NASA/TM--1998-208658

Determination of Yield in Inconel 718 for

Axial-Torsional Loading at Temperatures

up to 649 °C

Christopher M. Gil and CliffJ. Lissenden

Pennsylvania State University, University Park, Pennsylvania

Bradley A. Lerch

Lewis Research Center, Cleveland, Ohio

November 1998

https://ntrs.nasa.gov/search.jsp?R=19990008650 2018-05-11T17:15:31+00:00Z
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NASA/TM--1998-208658

Determination of Yield in Inconel 718 for

Axial-Torsional Loading at Temperatures

up to 649 °C

Christopher M. Gil and CliffJ. Lissenden

Pennsylvania State University, University Park, Pennsylvania

Bradley A. Lerch

Lewis Research Center, Cleveland, Ohio

National Aeronautics and

Space Administration

Lewis Research Center

November 1998
NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

Price Code: A03

Available from

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Price Code: A03
DETERMINATION OF YIELD IN INCONEL 718 FOR AXIALTORSIONAL LOADING AT TEMPERATURES UP TO 649 °C

Christopher M. Gil and Cliff J. Lissenden

Pennsylvania State University

University Park, PA 16803

and

Bradley A. Lerch

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, OH 44135

SUMMARY

An experimental program has been implemented to determine small offset yield loci under axial-torsional

loading at elevated temperatures. The nickel-base superalloy Inconel 718 (IN718) was chosen for study due to

its common use in aeropropulsion applications. Initial and subsequent yield loci were determined for solutioned

IN718 at 23, 371, and 454 °C and for aged (precipitation hardened) IN718 at 23 and 649 °C. The shape of the

initial yield loci for solutioned and aged IN718 agreed well with the von Mises prediction. However, in general, the centers of initial yield loci were eccentric to the origin due to a strength-differential (S-D) effect that

increased with temperature. Subsequent yield loci exhibited anisotropic hardening in the form of translation

and distortion of the locus.

This work shows that it is possible to determine yield surfaces for metallic materials at temperatures up to

at least 649 °C using multiple probes of a single specimen. The experimental data is first-of-its-kind for a

superalloy at these very high temperatures and will facilitate a better understanding of multiaxial material

response, eventually leading to improved design tools for engine designers.

INTRODUCTION

Aeropropulsion components, such as disks, blades, and shafts are commonly subjected to multiaxial stress

states at elevated temperatures. Nickel-base alloys are often used for these applications because of their excellent elevated temperature mechanical properties. Experimental results from loadings as complex as those felt

in-service are needed to help guide the development of accurate viscoplastic multiaxial deformation models

that can be used to improve the design of aeropropulsion components.

Inconel 718 (IN718) is a popular nickel-base alloy which has been extensively researched in terms of

strengthening mechanisms and fatigue behavior (e.g., Oblak, et al., 1974; Fournier and Pineau, 1977; Sundararaman et al., 1988; Worthem et al., 1989; Kalluri et al., 1997). In addition, the viscoplastic behavior of

IN718 at 649 °C has been characterized for the Chaboche and Bodner-Partom viscoplasticity models using

tensile loading at several strain rates (Abdel-Kader et al., 1986; Li, 1995). In this investigation, tubular IN718

specimens were subjected to isothermal combined loads over a wide range of temperatures (23 to 649 °C) to

map out yield loci in the axial-shear stress plane. The results over this broad temperature range are unique and

will lead to a better understanding of time-dependent multiaxial behavior of IN718 in service at elevated temperatures.

Multiaxial experimental investigations often use a yield surface to delimit the elastic region, describe

hardening, and determine if an associated flow rule applies by checking for normality (Michno and Findley,

1974; Phillips and Moon, 1977; Khan and Wang, 1993). These experiments involve determining enough yield

points in one or more stress planes to construct the yield surface. This can be accomplished using several

specimens, where each specimen is used to find a single yield point, or by using a single specimen to determine multiple yield points. The latter technique is more common since using several specimens is not cost

efficient and the results may be affected by specimen-to-specimen scatter. For an in-depth (albiet dated) literature review of multiaxial experimental investigations, see Hecker (1976) and Michno and Findley (1976).

NASA/TM--1998-208658 1
Thesuccessof usingasinglespecimentocompletelymapoutayieldsurfacedependsstronglyonpreservingthematerialstateduringprobing.Sinceyieldingdefinestheonsetof plasticdeformation, anychange

in materialstateassociatedwithdetectingayieldpointmustbeinsignificant.Otherwise, thematerialstate

(andalongwithit thesizeandshapeoftheyieldsurface)ischangedbyeachprobe.

Historically,threetypesof yielddefinitionshavebeenusedfor yieldsurfacexperiments: (1)deviation

fromlinearity,(2)offsetstrain,and(3)back-extrapolation. Thesmall offset strain definition is frequently used

to give an indication of the proportional limit. As the name implies, yielding is defined to occur when an

equivalent offset strain on the order of a few microstrain (He) has developed.

There is some flexibility in using the small offset definition of yielding since there are a wide range of

offset magnitudes that can be considered small. Helling et al. (1986) detected offset strains of-5 He to determine yield surfaces for aluminum and brass, whereas at the other extreme Nouailhas and Cailletaud (1996)

used a target value of 100 He when conducting similar tests on a single-crystal superalloy. For elevated temperature experiments, where 'heater noise' (thermal fluctuations and electronic noise) can decrease the strain

signal-to-noise ratio, a large enough offset strain must be used to determine yield points consistently. Thus, in

the present work we investigated the effect of using target values between 10 and 30 He for determining the

yield points.

The accuracy of the experimental results is strongly dependent on the strain measurement device. High

precision strain gages work well for detecting small increments of strain at room temperature (Helling et al.,

1986; Wu and Yeh, 1991). However, for high test temperatures, where strain gages cannot be readily used, a

different method must be applied to detect yielding, such as an acoustic emission system (Winstone, 1983) or

a high temperature biaxial extensometer (Battiste and Ball, 1986; Lissenden et al., 1997).

In the present study, a biaxial extensometer was used to determine yield loci in the axial-shear stress

plane for tubular IN718 specimens over a wide range of temperatures (23 to 649 °C). The specimens were

tested in two distinct material states: solutioned and aged. The aged material contains precipitates that are

expected to hinder dislocation movement and may lead to large back stresses (Stouffer and Dame, 1996),

while the solutioned material is generally a single-phase composition. Clearly, the two materials will exhibit

different yielding and hardening behavior.

The objective of this study was to demonstrate that yield loci (initial and subsequent) can be determined

for metallic materials (such as IN718) at temperatures up to 649 °C by probing a single specimen multiple

times and measuring strains with a biaxial extensometer. This work opens the door for a more in-depth study of

multiaxial response at temperatures in the service range of aeropropulsion systems. The data presented here

will be further analyzed in a companion paper (Gil et al., 1998a) to obtain loci of rate-dependent flow surfaces

in the axial-shear stress plane.

EXPERIMENTAL SETUP AND PROCEDURE

Material and Specimens

The wrought Inconel 718 superalloy used in this study was obtained in the form of extruded 31.8 mm

diameter bar stock, all from the same heat. The material composition as provided by the fabricator is listed in

Table I. The bars were machined into tubular specimens having the final dimensions shown in figure 1. After

machining, the specimens were solutioned at 1038 °C in argon for 1 hr and air cooled. Select specimens were

further heat-treated as follows: aged at 720 °C in argon for 8 hr, cooled at 55 °C/hr to 620 °C and held for 8 hr,

then air cooled to room temperature. Henceforth, the material state will be referred to as either solutioned or

aged.

