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APPLtCATION OF

F UeE CY"MODIFIED LIFE APPROACH TO

THE LOW-CYCLE FATIGUE BEHAVIORiJw

OF TYPE 304 STAINLESS STEEL

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Distribution Category:LMFBR Fuels and MaterialsEngineering and Development(UC-79b)

AN L-76-40

ARGONNE NATIONAL LABORATORY9700 South Cass Avenue

Argonne, Illinois 60439

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APPLICATION OFFREQUENCY-MODIFIED LIFE APPROACH TOTHE LOW-CYCLE FATIGUE BEHAVIOR

OF TYPE 304 STAINLESS STEEL

by

P. S. Maiya and S. Majumdar

Materials Science Division

May 1976

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . .

I. INTRODUCTION . . . . . . . . . . . .

II. LIFE PREDICTIVE PARAMETERS . . . . .

III. PREDICTION OF LOW-CYCLE FATIGUE DATA

A. Prediction of Continuous CyclingWaveform) Fatigue Data... ..

B. Prediction of Hold-time Data .

IV. DISCUSSION OF RESULTS . . . . . . .

V. CONCLUSIONS . . . . . . . . . . . .

REFERENCES . . . . . . . . . . . . . . . .

(Triangular

.. . . . . .

Iii

Page

1

1

3

5

5

5

8

14

15

LIST OF FIGURES

No. Title Page

1. Variation of Life Predictive Parameters with Frequency for

Type 304 Stainless Steel at 593*C . . . . . . . . . . . . . . . . 4

2. Series of Scanning-electron Micrographs Showing Effect of StrainRate on Fracture Appearance in Type 304 Stainless Steel...... 4

3. Comparison of Continuous Cycling Fatigue Data with CalculatedLife Using TFM Constants . . . . . . . . . . . . . . . . . . . . 6

4. Comparison of Continuous Cycling Fatigue Data with CalculatedLife Using IFM Constants . . . . . . . . . . . . . . . . . . . . 6

5. Comparison of Continuous Cycling Fatigue Data with CalculatedLife Using MFM Constants . . . . . . . . . . . . . . . . . . . . 6

6. Comparison of Hold-time Fatigue Data with Calculated Life

Using IFM Constants . . . . . . . . . . . . . . . . . . . . . . . I

7. Comparison of Hold-time Fatigue Data with Calculated Life

Using MFM Constants . . . . . . . . . . . . . . . . . . . . . . . 7

8. Plot of Frequency-modified Plastic Strain Range vs FatigueLife for Type 304 Stainless Steel at 593*C . . . . . . . . . . . 8

9. Series of Scanning-electron Micrographs of Fracture SurfacesShowing Effect of Hold Times in Tension and Compression andHold Times in Both Tension and Compression . . . . . . . . . . . 9

10. Prediction of Compressive and Symmetric Hold-time Data withTFM Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 10

11. Prediction of Compressive and Symmetric Hold-time Data withMFM Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 10

12. Comparison of Damage Resulting from Tensile Hold TimeEstimated from Frequency-modified Life and IncrementalDamage Approaches . . . . . . . . . . . . . . . . . . . . . .. . 12

13. Sawtooth Waveforms . . . . . . . . . . . . . . . . . . . . . . . 13

LIST OF TABLES

I. Fatigue Life Predictive Parmeterb . . . . . . . . . . . . . . . 5

11. Expected Results from Incremental Damage Approach ior SawtoothWaveform Acp a 0.007, Type 304 Stainless Steel, T " 593*C . . . . 14

iv

APPLICATION OF FREQUENCY-MODIFIED LIFE APPROACH TO THELOW-CYCLE FATIGUE BEHAVIOR OF TYPE 304 STAINLESS STEEL

by

P. S. Maiya and S. Majumdar

ABSTRACT

The application of the frequency-modified life equation tofatigue life prediction has been critically examined using theextensive fatigue data generated for Type 304 stainless steel at1100*F (593*C) under a variety of cyclic-loading conditions.The paramet.?rs that enter into the frequency-modified life equa-tion vary with strain rate and show a transition coinciding withthe frequency of cycling at which a change in the fracture appear-ance from predominantly tiansgranular to predominantly intergranularfailure mode or vice versa occurs. The accuracy in life predictionis improved when the effect of strain rate on life-predictiveparameters is considered. It is shown how the effect of compres-sive and symmetric hold time on fatigue life can be taken intoaccount. A comparison between the frequency-modified life approachof Coffin and the damage-rate approach recently developed byMajumdar and Maiya is also made to show the importance of wave-shape effects on low-cycle fatigue life.

