ELSEVIER

Int. J. Fatigue Vol. 19. No. 2, pp 109- 115, 1997 © 1997 Elsevier Science IAmiled. All rights re,,,erved

Printed in Great Britain. () 142- I 123/97/$17.(X)+.00

PII S0142-1123(96)00065-S

Low cycle fatigue life prediction--a new model

Tarun Goswami*

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA (Received I August 1995; revised 15 October 1995; accepted 15 September 1996)

A new creep-fatigue life prediction method has been developed in this paper to correlate high temperature low cycle fatigue (HTLCF) data on Cr-Mo steels. The new method has been developed within the premise that with the application of cyclic loading, which is plastic strain dominated under HTLCF conditions, damage accrues by means of viscous flow. Concepts of dynamic viscosity were used to describe such a flow behavior and assumed as damage parameter. When the ability of a material to accommodate viscous flow ceases, failure occurs. When these two terms namely; dynamic viscosity and material toughness, equated, produce a life prediction expression, that has been derived in this paper. The assessments of HTLCF data were performed with the new model developed in this paper for 1Cr-Mo-V, 2.25Cr-Mo, and 9Cr-lMo steels. Numerous test conditions were employed by the National Research Institute for Metals, Tokyo, Japan, in generating HTLCF data where the assessments show that the new method correlates the data. Copyright © 1997 Elsevier Science Ltd. All rights reserved

(Keywnrds : low cycle fatigue; life prediction; strain range; cyclic s t r e s s - s t r a in ; factor of 2)

INTRODUCTION

The high temperature low cycle fatigue (HTLCF) is an interactive mechanism of different processes such as fatigue, creep, corrosion, oxidation, etc. which produce premature failures in engineering components used in power generation, gas turbines, space propulsion engines, structures, and other systems and sub-systems. The components in the examples cited experience a period of steady loading together with high mechanical, thermal, and other stresses at high temperatures. As a result, such failures occur prematurely, and require knowledge of failure analyses and development o f life prediction methods applicable under a wide range of laboratory test conditions. Several such failures have occurred in aviation and power generation industry since 1950 and have required study of high temperature low cycle fatigue. Typically, these failures associated a cyclic life range from a few hundred cycles to tens of thousands of cycles.

In the early 1950s, Manson j and Coffin 2 presented plastic strain and cycles to failure correlations, which accelerated the development of many empirically based, phenomenological methods. A recent review 3 describes some of the popular methods of life prediction developed since 1950. Halford 4'5 summarized over 100

* Presently at Damage Tolerance and Fatigue Group, Department No. 178, MS 9, Cessna Aircraft Co., 2617 South, Hoover Road, Wichita KS 67215 and Mechanical Engineering Department, Wichita State University, Wichita, KS 67260-0035, USA.

methods of life prediction under isothermal and thermo- mechanical fatigue published from 1953 to 1991. The life prediction methods summarized by Halford 4"5 were classified in terms of two frameworks namely "initiation of crack growth" to a "detectable" size and LCF as a full "crack growth" process, respectively.

Extensive reviews, proprietary reports, and other ref- erences j-3° provide the scope of research in the area of HTLCF and life prediction since the 1950s. A few empirically based, phenomenological life prediction methods t~2° received much attention and assessments were performed with limited HTLCF data to determine their applicability. In the case of low alloy steels, no life prediction method t°-2° was found universally applicablefl j'22 Every method had mixed success and limitations 821'22 where modifications were made on a specific method to analyze a particular type of data. 2t-22 Such modified versions of life prediction methods remain isolated in the literature 2t'22 as no attempts have been made to extend the assessments to new data. Only three methods became major analytical tools in the area of HTLCF life prediction of engineering equip- ment that operate at high temperature. These are as fol- lows:

1. ASME nuclear code case N-47; "~ 2. strain range partitioning technique (NASA Lewis); t3 3. continuum damage mechanics approach (ONERA

France). 23

The first two approaches ~°'~3 are very popular all over the world despite their limitationsfl L22 whereas, the