Metallography was performed on transverse and longitudinal sections taken from the grip ends (undeformed) and from the gage sections (deformed) of both solutioned and aged tubes. No difference was observed

between the grip and the gage sections. Furthermore, both the solutioned and aged microstructures appeared

similar (fig. 2). The grain structure consisted of equiaxed grains having an ASTM grain size of 4 (a nominal

diameter of 90 Hm). The solutioned material had a hardness of HRB 90, while the aged material was HRC 45.

Carbide stringers were aligned parallel to the tube axis (i.e., the extrusion axis) and were observed distributed

throughout the microstructure.

Transmission electron microscopy was performed on the solutioned and aged IN718. The aged material

was observed to have a fine dispersion of y" within each grain (fig. 3). The precipitate particles were observed

to be platelets -10 to 15 nm in length. The solutioned IN718 did not show any precipitation. Texture analysis

was also performed, which showed there to be no preferred grain orientation for either heat treatment.

NASA/TM--1998-208658 2
TestEquipment

Theexperimentswereperformedonacomputercontrolledbiaxialservohydraulictestmachinecapableof

applyinganaxialloadof +222,000 N and a twisting moment of +2,260 N.m. The specimen was held in place

by water-cooled, hydraulically actuated grips. The top grip remained fixed throughout a test while the bottom

grip is attached to an actuator capable of independent rotation and vertical translation. An analog controller

was used to command the motion of the actuator. Additional details regarding the biaxial test machine are

provided by Kalluri and Bonacuse (1990).

The test machine is equipped with a closed-loop induction heating system (Ellis et al., 1997) capable of

specimen temperatures in excess of 800 °C. The system consists of a 5-kW radio frequency induction heating

unit and three adjustable, water-cooled copper coils that surround the gage section of the specimen (fig. 4).

The specimen temperature is controlled by spot welding a thermocouple to the gage section of the specimen.

Three additional thermocouples were spot welded to the specimen to help achieve an acceptable thermal gradient (+ 1 percent of the test temperature).

Strain Measurement

The ability to measure very small increments of strain (precise to the microstrain level) is necessary for

yield surface experiments, since the goal is to detect yielding and then unload the specimen before significant

permanent deformation occurs. Furthermore, the strain measurement device must maintain this level of performance for a wide range of specimen temperatures. This is especially difficult at elevated temperatures,

where thermal fluctuations can hinder high resolution strain measurement.

In this investigation, axial and shear strains were measured using a water-cooled biaxial extensometer

(fig. 4) that is capable of operating over a large temperature range. The extensometer uses two high-purity

alumina (A1203) rods, spaced 25 mm apart, to precisely measure axial deformation and twist. Strain values are

recorded to one tenth of a microstrain (_te). Lissenden et al. (1997) have supplied more details on the biaxial

extensometer.

For transverse strain measurement, a diametral extensometer was employed. The diametral extensometer

is similar to the biaxial extensometer in appearance, although it contains longer rods that rest on either side of

the gage section of the specimen to directly measure the change in diameter. Transverse strains were measured to determine Poisson's ratio (which will be used to calculate the equivalent strain rate) and to determine

whether Poisson's ratio changes during the course of a yield locus probe.

Test Control

With one exception, all of the experiments were conducted in strain control. An equivalent strain rate of

10 _te/sec (10 s s 1) was used. For axial-torsional loading and a Poisson's ratio of 0.34,1 the equivalent strain

rate is

Eeq=_f_EijEij = _(0.906)2E121 + 4 E122 (1)

where _ij is the strain rate tensor and Ell and El2 denote the axial and shear strain rates, respectively.

Custom written software and a personal computer, equipped with analog-to-digital (A/D) and digital-toanalog (D/A) conversion hardware, were used to control the experiments. The D/A hardware was commanded

to send strain increment data to the electronic controller 1000 times/sec. Similarly, the A/D hardware collected load, torque, and strain data from the controller at 1000 Hz. Every 100 data points were averaged to

help minimize the effect of heater noise, which resulted in a maximum of 10 data points per second being

written to a file.

Two different software programs were developed for controlling the experiments. One program was used to

determine the individual yield points that were used to map out initial and subsequent yield loci and the other

program performed the radial prestrains.

1Measured at 23 °C. Abdel Kader et al. (1986) obtained a value of 0.3356 at 649 °C.

NASA/TM--1998-208658 3
YieldLoci

Eachlocuswasdeterminedbystrainingthespecimeni 16uniquedirections, accordingto aspecified

angleinequivalentaxial-torsional strainspace(fig.5).Theorderinwhichtheprobeswereconductedwas

chosentominimizechangestothematerialstate.Forexample,figure5 showsthateacheven-numbered probe

wasintheoppositedirectionfromtheprecedingodd-numbered probe.Byusingthissequencewehopedto

counterbalancetheeffectsof thepreviousprobe.Furthermore, eachsurfacewasrepeatedatleastonceto

ensurethattheresultswererepeatableandto verifythatthematerialstateremainedessentiallyundisturbed.

Eachpointontheyieldlocuswasdeterminedusingthefollowingprocedure.

• Calculatethecoefficientsof theaxialandshearelasticloadinglines(E,¢Y]1, G, and ¢Y]2) over a predefined strain range during the initial (assumed to be linear elastic) portion of the loading using a least

squares regression technique (fig. 6). E and G are the axial and shear moduli; ¢Y]I and (Y]2 are the axial

and shear initial stresses.

• Continually calculate the offset strain components (fig. 6)

" (Yll --(Y_I (2)

E_{)' = E11 E

qff O12 -- (Y]2 (3)

El'2 ----El2 2G

where o11, o12 are the axial and shear stresses and E11, E12 are the axial strain and tensorial shear strain

(E12 = 1/2 712).

• When the equivalent offset strain,

- 3k 12] = ) +3k 12] ,

(4)

reaches the target value (usually 30 _tE), write the current stress values (axial and shear) to an output

file, unload the specimen and then begin the next probe.

Equation 4 is the equivalent offset strain, simplified for axial-torsional loading of a material exhibiting

inelastic incompressibility (v = 0.5). Although the incompressibility condition may not be met for small offset

strains, where the instantaneous Poisson's ratio is transitioning from its elastic value to its fully inelastic

value, this relationship for the offset strain components has been traditionally used by researchers for determining yield surfaces (e.g., Wu and Yeh, 1991; Khan and Wang, 1993; Lissenden, et al., 1997). Additionally, the

equivalent offset strain refers to an offset during loading and does not necessarily have the same magnitude as

the permanent set (i.e., permanent strain at zero load).

Radial Prestraining

After determining the initial yield loci, hardening behavior was studied by applying radial prestrains at

elevated temperature (except in one case a cyclic radial prestrain was applied at room temperature). Two

radial prestrain paths were used. One path was combined tension-torsion, corresponding to an angle of Z45 ° in

the equivalent strain plane (fig. 7(a)). This was equivalent to a Z45 ° path in the equivalent stress plane. A

schematic of the equivalent stress-strain response is shown in figure 7(b). The maximum prestrain point was

determined by detecting a particular value of equivalent offset strain. The other prestrain path consisted of

straining the specimen in pure tension until a predefined total axial strain was achieved.