I. INTRODUCTION

The low-cycle fatigue behavior of many materials at room temperature canbe described by the well-known Coffin-Manson relationshipl 2 expressed as

N' Ar - C, (1)

where a and C are constants, Atp is the plastic strain rage, Nf is the numberof cycles to failure, and L is related to ductility. The importance of plasticstrain in fatigue failure was recognized when Eq. (1) was proposed. However,at elevated temperatures ( 0.4 TM, where TM is the absolute melting tempera-ture), plastic strain alone does not provide a sufficient description offatigue because the time-dependent effects (e.g., creep and other effectsassociated with an active environment) become important. The time-dependenteffects play an increasingly important role when the cyclic strain rate of thefatigue tests is reduced and hold time are imposed during cycling. Colesand Skinner' included time dependency through frequency in the following re-lation:

k. tf W constant, (2)

where v is the frequency of cycling, tf is time to failure, and vk tf is con-stant for constant Atp. The parameter It changes from unity in the fatiguedomain to less that, unity in the creep sensitive region. To incorporate

2

time-dependent effects at elevated temperature, using Eqs. (1) and (2),Coffin proposed the frequency-modified Coffin-Manson relation given by

rNfvk-1) s AE C2

or

N - , (3)f AC

where C2 and B are constants. The detailed description of Eq. (3) and itsapplication to fatigue-life prediction have been discussed extensively byCoffin in a series of papers.5-8 Also, a frequency-modified life relation-shipa exists between elastic strain range and fatigue life, which we will notdiscuss in the present report inasmuch as it is primarily applicable to high-cycle fatigue.

In strain-controlled low-cycle fatigue tests involving continuous cy-cling, the frequency and strain rate are related by

vWft Ep (average) (4)2t pA

where Ac is the strain range, E is the strain rate, and the subscripts t andp refer to total and plastic strains, respectively. However, when hold-timeperiods are imposed in each cycle at constant total strain, the stress relaxeswith time and the plastic strain rate decreases continuously with time. Thedamage occurring in the material during hold time depends on the plasticstrain rate (and also depends on the plastic strain, which remains approxi-mately constant during hold time). 9 Furthermore, it depends on whether thehold-time period is introduced in tension or compression or both. For stain-less steel, it is observed that compressive and symmetric hold times produceless damage than tensile hold only. 0 Consequently, the use of frequencycalculated without regard to the details of wave shape* in Eq. (3) leads toconservative life prediction for tests with symmetric and compressive hold-time periods and nonconservative life prediction for tests with tensile holdonly, as has been shown in previous investigations.

1 0-1 .

Recently, a damage-rate equation has been proposed for creep, fatigue,and creep-fatigue interaction.I The damage-rate equation can be used tocompute the incremental damage along the deformation path. The approach hasbeen successfully applied to quantitatively analyze the extensive lw-cyclefatigue data generated for Type 304 stainless steel at Argonne NationalLaboratory (ANL) under a variety of cyclic-loading conditions. One of the

*Recently Coffin (private communication) has proposed a frequency-separationtechnique to take into account the wave-shape effects on fatigue life. Thepresent paper does not concern this method, which is currently being investi-

Cated by Coffin.

3

results that emerged from this study 9 is the rather weak dependence of fatiguelife on the wave form of the strain cycling with tensile hold times in therange from l to 600 min. Also, the Coffin-Manson frequency-modified lifeequation for the case of continuous cycling can be derived from the damage-rate equation. In view of th's observation, it was decided to criticallyexamine the constants that enter into Eq. (3) and to determine the extent ofcapability of the frequency-modified life approach to predict hold-time datagenerated with tensile hold time, compressive hold time, and symmetric holdtime (where tensile hold time equals compressive hold time in a cycle). Also,using the incremental damage approach, certain limitations of Eq. (3) as wellas conditions under which wave shape effects become important are presented.