109

110 7-. G o s w a m i

third framework 23 is being developed and used as a tool for life prediction in France and Europe. Priest and Ellison 2~ provide a discussion on the limitations of various life prediction methods for 1Cr-Mo-V steel tested at 565°C under various test conditions. Though these methods jw2° are material models that have been developed for specific applications, a list tabulated in Table 1, shows that strain range partitioning technique alone has 22 such specific versions, s

The new model

The model 24 developed in this paper assumes that the deformation is produced under HTLCF by creep- fatigue interactions by means of a viscous flow. A viscous flow occurs as the loads are applied in the elastic and/or plastic regimes. A typical example of this flow process is the generation of slip networks in some materials. With the application of loads, which in the case of LCF is plastic strain dominated, or total strain range above elastic strain range, produce deformation depending upon time at a rate measured by strain rate. The dynamic viscosity was assumed as a damage parameter in the new model. Cyclic and/or static loading begins the initiation of viscous flow accommodation process in a material. When the ability of a material to accommodate any further viscous flow ceases, the failure occurs. Therefore, when the two terms namely; dynamic viscosity and material tough- ness equated, produced a new life prediction equation. The damage parameter at failure can be described by Equation (1) by including the cycle time as follows

dynamic viscosity -- Ao-.(A~,/e) ( 1 )

where Ao- is the stress range, AE, is the total strain range and ~ is the strain rate.

Failure criterion was assumed in terms of dynamic viscosity becoming equal to toughness of the material. Toughness is a product of ductility and cyclic strength where it was represented in terms of saturated stress at half-life. Ductility was determined from the expression used by Edmund and White 25 as follows:

Dp = NfA% (2)

Table 1 Modified versions of strain range partitioning (SRP) technique 4

where D o is the ductility, Nr is the cycles to failure, and A% is the plastic strain range.

Cyclic strength in a fatigue test was used in terms of saturated stress range at half-life (AG,) represented in the following form:

Toughness = A% • N f . Ao-~ (3)

Equations (1-3) presented above must be represented in terms of a mechanical equation of state for life prediction. Such representations were presented by Hart 26 and Hart and Solomon. 27 They 26"27 accounted for the experimental fact that there is a scaling relationship by constructing curves for stress and strain rate among the curves of different hardness. These curves were translated along straight lines of slope m. In this particular case, since the fatigue litE is a variable of the test parameters employed, a scaling relationship was developed in terms of plots between the strain range to strain rate ratio, or cycle time, with number of cycles on the log-log scale. A curve between 'cycle time' and cycles to failure had a slope m as shown in Table 2 schematically, that was used in the equation of state for life prediction, as follows:

Aft. (Act/&),,, = A AEp. Nf. AG~ (4)

In the above equation A is a material parameter which balances the units of the equation and is a variable. The value of A depends upon the test parameters employed. In the case of continuous fatigue data at higher strain rates (from 0.5%/s to l%/s) the value of

Table 2 Material parameters used in the new model ik)r ICr M o V steel

K Temperature Strain rate Materials (MPa) n m (°C) (%/s)

IC r -Mo-V 1082 0.128 -0 .32 Room temp. 0.1 IC r -Mo-V 912 0.128 -0 .32 400 (1.1 ICr -Mo-V 815 0.143 -0 .30 500 0.5 ICr -Mo-V 815 0.143 -0 .24 500 (1.1 ICr -Mo-V 815 0.143 -0 .40 500 0.01 I C r - M ~ V 815 0.143 -0 .72 500 0.001 1Cr-Mo-V 693 0.133 -0 .36 550 0.5 ICr -Mo-V 693 0.133 -0 .29 550 0.1 1Cr-Mo-V 693 0.133 -0 .4 550 0.01 1Cr-Mo-V 693 0.133 -0.41 550 0.0(11 I C r - M o - V 693 0. ! 33 -0 .24 600 0.1

Original strain range partitioning technique Interaction damage rule Product damage rule Inelastic thermal fatigue Pratt and Whitney combustor model Multiaxiality factor Ductility normalized strain range partitioning technique Strainrange conversion principle Mean stress effects Combustion engineering model Total strain version of SRP Diesel engine piston Non-linear damage rule Statistical data analysis Exposure time modified Steady state creep law Time to failure modified Thermomechanical fatigue Fracture mechanics based Partitioned energy method Strain energy partitioning

The parameters of cyclic stress-strain relations were determined by incremental step tests by linear regression analysis of log o- to log % for plastic strains from 0.001 to 0.01. 28 The m was determined as follows, where cycle time = Aet/eTe,~,,,.

