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NACATN2890c .1

NATIONAL ADVISORY COMMITTEE --- -

FOR AERONAUTICS

TECHNICAL NOTE 2890 Gl~~

l@Abl COPY: REti ‘is ~M=WL (DOG’ ~>

1KIR’TLAND AFB, 3 I

TIME-TEMPERATURE..—

RELATION FOR EXTRAPOLATION

OF CREEP AND STRESS-RUPTURE DATAI

By S. S. Manson and A. M. Haferd

Lewis Flight Propulsion Laboratory

Cleveland, Ohio

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Washington

March 1953

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TECHLIBRARYKAFB,NM

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IIRMTA NO. 1

NACA TN 2890

A LINEAR TIME—TEJPJ3MTUM RELATION

llllMlllullluolllll!lMIICIL5792

FOR EXTMPOIATIONOF CREEP AND STRESS-RUPTURE DATABy S. S. &IM30?land A. M. Hsferd

March 1953

The words “determined in figure 7“ should be omitted from the legendof figure 7.

The legends of figme 8 should reference figure 7.

The legends of figure 10 should reference figure 9.

The legends of figure 13 should reference figure 12.

The legends of figure 14 should reference figure 13.

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NATIONAL ADVISORY C~ FOR AERONAUTICS

‘J31CBNICALNOTE 2890

A LINEAR TIME—~ IIEIATIONFOR EXTRAPOLATION

OF C!lWEPAND STRESS—RUF?JKE D&CA

By S. S. &son and A. M. Haferd

SUMMARY

A time-temperaturepsrameter based on examination of the publishedstress-rupture data for a variety of materials, rather than on physicaltheory, is proposed in the form (T - Ta)/(logt - log ta), where T istemperature in degrees Fahrenheit, t is rupture time in hours, and Ta~d log ta are material constants which appesr,to be determinable fromrupture data in the the range between 30 and 300 hours. This pameterexpresses the observed a~roximate linearity of the function log tagainst T for constsnt nominal stress in the rupture-time range above10 hours and the tendency for lines of constant stress to converge to

8 a single point (Ta, log ta). A plot of this psrameter against stressfor a given material results in a single curve with relati=ly littiescatter for various combinations of time, temperature, and stress in the

. rupture-time range above awroximately 10 hours. For 40 materials investi-gated, the use of data in the time range below 300 hours resulted in verygood extrapolation to longer times (up to 10,000 hr when data wereavailable) compared with corresponding predictions obtainable from aparsmeter recently proposed in the form (T + 460)(20 + log t), where(T+ 460) is the absolute temperature in degrees Rankine. Theparsmeter (T - Ta)/(log t - log ta) also appears to be applicable

in the correlation of total creep elongation data. In order to cor-relate minimum creep rate data, however, the parsmeter used is inthe form (T - ‘a)/(log r + log ra)) where log r is the minimum creep.rate and log ra is a material constant.

INTRODCK!TION

The subject of extrapolation of creep and stresfi-rupturedata onmaterials at high temperature is of considerable current interest. Thisinterest arises in part from the large number of materials under con-sideration for application in steam- and gas-turbine blading. Becauseextensive testing cannot be conducted on all these materials, an extrapo-lation procedure materially assists in the identification of the more

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promising materials, which can then be subjected to more intensive“

development and testing. In some cases, the intended life of the appa-ratus is well in excess of 10,000 hours, and since rupture tests extend-ing to such a long expected service life are expensive and introduce

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considerable delay in material selection, an approximation of materialbehavior in the high time range is of considerable value. (

Two interesting contributions have recently been made to the subjectof creep and stress-rupture data extrapolation. ~ reference 1, a newmethod has been applied to the analysis of high-temperature cobalt-basealloys, S-816 and S-590. The method makes use of the locations of dis-contixmdties in the conventional logarithmic stress-rupture plots ofnominal stress against time at constant temperatures. The authors attri-bute the discontinuities to changes in metallurgical behavior and in themode of rupture, and make use of metallurgical examination to assist inthe determination of the exact location of these discontimuities. Theypoint out that the discontinuities maybe gradusl rather than sharp,but that treating them as sharp is helpful in the analysis. Use is alsomade of very short-the data to obtain additional points of disconti-nuity for purposes of analysis.

Another method of creep and stress-rupture extrapolation which has u

the great advantage of s~licity is presented in reference 2. Thismethod is based on the rate-process equation, from which a deduction wasmade that at a given nominal stress, the par&ter (T +460)(C+logt) - ‘is a constant, where T is temperature in de-es Fahrenheit (T + 460is the absoltie temperature in de-es Rankine), t is the rupture timein hours, and C is a constant which depends upon the ma%erMl and pos-sibly the stress. For a nuniberof materials examined,C was found torange between 14 and 22 when considered as a material constant. Sticethe usefulness of the method is greatly enhanced by considering C as auniversal constant, C was selected equal to 20 as an approximation forall materials at ti stress levels. Thus a plot of {T+ 460)(20+ logt)aga~t stress should yield a single curve for each material irrespectiveof the individual values of time, temperature, and stress. If this curveis establ.ishedbyuse of data at shorter rupture times (and correspondinglyhigher temperatures), then it shouldbe usable to det~e rupturebehavior at longer times and lower temperatures. The selection of Cequal to 20 greatly reduces the amount of testing required for the pre-diction of the behatior of a given material, and for many applicationsthe results obtainable by this approximation are very useful. For example,this approximation has found considerable use in the evaluation of therelative merits of alloys under development. Accompanying the shplicityof the universal relation there is, however, a sacrifice in accuracy forcertain applications. For example, if the stress and temperature arespec~ied, a very considerable error, b some cases by a factor of 10,may result in the prediction of rupture time in the very long-time rangewhen only short-time data are available for the extrapolation.