II. LIFE PREDICTIVE PARAMETERS

At ANL, a large body of elevated-temperature low-cycle fatigue datahave been generated for Type 304 stainless steel (Heat 9T2796) for variousloading conditions. Prior to fatigue testing, the hourglass-shape specimenswere solution annealed at 1092*C for 30 min and aged at 593 C for 1000 h.The tests were done in axial strain control using hydraulically actuated

fatigue machines and the testing procedure described in detail by Slot et al. 1 3

For the purpose of the present discussion, we will consider only the data at1100*F (593*C), inasmuch as the data obtained at this temperature are moreextensive than those at other temperatures and are thus amenable to a more

rigorous testing of the data predictive methods.

The constants C2 , , and k were obtained by a least-squares it of thecontinuous cycling fatigue data to Eq. (3). Only the fatigue data obtained at

t from 4 x 10-2 to 4 - 10-6 s-1 and Act between 0.5-2.0% were used. Thevalues for Atp were obtained at half the fatigue life. The regression analysiswas performed so that the values of constants were obtained over different fre-quency ranges. When a geometric mean value was assigned for the frequencyrange (used in determining the constants), it was found that the predictiveparameLers vary with frequency in a systematic manner as shown in Fig. 1.All the parameters show a gradual transition with frequency. In all cases,it appears that the values vary more slowly with frequency both at the higherand lower end of the frequency spectrum. The transition in the variation ofthese constants with cyclic frequency coincides approximately with thetransition in failure mode from intergranular to transgranular or vice versa.Experimental evidence for this comes from an examination of fatigue fracturesurfaces and the series of scanning-electron micrographs shown in Fig. 2.The transition from transgranular to intergranular failure occurs approxi-mately at frequencies ,0.1 :pm, which is consistent with the transition inthe values of the constants observed. Three sets of constants were used inlife prediction, and the values are listed in Table I. The constants deter-mined from the data at ft between 4 x 10-2 and 4 10-3 8-1 will be referredto as transgranular failure mode (TFM) constants and the values obtained atit between 4 x 10-5 and 4 x 10-6 s-1 as intergranl.r failure node (IFN)constants. The values of the constant. detcrrir ' aver the entire spectrumof t (4 x 10-2 to 4 x 10-6 -1) will be i:entifiod as mixeu failure mode(MFMI constants.

C2

0.9 " kI

0.8' -

--

. . . . . Ial

.1 ' l .11.0

FREQUENCY. cpm

10 1.

Fig. 1. Variation of Life Predictive Parameterswith Frequency for Type 304 Stainless Steel at593*C. Neg. No. MSD-61840.

00 (c)E4 10-5 -I

J rr

-N

(d) Ott4 x 10-6 s1I

501L

Fig. 2. Series of Scanning-elect:on MicrographsShowing Effect of Strain Rate on Fracture Appear-ance in Type 304 Stainless Steel. T = 593*C,

Att = 1%. Neg. No. ANL 306-75-230.

0 20.o

a i i l i a i i i i l l

*

5

TABLE I. Fatigue Life Predictive Parameters

Type of Constants C2 8 k A m

Transgranular FailureMode Constants 0.303 0.475 0.866 15.42 1.2

Intergranular Failure

Mode Constants 1.03 0.641 0.614 0.45 0.93

Mixed Failure ModeConstants 0.39 0.535 0.74 5.62 1.13

III. PREDICTION OF LOW-CYCLE FATIGUE DATA

Using the set of parade ''sted in Table I and contained in Eq. (3),the fatigue life was calculat d :1, -ompared with the experimentally deter-mined fatigue life. The root-..i. . uare error (RMSE) is used as a measureof predictive capability for the appropriate case. The RMSE is defined as

N

RMSE - IZ [in Nf (calculated) - In Nf1 (experimental) (5)

1

In the plots of calculated versus experimental fatigue life discussed inSect. IIi.A and B, deviations of a factor of two from the calculated livesare shown by means of dashed lines.

