FACTORS AFFECTING TEST RESULTS

CHAPTER VI

FACTORS AFFECTING TEST RESULTS

SECTION 60. GENERAL

When WOhler in 1852 started thefirst fatigue test, his aim was to find outhow different materials respondedto different ranges of stress reversal.Thesetwo factors,the material and thestressamplitude, are still themainfactors in any fatigue test, although Wohler himselfvery soonrealized thatother factors, for example, the mean stress,had some influence on theresult.

Sincethenthenumberof factorsknown to influence the behaviourof thetestpiecehasincreasedmanyfold. It hasalsobecomeapparentthat minordifferencesin them may frequently causeconsiderabledifferences in thefatigue life. A review of the early literature discloseswide variations inresultsowing to lack of understandingof the important influence of manyfactors. This neglect is quite understandable,considering the difficultiesinvolved first in suspectingwhich they are and then in discoveringtheirquantitative effect.

It is now quite clear that in a fatigue test thereis a numberof extraneousfactors which mustbe kept constantif large variations in resultsare to beavoided; or at least they must be known and specified if the observedresultsareto beinterpretedproperly. Their effectson the test resultswill bediscussedin thefollowing sectionsof the presentchapter.

References:ASM Publ. “Fatigue durability of carburizedsteel.” (1957),CAZAUD (1949), DOLAN (1954), SAdus,MURnT andKLIER (1957),TEMPLIN

(1954).

SECTION 61. MATERIAL

61.1 Composition and Heat Treatment

For many test purposesa material is sufficiently well defined by itscompositionand heat treatment, and for standardizedmaterials thesearemost easilyindicated by various symbolsand abbreviations.

Thecompositionlimits ofsteels,standardizedby theSocietyofAutomotiveEngineersand the American Iron and Steel Institute together with corre-spondingSAE and AISI numbers, for example, will be found in the ASMMetals Handbook, 1948 edition, pp. 307—308. Generalprinciples of heattreatmentandindividual specificationsfor differentgroupsof steelsaccordingto theabovespecificationsaregiven on pp. 607—652.

The composition of aluminium alloys, standardizedin the U.S.A. withcorrespondingdesignationsfor trade name, ASTM number, Governmentnumber,andforeign equivalents,arepresentedin datasheetsonpp. 810—840

of thebook cited togetherwith temperaturerangesfor heat treatmentandthe physical properties thus obtained. General principles for the heattreatmentof aluminium alloys arediscussedin anarticleon pp. 775—777 andtemper designationsfor aluminium alloys arelisted on pp. 808—809.

An index of British Standardsand Aircraft Specificationsfor aluminiumand its alloys is given in a publication by the Aluminium DevelopmentAssociation. Other referencesareto be found below.

Forsometestpurposesa more elaboratedescriptionof thematerial anditsproperties is neededin order to distinguish between nominally identicalmaterials and to understandthe subtle but important factors of qualitywhich cannot be explainedby thecompositionof thematerial as ordinarilyreportedin the usualanalysis.

References: ASM Metals Handbook, 1948 ed., ADA Inf. Bull. (1955),Structural Aluminum Handbook, ALCOA (1940), Alcoa aluminum andits alloys, ALCOA (1950), FRITH (1948, 1956), JACKsoN and PO0HAP5KY

(1947), Monass (1947).

61.2 Structure in General—Grain Size

The structure may be regardedfrom three levels of observation: themacroscopic,the microscopic, and the submicroscopic. The first level ischaracterizedby visual observation,thesecondby therequirementof specialequipment (microscopesand X-ray diffraction pattern), and the third bythe statementthat structural changescannot be observeddirectly. For thepresent purpose, the microscopic level will be the only one that will beconsidered.

If a polished and etchedsurface is examined under a microscope,anetwork of crystal grain boundariesis observed. The size of the grainsthus detectedhasbeenfound to have a markedinfluence on the quality ofthe material which could not be explained by the composition alone. Ameasureof grain size was therefore strongly needed. The actual unitsemployedin suchestimatesof grain size vary from country to country.

The mostusualtermsfor grain sizeare:

(i) number ofgrains (n) (permm2

);(ii) averageareaof grain (in mm

2);

(iii) meandiameter (arithmetic cw geometric)of grain;(iv) an arbitrary number (N).

For example, the Timken, AS’l’IvI, indexof grain size is definedby

N: I -f- Ing n/log 2

where a numberof grainsper in2

at a magnification of 100.The number a is estimatedeither by counting the number of grainsover

aknownareaofimageatknownmagnificationor by matchingthemicroscopeimagewith charts that have standardgradedpatternsof an idealizedhexa-gonalnetwork. If themagnification is lower or higher than 100, say lOOk,the index N may be computedby

N= 1 + log (nk2

)/log2 = 1 + log n/log 2 + 2 Iogk/log2

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FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TFST RESULTS

In generalthebondsbetweenatomsat theinterfacebetweentwo crystalsappearto be strongerthan within the crystalgrain. For thesingle-phasemetals it thereforeseemsplausible to assumethat the fatigue strengthincreaseswith the reciprocalof the grain size. This hypothesishasbeenconfirmedby KARRY andDOLAN (1953)who demonstratedthat thefatiguestrengthof alpha-brassspecimensdependson the largestcrystal present,andalso found increasingnotch-sensitivityfor fine-grainedconditionsof themetal.

The effect of grain size in the ferrous metals and in the precipitationhardeningalloys is quite different, andlittle influenceon thefatigue pro-pertieshasbeenobserved. GEN5AMER, PEAR5ALL, PELLINI andLow (1942)havesuggestedthat theresistanceto inelasticdeformationsis proportionalto the logarithm of themeanstraight path through the continuousphase,i.e. theamountof hardparticleshas lessinfluence thanthemeanfreepathfor slip from onehardparticle to anotherin the soft matrix.

Studiesby DOLAN andYEN (1948) andby SINCLAIR and DOLAN (1950)have indicatedthat the fatigue strengthswere improved for a variety of’steelswhentheheattreatmentsinvolvedrelativelyrapid cooling to producefinely dispersedhardeningconstituents. The effectof graindirectionon thefatiguepropertiesof aluminium alloys hasbeenexamined,amongothers,by TEMPLIN, HOWELL and HARTMANN (1950) who found that the fatiguestrengthsin a direction transverseto the rolling fibre were not significantlydifferent from thosein the longitudinal direction. The influenceof grainsizeon thefatiguepropertiesof high-purityaluminium hasbeenstudiedbyDANIELS andDORN (1957).

References: AITCHI5ON and JoHNsoN (1925), BARRETT (1943), DANIELS

and DORN (1957), Donkmc andYEN (1948), GENSAMER, PEARSALL, PELLINI

and Low (1942), KARRY andDOLAN (1953), SINcLAIR andCRAIG (1952),SINCLAIR and DOLAN (1950), TEED (l952a,b), TEMPLIN, HOWELL andHARTMANN (1950), WALKER and CRAIG (1948).

61.3 Inclusionsand Inhomogeneities

The influenceof inhomogeneitiescausedby thepresenceof slag, oxides,sulphides,andthelike, dependsmoreupontheirshapeanddistributionthanon their size. They mustbe consideredin relation to their effect on thebehaviourof the surroundingmatrix. SnRm (1951) found, for example,thathigh-strengthhardsteelsaremoreadverselyaffectedby inclusionsthan

a low-strengthductile steel. Accordingto GRANT (1950), specially treatedeast iron with spheroidal graphite exhibits a fatigue strengthwhicls isdefinitely Superiorto thatofthesameeastironwith thesametensilestrengtlsbut with thecharacteristicstringy dispersionof graphiteflakes.

The effect of inclusions on the endurancepropertiesof steelshas beenstudiedby severalinvestigators,amongwhommay bementionedSTEWART

andWILLIAMS (1948)andRANSOM (1954). A comprehensiveprogrammeoffatiguetestshasbeencarriedout by FaITH (1954)who aimedat establishingmore definitely the influence of various metallurgical factors, includingnon-metallicinclusions,on thebehaviourof steelsin service. Oneresultof

Frith’s work was that only certain types of inclusion, particularly non-deformablesphericalsilicates,were found to be harmful.

An unusually largetestseries,involving more thanonethousandsmoothspecimens,has been carried out by CUMMINGS, STULEN and ScHULTE(1955, 1956) for the purposeof clarifying how non-metallicinclusionsactasmicroscopicstress-raisers.Someof the important resultswill be reportedhere. All thespecimensweretakenfrom asingleheatof SAE 4340 aircraftqualitysteel, heattreatedto give nominal ultimatetensilestrengths140,000,190,000and260,000lb/in2. Theinclusions,identifiedascomplexmanganesealuminosilicatetype,wereessentiallysphericalin shapewith noappreciableelongationin the longitudinaldirection. The size of eachinclusion fromwhich fatiguefailure hasoriginatedwasmeasured.The geometricmeandiameter,definedby multiplying thelength normalto thespecimensurfaceby thewidth parallelto thesamesurfaceandthentakingthesquareroot ofthis product,wasusedasameasureof thesize. None of the inclusionswaslargerthan 0~OO25in. in diameter,abouthalfweresomewhatover0~0010in., andtheotherSmallerdown to about0~O004in.

A plot of inclusion sizeagainstkilocycles tee failure showedstrongcorrela-tion for a setof 170 specimensof 140,000lb/in2 ultimate tensilestrength,stressedat 86,000lb/in2 asestimatedby thenonparametriccornertest (seeSection90.8),thefatiguelife increasingwith decreasingdiameterof inclusion.This simple correlationwasnot so apparentat high stresslevels, at leastnotin the ease of steel of the samequality, heat treatedto 190,000 lb/in.2

ultimate tensile strength, probablyowing to the fact that multiple nucleiappearedin increasingnumbers ofspecimensasthestresslevelwasincreased.The averagenumberof nuclei, beingonly oneper rotating-beamspecimen(190,000 lb/in2 ultimate tensile strength) at alternating Stressesfrom93,000to about120,000lb/in2, increasedgraduallyto 12—14at analternatingstressof 180,000lb/in2. Thesenuclei offailure crackswere in all easescloseto the surface, but in some casesa rather large inclusion appearedin anucleus at a measurabledistance (some thousandthsof an inch) below thesurface in long-lived specimens. It is possiblethat, at higherstresslevels,other microscopicstress-raisersthan inclusionsmight havebeenresponsiblefor the fatigue failure, as suggested by DIETER and MEHL (1953). Theappearanceof multiple nuclei at higherstresslevelshasalso beenobservedhy MAlter andSTARKEY (1954).

Refcrcnces: CUMMINGS, STULEN and SCnULTE (1955), DIETER and MEHL

(1953), FRITII (1954), GRAN’r (1950), MARCO and STARKEY (1954),RANSOM

(1954), STEWART and WILLIAMS (1940), STULEN (1951), STULEN, CUMMINGS

andSCmIULTE (1956), STTRI (1951).

61.4 Structural SurfaceConditionsProducedby HeatTreatment

The heat treatment may have thepurposeof improving thestructureofthematerialorrelievingstressesafterturningorpolishing,but it is sometimesaccompaniedwith thedetrimentaleffect of decarburization. HANKINS andBECKER (1931) and HANKINS, BECKER and MILLS (1935) were amongthefirst to study this effecton the fatigueresistanceof steel. They found that

96 97

FACTORS AFFECTING TEST RESULTSFATIGUE TESTING AN!) ANALYSIS OF RESULTS

thedecarburized material had poorer durability at all stresses. There aremany investigations whichSupport this opinion, including thosereportedbyJACKsoN and POcHAP5KY (1947) andby GARWOOD, ZURBURG and ERIcKsoN(1951). There are, however, other testswhich haveexhibitedlittle ornoeffect of decarburization(WEIBULL, 1952) andevena beneficialeffect, asfound by GILL andGoonAcxx(1934). Decarhurizedwires showedagreaterfatiguestrengththan homogeneouswires at high stresses.

The detrimental effect of decarburization is usually eliminated by grindingandpolishing. Theeffectof grindingon thephysicalpropertiesofhardenedsteelhasbeenexaminedby BOVER (1948).

Modern heat-treatmentmethods, however, have made it possible tokeepthefinishing to aminimumafterheattreatment. In manyapplications,no post-heat-treatmentfinishing is required. In viewof this trend,ROBINSON

(1957)found it desirableto investigatethemannerin whichthemetallurgyof thefirst few thousandthsof an inch of materialat the surfaceinfluencedthepropertiesof the test piece. Three factorswere studied, namely: (i)surfacedecarburizationon springsteel; (ii) networkcarbidein a carburizedcase; and (iii) subsurfaceoxidation, oftenobservedin thecarburizedcaseof steelstreatedin conventionalcarburizingmedia. Oneremarkableresultof this investigationwasthat theeffect of surfacedecarburizationdependson the magnitudeof the test stress. At a stresslevel producingfailure in50-400ke decarburizedsteelshoweda superiordurability. At lower stresslevelsnear theendurancelimit, surfacedecarburizationwas shown to bedetrimental, and slight reductionin surfacecarboncontent appearedtolower durability as muchas severedecarburization.Theeffect of carburi-zationhasalso beenstudiedby ROBERTS andMATTSON (1957)who investi-gated the influence of materialcomposition,case depthand section size,tempering,refrigeration,and electro-polishing. Theyfound that removing0~002in. from an as-heat-treatedsurfaceby clectropolishingis tantamountto removingmaterial that is damagingto fatigueproperties.

References: BOYER (1948), GARwOOD, ZURBURG and ERIcKSON (1951),GILL and GOODAcRE (1934), HANKIN5 and REeKER (1931), HANKINS,

BEcKER andMILLS (1935), JAcKSoN and POeHAPSKY (1947), RoBERTs andMATTSON (1957), ROBINsoN (1957),WEIBULL (1952).

61.5 Structural SurfaceConditionsProducedby MechanicalTreatment

Cold working generally improves the fatigue strength. It is not quiteclearwhetherthis effect is causedmainly by an improvementof thematerialowing to reductionof thecrystallite sizeor mainly by residualstresses,hutprobablyboth effectsare important.