Cycles to fa i lure log

Low cycle fatigue life prediction 111

A was found to be approx. 4 and higher, and for lower strain rates ( from 0.01%/s to 0.001%/s) it var ied from 5 to 10 for the three low al loy steels. It may be pointed out that for every data type the value o f A is l ikely to be different and to s impl i fy the model and the analysis the value of A was kept constant at 1 for all strain rates, s low-fas t , and tensile hold waveforms and assessments performed.

Equat ion (4) was further modif ied by subst i tut ing a cycl ic s t ress-s t ra in equat ion as fol lows;

K.(A%)".(AE,/~) m = A.AEp.Nf-Ao'~ (5)

Rearranging various terms in equat ion (5) resulted in the fo l lowing equation:

N, = { K-(Aep)"-t.(Ae,/~) '~ }/Ao-~ (6)

Equation (6) was der ived as a life predic t ion equat ion which was appl icab le under cont inuous fat igue and s low- fa s t waveforms.

A hold t ime correct ion was made from data fitting since hold t imes al tered strain rates in terms of the fol- lowing:

Hold t ime correct ion =

strain rate/{ 1 + log( t ime of hold in s)} (7)

The above factor was used only for the cycles that conta ined hold t imes in the life predic t ion Equat ion (6).

Like other methods o f life predic t ion ' ' , ' 5 this method also uses the strain rates only in one direction. Tensi le strain rates are used in the express ion for life predic- tion. Other methods, '°''3"~4"17 2o do not use the strain rates in life predic t ion express ion. However , fo l lowing approaches use strain rates ' ' - '5 or f requency '2''6 that have not been used ex tens ive ly in the life assessments as the other two methods. '°l-~ The N R I M data used in this paper have not been analyzed with life predic t ion methods m 2o and analyses are not ava i lab le in the open literature. Only the modif ied Diercks equat ion was used to assess the life predic t ion o f C r - M o steels. 24 General comments on the appl icab i l i ty of methods with two data sets : ' ` = examined by the author will be d iscussed briefly from Ref. 3.

L O W CYCI ,E F A T I G U E D A T A

The H T L C F data were obta ined f rom the Nat ional Research Insti tute for Metals , Tokyo, Japan. The detai ls o f mechanica l proper t ies o f the materials , condi t ions , and s t ra inqi fe data are d iscussed in references 28'3°. Therefore , interested readers are d i rec ted to or iginal references,28 3o only assessments of data with the new model will be d iscussed below.

D I S C U S S I O N O F THE A P P L I C A B I L I T Y O F THE N E W M O D E L

In this section, appl icabf l i ty o f the new model presented in this paper has been assessed with H T L C F data. The data compr i sed five temperatures ; f rom room to 650°C, four strain rates; f rom 0.5%/s to 0.001%/s, two s l o w - fast strain rate combina t ions ; two hold t imes; 6 and 60 rain, respect ively . Tests with total strain ranges from 0.2 to over 1% were used that p roduced cycl ic l ives ranging from a few hundred cycles to several hundred thousand cycles. Several mater ial parameters

Table 3 Material parameters used in the new model for 2.25Cr 1Mo steel

K Femperature Strain rate Materials [MPa) n m ¢'Ct I<i/s)

2.25C>1Mo 796 0.100 -0.3 Room temp. ILl 2.25Cr-1Mo 741 0.109 -0.26 ~0(1 il. I 2.25Cr- 1Mo 73(1 0.096 -0.35 400 i I. I 2.25C~1Mo 652 0.105 -0.4 500 i1.5 2.25C~1Mo 652 0.105 -0.5 5011 ILl 2.25Cr IMo 652 0.105 -0.32 500 0.01 2.25Cr 1Mo 652 0.105 -0.55 500 1).001 2.25Cr-lMo 428 0.082 -0.3 600 0.s 2.25Cr-1Mo 428 0.082 -4).43 600 t). 1 2.25C~1Mo 428 0.082 -0.44 600 t).lll 2.25Cr-IMo 428 0.082 -038 600 0.I)01

The parameters of cyclic stress strain relations were determined by incremental step tests by linear regression analysis of log ~r to I~g ep lk~r plastic strains from 0.001 to 0.01 >'

were suppl ied by NRIM 2* 3o and other parameters namely : A and m were de te rmined for three mater ia ls under different condi t ions tabulated in Tables 2-4. The appl icab i l i ty of the life predict ion Equation (6) was de te rmined for the three materials under fol lowing test combinat ions .