A. Prediction of Continuous Cycling (Triangular Waveform) Fatigue Data

Although the waveforms chosen for continuous cycling are triangular inall cases, the rate and extent of fatigue-damage accumulation and the param-eters C2, 8, and k depend upon the cyclic strain rate. Therefore, it isnecessary to use the appropriate values for the constants in Eq. (3) toachieve reasonably good life prediction (prediction of life within a factorbetter than two). This is demonstrated by plots of calculated versus observedfatigue life in Figs. 3-5 using the three sets of constants. It is clear thatthe TFM and IFM constants determined over a narrow range of frequencies yieldpoor results, whereas the use of MFM constants results in a fairly good pre-diction (Fig. 5). Therefore, even for the simple case of triangular waveshape prediction can be unduly conservative or nonconservative if the appro-priate values for the constants are not used.

B. Prediction of Hold-time Data

We now consider fatigue test results obtained at ANL for Type 304 stain-

less steel under loading conditions that involve various wave shapes. Inone type of test, in addition to cycling at a given strain range with zeromean strain, a predetermined period of hold time at constant total strain is

0

.W(

" " - . 1 0 T

a

10o 10 10" b0

LJ -

I

10' I L) I U,l: tr l.T. 0e' T1 q, r,' -r If(. CTCU

Fig. 3. Comparison of Continuous Cy-cling Fatigue Data with CalculatedLife Using TFM Constants. RMSE -0.50, Type 304 stainless steel.T - 5936C ,it a 4 x 10-2 to4 x 10 s- . Neg. No. MSD-62315.

C-0.39, BETA-C.53, K-0.74

-

-i-

-/

I'../

'7

V4/b

a

u0- so, tocW ITRa rwyle LR, Crt.coL

.4

Fig. 5. Comparison of Continuous Cy-cling Fatigue Dista with CalculatedLife Using MFM Constants. RMSE0.25, Type 304 stainleab steel,T- 593C, It u 4 x 10-2 to4 10- s-1. Neg. No. NSD-62312.

Fig. 4. Comparison of Continuous Cy-cling Fatigue Data with CalculatedLife Using IFM Constants. RMSE -0.56, Type 304 stainless steel,T -593C, t - 4 x 10- to4 x 10 1. Neg. No. MSD-62313.

imposed both at the maximum tensilestrain and maximum compressive strainlimits. In symmetric hold-time tests,the holi times in tension and compres-sion are equal, and the shape of thestrain cycle is trapezoidal. Also,fatigue tests have been run with onlytensilp hold time imposed in each cycleor compressive hold time or vice versa.The tensile hold-time tests have beencompleted with hold times ranging from1 to 600 min. In the compressive andsymmetric hold-time tests, the holdtimes varied from 1 to 4 min. Duri'agthe hold time at constant strain, thestress relaxes, which results in addi-tional plastic strain. In u few tests,the tensile stress was held constantduring the hold-time period of eachcycle, and the specimen was allowed tocreep until a predetermined amount oftotal strain was rcached. When Eq. (3)is used for life prediction, the wave-shape effects are generally ignored

6

- ETH-ll. lI, K-0.61

10'

"-1

--. Inc Kao Ti I

7

so that the average frequency vav is fined as

1v -

v cont + Hold(6)

where Tcont is the time spent in continuous cycling and T Hold is the hold-time period. In the cyclic creep tests performed at ANL, the frequency variedfrom cycle to cycle so that an average time period for each cycle is estimatedby dividing the total time to failure by the number of cycles to failure. Thefrequency-modified life equation together with IFM and M M constants yieldreasonably good prediction of the hold-time data (so far generated at ANL forone heat treatment) within a factor of two (Figs. 6 and 7). Another point tomake is the slightly improved accuracy in life prediction using IFM constantscomp:.red with the prediction by means of MFM constants.

r-:.C3, BETA-0.641, K-0.614

Ai

U

Q

.p(!'wi4,1 .ra,,, LV r[, Ciac

Fig. 6. Comparison of Hold-timeFatigue Data with CalculatedLife Using IFM Constants.RMSE - 0.36, Type 304 stainlesssteel, T - 593*C. Neg. No.MSD-62319.

