j.o. almen_general motors - shot blasting to increase fatigue resistance

8/12/2019 J.O. Almen_General Motors - Shot Blasting to Increase Fatigue Resistance

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S H O T B L S T I N G T O I N C R E S EF T I G U E R E S I S T N C E

b y I 0 ALMENResearch Laboratorler DlvlslonGoneral Motors Corp.


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S H O T B L S T I N G T O I N C R E SW HILE great strides have been made in most phases ofengineering and metallurgy, it is doubtful that indynamically loaded parts we are getting more net workfrom our metals today than was obtainable 25 years ago.The fact that modern airplane engines weigh only aboutone-half as much per horsepower as the engines of WorldW a r I is primarily due to im prov emen ts in fuels, andincreases in engine speed. T h e speed an d performance ofairplanes have increased because of the better pow er-weightratio of engines and aerodynam ic improvements in pro-pellers and airplane structures. Ne w fabrication techniqueshave made possible many design improvements, betterbearing materials arc available, lubricants have been im-proved; but the basic useful stre ngt h of ou r structuralmaterials remains unaltered.

Although no super-strength alloys have been discoveredand no such discoveries seem to e imminent, there is muchthat can be done to increase materially the fatigue strengthof many machine parts made from our ordinary structuralmaterials. Thi s fatigue strength ening does not requirechanges in design or in material, and in fact it does notrequire processes that are fundamentally new or untried.It is merely the extension of processes that, on the whole,have long and honorable histories, and the avoidance ofprocesses and practices that are now known to reducefatigue strength. The significance OA these processes hasonly recently become clear through the introduction ofnew concepts of fatigue ph enomena by which n ew avenuesof reasoning are opened to us. These new concepts are:Fatig ue failures result only from tension stresses ne verfrom compressive stresses and any sul-face no matter howsm oot hly finished is a stress-raiser.

atigue Vulnerabilityhe surfaces of repeatedly stressed specimens, no matterhow perfectly they are finished, are much more vulnerablzto fatigue than t he deeper layers. It has long been appre-ciated that the vulnerability to fatigue increases as thesurface roughness is increased, particularly if the roughnessconsists of sharp notches, and more particularly if thenotches are oriented at right angles to the principal stress.T h e practice of carefully finishin g fatigue test specimensand engine parts is, of course, a recognition of this vulner-ability in so far as visible marks or scratches are concerned,even down to being sure that the final polishing marks areparallel to the direction of the applied stress. These pre-

cautions are kn ow n to be effective in increasing th e fatigucstrength of the specimens, and specimens finished in thisma nne r have, therefo re, come to be kno wn as "par" bars.This name implies that fatigue specimens and machincparts approaching perfection in finish give the highestpossible fatigue endurance for any particular material, andthat they accurately measure the ultimate fatigue propertiesof that material..[This paper was presrnrrd ar the S.\E War Nateriel X1ceti:lg. Dctrwt Mich. June 9 1943 and the Kational Aeronautic Uertmr: of theSAE K\ w York City Apr~l8 1943.1

T is doubtfu l whe ther we a r e ge t t ing more ne twork from metals today in dynamically loadedpa r t s t ha n wa s ob ta ina b le 5 y e a r s a g o , a n d n osuper-strength-alloy discoveries seem imminent;however , much ca n b e do ne t o inc rease the ' f a -t i gue s t r e ngth o f m a ny m a c h ine pa r t s m a de f romordinary structural materials by merely extendingprocesses a l rea dy known to be sa t i s fac tory , anda vo id in s ~ r a c t i c e shat r e duc e f a t i g ue s t r eng th ..We have to da y new concepts of fa t igu e fai l-ure: Fati gue fai lures result only from tensionstresses, never from comp ressive stresses. Any sur-fa ce , no ma tte r how smoothly f inished, is a stress-raiser.S t ructura l mate r ia ls a r e not r ig id. Ma ny fa t igu efa i lures can be t rac ed t o e last ic def lect ion forwhich no allowance was m ad e in design.From experien ce with pr acti cal mach ine parts ,we can only conc lude tha t s t ress ca lcula t ions bytextbook methods a r e wholly inad eq ua te unlesswe generously temper our calculations with expe-r ience. The accu racy of s t ress d a t a f rom photo-elasticity, br it t le lacque rs, extensometers, an d sim-i la r methods is usual ly gre a te r than by m athe-mat ica l ana lysis , but these a re f a r f rom re liable .As a working hypothesis , i t seems reasona ble t oassume, except possibly for very ductile metals,

thatThe slope of the f a t i gue c u r ve, a s m e a su r ed ona log-log plot, is a m easure of ef fed ive stress; andfa t igue curves for va rying s t ress concentra t ionsconve rge toward a point near the tens i le s t rengthof the mate r ia l at some considerable number of

stress cyc es.Fully 90% of all fatigue failures occurring inse r v i c e o r du r ing l a bo r a to r y a nd r oa d t e s t s a r et r a c e a b le t o de sign a nd p r oduc tion de f e c t s , a ndonly the remaining 10% ar e pr imar ily the respon-sibil ity of th e metallurgist a s defects in mate rial ,m a te ri a l spec i fi c at ions o r he a t - t r e a tm e n t .Study of fatigue of materials is the ioint dutyo f t he m e tal lu r gi c al , e ng ine er ing , a n d ~ r o d u d io ndepar tments . There i s no def in i te l ine be tweenmechanica l and meta l lurgica l fac tors that con-t r ibutes to fa t ig ue . This over lapping of responsi -bility is not sufficiently unders tood. Until moret ime is dev oted t o sea rching for mechanicalcauses ra the r than meta l lurgical ones , we canno tmake full use of our materials.THE AUTHOR: J . 0 LMEN has long becn acrivc inGcncral Motors rcscarch dcvclopmcnt work He is head of theMechanical Enginccrin~Dcpartmnt No. of the GM RcscarchLaboratorics.

It can be sho wn, however, that the so-called "par" barsare not th e best specimens, but that influences aki n to


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F T I G U E R E S I S T N C Enotches, so far as fatigue vulnerability is concerned, arcretained by the par specimens. It seems that the speci-men surface is highly vulnerable simply because it is nsurface; that there is an extra hazard in the surface layer-not shared by the deeper layers. Th is extra surface hazardmay be due to subm icroscopic notch effects, or to th e factthat the surface is a discontinuity, since the outer crystalsare not supported o n their outer faces. Whatever the reasonfor surface vuln erability, the evidence of its existence isstrong.

Fatigue Life IncreasedT h e fatigu e stren gth of the most carefully prepared speci-men will be increased if a thin layer of the specimen ispre-stressed in compression1 by a peening operation suchas peen hammering, swaging, shot blasting or tumbling,or by pressure operation s by balls or rollers. Th is increasein fatigue strength resulting from the surface layer being

stressed in compression is clearly shown by the S-N curves,Fig. I , which compare normally finished railway axleswith axles that had been subjected to a rolling operation2.Th is and many other tests- show that the-compressivestressed surface is effective in increasing th e fatigue s tren gihwhether applied to highly finished specimens or to speci-mens having rough surfaces.We are a ll f ami liar w ith the im~ rov em entn fatigue thatmay be obtained by a few cycles of overload sufficient toproduce a set in such parts as springs. Local tensionstresses from the overlo ads exceed the elastic limit of thematerial and, therefore, the tension stress at the workingload is decreased. Th is treatment, w hich has long beenpracticed on many production items, is similar in effect torolling or peening since, in the unloaded state, thc memberis stressed in compression in the areas where yield occurredduring the overloading.The bar char t , Fig. 2, 'records the increased fatiguedurability resulting from shot peening of a few typicalmachine parts. I t will be seen that the fatigue durabilityis increased whether the parts are hard, such as carburizedgears, or soft, such as steering-gear parts, and whether thestress is completely reversed, as in crankshafts, or the stressrange is small, as in preloaded springs.Note that th e fatigrie durability of peened axle shafts wasnot increa5ed as mu ch as most of the other specimens. T hework on these shafts was conducted a num ber of years agobefore the technique of peening machine parts had beendeveloped, and the relatively small increase was probablydue to insufficient peenin g. Simila r fatigue results havcbeen obtained fro m a large variety of machine parts an dfrom aluminum specimens, and there are reasons to expectthat the treatment is equally effective for all metals.The bar char t , Fig. 2, shows the fatigue durability in-crease as per cent gain abo ve the durability of the sam emach ine part before peening. Actually, durability corn-

S e e Srobl find Eiserr 1'01. 49 April 25, 1929 pp. 5 7 5 5 7 i : "DasDriicken der Oherflache von Bautei en a us Stahl," by 0 Foppl.- S e e A S M E Transactions, Vol. 58 Septemher, 1936 pv A 91 A M:"Increasli ig the Fatlgue Stren gth of Press-Fitted Axle Assemblies byS:lrfarc Rolling," by 0 . J. Horger and J L. Maulbetsch.

b y I 0 ALMENResearch Laboratories Division.General Motors Corp.

