Calculation of Thermal-fatigue Life Based on Accumulated Creep Damage

7/27/2019 Calculation of Thermal-fatigue Life Based on Accumulated Creep Damage

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111 I 1 1 1 1 1 1 1 1 1 1 1 1 1 I., . . . . __

LOAN COPY: RETURN TOKIRTLAND AFB, N MEXAFWL IWLOL-2f

CALCULATION OF THERMAL-FATIGUE LIFEBASED ON ACCUMULATED CREEP DAMAGE

by David A. SperaLewis Research CenterCZeueZmd, Ohio

N A T I O N A L A E R O N A U T I CS A N D SP AC E A D M I N I S T R A T I O N W A S H I N G T O N , D . C . O C T O B E R 1 9 6 9


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TECH LIBRARY KAFB, NM

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1. Report No.NASA TN D-54 89

4. Ti tl e ond Subtitle

2. Government Accession No. .

CALCULATION OF THERMAL-FATIGUE LIF E BASEDON ACCUMULATED CREEP DAMAGE

7 . Authorls)David A. Spe ra

Lewis Research C enterNational Aeronau tics an d Space AdministrationCleve land, Ohio, 44135

9 . Performing Organization Name and Address

12. Sponsoring Agency Nome and AddressNational Aeronau tics and Space AdministrationWashington, D. C. 20546

15. Supplementary Notes

16 . Abstroct

3. Recipients Catalog No.5. Repor t DateOctober 19696 . Performing Organization Code

8. Performing Organization Report No.E-4950IO . Work Unit No.129-031 1 . Contract or Grant No.

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A method is presen ted fo r predicting the onset of the rmal-fatigue cracking in high-temperature components under service conditions.ties, l ife is calculated by considering two distinct failu re modes: (1) cyclic creep-rupture, using a modification of the well-known life-fraction ru le propo sed by Robinsonand Ta ira , and (2) conventional, time-independent, low-cycle fatigue, using empi ric alequation s of the Method of Uni ver sal Slopes develop ed by Manson. The method is illus-trat ed by using Glenny-type thermal-fatigue tes t data on the nickel-base alloy Nimonic 90.In 24 of the 28 ca se s analyzed, cyclic cree p-r upt ure was the dominant fai lur e mode.

Start ing from basic mater ial proper-

17 . Key Words ( S u g g e s t e d b y Au t h o t ( s ) )Thermal fatigueC r e e pLife calculation

18 . Distribut ion StatementUnclassified - unlimited


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C A L C U L A T I O N OF THERMAL-FATIGUE LIFE BASEDON ACCUMULATED CREEP DAMAGE

by D a v i d A . S p e r aL e w i s R e s e a r c h C e n t e r

S U M M A R YA method is presented fo r predicting the onset of thermal-fatigue cracking in high-

temperature components such as turbine blades and disks which a r e subjected to arb i-t ra ry , complex cycles of temp era tur e and load. It is proposed that thermal-fatigue lifecan be determine d solely from the basic mechanical propert ies of a mat eri al by calcula-ting liv es for each of two distinct and independent failu re modes: (1) cyclic creep-rupture, using a modifica tion of the well-known lif e-fraction ru le proposed by Robinsonand Tai ra, and (2) conventional low-cycle fatigue, using the empiri ca l equations of theMethod of Universal Slopes developed by Manson. Equations a r e pre sen ted in sufficientdetail t o completely define the analytical procedure.

The proposed method of life ana lysis is illustrated and evaluated by using data fromGlenny-type thermal-fatigue tests, as reported in the literature.disk specimens of the nicke l alloy Nimonic 90 were hea ted and cooled in beds of fluid-ized sand to produce c ra ck s si mi la r to those found on the leading and trailing edges ofturbine blades and vanes aft er service. In this study, temperatures , strains, st re ss es ,and finally lives a r e calculated fo r the disk specimens, which we re cycled under a varietyof tem per atu re and tim e conditions, with and without int ern al air-cooling . It is found in24 of the 28 ca se s analyzed that cyclic creep -rupture is the dominant failure mode.culated and observed lives gener ally a r e in good agreemen t.that ef fo rt s to predict and eventually improve the thermal-fatigue resis tanc e of a high-temperature alloy or component should be focused on the calculation and reduction ofcr ee p damage.

In these tests, tapered-

Cal-This investigation indicate s

INTRODUCTIONThis investigation w a s conducted to develop a method for pred icting the onset of

thermal-fatigue cracking in a high-temp erature component such as a turbine blade or


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disk. Th erm al fatigue is defined as the cracking of a mate rial primarily by repeatedheating and cooling which induc es cyclic inter nal t he rm al stresses. In addition, stresscaused by external mechanical loads may al so contribute to thermal-fatigue failure. Eathermal-fatigue cycle is a complex combination of changing stresses, strains, temperatu re s, and mate rial properties. Stres s, temperature , and tim e conditions may be suf-ficient to cau se both instantaneous plastic st ra in and time-dependent cr ee p str ai n duringeach cycle. Therefore, a gen era l method for calculating thermal-fati gue life mus t applt o a cycle in which variou s types of mat eri al behavior are present i n arb itr ary combinations. This study pres ents a method of life calculation which can be used to predict thestart of thermal-fat igue cra cki ng caused by a gene ral thermomechanical cycle.

A review of the re se ar ch which fo rm s a background fo r this investigation has beengiven in referen ce 1 . Some 30 references were discu ssed to t ra ce the development offatigue theory during the last 110 yea rs. In gene ral, the thermal-fatig ue theory proposein references 1 to 3 and furth er developed herein diffe rs from previo us work in one orm ore of the following ways:

than a modification of conventional roo m- tem per atu re fatigue.rat her than being limited to cycles which contain tensile mean st re ss .

temp eratu re, rat her than being limited to a specific idealized laboratory test such as isthe rma l strain-cycling.

ru ptur e under nonsteady conditions to account fo r the potentially benefic ial effect of e liminating net creep strain.life of variou s cycle par am ete rs such as maximum and minimum temperature s, ra te s ofheating and cooling, and hold periods.

P. W. H. Howe at the National Gas Turbine Es tablishmen t (England).published what c an rightly be te rme d the first complete thermal-fatigue analysis (ref. 4)The te rm "complete" ste ms from the fact that all sta ges of the g ene ral thermal-fatigueproblem we re tr ea te d (1) determining transient tempe ratu re distributions, (2) estima-ting the s tr es se s using creep data, and (3 ) obtaining thermal-fatigue life by using isothema l mechanical endurance data fo r slowly repeated cycles of tension. It w a s emphasizethat the impo rtant fact or in determining life w a s time-dependence of the sa me type asexpressed in cre ep data, rath er than a time-independent effect such as plastic deforma-tion.dire ctly to conventional cr ee p life, without recou rse to the cyclic mechanical test s usedby Howe.