10,[DN iIFTk.T r"TIQ Lire Uvr -

Fig. 7. Comparison of Hold-timeFatigue Data with CalculatedLife Using MFM Constants.RMSE a 0.41, Type 304 stainlesssteel, T * 593*C. Neg. No.MSD-62314.

Another way in which the frequency effect on fatigue life is expressed7'8

is by constructing plots of frequency-modified plastic strain range versusfatigue life. Equation (3) is rewritten as

(k-l) 0 C2 Nf B9 (7)

where the term on the left-hand side is defined as the frequency-modifiedplastic strain range. When the IF1M constants and Eq. (7) are used, a plot isconstructed to illustrate that wave-shape effects do not show up signiti-antlyin life prediction, as shown in Fig. 8. The solid line is the calculated line,and the symbols are the experimental points; good correlation exists betweenthe two.

"*

*IS IM t~hilOm .0A0"-60 "lb rmr~l .0.0

9 ~~ .. 6SO 0i1% ?1buI) .00a. -r IMCII 1(iiOD.

"a

" " " * It 01IC IO HU

" - 60 "l1b TaS I O. PQOI" " 00142 TENSIi O. "oa

- 60 aiM M1N51021 M".0 -COPW~rIlc ae0.0L

10"

C-0.-4 3T-0.53, 1(-.74

N C]

u

J

1

V

8

TI. 30J1 T1IP&MS ST(LL

Fig. 8. Plot of Frequency-V modified Plastic Strain

Range vs Fatigue Life forType 304 Stainless Steelat 593*C. IFM constantswere used in determiningsolid line. Symbols indi-cate experimental points.Neg. No. MSD-62316.

101 0Cl~ FI , 1C ., C C C

IV. DISCUSSION OF RESULTS

The low-cycle fatigue data generated at ANL for Type 304 stainless steelat 1100*F (593*C) for a variety of cyclic-loading conditions can be predictedwithin a factor better than two from continuous-cycling data using thefrequency-modified life equation. However, a trend does exist, as has beennoted by several other investigators, 10-1 2 that the life prediction is non-conservative for tensile hold-time data and conservative for compressive andsymmetric hold-time data. These results can be examined in light of the ex-perimental observation that, for Type 304 stainless steel, the tensile hold-time period produces more damage than compressive or symmetric hold-timeperiods introduced per cycle. Microstructural evidence is presented by aseries of scanning-electron micrographs of fracture surfaces for short hold-time periods involving a few wave shapes (Fig. 9). It is clear that tensilehold time as short as 1 min produces both transgranular and intergranularfracture, whereas symmetric and compressive hold times of the b4me durationproduce transgranulaz fracture surfaces. These observations are consistentwith the work of Cheng and Diercks. 14 Similar results are observed for the2-min hold-time tests (Fig. 9). It should also be mentioned that compressivehold time as long as 4 min also produces well-defined fatigue striations.15

Inasmuch as continuous cycling at strain rates >10 s-l also causes trans-granular fracture mode [well-defined fatigue striations visible on thefracture surfaces of specimens (Fig. 2)), it should be possible to predictfatigue life (with TFM constants) when compressive and symmetric hold-timeperiods are imposed. This is demonstrated in Fig. 10, and a comparison ofFigs. 10 and 11 shows how the accuracy in life prediction is improved whenthe variation of predictive parameters with frequency is considered. However,longer compressive and symmetric gold times may be more damaging, resultingin intergranular fracture, and, furthermore, the deformation behavior mayalso be influenced by strain-rate effects. Therefore, additional tests thatinvolve longer compressive and symmetric hold times may impose a limit uponthe extent of prediction by means of TFM constants.

(o) ZERO HOLD

(c) Iin COMPRESSION HOLD

(e)2 min COMPRESSION HOLD

(b) I rn TENSION HOLD

(d) Imin SYMME TRIC HOWD

(d) 2 min SYMMETRIC HOLD3O&

-4

Fig. 9. Series of Scanning-electron Micrographsof Fracture Surfaces Showing Effect of HoldTimes in Tension and Compression and Hold Timesin Both Tension and Compression. Type 304stainless steel, it n 4 x 10-3 s-1, Ac - Itand T - 593*C. Neg. No. ANL 306-76-11.