NOT ROLLED

o l o 2 1 0 l o 4 1 5 l o 6 1 0CYCLES T FAILURE

Fig. I S N diagram for railway axles showing change of slopdue to rolling1

Fig. 2 Bar chart showing the benefits of surface-peening bore don fatigue l ife

parisons cannot be made on a percentage basis alone, asis apparent when we examine the improvement in fatiguedue to rolling, as shown in Fig. I If, in this chart, thedurability comparison is made at a load equal to 55% ofthe ultimate stre ngth , the percentage improvement is zero;if the durability comparison is made at a load correspond-ing to 20 of the ultimate strength, the percentage im-provement is infinite, and, at intermediate loads, the per-centage gain will, of course, be somewhere between thesclimits.It is essential that this be kept in mind when interpretingthe fatigue data. T o illustrate, suppose that the averagefatigue durability of a gear tested at high load is increasedfrom 30,000 cycles to 70,000 cycles by suitable surface-peening, a gain of 13 0% . No w if this comparison is ma de


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at a lower ,load such as to cause initial failure at 300,000cycles, the treated gear might run 6,000,ooo cycles beforeiailu re, a g ain of possibly zoooC/C~. Th is is because of thcdifference in slope of the fatigue curve representing thenormal ge ars and the fatigue curve representing the peenedgears.Explanation of Peening Effectiveness

T h e most plausible explana tion of the effectiveness ofsurface compression stress is that w hen a load is appliedto such specimens the tension stress in the surface layerbecomes less by the amount of the compression pre-stress,and since fatigue failure starts from tension stress thefatigue durability of t he w eak surface layer is increased.However, the tension stress in the material below thepre-stressed layer is not reduced but may be actuallyincreased, notwithstanding which, the fatigue strength ofthe specimen is increased. It follows , therefore, that thelower layer is inherently stronger than the surface layer.Fopp14 shows that t he fra ctur e in rolled specimens docsnot originate at the surface but in the material below thcpre-stressed layer, as wo uld be expected if the surfac e issufficiently pre-stressed in com pression. Sim ilar subsurfa cefatigue failures, usually called fissures and attributed tofaulty material, have long been known to occur in railroadrail, in which the surface is stressed in compression as aresult of the cold work of heavily loaded locomotive andcar wheels.T h e situation can perhaps be clarified by the use of theconventional textbook stress diagram of a loaded beam, asillustrated in Fig. 3, in which a beam supported at thc

COMPRESSIONI Cl

i ..-.I..i: NEUTR L AXIS.-

Fig. 3 -Conven tional stress diagra m of a loaded beam

ends is loaded in the central plane, P-PI . The stress at anypoint in the beam is measured by the horizontal distancefrom the plane P in which the load is applied, to thcdiagonal line T1-C1. Th e distance P-Cl represents the com-pressive stress at the upper surface, the stress at the neutralaxis 0 0 is zero and the tension at the lower surface isrepresented by the distance T I - P I .-- be S t ah l un Eiserz Vol. 53 Dec. 21 1 9 3 3 , pp. 1 3 3 0 - 1 3 3 2 : DieWirkung von Eienspannungcn kuf die Biegeschn,ingtmgsfestiskeit, .by Hans Bull ler and Herbert Buchholtz.' S e e TO*& Ag c . Vol. 126, Sept . 18 1930 pp. 775.777. 829: ColdRolling Raises Fatigue or Endurance Limit, hy C S. von Heydckan~pf .

While this is a satisfactory enough stress diagram forstatic loads, it does not agree with the behavior of fatiguespecimens. However, if we modify the diagram Fig. 3 asis shown in Fig. 4, in which T I - T 2 represent an added

COMPRESSION

Fig. 4 - Modified stress diagram of a loaded beam showing rur.face vulnerability

increment of tension stress in the surface, we have areasonable representation of the surface fatigue vulner-ability. Fo r a sharply notched surface, the addition al stressincrement TI T2 s relatively great. As the surface rough-ness is decreased, the increment T I - T 2 decreases, but nomatter how well polished the specimen may be, there stillremains an additional surface stress as measured by fatiguetests.Stress Patterns

Fig. 5 represents the residual stress pattern in an un-loaded beam that has been rolled or peened, as has beendescribed, in which C3-P and C 3-P represent the magni-tude of compressive pre-stresses, and Ts -A represents tilema gnitu de of the tension pre-stress to balance the corri-pressed stresses in the surfaces. Af ter this beam has beenloaded from either side through one stress cycle, as in areversed fatigue test, the compression pre-stress will bereduced i the applied load raises the total co~npressio~l

, COMPRESSION--

Fig. 5 - Probable stress diagram of an unloaded beam with pro-stressed surfaces

250 SAE Journal Transactions), Val. 51,N o - 7


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stress above the yield point. The stress diagram tor sucha ]we-stressed beam supporting an external load is shownin Fig. 6 in which the effective tension stress, T t thcsuriacc may be less than the stress T elow the surface,

C C S R E C S I O NA e L jINTERNAL rAPRE-STRESS-\\TOTALJ?+ LOAD

COMPONENT

rn Fig. 6 -Stress d iag ram for o loade d pre-stressed beam

in which case h i lu re would s tar t be lo\\ the surface , asnoted by Fijpp l. Note also that the ne utral axis is displacediron1 the geome:ric center of the heam and th at the tensionstress, T; below the surface is greater than in the hcanlth at had not been p re-stressed, as is sho wn by t he clottedlines.T h e mag nitude of the su hsuri ;~ ce ens ion s t ress in ;Iloaded beam hav ing pre-stressed surf;~c es will vrlr); witht he a m ou n t of co mpression pre-stress ~ n ~ lvith the clcpthof the pe -s tre s sed Iayc r. F ig. l io \\ .s thxt t h ~u h s u r t : ~ ~ ~

SHALLOW LOAD

T E N S I O NFig. -Stress d ia gr am for a loa ded pre-stressed beom show-ing the influence of the dep th of the pre-stressed layer

tension stress may he greater for deeply prc-stressc. il la y uthan for a layer ot ' lesser depth.I t s eems ev iden i tha t the in lp ro vc~ l~e n tn i ;~ t i gue trcng thby conlpressive prc-stress is due to the reduction in tensions tre ss w h en l oa de d in th e vu ln er ab le s ur ta ce la ye r a n d t h ~the increased compressive stress in a specimen stressed tromzero to a m ax im un ~ in e i ther direc t ion docs no harm.probably beczuse oi a djus tm ent ot compress ion s t ress ~th e 1"'-stressed layer th ro ug h yield.Further evidence of the extra vulnerahi l i ty ot the suri ;~cclayer is found in the behavior oi specimens having in-creased strength in a thin surtace layer. as in thinly car-l m h x l o r cyan ided s pec imens o r in thin ly n i t ridcdspecinlens. Fatigue failures in such specimens also startlxlow the surface and show greater ia t igue s t rength thanthe sa lne n~ ateri a l n the unclad s ta te . A ni tr icled specimenis prolxthly superior to the other torms 01 h;lril clntlding

because. in adJition to the higher physical properties ofthe surface layer, this layer is in a state of compression,and i t i s, t h x i o r e , le ss no tch s ens it ive .

Residual Thermal SiressesWhile on the subject of beneficial internal stresses, men-

tion should hc made of the surface compressive stressobtninable by heat-treatment. B a rapid quench, it ispossible, through thermal contrac t ion a lone , to t rap corn-pressivc stress in the suriace and corresponding tensions tress in the core , but this method, a l though showing som ehenefit in fatigue, is not as effective as the other methodstha t have been discussed. Th is subject will be discussedInter in this paper.

Perhaps the most spectacular use of surface compressionstress by heat-treatm ent thro ugh therm al contraction aloneIS tempered glass which, because of its great strength, isused in some parts of mode rn automobiles. Th is glass sprepared from normal glass by rapidly cooling the surfacesby means of air jets. T h e cooled surfaces contract causingthe relatively plastic center to yield in compression. sthe center of th e glass cools an d contrac ts it becomesstressed in tension, with consequent compressive stress inthe surfaces.

First Use of Surface CompressionT h e iclcaoof surface com pression t.) improve the s t rength

of steel is pr ol~ ably as old as steel itself. It has probablyIxen discovered, torgotten and rediscovered many times.Certainly every village blacksmith knew and practiced theart in m aking \vagon an d bug gy springs , axles , and otherhe;~v ily oaded parts , After these parts were forged intoshape they \vere severely hammered to improve theirstrength an d, no do d )t . the same procetlure \vas t 'ollowedby the anc ien t s \v o~ d make rs . I,ike\vise, mill and shipshafts were cold-\\,orlied hy the application of small rollersat high pressure aftcr machining hecause of the greaters t rength tha t was known to rcsul t .C o l d- w o rk i ng of ~ , . m l s ncre:~ ses he hard ness of mostmetals, including steel. at least in the range of lo\\ hard-ness. i t usually results in internal stresses of varying degrersand patterns, i t alters the physical properties and sometime..frac tures the materia l . With the known sens i t ivi ty oftnaterials to fatigue. it is obvious that we must learn howto control cold-work just as we have had to lea n how tocontrol heat- t rea tment in order tha t we may be :tit by the~ o o t l ffec ts and overcome the evil e ffec ts . i t .vouldn ot t h i n k o f s pe ci fy in g a h ea t- t re a tm e n t w i t l i ~ t s h n g\yhcther the temperature should be ra ised or loncged anJin which order and to what extent; yet that is tne way\W now thin k of cold -wor k. Cold -tvork ing can be good orb; ld depending upon how i t is done and for what purpose.