Theeffectof shot-peeninghasbeenstudiedby ALMEN (1943)andalso byMATTSON and COLEMAN (1954). The beneficialeffect of this surfacetreat-ment as well as such treatmentsas polishing, carburizingor nitridingdepends,accordingto ALMEN (1950, 1951), upon the fact that thesurfacematerial is inherently weakbut is improvedby thesetreatmentsboth byphasetransformationof thematerialandby residualstresses.Theseparation

of thesetwo effectson the phenomenologicalscaleis very difficult. CooMBs,SHERRATT and POPE (1956) concludethat removal of material from thesurfacelayersof ashot-peenedspecimenresultsin a variationof fatiguelifeat constantstress. Thelife increasesup to amaximumvalueseveraltimesas greatasthat for a peenedor an untreatedpolished specimen,and thendecreasesagainto valuescommensuratewith thoseof untreatedpolishedspecimensof thesamediameter. Greatcaremustbe takenin establishingpeeningconditionssince,if thematerial is overpeened,surfacecrackswilloccurandsomeof thebeneficialeffectswill be lost. The correctconditionsvaryconsiderablywith thehardnessof thematerialto betreated. LE55ELL5and BRODRScK (1956) found that shot-peening,if properly controlled,considerablyimprovesthefatiguestrengthofsubsequentlydamagedsurfaces.Thesebenefitsweremoremarkedas thehardnessof the steelwasincreased.Improvementsup to 110 per centwereobserved.

The beneficial effect of surface-rollingon the fatigue strengthof largeaxles hasbeen demonstratedby HORGER and MAULBET5cR (1936) andBUcKwALTER and HORGER (1937). Fatiguestrengthof screwthreadsbeforeand after prestressingwith rollers hasbeendeterminedby ALMEN (1951)who foundthatthefatiguedurabilitywasgreatlyincreasedby this treatment.

References:ALMEN (1943, 1950, 1951), BUcKwALTER andHORGER (1937),CooMBs, SI-IERRATT and POPE (1956), HEMPEL (1937), HORGER (1935),HORGERandMAULBETSeH (1936), LESSELLSandBRODRIcK (1956),MAnsoNand COLEMAN (1954).

61.6 Structural Changesrelating to Sizeof Test Piece

Theeffect of sizeon fatigue strength is a complex problem. It frequentlydependsboth upon structural changes in the material and upon the“statistical sizeeffects”. Only theformer effect will be discussedhere. Thelatter effectwill be discussedin Section63.1.

The best known effect of size on the strengthpropertiesof a materialrelatesto castiron. It is an old observationthat its strengthis in generalmuchbetter in barsof small thanof largediameter. This effect is readilyexplainedby thedifferencein cooling rate. An investigationseparatingthiseffect from thestatisticaleffect hasbeencarried out by MEYER5BERG (1952)by meansof different typesof static tests.

In tlse sameway, theeffectof heattreatmentofthematerialmaydependon the size, andfabricationprocessessuch asrolling andwire drawingmayturn out productswlsicls differ witls regardto the material owing to thedimensions.

A comprehensivesurvey of fatigue characteristicsof large sectionshasbeenpresentedby HORGER (1954). Investigationsinto thecompositesizeeffect have beenperformed by HORGER and MAULBET5GIJ (1936) whocomparedtheir early work on size effect in plain specimenswith thatreported by PETERsON (1930). They found that in general the fatiguestrengthof 0~3-in.plain specimensis 10 to 15 per centhigher than thatobtainedfor specimensof about1 in. diameter. Other investigationsto bementionedare thoseby BUcKwALTER and HORGER (1937), MOORE and

98 99

FATIGUE TESTING AND ANALYSIS or RESULTS FACTORs AFFECTING TEST RESULTS

M0RK0vIN (1943), MORKOVIN and Mooa~(1944), MOORE (1946) andMOORE, Da&N andHANLEY (1948). Hereagainspecimensizesof 0~l25in.showedasmuchas 15 percenthighervaluesthan I-in, specimensin thecaseofsomematerials,whilefor someothersthedecreasewasmuchless. HORGERand NEIrERT (1952) found thatplain specimens6 in. in diameterhad aminimum endurancelimit 35 percentlower thanthatfoundfor theconven-tional 0’3 in. diameterplain specimenfrom untreatedsteel. No Significantsize effect was exhibited however, betweengeometrically similar filletspecimensfrom normalizedand temperedsteel If and Sf in. in diameterfor two r/d ratios. A hypothesisto explaintheeffectsof sizeofspecimenshasbeensuggestedby YEN (1950).

References:BUCKWALTER andHORGER (1937), HORGER (1954), HORGER

and MAULBETSCH (1936), H0RGER and NEIPERT (1952), MEYERSBERG

(1952), MOORE (1945), MOORE, DOLAN andHANLEY (1948), Mooax andMORKOYIN (1943), M0RK0vIN and MOORE (1944), PETERSON (1930),YEN (1950).

61.7 Structural Changescausedby Preloading and Prestressing

Crystalline structurein relation to prestressingwas studied by GOUGH(1933). Structuralchangesin ingotiron causedby repeatedplasticstressingwerestudiedby LOVE (1952). Similar studieshavebeenmade by BULLEN,

HEAD and WooD (1953). Observationson the fatigue processin purealuminiumweremadeby FORSYTH (1952),whoalsocomparedthebehaviourof cold-workedpurealuminiumandage-hardeningalloy (1956). He foundthat both materialsdevelopedsoft spotsundertheactionof fatiguestresses,thecold-rolled material by locally recrystallizingandthe alloy by an over-ageingprocess. Both of theseprocessesaredescribedas “shakingdown”processes. THOMPSON (1956) hasattemptedto detectthe beginning of afatiguecrackasearlyaspossible,andto follow its gradualprogressin copperand in nickel. This hasbeendoneby acarefulandthoroughmicroscopicexamination. The interpretationof theobservationsis that thecrackstartsin a slip-band,in asinglegrain, at anearlystageof thetest. Thepresenceof thecrackproducesa regionof low stresson either side of itself, so thatfurtherslip is inhibited there. Nearthetipsofthecrack,thestressis increasedso that an extradensepatch of slip is produced,throughwhich thecrackpropagates further. The changesin hardnessduring fatigue testson copperhave been examined by DAVIES, MANN and KEMSLEY (1956)andtheinfluenceof preloadingand prestressingon the fatiguelife by DRGZD, GEROLD and

SCHULTE (1950).References:BULLEN, HEAD andWooD (1953), DAVIES, MANN and KEMS-

LEY (1956), DROzD, GEROLD and SCHULTE (1950), FORSYTH (1952, 1956),COUGH (1933), LOVE (1952), THOMPSON(1956).

61.8 Anisotropy

The importance of anisotropy as a factor influencingthefatiguestrengthhasbeenrecognizedfor a long time, andalso that all real materialsareanisotropic on a microscopiclevel of observation. For thepresentonly

macroscopic anisotropy will be considered; that is, a material may beregardedas isotropic if it hasthesamefatiguepropertiesat all points andin everydirection,evenif it hasmicroscopicstressraisersdispersedoverthevolume.

Two different types of anisotropymay be distinguished:location aniso-

tropy anddirectionanisotropy. Thefirst type is represented,for example,by a material having spherical inCluSionS of different density in differentparts of the volume. Consideringthe fact that the surface material isinherentlyweak, as pointed out by ALMEN (1950) andsubstantiatedwiththe observationthat fatigue strengthis improved by cold working, shot-peening or nitriding which makesthe surfacemore fatigue resistant, itcould be postulatedthat all specimenshave locationanisotropy. Thisstatementagreeswith the observationmadeby STULEN (1951) that “incarefully prepared specimens, the origin of failure is almost alwayl at amicroscopicnon-metallicinclusionwhich is opento thesurfaceor is slightlysubsurface.” It may be pointed out that an experimentaldecisionas towhether a specimenhassuch a surfaceanisotropyor not is possiblebysubjectingcylindrical specimensto axial load androtatingbendingof thesame maximum stress. If thesamefatiguestrengthis obtained,this typeofanisotropy is proved; otherwisetherotatingbendingwill indicateahigherfatigue strength. Such a test serieshas beencarried out by CHADWICK

(1954) who found a close agreementbetweenthe fatiguestrengthof lightalloy specimenssubjectedto axial androtating-bendingloadings.

Direction anisotrGpymay, for example,appearin amaterialcontaininginclusionsof stringer type. The literatureon aniSotropyof thestaticpro-perties, giving an indication also for fatigueproperties,hasbeenreviewedin abook by BARRETT (1943). In this casethematerialhasdifferentfatigueproperties in different directions and the orientation of the specimeninfluencesthe result. A comprehensivesurveyof results from fatiguetestsin plainbendingis presentedby FINDLEY andMATHUR (1955). Thefatiguestrengthof aspecimencutperpendicularto thedirectionof grain may insomecasesbe considerablyless than that of a specimencut parallelto thisdirection. Reductionsof up to 48 per centhavebeenobserved(SAE4340,steel forging).

A very Isigh degreeof anisotropywas alsoobservedin several studieson

SAE steelfnrgillgS by RANSOM and MeuL (1952, 1953), on heat-treatedsteelsby CORNELIUS and ICRAINER (1941), and on various nickel and nickel-chrnlnium steelsby P0MEv and ANeELLE (1935—36), JUNGER (1930), andMAILANDER (1936).

Fatiguetestson aluminium alloys by BERNER and KASTRON (1938) andby MARIN andSIIEL50N (1949)indicatehighanisotropy,whileAITCm50N andJOHNSON (1925), MORRIS (1946), and TEMPLIN, HOWELL and HAETMANN

(1950), studying various Steels and aluminium alloys, reported very littleor no evidenceof anisotropy.

FINDLEY and MATHUR (1955) investigatedanisotropyin fatigueundertwodifferent states of stress, bending and torsion, applied to two aluminiumalloys and a steel. The fatigue strength in bending decreasedas the

100 101

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

orientationchangedfrom longitudinalto diagonalto transverse,whereasthefatigue strengthin torsion was nearly constant for all three orientations.The authors concludedthat cyclic principal shearstress is the primarycauseof fatigue, but theability of theanisotropicmaterialsto withstandthisaction is affectedby themagnitudeand directionof the complementarynormal stressacting on planes of principal shearstress,as well as by theanisotropyof thematerial. Thebendingfatiguestrengthin transverseandlongitudinaldirectionswas determinedby voIc R05SING (1942).

Theeffectof fibreorientationin ball racesandball bearingsunderrollingcontacthas beenexaminedby BUTLER, BEAR and CARTER (1957) andCARTER (1958).

References:ALMEN (1950, 1951),AITcHI50N andJOHNSON(1925), BARREn(1943), BERNER and KA5TRON @938), BUTLER, BEAR and CARTER (1957),CARTER (1958), CHADWICK (1954), CUMMINGS, STULEN andSCHULTE (1955),CORNELIUS and KRAINER (1941), FINDLEY and MATHUR (1955), JUNGER(1930), KRAINER (1942), POMEY and ANCELLE (1935—36), RANSOM (1954),STULEN (1951), SCHMIDT (1937—38), TEMPLIN, HOWELL and HARTMANI~I(1950), MAILANDER (1936), MARIN and SHEL5ON (1949), MORRIs (1947),RANSOM and MEHL (1952, 1953),vo~cRossINc(1942).

61.9 OriginIf is obvious from the abovethat the processof fabrication may cause

considerabledifferencesin thepropertiesof the material in different partsof theproduct. For this reasonit maybe useful to know theorigin of thespecimen,i.e. from which part of the ingot, bar or sheet thespecimenistaken,andtheorientationin relationto therolling direction,or whetherthespecimensare takenfrom different batchesor from different manufacturers.

As an examplereferenceis madeto a comprehensiveinvestigationmadeby INE50N, CLAYTON-CAvE andTAYLOR (1956)to establishwhetheror notthefatiguepropertiesof the rolled productsof commercialsteel ingots varysignificantly firstly within an individual ingot, and secondlyfrom ingot toingotin agivencastofsteel. It wasconcludedthatsmall,statisticallysignifi-cant variations existedwithin an ingot, but they werenot thoughtto be ofany practical importance. The fatigue limit of the material from the topportion of one of the ingots examinedwas 34~3tons/in2, comparedwith32~9and 32~5tons/in

2for material from themiddle andbottom portions of

thesameingot. Thisdifferencewascloselylinkedwith variationsin hardnessand tensile properties(i.e. no significant difference in the fatigue limit,measuredasa percentageof the tensilestrength5,,, wasfound).

Reference: INE5ON, CLAYTON-CAVE andTAYLOR (1956).

62.0 GeneralSECTION 62. TYPE OF STRESSING

Themostgeneralway of describingastateoffluctuatingstressat a pointin a solid is by a combinationof a static (steady)stresstensorsuperimposedupon acompletelyreversedstresstensor,thelatter satisfying theconditionthat eachof the threeprincipal stressesarecompletelyreversed. The state

is thus definedby six components: threeprincipal meanstressesaod threeprincipal stressamplitudes. This pair of tensorsmay vary from point topoint, and the fluctuating stressfield distributedover thevolume of thespecimenis consequentlydefinedby the distribution of this pair of tensors.This is averyabstractwayofdescribingthis typeofstressing,andsomeofthetheoreticalpossibilitiesareimpossibleto reproduceby known testingdevices.

From a practicalpoint of view it thereforeappearsmore convenient toclassifythevarioustypesofstressingaccordingto thestressfieldsobtainedbyplacing the specimensin machinesactually used for testing purposes.Thismethod of classification eliminates types which are of purely academicinterest. Even so, each type must be defined by a stateof stressand adistribution of this state, although the latter is limited to a few simplealternatives,the uniform and the linear distribution, which canbe definedby astressgradient. A steadystress,uni- or multi-axial, may then besuper-imposed upon these reFersed stresses. By appropriate comparisonof thedifferent typesof stressing,the effectsof theStateof stressand of thedistri-bution canbe separated. It must be pointed out, however, that duecon-siderationmust be taken of possibleinfluencesof anisotropyin thematerial,which havebeen discussedin Section 61, and of size and shapeof thespecimen,whicis will be discussedin Section63. Thesefactorsmay be ofconsiderableimportance,and if not properly consideredmay upset thecomparison.

The simplest type of stressingis obtainedby subjectingthespecimento areversed,tension-compressionload. The stresswithin asmooth,unnotchedspecimen,is thenuniaxialanduniformly distributedover thevolume. Thistypemaybetakenasthereferenceto whichtheothertypesmaybecompared.

The following types will now be discussed: (1) tension-compression;(2) repeatedbending; (3) rotating bending; (4) torsion; (5) combinedbendingandtorsion; (6) biaxial andtriaxial stresses(otherthancombinedbendingandtorsion andusually producedby subjectingtubular specimensto internalor externalpressure); (7) surface-contactstresses;to which (8)failure criteria for multi-axial stresseswill be added.