9

10

Fig. 10. Prediction of Compressive Fig. 11. Prediction of Compressive

and Symmetric Hold-time Data with and Symmetric Hold-time Data with

TFM Constants. Tyr.., 304 stainless MFM Constants. Type 304 stainless

steel, T w 593%C. Continuous- steel, T a 593*C. Continuous-

cycling data obtained at et between cycling data obtained at it between

10-' and 10-4 s-1 are included, 10-2 and 10-4 s-1 are included,

RMSE " 0.18. Neg. No. MSD-62317. RMSE - 0.36. Neg. No. MSD-62318.

From what has been said so far, the low-cycle fatigue data generated

with tensile hold times. varying from l to 600 min, with symmetric and com-

pressive hold times <4 min, and cyclic creep data for Type 304 stainless steel

(at 593*C) can be predicted within an accuracy of 30-40% using the Coffin-

Manson frequency-modified life equation. In the following discussion, we

would like to show why the frequency-modified life approach works for the

cyclic loading variables (except rising mean strain--rate effects) considered

at ANL..

In an earlier report,9 an incremental damage (ID) approach for creep,

fatigue, and creep-fatigue interaction was discussed. Basically, the ID

approach assumes a failure criterion that involves the growth of an initial

microcrack length so to a critical crack length ac and proposes a damage-rate

equation

aT~cri |e |p k (in the presence of a tensile stress)

da/dt

FaC. 1|m Preik (in the presence of a compressive stress)

(8)

where a, cp, and H- are the current icrocrack length, plastic strain, plasticstrain rate, respectively, and t is time. The approach is versatile in thesense that the damage accumulation along arbitrary deformation path can be

11

computed by integrating Eq. (8). Because the ID approach has been success-fully applied9 to the same creep-fatigue data as those considered in thepresent report and also the frequency-modified life equation can be derivedfrom the ID approach, a direct comparison of the life predictions of the twoapproaches is possible. Integration of the damage-rate equation for continu-ous cycling over a plastic strain range Acp at a constant plastic strainrate cp yields the following relations: 9

N f m + 1 A2J E)l-k

f 4A 2 p

where A - C + T in ala

or, in terms of frequency v (v is in cpm),

( c -(m+k) -

Nf- m + 1 ( 4v)1-k.()f 4A 2

Equation (9) is identical to the :requency-modified life equation, Eq. (3),if

B - S +k m

and

(a+ 1 tB 2(m-k) S

C2 1 A (1-Wk) '(10'60

The values of A and m corresponding to 8 and C2 are listed in Table I.Therefore, under continuous cycling, the incremental damage approach yieldsidentical results, provided the same constants are used.

When hold times are imposed in each cycle, the damage-rate equationupon integration yields damage/cycle given by9

1 4A AEm c k-1 + 2AT ft H 1c1 k dtN )m+ ( 2 +1p) T+C m p P

+ Cpmn m f H 1pk dt , (11)

Jo

where cm is the plastic strain at the beginning of the tensile hold time,

cPmin is the plastic strain at the beginning of compressive hold time, and

tH is the hold time. The first term on the right-hand side of Eq. (11) isthe damage per cycle during loading and unloading, the second ter' is thedamage per cycle during the tensile hold time, and the last term is the dam-age per cycle associated with compressive hold time.

12

Let us consider and compare the extent of damage produced during tensilehold time up to 600 min using the two approaches. For this purpose, we in-clude fatigue test results at 593*C for Type 304 stainless steel with the same

Et . 4 x 10-3 s-l and Act - 1.0% but with different tensile hold times rangingfrom 1 to 600 min. The damage per cycle in the frequency-modified approach is

1 m+k T-k

N m + 1 2 4k (12)