(1 ) Thermal fatigue is considered to be primar ily a creep-rupture phenomenon rath(2) Creep-rupture is assumed to be a possible failure me chanism in any cycle,(3) The proposed theory applies di rectl y to the complete s er vi ce cycle of load and

(4)Modifications are presented to existing cumulative damage rules for creep-

(5) The proposed theory pred icts in quantitative te rm s the effect on thermal-fatigue

.In many ways thi s investigat ion is a continuation of pioneering work performed byIn 1962, Howe

Following th is hypothesis, the presen t investigation w i l l re la te thermal-fatigue lif

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Thermal and mechanicalproperties II

Method ofUniversal 4Slopes

Creep-ruptureproperties

Robinson-Tairatheory

fatigue life(tim e dependent)I IIIfatiaue lifeI I

Figure 1 - Proposed thermal-fatigue theory.

The method of a na lysis which w i l l be used in this investigation is illustrated in fig-u r e 1 .mechanica l cycle can be determined solely from the conventional mechanical and ther ma lpro per tie s of a ma te ri al by calculating lives fo r each of two distinct and independent fail-u r e modes: (1 ) cyclic creep-rupture , and (2) conventional low-cycle fatigue. As impliedin figure 1, cyclic creep-ruptur e is the most common failu re mode, particularly in thesh or t and intermediat e life ranges. Life in this mode is calculated from conventionalcreep rates and rupture tim es by a modification of the li near cumulative damage ru leproposed by Robinson (ref. 5) and Tair a (ref. 6). The modified Robinson-Taira theoryunifies two apparently different phenomena - cyclic thermal fatigue and static creep-rupture - without the us e of emp irica l constants derived from cyclic tes ts .

Conventional low-cycle fatigue is considered to be an alter nate failu re mode whichmay be dominant for longer thermal-f atigue lives. Low-cycle fatigue life is calculatedfro m conventional sho rt- tim e te nsi le prop ert ies by the existing Method of UniversalSlopes developed by Manson (ref. 7). Th is method re la te s cyclic life to the mechanicalst ra in range experienced by the mate ria l and is independent of tim e par am et er s such asfrequency. In its original for m, the Method of Universal Slopes applies only to fatiguein the absence of any cr ee p effects. However, simp le modifications have been proposedin the lit era tur e to extend its range of application to include high-temperature fatigue.These modifications a r e discussed herein and ar e particularly appropriate for thoseca se s in which it is impractical to make a complete s tr es s analysis.ficient detail to completely define the proposed analytical method.

It is postulated that the thermal-fatigue life resultin g fro m any thermal--

c

Th is study is presented in the following manner: First, equations are given in suf-Secondly, these equa-

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tions are used to calculate thermal-fatigue lives for comparison with Glenny-typethermal-fatigue data fo r the nickel-base alloy Nimonic 90. Thirdly, the calculatedand observed live s are used as a ba si s fo r drawing gen eral conclusions about thephenomenon of the rm al fatigue and the usefulness of the proposed life analysis meth-od.

tion during t he rm al fatigue of a turbine blade is often the s am e as the pr oc es s of rupt urduring conventional monotonic creep . Th is leads to a proposed method of li fe ana lys iswhich is evaluated by using the r es ul ts of thermal-fatigue tests obtained fr om the liter-ature.

In summary, th is investigation us es the hypothesis that the pro ce ss of c ra ck initia-

GLENNY -TYPE THERMAL-FATIGUE TESTINGGlenny-type thermal-fatigue testing r e fe r s to the us e of tapered-disk speci men s

which a r e alter natel y heated and cooled rapidly in beds of fluidized sol ids (ref. 8). Adiagr am of the fluidized-bed facility developed by Glenny and his as so ci at es is shown infigure 2. In this facility, the beds a r e used in pairs, one each for heating and cooling.Compressed air en te rs diffusion c hamb ers below each bed and pas se s upward throughperforated plates which support the actual beds. The beds are filled with ce ra mi c partcle s such as zircon sand. As the air pa ss es upward through the partic les they becomeleviated or "fluidized" under the action of drag fo rc es and develop a churning actionanalogous to that of a rap idly boiling liquid. Heating is accomplished by electric-resist ance elements im me rs ed directly in one bed, while cooling is achieved in the othebed by a water jacket. The la rg e heat capacity of the bed s and the churning action of th

I ----_ l ,r SpecimenTransfer actuators T- - - -! I

Heating elements--,' -'.-Air +'Perforated plate .-

-Waterjacket

Figure 2. - Diagram of fluidized-bed therm al-fatigu e facili ty developed byGlenny, et ai. (refs. 8 and 12).

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aI

L O . 754 - 0.094(0.70) (0.24)(a) Standard tapered disk (ref . 81.

I Cool ins a i r

0.015

0.200 (0.51)0.312 (0.79) 1 .-1.219 (3. IO) - -

(b)Co rew o l e d t ap e red d i sk ( re f. 12).Figure 3. - Thermal-fa t igue specimens. Dimensions ar e in inch es (cm).

par tic les a r e conducive to rapid heating and cooling. Also, the high the rm al inertia ofthe beds per mi ts ac curat e temp eratu re control over an extended period of time.

Glenny-type thermal-fatigue te st s were first conducted using a "standard" tapered-disk specimen such as the one depicted in figur e 3(a). During rap id heating and cooling,the thin periphery of the disk experiences f as te r tem perat ure changes than the bulkierco re section. The cor e constrain s the fr ee therm al expansion and contraction of the pe-riphery, inducing cyclic thermal st re ss es which eventually cause radial cra cks to appearat the thin edge, as shown in fig ure 3(a). Thus, fai lur e in a tapered disk occur s underconditions of (1) rapid tem perat ure range with respec t to both time and distance, (2) in-determinate uniaxial stress, and (3) high ra ti o of sur fac e to volume. Thes e conditionsar e a lso typica l of the leading and trailing edges of turbine blades and vanes. The stand-

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a r d d i sk w a s used extensively by Glenny et al. (refs. 8 to 10) and al so by Franklin, Helop, and Smith (ref. 11 ) for the ir c omparative study of th er ma l fatigue in 24 differenthigh-temperature alloys.

The central or "core" porti ons of so me turbin e blade s a r e cooled by air flowingthrough spanwise passages. Th is airflow ca us es a dec reas e in average section temperture and a corresponding i ncr eas e in creep-rupture strength with.which to r es is t centriugal loads. J. T. Roberts (ref. 12) conducted tes ts in a fluidized-bed facility to see ifcore-cooling would a ls o inc re as e thermal-fatigue life. Figure 3(b) shows how the standard tapered-disk specimen w a s modified to provide for core-cooling in these tests.

The genera l si ze of Glenny's standard disk was incre ased by 50 perce nt, while thecen tra l hole w a s further enlarged to receive a hollow support shaft with two concentricpassages. Air at 100' F (310 K) and 0.018 pound per second (8.2 g/sec) w a s conductedto the specimen through the inner passage, separ ated into 12 jets by radial holes in theshaft, impinged on the periphe ry of the ce nt ra l hole in the disk, and then exhaustedthrough the outer passage in the s upport shaft.