Pre-Stressing M a y Be Overdone1';lpers have Iwm publish ed shelving that cold-\vorkingot thc surf:~ce so ;IS to produce a layer stressed in com-pression increases the fatigue strength of the parts to which

t is :~ppl ic t l , >ut we ar e not told the a mou nt o i the prr-stress or the depth ot the pre-stressed layer. Both of the srvalues are presuln:~hly important in obta ining opt im umresults tor ;In , p r t i c d 3 r sjxcimen . hut it is probable thatthe values sho11ld not he th e sa me ior a11 sizes oi specimens,lo r ;dl ~ n ;~ t r . r i ;~ l s .r i11r hclr~l lnd ior soit spe cimen s.Sevcr;~l ns~. tn~.eslrc kno\vn in tvhich the strength of~ n x h i l l c .trts ; I I ~ pecimens hns h e n decreased by too


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intense surface peening. Fig. 8 is presented as showingthe probable effect of peening or rolling, particularly onthin sections. Th e fatigue strength is increased as thcintensity of peening or ro lling is increased until a maxi-mum improvement is obtained. With more intense peen-ing or rolling, the fatigue strength rapidly decreases belowthe original strength and the part will be damaged due toexcessive internal tension stresses.

Fig. 8 -Effe ct of peening intensity on fotigue l ife

It would, therefore, seem important to control the com-pression stressed layer as to stress magnitude and depthwith considerable accuracy by proper selection of thecurvature of the rolling or peening instruments and by thepressure that is applied. Th e precise amo unt of surfacecompressive stress that is required for optimum fatiguestreng th is kno wn f or a few specimens only. It will varywith the shape and section thickness of the machine part,with the hardness, and with the kind of metal beingtreated. For the present, we mu st frequently rely upon thenot too accurate sens e of pro portio n th at is developed byexperience to indicate the treatment that should be appliedto any given machine part.When the layer is stressed in compression (by applyingsufficient pressure on the work by rollers or by peening)to a degree exceeding the yield strength of the metal incompression, the amount of residual stress is presumablyat least equal to this yield strength.The depth of the stressed layer is probably roughly pro-portional to the instantaneous area over which the pressureis applied, and to the pressure intensity. T he dep th of thecomp ression stressed layer in a railroad rail h ould begreater than the depth of the compression stressed layerin the same material if small rollers at the same pressureintensity were used insread of large car wheels. Underthese circumstances, the initial point of fracture shouldappear at correspon ding depths. Such evidence as is avail-able indicates this to be true.w Instrument Measures Peening

simple and practical method for indicating the com-pression in the stressed layer consists of a thin flat strip,Fig. gB that is attached to a heavy base as shown inFig. gA This strip is rolled or peened with the sameintensity that is given to the machine part, and when itSee l o u r ~ ~ lf the r on and Steel Institute Vol. 66, N$ 11 1927PD. 265-282: The Work-Hardening of Steel by Abrasion, by E. CHerbert.

Fig. 9 Apparatus for indicating the com pr~ssion n the stressedlayer

is removed from the base it will be found to be curved,as shown in Fig. IOA , with the convex surface on thecold-worked side. T he curv ature of th e strip may bemeasured by an indicator, as shown in Fig. 11, which canthen be interpre ted in term s of the de pth of the stressedlayer.

A COLD WORKED

Fig. I0 Measuring strips

r f i g . I I Curvature indicator252 SAE Journal (Transactions), Val. 51 No. 7


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The chart shown in Fig. 12 records the stress magn itudeand the depth of the stressed layer at constant cold-workintensity of two such test strips. T he cold-worked surfacesof these strips , the Kock well hardness being respectively64 and 40, were honed away in small increments and thecurvature was measured with the removal of each thinlayer. T h e chan ging curvature as metal was removed pro-vided data from which the compressive stress in each lavercould be calculated, with the results shown in the chart.As would be expected, because of the higher yield point,the harder specimen was found to be more highly stressedthan the softer specimen.

SURFACE PEENEDROCKWELL C -40wV SURFACE PEENEDV)

COMP. STRESS IN 1000 PSIr Fig. I 2 Magnitude and depth of stress imposed by various

surface treatments

Also shown in this chart is the surface compressive stressin a nitrided specimen as a result of the nitriding . T heprocedure for this experiment was the same as for measur-ing the stress due to peening except that the face of thespecimen that was in contact with the heavy base wasplated to limit the nitriding 1 the outer face of the strip.On removal from the base after nitriding, the strip wascurved convex on the nitrided side, as is shown in Fig . IOB.It seems, therefore, that the well-known resistance olnitrided specimens to fatigue is primarily due to the com-pressively stressed surface layer.

Overdose of NitridingAlthough the usual experience with nitriding is that itgreatly improves fatigue strength, it is possible to overdonitriding just as it is possible to overdo surface stressingby peening and rolling. T h e high compressive surfacestress that results from nitriding must, of course, be bal-anced by inte rnal tension stress of equ al total value. W he ndeep nitriding is applied to light sections, the unit internaltension stress may reach dangerous proportions.Fig. 13 hows a part that was greatly reduced in strengthas a result of nitrid ing, its fatigue durability being o nly

I or 2 as great as the fatigue durability of the same partnot nitrided. Th e diameter of the part at the point offailure was approximately /s in. Th e dept h of the nitridedlayer was about 0 020 in., the area of w hich is equ al toabout 60% of the area of the section, as is shown bythe circle in the enlarged view. From the nitriding,compressive-stress diag ram s hown in Fig. 12, it is evidentthat the internal tension stress must have been very great.It is also known that internally nitrided cylinder barrelsare more prone to fail by cracking than cylinder barrelsthat are not nitrided, the reason being that the stress due

rn Fig. I The effect of deep nitriding failure from severe tension stress

to nitridi ng is adde d to the stress from gas pressure. Caremust, therefore, be used in nitriding thin sections to gagethe dep th of the nitrided layer in propo rtion to the thick-ness of the section being nitrided.Residual Stress from Honing

While the peened specimens used for the experimentshown in Fig. 12 were being honed as has been described,it was found that the strips did not fully recover theiroriginal flat form. T o determine if this residual curvaturewas due to a set in the material or was the result ofhoning, other flat strips that had not been peened werehoned. The se strips developed the same curvatu re as theresidual curvature in the peened specimens, dtmonstratingthat h oning produces a compressively stressed layer. T heapproxim ate mag nitud e of this honin g stress is also shownin the chart given in Fig. 12. This raises a question as tothe state of surface stress in the carefully prep ared fatigu especimens favored for laboratory fatigue tests, since addi-tional tests have shown that lappi ng also introduces surfacecompressive stress.rn Residual Stress from Carburizing

The carburized layer in a carburized part is stressed incompression, as is graphically shown in Fig. 14. T w o

A BEFORE SPLITTlNG

B FfER SPLITTING aFig I4 - Residual compressive stress resulting from carburizing

and hordening the upper and lower faces of a specimen

opposite faces of t h ~ s%-in . squ are specimen were carbu-rized, while the other two faces were protected by copperplating. T he specimen was quenched and tempered in theusual manner, after which it was split with a saw as shownin Fig. I ~ B .Note that the parts are curved convex onthe outer faces, indicating compressive stress in these faces.Analysis of th e internal stresses in ano ther carbu rized m em-ber by a method similar to that described for peened andnitrided strips indicated the internal stress pattern shownJuly 1943 253


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in Fig. I j Of intere st here is the m agn itude of th e con;-pressive stress in the carburized layer and the reducedcompressive stress, possibly even tension stress, in a thinsurface layer. When carburiz ed parts, such as bearing races,wristpins, and gear teeth, are ground we may expect thrsurface to be stressed in tension, as is indicated by thedotted lines shown at the right in Fig. 15

r Fig. I 5 Ma gni tud e a nd de pth o f re sidua l s tres s due to c a rburizing and hardening

The compressive stress in the carburized layer may bea hazard for members stressed in tension, as was shownfor the nitrided part, Fig. 13, because the tension stress inthe core is equal to the working load plus the tension loaddue to the compressive pre-load of th e case. Fo r mem bersstressed in bending and in torsion, however, the internalcompressive stress in the carb urized case of o rdinary depthimproves the fatigue strength of the part except for the thinsurface layer which, especially after grinding, is severelystressed in tension. It is, however, a simp le ma tter toconvert this thin tension stressed layer into stress in com-pression by suitable peening or rolling operations, as wasindicated in Fig. 12 with resultant large gains in bendingand torsion fatigue strength.The residual stress in crankshafts and other partshardened by induction heating and probably also in flame-hardened parts resembles the residual stress in carburizedand hardened parts, as shown in Fig. 16 The hardened

r Fig. 16 The ef fect of induct ion harden ing the convex curveof the upper surface indicates compressive stress

upper surface of this specimen was straight at the originaithickness. Note that af ter removal of the material indi-cated by the dotted line, the u pper surface is curved convex,indicating compressive stress. More complete analysis indi-cated that a thin surface up pe r) layer was possibly

stressed in tension. In these treatme nts as in carburizing,the hardened layer is stressed in compression because inundergoing the phase change to the hard state, the densityof the steel is reduced and therefore the hardened layerseeks to occupy mor e space. A th in surface layer howevermay be stressed in tension.W ith internal stresses of the magnitud e show n in Fig. 15we can readily understand why carburized parts are proneto w arp duri ng heat-trea tmen t, especially if the design isnot symmetrical with respect to the internal stresses.