(z is the time period per cycle in seconds), and the damage per cycle for theID approach is given by Eq. (11). Note that in the frequency-modified lifeequation, no distinction is made between the continuous cycling and the hold-time damages, but a distincticn exists in the ID approach. Using the appro-priate constants, life with hold time/life without hold time is computed andplotted versus the tensile hold time for the two approaches (Fig. 12). Theresults obtained are in close agreement and imply that, in th. frequency-modified approach, wave-shape effects can be ignored for this type of loadingconsidered at least up to tensile hold time <600 min. However, it should bementioned that the frequency-modified approach continues to predict a decreasein life with longer hold time beyond tH - 600 min, whereas the ID approachpredicts a decrease in life as long as cp # 0 and predicts zero damage(saturation) when E 0 0. The latter situation is of particular interest todesigners but no data exist beyond tH * 600 min to verify whether saturationoccurs. For handling the damage during long compressive and/or symmetrichold times, the frequency-modified approach presents problems, whereas in theID approach it is incorporated into Eq. (11).

ICREENTAL DAMAGE APPROACH14- - - - FREANCr -MODE iE D LIFE APPROACH

W OA

Q2 -

g ~~ 11 i 11 1 : J .1 La 1 1. L-1 It I. _ -I -U

00' 1o: "o' le 105TENSILE HOLD TIME. S

Fig. 12. Comparison of Damage Resulting from Tensile Hold TimeEstimated from Frequency-modified Life and Incremental DamageApproaches. Type 304 stainless steel, T " 593*C. Neg. No.ANL 306-76-115.

13

Another situation where wave-shape effects become important involvestests with sawtooth waveforms. Two types of tests that are of interest arethe following: one with slow loading followed by fast unloading (slow-fast)and the second with fast loading followed by slow unloading (fast-slow). Inthe frequency-modified approach, the preceding two loading sequences are notdistinguished and additional assumptions are necessary to handle the situa-tion.* To examine the damage using the ID approach, we consider two typesof tests that involve sawtooth waveforms as shown in Fig. 13. From straincycling and the corresponding stress

0"

a~

I-

I J

(a) ko-FasT

(b) FAST -SOW

Fig. 13. Sawtooth Waveforms.Neg. No. MSD-62311.

and in the fast-slow test

N- 5(1) (0.0035)m+1f ( )

cycling waveforms, shown in Fig. 13, itis clear that in a slow-fast test moretime is spent when the stress is ten-sile (also note that a mean compressivestress is present) than when the stressis compressive. Inasmuch as tensilehold time is more damaging than com-pressive hold time, we conclude thatslow-fast cycling is more damaging thanfast-slow cycling. To estimate theorder of magnitude of life differenceinvolved in sawtooth waveforms, we con-sider two sets of slow-fast and fast-slow tests, all with At - 0.007. Thestrain rates for the fist set are10-6 ,-( ( ) and 10-4 s8- (P2), and,

for the second set of tests, E - 10-6

-1 and P2 . 10-3 *-1. The damage per

cycle in the slow-fast test** is givenby

1 . 16A (0.0035)34.1 (. k-lN 5(m + 1) ( 5pk

+5(m + 1) (0.0035)0+1 g k-1

(13)

p )k-l + 5m 1 (0.0035)+ ( k-1

{ 2/ 5( ) pl

(14)

"Recently, the authors have learned that Coffin has proposed a frequencyseparation technique to handle wave-shape effects (private communication).

**The tensile hold time is assumed to be four times more damaging than com-pressive hold time to be consistent with our previous work.

-

14

Using the appropriate constants* from Table I, the fatigue lives calculatedfor sawtooth waveform are listed in Table II. The magnitude of the wave-shapeeffect on fatigue life estimated (slow-fast loading produces three to fourtimes more damage than the fast-slow loading) is consistent with the recentexperimental findings of Coffin for Type 304 stainless steel and the A286alloy.16

TABLE II. Expected Results from Incremental DamageApproach for Sawtooth Waveform Ac - 0.007,

Type 304 Stainlesh Steel, T * 593*C

Type pt 5 1'la cpc' 8-la Nf, cycles

Slow-fast 10-6 10-4 338

Fast-slow :0'4 106 1032

Slow-fast 10-6 10-3 378

Fast-slow 10-3 10-6 1470

a. and Epc are the plastic strain rates in tensionaS compression, respectively.