METHOD OF ANALYSISThe following descrip tion of t he analytical method contains so me deta ils which per -

tain specifically to the Glenny-type thermal-fatigue te st s describ ed in the previous se c-tion. However, the gen era l method is applicable to any high-tempera ture component suas a turbine blade, vane, or disk. The complete analyti cal proce dure con sis ts of fivesteps:

Step 1: Calculation of trans ien t tem pe ra tu re s throughout the specimen, using measured transient tem per atu res from r efe ren ces 12 and 13 to determine surfaceheat- trans fer coefficients between the sp ecim en and the fluidized beds

of step 1 and equations from re feren ce 14using the res ul ts of st ep s 1 and 2 , thereby obtaining the transient p eriph erals t r e s s e s

Step 4 Calculation of the cr ee p damage pe r cycle using the re su lt s of st ep 3, themonotonic cree p-r upt ure stren gth of the alloy, and a linear cumulative damagetheory, there by obtaining the number of cycles to failure in the c re ep mode

Step 5 Calculation of the number of cyc le s to fail ure in conventional low-cycle fa-tigue, using the range of s tr ai n calculated in st ep 2, the short-time tensile proer ti es of t he alloy, and an em pir ica l fatigue equation

Step 2: Calculation of tra nsi ent st ra in s at the perip hery of the disk using the res ul tStep 3: Calculation of the elast ic, plast ic, and cr ee p components of peri phe ral str a

The temperature, str es s, and stra in conditions at the perip her al sur fac e of the disk are

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used to calculate cr ee p and fatigue damage. Therefore, the te rm "calculated life" is de-fined here in as the theor etica l number of cycles re quir ed to cause failure of the surface.This w i l l be compared with th e observed number of cycles r equi red to initiate cracking ofthe periphe ry of the specim en.

Step 1 Calculation of TemperaturesIn a thermal-fatigue specimen or an engine component, two types of temp erature

data are usually required: (1) the gen er al distribution of te mpera tur e throughout thepart, with which to calculate total st ra in s during the cycle and (2) the temperature at theprobable points of fa ilu re in the part, with which to calculate local the rm al expansion andma ter ial properties. A method for calculating these temperature s is generally requiredbecause temperature measurements can normally be obtained only at a sm al l number ofpoints in the pa rt and often not d irec tly a t the probable points of failure. For these rea-sons, a gr ea t deal of effo rt has been given to the development of heat- transfer theory andprac tice which can be used to expand limited temp eratu re m easu reme nts into completetemperature distributions.

In thi s investigation, an existing computer code called TOSSA (acronym for Tr an s-ient or Steady-State Analysis) w a s used to calculate temperatures. The heat-transferanalysis w a s st ar te d by constructing the nodal diagram shown in figure 3(a). Th is dia-gra m co nverts the disk specimen into a lumped-parameter syst em in which all heat isstored at the node points (shown as black dots) or is conducted between nodes along con-ne ct er s which may be internal, surf ace, or bed connecters. The ra te at which heat istra nsf err ed along connecters or stored at nodes is determined by (1) the surfa ce heat-transfer coefficients, (2 ) th er ma l conductivity, (3) specific heat, (4)density, and (5 ) thedimensions of the nodes and connecte rs. Quantitie s (1) and (2) we re adjusted until thecalculated periphe ral and volume average tem peratures agr eed with measure d values asreported in refe renc e 13.erence 3.

Details of the trans ient tem pera ture a naly sis a r e given in ref-

Step 2: Calculation of StrainsThe calculation *of perip hera l e lasti c st ra in s w a s ca rr ie d on simultaneously with the

calculation of transie nt tem pe ra tu re s (step 1) by adding a new subroutine to the existingTOSSA code.peated in refer ence 3. The disk is assumed to be composed of a s e ri e s of concentric cy-lindrical layers of variable length which are assumed to remain cylindrical during heating

Equations for thi s subroutine were taken fro m referen ce 14 and ar e re-

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and cooling. Each cylin drica l lay er is assumed to be uniformly at its average temperature , s t re ss , and s t ra in states. It is assumed that the disk specimens are thin enough make t hi s one-dimensional analy sis acceptable.that a mor e complex two-dimensional ana lysis would be justified to deter mine th e effectaxial temperature gradients on the calculated peripheral str ain s.

Th e calculation of the elast ic, plastic, and c re e p components of s tr ai n is based onth e assumption that the calculated total st ra in s are approximately the sam e for a giventemp eratu re distribution whether or not plastic strain is ass um ed to occur. Thus, fo runiaxial state of s t r e s s such as that which exists at the disk periphery,

However, th is investigation indic ates

in whichE peripheral strain, percentt, m, T total, mechanical, and thermal, respectively

calculated total strain, assuming completely elasti c behavior, percent 0Also,

and

in which

-E m = E e + E + E CP 7

e, p, c elastic, plastic, and creep, respectivelya,T temperature, OF (K)RT

- mean coefficient of ther ma l expansion, percent/OF (percent/K)

room temperature, 70' F (290 K)Equation (la) defines the "method of st ra in invariance'' which was proposed by Men

delson and Manson (ref. 15) on the basis of their analy sis of s ev er al kinds of the rmoe lastopla stic problems. Relative constancy of total st ra in with and without plast ic flow indi-cates that, fo r therm al loads, st ra in s depend almo st completely on compatibility condi-tions which are geometric relations independent of the actual str es s- st ra in behavior.

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Step 3: C a l c u l a t i o n o f S t r e s s e sEquations (1) may be combined to give

-- c 0 - E - - c~(T RT)Po r

s = E E o E - c C - Z ~ ( T RT]Pin whichSE

peripheral stress, ks i (kN/cm 2)Young's Modulus, ksi /pe rcent (kN/cm 2 percent)The amount of instantaneous plas tic s tr ai n E is calculated by assuming ideallyplastic behavior at known minimum and maximum s t r e s s limits, so thatP

The minimum and maximum stresses are reach ed during the heating and cooling half-cycles, respectively. Therefore , combining equations (2a) and (2b) gives

'p, i- 1

10.

Smin < s. < smax

s. = sm inE i ' c , i - 'T, i 1 min---

or

'maxEi ' c , i - 'T, i 'i = Smax

--0,in which i is the time-increment index. The minimum and maximum s tr es se s a r e actu-ally the yield strength of the alloy at the te mp er at ur es which coincide with the minimumand maximum mechanical s train s. Th ei r exact values cannot be determined accurately inadvance because of the possibility that cyclic strain-hardening or strain-softening w i l l

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r a i s e or lower the yield strength, respectively.fatigue life is not sensitive to moderate v ariations i n yield strength, s o the conventionaltensi le-tes t val ues of yield stren gth are usually satisfactory.