Low Temperature Quenching StressesResidual stresses due to quenching from relatively lowtemperatures may reach considerable magnitudes and maybe harmful or helpful to fatigue durability dependingupon whether the trapped stresses augment or diminishthe tension stresses from the applied loads. An interestingcase of this kind occurred in a water-cooled aluminumcylinder head, as show n in F ig. 17, that failed by fatigue

r Fig. 17 Meth od o f indicat ing quenching stresses in a watercooled a luminum cyl inder head fat igue fa i lure occurred on thewate r side of the combustio n chamb er wall

on the \vater side of the combustion-chamber wall. Mea-sure me nts of residual stress disclosed that th e water sideof the combustion-chamber wall was stressed in tensionand the combustion-chamber side of the wall was stressedin compression. Th is internal stress pattern was one ofthe same kind as the stress from the gas pressure againstthe combustion-chamber wall, and the resultant stress was,therefo re, the sum to tal of th e residual stress an d the gaspressure stress.The residual stresses in this case were caused by quench-ing the cylinder heads from 980 F by immersion in coldwater. T he ou ter surfaces of th e casting were cooled whilethe inner water-jacket surfaces, especially at the thicksection, were still hot. Th er m al contraction o the outersurfaces imposed cornpressive stresses of such ma gnitu deas to cause yield in the still hot and therefore weakerwater-jacket surface. As cooling progressed, the metal thathad been stressed beyond the yield point contracted ther-mally, leaving tension stress on the water-jacket side andthe corresponding compression stress on the combustion-cham ber side. T he retention of the residual stress in thethick combustion-chamber wall was aided by the thinnerouter wall of the water jacket, which was stressed illcompression.A visual indication of the residual stress pattern is shown

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by the scribed arcs at the left in Fig. 18. These arcs weredrawn from centers in a steel bar bolted to the oppositeside of the ca sting section, as is shown in Fig. 17. T h earcs indicated by the numeral I were drawn when thccylinder head was intact. T he casting was then sectionedas shown in Fig. 17 except that the outer side of the waterjacket had not been cut and the arcs indicated by thenumeral 2 of the same radius as before, were drawn.Finally the outer side of the water jacket was removedand the arcs indicated by the numeral 3, still of the sameradius, were drawn. Note the direction of movement of

r Fig. 18 Var ia tion in internal stresses from different quenchingmethods

the metal with each operation and the order of the stresstha t is indic ated . As a correction of the undesirable residualstress shown by this test, another cylinder head was giventhe same heat-treatment except that it was quenched inter-nally by forcing cold water through the water jacket. Th eorder of internal stresses was measured in the same manneras has been described, with the results sho& at the rightin Fig. 18. Note that when internally quenched, the stresspattern in the combustion-chamber wall is reversed, leavingthe inner side in compression and the outer side in tension.Since these trapped stresses are of opposite sign to th eoperating stress, the resultant stress is the difference be-tween the residua l an d operating stresses instead of theirsum as w hen the casting was quenched externally.

Fatigue Life IncreasedFatinue tests were conducted on cvlinder heads auenche dby both methods, the results of which were 2,000,000 to3,000,000 stress cycles to failure for t he externally qu ench edheads, and 5,000,000 to 6,000,ooo stress cycles for the in-ternallv wenched heads.~ d d it io n a l fat igue tests were made on internallyquenched heads in which the aging treatment at 350 Fwas omitted in order to avoid reduction of the favorablestress Dattern. These heads endured more than ~~.ooo.ooostress cycles at the same test load without failure.Similar residual stresses are known to occur in manvother heat-treated and quenc hed alum inum parts. I t is alsoknown that many aluminum parts show better fatigueresistance when they are drawn to a higher temperaturethan that which gives the greatest tensile strength, pre-sumably because unfavorable residual stresses resultingfrom quen ching a re thereby reduced. It is probable that

s ee Engineering Voi. 154, Aiig 14, 1942 pp. 134-135: Ooench-in of Steel after ?cmperina end the Impact Test, by L. E. Benson.See etals and Al loys Vol. 5 J une , 1931. pp 129-130: Effect ofNotches on Nitrided Stee l, by J B. Johnson and T T. Oberg.

similar stresses can be trapped in steel by quenching fromtem pering tem peratures0. Sucli residual stresses may befavorable or unfavorable depending on the shape of thepart, the temperature gradient, and the direction of heatflow.r Corrosion Promotes Fatigue

Fatigue failures in many machine are traceable tocorrosion of several kinds or to other forms of surfacedamage that occur in service. In normal machine parts,even slight corrosion or bruising is very potent in encour-aging fatigue fractures because each pit interrupts thecontinuity of the surface and increases the local stress.The damaging effect of corrosion or bruising is preventedon the surfaces that are adequately protected by compres-sive pre-stress because the local tension stress cannot reachdangerous values until the pits or bruises have progressedsufficiently to penetrate the compressively stressed layer.This was forcefully demonstrated in fatigue tests of amachine part that failed alternately in a badly formedfillet or in the region of a clamp remote from the filletwhere fretting corrosion occurred. Th e durability of thepart could not be increased by improving the fillet becausethis would merely transfer all failures to the fretted areaat about the same durability. After peening, however, th efatigue durability was found to have increased severahundred per cent and large additional gains were thenpossible by im provin g the for m of th e fillet without failu rein the corroded area. Th e peening did not prevent corro-sion but it did prevent the ill effect of corrosion in pro-moting fatigue.Similar protectidrl against the effects of corrosion and ofsurface bruises is afforded by nitrid ing7, carb urizin g, andother treatments that produce compressively stressed sur-faces. The working face of a gear tooth may be severelypitted, creating a fatigue hazard, but the bending fatiguestrength may not be impaired because the carburized layeris compressively stressed and the surface is compressivelystressed by the c old-work of m ating teeth.

Surface FinishesEfforts to improve products by improving surface finishmay sometimes have the opposite effect. Highly finishedsurfaces and fillets may lead to a false sense of security if,as the result of machining or straightening operations, theparts have high internal stresses of the wrong kind.When machine polishing is done by the use of abrasivepaper, cloth wheels, or abrasive-covered felt wheels, su6-cient heat is often generated to induce serious surface-tension stresses an d thus prom ote instead of prevent fatigu efailures.In groun d surfaces such as shafts,. wristpins, an d gearteeth, the grinding operations may introduce high surfacetension stresses that, from the standpoint of fatiguestrength, often do more harm than good. T he surface-tension stresses from grinding are often so great as toproduce visible or magnaflux surface cracks, but whetherdetectable or not, su rface tension is frequently very serious.Fig. 1 9 is a magnaflux transfer print on transparentcellulose tape showing surface fractures in a ground geartooth. Th is tooth failed by spalling originating in thesesurface fractures. Sirice fatigu e cracks start on the side ofthe gear tooth that is loaded in tension, the effective stressis the grinding pre-stress plus the working stress. Fre-

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r Fig. 19 Surfoce fractures in o ge ar tooth he result of grinding

quently, we find that a hardened part will show a file-softskin after grinding, which not only promotes fatigue butis also susceptible to seizure and galling.Internal stresses of th e wro ng kin d a re perhaps the mostinsidious of all fatigue ha zard s because we can seldomknow their magnitude or the pattern in which they aredistributed within the material or whether they are alikefor all commercially identical machin e parts. Inte rnalstresses may be the result of o pera ting conditions such asoccur in brake drums, clutch plates, or other frictionsurfaces where the instantaneous temperature in a thinlayer is so great that, under thermal expansion, the surfacelayer is stressed beyond the yield point in compression.When the source of heat is removed, the heated surfacelayer is quenched by the adjacent cool metal and, underthermal contraction, it is so severely stressed in tension thatfractures often occur. Th is is, of course, the same thin gthat happens in machine polishing and in grinding unlessgreat care is used.The magnitude of surface tension stress in a specimenthat was ground in accordance with xiorma1 commercialpractice is shown in Fig. 20 specimen of annealed

r Fig. 20 Ma gnit ude a nd d ept h of the residual stress caused ygrinding a spring steel specimen

spring stock, 1/16 in. in thickness, I in. wide, and 7 in.long was ground to a depth of 0 002 in. After gr inding,the previously straight specimen was found to be curvedconcave on the gr oun d side, indicating tension stress. Verythin layers were then removed from the ground surfaceby hand honing until the specimen regained its initialstraightness. Measurements of the change in curvaturewith each thin layer removed permitted calculation of thestress distriburion as is shown in the ch art. Surface stressesof this magnitude are not unusual in ground productionparts, but we are seldom aware of their presence unlessactual failure has occurred.Obviously, a stress of 270,000 psi, a stress just below the

r.. .

v

W

'

fracture point oi tull-hard steel, could not be supportedby the steel in the annealed state, from which it followsthat the stress layer was hardened by the heat cycle of thcgrinding operation to not less than Rock.-:ell C jj T h cextrem e thinness of the h ardene d layer presents an inter-esting problem in hardness measurements, as is shown inTable I

- 5 0 0 I 0 0 2 0 0 3 0 0-COMP. TENSION IN 1000 PSI -

TABLE IUngrwnd GrwndRolwell B 88RockwellC 5 5V~ckersBr~nell 183 199

'This table demonstrated the futility of our normalhardness-measuring technique for measuring the hardnessof the most significant portion of our machine parts, thesurface layer.Inte rna l stresses often result from the cooling of castingsand forgings or from the vigorous heat transfer of heat-treating . Many parts, such as crank shafts, axle shafts, andcamshafts require straightening du ring processing. Sinccthe straightening operation is usually done at room temper-ature and since the part is rarely stress relieved afterstraigh tening , th e result is severe internal, stresses.