1. constant strain ampl i tude tests: 2. s l ow- fa s t waveforms: 3. tests with tensile hold.

These are d iscussed for I C r - M o - V , 2 . 2 5 C r - M o and 9 C r - l M o steels below.

1Cr-Mo-V steel

Constant strain amplitude tests. Various material parameters summar ized in Table 2 were used in the assessments of N R I M data on 1 C r - M o - V steel. 2s Pre- d ic ted and observed cycl ic l ives are plot ted in Figure 1. It shows that the life predic t ion is conservat ive as scatter in the data is be low one- to-one line. As the exper imenta l l ives increase from l04 cycles conserva- t ive life predic t ion was observed. The same was true with decreased strain rates. A decrease in strain rate increases the cycle t ime at the same strain range and as a result predic t ions are very conservat ive .

It may be noted that there is a range of temperature ,

Table4 Material parameters used in the new model tier 9Cr-lMo steel

K Temperature Strain rate Materials (MPa) n m C'C) (%/s)

9Cr-lMo 975 0.117 -0.29 Room temp. 0.1 9Cr-lMo 693 0.132 -41.32 500 O I 9Cr-lMo 609 0.142 -4).36 550 0.5 9Cr-lMo 609 0.142 -I).29 550 0.1 9Cr- 1Mo 609 0.142 -0.45 550 0./) 1 9Cr-lMo 609 0.142 -0.42 550 0.00I 9Cr- 1Mo 443 0. t 21 -4J.5 600 0.5 9Cr-lMo 443 0.121 -0.35 600 0.1 9Cr- 1Mo 443 0.121 -0.42 600 0.0 I 9Cr-1Mo 443 0.121 -4).58 600 0.001 9Cr-1Mo 343 0.125 -4).46 650 0. I

The parameters of cyclic stress-strain relations were determined by incremental step tests by linear regression analysis of log cr to log ~p for plastic strains from 0.0005-41.0091. ~'

112 7-. G o s w a m i

u

e_

10 6

10 5 ,

10 4

10 3 ,

10 2 .

101 101

~ 500"C 0.5%/sec. "l f • 550"C 0.5%/sec. "I / I' 5oo'c, 0.i%/~. / / , 5s0"c'0 i%/~c / / I = 5oo'c, O.Ol%/sec I I" 550"C~ 0.01%/~c. | ~

• , . . * , . . ~0,00c 000,%,,,c: l ÷ , , o . c ~

. / : .

/ "~ ° I ~ } i ~ ; . ...... I / ~ ~ . t" 6oo'c,o.1%/=. j

i ~ Conservative prediction

. . . . . . ; ' : . . . . . . ;'o3 . . . . . . ;%, . . . . . . ;'05 . . . . . . ; Observed life

10 5 •

.u

e.

10 4 .

10 3 -

10 2

101 101

I B 500'C,0.01%/sot. / • 500"C, 0.001%/sec. • 550"C, 0.01%/sec. • 550°C, 0 . 0 0 1 % / s e c . . ~

f ; : / ~ Conservative prediction

. . . . . . . . i . . . . . . . . i . . . . . . . . v . . . . . . . . 10 2 10 3 10 4 10 5

Observed life

Figure l Life prediction of 1Cr-Mo-V steel under continuous fatigue conditions

Figure 2 Life prediction of 1Cr MfFV steel under slow fast wave- forms

strain rate, and strain range where the life predicted by the new model is very close to the experimental lives. In the case of 1Cr -Mo-V steel under symmetrical test conditions such combinations were 500°C, 0.5- 0.1%/s, and total strain ranges above 0.25% and 550°C, 0.5-0.01%/s and at all strain ranges. However, as the strain rate decreased to 0.001%/s, the predictions were very conservative.