Fortunately, the calculated therm al-

The creep strai n at time i may be expressed as

+c, i - c, i-1 2, dtJi- 1 (4in whichi c creep strain rate, percent/hrt time, hrThe creep rate is calculated by using the assumption that cr ee p ra te and ruptu re time a rinversely proportional for the sa me s tr es s and temperature.tion is consistent with creep-rate data on Nimonic 90 at relative high stress levels(ref. 1). The constant of proportion ality between the cr ee p ra te and the inv ers e of th erupture time is assumed to depend on the temperature, or

Th is simplifying assump -

in whichK known function of temp era tur e, per cen ttr time to rupture, hr

and tem per atu re by using the following equation developed in ref ere nce 1:In this investigation, the ruptu re ti me s tr a r e calculated from the values of s t re s s

in whichlog logarithm to the base 10

temperature-dependent param eter, interpolated from a table of valuescurve -fit constants, independent of temp eratur e

ATB, C , DTh e derivation of equation (6) is given in referen ce 1.10


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The integral in equation (4) is evaluated by using a standard RungerKutta technique,as explained in the appendix.

Step 4: Calculation of Cyclic Creep LifeThe calculation of accum ulated cr ee p damage is performec at the end of each time

increment A t by using th e following equations (see fig. 4):

and

C~cp, 1 at failurein whichq c cre ep damage per cyclet ltrThis is the so-called "linear damage rule" or "life-fraction rule" originally proposedby Robinson (ref. 5) to account fo r temper ature variations during conventional creep. Itw a s lat er modified by T ai ra (ref. 6) through the addition of the absolute-value sign to the

duration of 1 cycle, hrcreep-rupture time at 1 S I and T, the average stress magnitude and temp eratu re

during At, hr

I /-Smooth

- - - --- -

Time to rupture, t,

v)i;I 0p(JTime, tRobinson-Taira theory: creep damage, Ap, % CAt/tr,,Proposed modification: CAt/tr,,


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I I ,,,,,,,, 11 ,,.,,,,,...,,,,, I. ,,....-,. 111 ... 111 111 I,... . . . .. . .... .. . .- .....I

s t r e s s in ord er to give full weight to damage by compr essive s tr es se s. The role of compressive st re ss i n causing creep damage is discussed further in this report, and a tentative hypothesis on the subject is proposed.

Over the yea rs the simple linear damage rul e has been very useful in estimatingc reep life under nonsteady conditions of s t r e s s and/or tempe rature. However, the dam-age fractions A t& are ass ume d to be independent of the st ra in histor y of the ma teri al.Thus, no distinction is made between a te st with net s tr ai n (such as a conventional creeprupt ure test) and one without net s tr ai n (such as a strain-cycling test). A sim ple modifi-cation to equations (7) was proposed in re fer enc es 1 and 2 to account fo r s ome of the ob-se rv ed effects of net stra in.

s t ra in is potentially detrimental to cre ep-rupt ure life, because it can lead to'increasingt rue stress and tensil e instability. Then, fo r a given nominal s tr es s and temperature, iis assum ed that a smooth c ree p specimen w i l l have the shortest possible life, becausesuch a specim en experi ences the maximum amount of necking and, theref ore, net stra in.It is further assum ed that a mildly notched cre ep specimen can be used t o approximate thinc rea se in creep-rup ture life which can be expected i f net strain is eliminated. At theoret ica l stress-concentration fa cto rs of 2 to 4 many alloys experience notch-strengtheningRupture ti me s ar e often considerably longer than those for smooth specim ens at the samnominal stress and temperature. The triaxial st r es s stat e at the notched section severellimits necking and thereby substantially reduces net strain. It might b e said that the benfici al effects of reducing c re ep st ra in mo re than offset the detr iment al effect s of the moderat e st re ss concentrat ion at the notch. On the basis of these assumptions, the rupt uretime in equation (7a) may va ry between lim its as follows:

To derive this modification t o equations (7), the assumption is first made that net

e t -= ttr , s - r - r , nin which the subscripts s and n designate conventional cree p-ru ptu re data obtained witsmooth and notched specimens, respec tively . In th is way, upper and lower bounds on lifa r e calculated. In the ca se of actua l notch-weakening (t < t,, s) only the smooth rup-ture t ime is used. The thermal-fatigue specim ens a r e not notched, theref ore, the det ri-men tal effects of the str ess -concentra tion should not be included. Notch-weakening s im -ply indicates that any benefit to be deri ved from reducing net st ra in can be neglected.Equations (7a) to (7c) define what is called the q'modified Robinson-Taira theory'' fo r cal -culating cyclic cr ee p damage. The se equations depend only on the instantaneous values ofs tr e ss and temperature, and they can therefo re be applied to any cycle, however irregu-lar or intricate. Th is flexibility is part icu lar ly useful for the life anal ysi s of componentswhich have complex s er vi ce cycles.

The application of equat ions (7) is illustrated in figure 4. The s t r ess S is the abso-

r, n

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lute value of the average s t r e s s during the time increm ent A t . The rupture t ime s forsmooth and notched specimens are then dete rmined fro m equation (6) for this st re ss levelacting continuously at the average temperature during A t , and these quantities a r e des-ignated as t and t r ,n , respectively. The increment of cre ep damage during A t isthen assum ed to be g re at er than or equal to the fraction A t / tthe fraction A t / t r , s. The accumulated c re ep damage at failure is assumed to be 1, sothe theoret ical number of cycles , each with duration tl, which would cause cyclic c re epfailure is

r, s and less than o r equal tor, n

1orNf 2

0

and1orN, I

in which Nf is the number of cycl es to failure.

S t e p 5: C a l c u l a t i o n o f L o w -C y c le F a t ig u e L i feThe number of cycles required for conventional low-cycle fatigue failure is calculated

fro m the following empi ric al equations which com pri se the Method of Universal Slopes(ref. 6):

Ace = 3.5-UTS N i 0 . l 2E0.6 -0.6= 100 Dt Nf

in which13


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A str ain range, percentm y , i mechanical, elastic, and inelastic, respectively

number of c ycle s to fai lur e2ultimate tensile strength, ksi (kN/cm )

NfUTSE Young's Modulus, ksi/percent (kN/cm 2 percent)

tensile ductility, -1 n(l - RA/lOO)RA reduction of area, percentDt

Figure 5 ill ust rat es how equations (9) are used to predict low-cycle fatigue life for t

1Icc

aULnW-mccm.-m 1cImcmc

-.-P

Temperature,"F (K)-

10-1102 103 104 105Cycles t o fa i lureFigure 5. - Conventional fatigue resistance of Nimonic 90 ,predicted by Method of Univers al Slopes.

alloy Nimonic 90.cycles to failure at 1600' F, while line CD is the relation between the inelastic str ai nrange and cycles to failure. In this simplified analysis, the slopes of -0. 12 and -0.6 onfull logarithmic coordinates a r e used for-ll meta ls, which lead s to the designation "uni-versal" slopes. The sum of the ordinate s from lines AB and CD produces the line EF,allowing a prediction of life solely fro m the mechanical str ai n range. The analyst neednot determine the individual elas tic and inelastic components, which a r e often mo re diffi-cult to compute and subject to gre ate r e r r o r than the mechanical str ain range.

tively iwlependent of tim e effects. Cyclic frequency and cr ee p we re assumed to be var i-able s of minor importance. Thes e sam e assumption s a r e inherent when equations (9 ) a r eused to calculate high-temperature life. A s the test temperature is raised, a fatigue failure without any cr ee p effects beco mes mo re of an idealization. In refer ence 16, Manson

Line AB is the predicted relation between the elastic st ra in range and

Equations (9) we re originally developed to descri be fatigue behavior which is rela-

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discuss ed the effects of cr ee p on fatigue and proposed a sim ple modification to the Methodof Unive rsal Slopes which leads to a mo re realis tic prediction of high-temperature fatiguelife. A s a fi rs t approximation, various cre ep effects w e r e assu med to combine to reducehigh-temperature life to about one-tenth the value computed fr om equations (9). This"1Wo rule" w a s evaluated furt her in refere nce 17 and w a s found to provide a reasonablelower bound on life for a variety of alloys, tes t temper atures, and cyclic frequencies.Thus, equations (9) and the 1% ru le can be used t o predict cycle-dependent lives neglect-ing and including cr ee p effects, respectively.