The same procedure was followed for both strain paths and is outlined in the following:

• The stress-free specimen was heated to the desired temperature (in load and torque control).

• After thermal equilibrium was reached, the specimen was strained until the target prestrain value was

achieved (point AI (or BI) in fig. 7(a)).

• The mode was switched to load/torque control and the specimen was held at a constant stress for several

minutes. During this time creep strains were monitored on X-Y plotters and recorded by the data acquisition software.

NASA/TM--1998-208658 4
• Afterseveralminutes,thecontrolmodewasswitchedbackto straincontrol.Thereverseyieldpointwas

found(pointA2(orB2)infig. 7(a))byunloadingthespecimenuntiltheequivalent offsetstrainexceededthetargetvalue.

• Thespecimenwasreloadedtoapoint(pointA3(orB3)infig. 7(a))midwaybetweentheprestrainpoint

andthereversepoint.Thesubsequent yieldlocuswasthendeterminedusingthispointastheprobe

origin.

EXPERIMENTALRESULTS

SolutionedIN718

Whenusingtheoffsetstraindefinitionofyieldingit isimportanttorelatetheoffsetstrainduringloading

tothepermanent setthatis measuredafterunloadingiscomplete.In anattempttocomparethesetwoquantities,theoffsetstrainforasmalloffsettensiontestwasplottedversusthetotalaxialstrain(fig.8).Theoffset

strainaccumulatesto-30_tEduringloading,howevertheoffsetstraincontinuestoincreaseduringunloading

toatotaloffsetof-44_tE.

Thediscrepancybetweentheoffsetstrainduringloadingandthepermanent setisbelievedtobedueto

inaccuracyof theextensometer afteraloadreversal,ratherthantruematerialbehavior.Datafromprevious

testsontype316stainlesssteel(Lissendenetal.,1997)wereanalyzed,whereanextensometer andstrain

gageswerebothusedtomeasurestrain.Acomparisonof straindataobtainedfromtheextensometer andfrom

thestraingageshowedthattherewasgoodagreement betweenthetwomeasurement devicesduringloading.

However,aftertheloadreversaltheextensometer offsetstrainsoftencontinuedtoincreasewhilethestrain

gagesindicatedlinearelasticunloading(constant offsetstrain).Thissuggestshatstrainsmeasuredby the

extensometer duringloadingareaccurate, butthatacorrelationbetweentheoffsetstrainandpermanent set

cannotbemade.

Nowthatwewereconfidentthattheextensometer wasaccuratelymeasuringtheoffsetstrain,specimen

IN-15wasusedtodeterminewhichcontrolmode,stressorstrain,gavemoreconsistent resultsat23°C.

Phillipsetal.(1984)investigatedtheyieldbehaviorof aluminumusingstressandstraincontrolledloading,

howeveradirectcomparisonoftheresultswasnotshown.In thispreliminaryworkwewereinterestedin comparingthesizeandshapeof theyieldlocususingstressandstraincontrolandwewantedto determineif there

wasmoreorlessscatterintheresultsforstraincontrolcomparedto stresscontrol.

InitialyieldlociforspecimenIN-15weredeterminedunderstressandstraincontrolledloadingatroom

temperature. In theseteststhetargetvaluewasanequivalent offsetstrainof 20_tE.Theresultinglociareplottedinthemodifiednormal-shear stessplane(_/3.cy12 -cyH)infigure9.Theeccentricityof thelocusinthe

compressiondirectionmayormaynotbesignificant,sincespecimenIN-15wasnotinthepristinestateprior

tothesetests.Clearly,thecontrolmodehadlittleeffectonthedata.Repetitivetestsweremadetoverifythis

result.Straincontrolwasusedfortheremainingexperimentstobeconsistent withprestraining.

Next,theelasticPoisson'sratio(whichwasneededforeq.(1))wasdeterminedduringatensileprobeby

measuringthediametral strain.SpecimenIN-9(apristinespecimen) wastestedin tensionuntila 10_tEoffset

wasreached. Figure10showsthediametralstrain(E22)plottedversustheaxialstrain(E11). Theslopeof figure10,whichisPoisson'sratio,is0.34andremainsconstant uptotheloadreversal.Thissuggestshatthe

elasticPoissonratio(0.34)is amoreappropriatechoiceforuseinequation(4)whenperformingsmalloffset

yieldexperimentssincenosignificantchangein thePoissonratiooccurs.However,esultsnotshownhere

indicatethatyieldlociarerelativelyinsensitivetothePoissonratiofor valuesrangingbetween0.25and0.5

(Gil, 1998).

Theeffectofusingtargetvaluesbetween10and30_tEto determineyieldlociwasexaminednext.Three

lociweredeterminedfor eachtargetvaluetojudgerepeatability. Ateachtargetvalue,theresultsof thethree

lociwerenearlyidentical(Gil, 1998);indicatingthattargetvaluesin thisrangedonotsignificantlychange

thematerialstate.Additionally,nosignificanthardeningoccurredin theoffsetstrainrangeof 10to30_tE.We

chosetouseatargetvalueof 30_tEfortheremainingexperimentstoobtainamaximumamountof offset

straindatatoanalyzeintermsofrate-dependent flowdefinitions;whichforviscoplasticmaterialsaremore

importantthantheyielddefinition(Giletal.,1998a).Here,arate-dependent flowdefinitionreferstoonethat

dependsontheinelasticstrainrate,ratherthanthetotalinelasticstrain.Additionally,atelevatedtemperatures

thermalfluctuationsdecreasetheresolutionof themeasuredstrain,makingalargertargetvaluemore

practical.

NASA/TM--1998-208658 5
Afterthesepreliminaryissueswereresolved,theinitialyieldbehaviorof solutionedIN718wasinvestigatedat23°Cusingtwopristinespecimens(IN-6andIN-25).Therewasremarkablyverylittlespecimen-tospecimenscatterbetweentheinitialloci(fig. 11).Furthermore, eachtestwasrepeatedonceto confirmthatno

significantchangeinmaterialstatetookplaceduringprobing.

ThevonMisesandTrescayieldcriteria(see,forexample,KhanandHuang,1995)arethetwomostpopularcriteriaforpredictingyieldinginisotropicmetals.ThevonMisescriterionplotsasacircleinthemodified

axial-shear stressplane0/3"%2- %_),whiletheTrescacriterionplotsasanellipse.Thesecriteriaarecomparedwiththeexperimental datainfigure11.ThevonMisescircle,centeredatthestressplaneoriginwitha

radiusof 248MPa,appearstofit thedatawell.TheTrescaellipseprovidesamoreconservativepredictionof

yieldingwhentorsionalloadsarepresent.

Beforeinvestigatingtheinitialyieldbehavioratelevatedtemperaturetheheaternoiseinthestrainsignals

atelevatedtemperaturewasevaluatedthroughcomparisonwithroomtemperaturemeasurements (fig. 12).The

peak-to-peak amplitudeof theelectronicnoisewaswellbelow1_teforbothaxialandshearstrainatroom

temperature. At elevatedtemperature(454°C),theamplitudeislarger(especiallyin theaxialstrain)dueto

smallthermalfluctuationsandelectronicnoiseassociatedwiththeinductionheatingsystem.Clearly,heater

noiseisimportantwhenattemptingtomeasurestrainsprecisetoafewmicrostrain. Afteragreatdealofeffort

tofurthereducetheheaternoisewithoutsuccess, it wasviewedasacceptable.