For each type, commentswill be madeon general characteristicsandcomparisonwith theprecedingtypes, the influenceof superimposedsteadystresses,anddifferentcriteria.

62.1 Tension-compression

This type of stressingis characterizedby a uniaxial stateof stressand auniform distribution.

The effect of a steadystresssuperimposedupon reversedaxial load wasinvestigatedasearlyasin 1874by GERBER (1874),whosummarizedtheresultsby introducing a diagram, now called the Gerber diagram (see Fig.82.7), basedon a parabolic relation betweenthestressamplitude 8

a andthemeanstress5m• Thequadraticterm (

5m)

2 impliesasymmetricaldiagram.A fair amount of work has beencarried out since then to determinesaferangeswith variousmeanstresses.Someof thetestshavesupportedGerber’sassumption(HAIGI-I 1915, 1917)but somehave led to modified diagramsas

102 103

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

demonstratedin Section82.2. Referenceis madeto thework ofJ. H. SMITH(1910) andBOLLENRATH and CORNELIUS (1938). A summaryof theworkup to 1942 is containedin a paperbyJ. 0. SMITH (1942).

Thelargenumberof datacompiledbyJ.0. Smithwereusedby PETERSON(1952) who found that the ~ diagramcouldbe representedwith goodaccuracyby a cubiccurvefor both unnotchedandnotchedspecimens.It isof particular interestthat thesetwo curvesdiffer only by thefatiguenotchfactor K,, which implies that thevalue of K, is independentof thesteadystressvalue.

The cubic relation meansan unsymmetricaldiagram with an increasedrangeon thecompressionside. This type of diagramis particularlymarkedfor a material suchas cast iron, aswas earlier demonstratedby POMP andHEMPEL (1940).

Fewertestshavebeenreportedin which themeanstressof thecycle wascompressive,but the resultsof suchtestshavebeenreviewedby NEwMARK,

MOSBORG, MUN5E and ELLING (1951), by GROVER, BISHOP and JACKSON

(195la,b,c)andby WALLGREN (1953).Experimentscoveringa verywide rangehasbeenperformedby FINDLEY

(1954). Axial-load fatigue tests at mean stressesfrom 40,000 lb/in2 intensionto not less than 135,000 lb/in2 in compressionon SAE 4340 steelspecimensresulted in the conclusion that the fatigue strengthdecreasedslightly as themeanstresswas changedfrom compressionto tension. Athigh compressivemeanstressthe fatiguestrengthincreasedsubstantially.Fatigue cracks, which were initiated at the surfaceand progressedto acertaindepthandstoppedthere,havebeenobserved.

Two other recent investigationswill be mentioned. The first one byO’CONNOR and MORRISON (1956) wasconducted at mean stressesof such

magnitudesthat the upperstressexceededthe lower staticyield both intensionand compression,thematerial beingan alloy steelwith an ultimatetensilestrengthof 55 tons/in2. The 5

a~~5

mdiagram was composedof threestraight lines with markeddiscontinuitiesat thecompressiveyield, at thetensile yield, and at theultimate stress. No evidentreasonwasfound todrawthecurveother thanstraight.

Thesecondinvestigation,carriedout by WOODWARD, GUNN andFORREST

(1956) establishesthe diagrams of sevendifferent aluminium alloys repre-sentinga rangeof materialsusedfor stressedpartsin structural engineering,marineengineering,and aircraftconstruction.

The resultsfall into two groups;onegroup, comprising NS 41 H andallthe heat-treatablealloys excepta sampleof DTD 363 A, is typified by acurve lying betweenthe Goodmanand Gerberlines (see Section 82); theother group, comprising the soft aluminium—magnesium alloys and one

sample of DTD 363 A, gave results lying below the Goodmanline. Thediagramsare convexupwards, which is the orthodoxshape. There is onlyoneconcavediagram(DTD 363A); it is suggestedthat this maybeduetothe presenceof micro-constituentsacting as inherent stressraisers. If thishypothesis is accepted, the similarity betweenthis diagram and those fornotchedspecimensis understandable.

It appearsto begenerallyacceptedthat thereis a reductionin thefatiguestrength with increasing mean tensile stress, but thereis somedivergenceasto the explanation of this observation. GOUGH and CLEN5HAW (1951)suggestthat the decreasemay be due to damagecausedto thecrystalstructureof thematerialby deformationproducedby themaximumstress,andthat theeffectof meanstress,assuch,is negligible. On theotherhand,FINDLEY (1954) is of theopinionthatresistanceto fatigueis influencedby themagnitudeand sign of the complemeatarynormal stressacrossthe planesstressedin shear,the resistanceto fatigue being reducedby tensile andincreasedby compressivestresses. This effect of the normal stress hasfrequently beenassumedto be linear [(STULEN andCUMMINGS (1954)], butFINDLEY, COLEMAN andHANLEY (1956)have concludedon thebasisof testson SAE 4340steelat a Rockwell hardnessof C—25 that thereis a likelihoodthat the influenceof thenormal stresson the shearplane is non-linear.

References:BOLLENRATH andCORNELIUS (1938), FINDLEY (1954), GERBER(1874), GOUGH and CLENSHAw (1951) HAIGH (1915, 1917), NEwMARK,

M05B0RG, MUNSE and ELLING (1951), O’CONNOR and MORRISON (1956),PETERSON (1952), POMP and HEMPEL (1940), J. H. SMITH (1910),J. 0.SMITH (1942), WoonwARn, GUNN and FORREST (1956), STULEN and

CUMMINGS (1954).

62.2 RepeatedBending

Thestateof stressis thesameasthat obtainedby axial load but thestressdistribution is differelst. If thesetwo typesof stressingare comparedon thebasis of the maximum stressin the specimens,it is generallyfound that thefatiguestrengthis higherin bendingthanunderaxial load. Twoexplanationsof this observationhave beenproposed; the first is thestatistical concept(WEIBULL, 1 939a,b) which will be discussedmore thoroughly in Sections63.1 and63.2; the secondpostulatesthat thestressgradient is responsiblefor theimprovementin endurance.Theresultsofbendingtestson specimensof different diametersled SIEnEL and PFENDER (1947) to introduce the“relative stressgradient” definedby (I/a) da/dxwhereder/dx is the stressgradient. Varying tisis factor from 03 to 2~0mm1, it was found that thefatigue strength remains nearly constantwith variations of its Value when itis above 10 mc

1. A physicalinterpretationof the influenceof the stress

gradienthasbeensuggestedby FORREST(1955)on thebasisofablocktheory.This theory supposesthat fatigue failure occurs, not when themaximumstressin a specimenreachesa critical value, but when theaveragestressover a block of finitesizereachessucha value. Thus, wherea steepstressgradient exists, a higher nominal strengthwould be obtained thanwith ashallow, or non-existentgradient. This theory will also be discussedinSection63.

The effect of superimposedstatic bendingon the endurancelimit inbending of SAE 1020 steel is illustrated by a remarkable curve in thediscussionof a paperby FINDLEY (1954). The endurancedid not decreasemorethan 3 per centwhena steadybendingstressas high as 24,000lb/in2

wasapplied.

104 105

FATIGUE TESTING AND ANALSYIS OF RESULTS FACTORS AFFECTING TEST RESULTS

Theeffect of meanstressesof variousmagnitudeshasalso beenexaminedby MoRRISoN, CROS5LAND and PARRY (1956) andrepeatedbendingtestsandrepeatedbendingtestswith superimposedsteadytorsionalstresseshavebeencarriedout by LEA (1926)and LEA andBUDGEON (1956).

References: FINDLEY (1954), FORREST (l955a,b),LEA (1926), LEA andBUDGEON (1926), MoRRIsoN, CROS5LAND and PARRY (1956), OBERG andTRAPP (1951), SIEBEL and PFENDER (1947).

62.3 Rotating Bending

This stateof stressis thesameasin thetwo precedingtypesbut thestressdistribution is different. Sincemost fatiguefailuresstart at thesurfaceorslightly below (STULEN, 1951), little differencebetweenrotating-beamandaxial tests should be expected. In general,theaxial load gives somewhatlower fatiguestrengthsthan the rotating-beamtest using solid specimens,but comparabledataareobtainedif thin-walledtubular specimensareused.

Referenceis madeto aninvestigationby WoonwARn,GUNN andFORREST

(1956) in which resultsobtainedfromaxial-loadtestsandrotating-cantilever~testson theSamesampleswerecompared.With theexceptionof onematerialall theaxial testresults arewithin 5 per centof the rotatingbeamfigures.CHADWICK (1954)hasfound similar closeagreement.

Fatigue characteristics of rotating-beam and rectangular cantileverspecimensof steeland aluminium alloys havebeencomparedby FULLER

andOBERG (1947).Usually theplain-bendingtest is reported to give results in reasonable

agreementwith the rotating-beamtest. It must, however, be pointed outthat dueregardto the influenceof theshapeof the specimenis not alwaystakenwhen comparingthe effect of the two types of stressing. From astatisticalpoint of view a definite differenceis to be expected.

The rotating-beamtestis averyeasyoneandmuchusedfor determiningthe fatiguepropertiesat completelyreversedstresscycles, but it is not wellfitted for applicationof steadystressesto thespecimen. MOORE andJASPER

(1923) solved the problem in an interestingway. The meanstresswasapplied by meansof a helical tension spring, acting along the axis of thespecimen,while theappliedrangesofstressweredueto deadweightloading.In this way, theystudied the influenceof meanstresseson nickel steelandcarbonsteelspecimens.

References: CHADWICK (1954, FULLER and OnERG (1947), MOORE and

JASPER (1923), STULEN (1951), WOODWARD, GUNN and FORREST (1956).

62.4 TorsionThe torsion test provides theeasiestway of producing a biaxial state of

stress. The stressdistribution is identicalwith thatobtainedin a rotating-beamtest,andfor this reasonthecomparisonbetweentheresultsfrom thesetwo typesof test offers an excellentway of studying the influence of thenormal complementarystresson a critical shearplane,providedduecon-siderationis taken to possibledirection anisotropyin thematerial. Thisprecautionhasfrequentlybeenoverlooked.

TIse problemof anisotropyin this connexionhasbeencarefullyexaminedby FINDLEY andMATHUR (1955a)by comparing theresultsof bendingandtorsion tests on a steel andtwo aluminium alloys. It was found that thefatigue strengthin bending decreasedas the orientationchangedfromlongitudinal to diagonalto transverse,while the fatiguestrengthin torsionwas nearly constant at all threeorientations. This remarkable result wasexplained by the concept that cyclic principal shearstressis theprimarycauseof fatigue; but theability of the anisotropic materials to withstandthis action of cyclic shearis influenced by themagnitudeand thedirectionofthecomplementarynormalstressactingon planesof principal shearstress,aswell as by theanisotropictexturesof thematerial. It maybe mentionedthat ALMEN (1951), on theother hand,postulatesthat the directcauseoffatiguefailuresfrom repeatedlyappliedtorsionalloadis alwaystensilestress,andthat the compressivestressescontributeonly indirectly throughalteringthe yield strengthof the material.

Several investigatorshave comparedthe endurancelimit of a largenumberof materialsin torsion and bending. Among earlier investigatorsMOORE, JASPERandMACADAM found a ratio whichvariedbetween0~49and0~60.According to FöPPLthe ratio for steel lies between048 and0~75andfor aluminium alloys between0~54and 0~65(cf. GOUGH 1949). LUDWIR

(1931)suggestsaratio equalto 0~58for alargenumberof differentmaterialsandROUCHET (1934) proposes0~58for a mild steeland0~65for a nickel-chromiumsteel. Someof thesevaluesare very probably biasedby uncon-trolled anisotropyin the material.

Most of the availableliterature hasbeenreviewedin papersby GOUGH(1949) andFINDLEY (1953). In thelatter paperathoroughexaminationoftheresultsfrom alargenumberof testsin bendingandtorsion hasdisclosedthat the ratio b/t, whereb is the fatiguestrengthin bendingand it that intorsion, varies considerably; for metalsalone its value lies between0~9and2~6.If however, differenttypesof materialaregroupedtogethermuchlessvariationwasobserved; thegroupingbeing (i) cast irons and iron alloys,(ii) unnotched steels and aluminium alloys, (iii) notchedsteels, (iv) copperalloys, (v) plasticlaminates. In a morerecentpaperby FINDLEY, COLEMANand HANLEY (1956) it is shown that the ratio b/it dependsalso upon thenumber of cycles to whirl’ thefatiguestrengthcorresponds.For example,for SAE 4340steel,Rockwell C25, the ratio is largerat smallnumbersthanat large nombers,varying from a maximumof b76 to l~5at a minimumpoint.

Dueregard to the anisotropyis takenin aninvestigationby CHonoEowsKl(1956). He statesthat tlse effect of anisotropyon the fatiguestrengthinshearof anickel—chrnmium—molybdenumsteelis measurable,thoughsmall.Longitudinal and transversespecimens gave almost identical results;oblique specimensgave a slightly higher strength. He statesthat solidspecimensareunsuitablefor investigationsinto the effect of meanstressonthetorsional fatigue strength,becausethe stress—strainrelationshipchangesunder cyclic stresses. Thin tubular specimensare therefore preferable.Testsmadeon suchspecimensshowedthat the fatiguestrengthin shearis

106 107

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

affectedby even a small meanstress,and decreaseslinearly with increasein meanstress.

A considerableeffectof largehydrostaticpressureson thetorsionalfatiguestrengthof an alloy steelis reportedby CROSSLAND (1956). Thesemi-rangeof torsion was raised from l9~2tons/in2 underatmosphericpressureto 254tons/in

2at 20 tons/in

2pressure,provided that thespecimen surface was

protectedby someimpervious layer from the pressureoil, which had adeleteriouseffectif the fluid was in direct contact with thesurfaceof thespecimen.

References: ALMEN (1951), CHonoRowsKI (1956), COATES and POPE(1956), CROSSLAND (1956), FINDLEY (1953), FINDLEY and MATHUR (1955),FINDLEY, COLEMAN and HANLEY (1956), GOUGH (1949), LUDwIK (1931),ROUCHET (1934).