Slow-fast waveforms. Slow-fast waveforms, in which the strain rates in tension and compression directions vary are difficult to model. Since the model developed in this paper is a continuum model, micro- mechanistic changes that strain rates cause are difficult to incorporate in the model. This was the case for all other life prediction methods. '~2° Like most methods, this method also assumes strain rates in the tensile direction. The strain rates were 50-500 times lower in tension than compressive strain rates. Variable strain rates in tension and compression directions have been found to alter the HTLCF lives as seen in the NRIM data sets? 8-3° The predicted and experimental lives under slow-fast waveforms are presented in Figure 2. For a combination of higher strain rates (>0.01%/s), higher total strain ranges (>0.3%) and higher test temperatures (>550°C) the new model predicted lives conservatively within a factor of 2-4.

Tests with tensile hold. Assessments were performed for tensile hold cycles of 6 and 60 min. In these cases the predicted lives were very similar to that of experimental lives for 6 min hold above 0.3% total strain range at 500°C. However, with 60 min hold at 550°C, the predicted lives were slightly higher than experimental lives above 0.5% total strain range, shown in Figure3. In all the cases the cyclic lives were predicted in a factor of +2. A factor of two criterion has been used extensively in life prediction analyses. 3-24 One point over-predicted in Figure 3 was as a result of experimental error.

10 4

f" ~oo.¢,~ hold - - / / |e 500"C, 6min. hold J • / "

[ • 550"C, 60 rain. hold / /

lo3. / / , _ . o o ,

i />": ~ ~ / / / A e ~ A e ~-- Conservative prediction

I / lo 2 I" . X . . . . . . . . . . . . . . .

10 2 10 3 10 4

Figure3 Life prediction of 1Cr-Mo-V steel under tensile hold waveforms

2.25Cr-1Mo steel Constant strain amplitude tests. Analysis of HTLCF

data on 2.25Cr-Mo steel with the new model, using the material parameters from Table 3, was found to exhibit a similar trend shown for 1Cr-Mo-V steel. At constant strain rates of 0.1%/s, the predicted lives were very conservative below total strain range of 0.5% at room temperature. At the outset, the prediction by the new model can be seen within a factor of +2 in Figure 4. It was also noticed that with a decrease in strain rate and an increase in temperature the new model predicted conservative lives. A range in test temperatures, strain rates, and strain ranges was found to exist for this material where the prediction was found very similar to experimental lives as shown in Figure 4. These combinations usually were strain rates from 0.5 to 0.01%Is at temperatures 500°C and above.

Slow-fast waveform. Assessment of HTLCF s low- fast data with the model shows that at 500°C with tensile strain rates of 0.01 and 0.001%Is the lives

L o w cycle fa t igue l i fe p red ic t i on 1 1 3

Observed life 105 .

! f• RoomTemp. 0.1%/sec: / / : / e 300"C,O.l%/sec. / / m

/ • 400"C, O.l%Isec. / / l ° see'c, o.5%/~. / / / • 500"C,O.l%lsec. / AM

~o4~ [ * 5oo'c,o.ot%/scc. / / * [] i I, • 5oo'c, oooi%,sec , //.~('+ . * -

1o3 /;/.,_ ,; : x •

_ ~ / / + . x k f" 600"C, 0.5%/sec

! / ~ " I " 6oo~c,o.o]%/~.

t//- : :°or Conservative p i

101 " • . . . . . . . , . . . . . . . . , . . . . . . . . i . . . . . . .

101 102 103 104 05

Figure4 Life prediction of 2,25Cr-Mo steel under continuous fatigue conditions

Observed life 104 /

• 500"C, 6 rain. hold / /

• 500"C, 60 rain. hold / /

103. - - ~ ~ •

/ , []

@

102- / & •

t f " Conservative prediction 101 If" . . . . . . . . , . . . . . . . . ~ . . . . . . . .

101 102 to 3 104

Figure 6 Life prediction of 2.25Cr-Mo steel under tensile hold wave forms

were predicted very conservatively. However, as the temperature increased to 600°C, the predicted lives were in a factor of +2 as shown in Figure 5. Some of the mechanistic aspects of deformation for this parti- cular material are very complex, where the interaction of strain aging, MoC clusters, oxidation, and other mechanisms which depend upon the temperatures and other test parameters effect the HTLCF resistance and are not very well known.