InitialyieldlociforspecimensIN-6andIN-25determinedat371and454°Careshownin figures13and

14,respectively. SolutionedIN718wasnottestedat649°Cbecausethatis felttobetooclosetotheaging

temperature. Asthetemperatureincreases, theyieldlocidecreasein size,butretainthesameshape.In addition,thecenterofthelocusisnotlocatedattheoriginof thestressplaneasit wasat23°C.AvonMisescirclewitharadiusof 207MPacenteredat(-13.8,0.0)MPainthemodifiedaxial-shear stressplaneappearsto

fit thedataat371°Cverywell(fig. 13).At454°C(fig.14),avonMisescirclewitharadiusof 193MPaand

centeredat(-27.5,0.0)wasfit tothedatabyeye.Theseresultsindicatethatasthetemperatureincreases, the

yieldlocusdecreasesinsizeandbecomesmoreeccentricto theorigin.Theeccentricityin thecompression

directionwill bediscussedlaterinconjunctionwiththeagedIN718.

Next,specimenIN-6wassubjectedtocombinedaxial-torsional prestraining, asshowninfigure15.Point

A corresponds to thelocationwheretheinitiallociweredetermined(zerostress).Subsequent yieldlociwere

determinedatlocationsC,O,Q,andS.

Thefirstprestrainconsistedof combinedtension-torqueloadingat454°C.SpecimenIN-6wasstrained

alongaZ45° radialpathinequivalent srainspace(pathOA_A2A3infig.7(a))untilanequivalent offsetstrain

of500_tEwasattained(whichcorresponded toastresstateof cy_ = 173.5 MPa, %2 = 92.0 MPa; point B in

fig. 15). The center of the elastic region (point C) was then found, as described in the previous section, and

two subsequent loci were determined.

The first subsequent yield locus (Locus C) is shown in figure 16, along with the prestrain point B. A spline

fit of the yield locus is included to aid in interpreting the data. There is clearly some translation of the yield

locus toward the prestrain point. Furthermore, the back of the locus has become flattened indicating some distortional hardening. Various researchers have observed similar results for monolithic metals such as aluminum

(Phillips et al., 1972), brass (Helling et al., 1986), and stainless steel (Wu and Yeh, 1991). Figure 16 also

indicates that neither isotropic hardening (a pure expansion of the yield surface), nor kinematic hardening (a

pure translation of the yield surface), nor a simple combination thereof accurately describe the hardening

behavior of solutioned IN718 at 454 °C. Furthermore, the locus shows a small amount of cross effect, that is,

an expansion of the locus in the directions perpendicular to the prestrain direction.

Solutioned IN718 exhibited very little hardening behavior during the first prestrain cycle at 454 °C. Upon

reaching prestrain point B, the axial and shear responses were nearly perfectly plastic. In an attempt to determine the effect of fully reversed cyclic loading on material hardening, specimen IN-6 was subjected to five

strain-controlled cycles of combined axial-torsional loading at 23 °C, beginning and ending at zero stress

(figs. 15 and 17). The radial strain path was oriented at an angle of Z45 ° for positive strains and Z225 ° for

negative strains (as measured counterclockwise from the positive axial strain axis) and had limits of

E11= +2500 _tE and E12= +1875 _tE.

The last cycle ended when the axial and torsional loads reached zero, thus the final loading was in the

Z225 ° direction. Terminating the final cycle at zero stress (point O in fig. 17) led to an equivalent offset strain

of 1625 _tE between points O and D. Specimen IN-6 was then reheated to 454 °C and a subsequent yield locus

was determined. Figure 18 shows the subsequent locus (Locus O) as well as the cyclic prestrain path. As

expected, the locus has been translated and distorted in the Z225 ° direction compared to locus C and its center is located at approximately the same position as the initial Mises circle. It also appears that the cyclic

loading may have slightly increased the yield strength in the directions perpendicular to the loading path (i.e.,

cross effect).

NASA/TM--1998-208658 6
SpecimenIN-6wasagainprestrainedin theZ45° directionat454°Cuntilanequivalent offsetstrainof

1000HE was achieved (which corresponded to a stress state of %1 = 162.0 MPa, %2 = 86.0 MPa; point P,

fig. 15). Locus Q was then determined, as shown in figure 19, and was again translated in the direction of prestrain and distorted. From this point, specimen IN-6 was then further prestrained until an additional offset strain

of 500 HE was reached (corresponding to a stress state of cy_ = 177.0 MPa, %2 = 100.0 MPa; point R, fig. 15),

and locus S was determined (fig. 19). For each locus shown in figure 19, the corresponding prestrain point is

shown to provide a reference. Loci Q and S are very similar in shape and size, however locus S is shifted

slightly more in the prestrain direction with respect to locus Q due to the additional prestrain. Additionally, the

loci exhibit a cross effect, that is they have expanded slightly in the direction perpendicular to the prestrain

direction.

Aged 1N718

Experiments to determine yield loci for aged IN718 were hindered by an anomalous material response,

termed stiffening (Gil et al., 1998b), that occured during compressive loading. Stiffening is a nonlinear material response that is characterized by a slight increase in the stiffness. This behavior is shown in figure 20,

where the offset strain initially has a positive sign for compressive loading. At some point, as indicated in

figure 20, the direction of the offset strain reverses. Again during unloading, the offset strain continues to

increase. As mentioned, the permanent set shown in figure 20 may not be representative of the true material

behavior since the extensometer appears to exhibit hysteresis upon reversing the load. If the true material

response were elastoplastic, then the permanent set should be 30 HE, which would make the error in the extensometer results after complete unloading -17 HE (the maximum compressive strain was 3720 HE).

Stiffening could be associated with nonlinear interactions between dislocations and precipitate particles.

Hirth and Cohen (1970) proposed a theory to account for the strength-differential (S-D) effect in steels, in

which dislocations interact with solute atoms causing local distortion of the lattice and leading to local elastic

strains that are nonlinear. According to the model, the compressive nonlinear elastic region has an increasing

instantaneous stiffness. Thus, the yield stress is higher than that of a material having a linear elastic region

(given the same amount of elastic strain). Additionally, the tensile nonlinear elastic region has a decreasing

instantaneous stiffness and therefore the yield stress is lower than that of a material having a linear elastic

region. Kalish and Cohen (1969) suggest that this theory can also apply to the coherency strains around precipitated particles.

Stiffening presented a real challenge to our procedure for detecting yielding because our existing procedure explicitly assumes an initial linear elastic response. If stiffening is an elastic response (which appears to

be the case), then inelastic strain begins to occur when the stiffening offset has reached a maximum (fig. 20).

Therefore, in the presence of stiffening, we took the inelastic strain to be the offset strain plus the maximum

stiffening strain. Doing so essentially shifts the elastic loading line in the direction of the stiffening.

Two pristine aged IN718 specimens (IN-8 and IN-10) were tested at 23 °C and the initial yield loci are

shown in figure 21. The tests were repeated once for each specimen with nearly identical results. Avon Mises

circle of radius 655 MPa appears to fit the data well, that is 2.64 times larger than the initial von Mises circle

for solutioned IN718 at 23 °C. Clearly, the aging process (precipitation) effectively strengthens the material.

However, unlike the solutioned specimens (fig. 11) the locus is extremely eccentric to the stress origin and

centered at (-138, 0) MPa. The eccentricity of the locus in the compression direction is representative of the

S-D effect that has been observed in select materials (martensitic steels and other alloys as well as plastics).