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The object of this report i~ to present the results of a critical ,analysis conducted at the NACA Lewis laboratory to determine the sourcesof discrepancy srising from the use of the (T + 460)s(20+ log t) psram-eter, and to propose a different time-temperatureparameter involvingtwo material constsmts derived as a consequence of the analysis that hasbeen found to yield considerably improved accuracy when used for long-time extra@ation.

~ION OF P~ (T -I-460)(20 -I-log t)

Plots of the psmmeter (T + 460)(20 + log t) against stress forseveral materials, as shown in figure 1 for 18-8 stainless steel, arepresented in reference 2. Although, in general, there is a tendency forthe various experimental data points to establish a single curve for agiven material, the deviations are too systematic to be attributed toexperimental scatter. Consideration of sll the data shows that the pointsrange about a mesn curve; but at various condxmt temperatures, they fallon different individual smooth curves considerably removed from the meancurve. Likewise, data obtained only at low rupture times establish adifferent curve from that obtained using data covering a wide range ofrupture times. For example, if a curve is drawn using data at rupture

I times less than 100 hours, it is considerably different from the meancurve.. .,

b a plot of this nature, minor displacements of the data pointsfrom the mean curve can result in rather large errors in predicted rupturetime at a given stress and temperature. Figure 2(a) shows a conventionalstress-rupture plot for 18-8 stainless steel, together with the curvespredicted from figure 1 using data for less than 100 hours for comparison.Figure 2(b) shows a similw plot for DM steel, and in each case there isa considerable discrepancy between the predicted curves and the experim-ental points. For a specified rupture time and temperature, the errorin stress in the medium-time range is rsrely greater than10 to 20 per-cent, as indicated in reference 1. At the higher times, however, con-siderably greater error in stress may be observed, and for a specifiedtemperature and stress, the error in rupture time frequently exceeds afactor of 5, the predicted rupture time being, in general, too high for18-8 stainless steel and too low for DM s“teel.

An attempt was made to find the possible source of errors srisingin the use of the (T + 460)(20 + log t) parameter by investigating the

1assumed linearity of plots of ‘log t against — at constant

T + 460

nominal stress and the hypothesized convergence of the constant-stress

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‘lines at1

0. Since very few points at a given stress wereT+ 460=

directly obtainable from conventional curves, cross plots were made toobtain a better delineation of the curves at constant stress. b thepreparation of these plots, the variation of the logarithm of stresswith temperature was first cross’plottedwith time as a psmuneter.Figure 3 shows schematically the nature of such plots obtainedby fairingthe data to be consistent with the family relation smong various materials.

When plots of log t against T +1460 based on the cross-plotted

constant nominal stress curves were examined for a number of materials,deviations from the assumed relation were observed, as shown schematicallyin figure 4. The nonlinearity trends were tio general and systematic tobe attributable either to cross-plotting or to experimental scatter.(The appendix shows a detailed analysis of 16-13-3 steel for illustrationpurposes.] These deviations from linearity have been emphasizedbyetiension of the constsmt-stress curves as indicated by the dotted lines,but the trends shownby the curves in this figure are characteristic ofthe data for the materisllsexsmined. It is seen that curvature occursat very short and very long rupture times; thus the use of short- andmoderate-time data can be expected to lead to error in the prediction oflong-the data due to the nonlinearity in the range of extrawlation.

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The assumption of (T + 460)(20 + log t) as the correlating psrameteris representedby the straight lines converging at the point log t = -20on the vertical sxis. Further e?xroris therefore introduced when theexperimental curves dn not converge to a point on the log t SX3.S2andinparticul.ar,when they do not tend to converge to the point log t = -20.Considerable improvement b correlation for times between 1 and 1~ hourswould be obtained if a value of C other than 20 were used for a partic-ular material (in the illustrative case a better average value might bec = 30); however, some error results in any case from nonlinearity ofthe experhnental curves and the kck of true tendency for these curvesto converge to a single point on the log t axis.

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Assumed Relation and Materisl Constants

Reference to the schematic cross plot in figure 3 shows that at agiven stress, equal increases in log t result in approximately equalincreases in T in the range of log t geater than unity, su~estingthat a plot of log t versus T at constant stress should be approxi-mately linear for times over 10 hours. Figure 5 shows the typical sche-

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matic results obtained when plots are made of this function. At the veryshort rupture times there iS co~iderable c~tme h the constant-nominal-stress lines (increasedby the use of the direct scale for tem-perature rather than the reciprocal scale), but in the practical range,for most ap@ications between 10 and 10,000 hours the lines are quitestraight and tend to converge to a common point. Therefore, over thetime r~-e in which the relation is approximately linesr, a new ttie-temperature parameter can be derived based on the assumption of the con-vergence of all stress lines to a common point (Ta, log ta), where Ta- 10g ta are material constants. The equation of each line is

T-Ta= s

log t - log ta(1]

where T and log t are corresponding temperature and rupture timeand S is the slope. b equation (1) the only term dependent upon the

T-Tastress is S; hence, a plot of

log t -against stress should

log ta

result in a single curve”which, if once determined from data at moderaterupture times, should be useful for exha~lation to longer rupture times.