62.5 CombinedBendingandTorsion

Themajority of combinedfatiguestresstestsreportedhavebeenmadebysubjectinga specimenof circular cross-sectionto combinedbendingandtorsion. Therangeof biaxial principal stressratios is then limited to valueslying between0 and—l~0,i.e. to combinationsofbiaxial stressesof opposite

signs.Mostoftheavailableexperimentaldataon thefatiguestrengthsofmaterials

for combinedstresseshavebeenobtainedfor completelyreversedstresses,using solid round specimenssubjectedto fluctuating bendingand torsion.Such tests have been conducted by NISHINARA and KAwAMOTO (1940),CORNELIUS (1941), FRITH (1948), GOUGH (1950, 1951), GOUGH and CLEN-snAw (1951), GOUGH, POLLARD and CLENSHAW (1951), HANLEY andDOLAN (1951). SAWERT (1943) varied the shapeof the specimenandobtained in this way different ratios of biaxial completely reversedstresses.

Some tests have been conducted on cylindrical specimenssubjectedtocombinedreversedtorsionand reversedbendingwith superimposedstatictorsionandstaticbending,or by acombinationofstatictorsion andreversedbending. Testsof this typehavebeencarriedoutby SAUER (1948),PUCHNER(1948, 1951)andFINDLEY (1956).

References: CORNELIUS (1941), FRITH (1948), FINDLEY (1952, 1953a,b,1956), FINDLEY, MITCHELL and MARTIN (1954), FINnLEY, MITCHELL and

STROHBECK (1955), GOUGH (1950, 1951), GOUGH and CLEN5HAW (1951),GOUGH, POLLARD and CLEN5HAW (1951), HANLEY and DOLAN (1951),NISHINARA and KAwAMOTO (1940), PUCHNER (1948, 1951), SAUER (1948),SAwERT (1943), SINES (1955).

62.6 Biaxial andTriaxial Stresses

A much wider rangeof biaxial principal stressratios is obtainablebymeansof thin-walled tubular specimenssubjectedto internal fluctuatingpressurethanby a combinationof bendingandtorsion,wheretheratio islimited to valueslying between0 and — l~0.Testsof this type havebeencarried out by severalinvestigators,as mentionedin the list of references.

If the ratio of the externalto internal diameterof thetubularspecimenisincreased,it is possibleto obtaintriaxial statesof stress. As pointed out byPARRY (1956),athick cylindersubjectedto internalpressurewhensupportingits own endload can be consideredas subjectto a uniform triaxial tensilestressactingthroughoutthe wall thicknesswith a superimposedshearstresswhich variesfrom aminimum at theoutsideto a maximumat thebore. Theratio of the triaxial tension to the shearstresschangeswith theratio of theexternalto the internal diametersof the cylinder. In a bai subjectedtorepeated torsion, the shear stress is unaccompanied by triaxial stress.Comparison betweenthe resultsof these two typesof test thus offers thepossibility of investigatingthe influence,if any, of an addedtriaxial tension.

The developmentof sucha testing machineand preliminary resultsaredescribedin a paper by MoRRIsON, CRossLANn and PARRY (1956) andfurther resultsof fatigue under triaxial stressin thepaperby PARRY (1956).The testsreportedarenot conclusivebut only exploratory,andthe work isbeingcontinued.

References: Biaxial stresses: BLA5ER, TUCKER and KooIsTax (1952),BUNnY and MARIN (1954), BOWMAN (1955), BOWMAN and DOLAN (1953),MAJORS, MILLS and MACGREGOR (1949), MARIN (1949), MARIN andHUGHES (1952), MARIN and SFIEL50N (1949), Ro~(1950), TUCKER (1955).Triaxial stresses: MORRISON, CROS5LANn and PARRY (1956), PARRY (1956).

62.7 Surface-contactStresses

When two elasticbodiesare pressedagainst eachother very high stressesresult, evenfor small loads. The stressdistribution is complicatedeven ifthesimplecaseof two spheresis considered. Theprincipalstresscomponent,acting in thedirectionoftheline ofsymmetryjoining thecentresofcurvatureof the spheres,reachesa maximum value at thesurfaceof the material.This value is generallyreferred to as the maximum Hertzian pressure,butas all three principal stressesare compressivethis is not the dangerpoint.There are, however, tWo other points of interest. In either spherethemaximum shearstressoccurson theline of symmetry, but at a certaindepthbelow the contact surface; and aho at the boundaryof the contact areathere is a maximum tensile stressacting in a radial direction,accompaniedby anequalcompressivestressin the tangentialdirection. Consequently,ashearexists at this point with a magnitudeequal to either of the directstresses.

‘Fire examinationofthe fatigne damagingeffect of sucha stressfield is ofgreatpractical importancein eonnexionwith ball-bearingand geardesigns.Evenif a very largeamoont of work hasbeencarried out to determinethefatigue behaviourof actualmachineparts,very few testsof a basicnatureinthis respecthave been reported. Quite recently a study of the fatigue ofcurved surfaces in contact under repeated load has been performed byKENNEDY (1956). The cyclic loading was introducedbetweentwo ball-bearingballs by meansofa crankconsistingof a doubleeccentricconnectedto a rotatingshaft anda spring. The testpieceswereregularly inspectedbymeansof anultrasonicmethod ofcrack detection. From the testson balls of

108 109

FATIGUE TESTING AND ANALYSIS OF RESULTS

two different hardnessesit was concludedthat the maximum snbsurfaceshearing stressdid not play a significant part in the destruction of thecontactsurface; but themarkeddamagesustainedat or nearthecontactboundary indicated that the material is subjected to conditions in thisregion which are morecritical. This result agrees,in fact, with static testswherethe crackalwaysStartsat or near thecontactboundary.

Fatigue failures underrolling-contact conditions havebeenstudied byBUTLER, BEAR and CARTER (1957) and by CARTER (1958), using a rigconsistingof two balls drivenat high speedontheinnersurfaceof acylinderraceby anairjet. Theball loadingresultedfromcentrifugalforcesoftheballs.

The processof initiation andgrowth of pittingS on thesurfacesof gearteethhasbeenstudiedamongothersby H0SHIN0 (1956)who concludedthatthe pitting phenomenonis not a simple compressivefatigue failure, but afailure of surface layers deformedplastically by shearingstressescausedbyfrictional forcesof slidingcombinedwith compressivestressesdueto contactpressure. Fine crackshavebeenobservedto emanatealong the flows ofmetal. A theoreticaldiscussionof pitting failuresis given by BEECHING and

NIcKOLLS (1948).References:BEECHING and NICKOLLS (1948), HosusNo (1956), KENNEDY

(1956).

62.8 Failure Criteria for Multi-axial Stresses

Many attemptShave beenmadeto apply the theoriesfor yielding undercombinedStatic stressesto fatigue failures. Such theories are basedonprincipal stress,strain or shearstresses,total strainenergy and distortionenergy criteria. None has, however, been completelysuccessful,and thereasonappearsto be dueto theinfluenceofanisotropyandthestateofStress.Theinterpretationof experimentalresultshasfrequentlybeenhamperedbyneglectof theeffectof sizeandshapeof thetestpieces. Anotherreasonmaybesoughtin thefact that therelationbetweenfatigue strengthcorrespondingto differentstatesofstressdependsuponthefatigue life preassignedasalreadymentionedabove.

Most of the theoriesproposedhave beenapplicableto combinationsofbendingand torsion only, but in recentyearsmore general theorieshavebeensuggested.

One of the earliest of the first type seemsto be the ellipse quadrantexpression,GOUGH (1949). In a recentinvestigationby CR055LANn (1956)it was found that on the basisof this hypothesisall theexperimentalresultson alloy steel specimenssubjected to torsion and very high hydrostaticpressurescould be correlated,providedallowancefor anisotropywasmade.In severalpapersby Findley andco-workersexistingtheorieswerecorrectedby introducinga suitableconcentrationfactor in thetorsionalstresstermoftheprincipal shearstresstheory,thusreducingsix of thetheoriesto thesameform as that proposedby Gough. The equationsdevelopedare in goodagreementwith data on ductile metals. Other modifications reduced theprincipalstresstheoryto aparabolicform, whichis in goodagreementwithdataon castiron andnotchedductilemetals.

rFACTORS AFFECTING TEST RESULTS

STULEN and CUMMINGS (1954) haveformulated a mathematicalrelationfor theinfluenceofthenormalstressonacritical shearplanein fatiguebasedon theassumptionthat this influenceis linear. This assumptionappearstobevalid for somematerialsbut not for others.

In a recentpaperby FINnLEY, COLEMAN and HANLEY (1956)a refinedtheory is obtainedby a properconsiderationof the influenceof the normalstresson theplaneof failure andtheanisotropy. This theoryrepresentstheexperimentaldatabetter than the other four theorieswhich have beenexamined.

An attempt to find a very general expressionfor criteria of failure ofcombinedfatigue stresseswith superimposedstaticstresseshasbeenmadebyMARIN (1956). Startingfrom thedistortion energycriterion of von Mises-Heneky, a general expression, including three-dimensional directionanisotropy,is obtainedfor theequivalentuniaxial stressamplitudeandmeanstress. A comparison betweentheory and test results is presented.Theagreementis good for completelyreversedstressesbut not quite assatis-factoryif superimposedsteadyStressesareintroduced. This discrepancywasbelieved to be due to the uniaxial equivalentused.

References: CRO5SLAND (1956), FINDLEY, COLEMAN and HANLEY (1956),FINDLEY and MATHUR (1955), GOUGH (1949), HAHNEMANN and PRAGER

(1933), MARIN (1956), STULEN and CUMMINGS (1954).

63.0 GeneralSECTION 63. TEST PIECE

The factors relating to thetest piecewhich have an influenceon the testresultmay be classifiedas follows: (1) size; (2) shape; (3) stressconcen-trations; (4) surfacecondition; (5) residualstresses.The effectsof thesefactorson thefatiguepropertiesof the testpiece,illustratedby resultsfromexperimentalinvestigations,and also proposedexplanationsand theories,will now be discussedandcommentedupon.

63.1 Size

It hasbeersknown for a long time that dimensionshavea definiteinfluenceon the static strengthof the test piece and that the strength, in general,decreaseswit ii increasingsize. Several investigatorshave presentedevidence

that this rule also applies to the fatigue strength, among whom may bementioned PETERSON(1930), FALLHAI3ER, BUCHIIOLTZ and SCHULZ (1933),and LEHR and MAILANOER (1938).

Test pieceswith very large sections have been tested by H0RGER andNEIFERT (1939, 1952) and by HORGER (1954) who found that 6 to 7 in.shaftshave a fatigue strengthin bending which is 25 to 50 per cent lowerthan that of 0~3in. specimens. Differences in surface finish and slightcorrosion make it questionablewhether this effect is entirely due to size.Other factorswhich maymaskthis effect andproducemisleadingresultsareanisotropyof thematerial and unintentionalstressraisersvarying with thesize of the specimen.

110 111

FATIGUE TESTING AND ANALySIS OF RESULTS

It is possibleto eliminateall suchirrelevantfactorsby testingSpecimensofdifferentlengths,providedthat the anisotropyand thesurfacefinish do notchangewith thelength,e.g.by cutting thespecimensat randomfrom alongwire. Sucha testwas carriedout by WEIBULL (1946; 1949, pp. 33—35).Specimenswith gaugelengthsof 25 and50 mm weresubjectedto rotatingbendingin awire testingmachine. Thestressamplitude was 3l~6kg/mm

2

whichresultedin 18 failuresout of 26 long specimensbut only 10 out of 26shortspecimens.The distributionsof fatiguelife for thetwo sizeswere invery good agreementwith theexpectationfrom thestatistical theory.

Rotating-beamtestswith various sizesof specimenhave beenconductedby MOORE and M0RK0vIN (1943), MOORE (1945), SIEBEL and PFENDER

(1947), andD0LAN and HANLEY (1948). Torsionaltestshavebeencarriedout by DOREY (1948) and DOREY and SMEDLEY (1956). They found bymeansof largesteelshaftsof 3, ~I and 9~in. diameterthat sizeeffect is areal phenomenon.The combinedeffect of sizeandStressconcentrationdueto various diameters of fillet could be represented by one simple

expression.UnnotchedandnotchedspecimensofvariousSizesfrom two typesofsteel,

one wild steel (25 tons/in2

) and one nickel-chromium steel (65 tons/in2

),

weresubjectedto axial loadingasrecordedin a paperby PHILLIPS andHEX’-wooD (1951). Fatiguestrengthswereascertainedfor specimensof diametersin the rangefrom 0~l9to 24 in. No intrinsic size effect with the plainspecimenswasobserved,however. The specimenswhich werenotchedbya transversehole andwhich weregeometricallysimilar, showeda fatiguestrengthdeclining from 84 to & 1 tons/in

2when thediameterwasincreased

from 0~33to l~7in. for mild steel. A similar sizeeffect wasfoundwith thenotched alloy steel specimens. Fatigue limits of 17~1and 13~9tons/in2

respectivelywereobtainedfor thesetwo sizesof specimen. Among others,contributionsto thestudyof sizeeffect arereportedin papersby LEHR andRUEF (1944) and by HELMS (1950).

The explanationof size effect has been approachedfrom two differentviewpoints. According to thefirst conceptit is assumedthat fatiguefailuresoriginateat small local inhomogeneities(inclusionsor the like) which arestatisticallydistributedoverthevolumeof thespecimen. Eachsuchnucleushasits individual endurancelimit, no failure being started from it if thenominalstressis belowthis value. Theprobabilityof encnunteringanucleusof a certain severity increaseswith the volume. This concept, initiallyintendedas an explanationof size effects in brittle materials (WEInULL,

1939a,b) subjectedto static strength (N = 0), is directly applicableto thefatiguestrength(but not to the fatiguelife) at anarbitrarily preassignedlifeN. For somematerialsat leastthis conceptis arealistic one, whichhasbeenmathematicallytreatedby MCCLINT0CK (1955). It is supportedby severalobservations,aspointed out, for example,by STULEN (1951), who statesthatthematerialexaminedindicatesthat“the origin of failure is almostalwaysat a microscopicnon-metallicinclusion which is open to thesurfaceor isslightly subsurface.” Investigationsby EPREMIAN and MEHL (1952) andCUMMINGS, STULEN and SCHULTE (1955) confirm this statement. From the

iF

FACTORS AFFECTING TEST RESULTS

above-mentionedremarkby Stulen it follows that in many,if not all, casesthe surfaceandnot the volumeis theappropriate“size”.

Theother approachto thesize-effectproblemtakesinto considerationthestructureof the material, in particular the grain size. This quantity is arelevantfactorwhen thestressdistributionis non-uniform, andwill thereforebe discussedin connexionwith the influenceof stressdistribution.