For the Glenny-type tests, the stra in ranges are defined by the minimum and maxi-mum s tr ai ns which occur during the heating and cooling half-cycles, respectively. Whentemperatures vary during a cycle, it has been recommended that a conservative approachbe taken, namely that the tempera ture which leads to the sh ort es t calculated life be used.This procedure w a s followed in this investigation, and generally produced th e be st co rr e-lation between theory and expe riment of se ve ra l assump tion s which could be used to obtainan "equivalent" tem pera ture .

R E SU LT S A N D D I S C U S S I O NComparisons of calculated and observed thermal-fatigue lives a r e presented in thr ee

groups: (1) th er ma l fatigue of s tand ard disk specimens, (2 ) th er ma l fatigue of ov ers izedisk specim ens with and without core-cooling, and (3) combined res ults .

In or der t o perform the complete five-step analysis which w a s summarized in thepreceding sections, the following mat eri al properties w ere required:

(1) Th er ma l conductivity(2)Specific heat(3) Density(4) Mean coefficient of t he rm al expansion(5) Young's Modulus (dynamic)(6) Yield strength(7 ) Ultimate tensile strength(8) Reduction of a r e a(9) Creep-rupture strength(10)Creep s t r a in r a t eThe rat io of the cre ep- rat e par am ete r K in equation (5) to the t ensi le elongation

These quantities are given fo r Nimonic 90 in table I .was found to be 0.14 both at 1400' and 1800' F (1030 nd 1250 K). These two tempera-tur es re pres ent the ex trem es in elongation for this alloy, s o the sa me r ati o of 0.14wasassumed t o apply at all tempera tures, leading to the values of K shown in table I.

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TABLE I. - MECHANICAL AND THERMAL PROPERTIES O F NIMONIC 90(a) U. . customary units

Temperature, T, O Froperty~

16000 1000 1200 1400Ultimate tensile strength, UTS, ks:Yield streng th, S ksi

Y'Reduction of are a , RA, percentCreep-rate parameter, K, percentCreep-rupture temperature param-

eter, log(hr):Smooth, ANotched, AT, sT, n

1608642

3.8

15.0015.26

1518 43 1

1. 7

12.7012.96

1227814

1.6

656322

3.4

7.928. 18

10.4010.66

Creep-rupture time(S = stress, ksi), log(hr):

Notched, log(t,- ,Smooth, lodt,, s) 2A T,

AT.- 4.95 log(S) + 0.00660 S - 0.000277 S2- 3.68 lOg(S) - 0.0669 S + 0.000206 S

Young's Modulus (dynamic), E,ksi/percent 332 - 8 8 ( 2 )800 - 3 6 ( 2 ) 3800

Mean coeff icient of therma l expan-sion (from 70' F), 5,percent/OF

p .30 + 2. 40(&0) + 1.75(&)1 xThe rma l conductivity, k,

Btu-in. /ft2/hr/'F 5 6 + 9 1- 17-o ) (103Specific heat, y , Btu/lb/OF 1.108 + 0.0000244 TDensity, p , lb/in. 3 1. 296

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TABLE I . - Concluded. MECHANICAL AND THEFMAL PROPERTIES OF MMONIC 90

Property

2Ultimate tensil e strength, UTS, kN/cmYield strength, S kN/cm2Y'Reduction of area, FtA, percentCreep-rate parameter, K, percentCreep-rupture temperature parameter,

log(hr):Smooth, ANotched, AT, sT, n

Creep-rupture time(S = stress, kN/cm ), log(hr):Smooth, log(t )r, sNotched, log(t )r, n

2

Young's Modulus (dynamic), E,2W/cm /percent.__Mean coefficient of thermal expansion

(from 290 K), z, percent/KThermal conductivity, K, W/m/K

% _

.- .--Specific heat, y , J/g/K

3Density, p , g/cm

(b) SI unitsTemperature, T, K

1105942

3. 8

14.2014.66

9201045831

1. 7

11.9012.36

1030845414

1.6

9.2010.06

1140454322

3.4

7.127.58

~

125C

AT, - 4.95 log(S) + 0.00957 S - 0.000583 S2AT, - 3.68 log(S) - 0.0970 S + 0.000433 S2

9 . 5 + 131(-) 1000 + 2. 4 ( e ) 30000.452 + 0.000184(T - 256)8.20

Standard Disk SpecimensPreliminary.- calculations. - In figures 6 and 7, calculated and observed tempera tures

a r e compared for a sta nda rd disk specimen during rap id heating and cooling between70' and 1690' F (290 and 1190 K).tr an sf er coefficient s of 200 and 130 Btu per squ are foot pe r hour per OF (1130 and 740W/m /K) or heating and cooling, respectively .in reference 7. In orde r t o match observed tempera ture gradien ts in the disk, it w a snece ssary .to reduce the t her ma l conductivity to 70 percent of the nominal value given intable I. Th is reduced conductivity probably res ul ts from the lumped-parameter approxi-mations in the heat-transfer analysis.trans ient temp eratu res, assuming completely elastic behavior. The minimum and maxi-

Good agreement w a s obtained by using sur fac e heat-2 These are the same coefficients reported

Figure 8 shows the mechanical strai n cycle at the periphery as calculated from the

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-Calculated

Heating time, secFigure 6. - Calculated and observed temperatures d ur in gheati ng of standard disk specimen of Nimoni c 90. Tem-perature range, 70" F - 690" F (290 K - 1190 K) .

250

1250

zal-L3cmLlnEc 500

250

2 W O r - T r a n s f e r timeU !16

120 Periphery }Ref. 13

00 -Calculated

800

4 0 0 1 II 10-5

I n0 5 10 15 20 25 " 60Coolin g time, sec

Figure 7. - Calculated and observed temperatures d ur in gcooling of standard disk specimen of Nimonic 90.Temperature range, 1690" F - 0" F (1190 K - 90 K) .

u.-

Elapsed time , secFigure 8. - Calculated periph eral stra in in standard diskspecimen of Nimonic 90. Temperature range, 70" F * 1690" F(290 K Z 1190 K).