T - TaBecause the relation

log t - log taarises from the assumption that

constant-stress lines are linear on the log t againkt T coordinates,it will hereinafter be cslled the linear time-temperatureparameter.

The assumption of convergence of all constant-stresslines to a

r cdmmon point (Taj log ta) is consistent with the observed trend of theexperimental data; it also simplifies the form of the time-temperaturerelation and reduces greatly the amount of experimental data requiredfor a complete characterizationof a material., Use of the linear approxi-mation results in predicted trenti of constsnt-temperaturecurves (inconventional stress-ruptureplots) that have a very reasonable appearancein the time range immediately beyond the experimental range. However,the extent to which extrapolationmaybe performed in the time range con-siderably above 10,000 hours cannot be predicted in the absence of suita-ble experimental data. The point (Ta, log ta) is not considered to havephysical si@fic~cej it is considered cml.yto be the point of conver-gence of the tangents to the curves of log t against T in the timerange from approximately 10 to 10,000 hours. Since there is relativelylittle curvature in this time range, the tangents represent a goodapproximation to the experimental curves, but no conclusions can be drawnabout the linearity in longer the ranges.

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It is probably also true that a~lication of the linear relationwill be invalidated in any temperature range where major metallurgicaltransformtions take place. Hence, caution must be exercised in theprediction of properties at temperatures beyond the range of experience.

Illustrative Examples

The methodof determhing the optimum values of Ta and log tafor a given material requires a certain amount of data analysis whichdepends on the amount and type of rupture data available. The methodused in the investigationwill be discussed in a later section. Thepresent intention is to demonstrate that for the materials consideredalJ the available data at rupture times above approximately 10 hourscan be well correlated once Ta and log ta have been determhed.

Analyses of the type presented have been made on 40 differentmaterials. These materials represent ferritic snd austenitic steels(ref. 2], high-temperature alIloysof the nickel-base type (refs. 3 and 5),high-temperature alloys of the cobslt-base type (ref. 4), and aluminum(ref. 6), as well as various experimentsllhigh-temperature slloys forwhich data sre not published. The materials used for illustrative pur-poses are not necessarily those best correlated by the linear time-temperature relation, but rather they are representative of the varioustypes encountered. DM steel and 18-8 stainless steel, respectively,represent ferritic and austenitic steels which correlate well with thelinesr time-temperature relation but poorly with the (T+ 460)(20+ logt)relation. The alloy S-590 represents a cobalt-base slloy for which alarge smount of very short-time data was available and which shows rela-tively good correlation with the (T + 460)(20 + log t) psrameter. The25-20 stainless steel is a relatively unstable materisl compared withother steels, such as DM steel. Inconel X is included to illustrate atypicsl nickel-base high-temperature alloy for which data sre availableover a large range of stress values.

Figure 6 shows the basic data for the five illustrative materialstaken from references 1 to 4. Cross-plotting and fairing the data give .

the constant-time curves for these materials suchas shown in figure 3.From the intersections of these curves with horizontal constant-stresslines, a sufficient number of points became available to constructlog t against T plots such as those shown h fi~ 5. Rupturedata above approximately 30 hours were used to determine the point ofconvergence of the constant-stresslines (Ta> logta). (It hasbeen found that the best results are obtained if data involving rupturetimes between 30 and 300 (or more) hours are used in determining theconstants. After the constants have been determined, however, allrupture data above 10 hours can be used to construct the mastercurve.) Although the values of Ta determined for most of the

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materials examined ranged from 0° to 200° F,were found in several cases. However, since

values as highthe results in

as 700° Fextrapola-

tion depend largely upon the use of the proper combination of Tm andlog ta, rather than on the individual values of these constants,“it ispossible that a single value of Ta can be used for all materials toreduce the amount of testing. A low value of Ta, such as 0° F, ~in general result in relatively little error in the usual t* rangeof interest.

T - T_Master plots of logarithm of stress against

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log t - log tautiM.z-

i.ngconstants so determined are shown in figure 7 for each of theillustrativematerials. Only the actual experimental data pointsfrom figure 6 are used in the construction of the master plots. Foreach material the experimental points satisfy a fairly universal relationwhich is shown by the solid curves in figure 7. Figure 8 shows thecomputed constant-temperaturecurves on conventional stress-rupture plotsof stress against time on logarithmic coordinates. These curves couldbe obtained either by computation from the master plots in figure 7 ordirectly from constad-stress plots.

In figures 9 and 10 a corresponding analysis of the same ~terialsbased on the (T + 460)(20 + log t) parameter is shown. Figure 9 shmmthe master plots based on this parameter for all data points in figure 6.Two curves are drawn through these points, the mesm curve for all the .data and a curve representing rupture times below 100 hours. Conventionalstress-ruptureplots derived from these curves are shown in figuxe 10.Since the master curve obtained from using aJl the data covers a widerrange of rupture times, the resulting derived constant-temperaturecurvesaverage all the data but do not properly represent the basic shape ofcorresponding experimental curves. Usually the experiment&1 data fallabove the predicted curve in some ranges, below in others. Thus, if dataare available over a wide range of rupture times, the parameter(T+ 460)(20 +logt) can be successfdlya ppliedfor approxbnate interpo-lation purposes. Extrapolation, however, results in greater error; con-siderable deviations occur between the experimental data points and the

. predicted curves in figure 10. This is true for all the materials examined.The best agreement among the 40 materials was the S-590 alloy. h thiscase, the parameter (T + 460)(20 + log t) gives better results than thelinear parameter in the range of low rupture times and relatively goodlong-time predictions.