Test with tensile hold. The assessment of data with the new life prediction model is shown in Figure 6 for the tests with hold times of 6 and 60 min. Below total strain range of 0.25% at both the temperatures (500 and 600°C) the predicted lives were quite similar to experimental lives. However, the new model was found to be conservative for longer tensile holds of 60 min.

9Cr-lMo steel Constant strain amplitude tests. The assessments

were performed using the HTLCF data and material

parameters from Table 4 for 9 C r - l M o steel under con- tinuous fatigue conditions. The predicted and experi- mental lives are plotted in Figure 7. At room tempera- ture, the predictions were very conservative. As the total strain range increased from 0.9%, the prediction of HTLCF lives were in a factor of 2, however, below that total strain range, conservative lives were predicted. At 500°C the prediction was in a factor of 2 above total strain range (>0.25%) and for 550°C and strain rates of 0.5%/s, the predicted lives were very similar to experimental lives. A decrease in strain rates the model predicted lives conservatively. The predicted lives were conservative for the very slow strain rates such as 0.01 and 0.001%/s at higher tem- peratures. However, for other strain rates the predicted lives were conservative in a factor of 2-4. Other methods t~2° were also found 2~'22 to be conservative in a wide spectrum of test conditions such as hold times and strain rates.

10 4

103

102 .

101 10

Observed l i f e

I A 500"C, 0.01%Isec. / • 500kC, O.O01%/sec

• 600"C, 0.Ol%Isec. / •

L 600"C, O.001%/see. / •

e • •

J : .

. . . : :onse tive prediction

. . . . . . . ;o~ . . . . . . . ;~,3 . . . . . . . ~o'

~=,

u

10 5 ,

104

t03.:

102-:

Observed life

m ' Room temp. 0.1%/sec~ / • 500"C, 0. l%/s~c. / u 550"C, 0.5%/see. • 550"C,O.l%/sec. • / • 550"C, 0.01%/see. / o 550"C,O.O01%/sec. / / A u -4- • 6 0 0 " C , 0.5%/see. ~ ¢ - - "~ _ + 600"C,O.l%/sec. / /_ x + • " x 600"C,O.0l%/scc. 0 / ~1~ , [] • m m 600"C, 0.001%Iscc. ~ -r A 650"C,O.l%/seC. /~: ~ + ~ 4n

" _ / a $ • [] ,R, • X o

_ d . , c

/ & ~ []o -

/ • II •

~ m ionservative prediction 101 / r

101 . . . . . . 1"02 . . . . . . . 1"~3 . . . . . . . 1"~4 . . . . . . . 1"05

Figure 5 Life prediction of "~ 25 ~ "" .. _t~r-mo steel under slow-fast wave- Figure 7 Life prediction of 9Cr- IMo steel under continuous forms fatigue conditions

114 1-. G o s w a m i

10 4

10 3

10 2

101 101

Observed life

{ ~ 550"C,0.01%/s¢c. 550"C, 0.001%/sec. / I 600"C, 0.01%/scc. / •1 600"C, 0.001%/sec. / • a I

/

J ;" • ..-.i" " • O&

~ Conservative prediction

. . . . . . . . i . . . . . . . . i

10 2 10 3 10 4

F i g u r e 8 Life prediction of 9Cr 1Mo steel under slow-fast waveforms

Slow-fast waveform. The predicted versus experi- mental lives are plotted in Figure 8. It shows that the predicted and experimental lives under slow-fast waveforms are very conservative for both temperatures and strain rates.

Test with tensile hold. The predicted versus observed lives were plotted in Figure 9. With 6 min tensile hold the predicted lives were in a factor of 2 for both temperatures. However, as the hold time increased to 60 min, conservaive life prediction occurred for 550°C and 600°C in Figure 9.