Hirth and Cohen (1970) and Drucker (1973) provide possible explanations for the S-D effect. The Hirth and

Cohen explanation involves nonlinear elasticity and was mentioned previously. Drucker's explanation is based

on the experimental observation that materials that exhibit a S-D effect also have a permanent volume

change, which implies that yielding is dependent upon the mean stress (cym = [CYll+ cY22+ cy33]/3). Permanent

volume change is generally related to an increased dislocation density required for inelasticity in dispersion

hardened materials. If yielding is a linear function of mean stress, then there is a S-D effect. See also Radcliffe and Leslie (1969), Drucker (1973), Ranch et al. (1975), and Spitzig et al. (1975) for more on the

strength-differential effect.

There appears to be more scatter in the aged IN718 results than for the solutioned IN718 results. This is

probably due at least in part to the gradual yielding exhibited by the aged material relative to the solutioned

IN718. Figure 22 shows the normalized von Mises effective stress, cye_. = 3_f2/cYt, L for equivalent offset

strains up to 30 He for both materials under combined tension/torsion (0 = 57 °) at 23 °C. Here, J2 is the second

invariant of deviatoric stress and cypL is the proportional limit. The smaller hardening modulus of the solutioned

IN718 results in minimal scatter because of the smaller resulting stress increment relative to the aged IN718.

NASA/TM--1998-208658 7
SpecimensIN-8andIN-10werethentestedat649°C(fig.23).Followingthesametrendthatwas

observedforsolutionedIN718,thelociaresimilarinshapetothelociat23°C,yetsmallerinsizeandtranslatedfurtherinthecompressiondirection.AvonMisescirclewitharadiusof 448MPaandcenteredat

(-145.0,0.0)MPaappearstocloselyfit thedatafrombothspecimens. Morescatteris observedat649°Cdue

totheeffectof heaternoise.TheyieldlociforbothsolutionedandagedIN718appeartotranslatein thecompressiondirectionwithincreasingtesttemperature, asindicatedin tableII. ThismeansthattheS-Deffect,

whichis definedmathematicallyin thediscussionsection,increaseswithtemperature, butRauchetal.(1975)

reporthattheS-Deffectdecreaseswithtemperatureforsomesteels.AdditionalinitialyieldsurfacedeterminationsforagedIN718at371and454°C(notreportedherein)indicatethatthetemperature-dependence of

yieldingis differentforIN718intheagedstatethanit isinthesolutionedstate.

SpecimenIN-10wassubjectedto acombinedaxial-shear prestrain(Z45° inequivalent srainspace)at

649°Cuntilanequivalent offsetof 500_tewasdetected. Thesubsequent yieldlocusis shownin figure24,

wheretheinitialMisescircleisalsoshownforreference. Duringtheprestrainprocedurethecenterof thelocus

wasnotaccuratelylocated,possiblydueto theinfluenceof heaternoise,whichmayhaveledto thescatterin

thedatapointsontheyieldlocus.Nevertheless, afewimportantcharacteristics canstill beobserved. First,the

locusistranslatedfurtherinthedirectionof theprestrainthanwasobservedforsolutionedIN718(fig.16).

ThisverifiesthatprecipitationhardeningIN718notonlyincreasestheyieldstrengthof thematerialbutalso

increasesitsabilityto strainharden(Dieter,1988).Additionally,thereappearstobenocrosseffect,however

it isdifficultto makeanystrongconclusionsbasedonthelimitedamountof data.

Theotheragedspecimen(specimenIN-8)wassubjectedto apurelytensileprestrainuntilatotalaxial

strainof 9000_te(0.9percent)hadbeenreached. Thefirstsubsequent yieldlocusisshowninfigure25.The

locustranslatedinthedirectionof prestrainanddistorted.Thedistortionis anelongationithedirectionof the

prestraininadditiontoaflatteningof thebackside.Nocrosseffectisobserved.

DISCUSSION

All initialyieldlociexhibitanS-Deffect(exceptfor solutionedIN718atroomtemperature) fora30_tc

offsetstrainyielddefinition.TheS-DeffectincreasesasthetesttemperatureincreasesandforagedIN718at

649°Cis65percentbasedonthedefinitionof strengthdifferentialcommonlyused(Spitzig,etal.,1975),

SD=2 (5)

where % and (Yt are the yield strengths in compression and tension, respectively. Equation (5) was used to calculate the strength-differential shown in table II. When interpretting this definition based on the Mises yield

locus in the modified stress plane shown in figure 23, SD is the percentage of the ratio of circle center to

diameter. Whether the S-D effect that we have observed is real or apparent is currently being investigated.

A real S-D effect remains during gross plastic deformation, while an apparent S-D effect is only present at

the initiation of plastic deformation and could be due to residual stresses or microcracks among other things

(see Hirth and Cohen, 1970 and Drucker, 1973). The real S-D effect in 4310 and 4330 steels was found to be

5.5 percent by Spitzig et al. (1975). We suspect that a large portion of the 65 percent S-D effect that we have

observed is apparent rather than real. However, in order to mathematically predict our experimentally determined yield loci the S-D effect, real or apparent, must be taken into account. One way to do that is to use a

Drucker-Prager (1952) type yield criterion, that is, one that depends on the first stress invariant, I1 = 3(Ym, and

thus depends on the mean stress. Alternatively, the third deviatoric stress invariant, J3, could be used if yielding is independent of the mean stress.

The subsequent yield loci indicate that IN718 exhibits kinematic hardening, which results in a

Bauschinger effect, as well as distortional hardening, which is commonly observed in yield surface

experiments when a proportional limit or small offset strain definition is used. It is commonly observed that

small offset strain definitions result in hardening that is primarily kinematic and distortional while large offset

strain definitions (e.g., 2000 _te) result in isotropic hardening (Williams and Svensson, 1971 and Khan and

Wang, 1993). However, solutioned IN718 exhibited only a small amount of hardening relative to aged IN718.

Experimentally determined subsequent yield loci have two primary purposes. In one case, they can provide

guidance for the development of evolution equations that are necessary for materials that exhibit hardening. In

another case, they can be used to validate material models that have been developed and characterized from

other, perhaps uniaxial, data. We view the limited subsequent yield loci presented herein as insufficient for

NASA/TM--1998-208658 8
eitherof thesepurposes, butpresentit asademonstrationthatthistypeof datacannowbeobtainedandwill

undertakeadetailedstudyof hardeningbehaviorinthefuture.

SUMMARYANDCONCLUSIONS

Theeftorttodetermineinitialandsubsequent yieldlociforIN718attemperatures upto649°Chasbeen

successful. YieldlociweredeterminedforsolutionedIN718attemperatures of 23,371,and454°Candfor

aged(precipitationhardened) IN718attemperatures of23and649°C.Thisworkopensthedoorformore

detailedstudiesonhardeningbehaviorathightemperatures. Thefollowinggeneral conclusionscanbemade

basedontheexperimental resultsofthiswork.

• ThevonMisesyieldcriterionfit theinitialyieldlociin theaxial-shear stressplaneverywellif aninitialeccentricityisconsidered(seetableII), suggestingtheuseof aDrucker-Prager typeyieldcriterion.

• Eccentricityof theinitialyieldlociforagedIN718definesthestrength-differential effectthatmaybe

dueto nonlinearelasticity(dislocation-precipitate interactions) and/ortheeffectof meanstress

(increaseddislocationdensity).

• AgedIN718displaysignificantlymorehardeningbehaviorthansolutionedIN718.