Determination of Constants

The analytical approach depends upon the amount and type of experi-mental.data available. For the analysis of data obtained in a series ofconventional tests at several constant temperatures, the approach used

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8 NACA TN 2890

must be different from that employed when constant nominal stress testshave been conducted to fit the needs of the analysis. Each of thesecases will therefore be considered separately.

Constant rupture-tti curves, such as shown in figure 3, are usedh analyzing conventional data. For tbe construction of such curveswhen the available data are 13mited, use can be made of the general fea-tures of such families of curves. Generallyj the rupture-time curveshave a convex curvature, converging at a stress level near the room-temperature ultimate tensile strength of the material. (In some cases,the curvature tends to reverse at very low stress levels.) Elevated-temperatwe tensile data may be used as a guide in fairing the rupturedata. Thus, M a plot is made of tensile strength against temperatureover the range of temperatures covered by the rupture tests, it w511 befound that the curve so obtained agrees approximately in shape with thatfor O.l-hour rupture data. Further, since such curves are to be used inestablishing the best constants for a linear time-temperature parameter,curves of equal ticrements.of log t should be equald.yspaced, at leastin the time region above 30 hours. When the constant-stress curves areto be constructed from the cross plots, as - stress levels as desiredcan be used ti the analysis, provided they are h the range where suf-ficient data are available for interpolation. On the bases of the_ses ~de, the most satisfactory stress range for determining thepoti~ of intersection is between approx3mtel.y 10 amd 40 percent of theroom-temperature ulthnate tensile strength of the material.

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If the ~erhental data are to be obtained frm a minimum numberof tests expressly for such an analysis, a series of constant-nom3nal-stress tests best serve for the determination of Ta and log ta. Itis deskble to obtain data in the range of apprwimately 30 through300 hours for at least two stress levels, at about 10 percent and 40 per-cent of the ultimate tensile strength. Once these constmts have beendetermined, the master plot of the logarithm of stress(T - Ta)/(log t - log ta) can be constructed using anytitel.y 10 hours at other stress levels as necessary.

Extrapoktion of Short-Time Data

Experience with analysis of a nuniberof materials

againstdata above approx-

has suggestedthat the clifferences which can be introduced in the detemina~ion of -these constants by use of data in the range between 30 and 3W hours,as compared with the use of data for longer times, have relatively littleeffect on the results of exbrapolation up to at least 10,000 hours. How-ever, the question of precisely how many tests in the 30- to 300-hourrupture-time range might be required in say specific case is left toexperimental investigation.

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n figure 7 the solid points represent the data belowrupture time. If the same values of Ta and log ta arematerial as were determined using longer rupture times, it

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100-hourused for eachcan be seen

that the master curves will be almost exactly the same when data arelimited to the 100-hour time range as when all the data are used. Hencethe plots in figure 10, including the extrapolated data to 10,000 hours,would be erectly the Samej although only the data below 100 hours areused to obtain the master curve. However, it should be emphasized thatdata below approximately 10-hour rupture time often deviate sufficientlyfrom the linear portion of the constant nominal stress curves to intro-duce error in the master plot. Fof example, in the case of S-590 alloy,the low-time data are not included in the master plot, and correspond-ingly, the conventional plot in figure 8(e) based on the master curveof figure 7(e) does not fit the low-time data.

APPLICATIONTO CREEP

Only limited creep data are available in the literature suitablefor a critical analysis of the applicability of a given time-temperaturerebtion. Analysis of suitable available data indicated, however, thatthe use of the parameter (T + 460)(20 + log t} to correlate creep dataat a given stress, where t is the time to produce a given totalelongation, leads to the same type of discrepancies as its use to cor-relate stress-rupture data. On the other hand, the linear time-tempe?.aturerelation was found to yield an improved correlation. Fig-ure U. shows a master plot for Nimonic 80 based on the linear parameter.These data are presented in reference 5 in the form of average curvesrather than experimental data points, and the data points used for fig-ures Kl represent values from these curves. The three curves shown arefor rupture, for 0.2-percent plastic creep strain, and for O.1-percentplastic creep strain. For each of these conditions, stress is plotted

Tagainst - 100

logt - 17’where T is the temperature in de-es Fahrenheit

and t is the time in hours. It is seen that the data points at alltemperatures correlate very well with the master curves drawn throughthem. b this case, Ta and log ta for rupture and for each of thetwo conditions of plastic creep strain are the same, although it ispossible that for other m.terial.sdifferent values of Ta and log ta

will apply to fracture and to creep.

Reference 2 recommends the use of the ~eter (T + 460)(20 - log r]to correlate minimum creep data, where r is the minimum creep rate.Data covering a sufficiently wide range of the creep variables to permitan adequate critical analysis of this parameter are not genersJly availa-ble. However, the linear parameter in the form (T - Ta)/(log r + log ra)L.where r is the minimum creep rate and ra is a material constant, has

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been applied with good results inavailable - principally for S-590The value of Ta was found to bethe stress-rupture data for these

NACA TN 2890

several cases where -e~ive data arealloy (ref. 1) and Monel (ref. 7].about the same as that for correlatingmaterials; the value of log r. was

found to be a~proximately 2 to 4 units lower than log ta [t~e ~orre-lating constant for stress-rupture data) when r and ra are expressedin percent per hour and t and ta in hours.