SPRINGSTEEL

M a c h in in g D a m a g eIn turning, milling, and other machine operations, it isnecessary that metal be removed at a minimum cost, andtherefore the cutting tools must often take deep cuts athigh feed rates. Since metal cuttin g is more accuratelydescribed as a metal-tearing operation so far as stresses arcconcerned, we need not be surprised to find serious internalstresses to considerable depth s after machining. W henmetal cutting has been unusually severe or after operationssuch as punching and shearing, we often find that thesurfaces are actually fractured. Finish m achinin g or grind-ing rarely goes deep enough to remove the internallystressed metal from previous rough machining and, ofcourse, these finishing opera tions add stresses of t heir ow n.Whenever it is economically practicable, internal stressesthat produce tension in any surface layer subjected to cyclictension stress should be reduced or removed or, better still,converted to compressive stress by suitable treatment be-cause all fatigue failures are due to tension stresses.In connection with machining damage, an interestingand perhaps important observation has recently been madcwhich indicates that the layer injured by mach ining isdeeper tha n is generally believed. It also shows that theinjured material does not recover by hea ting for lon gperiods at high temperatures. Fig. 21A shows a bar of4615 steel as it appeared after rough machining on ashaper. Th is piece was then carburized for 8 hr at 1700 Fcooled in the box, reheated to I500 F quenched in oil,and drawn at 300 F for I hr. T he machined surface wasthen ground in a direction at right angles to the shapermarks to a depth of 0.0055 in. below the last visible toolmark, after which it was polished as shown in Fig. 21B.Finally, the polished surface was shot blasted, whereuponthe machining marks (vertical l ines) and the grindermarks (horizontal lines) reappeared as shown in Fig. 21C,showing that the material is not uniform in resisting theshot blasting, notwithstanding the long period at elevatedtemperature. Th ere is no evidence at present that the effectbrought out by this experiment is significant in fatigue.

I-.A......

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LIFE IN 100,000 S OF CYCLESFig. 23 Effect of in it ia l tightness on bolt l i fe

tatigu e than long ones. Th eir elastic extension is small,a n d . therefore a slight loss of dim ension by corrosion,plastic defo rmation, o r w ear will lose preload and they willfail by fatigue.T h e practice of plating screw threads with soft metal toavoid corrosion is a definite fatigue hazard and should cavoided. T he soft plate is so weak that it squeezes ou tfrom between the loaded thread surfaces and reduces thestud or bolt tension, thus promoting fatigue failure. Aslackening of 0 001 in. on a stud holding a %-in. flangemay result in a loss of 50,000 psi preload. If protectiveplating must be used, it should be of a hard metal and ofmin imu m thickness.The initial tension applied by the nut is difficult todetermine unless the elongation of the bolt or stud can bemeasured. Measurem ent of the torque applied to thewrench is very unreliable because of the variability of thefriction. Fig. 24 records tension measurem ents plotted

TENSION ON BOLT--1000 LBSFig. 24 Effect of lubricants on bolt tension

against wrench tor que in lb-ft for j/16-in. diameter cap-screws havin g 24 threads per in. It will be seen that thebolt tension varied as much as 1 to I for constantwrench torque depending upon the lubricant that wasused. T h e mechanical efficiency of this bolt varied fromI to lo%, as may be calculated from the chart .There is l i t t le need for metal lurgical examinat ion otfailed bolts or studs, or for considering design' changesuntil i t has been shown that the failure was not the faultof the m an o n the wrench.

I'reloading oi cyclically stressed m em lx rs to reduce thestress range and thus to increase their fatigue durabilityis not restricted to bolts but may be applied to manymachine parts. Fo r example, the stress range in leaf-springeyes can be reduced by pressing a bushing tightly into thespring eye.ater ia ls Are Elastic

A common cause of fatigue vulnerability is the beliefapparently held by many des igners and engineers that ourstructural materials are rigid. Many fatigue failures canbe traced to elastic deflection for which no allowance wasma de in the design. Elastic deformation of matin g partsmay be such as to concentrate the load in a small region,as occurred under the conditions described for the bolt inFig. 22A.Under operating conditions, a crankshaft may be soelastically deformed in twisting and in bending that thebearings are only partially effective in supporting the load.The bearings are frequently found to be plastically de-formed or worn bel l mouthed to accon~modate he elasticgyrations of the crankshaft.

Perhaps the most generally misunderstood of all machineelem ents are the several classifications of gears. As ordi-narily designed, there is only one thing certain about gearsand that is that they will not function as intended by thedesigner. W he n laying out a set of gears on the draftingboard, the mating gear teeth are represented by parallelstraight lines over which the load is assumed to be uni-formly distributed, but no matter how carefully the gearsare cut and heat-treated the mating teeth will never againbe parallel, except by accident and then o nly thr ou gh asmall load range.The nature of the contact between two mating gear teethis influenced by:

I T h e elastic characteristics of the h ousing in whichthey are contained.2 The elastic characteristics of the bearings by whichthey are supported.3 The elastic characteristics of the shafts upon whichthey are m ounted.4. The elastic characteristics of the gears themselves.5. The accumulated dimensional errors in all the sup-porting parts as well as the errors in the cutting of thegears.6. The necessary and accidental clearances in the sup-porting parts.j Misalignment of supporting parts through thermalexpansion.8. T he amo unt and nature of the warpage in heat-.treating o give the metallurgist some of the responsibility.T h e result of all this is that it is virtually impossible forthe parallelism between mating teeth, as visioned by thedesigner, to exist in practice. If i t should chance that twomating gear teeth are parallel at some load, they cannotbe parallel at any other load because the elastic deflectionof some of the supporting parts is not linear with respectto the load. As ordinarily designed, the load on gear teethis never uniformly distributed over the length of the teethbut is always concentrated toward o ne end of the teeth.This localization of the load is shown in Fig. 25, which isa record of the contact impressions of gear teeth underload in a commercial gear box. Load localization cannotoften be seen by examination of a gear that has been inservice because, usually, each tooth of each gear makes

258 SAE Journal Transactions), Vol. 5 1 No. 7


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Fig. 25 -C on ta ct impressions of gear teeth under load in acommercial gear box

contact with all of th e teeth in the m ating ge ar and , there-fore, the summ ation of all contacts und er all load conditionswill e seen by the exa miner.Localized Gear-Tooth Load

T he illustration shown in Fig . 26A is of a gear thatfailed in service. T his gear was rescued while on its wayto the metallurgical department to find out what waswro ng with the material to cause the fatigue failure. Notethat the failed tooth is broken at one end which, inciden-tally, is typical of almost all failed gear teeth. An a djo inin gunbroken tooth shown in Fig. 26B tells us that failureFig. 2 6 - Localized tooth load of a gear that failed in service

A Gear tooth that failed in service

- Na tu re of contaci as shown by adioining unbroken toothload was concentrated on left end

occurred because only a small part of the tooth was actuallysupp orting th e load in spite of the generou s tooth lengththat was provided by the designer. Th is gear would havebeen just as durable had it been designed to one-fifth thetooth wid th tha t was actually provided. Clearly, this is amechanical and not a metallurgical problem. T h e realtrouble was inadequate support of the gears and othermechanical errors as enumerated.It may fairly e argued that this is an unusually severecase and that it is not typical of gear fatigue. Actually themost unusual thing about it was that it could be diagnosedbefore it was cut into sections and the evidence etchedaway, as so often happens in metallurgical examinations.In t he case of fatigue failure of matin g helical gear teethof equal srrength, fatigue will always occur in the tooththat is loaded on its acute-angled end because the section

See Antomot irc I n d~ i s t r i c s Vol 77, Sept. 25. 1937, p ,. 426.432,Oct 9 1957, pp. 488-443: ' ,'Factors Influencing the Durabilrry o i Automobile Transmrssion Gears, y J . 0 Almen and >. C. S t m u h .o See STM Proceedrnge, Vol. 3 5 , an 11. 1933 pp. 99-135: '*Real.A x l e G e a r s ; F ~ c t o r swhich Influence their Life. b y J. 0 lrnen and-4. L. Boegehold.

is weaker a t this end. Ma ting helical gears should be offsstSO that contact cannot occur on the acute-angled end byany mode of deflection. This is possible only where thetorque is constant in direction?All gear teeth should be designed to afford a degree oftolerance for deflections. machining errors, and warpageas has long been stan dard practice in spiral bevello, hypoid,and in some spur and helical gears. In rigidly moun tedgears, this is accomplished by curving the teeth barrelshape or the equivalent in such a mann er as to concentratethe load near the centerline of the gear width and thusavoid load concentration at the weaker extreme ends ofthe teeth.Load concentrations at the ends of gear teeth can some-times be avoided by increasing the elastic deflection, as isdone in simple spur reduction gears by providing the gearwith a thin diaphragm web located central of the gearwidth, or by more complex construction in other forms ofgears, but it cannot be done by accurate dimensions alone.