From theprecedingit is safe to conclude that the size effect exists, butthat it is not easilyestablished,thereasonfor this beingthemany irrelevantfactorswhich maskthe resultby simulatingthepropersizeeffect. There is,however, anotherreasonof even greatersignificance, and that is that thelawsof size effect must bequite different for the pre-craekandfor the post-crackstagesof thefatigueprocess.In astudyof crackinitiation andpropa-gationin flat specimensnotchedby a centralhole, size effect wasfound(WEIBULL, 1 956a) on geometricallysimilar specimensonly in thepre-crackstage; but thepropagationtime of thecrackwasindependentof the sizeof the specimen. The relevantsize in this caseis thediameterof the hole(or perhaps,more exactly, thecircumference). This conclusionis supportedby observationsmadeby PHILLIPS and FENNER (1951) who found that littleor no reductionin fatiguestrengthis producedby drilling averysmallholein a large flat specimen subjected to reversed axial load. The fatiguelimitsof 44 in. panelswith ~4in. diameterholes and 9 in. panels with ~ in.diameter holes were substantially the sameas thoseof the correspondingundriled panels.

References:DOLAN and HANLEY (1948), DOREY (1948),DOREY andSMED-LEY (1956), FALLHABER, BUCHFIOLTx and SCHULZ (1933), HELMS (1950),HORGER (1954), ITORGER andNEIFERT (1939, 1952), LEHR and MAILANnER(1938), LEHR and RUEF (1944), MCCLINTOCK (1955), MOORE (1945),MOORE and M0RR0vIN (1943), PETERSON (1930, 1949), PHILLIPS andHEvwooD (1951), PHILLIPSand FENNER (1951),SIEBEL andPFENnER(1947),WEIBULL (1939a,b; 1946; 1949; 1956a).

63.2 Shape

The influence of shapeon the fatiguestrengthof a specimenhas beenproved by ~nany investigators. Different factors in connexion with thisproblem have beendiscussedby CAzAtID (1950).

A comparisonof theendurancelimits of cylindrical andof torus-shapedspecimensof cmimmal lmlininmmmmn di;mmct i, axially loaded, hasbeenmadeby(JAzAun (1952), who foumid l7~6kg/mom2 lhr cylindrical and2l~2kg/mm

2

lbr torus-shapedspecimensat a frequency of 2475 c/mm. Correspondingvalues were 194 and 2l~9kg/mm

2respectively for a frequencyof 9500

c/mm. This result has beenverified by Rol and EICHINGER (1950). Forcylindrical specimensfrom two different steels they found an endurancelimit of 30~6and40~2kg/mm2 respectively,comparedwith the values33~5and42~1 kg/mm2for correspondingtnrus-shapedspecimens.

This resultagreeswith thestatisticaltheorybecausethehighly stressedvolume is smallerin the torus-shapedthan in thecylindrical specimensdueto thefact that the cross-sectionof tlse former increasesgradually with the

112113

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

distancefrom the centreof thespecimen. Consequently,the nominal stressfor off-centrefracturesis less thanthat at thecentresection. This particularproperty of this typeof specimenis of interestbecausethedistribution of thelocation of failure has a definite relation to the scatterin fatiguelife, aspointedout by MCCLINTOCK (1955a,b; 1956)whogivesaformulaaffordinga check on whether or not there are present any extraneousvariablesaffecting the scatter in fatigue life other than local variations within thevarious specimens. This relation betweenscatter in life and scatter inpositionof failure hasbeenverified by theuseof datafrom FLUCK (1951).

The effect of specimenshapeon the resistanceof metals to combinedalternatingstresshasbeenstudiedby GOUGHand POLLARD (1936). Repeatedstressdiagrams of round and flat steel bars, T-beams, and wires have been

presentedby HEMPEL (1937).Testsweremadeby Roos,LEMMON andRAIc50M (1949) on flat and round

specimensof anSAE 4340steelin purereversedplanebendingandonroundspecimensacting as rotating beams. Data show that a higher endurancelimit is obtainedin plain bendingthanin rotating-beamtests; andin roundspecimenssubjectedto plain bendingthan in flat specimenssimilarly tested.Similar resultswereobtainedby OBERGandROONEY (1949a,b)with reversedbending for cantilever round section, simple rotating-beam, cantileversquare section, cantilever constant strength, and cantilever rectangularsection. According to investigationsby DOLAN, MCCLOw and CRAIG (1950),theflexural fatigue strengthsofspecimensfrom two typesofsteelwere found

to be, in order of decreasingendurancelimits for both steels: round,diamond, modified diamond, and square. The fatigue propertiesof Z-section test piecesmachined from an aluminium extrusion conforming toDTD 364B havebeendeterminedby FORREST,GUNN andWOODWARn(1953).

The tendencyof all theseresults reportedis in agreementwith thestatistical theory of stressedvolume effect, but various factors, thoroughlydiscussedby DOLAN, MCCL0w and CRAIG (1950), hascertainly contributedto this result.

References:CAZAUD (1950, 1952), DOLAN (1951), DOLAN, MCCLOW and

CRAIG (1950), FLUCK (1951), FORREST, GUNN and WOOnWARD (1953),GOUGH and POLLARD (1936), HEMPEL (1937), MCCLINTOCK (l955a,b;1956), OBERG and ROONEY (1949a,b),Roos, LEMMON and RANSOM (1949),Rol andEICHINGER (1950), WEIBULL (1939a,b).

63.3 StressConcentrations

According to thestatistical theoryof strength,a non-uniform stressdistri-bution is equivalent to a uniform distribution of the samemaximum stressactingon a reducedvolume. This implies that the probability of failure isless in a given volume subjected to a non-uniform stressfield than to auniform distribution of thesamemaximumstress.

A non-uniform stressdistribution in a specimenmay be producedeitheras a consequenceof thetypeof Stressing,bendingor torsion, and by inten-tional notchesand fillets, or by unintentionalstressraiserssuchas scratchesand inclusions. Unintentional stressconcentrationsmay also be causedby

too smalla radiusof thefillet betweenthegrip endandthegaugelengthofa specimen. In any case, the theoreticalstress-concentrationfactor K

1determined by the theory of elasticity with simplifying assumptionsofisotropy, which is definedas theratio of thepeak local stressto thenominalstressat the section, might be expectedto reduce the fatigue strength inproportion to its value, bnt in reality it is always found to be less severethan theory predicts. For this reasona correction term, the fatigue notchfactor 1(1, hasbeenintroduced. It is definedby

K1

= (fatiguestrengthof a plain specimen)/ (fatigue strengthof thenotchedspecimen)

both strellgthS taken at the samenumberof cycles. In generalK,. tendstoincreasewith K

1, but the scatteris very largewhich indicatesthat thereare

other factorsof influence. As a result of rotating cantilever testson 24S—Tspecimenswith V-notchesproducinga valueof K

1varying from I to 10,

MANN (1953) found thattheexpression

K1

= K1(l~09— 0~09K1

)

fitted theobservations.This equationimplies theexistenceof a maximumstrengthreduction, thevalue in this casebeingK

1= 3~2correspondingto a

notchhaving a value of K1

= 5~8.It hasbeensuggestedby NEUBER (1946)that a moreplausiblefactorfor stressconcentrationis obtainedby thefactorKN definedby

KN=(Kl— l)/{l + (A/R)’]

where A is aInaterialconstanthaving the dimensionof length andR is theradiusof thenotchroot. KUHN and HARURATH (1952) have evaluatedtheNeuberconstantA for a large number of fatigue testson steelspecimens,and they have found that the fatigue factor at the endurancelimit canbeestimatedfor steelswith reasonableaccuracy,assumingtheconstantA tobe a non-linearfunctionof thetensilestrengthof the steel. Thevalue of Ais representedby agraphin thepapercited.

This method does not takeinto accountthesize effect. An expressionwhich includesthe effect of size as well as that of stressconcentrationisproposed by DOREY and SMFnLEY (1956). Summarizingthe results fromtorsionalfatiguetestson solid forged steelshaftsup to 9~in. diameterwithfillets of varying radius, it was found that the torsionalfatiguestrength~T

could,with good accuracy,be expressedas

= a — bD + c\/r

whereD is thediameterof theshaft,r is therootradiusanda, b, carematerialconstants. It is of interestto note that there is a limiting fatigue strength

no matterhow sharpthefillet radius, i.e. in spite of a theoreticallyinfinitestress.

Insteadof using the statistical approach,the other conceptis that thestressgradient is the relevantquantity when correlatingdata on stress-Concentrationspecimens. This suggestionhasbeen madeby H0RGER and

114 9 115

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTs

MAULEET5CH (1936). If theStress field is concentratedin a small volumeit seemsplausible that the grain size of the actual material must beconsidered.

By a combinationof thegrain sizeandthe Stressgradientdivided by theendurancelimit of the material, PETERSON(1938) arrived at a criterion fornotch-sensitivity. By plotting thedatafrom a largenumberof testshefounda relation betweenthe notch-sensitivity index (K

1— 1 )/(K5 — 1) and the

relative decrementin stressacrossonegrain.Observingthat thestressgradientsfor stressraiserssuchasfillets, grooves

and holeswereapproximatelyproportional to 1 /r, wherer is theroot radius,PETERsON(1954)modified hiS methodby usingr asa measureof thegradientand plotting it againstthenotch-sensitivityindexwhich is given theslightlymodified form (K

1— l)/(Kr — 1), where Kr is thetheoreticalshearenergy

concentrationfactor. Referenceis madeto a critical review of the criteriafor notch-sensitivityby YEN and DOLAN (1952).

The precedingformulae are limited to stressesin the elastic range. Anextensionto theplasticrangefor acircular hole in aniafinite platehasbeenpresentedby STOwELL (1950). In orderto determinethestressconcentrationfactors in both theelastic and theplastic ranges,HARDRATH and OHMAN

(1951) testedsheetspecimenscontainingvariousnotchesandfillets. It wasfound thatstressconcentrationfactorsdecreasedasthe stressesat thecriticalpoints enteredtheplastic rangein accordancewith a generalizationof theStowell relation.

A stressraiserof particular interest is the fatigue crack. It is obviousthat the theoreticalstressconcentrationof a crack is extremelyhigh, andfor this reasonit was generally believed that the fatigue crack shouldproducethehigheststressconcentrationpossiblewithin amaterial. Thereisevidencethat this assumptionis not correct. BENNETT (1946) found thatcracksof 12—17 percentof theoriginalareahadastrengthreductionfactorof about2 only, andfor specimenscracked50 per centof theoriginal areathefatiguestrengthwasgreaterthan in proportionto this value. This resultis confirmed by POPE and BARS0N (1956) who state that the strength-reductionfactor for a quenchingcrack wasfound to be l~78relativeto an“as-heat-treated”specimen. FROST and PHILLIPS (1956) have also deter-mined the fatigue strength of specimenscontaining cracks. They report thatthestrength-reductionfactor of a crack is independentof its size, the sizeof specimen,formation conditions,andtype of loading, when the stressiscompletely reversed; and also that cracks have lower fatigue-strengthreductionfactorthanmechanicallyformedsharpV-notches. Thisstatementis confirmed by the resultsof statictests on specimenscontainingfatiguecrackswhich havebeencarried out by MCEvILY, ILLG and HARaRATH

(1956), by ILLG andMCEvILY (1951) andby WEInULL (l956a).References: BENNETT (1946), BUNYAN and ATTIA (1953), Cox (1956),

DOREY andSMEDLEY (1956), FORREST (1956b),FROST and PHILLIPS (1956),GROVER (1956), HORGER and NEIFERT (1952), ILLG andMCEvILY (1951),KUHN and HARDRATH (1952), LEHR and MAILANOER (1938), MCEYILY,ILLG and HARDRATH (1956), NEUBER (1946, 1958), PETERSON(1938, 1945),

PHILLIPS and FENNER (1951), POPE and BARSON (1956), IJZHIK (1956),WEIBULL (1939b, 1956a),YEN and DOLAN (1952).

63.4 SurfaceCondition

The effect of the surfacecondition on fatigue strength in relation todifferent methodsof preparingthespecimendependsupon three factors:stressconcentrationsdue to surface roughness,scratchesand the like;changesin the structureof surfacelayers; andresidualstresses.Theeffectson fatigue strengthof thesefactors arenot easilyseparatedand thereforelaws of generalvalidity coveringdifferent materialsandmodesof stressingarenot available,in spite of thefact that this problemhasbeenthesubjectof extensiveinvestigations as indicated by the bibliography. There is afurtherdifficulty arising out of the fact that themeritof a given procedurefor finishing thespecimencannotbe definedby a single figure, becausetheshapeand theslopeoftheS—Ncurvedependsonthefinenessofthefinish andin many casestwo different finishes will result in intersectingS—Ncurves.Consequently the appraisalis entirely dependentupon which part of thefield is madethe basisof the comparison.

This statementwill be illustratedby datafrom an extensiveinvestigationby MANN (1950) who testedmore than 350 specimensin rotatingbendingusing nine different finishes: two turned, four ground, and threehandpolished. It wasfound that at 10°cyclesa 220 grit circumferentialhandpolish gavethe highestfatiguestrength(25,000lb/in2), whereaslongitudinalgrinding to 46 silicon carbide and coarseturned gave the lowest value(19,000 lb/in

1). If, however, the comparison is made at 106 cycles the

order will be completely changed, and the bestmethod will be 400 gritlongitudinal polishing. Thesedatahave also beenevaluatedby WEIBULL

(1958a) with the result that grinding to 60 grit silicon carbidegave thehighest endurancelimit and 400 grit longitudinal grindingthe lowest one.Mannhasahocomparedtheactualand percentagescatterin strengthforthe different finishesat l0~,106, l0~and 10~cycles. The order differs foreachlife andalsofrom theorderobtainedby Weibull, usingthevarianceinfatigue strengtlsas a measureof the scatter. It is obvious that a definiteappraisal of a finishing procedurerequires the complete P—S—Ndiagram(seeSection 81).

‘l’lie ellèetsof machining,grinding, and polishingare reportedin severalpaperslisted below.

The influenceof thevat-ionsprocedureson thefatiguepropertiesmay besumlnarizedasfollows.

Polishing is favourablenot only becauseit providesa surfacefree fromscratchesbut also becauseof compressiveresidualstressesproducedin thesurfacelayers. This is confirmedby theobservationthat areductionof theendurancelimit results if the residual stressesin the polished specimenarereleased,for example,by heattreatment. Someinfluenceof thepolishingdirectionhasalsobeenobserved.