CONCJXJSIOI?S

The examination of ptilished data on 40 mterials representingferritic and austenitic steels, high-temperature alJoys, and aluminumdhys has led to the following conclusions, which have been found toapply in the range of rupture times between 10 and 10,000 -hours:

1. The experimental data justify the assumption that when thelogarithm of the rupture time is plotted directly against temperaturewith nominal stress as a parameter, reasonably straight lines,resultand these lines tend to converge to a single point (Ta, log ta). Basedon this assumption of linearity and convergence, a t--temperatureparameter in the form [T - Ta)~(log t - log ta) is proposed’for thecorrelation of rupture data and the prediction of long-time bekviorfrom data in the moderate-rupture-th range. It is believed that datain the ruptuxe-time rmge below 300 hours should suffice to determinethe constants Ta and log ta, and the greater portion of the data usedto determine the master plot can be in the 10- to 100-hour t~ range.In ald cases examined, the use of data at rupture times below 300 hoursresulted in accurate predictions of rupture times in the 10,000-hourrange. /

2. Examination of limited available creep data indicates that aparameter in the form (T - Ta)/(log t - log ta) is suitable for corre-=t ion and prediction of time to produce a given total creep elongation;and a prameter in the form (T - Ta)/(log r + log ra) is suitable forcorrelation and prediction of ndn.imm creep rate.

3. The parameter (T + 460)(20 + log t) was found in some cases toyield rupture tties In error by a factor of 10 when 10,000-hour data arepredicted from 100-hour data. These discrepancies arise from the use ofa universal constant equal to 20 and also from the nonlinearity of therelation between the logarithm of the rupture time and the reciprocal ofthe absolute temperature (at a given stress).

Lewis Flight Propulsion LaboratoryNational Advisory Commitiee for Aeronautics

Cleveland, Ohio, December 11, 1952.

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Al?Hmmx - CRITICAL EXAMINATION OF LINMHTYOFJ?LCTOF

LOG t AGAINST1

T + 460

The following analysis of 16-13-3 steel is presented in order todemonstrate by numerical example the basis for showing in figure 3 the

1typical shapes of plots of log t versus —

T + 460”

Figure 12 shows the conventional stress-rupture data for 16-13-3 steelas taken from reference 2. The solid lines are drawn for reasonable fitwith the data in the experimental range. Extrapolations of one-halfa time cycle for the 1200° F and 1400° F curves are shown by the dottedlines. Figure 13 shows constsmt rupture-time curves derived by cross-plotting the values from the curves in figure 12. The constant rupture-time lines from log t= - 1.0 to log t= 3.5 sre shown as solid lines;the dotted lines for log t = 4.0 and log t = 4.5 are based on the pointsA, B, C, and Destablished in

Figure 14.

and on the general family relation among such curves asthe range of actual experimenteildata.

shows cross plots from figure 13 of log t against T +1460.

The stress ramge of primary interest for anslysis is between 5000 and20,000 pounds per square inch, where the.high-rupture-time data are estab-lished with the most certainty; the curve for 30,000 pounds per squareinch, which involves only low rupture times, is also included for lateruse. For various constant stress values, curvature is observed at thehigh rupture times. To ascertain the significance of this curvature inrelation to extrapolation of short-time stress-rupture data,straightlines are drawn to best fit the experimental data in the rupture timerange up to about 300 hours. If only the rupture data below 300 hourswere available, the best extrapolationbased on the linearity of plots

1of log t against

T + 460would be therefore by extension of these

lines. (This case represents the assumption that C in the relation ofref. 2 varies with both material.and stress, and should therefore @vethe best over-all results available from the rate-process equation.) Hthe 1200° F curve in figure 12 is to be determined by extrapolation fromdata below the 300-hour rupture-time range, points on this curve aredetermined from figure 14by the intersection of the vertical line at1200° F with the extensions of the straight lines representing the datain the rupture-time range below 300 hours. These points establish thecurve EF in figure 12, where it differs appreciably fran the experi-mental curve even in the rsmge where data are available.

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,Figure 15 shows constant stress cross plots of log t against tem-

perature using the same data as those used for the construction of fig-ure 13, and the linearity is considerably improved. Establishment ofthe 1200° F curve in figure 12 by linear etiension in figure 15 of therupture data below 300 hours to the points of intersection with the1200° F line is seen to be in better agreement with the experiment.%11200° F curve.

REFERENCES

1. Grant, Nicholas J., and Bucklin, Albert G.: On the ExtrapolationShort-Time Stress-RuptureData. Trans. A.S.M., vol. 42, lg50,pp. 720-751.

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f2. Lsrson, F. R., ~ ~er~ J~-: A Time-TemperatureRelationship

for Rupture and Creep Stresses. A.S.M.E. Trans., vol. 74, no. 5,July 1952, PP. 765-771.

3. Anon.: Digest of Steels for High Temperature Service. Fifth cd.,Steel and Tube Div. (Canton, Ohio), The Timken Roller Bearing Co.,1946.

4. Anon.: Ihconel “X” - A High Strength, High Temperature Alloy. Rev. cd.,Dev. andRes. Div., The International Nickel Co., Inc., Jan. 1949.

5. Anon.: The Nimonic Series of Alloys - Their Application to Gas Tur-bine Design. Rev. cd., The Monel Nickel Co., Ltd., 1951.

6. Flanigan, A. E., Ted.sen,L. F., and Dorn, J. E.: Stress Rupture andCreep Tests on Aluminum-alloy Sheet at Elevated Temperatures.Tech. Pub. No. 2033, Am. Inst. Mining and Metall. Eng., Sept. 1946.

