsin a smallvolume nearthepoint of origin, while thepropagationis affectedby condi-tions throughoutthe cross-sectionof the testpiece. It is thereforeapparentthat general information on the effect of a given variable on the fatiguestrengthof a metal will be obtainedonly by studying thecrackinitiationseparatelyfrom thecrackpropagation. “Failureto distinguishbetweenthesetwo stagesof thefatigue processleadto erroneousand sometimesdangerousresults” as emphasizedby BENNETT (1956).

Two stagesmay be distinguishedin the process. En the first stagethematerialundergoesbulk deformationandwork hardening. Slip lineswhichgradually thicken arethen formed. When this processhasproceededfor awhile, final ruptureof thelatticeoccursandsubmicroscopiccracksappear.During thesecondstagethesecrackscoalesceto form visible cracksresulting

in thecompletefractureof thetestpiece. It will beapparentevenfrom thisbrief descriptionthat theseparationpoint betweenthe two stagesis to someextent a matterof definition.

Various methods have been employed to detect early cracking, and acomprehensiveand thorough examination of these methods has beencarried out by DEMER (1955). He also gives a systematiclist of factorsinvolved in the selection of crack detection methods which is presentedbelow. The factorsare:

Typeof material.Natureofdetectionmethod.

As a crack can vary from a discontinuity barelyvisible under the resolving power of an electronicmicroscope to one of a macroscopic length, thechoiceof methoddependson thesensitivityrequiredfor the purposeof thetest.Machine affords easy removal of specimen ornecessitatesexamination in situ.Componentor specimen,the testpiecebeingsolidround, hollow, strip, wire.Uniform stressor stressconcentration.

Alternating tension-compression,reveihed flexure,rotating bending, reversedtorsion, combinationsofabove.

Time availablefor crackexamination.Equipmentavailablefor detectionpurposes.

The detectionmethods may be classified into two main groups, non-destructive and destructive methods. The former have the advantageofreducingboth thenumberof specimensand the time requiredfor a giveninvestigation. In addition, the progressof failure may be followed on asingle specimen,which contributesto thereduction of the scatter. In fact,WEIBULL (I 956a, I 956b) hasdemonstratedthat the scatterin thetime ofpropagation, measuredon a single specimen,is considerablyless than thatof the total fatigtse life, wInch implies that the main reasonof scatterinfatigue life is the initiation andnot tile propagation stage.

ihe various methtsdsfor detectionof fatigue cracksin laboratoryfatiguetest specimenshavebeenclassified (bc. cit) as follows, someof them alsobeing applicablefor thedetectionof cracksin actual components.

Non-destructiveTests

(a) Microscopic tests. Optical microscopemethodsor electronmicroscopemethods.

(b) Magneticparticle testing.(c) Penetranttests. Oil-whiting, fluorescentpenetrant,dyepenetrantOr

bubblemethods.

(a) Desiredsensitivity.

(b) Typeoffatiguetestingmachine.

(c) Typeoffatiguespecimenemployed.

(d) Natureofappliedstress.

(e) Mode offatiguestressimposed.

(f)

(g)

(h)(i)

Magneticor non-magnetic.

Non-destructiveor destructive.

22 23

Documents

Fatigue Testing and Analysis of Results