The effectof grinding is twofold: (i) notcheffectsdueto grindingmarksand (ii) detrimental or beneficial effects due to residual stresses.Poor

116 117

FATIGUE TESTING AND ANALYSIS OF RESULTS FAcToRS AFFECTING TEST RESIJLT5

grindingtechniquecausesa reductionin thefatiguestrength,butanincreaseof surfacesmoothnessbeyonda reasonablevaluehas no significant effect.Residual tensilestressesare producedin thegrinding directionwhile theresidual stressesin the perpendiculardirection are mainly compressive.By choosingasuitablegrindingfluid, only beneficialcompressivestressesinthesurfacemaybe produced.

The effectof turning dependsupon cutting speedanddepthof cut. Forthebestfatigue conditionsthereexistsanoptimumspeedwhich dependsonthe tool and thematerial. The beneficialeffectof work-hardeningin thesurfacematerialincreasesto acertainextentwith thedepthof cut.

The effectof scratcheson thefatiguestrengthof steelhasbeenexaminedby THOMAS (1923), and of unintentional stressraiserssuch as scratches,longitudinal cracks, discontinuitiesin handforging andin sand castingonstructuralcomponentsfrom aluminium alloys by HARTMANN (1956). Thesurfacepreparationof electropolishingis describedby FAUST (1948).

Extensive reviews of the influenceof Surfaceconditions on the fatiguepropertiesaregivenby HORGERandNEIFERT(1941),LOVE (1952) (including157 referenceson varioussurfacetreatments),MANLEY and DOLAN (1954),andNELSSON (1957).

References: BOTER (1948), CLEDwYN—DAVIES (1954), FAUST (1948),FERGUSON (1954), FLUCK (1951), HANLEY and DOLAN (1954), HARTMANN

(1956), HEAD (1950), HORGERand NEIFERT (1941), LOVE (1952), MANN

(1950), NEL550N (1957), RUSSELL, GILLETT, JAcKsON and FOLEY (1943),SIEBEL and LEYENSETTER (1936), SIEBEL and GAIER (1956), SINCLAIR,CORTEN andDOLAN (1955),SFEAR, ROBINSONandWOLFE (1953), TAm’sOvand GROVER (1950), THOMAS (1923), WILLIAMS (1949).

63.5 Residual Stresses

Residual stressesin specimensare caused by mechanicalfabricationprocessessuch as turning, grinding, shot-peening,surface-rolling and byheat treatment, flame-cutting, etc. It is now generally acceptedthat themacro residual stressesmeasured,for example,by dissectionmethods orX-ray techniques,are additivewith stressesresultingfrom externalloads.For this reasonresidualstressesmay beeither beneficialor detrimental.

The measurementof residual stressesis rather difficult. Two differentmethods have been developed. The oldest one is a destructivemethod,basedon the removalof part of thespecimenand measuringthe resultingstrainin two directions. Thesecondmethodis theX-ray diffraction method.Thanks to a co-operativework within Division 4 of the Iron and SteelCommittee of the Society of Automotive Engineers,New York, differentmethodshavebeenthoroughlyappraised.ResidualStressdistributionshavebeen determinedon six Standardspecimensby twenty different researchlaboratoriesusingfive differentmethodsof analysis.

Thesemethodswere: (i) Saehs’boring and turning method,developedby SACHS (1939); anumericalexampleof this methodis given by HANSLIP(1952); (ii) layerremovalmethod,describedby LETNER (1953)andLEESERand D&Arix (1954); (iii) beam dissectionmethod, describedin detail by

SIMPSoN and COLEMAN (1957); (iv) hole drilling method, describedbyKELSET (1956); and (v) X-ray diffraction method, using two exposuremethods,describedin theHandbookof ExperimentalStressAnalysis,JohnWiley, 1950, andby BARRETT (1943).

Theresultsareexhibitedin the technicalreportSAETR-147, by MARTIN(1957). It is statedthat the reproducibilityof the methodscould be greatlyimproved by standardizationof certain experimental techniques. Inparticular,the resultsobtainedby theX-ray diffraction methodaresaid toindicatethat different laboratoriesareable to measureresidual stressesbythis methodwhich will be in agreementwithin 5000lb/in2, providedthattheexperimentaltechniquesused by eachlaboratoryareidentical.

In the preceding,it wasmentionedthat thebeneficialeffectof polishingandgrindingwascausedby residualstresses.An exampleofsuchinfluencesis reported by ALMEN (1951). Nickel deposits were plated to fatiguespecimensin suchaway that thedepositon onegroupdevelopedresidualtensile stressesof 25,000lb/in2 andon a secondgroup a residualcompressivestressof 6000 lb/in2. The endurancelimit of thepolished basesteelwas45,000lb/in2, which droppedto 29,000lb/in2 when platedwith the25,000lb/in2 tension stressednickel. In contrastto this loss of 35 per cent, thespecimensplatedwith nickelstressedto 6000 lb/in2 compressionindicatedasmall gain in strength—too small, however, to be significant.

Anotherexampleof beneficial residualstressesis the scraggingprocessofsprings,where thesurfaceof the spring material is subjectedto a torsionaloverstraiu. When this overstrainis removedresidualstressesremainon thesurfaceofthebar, which act in a direction oppositeto thosestressesproducedin subsequentserviceloading. In an experimentconductedby COATE5 andPOPE (1956) thefatiguestrengthat 10°cyclesof a spring as-receivedwas11 ~1tons/in2andafter scraggingan increaseto 131 tons/in2 wasobtained.Scragging is much milder than shot-peeningand it was found that, ifpeeningfollowed the scraggingprocess, the fatigue strengthwasfurtherincreased, taking a value of l9~7tons/in2. If, however,thesequenceof thesetwo processeswas reversed, the fatigue strength took the value 15~9tons/in2.

In addition to these results thebeneficial effect of shot-peeningmay bedemonstrated by d;ita taken from an investigation by WATICINSON (1956).Resultsof testson diot-peeneddeearburizedspring steel showan increaseof thetorsionalendurancelimit from 35~5to 54~0tons/in2afterpeening,andon heavily oxidized anddeearburizedspecimensfrom 22~2to 37~5tons/in

2.

Similar results have been obtained by CooMBs, SHERRATT and POPE

(1956). It wasfound, however, that removalof material from thesurfacelayers of a sisot-peenedspecimenresults in a variation of fatigue life atconstantstress. The life increasesup to a maximumvalue severaltimes asgreat as that for a peenedor an untreatedpolished specimen, and thendecreasesagain to valuescommensuratewith thoseof untreatedpolishedspecimensof the same diameter. LESSELLS and BRODRICK (1956) havefound that the fatigue strength of subsequentlydamagedsurfacescan -beconsiderably improved by properlycontrolledshot-peening.

118 119

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

A review of residual stresses, their measurementand their effect onstructuralparts, is given by SAcH5 (1947) and a bibliographyon residualstressby HUANG (1954).

Thepresentstatusofour knowledgein this field is summarizedby MATTSON

(1956) as follows. Best prediction can be made of residual stressesfrom

mechanical treatmentssuch as shot-peeningand surfacerolling. Stressesdue to heat-treatmentarestill not predictablein practice. Informationofgrinding stressesreveals almost unbelievablehigh stressmagnitudesandgradients. Stressesdue to surfacecold-working vary in magnitudewithmaterialandin depthwith severityof surfaceworking.

Another processby which thesurfacelayerof thespecimenis affectedisby flame-cutting. The fatigue strengthof suchspecimensfrom bright andblack mild steelhasbeendeterminedby KOENIGIBERGER (1955a,b).

References: ALMEN (1951), BUHLER (1952), COATES and POPE (1956),COLEMAN and SIMPSON (1957), CooMus, SHERRATT and POPE (1956),HAN5LIP (1952), HENRIR5EN (1948, 1951), HUANG (1954), KELSEY (1956),KOENIGIBERGER (1955a,b), LEE5ER and DAANA (1954), LEISELL5 and

BRODRIcK (1956), LETNER (1953), LETNER and SNYDER (1953), MARTIN

(1957), MATTSON (1956), SAcH5 (1939, 1947), SIGwART (1956), SIMPsoN

and COLEMAN (1957), WATKINSON (1956).

64.0 GeneralSECTION 64. TESTING MACHINE

It is a well-known fact that the resultsof testswhich are supposedto beconductedidenticallymay be quite different. Therearemanycausesofthis deplorablefact, someof which are attributableto the testingmachine,and will be discussedin the presentsection.

The desiredfluctuation of stressand strainin a given specimencan beproduced by meansof two basically different types of loading, namely,by applying eithera constantamplitudeof forceor aconstantamplitudeofdisplacement. The different effect of thesetypes will first be discussed.Otherfactorsarethe individual propertyof themachinedueto its designandthespeedactually used.

Even if two machinesareof thesamedesignandarerun with thesamespeed, they may give different results becauseof differences between thenominal and theactualload. This error can bestatedand eliminatedbya propercalibrationof themachine.

All thesefactorscontributetoadifferentbehaviourofevensimilarmachines.The variations thus obtainedwill be discussedand somedata will bepresented.

64-1 Typeof Loading

If the specimenrespondedto theapplied stressesas a perfectly elasticcody, there would, of course,be no difference betweenthe two types ofloading: but this condition is neverfulfilled for loadsabovetheendurancelimit, becausethefirst stageof thefatiguedamageconsistsofthedevelopment

of submicroscopicslip bandswithin the individual grains,followed by theformation of fine cracks.

It is obvious that the stiffnessof the specimenis graduallychangedbytheseoecurenceswhich start at an early stage, and that the specimenswillact differentlyunderthe two typesof loading.

Internalfriction andthepropagationof cracksin thematerialmay some-timescausea temperaturerise in theSpecimensufficientlyhigh to changethemodulusofelasticity,with aneffect equivalentto thatproducedby numeroussmall fatigue cracks. This precludesthe correlationof the results of thetwo types by meansof a stress—straincurve determinedon an undamagedSpecimen.

This differentbehaviouris reflectedin thedifferent shapeof thestrain-against-endurancecurve and the conventional S—Ncurve. The formerappearsto be characterizedby a breakwhichdoesnot exist in theconven-tional S—Ncurve. As an illustrative examplereferenceis madeto a studybyTORRET and GOHN (1956) on phosphorbronzestripssubjectedto reversedbending with constantamplitude of deflexion. A similar kneeis found atasomewhatlower value of N in strain-against-endurancecurves establishedby Low (1956) for many different materialssubjectedto reversedbending.As a third example,an investigationby CORTEN and SINCLAIR (1955) ismentioned,wheresteelwires, actingasdeflectedrotating struts,indicate thesame break at about the samenumber of cycles as in the first examplementioned.

It seemssafe to say that a conversionfrom displacementlevels to stresslevels will be very dubious, and that a correlation between the resultsfrom tests basedon the two types of load is impossible. It seemsplausiblethat an equal endurancelimit will be obtained, but this question is notdefinitely answered.

References: CORTEN and DOLAN (1956), CORTEN and SINCLAIR (1955),Low (1956), TORRET and GOHN (1956).

64.2 Design of Testing Machine

There are many minor details of the machine which may contribute toa changein theresults. Oneof theseis thegripwhich, dueto misalinement,may causeunintentional betidingmomentsin axial-loadmachinesorpreventthespecimenfront running true in a rotating-beammachine.

\7

ibrations maysometimesgive trouble. If the machineis not sufficientlyrigid, resonantvibrationsmaybegenerated. Theyareofparticularinfluenceif thespecimenis causedto vibrate in a transversedirection,and prematurefailure may occurat somedefinite stresslevels.

Fretting corrosion may occurin somemachinesat thejoints at the endsof thespecimen,and fracturemayresult at thejoint. Thesameresult maybe obtainedby clamping effects.

Constantcheckingof thetestingmachineis thereforerequired,comparingwith previousdata andwith other machinesof thesame type and design.

References: CORNELIUS (1944), MOORE (1941), RES. Cossr~I.FATIGUEMETALS (I 941), WALFORD and WISTREICH (1950).

120 121

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

64.3 Speed

The fatigue strengthsof metallic materials are usually found to beindependentofspeedup to 10,000rev/mm,whileabovethis valueanincreasewith increasingtestingspeedhasbeenobserved. It is, however, to benotedthat in manycasesthespeedeffect hasbeendeterminedby comparingresultsfrom different typesof machineand different specimens. It is thereforenotimpossible that extraneousfactors might have maskedreal speedeffectsactually existing.

Among investigations carried out under uniform conditions may bementionedKROUSE (1934), OBERGandJOHNSON(1937) and Roos,LEMMON

andRANsOM (1949).Another experiment is reported by MANN (1954) who found that the

effect of rate of cycling on thefatigue propertiesof 24S—T aluminium alloyis insignificant at low stresses,whereasat higher stressesthereis a rangeoftestingspeeds(for this material between200 and 600 rev/mm)where theincreasein fatigue strengthwith speedis morerapid. Similar observationshavebeenmadeby WOOD andHEAD (1951)on annealedcopperwherethisrangewas between300 and400 rev/mm. In thetestsof Mann, thefatiguestrength was observedto increase,for example,at a life of 4 x l0~cyclesfrom 29,000 lb/in

2at 170 rev/mm to 35,000lb/in

2at 12,000rev/mm.

Very high speedshaverecently beenattained. By meansof a torsionalvibrator, WADE andGROOTENHUIS (1956) testedHiduminium alloy, RR56,in reversedbendingfrequenciesfrom 24 c/s to 3835 c/s. A definite speedeffect wasobserved,the increasein fatiguestrengthbeingonly 2 per centfor 200c/s (comparedto afrequencyof 24 c/s) while an increaseof 12 percent was recordedat a frequencyof 3385 c/s. Therewas no evidencethat alimit hadbeenreached.This problemhasbeeninvestigatedfrom a physicalstand-point by DANIELS andD0RN (1957) who have attemptedto correlatespeedand temperature. VALLURI (1957) suggests,however, that criticalfrequenciesassociatedwith roomtemperaturediffersubstantiallyfrom thosefrequenciescustomarilyusedin fatiguetesting.