7. Grsnt, Nicholas J., and Bucklin, Albert G.: Creep-Rupture andRecrystallization of Monel from 700 to 1700° F. Trans. A.S.M.,.Preprint no. 5, 1952.

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32 36 40/ (T+ 460)(2%+log

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. ,- Figure 1. - Minterrupturecurvesfor 18-8steel-using

,)

Temperature,T,OF E

o L2001300

: 1400A 1500v 1600A 1800 F

100X103

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< 10~ ‘tx \

.mm \

E%

\~ Curve forrupturetimes

\ \\”,

alldatapotits

)1

48t)

parameterT

(T+460)(20+ log

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1

Temperature,T,%

o 12001300

: 1400A Moov 1600h 1800

—Curvee preaictedby fig.1(dataforlessthap 100hr)

.

-1 0 1 2 3 4Logt, hr

(a)18-8stainlesssteel.

Figure2. - Conventicmalstress-ruptureplotsderivedfrom (T+ 460)(20+ logt)parameterusingdatafor lessthan100hours.

— ———

.

a

.

\

m

*

— . -...——

15

.,

.

*

2890

F100MO3—

10

1

-1

I

o 1

-.i

Temperature,T,%1000

: 11000 1200A 1300v 1400

CurveS predictedfmmdatafor lessthan100&s

.

\\

k,\

\ \-\

\ L\ \\

\ \ L .Y

\

\ “\\

\\ u

\

~

‘\\

\ \

> \\

I2

Log t, hr

(b)DM steel.

4

Figure2. - Concluded. (conventionalstress-ruDtureDlotsderivedfrom (T+ 460)(20+ logt) parameterusingd~taf& lessthan100hours.

——..—. ________ —— — .— — .——

16 NACA TN 2890

100(I.O3 1 t I I I 1 1

10

1

‘— Typioal range ofexperimental data

-— —— Erhapolatedrange

\,

\ ~

\ \\\

\\

\\ \\

\ \\

I ●

\ k \ l\ \ \ k%

. \ \ , .\ \

\ II

1 \*

\ \ \ \ \ \.

\ \ \ \ \ \

\

i \ \ \\

\\\ \

\b

\

\‘\ ‘\ i, \

\ \ \ \\ \ \ \ \t \\ \

\\ \ ,

\ \1 ●

\ ‘\ \, \\ \

J \

\ \ i.

’600 800 1000 lmo 1400 1600 1800

.

/,

.

Temperature,T, %-

Figure3. - Schematicdiagramshowingtypic-alconstant-ttiecrossplotusedinanalyslsof data.

.

@

— —

17

.

“

12

8

4

0

-4

-8

-I-2

-16

-20

Figure

o .1 . .3 .4 .1

T i-460

4. - Sohematicrepresentationccmrssuondtitofkure3 ah- ocmstant.namlnalstressourvasforlogar~tlmofrupturetimeaga~ reclpromlofabsolutetemperatuz=.

“

———— .— ...— — —....——— ---

18

.

“

o 200 400 600 800 10UO 1.2oo 1400 16Q0 1800

.

a

.

Temperature,T,~

F@lre5. - Sohemtio diagramcorrespondlmgto figure3 of oonstant-noinbldress curvesforlogarithmof rupturetime againsttemperature.

.— —.

19

.

.

-1 0

\

\

1

Temperature,T,‘?F

1200: 13000 1400a 1.3oov 1.6oo& 1800

4

(a) 18-8 stainlesssteel (ref.3).

Figure6. - Eaaia stress-rupturedata taken from publishedsouroes.

.

.

/

.—— ..— —— ———— _ _—.

20

200x

10Q

10

1

--- . -c

-- .

‘A \

-%

‘-%

x\

>

90011oo12CKl1350150016Q01800

0 1 2 3 4Log t, hr

(b)InconelX (ref.4).

-e 6. - Contkuea. Easic stress-rupturedata takenfrom publishedsources.

.

‘

.

.

(.

——— —.. .._. —

21

.

.

.

10CEU$

.— .

-- t

‘\

%\A\

10

1,-1

Temperature,T,%

1000: ~~o u?ooA 130Qv 1400

<\

\\

\

\

\\

I4

-6. - continued. Bsslostrees-rnpturedata taken from publlehsdsources. \

-- —..-..—. —— —— ————. —-——. ——

I

.

~10DQO3-

10

l_-1 o ‘1 2 3

IOg t, m

(d) 25-20 dxdnless steel (ref.3).

.

.

-6. - continues.I?asiastress-rupturedata‘takenfrom published

.

.

-3 -2 -1

ti

Temperature,T,‘%

0 lwo1350

: 1500A 1600v 1700h 1900

0 1 2 3L4Jgt,ti

(e)S-590 alloy (ref.1).

= 6. - Conoludea. Basio stress-rupturedata taken fran publishedeoorcea.

.

.—— ——— —. . ._—

10W

1-40 -t

Tempemtme,T,9

0 1.2oo1300

: 1400A 1500v 16CK)A 1800

Soltdfor

“\

\\

\

d

) -80 -100

.9ymbolsare usedruuturathe less

1

-120 -140T - 10+3logt-ls

(a)18-8 stainleaasteel.

m7. - Mastermpture aurvesfor expertientildata In the rangeabove1 hour USQ valuesof Ta and 108 ta detmed h f@LW 7.