• Subsequent yieldlociindicateanisotropichardeningthatis predominantlykinematicandsecondarily

distortional. In addition,theremaybeaslightcrosseffectforsolutionedIN718.

REFERENCES

Abdel-Kader, M.S.,Eftis,J.,andJones,D.L.(1986),"Modelingtheviscoplasticbehaviorof inconel718at

1200°F,"NASACP-10010:NonlinearConstitutiveRelationsfor HighTemperatureApplications,

pp.37-68.

Battiste,R.L.andBall,S.J.(1986),"Determinationof surfacesof constant inelasticstrainrateatelevated

temperature," NASACP-2444:TurbineHotSectionTechnology, pp.307-325.

Dieter,G.E.(1988),Mechanical Metallurgy. McGraw-Hill, London.

Drucker, D.C. (1973), "Plasticity theory, strength-differential (SD) phenomenon, and volume expansion in

metals and plastics," Metall. Trans., Vol. 4, pp. 667-673.

Drucker, D.C. and Prager, W. (1952), "Soil mechanics and plastic analysis or limit design," Q. Appl. Math.,

Vol. 10, pp. 157.

Ellis, J.R. and Bartolotta, P.A. (1997), "Adjustable work coil fixture facilitating the use of induction Heating in

mechanical testing," Multiaxial Fatigue and Deformation Testing Techniques, ASTM STP 1280, S. Kalluri

and P.J. Bonacuse, Eds., American Society for Testing and Materials, pp. 43-62.

Fournier, D. and Pineau, A. (1977), "Low cycle fatigue behavior of inconel 718 at 298 K and 823 K," Metall.

Trans., Vol. 8A, pp. 1095-1105.

Gil, C.M. (1998), "Determination of yield and flow surfaces for inconel 718 under axial-torsional loading at

temperatures up to 649 °C," Masters thesis, Penn State University.

Gil, C.M., Lissenden, C.J., and Lerch, B.A. (1998a), "Rate-dependent flow surfaces for inconel 718," In

preparation.

Gil, C.M., Lissenden, C.J., and Lerch, B.A. (1998b), "An investigation of anomalous behavior in metallicbased materials under compressive loading," NASA TM-206640, NASA Lewis Research Center, Cleveland, Ohio.

Hecker, S.S. (1973), "Influence of deformation history on the yield locus and stress-strain behavior of aluminum and copper," Metall. Trans., Vol. 4, no. 4, pp. 985-989.

Hecker, S.S. (1976), "Experimental studies of yield phenomena in biaxially loaded metals," Constitutive

Equations in Viscoplasticity: Computational and Engineering Aspects, ASME, pp. 1-33.

Helling, D.E., Miller, A.K., and Stout, M.G. (1986), "An experimental investigation of the yield loci of 1100-0

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Technol., Vol. 108, pp. 313-320.

Hirth, J.P. and Cohen, M. (1970), "On the strength-differential phenomenon in hardened steel," Metall. Trans.,

Vol. 1, pp. 3-8.

Kalish, D. and Cohen, M. (1969), "Anisotropy of properties in martensite as developed by thermomechanical

treatments," Trans. ASM, Vol. 62, no. 2, pp. 353-361.

NASA/TM--1998-208658 9
Kalluri,S.andBonacuse, P.J.(1990),"A dataaquisitionandcontrolprogramforaxial-torsional ftiguetesting,"ApplicationsofAutomationTechnologytoFatigueandFractureTesting,ASTMSTP1092,

A.A.Braun,N.E.Ashbaugh, andF.M.Smith,Eds.,AmericanSocietyforTestingandMaterials,Philadelphia,pp.269-287.

Kalluri,S.,Rao,K.B.S.,Halford,G.R.,andMcGaw,M.A.(1997),"Deformationmechanisms andfatiguebehaviorof prestrainedinconel718superalloy,"Proceedings of theFourthInternational SpecialEmphasis

SymposiumonSuperalloys718,625,706andDerivatives, Pittsburgh, PA,June15-18.

Khan,A.andWang,X.(1993),"Anexperimental studyonsubsequent yieldsurfaceafterfiniteshearprestraining,"Int.J.Plasticity,Vol.9,pp.889-905.

Khan,A.andHuang,S.(1995),Continuum Theory_ of Plasticity. John Wiley & Sons, New York.

Li, K. (1995), "Experimental evaluation of a viscoplastic constitutive model," AIAA/ASME/ASCE/AHS/ASC,

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Lissenden, C.J., Lerch, B.A., Ellis, J.R., and Robinson, D.N. (1997), "Experimental determination of yield and

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STP 1280, S. Kalluri and P.J. Bonacuse, Eds., American Society for Testing and Materials, pp. 92-112.

Michno, M.J., Jr. and Findley, W.N., (1974), "Subsequent yield surfaces for annealed mild steel under deadweight loading: aging, normality, convexity, corners, Bauschinger, and cross effects," J. Eng. Mater. Technol., Vol. 96, pp. 56-64.

Michno, M.J. and Findley, W.N. (1976), "An historical perspective of yield surface investigations for metals,"

Int. J. Nonlinear Mech., Vol. 11, pp. 59-82.

Nouailhas, D. and Cailletaud, G. (1996), "Finite element analysis of the mechanical behavior of two-phase

single-crystal superalloys," Scripta Mat., Vol. 34, no. 4, pp. 565-571.

Oblak, J.M., Paulonis, D.F., and Duvall, D.S. (1974), "Coherency strengthening in Ni base alloys hardened by

DO22 7" precipitates," Metall. Trans., Vol. 5, pp. 143-153.

Phillips, A., Liu, C.S., and Justusson, J.W. (1972), "An experimental investigation of yield surfaces at elevated

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Phillips, A. and Lu, W. (1984), "An experimental investigation of yield surfaces and loading surfaces of pure

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no. 12, pp. 2279-2287.

Spitzig, W.A., Sober, R.J., and Richmond, O. (1975), "Pressure dependence of yielding and associated volume

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NASA/TM--1998-208658 10
TABLE I. MATERIAL COMPOSITION

OF INCONEL 718

Element Content,

wt.%

Ni

Cr

Mo

(Nb+Ta)

Ti

A1

Co

C

S

Mn

Si

B

Cu

P

Fe

53.58

17.52

2.87

5.19

0.95

0.57

0.39

0.034

0.002

0.120

0.070

0.004

0.050

0.006

Bal.

TABLE II __ RADIUS AND CENTER OF EACH INITIAL YIELD LOCUS FOR SOLUTIONED

AND AGED IN718 AS A FUNCTION OF TEMPERATURE

Tenlperature,

°C

23

371

454

649

Solutioned Aged

Radius of Center of Strength

Mises circle, Mises cu'cle, differential

MPa MPa percent

248 (0.0, 0.0) 0

207 (13.8,0.0) 13

193 (_7.5, 0.0) 28

Radius of Center of

Mises circle, Mises circle,

MPa MPa

655 ( 138.0, 0.0)

448 ( 145.0, 0.0)

Strength

differential

percent

42

65

"91 228.6 I1_

I_1 635 I_1 j-- 82.6 R 82.6 R --,

! " ! / \

V//////////////'_/_ ........ _ ........ /-757//////////////

[////////////;/2.dJ ........ i..._ ..... _£////////-//////

I- 165.1 "_1

J_ _ 21.0

25.4

V

I _-- 15.9

Figure 1.--Typical specimen geometry (all dimensions are in millimeters).