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mum values occur within a few seconds after the start of rap id heating' and cooling, r e -spectively. The mechanical s tr ai ns become asymptotic to zero with time because of theuniform tem perat ure conditions approached in the disk. During slow cooling, mechanicastrain is assumed to remain zer o at all t imes.rapid cooling is approximately twice that fo r rapid heating and slow cooling, which leadsto considerably different calculated fatigue lives fo r the two conditions.

Figure 9(a) illustrates a typical st res s-s tra in hyst eres is loop containing time-independent plasti c flow as well as cre ep str ain . The minimum and maximum stresseswer e obtained fr om the yield stre ngth of the alloy (table I) at temperatures of 1280' and

The st ra in range for rap id heating and

Heating T C o o l i n gr

NEz-...

VIVIWcI

-20-40-60

30

-10-M20F

m-u)

cI2-Er,a.-LW

,-Creep100 -k4-1690" F (1190 K h /'

(1160 K), 15 sec? A0I620" F 7780" FT-%- 70" F 1290 K )-- -Idealized plastic.flow I/ - /--100

(a) Wi th plastic flow. Tempe rature range, 70" F = 1690" F(290 K * 1190 K).

1290" an d 1690" F(975 and 1190 K ) 725cn. t

'--Increment ofmean stress

-25 - First cyclev I I

.1 .2 . 3I I I

0Periph eral strain, percentI50 ~~-.3 -. 2 -.1

(b)Wit hou t plasti c flow. Temper ature range, 1290" F f 1690' F1975 K 1190 K).Figure 9. - Typical stress -strain hysteresis loops for standarddisk specimens of Nimonic 90.

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780' F (970 and 690 K ), respectively. In this way, the cr it ica l extreme conditions in thecycle are consistent combinations of st re ss , strain , and temp eratu re. At the start ofheating, compressive peripheral stress is induced which quickly reaches the yieldstrength of the alloy and rema in s the re until 3 to 5 seconds have elapsed. Thereafter,ela sti c unloading to z e r o s t r e s s is accomplishe d in anoth er 12 seconds, followed by re -loading in tension. Cr ee p st ra in is continuously occu rring during both the co mpre ssiveand tensile portions of the cycle. However, mo st of the cr ee p st ra in occur s during thetensile par t of the heating half-cycle. The resid ual tensi le st r e s s resulting from the pre-vious compressive plastic s trai n is considerably reduced by cr ee p relaxation, as shownin figure 9(a).

During rapid cooling, per iph era l stress reache s and rema ins at the yield for 3 to 5seconds and then unloads t o a res idu al comp ressio n condition. Because of lower temperatures , creep during cooling is not significant. Successive cyc les rep eat the pat ter n of thefirst cycle because tensile and compressive inelastic s tr ai ns become, and remain, equalin magnitude.

A second type of st re ss -s tr ai n loop is shown in fig ure 9(b). In th is type, the temper-at ur e range during the cycle is not sufficient to cause instantaneous plastic flow. On thefi rs t cycle, m or e cre ep occurs in compression during heating than in tension during cool-ing. Therefore, the second cycle is not a duplicate of the first but contains higherstr ess es for the sam e strains. This increase in average stress with cycling continuesuntil tensile and compressive cr ee p st ra in s balance and th e cycle begins and ends at thes a me s t r e s s . For this reason, "elastic" cycles req uir e an iterative calculation pro ces swhich is not necessary when plastic strain is present.

fo r thermal-fatigue te st s on the standa rd disk specimen of Mimonic 90 alloy. The effectson life of the following pa ra me te rs a r e shown: (1 ) assumed yield stress, (2) durat ion ofthe heating half-cycle, (3) minimum temperature fo r a constant maximum temperature,(4) maximum temperature fo r a constant minimum tempe rature , (5) maximum tempera-tureefor a constant temperature range, and (6) heating and cooling rates. The observednumber of cycles to cra ck initiation w a s determined by averaging the cycle numbers of thelast inspection without cracking and the first inspection with cr acks . Most of the re su lt sa r e the average lives of se ve ra l specimens.

In figur e 10, the calculate d number of cycles which cause cracking is presented as afunction of the ass um ed yield s t r e s s fo r the cycle which w a s shown in figure 9(a).upper and low bounds of th e band a r e lives calculated from equation (8) by using the rup-tu re strength of smooth and notched specimens, respectively. As the assum ed yields tr e ss dec rea ses in magnitude, cree p damage during compression is reduced and tensilecr eep damage is increased. This occurs because higher tensile st re ss es a r e induced asthe plastic stra in in compression increases. At yield stresses le ss than 90 000 psi(62 kN/cm ), the i ncr eas e in tensile damage is gre ate r than the decrease in compressive

Final results. - Calculated and observed cyclic lives are compared in figures 10 to 1-The

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0 Ref. 8

\ Fatigue theory:lo3kWitho ut creep effectII I- 10% RuleY

strengthJ. II I I u80 90 100 11010 160 70Assumed yield strength, ksiI - I I - I40 50 60 70 - 80Assumed yield strength, kN/cmZFigure 10. - Effect of assumed yield strength oncalculated life. Standard disk specimen ofNimo nic 90; tempe rature range, 70" F(290 K 1190 K) . 1690" F

0 Ref. 9Fatigue theory:

,-Without creep effect

! I I d10 102 103 104101 Heating period, secFigure 11. - Effect of the du ratio n of th e heating period ontherm al-fa tigue life. Standard disk specimen of Nimonic90; temp eratu re range, 70" F 1690" F (290 k 1190 K ).

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lo 45.-cm.-.-.E 103.m,Yu0YIlu-al 102 'mmLli

Fatigue theory:

L JL L A00 400 600 800 1000 120000 Minimum emperature, Tmin, "F

300 430 500 600 700 800 900Min imum temperature, Tmin, KFigure 12. - Effect of mini mu m tempera ture on thermal- fatigue life.

I I I I - I ;I- I

Standard disk specimen of Nimonic 90; temperature range,Tmin f 1690" F (Tm in 2 1190 K).

Fatigue th eor y (rapidcooling only):With out creep effect

0 Rapid0 Slow

10 I I I 1 1 A1000 1200 1400 1600 1800 2000Maximum temperature, Tmax, "F

I I I I I 1900 1000 1100 1200 1300 1400Maximum temperature, Tmax, KFigure 13. - Effect of maximum tempera ture on thermal-fatigue lifewit h constant min im um temperature. Standard disk specimen of

Nimonic 90; temperature range, 70" F =Tmax (290 K ZTmax).

damage, causing a reduction in calculated lives. Thus, i f compression is assumed to beas damaging as tension, the calculated cyclic life is relatively insensitive to e r r o r s in theassum ed yield s t re s s of the alloy fo r cycles which contain instantaneous plastic s train.Of course, cycles without plastic s tra in ar e als o not affected by e r r o r s in yield strength.Thi s leads to the conclusion that an accurate knowledge of the cyc lic yield stre ngth of thealloy is not always necess ary. Therefore, the initial yield strength was used in all theremaining life calculations to establish minimum and maximum st re ss es in a given cycle.22


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lo4E 0 Ref. 9Fatigue theory:

10 I I I 11200 1400 1600 1800 Zoo0Maximum temperature, Tmax, "F

I I 1loo0 1100 1200 1300 1400Maximum temperature, Tmax, KFigure 14. - Effect of maximum temperatu re on therma l-fatigue life with consta nt temper ature range. Standard

disk specimen of Nimonic 90; emperature range,Tmax - 1440" F =Tmax (Tmax - 1060 K =Tmax).