Gear-Tooth PiHingThe pitting of gear teeth is a form of fatigue that isinduced by tensile stress from compression loads on thecontacting tooth surfaces. T h e mag nitud e of the compres-sion stress varies with relative curvature of the contacting

teeth in accordance w ith th e H er tz formula, i t varies withthe deg ree of load concentration at th e ends of th e teethand with th e applied load. Th e load that may be carriedvaries with the hardness and, therefore, with the strengthof the m aterial, with the tempe rature, and with the m annerin which the lubricant is applied.The design factors that are effective in reducing the loadconcentration at the ends of the tooth barrel shaping oreqnivalent, also reduce the contact compressive stress. Therelative curvature and, therefore, the contact compressivestress can be varied by the choice of pressure angle. Ingeneral, there is little to be gained by designing wide facegears except the doubtful satisfaction of dealing with thesmaller stress numbers.In high-speed gears, pitting may occur when gears aretransm itting no load. Th is is sometimes seen in the reverseidler gear of the automobile transmission. Although thisform of transmission troub le is rare an d occurs only whenother co nditions, such as hardness, are unfavorable, it servesto emphasize the part played by the lubricant in promotingfatigue. A reverse idler runn ing submerged in oil will trapthe oil between th e gear teeth an d if the clearances aresmall will induce extremely high surface pressures. W eare all familiar with the high temperatures that are gen-erated in gear boxes when too generously supplied withoil, but we do not always interpret this as a fatigue hazar d.High-speed gears should be lubricated by jets of low-viscosity oil directed at the teeth as they are coming outof mesh, not on the incomin g side. Th is form of lubrica-tion will wash away the heat of friction while it is still onthe surfaces of the teeth and will prevent excess oil fromreaching the contacting teeth, provided, of course, thesum p is dry.Generalized Fatigue Laws

T h e conventional ap proa ch to studies of th e fatigue ofmetals is through laboratory tests on several arbitraryform s of fatig ue specimens. Du rin g the man y years tha:such tests have been made, a vast amount of fatigue datahave been accumulated. These data have enabled us toJuly, 1943 259


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formulate somewhat general ized " laws",on the behaviorof various specimens subjected to repetitive stresses of sev-eral k inds .W e have found that steel, under most laboratory con-ditions of repetitive stress has a fairly well-defined limitof stress, known as the fatigue endurance limit, belowwhich it will e ndu re for a n i n f nite num ber of stress cycles;that the fatigue endura nce limit of steel is roughly proportional to the ultimate strength of the material but that theproportionality varies with the range of the applied stress.W e also kno w that, und er certain other test conditions,steel does not have a fatigue endurance limit, that non-ferrous metals generally do not have a fatigue limit, thatrough surfaces, notches, section changes, and other dis-continui t ies are detr imental to fat igue s t rength . These andman y other "laws" have been established thr oug h labora-tory tests under controlled conditions.T he preferred laboratory fatigue test specimen is very care-fully prepared to avoid all surtace imperfections, abrup t sec-tion changes, internal stresses, and oth er stress-raisers. T hi s1s considered necessary because the investigator is usuallyinterested in the inherent properties of the material under-going test, and he naturally seeks to eliminate all factorsthat would tend to obscure these inherent properties. Therecan be no objection to this procedure as it refers to the testspecimens, but the data thus obtained have little bearingon the fatigue characteristics of machine parts made fromthe same material and g iven the same heat-t reatment , be-cause in machine parts surface irregularities, abrupt changesin section, and internal stresses are almost always present.Economic Requirements

In the design of machines and equipment for heavyduty , where weight is not important and where the num-ber of units produced is small, the present practice ofdesigning to large factors of safety is justified because theexpense involved in preparing designs to approach exactrequirements would far exceed the savings in weight andmaterial.The same economic considerations that justify overde-s ign in low-production-volume equipm ent dem and designsof low weight and high stress in many machine parts whereweight is all-important, as in airplanes or in large-produc-tion-volume machines, such as automobiles, where bothweight and cost mu st be considered. Obviously, the dy-namically loaded parts of such machines sh ould be designedwith accurate knowledge of their fatigue'strength.

Laboratory Fatigue DataWhen we try to apply quant i tat ively the accumulatedlaboratory fatigue data to such design problems, we findthat they are almost useless. Published data on fatigueassume that :I . The operat ing s t ress can be determined.2. Laboratory test specimens are representative of a ma-terial whe n that m aterial is formed in to a machine part .3 T he am ount an d nature of the applied load is know n.4. Load variations occur in an orderly and predictablemanner.5 Representative fatigue curves can be constructed froma dozen or less specimens.6 Machine parts must be stressed below the fatigue limitto be successful.These assumptions are not justified in practical design.

Stress Cannot Be CalculatedFrom the data on internal stresses that have been dis-

cussed, we may reasonably have some misgivings about thereliability of our stress calculations. From experience withpractical machine parts we can only conclude that stresscalculations by textbook methods are wholly inadequateunless we generously temper our calculated results withexperience. Fo r exam ple, by the usual me tho ds of calcula-tion, crankshafts may be stressed to 20 000 psi, connectingrods may be stressed to 40,000 psi, valve springs 90,000 psi,disc clutch springs to r80,ooo psi, while another form oidisc spring suppor ts, by calculation, 600,ooo.psi. Obviously,some of these stress values are ridiculous, but the formulasused in each case conform to the "laws" of mechanics.T h e actual stress in crankshafts is probably several times20,000 psi, while the 600,ooo psi in the disc spring is notreached because of yielding in local highly stressed regions.The unreliability of stress calculations has almost beenforgotten by seasoned designers because they no longertake the numerical values of their stress calculations lit-erally. Instead, they have learned by experience that, bythe usual methods of calculation, the numerical valueshave different meanings for different machine parts; thatis, somewhz t rough empirical correction factors are applied.

xtensometer Readings of Doubtful ValueThere is a growing interest in various devices employedto make direct measurements of stress, such as by photo-elasticity, brittle lacquers, extensometers, and similar in-strunlentation, in the belief that these devices will provideaccurate stress data. T h e accuracy of stress data fr om suchmeasurements is usually greater than can be obtained fromthe most involved mathematical analysis, but that they arefar from reliable can easily be shown by fatigue tests. T w ospecimens may vary widely in fatigue strength dependingupon minute differences in surface finish or internalstresses. Since internal stresses are often desirable and arefrequently unavoidable due to processing operations, suchas machining, heat-t reat ing, s t raightening, or grinding, as

has been discussed, and since surface finishes vary all theway from rough forgings to lapped or honed surfaces,there is little reason to expect accuracy from extensometerreadings, and even less for photoelastic tests, since photo-elastic specimens must be free from interna l stress and mus tbe made of another material.Photoelastic and extensometer readings are measures ofelasticity in which the changes in dimensions are the statis-tical average of all of the ma terial involved in t he mea surc-men t. Fatigu e tests provide a streng th measure of theweakest portion of the material involved, usually at thesurface, even though it be submicroscopic in size. Obvi-ously , we cannot expect agreement between fat igue mea-sures of stress and the stress readings obtained from elasticmeasurements alone.Even if stress could be determined, the fatigue datafrom laboratory specinlens could not be used because ma-chine parts c annot be finished wit h the ca re and exactnessthat is given laboratory specimens. Ab rup t section changescannot be avoided, high internal stresses are often presentas a result of processing or because of local heating as frombearing friction, surfaces are subject to bruises and to cor-rosion of various kinds. Th ese effects cannot be evaluatedin terms of arbitrary stress-raisers in controlled laboratorspecimens.

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Operating Loads Rarely KnownIn the kind of machines under d iscussion, the dynamiclo;& arc rarely constant for any appreciable time but varyup and.down the load scale in an unpredictable mann er.Only a sm all percentage of th e total num ber of stress cyclesarc : ~ tmaxim unl load, and this percentage will not be thesame in the hands of any tw o operators.Th is hrings u p the question of d ama ge by overstress an drecovery by understress as has heen observed by severalinvestigators in tests of laboratory fatigue specimens. N odoubt such effects occur also in dynamically loaded ma-chine parts, but how are such laboratory data to be appliedto machine parts wh en the schedule of overload an d und er-load is beyond control?T he developmen t of engineering materials, designs, anllprocesses requires that we conduct laboratory tests by whichthese factors may be evaluated, hut to devise a reliablelaboratory test is far from simple. T h e common belief thatwe can reproduce the conditions of service in a laboratorytest is wholly erroneous. By the time the laboratory in-vestigator on any particular part has provided for all ofthe conditions that occur in service he will have a com pletemachine in actual service.The useful strength of materials in dynamically loadedparts is the fatigue strength of such parts under actual ser.vice conditions. N o other measure will suffice. T h estrength of a part cannot e determined by tests of the kindt h a t a r e c o n ~ m o n l ymade in laboratories, many of whichare used because they are easy to perform and not becauscthey give useful information.

ompromise TreatmentsMany materials and processes have been graded and arestill being graded by laboratory tests which are now knownto have been very costly to industry. For example, thefiction that a carburized part should have a hard case toresist wear, and a tough core to resist breakage, arose fromlaboratory impact tests. In these tests, the strength of thepart was judged by the number or intensity of hammer

blows it would withstand before fracture. Since gear teethresisted impact fracture in accordance with the physicalproperties of the core, it seemed logical to specify heat-treatments to bring out the best compromise between theimagined requirements of the case and th e core. Beingcompromises, these heat-treatments were not the best foreither region.If, instead of counting the number of impacts or measur-ing the intensity of hammer blows to produce fracture, thegear tooth had been examined after the first impact, thetooth would have been found bent , and therefore ru ined,and i t would makc no difference how many more b lowswere required to fracture the tooth .Th is compromise heat-t reatment resulted in reducing thequality of ma ny millions of gears before it was realized thatgear teeth fai l by fat igue and that fat igue fai lure, for theusual depth of carburizetion, always originates at the sur-face of th e case. Fr om this evidence, it became clear theheat-treatment should consider the requirements of thecarburized case only, and that the properties of the corewere relatively unimportant, because, in bending and intorsion, the core serves mainly as a stuffing for the case.

Physical TestsScveral kinds of impact tests arc still being used and

impact specifications appear in many drawings, but no mancan explain and substantiate the significance of the test interms of the service strength of machine parts.