In aninvestigationby LOMAI, WARD, RAITT and COLBEcK (1956), speedsup to 150,000 c/mm were obtained by meansof a pneumaticresonancesystem. Eight different steelswere tested. Four standard engineeringmaterialsshowedasteadyincreasein endurancelimit with frequencyup toapeakvalue between1200 and 1800 c/s,andthena progressivedecreaseinendurancelimit asthefrequencyincreasedup to 2500c/s. The curveshavethe sametendencyas thoseofJENKIN (1925) for similar materials, but thepeakTaluesareobtainedatverydifferentfrequencies,whichis believedto beexplainedby differentdimensionsof the test piecesandmodesofvibration.

The effect of frequencyon the time of endurancewas representedbyECKEL (1951) from bending tests on lead at room temperatureby thefollowing expression

logL = log k — mnlogf

whereL is the life in days,f the frequencyand It a constant.

Sincethe time-to-failure and thenumberof cycles-to-failureis

we havefL = N

log N = log It — (m — 1) logf

HereIt is afunctionofthe appliedload5, andat is afunctionofthetempera-ture only. If we now postulatethat the S—Ncurveis representedby theequation

S = bN-°+ S’g

for a given temperatureand for f = 1, whereanyvalue of the frequencymay be taken as unity, it follows that the S—Nequation for an arbitraryvalue of thefrequeneyftakestheform

S = bf—°t~’—’~N—~+ S~

ALLEN and FORREST (1956) suggest that in = I in thelow-temperaturecase,while at = 0 in thehigh-temperaturecase. It was found by ECKEL

(1951) that in = 0~7for lead at room temperature. For other materials,valuesof in arequotedby ALLEN and FORREST (bc. cit.) at varioustempera-tures. For example,at = 0~75for 017 per cent carbonsteelat20°C.

It maybepointedout thataccordingto theaboveformula, theendurancelimit ~e is independentof thefrequeneyf. This conclusiondoesnot appearto be eonfirmedby the results mentioned in thepaperby LOMAS, WARD,RAIT and COLBECK (1956).

References: ALLEN and FORREST (1956), DANIELS and DORN (1957),ECKEL (1951), JENKIN (1925), KR0U5E (1934), Loins, WARD, RAIT andCOLBECK (1956), MANN (1954), Roos, LEMM0N and RANSOM (1949),VALLURI (1957), W~&nEandGROOTENHUIS (1956), Woon andHEAD (1951).

64.4 Accuracyof Individual MachinesIt is apparentfrom the abovethatdifferencesbetweenthe nominal load

andtheactualload appliedto thetestpiecemayeasilyarise. For thisreasoncalibration of the testing machineis an urgent requirement. Therearetwo ways of carrying out this procedure. The simpleroneis a staticcali-bratietn whiehincludescheckingof weights,springs,andhydraulicor othermlevieesby which theloading is produced, and theweighingofall leversandother parts of the lever system, and experimentaldeterminationsof thecentre of gravity ui thescparts. Theother wayof calibratingthe machineis calleddynamiccalibration. It is not assimplC asthestaticmethod,but,correctly performed, it is morereliable. More detailson calibrationaretobe foundin theASTM Manual on FatigueTesting (1949, pp. 49—52).

The necessityof calibrating fatigue testing machineswill bedemonstratedby somedata. WILKINs (1956) found as a resultofstatic calibration that thecorrection faetor of twenty identical rotating-beam machines of reputable

manufacture varied between l~05and 1 ~llExperiments designedto determine thevariationsin fatiguelife obtained

from individual testing machines are discussedin a paper by ERLINGER

(1936)andalso by CLAYTON-CAVE, TAYLOR and INE5ON (1955).

122 123

FATIGUE TESTING AND ANALY5I5 OF RESULTS PACTORS AFFECTING TEST RESULTS

Another control of hydraulic fatigue testingmachineshasbeenperformedby FINK and HEMPEL (1951). It is reportedthat tremendouserrors mayappearin hydraulicmachinesif appropriateprecautionsareneglected.

References:CLAYTON-CAVE, TAYLOR andINE5ON (1955), ERLINGER (1936),FINK and HEMPEL (1951), WILKINS (1956).

64.5 Variations of Similar MachinesIt seemsimportantto examinetheresultsobtainedby meansof different

machinesandto determinethevariationsobtainednot only from individualtesting machinesbut also from a battery of machines and from similarmachinesin differentlaboratories. SuchaninvestigationwasperformedbyGOUGH (1924, p. 96) who carefully comparedthe resultsof many rotating-beamtestsmadein EnglandandAmericaon materialsknown to be verysimilar in composition and physical properties. The resultswere found toagreewithin very small limits.

Some rotating-beam tests on the samesize materialswere carried out byDr. Hatfield at theNationalPhysical Laboratory.The averagedivergenceof thefatiguerangeswas2 percent,themaximumdivergencebeingSpercent.

Another similar comparisonhas beencarried out by CLAYTON-CAVE,

TAYLOR and INES0N (1955) on the reproducibility of Wohler-typefatiguetests. The tests were planned and analysed statistically. Some of theresultsarepresentedalso by TAYLOR (1956). It wasconcludedthat theeffect of machinedifferencesis to increasethevariability of resultsandtoreducethe precisionof conclusions. The analysisof varianceshowedthatthevariancedueto the testingmachinesequalsapproximately40 per centof the variancedue to all other causes.The investigationwas extendedtostudy the differencesbetween other laboratoties using the WOhler-typefatiguetest. Theresultsaremorecomplex. It wasstatedthatthevariationsbetweenlaboratoriesarehigher than that within laboratories,but it wasnot possibleto measurethe increasequantitatively.

Another investigationof this type was carried out by GROVER, HYLER,

KUHN, LANDERS and HOWELL (1953). This report presents axial-loadfatigue data on 24S—T and 75S—T aluminium alloy obtained at fourlaboratories. For the 24S—T material, the agreementbetweenresultsfromall four laboratoriesis said to be very good. For the 75S—T material,similarly good agreementexistsonly if thecomparison is confined to sheetmaterial testedat mediumstresses.If thecomparisonis extendedto includesheetmaterial testedat low stressesand rod material, discrepanciesappear.It wasnot clearhow muchof the discrepancyshouldbe attributed to varia-bility ofmaterialandhowmuchto unrecognizeddifferencesin testconditions.

References:CLAYTON-CAVE, TAYLOR and INESON (1955), GOUGH (1924),GROVER, HTLER, KUHN, LANDERS and HOWELL (1954), TAYLOR (1956).

65.0 GeneralSECTION 65. ENVIRONMENT

The environmentof the test pieceis definedby the temperatureandthesurrounding medium, which may consist of inert or chemically aggressivegasesor liquids.

A particulartypeofaggressionis obtainedby frettingcorrosion.Radiationmayin somecasesbeof influence; for example,plasticsandrubbermaybeaffected by sunlight or heat radiation. In recentyears nuclear radiation hasbecomean important subject of research.

65.1 Temperature

In a laboratoryfatigsie testat roomtemperature,it is assumedthat thetemperatureof the test piece is constantor at least that the rise in thetemperatureis negligible. This assumptionis not always true. The tem-peraturedevelopedin a specimendependson manyfactorssuch as size,damping,and heat transfer propertiesof the material, stressdistributionwithin the specimen (uniform distribution producing more heat thanconcentratedstresses),andfrequencyand amplitudeof the stressreversal.Since thedeterminationof anS—Ncurverequirestheapplicationof differentamplitudes, such a test, run at a constant—notvery low—speed andwithout a very efficient cooling, will result in a curvewherethe fatigue liveshaveactually beenmeasuredat different temperatures.

The distortion of the curve due to this fact dependsnot only upon theriseof the temperaturebut also on the relation betweentemperatureandfatigue strengthofthematerial. This is oneof the reasonswhy this relationhasto be known, theother being that somemachinepartsoperateat otherthanroom temperatures.

The dependenceof fatigue strengthon temperaturehasbeen the subjectof numerouspublications which will be reviewed briefly.

The tendencyfor practically all metals at roomtemperatureis that thefatigue strengthdeclineswith increasingtemperaturefrom zero to at least100°C. The slope of the curve relating fatigue strengthto temperatureisexceptionally large for titanium and aluminium alloy RR 59 up to 400°C.Thisproperty implies that in testsat constant speedtherewill bea tendencyfor measuredTallIes of the fatigue strength at higher stressesto be toolow.

Endurancetestsat high temperaturesmadewith varioussteelson rotating-beam machinesby MOORE andJASPER (1925), and on reversedaxial-loadmacitinesby TAP5ELL and CLEN5IIAW (1927), andmorerecentlyby FORREST

and ‘~‘APIELL (1954), and by ALLEN and FORREST (1956) indicate that thensaxilnuln endurancelimit is usually obtainedin therange300 to 400°C,while at 100 to 200°Cthe endurancelimit is lessthanat roomtemperature.It is of interest to note that the variation of tensile strengthfollows thevariat ion of fatigue strength,while the curve of the yield point hasquite adifferent shape. Experimentsalso show that the S—N curve at elevatedtemperaturesdoes not approach the asymptote as rapidly as at roomtemperature,and that more than l0~cyclesare requiredto determinethemagnitudeof theendurancelimit.

The fatigue strength of technical creep-resistingalloy declines steadilywith temperaturefor somealloys (titanium and aluminiumalloy RR 59).Someof them (Y alloy andDTD 424) haveaconstantfatiguestrengthup to200°C. From 400°Cand upwards all of them havea declining fatigue

124 125

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

strengthas demonstratedgraphicallyby ALLEN and FORREST (1956), whoalsogive severalsources.

Dataon notcheffectfor varioussteelsat room temperatureandat 500°Carepresentedby WEVER (1956). In everyoneof thesevensteelsexaminedthe fatiguenotchfactor is lower at 500°C,in someconsiderablylower thanat20°C.Theonlyexceptionis anausteniticchromium—nickel—molybdenum—niobium steel, which revealsexceptionallylow notchsensitivity at roomtemperature.

A verycompleteandsystematicsurveyof thefatiguepropertiesofa widevariety of alloys suitablefor high-temperatureservice is containedin thework by T00LIN and MOCHEL (1947), who presentdatafor more than70fatigue curvesobtainedat 1200 and 1500°F.The materialsareclassifiedinto six groups. It is observedthat all of thesedatashowtrendstowardsacontinuing downwardslopeof theS—Ncurve even at lives exceeding 108cycles, which is thenumbercorrespondingto which the fatigue dataaregiven.

Comparativeendurancetestsmadeat +20 and—40°Cwith Monelmetal,stainlesssteel,nickel steel, andchromium—molybdenumsteelperformedbyRUSSELL andWELCKER (1931) showin all casesan increasein theendurancelimit with decreasein temperature. Thefatiguepropertiesat low tempera-turesof anumberof alloysusedin theaircraft industry havebeeninvesti-gatedby ZAMBROw and FONTANA (1949) and by SPEETNAK, FONTANA andBROOKS (1951). HEMPEL and LUCE (1941) comparedthebendingfatiguestrengthofa numberofsteels,notchedandunnotched,at roomtemperature,at —78, andat—188°C.All thesteelsshowedan increasein fatiguestrengthwith decreasingtemperature,for carbonsteel 20—40 per centat —78°Cand 130—200 per centat —188°C,for alloy steels5—10 pet centat —78°Cand 40—70 per centat —188°C.

References:High temperatures:ALLEN and FORREST (1956), Dlx (1956),DOLAN (1950, 1952), FORRESTand TAPSELL (1954), Gsw~T(1952), JASPER

(1925),JONESand WILKES (1950), MOORE andJASPER(1925), TAP5ELL andCLENSHAw (1927), T00LIN and MOCHEL (1947), WEVER (1956), NACATN 3216 (1955).

Low temperatures: BOONE and WISHART (1935), HEMPEL and LUCE(1941), RUSSELL and WELeKER (1931), SPRETNAK, FONTANA and BRooKs

(1951), TEED (1950), WELLINGER and HOFMANN (1948), ZAMBROW andFONTANA (1949).

65.2 VacuumandAir

Experimentsin a vacuumperformedby GOUGH andS0PwITH (1 932a,b)showedthattheendurancelimit of steelwasaboutthesameas in air, whileexperimentswith copperandbrassin a vacuumdemonstratedan increasein theendurancelimit of 14 to 16 percent. Endurancetestsin anatmosphereof drysteamcarriedoutby FULLER (1931)showedno effecton theendurancelimit. When thesteamcontainedair or water, alowering of theendurancelimit was observed.

Humid air mayaffectstoredspecimensbyoxidationorcorrosion.Somepro-tectingfilm of non-corrosivemineraloil or greaseis thereforerecommended.

References:FULLER (1931), GGUGH andS0PwITH (1932a,b).

65.3 Non-corrodingEnvironment

It hasbeenobservedthat in somecasesa non-corrodingsolventmayhavea remarkableinfluenceon the fatiguelife. A few exampleswill bementioned.

In amachinedesignedfor thepurposeof subjectingthick-walledcylindersto repeatedhigh internal pressures,developedby MoRKIsoN, CROS5LAND

and PARRy (1956), it wasfound that the oil used,beingamixture of castoroil and about 16 per centof brakefluid, in spite of not showingany signsofcorrosion,hadaveryharmful effecton thefatiguespecimensif thefluid wasin directcontactwith thesurfaceof thespecimen.As yet thereis no satis-factoryexplanationof thisweakeningeffect. It maybecausedby penetrationof thefluid into thesurface or by someactionwhichis enhancedby pressure.If the specimenwas protectedfrom the fluid by a thin film of rubber, thestrength could be considerably raisedasdemonstratedby CRO5SLAND (1956)

andin anotherpaperby PARRY (1956).A similar effect wasobservedby WEIBULL (1954a). The propagationof

fatigue cracks were studied using flat specimensfrom aluminium alloy75S—T. In Some of the tests the specimenwas coatedwith kerosonewitha pencil. It wasfnund that thepropagationtime for coatedspecimenswasabout 70 per cent longerthan that for uncoatedspecimenssubjectedto thesamestressamplitude. No evidenceof corI-osionwasobserved.

References:CROS5LAND (1956), MORRISON, CROSSLAND and PARRY (1956),PARRY (1956), WEIBULL (1954a).