.— —. —

25

.

100

lC

Tamperatwe,T,%

o 1.2oolwo

: 14.00A “ I.soi)v 1600A 1800

Solid symbolsare usedfor rupturetime lessthen 100 ID?

T - 100logt-L5

(a)18-8 stainlesssteel.

E’iaure7. - Masterruuturauurvesfor exmrimentaldata in time ranaaabove1 hour ushg va-hes of Ta and & ta detezmimdh f~-T.

—.—— .—— —— ————. —

NACA TN 2890

I20@lo3—

---

100

10 -

1-30 -40 -50

\

—

—

-,

40 900

I.loo: 1200& 1350v 1.5ooh 1600v 1800

4 Solid eymbolaare UsedforrupturetimeBlessthan100br

L

b,

\

60 -70 -80 -90T - 100

log t - 24

(b)IhconelX.

Fiaure7. - Continued. Masterr’nDtureourvesforexmrimentaldataintime

.

rangeabove 1 lmur uElngvalues-of Ta and log t; determinedIn figure7. ,,

a

.

100X

-30 40

Temperature,T,OF

0 10QO11oo

; I-2(x)A 130av 1400

Solid S~b016areusedfor zmpturetimeslessthan 100 hr

T - 100log t - 22

(o)DM steel.

FY4cure7. - continued. MasterruptureCWVEISfor expartientildata h time%gaabove 1 hour usingvaluesof Ta and log ta deteminea infigure7.

,

.-. ——-—

T - 100log t - 14

(a)25-20at=dnleaasteel.

Figure7. - Conttiea. Maatarnptme onw’eafor erperlmentaldata h time rangeabove1 hom USing vahm of !ca ma 108ta dekm@d in f@ 7.

.

.

4

—-— .———— -–— ----- .———— ———-. _.— ..—

,.

“

1

,

.

Figore7. -abO-

) -60

!%

!cOmperature,T,%?

o 12001350

: 1500A 16(XIv 1700N Boo

a Solid symbolsare usedfor ruptoretjmeslessthan 100 w

\

v

-70 -80 -90T

log t-21

(e)S-590alloy.

3!!Ell-100 -1

Conoluded.Masterruptureowmes for erperlmentaldata h time range1 hour usingvaluesof Ta and log ta detemnirmdh f@we 7.

—.. — ._ —___.—z .—— — ...—. —. —___

.

100

.

10

1

‘F’ v 1604)A 1800

— Curvesbased cm linearttie-temperattire~ter

\ \y

L

\ vA \

\v \

A \

\ . \

\A u

\\ \

\

i7

n

\\

\ \\

\

-1 0 1 2 3 4 5Log t, Ill?

(a)18-8 stainlesssteel.

Figure8. - Conventionalstrass-ruptnreq-s deriwd frcm masterourvesIn

.4,

.

..

flgwe 9.

.

.

.

. I I I I Temperature,

Ourvesbased on ltiear T,time-tamperatuzw %?

parameter o 90011OQ

20WL 03 : “ 1.2ooA 1350v 1.500

I A 1600w, v MOO

10Q~ —

1.\

id~l-l.m 10m -b.

i!

\

\

\

\

z\

7

\

\

1 .0 1 2 3 4 5

Log t, h?

(b)InoonelX.

Figure8.,- Conttiued. Conventionalstress-tiptureourveaderivedl%cmb mwter ourvesh figora9.

——— -— ——- -—— — —— . .

-1

* i’z”e’I I I I I I A 1.3oo

v 1400

~— Ourveabased on llnem

o 1 2 3 4 :Iog t, ID?

(0)DM steel.

Fiuure8. - Continues. Ccmvantlonalstress-ruptureowwes derivedfhm masterOurvesti figure9.

.

.

.

. — .— —— ——– — .- —

33

.

.

1007

10

1-:

Tempemture,T,OF

o 1000; El

A 1300v 1400

,.3 ~ 1500

Logt, br

(d) 25-20 stahless steel.

Figure8. - Continued. Conventionaletrasa-zmptureourvesderivedfrommasterOurvesin figure9. -

NACA TN 2890

“

10Q d’ –

v

-3 -2

Tempemture,T,‘%

0 12001350

: 1500A 1600v 1700& 1900

Owves baaed on llnear

n tIme-temperatwraparemeter

,

a ve

L A

+’ \ \

\ . \ \

\ v \

-x \

-1 0 1 2 3 4

.

Logt, llr

(e)S-590alloy.

Figure8. - Cancluded. Conventionalstress-rupttumcurvesderiveilfrcnnmaaterourvesin figure9.

.

35

+

100lcF-

k

;+

10

A

0

MeallcUrvefor all date

132 36

(T +4:60)(20 + 1: t)

(a)).6-8atatilee~steel.

IMrm for rlessthan

-Tmparatma,T,%

o 1.2001300

: 1400A 1500v 1600A 1800

)twe tties

Figure9. - Masterrupturecorvesuelngperamater(T + 460)(20 + log t).(Datafromfig.6.)

.

w

.—. .— —_. —__ .—

(T + 460)(20 + logt)

(b)IncanelX.

(Datefrm fig. 6.)(T + 460)(20 + logt).

— -——— ..—. _______ __

,

.

“

10M’P—

1

Figure9.’-

8

— 01

3

Te f(

T

I

1

rnpk t:easthan 100hrsolidsymbols)—

~36

o 10000 IJ.oo Io lmoA 13(X3v 1400

>

Mean curw foralldata

v\

\es

40 44xl&

7

(T + 460)(20 + log t)

(c)I!Mukel.