Fatigue theory:yWit hou t creep effect

1400 1600 1800 2000 2200Maximum temperature, Tmax, O FI I I1100 1200 1300 1400Maximum temperature, Tmax, K

Figure 15. - Effect of compressive damage oncalculated thermal-fatigue l ife under slowheating and rap id cooling conditions.Standard disk specimen of Nimonic W:temperature range, 70" F =Tmax(290K =Tmax).

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Test resu lts from reference 8 are plotted in fig ure 10 at a yield st re ss equal to theinitial yield strength of the alloy. Thes e re su lt s ag re e with the calculated life range,demonstrating the reaso nabl enes s of the concept that th er ma l fatigue can be a form ofcreep-ruptur e. Cr ee p damage during the cooling half-cycle wa s negligible fo r these

' tests , so the assumed yield s t re s s in tension w a s not an important para mete r. The cal-culated low-cycle fatigue life fo r the se tests without c re ep effects w a s about 2500 cycles,which em phasizes the dominant rol e of cr ee p and the min or ro le of conventional fatigue incausing the thermal-fatigue cracks.

cycl es to failure. During these tests, the heat-transfer coefficient w a s always the sam e,so the r a t e of heating did not change. Thus, the st ra in limi ts we re approximately con-stant while the cr ee p st ra in varied. The data from refe ren ce 9 are an average of th re especimens and show a se ve re reduction in life as the heating period in cre ase s from 10 to100 seconds and no significant change for longer periods. It can be se en that the livescalculated with the lin ear cr ee p damage theory are in good agr eem ent with these data.The estimated fatigue life a gr ee s with the endurance of a 10-second immersion test.However, because longer imm ers ion tim es do not significantly change the str ai n rang efor the complete cycle, approximately the same conventional fatigue life would be calcu-lated for all heating times, which is inconsistent with the te st res ult s.

In figure 12, calculated and observed lives a r e compared for te st s in which the max-imum temperatu re w a s maintained at 1690' F (1190 K) while the minimum t emp eratu rew a s varied. Both heating and cooling were rapid. It can be see n that lives calculated bythe cr ee p theory ag re e with the experimental data, while fatigue theory greatly ov eres-tima tes the lives. The sh ar p change in calculated cr ee p life at a minimum temperatu reof 800' F (700 K) signifies the transition from cy cles-ith plastic st ra in to cycles withoutsuch strai n. It is apparent that e r r o r s in life calculation can resu lt i f the first-cyclest re ss es ar e used when plastic st rai n is absent. In general, la rg e changes in minimumtemp eratu re a r e required to cause significant changes in cyclic life.dominant rol e for the maximum temperatur e, which w a s held constant during this seriesof tests.at 70' F (290 K) and the maximum temp eratu re is changed.figure 13,temperature is increased fro m 1400' to 1700 F (1030 and 1200 K).per atu res above 1700' F (1200 K), lives rem ain approximately constant if cooling is rapidor they inc reas e somewhat i f the cooling ra te is slow.sul ts is predicted by the cr ee p theory, although the longer lives are overestimated.minor effect of cooling r a t e is al so predicted by this theory because most of the c reepdamage occu rs during the heating half-cycle f or maximum temp erat ures above 1600' F(1140 K).24

Figure 11 shows the effect of the duration of the heating half-cycle on the number of

-

This indicates a

Considerably different behavior is observed when the minimum temperature is heldData from reference 9 show a sharp d ecrea se in cyclic l ife as the maximum

Th is behavior is shown inFo r maximum tem -

The gen era l trend of the tes t re -The


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The fatigue theory indicates that, at maximum temperatures less than about 1460' F(1070K), thermal-fatig ue cr ac ks would f or m in accordan ce with conventional low-cyclefatigue experience. However, the indicated fatigue res is ta nc e applies only to tes ts withrapid cooling.leading t o calculated fatigue lives in exce ss of 10 cycles.

Figure 14 presents calculated and observed cycles to cracking for thermal-fatiguete s t s at a constant temp eratu re range of 1440' F (1060K). Comparis on with fig ure 13shows that the vari ation of cyclic life with maximum temperature w a s about the same,whether or not the temperature range w a s 1440' F (1060K). This conclusion w a s reachedexperimentally by Glenny and Taylor (ref. 9) and is reaffirmed herein on the basis ofcalculated lives, but only for l ar ge temp eratu re ranges.perature is a much mo re significant pa ram ete r in determining cyclic life than the tem-per atu re range when the range is la rg e enough to caus e plastic str ain. However, fig-u r e 12 shows that for c ycle s without plastic s train , calculated life is sensitive to changesin minimum temperature, and there fore tempe ratur e range, when the maximum temper -ature is held constant.

Slow cooling reduces the mechanical strain range by almost one-half,4

Apparently, the maximum tem -

To complete th is analysi s of thermal-fatigue te st s on standard disks of Nimonic 90alloy, figure 15 pr es en ts res ul ts fo r test cycles with rapid cooling but slow heating. Atthe end of the cooling half-cyc le, the per iph ery of the disk spec imen is in a stage of re -sidual compression at z er o mechanical stra in and room tempera ture . During the slowheating to the maximum temperature, the residual compressive st re ss relaxes while themechanical str ai n rem ain s approximately zero. In effect, t he s t r e s s e s are annealed outof the disk. During thi s slow heating period, significant c re ep damage is accumulated ifcompressive s t r es s is assumed to be fully as damaging as tensile st re ss of the samemagnitude, as state d by equation ("a). However, figure 15 shows that lives calculated byusing this assumption a r e an o rd er of magnitude sh or te r than those observed experimen-tally. On the othe r hand, i f damage is assu med to occur only during tension, agreementbetween experiment and theory is the same as that shown in figur es 10 to 14 for rapidheating and cooling. Th is behavior is very s imilar to that observed here at Lewis.Cyclic creep-rupture tests of the "square wave" type we re conducted on the cobalt-base alloy L-605 and on 316 stainless stee l. In this type of test, equal magnitudesof st re ss a r e applied alternately in tension and compression, and the s tr es s is held con-stant while the specimen cre ep s between fixed str ai n limits. The re su lt s of these testsare compared with monotonic creep-rupture time in figures 16(a) and (b). In the se fig-ures, nominal stress is plotted against rup ture time. If only the time spent in tension isplotted for the cyclic tests, the da ta points fall within or ver y near the range bounded bysmooth and notched monotonic strength. However, thi s ran ge significantly unde restima-t e s the total cyclic rupture time, particularly for the L-605 alloy.and 16 strongly indicate that compres sive Stress is not particularly damaging, at leastwhen the mechanical s tr ai n ra te is zero (conventional relaxation) or the stress r a t e is

Thus, figures 15

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60

50

u-...5

-m0.-E

30

25

.-v)

VIIzccn-mEz.-

Cyclic, square wave0 Tension t i m e only0 Totalt ime0

80

70

60

0

0

0

(a) L-605 at 1180" F (910 K).I

Time to rupture, hr( b ) Type 316 stainless steel at 1300" F (980 K).