65.4 Corroding Environment

In general,fatigue actingjointly with corrosion behavesas an intensifiedform of fatigue. There is a considerabledifference betweenthe resultsobtainedwhen the specimenis exposedto corrosion prior to the endurancetestandwhen thecorrosionand theapplicationof pulsatingstressestakeplacesimultaneously.This observationhadalreadybeenmadeby MeADAM(1926, 1927a,b). He testedsteels of vat-ious carbon contents, havingendurancelimits in reversedstressvarying from 20,000 to 40,000 lb/in2.When thespecimenswere subjectedto theactionofflesh waterduring thetests,theendurancelimits weregreatlydiminishedandvariedfrom 16,000to 20,000lb/in1. The explanationappearsto be that a metal exposedtoactivecorrosionfatiguehasasurfaceoxidefilm whichis brokendownby theinducedmechanicalstrainswhich, in addition, may removeany productsof corrosionthat otherwisemight have a stifling effect upon the electro-chemical action. The electrochemistryof corrosion-fatigueis treatedin apaperby EVANS (1947). An introduction to the studyof corrosion-fatigueis given by P0MEV and ANCELLE (1935). An extensivesurveyof corrosion-fatigue datais to be foundin thebook by CAzAUD (1948)containingdatafordifferent materials,corrosivesolutions andtypesof stressing.

126 127

FATIGUE TESTING AND ANALYSIS OF RESULTS FACTORS AFFECTING TEST RESULTS

Factors associated with Corrosion fatigue such as slip, composition andnature of the metal, nature and concentration of the corrosivesolution,temperature,scale, metallography,manner of testing, mean stressandelectrodepotential havebeendiscussedby GOULD (1956).

References: EVANS (1947), FULLER (1931a), GOODGER (1956), GOULD(1956), HA1L4 (1956), MCADAM (1926, 1 927a,b), P0MEv and ANCELLE

(1935), WESCOTT (1938).

65.5 Fretting Corrosion

Fretting is a frequentoccurrencein engineeringpractice,particularly inelementsin which mating surfacesrepeatedlyundergo relative motion,resultingin surfacedamagewhichmaycauseseizureor lossoffit andoriginatefatiguefailures.

Oneof thefirst observationswithin this field wasreportedby EDEN, RosEand CUNNINGHAM (1911) who detectedfretting corrosionin thegrip of afatiguetestingmachinewhich causedprematurefailure. A similar incidenthappenedto GILLETT and MACK (1924) who found failures in machinegrips which decreasedtheapparentfatigue limit by more than sixty percent.

Since then, fretting corrosionhas beenextensivelystudied both as aphysicalprocess(GODFREY, 1950),and alsoin relation to its influenceon thefatiguestrength(TOMLIN5GN, THORPE and GOUGH, 1939).

Basing their experience on many years’ studiesin theLubrication Divisionof the Mechanical Engineering Research Laboratory, mainly dedicatedtoferrous materials, FENNER, WRIGHT andMANN (1956)stateaswell-establishedfacts that fretting occursin thepresenceof inert gas, but is more seriouswhen oxygenis available,and then thedebris consists almost entirely offinely divided cc-ferric oxide. Thedebrisaccumulatesbetweenthesurfaces.Thedegreeof frettingdamageis greatestunderperfectlydry conditions,anddecreasesas thehumidity of theenvironmentis increased. Someresultsoffretting fatiguetestson specimensof aluminiumalloy L65 arealsoreported.Various stressamplitudes and clampingpressureshavebeenapplied. Asurprising feature of the testsis thatevenunderverysmallvaluesofnormalcontactpressurethefretting actionstill exertsanimportantinfluenceon thelocationof thefractureandon the fatiguelife.

Fretting corrosion in connexion with press-fittedassemblieshasbeenthesubject of several studies. PETER5QN and WAHL (1935) tested rotating-bendingspecimenswith pressed-oncollars and found that the highestradial pressure(16,000lb/in2) reducedthe fatiguelimit to halfthat of theplain specimenwithout collars, whereasalight press-fit (90 lb/in2) resultedin a 30 per centreductionin fatiguestrength. HORGER and NEIFERT (1941)and HORGER (1953) confirmedtheobservationthat thefatiguestrengthofpress-fittedassembliesdecreaseswith increasingpressure,and found thatshrunk-onwheelsresultin afatiguelimit for theaxleabout20 percentlowerthan with apressed-onwheel.

In a recentinvestigation,HORGER (1956) determinedthe influence offretting corrosionon the fatigue strengthof press-fitted assemblies,using

rotating-bending testson sixty-six shafts of ~1in. diameter. It wasobservedthattheflat portion of theS—Ncurverequirestestingfor at least30 millionstressreversals,indicatedby theresultthatbrokenshaftsfailed at 40, 45, 77and84 million reversals. It is concludedthatthefatigueresistanceof press-fitted assemblieswas comparativelyless influencedby: (i) type of steel;(ii) tensile properties; or (iii) whether the shafts were normalized and

tempered,or quenchedand temperedthan by subcritical quenching toobtainfavourableresidualthermal compressivestresseson thesurface,thusincreasingtheenduranceby at least64 percent.

Anotherstudyof theprocessoffatiguein thecaseofcontactfriction whichis worth mentioning is one by ODING and IvANovA (1956). Two kinds ofchromium-nickel-molybdenumsteel were used for the investigation. It isconcludedthat thereis no reduction in a medium of molecularhydrogen,but a continuousreduction was observedboth in air and an atmosphereofhydrogen. Theendurancelimit wasfound to hezerooratleastto haveaverylow value. ThereductiGnin thefatigue limit by contactfriction is explainedby the processof electricalerosionproceedingundertheactionof thermo-electric currents. By changingthe direction of the thermo-electriecurrentthrough theselectionof the proper contact material or by applying a countercurrent,it waspossihleto retard or entirely eliminatetheaction ofelectricalerosion and thus to raise the fatigue limit. The mechanismof fatiguefracture due to contact friction is understood as the formation of vacantsites in the crystal lattice during the transfer of metal in the processofelectrical erosion.

References:EDEN, ROSE and CUNNINGHAM (1911), FENNER, WRIGHT andMANN (1956), GILLETT and MACK (1924), GOOFREY (1950), HGRGER(1953, 1956), HORGER and NEIFERT (1941), ODING and IvANovA (1956),PETERSON and WAHL (1935),TOMLINSON, THORPE and GOUGH (1939).

65.6 SunlightandHeatRadiation

The heat radiation hasno discernible effect on the fatigue properties of

metallic materials other than a possible rise of temperature, the effect of

which is discussediii Section 65.1. On the otherhand,detrimentaleffectsofradiation are not unlikely on test piecesof plasticsand rubher.

65.7 NuclearRadiation

Sparsebut accumulatingknowledgeof the effects of nuclearradiation onmaterials is thepresentstatein this field. Two symposiaon radiationeffectson materialssponsoredjointly by ASTM and the Atomic Industrial Forumhavebeenheld. So far, no fatigue tests on irradiated materials have been

reported.

SECTION 66. TESTING TECHNIQUE

In this sectionthefollowing factors associatedwith thetesting techniquewillbediscussed:(1) definitionof fatiguelife; (2) runoutnumberof cycles; and(3) restinterval.

128 129

FATIGUE TESTING AND ANALYSIS OF RE5ULT5

66.1 Definition of FatigueLife

The term “fatigue failure” is an ambiguousone. Customarily and ifnothingelseis explicitly said, it meansthe final breakinginto two or morepiecesof the specimen. This end-point definition of fatigue life may beregardedasan acceptableonein laboratorytestson small specimens,but itis not entirelysatisfactory,becauseit doesnot takeinto accountthecompletelydifferent characterof thepre-crackandthepost-crackstagesof thefatigueprocess. Moreover, in somemachinesit is impossibleto continuethe testuntil completeruptureoccurs.

For thesereasons,otherdefinitionshavebeenproposedandarefrequentlyused. From a theoreticalview-point, thefirst appearanceof avisible crackwould be the mostrational definition. Thereare, however,practicaldiffi-culties. Theterm “visible” is not uniquely defined,asit dependsupon themethodof detectingthecrack,andthefirst visible crackmayevenbea non-propagatingone. Furthermore,at high stresslevelsmultiple nucleiappear,which all contribute towardsthe fractureof the specimen(ef. CUMMINGS,

STULEN and SCHULTE, 1 955b). Onewayout of this difficulty is to stipulateacertain crack length, not too small. DrETER, HORNE and MEHL (1953)haveproposeda lengthof 0~0l5to 0~030in.

A still moreelaboratemethodof defining thefatiguelife is to split up theprocessinto furtherstagesbasedontheuseoftheelectronmicroscope,being:(i) submicroscopicslip bandswithin individual grains, (ii) formation ofextremelyfine crackswithin individual grains, (iii) joining of cracksacrossgrain boundariesto form major cracks, and (iv) extensionof thesemajorcracksuntil sudden,complete,tensilefailure of thespecimenoccurs. Thisdivision is suggestedby HUNTER andFRICKE (1954) whohavealsopresentedS—N curves correspondingto the various stages. It is evident that thissplitting-up of the processis not workable in routine testing, but investi-gationsof this kind arevery important and may contribute to a rationaldefinition of fatigue life.

Other definitionswhich havebeenproposedarerelatedto theoperatingcharacteristicof the testing machine. Machinesof the resonanttype aredistinguishedby theproperty that thenatural frequencyof the system isreducedwhena fatiguecrack developsin thespecimen. This property isfrequentlyusedto define the endof thetest for this type of machine.

Anotherdefinition is relatedto the deflexionof the specimen. FINDLEY,

MITCHELL andMARTIN (1954)havesuggestedthattheend-pointbereachedwhen thestiffnessof thespecimenis reducedby the repeatedloading toseven-eighthsof its original value.

Thereliability of this definition hasbeenexaminedby CUMMINGS, STULEN

and SGHULTE (1955b). The deflexionof a smoothSAE 4340 steel R. R.Moore rotating-beamspecimenwas measuredat frequent intervals andplotted againstnumberof cycles. Inspectionof thecurvesshowedthat, ifthe limit-switch button hadbeenset0~04in. higher, all specimenstestedatalternatingstresslevelsequalto 90 per centor more of tbe ultimate tensilestrengthwould haveshownonly halfor less of the recordedcyclesto failure.

FACTORS AFFECTING TEST RESULTS

References:CUMMINGS, STULEN andSCHULTE (l955b),DIETER, HORNE andMEHL (1954), FINDLEY, MITCHELL and MARTIN (1954), HUNTER andFRICKE (1954).

66.2 RunoutNumberof Cycles

The testshaveto bestoppedafter a certainnumberof cycleswhetherornot the end-pointof fatiguelife is reached. The choiceof this thresholdvalue,herecalled the runoutnumber,hasaninfluenceon thedeterminationof theendurancelimit, in so far astoo smalla numberof cycleswill resultintoo high avalue of theendurancelimit estimated.

The appropriatevaluedependsupon the material, typeof stressing,andshapeof specimen. Other factors that may, in someeases,be consideredare the influenceof temperatureand corrosionon the fiat portion of theS—Ncurve.

In his book on fatigueof metals,GOUGH (1924)states,on thebasisof theexperienceof manyyears’ testingattheNPL,thatadirect-stressmachinewillrevealthe limiting rangeof stressata lower numberof stressreversalsthaneither a rotary bending machine or an alternating torsional machine.Further, hollow specimensreveal the limiting rangeafter fewer reversalsthan solid specimens, when a rotating bending machine is employed.“It is ourcustom”,hecontinues(1924), “to teston a12 x 106 reversalsbasisfor solid specimensand on a 6 x 106 reversalsbasisfor hollow specimens.”

Thesestatementshave beenproved for ferrousmetals. For light alloys agreaternumberthan l0~is required,he says,before thelimiting rangeisdisclosed.

The aboverule is still valid for ferrous materialsas confirmedin arecentinvestigation by TAYLOR (1956) who has analysedthe influence of therunout number (maximumnumber) on the 50 per centfatiguelimit of amild steel (B.S. 970En4), determinedby aprobitandby astaircasemethod.He found thattheestimateremainedunalteredfor anappreciablerangeofthresholdvalues, as demonstratedby the following Table:

Runout Number Numberof Estimateof 50%log N Non-Breaks FatigueLimit

(tons!in’)

7-50 60 32-40

7-47 64 32-437-00 64 32-436-50 66 32-43

6-25 76 32-556-00 122 33-60

A thresholdvalue of 10 x 106 (log N = 7~00)insteadof theusedvalue30 x 106 (log N = 7~47)would havegivena savingexceeding100 x 106cycles. If, on theother hand,N = 106 had beenchosen,a fatigue limit3~7per centtoo high would haveresulted.

130 so131

FATIGUE TESTING AND ANALYSIS OF RESULTS

At elevatedtemperatures(ToouNandMOCHEL, 1947) orundercorrodingconditions,a number of cycles higherthan l0~will be required. As anillustrativeexample,aninvestigationby HORGER(1956)maybementioned.He found thatthe flat portion of theS—Ncurve of a specimen subjected to

fretting corrosionrequirestestingfor atleast30 million stressreversals.Thisconclusionis basedon observedfatiguefailuresat 40, 45, 77 and84 millionreversalsin a sampleof sixty-six shafts, testedin rotatingbendingon thebasisof 85 million stressreversals.

References:GOUGH (1924), HORGER (1956), TAYLOR (1955), T00LIN andMOCHEL (1947).

66.3 RestInterval

Veryfrequently testsare sto1ped over-night and continuedthefollowingmorning. It is ofimportanceto knowwhetherornot suchrestintervalshaveany influence on thefatiguestr~ngthof thespecimen.

This problemhadalreadybeenexaminedby MOORE andPUTNAM (1919)withtheresultthatrest intervalshadnoinfluenceon thefatiguestrengthforstressesbelowthe yield point. A slight effect wasfound for higherstresses.This conclusionwas confirmed by BOLLENRATH andCORNELIUS (1940) whostatedthat restintervalsdid not affect theS—Ncurvesof alloy steels.

Divergentresults havebeenobtainedby DAEVES, GEROLO and SCHULZ(1940) as demonstratedby thefollowing Table correspondingto a steelof160 kg/mm2 ultimate tensile strengthsubjectedto reversedstressesof 55kg/mm2amplitude.

RestInteroal FatigueL!fe(days) (kc)

Uninterrupted 0 65Interruptedafter l3~Oke 3 82Interruptodafter6~5kc 3 100Interruptedafter 13~0kc 73Interrupted after6-5 kc 1 96

The effectwasstill more pronouncedwhen thespecimenwaskept at atemperatureof 50°C.

References: BOLLENRATH and CORNELIUs (1940), CORNELIUS (1941),DAEvES, GEROLD andSCHULZ (i 940), MOORE and PUTNAM (1919).

132