NASA/TM--1998-208658 11
0.10 mm

Figure 2.--Microstructure of solutioned Inconel 718

(optical microscopy). The microstructure for aged

Inconel 718 was similar.

Figure 3.--Transmission electron microscopy of aged

Inconel 718 showing _/" precipitation.

Figure 4.--Close-up of specimen, extensometer, and

heating coils.

NASA/TM-- 1998-208658 12
11

13

A

3 9

12

(0.906),sll

16

10

14

Probe Probe

Number Angle

1 12 °

2 192 °

3 102 °

4 282 °

5 57 °

6 237 °

7 147 °

8 327 °

Probe Probe

Number Angle

9 79 °

10 259 °

11 170 °

12 350 °

13 125 °

14 305 °

15 35 °

16 215 °

Figure 5.--Probe directions used in determining a yield locus.

NASA/TM--1998-208658 13
o0

o0

C].)

rJ3

S

I

I

I

I

I

I

/

Proportional

Limit

E,2G .

Stress-Strain Loading Curve

Extrapolated Linear Loading Curve

J

Figure 6.--Calculation of E, G, and Eoff during experiments.

Strain

NASA/TM-- 1998-208658 14
cc_

oo

¢0

¢0

oo

oo

8 2

0

A2

(a)

1 - Prestrain Point

2 - Reverse Yield Point

3 - Center (elastic) Point

A 1

_'45° B3

ct)

ct)

¢.D

e--

CJ"

UJ

8 1

A 0

v

Axial Stress or Strain

(b)

E iv ln r in

Figure 7.--Prestrain paths shown (a) in the stress or strain plane, and (b) as the equivalent stress-strain

response.

NAS A/TM-- 1998-208658 15
50 ' I ' I ' I ' I

cO

=L

v

o

cO

c--

c13

i_

03

03

O

40

3O

2O

10

-10

i............. ,oadin0 i • /

, I , I , I , I ,

0 300 600 900 1200

Axial Strain, _ (_)

Figure &--Offset strain versus strain during tensile loading for solutioned IN718.

1500

NASA/TM-- 1998-208658 16
c'_

I:1_

v

C_l

O'3

09

09

,,c

Cd')

,,c

c'_

c.-

Cd')

4OO

2OO

0

-200

-400

IN-15

[]

o

............................................................ L - -(_ ..................................

,,

,,

i

....................................................................................................

.......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L .........

.......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L .........

.......... _......... _................... "-....................... I_ .................................. ', ', 13D ',

i i ino 0

,, ,, ,,

i i i

.......... L ......... L ......... L ..................................................

I I .......... I .........

-I O[] Stress Strain Control 1 ........................................................

i i i i

i i i i

t t t t

t t t t t t t t t

-400 -200 0 200 400

Axial Stress, (MPa)

Figure 9.--Yield loci for solutioned, non-pristine IN718 determined under stress and strain control at room

temperature.

NAS A/TM-- 1998-208658 17
%-.

V

c_J

c_J

cO

cc_5

OO

E

c_5

-400

-300

-200

-I00

I 23°C IN-9 1

0.34

0 300 600 900 1200

Axial Strain, _11(_)

Figure lO.--The slope of the diametral strain versus axial strain gives a Poisson's ratio of 0.34.

NASA/TM--1998-208658 18
4OO

c_

EL

200

c'xJ

&

d o

r.D

c_ -200

(:1)

03

-400

23°C 1

.................................................. i ..................... _off = 30ps

i

i

i

i

i

.......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L .........

I I

--- 0 IN-6 .........................................................................

[] IN-25

Mises

Tresca

-400 -200 0 200 400

Axial Stress, _11 (U P a)

Figure 11 .--Initial yield loci for solutioned IN718 at room temperature. The yon Mises and Tresca yield

criteria are also shown.

NAS A/TM-- 1998-208658 19
-4

-6

-8

23°C

......... 454oc

Torsional

m , i

',.;t_ ,,_ _. ._ ] , t,"

., , _ .,'t' .-_,_..... _, _ , ,

_,_ .. . ,.,. ,, .

/ "_,_l!t,_' _' 'i%,,,_

, I , I , I

50 100 150

Time (sec)

Figure 12.--Comparison of heater noise at 23 and 454 °C.

I

200

NASA/TM-- 1998-208658 20
c_

CL

V

co

¢

d

co

CO

c_

CO

4OO

200

0

-200

-400

.......... L ......... L ......... L ......... L ......... L ......... L ......... 371°C t

_0ff = 30_ -

J

.......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L .........

© IN-6

[] IN-25 ..........................................................................

-- M ises

i i i i

-400 400

i i i i i

-200 0 200

Axial Stress, oll (UPa)

Figure 13.--Initial yield loci for solutioned IN718 at 371 °C.

NAS A/TM-- 1998-208658 21
c_

CL

V

C_J

co

d

Or)

(:1)

03

c_

(:1)

(--

03

4OO

200

0

-200

-400

1 1

f 4 4°° t

.......... L ......... L ......... L ......... L ......... L ......... L ......... L-- ----

_off = 30_

.......... L ......... L ......... L ......... L ......... _ ......... L ......... L ......... L ......... L .........

i

i

i

i

i

..........,_............................ ,_....._____,;__D .....i.......................................

iiiiiiiiiiiiiiiiiiiiiiiiii iiiiiiiiiiiii

© IN-6

[] IN-25

Mises

i i

i i

-400

i i i i i

-200 0 200

Axial Stress, oll (U P a)

Figure 14.--Initial yield loci for solutioned IN718 at 454 °C.

i

4OO

NASA/TM-- 1998-208658 22
F IN-6

400 -- Axial Stress

.......... Shear Stress

• * Loci ,

200 -

o

-200

-400

H isto ry

Figure 15.--Loading history for specimen IN-6 indicating where yield loci were determined.

NASA/TM--1998-208658 23
c_

1:3_

V

co

Or)

CD

OO

c_

CD

OO

4OO

200

0

-200

-400

I'= liiiiii 454oc ...............................................................

_off = 30ps

.......... iii ............ ................ iii...............

..........i........i............ _..........i.........i.........

i i o : : , i i

..........i........i....... L.........i.........i......I--i.........i.........i.........

.......... tt.................... Lt .............

.......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L ......... L .........

ii[ " Prestrain PointB

© Locus C

-- Initial Mises

,, ,, ,,

i i i

-400 -200

Axial

IIIIILIIIIIIIIILIIIIIII

I

i i i i i i

0 200 400

Stress, oll (MPa)

Figure 1&--Yield locus subsequent to a tension-torsion prestrain of 500 gE offset for solutioned

IN718 at 454 °C.

NASA/TM-- 1998-208658 24
c_

O_

v

09

03

i

c_

.i

x

<

c_

O_

v

oa

09

03

(--

03

200

0

-200

100

-100

I ' I ' I ' I ' I ' I ' I

E ,G ,I,

Axi K,M

F,H ,J,

L,N Specimen IN-6

I ' I ' I ' I ' I ' I ' I

E ,G ,I,K,M

Torsional

o D

m

F,H ,J ,L,N

I , I , I , I , I , I , I

-3000 -2000 -1000 0 1000 2000 3000

Strain (p_)

Figure 17.--Combined axial-torsional cyclic loading at room temperature (O = 45°). Five complete

cycles beginning and ending at zero stress.