(knMnned. Maaterzupturecurvesuahg ~ter (T+ 460)(~CI+ logt).(Ditafrm fig. 6.)

———— -—-..– —_—L......— —

38

----+Tamperatuzw,

T,CT

o 1000

A 1300v 1400

L.

Curvefor ruptm-atheeleesthan 100hr(solid symbol%)

\v\

v \h Y

N \\

, I vMean ourw for \ \

\all data— v

“\

V *

?lIi 40 44 40 52 56X--(T + 460)(20 + logt)

(d)23-20 stainlesssteel.

3

Figure9. - Collttiuaa.l!aaterruptureo=fu:~ Yter (T+ 460)(20+ logt). (Data. .

—

.

,,

39

10CMICF

10

128 32 3

Figure9.i-

0 1200

A 1600v 1700

v

all data

\.K,71U’vefor rupturetinlaslessthan 100hr /

>

(aolldsymbols) /

48(T +4:60)(20 + 1: t)

52 56xlo-

(e)S-5S0 alloy.

Conoluded. Masterruptureoorvasusingparamatar(T + 460)(20 + logt).(Datefranfig.6.)

,

.

-.. . . .... . —. -——.+ ..—

40

.

100

10

11

Tam--,.

l-z(x): 13000 1400A 1500v 1600Is Moo

=1 —— — Data under109 hr used—A1.laatansd

Iclgt, h’

(a) 18-8 .gt.dnlesssteel.

Figure 10. - Cmlventicmalstress-mptm?emrms derivedfranmaterPlotsIn

,,

fIgureu.

. . .. —

NACA TN 2890

I I I I I I I I 1 1

41

I——_Data under100 W “wed Tamperatnre,— AU. dati used T,

200)U03 %

o 90011oo

; zooa- ~ A 1350

100

\

\2 \ A

\\\

\ \

\\

\

\ \\

\

\

I lxI I . x

~ \ \\ I

\\ \ 1

\; \ \ \\ \y

\’ \ \ \\ \\

\\ k \

\. \ \=\

\

\

●

\~

\

\

\

\7

\.

1o 1 2 3 4 5

Log t, hr

(b) Ihoonel X.

Figure 10.- Conttied.Conventionalstress-ruptureourvesderivedfrcnnMater plots h figure11.

.

.

.-. __ —-- . -—— .——.

42 NACA TN 2890

.

I Temperature,T,

k

9

0 1000l-l 11111 0 11(H3

F’ I---

0 1200

I A UOQv 1400

Logt, hr

(c)DM steel.

Figure 10. - continued. Conventimal streaa-ruptwreploteIn flgul’a11.

cumes deri~adfrommaater

I

NACA TN 2890

low

I

10

rF’–

1

T

0

R@ure 10. - continued. Conventionalstress-rupturecurvesderivedfrommwter—plots in figure-Il.

./

43

l’empmture,T,%?

1 3 4 5L@:ti

(d) 25-20 stainlesssteel.

. . -—. —.— —. — -.--. —-—-—-—-—-———-—

NACA TN 2890

.

.

-3 -2 -1

concluded. Comantional

0 12001330

: lsooA 1600v 1700& 1900

—-- Data under 100 br usedAU data used

Iogt, hr

(e)S-590alloy.

-t-i

Q

-T!E3 4

stress-rupturecurvesderivedfrmnmasterplotsIIIfigureIl.

.

,

ma

.alm

i!

I I I II%wl.1

Tempe~ture,

o1112

A 1382~03

10

-0.2percentplaatio—

oreepstrain

1-50 -60 -70 -80 -90

Figure 11. - Maaterplot for totalplaatiooreepdata and ruptoredatafor Ntionio80. (Datafromref. 5.)

.,

.

*

— _ . . . .— ——

NACA TN 2890

Imgt,im

1

~

Temperature,T,‘%

F-r

\

—

—

—

—

—

—

6 7

.

.

- ~. - CCQVBIIZIO~l *ess-mpt- plot for16-H-3 steel. (Datafromref.z.)

NACA TN 2890 47

.,

“

100X

10

11

3—

1( 0

~g t,-br.1.0

-.5(

0’

.5(

1,0

1*5 (~

2,5’

3.0’

~

4.0

4.5

J-1.2oo 1400 )

‘\)

\\

\ 1 \

\\\

1800

-

Temperotore,T, %

IYgure 13. - Ccmstantmpture-time oroseplotsfor 16-13-3eteelderivedfromfigure14.

wJ-D

———-.——. .—— __ —————— ——. —

7

El

5

4

A3

+-

1

2

1

0

-1

.40 .44 .46 .52 .56 .60 .6&Xl$1

T + 460

1 I I I I I I I 12000 1900 1800 1700 1600 1500 1400 1300 1200

Temperaturej T, %

R@re 14. - Plots of logarithm of rupture the against reclprooal of absolutetemperature for 16-13-3 steel. (Data from fig. 15.)

— 1

I?ACATN 2890 ‘ 49

.

-1 I1000 1200 1400 1600- -1800 - 2000

12200

Temperature, T, %’

Figure 13. - Logarltbm of rupturetimeagainsttemperature for 16-13-3 steelshowing assumed linear relation above approximately lo-hour rupture time.

Material constants: Ta = l~; log ta = 17.

NACA-bnSIeY -3-20-54-125

—.—.- -- —_ — –—— -——.