Elon gation an d reduction of are a are carefully measuredand are prominent in our specifications, but we do notknow their meaning in terms of serviceability of machineparts. W e are told tha t brittleness must be avoided, butno matter how brittleness is defined it does not explainwhy this property is necessarily more harmful than duc-tility. Most m achin e parts tha t are plastically defo rmedare just as surely failed as i they were broken. W e areasked to believe that machine parts generally must possessrelatively high ductility and they must therefore be heat-treated to develop this property. How ever, when we reallyget down to applying severe dynamic loads, we forgetabout ductility and specify high hardness that certainly iswell within the range of brittleness in the usual meaningof the wo rd. Str ong fatigue-resistant gear teeth are filchard. Wris tpins, ball bearings, roller bearings, shafts, andcams are hard, and they are strong and fatigue-resistantbecause they are hard.gear tooth is just as surely a spring as the coil thatactuates a valve. Why , then , mus t the one e hard andbrit tle and the o ther be re la t i dy soft and ducti le ?Why can we not avail ourselves of stronger hardened ma-terials? T h e answer may lie in our concept of brittleness.W e do not fear brittleness from hardness whe n hardnessis obtained by nitriding . Nitrid ed surfaces are not notch-sensitive because they are stressed in compression.Notch sensitivity is probably the inability of a non-ductilematerial to yield locally and thus reduce tension stresses inlocal highly stressed regions, such as notches and scratches.T he am oun t of ductility that is required to overcome brit-tleness depe nds upon the am ou nt of yield that is necessarvto reduce local tension stresses. If the surface is sufficientlypre-stressed in compression, local yielding is not requiredan d therefore non-d uctile materials will not be brittle. Asme improve our understa nding of brittleness we may ex-pect to use steels at higher hardness in many parts foxwhich we now specify ductility. W e will then gain fromthe greater inherent strength as well as from the increasedstrength obtained by compressively stressed surfacLs.The most significant of our easily performed laboratorytests is hardness. Since the static streng th of most mate-rials is roughly proportional to hardness, we will b.now theapproximate static strength of a part if the hardness isaccurately measured. How ever, the popular hardness testerssuch as Brine11 or Rockwell are incapable of the accuracythat is required because they penetrate too deeply into thematerial being tested, and therefore they do not measurethe characteristics of that most i mpor tant part of the mate-rial, the surface laver.

Chemical analysis can only indicate the responsivenessto heat-treatment and can measure the potential strengthof a steel only by its probable harden ability . Since stre ngt his proportional to hardness, ail properly heat-treated steelsof equal hardness are equally strong regardless of theircompositions.

Laboratory hardenability tests are now coming into gen-eral use. Thi s test has much m erit vrovided that we under-s tand i ts meaning and that we do not debase i t, as we arcso prone to do hy applying arbitrary hardenability specifica-tions without considering the requirements of each par-ticular part. Thro ugh-h arden ability (approximately uni-form hardness through the section) can be very importantJuly 1943 6


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fo r parts tha t a re stressed in tension, but it is difficult tosee why through-hardness is necessary in parts that areloaded in bending or in torsion, because in such membersthe stress decreases somewha t linearly w ith depth, reachingzero at the neutral axis. For this kind of loading, it wouldseem to be more important to develop heat-treatments thatgive the type of inte rnal stress shown in Fig. 15 because,being pre-stressed negatively to the applied tension load,the dynamic load-carrying capacity is greatly increased.The standard laboratory tensile test is, of course, inca-pable of indicating the useful bending or torsion strengthof pre-stressed specimens, particularly when the pre-stress-ing is deep, as shown in Fig. 15 For such specimens, thetensile test cannot even distinguish between harmful andbeneficial pre-stressing. Both would probably show de-creased tensile strength, whereas under dynamic bendingor torsion loads one would show greatly decreased fatiguestrength and the other greatly increased fatigue strength.However, we have done a reasonably satisfactory job inthe past without worrying overmuch about the shortcom-ings of the methods used. W e may be certain that wewill do better in the future as more experience is gainedand it is in the accumulation an d organiza tion of thisexperience that we can best serve the needs of the fu ture.It is probable that fatigue studies will play increasinglyimportant parts in future designs; but these studies willbe based on fatigue tests of actual, full-scale mach ine partsinstead of on laboratory specin~ens.atigue Tests on Machine Parts

Fat igue tests of full-scale ma chin e parts have been mad eby many laboratories for a long time, but since these testshave usually been made for the purpose of comparing onematerial, design, or process with another material, design,or process, the tests have been run at arbitrary constantloads without thought to the fatigue-curve characteristicsand often without adequate correlation with service re-quirem ents. Because of this procedu re, we have madelittle use of t he vast quant ities of such fatigue d ata as arenow locked in our files in so far as establishing a basisfor evaluating material, design, or process for the future isconcerned.In the few cases where fatigue data on machine partshave been properly organized, we find that they revealastonishing amounts of fundamental information aboutthe many variables that are present in-m ac hin e elements,many of which are not even qualitatively revealed by ideallaboratory fatigue specimens.

F af ig ue u a f a A r e M o d a l i t y D a t aFatigue data are mortality data and it is just as absurdto expect that reliable actuarial tables can be constructedfrom mortality data on a half-dozen individuals as to

expect that reliable comparisons can be made from fatiguetests on a half-dozen machine parts. Wh en a sufficientnumb er of ma chine parts are fatigue tested at constantload and plotted in the manner of the well-known mor-tality curve for human life expectancy, we find remarkablesimilarity to hum an mortality experience. Heindlho ferand Sjovall" have show n life expectancy curves for com-mercially identical ball bearings, for commercially identical"Se e Merhanical Engineering Vol. 45 Octoby, 1923, pp. 579-581:"Endu rance-Test Data and their Intcrpretatlon, by K. Heind hoferand H. Sjovail.UPr ivate communication. R. S Carter. Goodyear Tire B Rubber Co.

mazda lamps, and for hum an beings. These curves arcshown in Fig. 27, n which the ordinate is the percentageof units surviving and the abscissa is durability in per centof average life.Fig. 28 is a life expectancy chart at constant lqad forcommercially identical transmission gears in complete auto-mobile transmissions, for commercially identical rear-axlegears in complete automobile rear axles, for commerciallyidentical automo bile fan belts12, for com mercially identicalbolts, and for a group of ideal laboratory fatigue specimens.Similar life expectancy curves will result whether appliedto mountain ranges or to the hairs on our heads.Alth oug h the gene ral for m of all life expectancy curvesis the same, they differ in detail. Not e that th e expectancycurves for machine parts (Figs. 27 and 28 do not extendto zero life as is the case in the human expectancy curve.Infant mortality is avoided in machine parts because theparts having a low potential life are rejected by factoryinspection, a practice that is not followed for humans.

r Fig. 27 C o m p a r a t i v e endurance i fe expec tancy curves forbal l bear ings and lamp s comp ared wi th th e l i fe expecta ncy curvefor human beings

LIFE PERCENT O AVERAGEFig. 28 imilari ty of var ious l i fe expectan cy curves - a s shownby m achine parts , be l ts , and laboratory spec imens

Variation in DurabilityAnother important difference is the relative life span forvarious machine parts. Note th at for automobile rear-axlegears, the life span of the most durable unit was aboutfour times the life span of the poorest unit, but for auto-mobile transmission gears the life ratio from the best tothe poorest was about 15 to I that is, childhood mor-tality is higher in automobile transmissions than in auto-mobile rear axles. Th e life span ratios given should not

262 SAE Journal Transactions), Val. 5 1 No. 7


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he taken literally because there are not enough test pointsin either curv e to define their limits. As the num ber oftest points is increased, the life ratio of the best to thepoorest will increase but the scatter will be greater fortransmission gears because the variability of stress resultingfrom end contact is greater.The percentage variation in life of machine parts willalso change as the test load or load range is changed.When tests are conducted at high load or high load rangeto produc e fatigue fa ilure after relatively few stress cycles,the percentage variation from the best to the poorest willbe less than if the test is conducted at a lower load toproduce fatigue failure after a relatively large number ofstress cycles. Thi s is shown in Fig. 29 in which the lifevariation of the bolts used to determin e Fig. 23 is recorded.Note short life and the small variation in life for the boltsthat were given low initial tightness (large stress range),and the greater life and relatively great variation in lifefor the bolts that were given high initial tightness (lowstress range ). Th e reason for this variable will becomeclear when we examine the form of scatter band of fatiguedata from a suficiently large number of fatigue tests.In the class of light machines where w eight must beconserved, it will probably never be possible to designmechanisms to withstand all the abuses that are encoun-tered in service. If a n airplane engin e, for example, shouldbe so sturdily designed that the shortest lived of each ofits numerous parts was failure-proof under all the abusiveconditions tha t may be experienced in service, the engin ewould be so heavy as to be impractical. As we learn howto increase the d urability of each machin e element, we willreduce but not eliminate failure hazards. Instead, progresswill demand that we take advantage of such improvementsby reducing the weight or by increasing the power output.

UFE THOUSANDS OF CYCLESFig. 29 Life variability of bolts for different stress ranges

Insufficient Test DataReliable life comparison of mach ine parts dem ands alarge number of tests unless the life difference is verygreat. It is obvious fr?m the mortality charts that havebeen shown that, on the basis of a few tests, the poorerdesign , ma terial, or process may rate highe r thaq.the betterJ c e I.' .LIIKIICf hlcti~l\, II\ hloore nd Kommers McCrow-Hill

lsoo Co.

design, mate rial, or process. Yet nowhe re in the literaturedo we find fa t~ gu e ata approaching even the minimumrequire me nts of reliability. T he reason is largely that mostof the investigators in this field, particularly in work onsteel, assume that we have no interest in data at any stressexcept the stress at which the specimen will endureindefinitely.In practical fatigue testing of machine parts, it should beobvious that comparisons of material, design, or processescannot be made unless the tests are run to failure and thecomparisons are m ade on th e n umb er of stress cycles eachwill endure. Thi s is true whether or not the part beingtested is require d to withstand , in service, a very largenum ber of stress reversals at m axim um load such as acrankshaft or a relatively small number of stress reversalsat max imu m load, such as chassis springs. Since all repre-sentative tests are made at loads that result in failure byfatigue, our interest lies not in the fatigue endurance limitwhere for steel, under most test conditions, life is infinite,but in that portion of the fatigue curve to the left of theknee whe re life is finite, that is, the sloping part of thecurve.