Figure 16. - Comparison of cyclic and monotonic creep-rup tur e l ives.

ze ro (conventional creep).On the other hand, the anal ysi s of other test data indicates that compressive s tr es se s

can be damaging under other conditions of s t r e s s and st ra in rate.L-605 specimens wer e strain -cycled sinusoidally at constant temp erature, calculated andobserved lives agree d much better when compressi ve damage w a s included than when i tw a s neglected (ref. 2). Another stro ng indication of com pressiv e damage is shown in fig-u r e 17 . In a se r ie s of te st s reported in reference 18, Hastelloy X specimens were ther-mally and mechanically cycled in th re e ways: with tempera ture s and st ra in s in phase,with tempera ture s and st ra in s 180 degr ees out of phase, and isothermally. The in-phasete st produced tension at 1800' F (1260 K), while the out-of-phase t e s t s contained com-pression at 1800' F (1260 K ). Of course, the isot herm al tests had both tension and com-

For example, when

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10c -

0 1800" F (1250 K) 1300" F (980 K )Tension } 2 Compression0 1800" F (1250 K) 600" F (590 K)Compression 1 (Tension

Isothermal. 1800" F (1250 K )

Cycles to fai lureFigur e 17. - Cr eep damage in Hastelloy X fromcombined strain and temperature cyclin g(ref. 18).

pression at 1800' F (1260 K). As shown in figur e 17, the cr eep damage at failure, in-cluding all com press ive damage, approaches approximately the sam e value for all three3t e s t s as live s approach 10 cycles. At this life, st re ss es a r e low enough s o that conven-tional cr ee p and relaxation in compression a r e small.st re ss and stra in rat es occurring in compression.now proposed to determine i f compressive st re ss cause s cree p damage:

Apparently, equations (7 ) may r eq ui re further modification to account fo r the actualThe following tentative criterion is

During an increment of time, compressive st r e s s causes c ree p damage if and onlyi f the alg ebraic product of the stress ra te and the mechanical st rai n rate is greaterthan zero .

Thus, equation (7c) might be rew rit ten as4 t - = X tX t r , s - r - r , n

in which(-1 for s L o

for S < 0 and &, > 0for S < 0 and &ms

and S and km are the stress and mechanical st ra in ra te s, respectively. The tentative natuof th is hypothesis must be emphasized. Considerable testing would be requir ed to establish i

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validity. However, it does appear to be consistent with the high-temperature te st dataanalyzed to date by the modified Robins on-Taira theory.

Overs i ze Disk S p e c i m e n sThermal-fatigue tests on overs ize s pecim ens with and without core-cooling (ref. 12)

we re conducted with a nominal tem per atu re cycle of room te mp era tur e to 1690' F(1190 K) at a frequ ency of 1/8 cycle pe r minute. When core-cooling w a s used, it w a snecessary to raise the maximum bed temperature to 1725' F (1210 K) n ord er to main-ta in the per iph ery of the specimen at 1690' F (1190 K) during the steady-state per iods.

. The resu lts of the trans ient tempe rature a nalys is for the core-cooled condition a r eshown in figure 18. In this case, three sets of data we re considered: perip heral ,

E 750nEa,

500

250L

U-

i I0 10 20 30 40 50 60Heating time, sec

heating of core-cooled disk specimen. Oversize diskspecimen of Nimonic 90; temperature range, 70" F = 1690" F(290 K 1190 K) .Figure 18. - Calculated and observed temperatures d ur in g

volume-average, and cor e temperatures. Only two variable quantities were used to f i tcalculated temperatures to these data: the bed and cor e heat-tra nsfer coefficients. Agood fi t of the temperature data w a s obtained when the bed and co re coefficients were 210and 380 Btu pe r squ are foot per hour pe r OF (1190 and 2150 W/m /K), respectively.Some deviations in the transient volume-average temp eratur e and in the steady-state coretemp eratur e were noted. Also, i t w a s nec ess ary to reduce the boundary tem perat ure forthe heat-transfer analysis to 1710' F (1200 K) ro m the bed temp er ature of 1725' F(1210 K). This is not unrealistic because the bed tem perat ure near the specimen mayactually have been reduce d somewhat by the cooled shaft supporting the specimen. The

2

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-Incooled -,\E- -.2

-E - . 3zcqrr. -. 4a.L.-0) -.5Q I-J7-O. 15 percent' X Y Y// '- I I10 20 30 40. 0 Heating time, se c

Figu re 19. - Calculated periphe ral strains, wit h and withoutcore cooling. Oversize disk specimens of Nimon ic 90; tem-perature range, 70" F 1690' F (290 1190 K).sa me bed coefficient w a s used fo r the disk without core-cooling, but with the bed temp er-a ture of 1690' F (1190 K).

Figu re 19 shows the variatio n of calcu lated per iph era l st ra in during the heating half-cycle: In 4 seconds, both s tr ai n cycl es reach minimum v alues with only minor differ-ences in s t rai n or temperature. Thus, core-cooling ha s had little effect on the tra nsi entpa rt of the cycle. The major difference in peri phera l st ra in between the core-cooled andthe uncooled cycles is found during the steady-st ate period. In the uncooled disk, a uni-form temperature is eventually reached throughout the specimen, and the mechanicalstr ain therefore approaches zero. In contrast, the core-cooled disk has a temperaturegradient even in the steady-st ate condition, and the hotter periphery susta ins a steadycompressive strain of about 0. 15 percent a t the end of the tr ans ien t period.shown in figure 20. In this figure, the compressive yield strengths a r e assum ed to maintain their first-cy cle values of 82 000 ps i (56 kN/cm ). No difference in the compressivestresses with and without core-cooling is observed for the first 10 seconds of the heatingua l comp ressi ve st ra in induced in the periphery by core-cooling caus es a significant r e-duction in tensi le stress. Without core-cooling, tensile stress reaches a peak va lue of31 000 ps i (21 kN/cm ), followed by considerab le relaxation. On the other hand, cor e-cooling lim its the tensile st re ss to values le ss than 16 000 psi (11kN/cm ) with very littlre axation.

Figures 21(a) and (b) show the res ul ts of the thermal-fatigue tests on the overs ize

The effect of thi s compressive str ain on the s tr es s cycle for the core-cooled disk is2

period. However, a maj or difference exists in the residual tension stre ss es . The resid

2 2

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-60

,-..-Uncooled--c'Lore-cooled

Calculation of Thermal-fatigue Life Based on Accumulated Creep Damage

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Transcript of Calculation of Thermal-fatigue Life Based on Accumulated Creep Damage