NASA/TM--1998-208658 25
c_3

O_

V

OJ

co

O0

O0

O0

c_3

(--

O0

200

0

-200

-400

i i

i i

i i

i i

i i

.......................... ......... ......... ........ .............. ........'......... o,....

i i i i i

.......... i....... i...... /i......... i....... i.......

i i /i i i

i i i io i i i

.......... " ......... L......... " ......... " .........

/ O

.......... L ......... L ......... L ......... L ......... L ......... _ ......... L ......... L ......... L .........

............................................................. ifo,ocuso Locus C ___

-- Initial Mises

, ', ,, ,,

i i i i

i i i i i i i i i

-400 -200 0 200 400

Axial Stress, Gll (UPa)

Figure 1&--Yield locus subsequent to cyclic loading for solutioned IN718 at 454 °C.

NASA/TM-- 1998-208658 26
c_3

EL

V

C'M

E)

co

oo

oo

(3.)

O9

c_3

(3.)

cOO

4OO

200

0

-200 .......... ,_......... ,_......... ,_......... ,_...........................................................

i i i

i i i

-400

f

• Prestrain Point P

© Locus Q

• Prestrain Point R

[] Locus S

,-- Initial Mise s

i I I

-400 -200

Axial

i

i

,liiiiiiiiiiiiiiiiiiiiiiii

i i i i i i

0 200 400

Stress, ( 11(MPa)

Figure 19.--Subsequent yield loci for proportional prestraining to 1000 gEoffset (locus Q) and 1500

(locus Q) and 1500 (locus Q) and 1500 gEoffset (locus S) for solutioned IN718 at 454 °C.

NASA/TM--1998-208658 27
10

CO

:=.

v -10

,.,._

to

¢-

cU -20

¢0

-30

O

-40

-50

' I ' I ' I '

- Maximum Stiffening Offset Strain

• " ¥ "'T P'" r"

I ............. Loading Unloading 1

i

,°

, • .° .'

°,,,"

o,"

,-%"

..°,

, ..,-°.,,'_s "_'_ .,.

,,.'

• -,.° .•-

,_%,',"

, I , I , I , I

0 -1000 -2000 -3000 -4000

Axial Strain, (lug)

Figure 20.--Offset strain versus strain during compressive loading for aged IN718, indicating

stiffening.

NASA/TM-- 1998-208658 28
IOO0

500

I::I...

OJ

d o

139

139

t- -500

-1000

23°C 7

........... 7............ [ ........... 7---£20...... [.... El-.... 7...... t I_°ff = 30_ I_ /

iiiiiiii iiiiiiiiiiiii

O IN-8 ]

........... 7 ............ r ........... 7 ............ r ........... 7 ........... l

[] IN-IO

Mises

-1000 -500 0 500 1000

Axial Stress, Gll (UPa)

Figure 21.--Initial yield loci for aged IN718 at room temperature. An eccentric von Mises circle is also

shown.

NASA/TM--1998-208658 29
m

13_

4

OO

OO

"- 3

03

o

"-'- 2

U_I

"O

U

E 1

O

z

0

5PL = 136 MPa

_PL = 97 M Pa

23 °C, 0 = 57o

o Solutioned

Aged

J

0

, I , I , I ,

10 20 30

Equivalent Offset Strain (g_)

Figure 22.--Stress versus offset strain for solutioned and aged IN718 under tension and torsion.

I

40

NASA/TM--1998-208658 30
cO

Q_

V

C_J

CO

d

OO

03

cO

03

1000

500

0

-500

-1000

...................................................................... i _off649°C = 30p_ 1-

............................................ Z_---_................................................. FI,

............................ D/ [].....i:_{i .........._--o.................... _,[ ............

................... ................. --°- ..... ,........ 4............

_ ___,,4_.0,0.01 !? _ _

Do

............ J ............ L ........... J ............ L ........... J ............ L ........... J ............

0 IN-8 /-/

[] IN-IO

Mises

-1000 -500 0 500

Axial Stress, oll (UPa)

Figure 23.--Initial yield loci for aged IN718 at 649 °C.

1000

NASA/TM--1998-208658 31
1000

Q_

V

C_J

d

oO

(1)

O0

(1)

eI

O0

500

0

-500

-1000

F IIN_IO I q I I

/ L _°ff = 3 0 _[_.__

........... j......... s_ ....... __...j..........

i i i

........... _............ ,_........... _..............................................................

,, ,, ,,

i i i

• Prestrain Point

© Subsequent Locus .................................................

Initial M ises

-1000 -500 0 500 1000

Axial Stress, _,, (UPa)

Figure 24.--Yield locus subsequent to a tension-torsion prestrain of 500 ME offset for aged IN718 at

649 °C.

NASA/TM--1998-208658 32
1000

500

a_

£,J

d o

139

r.D

139

t- -500

O0

-1000

I IN -8 t

6_9-_C ..................................................................

_o.= 30p_ i

( ' O

........................i...........i...........i...........i-- i--o........

, ,

i

• Prestrain Point 1 ..................................................

O Subsequent Locus[--

Initial Mises _J

-1000 -500 0 500 1000

Axial Stress, Gll (MPa)

Figure 25.--Yield locus subsequent to a tension prestrain of 9000 pE (0.9%) for aged IN718 at 649 °C.

NAS A/TM-- 1998-208658 33
Form Approved REPORT DOCUMENTATION PAGE

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

November 1998 Technical Memorandum

4. TITLE AND SUBTITLE

Determination of Yield in Inconel 718 for Axial-Torsional Loading at

Temperatures up to 649 °C

6. AUTHOR(S)

Christopher M. Gil, Cliff J. Lissenden, and Bradley A. Lerch

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135- 3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546- 0001

5. FUNDING NUMBERS

WU-523-21-13-00

8. PERFORMING ORGANIZATION

REPORTNUMBER

E-11380

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--1998-208658

11. SUPPLEMENTARY NOTES

Christopher M. Gil and Cliff J. Lissenden, Pennsylvania State University, University Park, Pennsylvania 16802-1009.

Responsible person, Bradley A. Lerch, organization code 5920, (216) 433-5522.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Categories: 26 and 39 Distribution: Nonstandard

This publication is available from the NASA Center for AeroSpace Information, (301) 6214)390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

An experimental program has been implemented to determine small offset yield loci under axial-torsional loading at

elevated temperatures. The nickel-base superalloy Inconel 718 (IN718) was chosen for study due to its common use in

aeropropulsion applications. Initial and subsequent yield loci were determined for solutioned IN718 at 23, 371, and

454°C and for aged (precipitation hardened) IN718 at 23 and 649°C. The shape of the initial yield loci for solutioned and

aged IN718 agreed well with the von Mises prediction. However, in general, the centers of initial yield loci were

eccentric to the origin due to a strength-differential (S-D) effect that increased with temperature. Subsequent yield loci

exhibited anisotropic hardening in the form of translation and distortion of the locus. This work shows that it is possible

to determine yield surfaces for metallic materials at temperatures up to at least 649°C using multiple probes of a single

specimen. The experimental data is first-of-its-kind for a superalloy at these very high temperatures and will facilitate a

better understanding of multiaxial material response, eventually leading to improved design tools for engine designers.

14. SUBJECT TERMS

Nickel alloy; Plasticity; Yield surface; Multiaxial loads

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

15. NUMBER OF PAGES

39

16. PRICE CODE

A03

18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

OF THIS PAGE OF ABSTRACT

Unclassified Unclassified

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-1B

298-102