The NRIM data 28 3o analyzed in this paper have not been assessed with methods of life prediction. 1°-2° At many occasions such data and analyses are classified 3~ and cannot be cited in the open literature. As a result it may not be possible to compare the capability of the new model developed in this paper with other methods of life prediction. In a separate study 3 life prediction methods were reviewed and trends in the life prediction of various methods with two data sets 2~22

10 5 , Observed life

10 4 -

10 3

10 2

[ • 550"C, 6rain. hold / • 550"C, 60 min. hold / • 600"C, 6 min. hold * 600"C, 60 rain. hold ~

- S " S : '

//¢'" • Conservative prediction

. . . . . . . . i . . . . . . . . i . . . . . . . .

0 2 10 3 10 4 10 5

F i g u r e 9 Life prediction of 9Cr - lMo steel under tensile hold waveforms

compared. In conclusion, it was found that applicability of life prediction methods depends upon the test para- meters employed. Test parameters such as temperature, hold times, variable strain rates, material conditions, and other parameters influenced the capability of methods.~O 2o Two methods used extensively in life prediction are damage summation approach ") (DSA) and strain range partitioning technique ~3 (SRP): where DSA was better applicable :~ at lower temperatures (<485°C) for quenched and tempered material con- dition than SRP. However, SRP was better applicable at higher temperatures, higher strain ranges, and higher hold times in annealed conditions?

SUMMARY

The model developed in this paper is within viscosity frameworks, where dynamic viscosity was assumed as damage parameter. A failure criterion of dynamic vis- cosity becoming equal to material toughness was found to correlate the high temperature low cycle fatigue data. In all the cases the predictions were conservative.

ACKNOWLEDGEMENT

The research reported in this paper is a part of authors' private research conducted at the University of Utah. Dr Koji Yamaguchi from the National Research Insti- tute for Metals, Tokyo, Japan provided the data and permitted their use for the analysis.

REFERENCES

1 Manson, S.S. 'Behavior of Materials under Conditions of Ther- mal Stress; Heat Transfer Symposium' University of Michigan Engineering Research Institute, Michigan, 1953, pp. 9-75

2 Coffin, L.F. Jr. Trans. ASME 1954, 76, 931-950 3 Goswami, T. High Temperature Mater. Processes, 1995, 14,

21-34 4 Halford, G.R. in 'Thermal Stresses II' (Ed. R.B. Hetnarskil.

Elsevier Science Publication, Oxford, UK, 1987, Chap. 6, pp. 33~428

5 Halford, G.R. 'Evolution of creep-fatigue life prediction models, ASME Winter Annual Meeting on Creep-Fatigue Interaction at High Temperature" (Eds G.K. Haritos and O.O. Ochoa), AD- Vol. 21, American Society for Testing and Materials, Philadel- phia, 1991

6 Miller, D.A., Priest, R.H. and Ellison, E.G. High Temperature Mater. Processes, 1984, 6, 155-194

7 Lloyd, G.J. and Wareing, J. Metals Technol., 1981, 809, 297 8 Brinkman, C.R. Int. Metals Rev. 1985, 30, 235-258 9 Anon, 'Nonlinear Fracture Mechanics' Vol. 1, Time dependent

fracture, ASTM STP 995 (Eds A. Saxena, J.D. Landes and J.L. Bassani) American Society for Testing and Materials, Philadel- phia, 1989

10 Anon, Code Case N-47, ASME Boiler and pressure vessel code, Criteria for design of elevated temperature, Class I components in Section III, Division 1, American Society of Mechanical Engineers, New York, 1976

I I Coffin, L.F. Jr. in "Proc. 2nd Int. Conf. on Fracture'. 1969, pp. 643`654

12 Coffin, L.F. Jr. in 'Symposium on. Creep-Fatigue Interaction', MPC-3 (Ed. R.M. Curran) American Society for Testing and Materials, Philadelphia, 1976, pp. 349-363

13 Manson, S.S., Halford, G.R. and Hirschberg, M.H. in 'Proc. ol Symposium on Design for Elevated Temperature Environment', American Society for Testing and Materials, Philadelphia. 1971. pp. 12-28

14 Halford, G.R., Saltsman, J.F. and Hirschberg, M.H. in "Proc. of Conference on Environmental Degradation of Engineering Materials', Virginia Tech. Printing Department, Virginia, 1977, pp. 599,612

15 Majumdar. S. and Maiya, P.S. in "Symposium Creep Fatigue

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