Fafigue Curve SlopeThe characteristics of the sloping part of the fatiguecurve have been obscured in most of the published S-Nplots (a) by never having enough test points and (b) bythe popular custom of plotting fatigue data on semi-logcharts. In the very few cases whe re published data containa considerable number of test points, we find that whenlots are constructed on log charts, the points tend to lieon a straight line instead af on a curved line as when theyare plotted on semi-log charts.Fig. 30 shows a series of fatigue specimens used byMoore and Kommers13 to determine the effect on fatigueof varying degrees of stress concentration.

Fig. 30 -Specimens used to study the effect of shape on endur-ance limit

The resulting fatigue curves, plotted on logarithmiccoordinates, are shown in Fig. 31 The authors comparethese specimens on th e basis of calculated stress at thefatigue endurance lim it; that is, the stress at the kneewhere the curve becomes horizontal. Howev er, as stated


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.Number o f Cycles f o r Fracturer Fig. 31 - S N curves for the specimens shown in Fig. 30

above, our interest is in the finite life region of the dia-gra m; tha t is, in the characteristics of the curve lying tothe left of the knee. Observe tha t as the notch severityof the specim en section is increased, the slope of the curv eincreases, an d tha t the curves, if e xtended leftw ard, tend tocross one another.Machine Parts Fatigue Curves

Fatigue curves of machine parts, no matter how wellfinished or how carefully rejected for detectable flaws,almost invariably show steeper slopes than are shown bywell-finished fatigue specimens and, therefore, presumablythe fatigue strength of a material as determined by idealtest specimens is not obtainable when that material isformed into a mach ine part. Permissible stress at thefatigue limit of a machine part may be less than 10 ofthe ultimate strength of the material, whereas laboratorytest specimen s may indica te 50 or mor e as obtainable.T h e difference in slope of the fatigue curves suggeststhat this characteristic promises a way whereby we mayeventually greatly improve our accuracy in determiningthe strength of mach ine parts. Th is is now being done inrating the load capacity of ball bearings, roller bearings,automobile transmissions, and rear-axle gears.The lines plotted in Fig. 31 are intended to representthe averages for the specimens tested. Note the widescatter of th e test points and the incre asing scatter of thepoints as the slope increases. No te alsc that, generally,the scatter decreases towa rd the left of the diagram. T h esignificance of this scatter is not apparent in the diagramdue to the limited number of test points, there being anaverage of only 12 failed tests for each type of specimen.

Slope Indicates Stress ConcentrationT he sca tter of test points is due to unavoidable differ-ences in test specimens no matter how carefully they aremade. Since these differences constitute varying degreesof stress concentration, the fatigue line representing thepoorest of a group of specimens should lie on a steeperslope than the fatigue line representing the best specimens.Th is is for the same reason th at the average slopes of thespecimens shown in Fig. 30 increase with the severity ofthe stress concentration as shown in Fig. 31.Se e Report of the Research Committee on the Fatigue of Metals.

STM Meeting June, 1941

Th e test points for any group of specimens would,therefore, be expected to lie within a scatter band divergingfrom th e region of h igh stress, an d will be of the ordershown in Fig. 32.If a sufficient num ber of specimens had been tested, andif the stress scale proportionality were the same for alspecimens, it is probable that the sloped lines in Fig. 31would all tend to converge toward a point in the vicinityof 1000 cycles and 90,000 psi, somewhat as indicated inFig. 32, in which t he fatig ue slopes of sp ecimens I and 4

CYCLES TO F ILUREr Fig. 32 Probable form of scatter band of specimens 1 and 4Fig. 30

of Fig. 30 are shown as converging bands rather thanlines. This region of intersection is suggested because theultimate strength of the material tested by Moore andKommers was approximately 95,000 psi and, obviously, ithe stress scale is correct for each type of specimen, theywould all have approximately the same strength at onstress cycle. T h e point of intersection would probably bat a considerable number of stress cycles because the ductility of the material permits adjustment of stress yield, thureducing the influence of local highly stressed points.Fo r very brittle mate rial, the intersection point of thefatigue curves for the type of specimens shown in Fig. 30would probably be near the ultimate strength and neareone cycle of stress.There are not now available sufficient data on any specimens to complete a gro up of fatigue diagrams to the regionof intersection. Kno wled ge of the characteristics of fatiguecurves at high stress would be valuable in industry sinceit would grea tly facilitate interpr etation of fa tigue tests onmachine parts. Such tests could e evaluated in terms othe slope of th e fatig ue curve, whic h wo uld also give clue to the actual stress, if desire d, in the part be ing testedT h e research committee of the A ST M recently sponsored a cooperative test program in which several laboratories conducted independent fatigue tests on identicamaterial (heat-treated SAE 4340) under similar test conditions. T h e results were reported in an A ST M researchreport14 from which the gr oup of plots shown in F ig. 3were taken. Note the wide disagreeme nt between thecurves from the several laboratories in the fatigue limit aswell as in the sloping part of the curves. W he n all of the59 individual failed points are plotted on a log-log chartas is shown in Fig. 34, we begin to see a semblance oforder, in that all of the points lie within a scatter band ofthe same converging form as is shown in Fig. 32.In passing, it is interesting to note that in Fig. 33 wefind nine test points at 85,000 psi load, which are thepoints plotted in the life expectancy curve, Fig. 28, to show264 SAE Journ al Transactions), Vol. 5 1 No . 7


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m Fig. 33 Semi-log plot of data reported by the ASTM ResearchCommi t tee on Fat i gue o f Meta l s

AM. S T E E L FO UNDl l

CYCLES TO F ILURErn Fig. 34 Log-log replot of da ta plo tted in Fig. 33

that the life variation of laboratory specimens is of thesame order as the life variation of gears and other machineparts.Published data on fatigue of metals contain numeroustests showin g the same general tre nd of increasing slopewith increasing- stress concentration w hethe r d ue to d iffer-ences in specimen shape, specimen size, mechanical work-ing of specimen surface, surface coatings, fillet radii,surfac e finish, or to variatio ns between identical speci-mens. As previously stated, this tendency tow ard con-vergence is-often nit apparent in the published curvesbecause the investigators have plotted their data on linearordinates and logarithmic abscissa, and always there areinsufficient test points. T h e following d iagram s copiedfrom published papers have, when necessary, been replottedfor the sake of uniformity on logarithmic coordinates tothe same scale as used bv Moore and Kommers in which2the stress scale is fou r times t he scale of stress repetition s.The slopes of the curves are calculated as the measuredhorizontal distance multiplied by the scale ratio divided by

(Abscissa X Scale Ratio)the measured vertical distance:OrdinateNote that this is the reciprocal of the slooe as ordinarilvused in engineering, but it is a more convenient form.

6 See ASTM Proceedings, Vol. 37, Part 11 1937 p. 199: FatigueProperties of Metals Used in Aircraft Construction a t 3150 and 10,600Cycles, by T. T. Oberg and J. B. Johnson.'See Mo d e r ~ r P l a s t i c s Vol. 19, Septentber, 1911, pp. 57.62 78:Mechanical Tes ts of Cellulose Acetate, by W. M. Findley.l7 See L ~ r j t f a k r t . F o r s c h t i r r n .Vol. 18, March 29. 1941, pp. 102-IOG:U k r d en Einfiiiss von Bohrungen mit .Gewinden und Kerbverzahnun-Ken auf di e Zeit- uncl Danerfestigkei: von I.eichtmetall.Flacl~stuben~ ~by H. Biirnhrim.

Oberg and Jol~nson report a comparison between pol-ished and notched s~ecimens.Fie. 2s. with results similard /to the exeperiments by Moore and Kommers, Fig. 31.Surface treatment of th e test specimens, other than the

CYCLES TO F ILUREFig. 35- S-N diagram for a metal used in aircraft construc-tion 134 steel

oo86

L4030mm L I Z E D AIJD tJNw 20 P O L I SHED

degree of smoothness, has a ma rked effect on fatiguestrength. Horg er and Maulbetsch2 compared norm al well-finished specimens with specimens that had been subjectedto a rolling operation which introduced compressive stressesin the surface layer with the results shown in Fig. I Sincethe rblled specimens were pre-stressed in compression, the

eu

subsequen t tens ion stresses du ring the test were reduced,as is shown in Fig. 6; hence the difference in the slope of

A NOTCHED. . .

the curves for the-two types of specimen s. Since this treat-ment would be ineffective in a tensile test, the lines should

10- I1 l o 2 l o 3 l o 4 to lo6 10

converge in the manner shown.When replotted on log-log charts, published fatiguecurves on other materials than steel exhibit the same ten-dency to converge toward the left and to increase theirslope as notch effects are increased.Findleyl onduc ~ed fatigue tests on cellulose acetatespecimens with the rcplotted results shown in Fig. 36. As

CYCLES TO F ILUREFig. 36 S-N dia gram for cellulose ac et ate

is usual, there are ncjt as many test points as are needed todefine the region of convergence but the trend is definite.Burnheim li reported fatigue tests on d uralumin (Fig.37 , and magnesiunl (Fig. 3 8 , in plain and variousnotched specimens. These rrplotted charts are more satis-factory than most published data in that the region ofconvergence is more clearly defined.Fig. 39 is the origin31 semi-log plot of t he fat igu e dataon magnrsiuln that is slio\vn in th e

j.o. almen_general motors - shot blasting to increase fatigue resistance

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