V. CONCLUSIONS

It is shown that the fatigue-life predictive parameters of the frequency-modified life equation vary with frequency or str. Ln rate for Type 304 stain-less steel. The constants show a transition coinciding with the frequency ofcycling at which a change in the fracture appearance from transgranular tointergranular failure mode or vice versa occurs. Although life prediction ofhold times can be made by etermining the constants over the entire strain-rate spectrum (10-2 to 10-0 s1), better accuracy in life prediction resultswhen the variation of the predictive parameters with frequency or strain rateis considered. Furthermore, the constants (C2 , 8, and k) determined fromcontinuous cycling fatigue tests, in which the fractured surfaces show fatiguestriations, accurately predict the effect of short compressive and symmetrichold times on fatigue life. Finally, a comparison of the creep-fatigue damageusing the frequency-modified approach and the recently developed incrementaldamage approach is made to show the importance of wave-shape effects on low-cycle fatigue life for Type 304 stainless steel.

For lO > 10-4 sl, TFM constants are used, and, for lO < 10-5 8-1, IFM con-stants are used.

15

RFFERENCES

1. L. F. Coffin, "A Study of the Effects of Cyclic Thermal Stresses on aDuctile Metal," Trans. Am. Soc. Mech. Engrs. 76, 923 (1954).

2. S. S. Manson, Behavior of Materials Under Conditions of Thermal Stress,Natl. Advis. Comm. Aeronatu. Tech. Note No. 2933 (1954).

3. A. Coles and D. Skinner, "Assessment of Thermal-Fatigue Resistance ofHigh Temperature Alloys," J. Roy. Aero. Soc. 69, 53 (1965).

4. L. F. Coffin, "Predictive Parameters and Their Application to High Tem-perature, Low Cycle Fatigue," in Fracture 1969 (Proc. of Second Intl.Conf. on Fracture), Chapman and Hall, London, 1969, p. 643.

5. L. F. Coffin, "A Note on Low Cycle Fatigue Laws," J. Mater. 6, 388 (1971).

6. L. F. Coffin, "Life Prediction of Metals Subjected to High Temperature,Low Cycle Fatigue," in Proc. of 1971 Kyoto Intl. Conf. of Materials II(1973), p. 234.

7. L. F. Coffin, "Fatigue at High Temperature," in Symp. on Fatigue at Ele-vated Temperatures, ASTM STP 520, 5 (1973).

8. L. F. Coffin, Fatigue at High Temperature, General Electric Company Tech-nical Information Series, Report No. 72 CRD 135, Class 1 (April 1972).

9. S. Majumdar and P. S. Maiya, A Unified and Mechanistic Approach to Creep-fatigue Damage, Argonne National Laboratory, ANL-76-58 (1976).

10. R. W. Weeks, D. R. Diercks, and C. F. Cheng, ANL Low-cycle FatigueStudies -- Program, Results, and Analysis, Argonne National Laboratory,ANL-8009 (November 1973).

11. Masaki Kitagawa and R. W. Week, "Analysis of Hold Time Fatigue Test Re-sults of AISI 304 Stainless Steel by Five Existing Methods," in Proc.1973 Symp. on ME ?hanical Behavior of Materials, Soc. of Matls. Science,Japan, 1974, pp. 233-238.

12. P. S. Maiya and D. R. Diercks. "Analysis of ANL High-temperature FatigueData for AISI Type 304 Stainless Steel Using Common PhenomenologicalMethods," Reactor Development Program Progress Report, Argonne NationalLaboratory, ANL-RDP-21, October 1973, p. 5.1.

13. T. Slot, R. H. Stentz, and J. T. Berling, "Controlled-Strain TestingProcedures," in Manual on Low Cycle Fatigue Testing, ASTM STP 465, 100(1969).

14. C. Y. Cheng and D. R. Diercks, "Effects of Hold Time on Low-Cycle FatigueBehavior of AISI Type 304 Stainless Steel at 593*C," Met. Trans. 4(2),615-617 (1973).

15. P. S. Maiya, unpublished research.

16. L. F. Coffin, private communication (1975).