NASA Contractor Report 190794

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Computational Simulation of ProbabilisticLifetime Strength for Aerospace Materials

Subjected to High Temperature,Mechanical Fatigue, Creepand Thermal Fatigue

Lola Boyce, Callie C. Bast, and Greg A. Trimble

University of Texas at San Antonio

San Antonio, Texas

November 1992

Prepared for

Lewis Research Center

Under Grant NAG3-867

N/ ANational Aeronautics and

Space Administration

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PREFACE

The University of Texas at San Antonio (UTSA) is a relatively new university. Itwas established in 1969 and opened for classes in 1973. As the only comprehensive publicuniversity serving the nation's ninth largest city, it was and is vital to San Antonio and theentire South Texas Region. In 1982, ten years ago, an undergraduate engineering programwas established at UTSA with the support of the community and its leaders. Today, allthree undergraduate engineering programs are ABET accredited and serve about 1000students, a significant percentage of whom are Hispanic. A new engineering building,containing laboratory facilities and equipment, opened in January, 1991. Furthermore, agraduate program has just been put in place at the M.S. level and one is planned at thePh.D. level. The first Master's Degree students enrolled in Fall, 1989.

Naturally, the engineering research environment is just developing at UTSA. Now,thanks in great measure to the UT System support and this ongoing NASA grant, goodprogress is being made. Specifically, the purchase of a UT System Cray-Y-MP inNovember, 1990 has provided a world-class analytical and numerical research environmentnot ordinarily available to a new university. As a result the UTSA Supercomputer NetworkResearch Facility (SNRF) was developed by the principal investigator, Dr. Lola Boyce.This has allowed the successful completion of this research project, an early one of its kindat UTSA.

This NASA research grant has allowed three undergraduate engineering students,Eddie Aponte, Greg Trimble and Paul Van Veen, plus the first UTSA MechanicalEngineering graduate student, Callie Bast, to work directly with the principal investigator,Dr. Boyce, providing them with a quality research experience they would otherwiseprobably not have had. All undergraduate students have expressed an interest in continuingtheir education at the graduate level.

In conclusion, and in view of the significant accomplishments in fundamentalresearch, enhancement of the engineering research environment at UTSA, and directsupport of Mechanical Engineering students, it is hoped that the proposed extension of thisgrant will receive favorable consideration at NASA. The principal investigator sincerely

thanks NASA for funding this fourth year grant.

COMPUTATIONAL SIMULATION OF PROBABILISTIC LIFETIME STRENGTH

FOR AEROSPACE MATERIALS SUBJECTED TO HIGH TEMPERATURE,

MECHANICAL FATIGUE, CREEP AND THERMAL FATIGUE

Lola Boyce, Callie C. Bast, and Greg A. Trimble

University of Texas at San AntonioSan Antonio, Texas 78285

ABSTRACT

This report presents the results of a fourth year effort of a research programconducted for NASA-LeRC by The University of Texas at San Antonio (UTSA). Theresearch included on-going development of methodology that provides probabilistic lifetimestrength of aerospace materials via computational simulation. A probabilistic materialstrength degradation model, in the form of a randomized multifactor interaction equation, ispostulated for strength degradation of structural components of aerospace propulsionsystems subjected to a number of effects or primitive variables. These primitive variablesmay include high temperature, fatigue or creep. In most cases, strength is reduced as aresult of the action of a variable. This multifactor interaction strength degradation equationhas been randomized and is included in the computer program, PROMISS. Also includedin the research is the development of methodology to calibrate the above-described

constitutive equation using actual experimental materials data together with regressionanalysis of that data, thereby predicting values for the empirical material constants for each

effect or primitive variable. This regression methodology is included in the computerprogram, PROMISC. Actual experimental materials data were obtained from industry andthe open literature for materials typically for applications in aerospace propulsion systemcomponents. Material data for Inconel 718 has been analyzed using the developedmethodology.

1.0 INTRODUCTION

This report presents the results of a fourth year effort of a research program entitled"Development of Advanced Methodologies for Probabilistic Constitutive Relationships ofMaterial Strength Models, Phase 4." This research is sponsored by the NationalAeronautics and Space Administration-Lewis Research Center (NASA-LeRC). Theprincipal investigator is Dr. Lola Boyce, Associate Professor of Mechanical Engineering,The University of Texas at San Antonio (UTSA). The objective of the research program isthe development of methodology that provides probabilistic lifetime strength of aerospacematerials via computational simulation.

As part of this fourth year effort, a material strength degradation model, in the formof a randomized multifactor interaction equation, is postulated for strength degradation ofstructural components of aerospace propulsion systems subjected to a number of effects orprimitive variables. These primitive variables often originate in the environment and mayinclude high temperature, fatigue and creep. In most cases, strength is reduced as a result.Also included in the research is the development of methodology to calibrate the multifactorinteraction equation using actual experimental materials data together with a regressionanalysis of that data, thereby predicting values for the empirical material constants for eacheffect or primitive variable. Material data for Inconel 718 has been analyzed using thedeveloped methodology. Sections 2.0 and 3.0 summarize the theoretical and computationalbackground for the research.

The above-described randomized multifactor interaction equation is included in thecomputer program, PROMISS. Calibration of the equation by multiple regression analysisof the data may be carried out using the statistical regression computer program,PROMISC. These programs were developed using the UTSA Supercomputer NetworkResearch Facility (SNRF) Cray Y-MP. The latest versions (Ver. 2.0) of these programsare obtainable from the principal investigator at the address given on the cover page of this

report.

Sections 4.0 through 7.0 address specific tasks described in the proposal for thisresearch "Development of Advanced Methodologies for Probabilistic ConstitutiveRelationships for Material Strength Models, Phase 4", 1991. Specifically, Section 4.0discusses the strength degradation model developed for the high temperature, mechanicalfatigue and creep effects of Inconel 718. Section 5.0 introduces the thermal fatiguestrength degradation model, a new effect included in the multifactor interaction equation.Section 6.0 presents experimental material data for Inconel 718 and displays the data in theform utilized in the multifactor interaction equation model. High temperature, mechanicalfatigue, creep and thermal fatigue data are displayed. This data may be used in thedevelopment of data for the PROMISS resident database. Section 7.0 presents anddiscusses cases for analysis that resulted from a sensitivity study, utilizing the PROMISS"flexible" capability. The cases show the effect on probabilistic lifetime strength for severaleffects, including high temperature, mechanical fatigue and creep. This sensitivity study isthe f'n'st such study to begin to account for synergistic effects.

A paper was produced documenting much of the effort of this fourth year researchprogram. It is entitled "Computational Simulation of Coupled Material DegradationProcesses for Probabilistic Lifetime Strength of Aerospace Materials", by L. Boyce andC. C. Chamis. It was presented at the AIAA/SAE/ASME/ASEE Joint PropulsionConference, Nashville, TN, July, 1992 and is published in the Proceedings. It has alsobeen submitted to the ASME Jo_m_l of Engineering for Gas T_lrbine_ and Power and a

copy is included with this report.

2.0 THEORETICALBACKGROUND

Recently,ageneralmaterialstrengthdegradationmodel,for compositematerialssubjectedto anumberof diverseeffectsorprimitivevariables,hasbeenpostulatedto.predict.mechanical.andthermalmaterialproperties[1,2,3, 4]. Theresultingmultifactormteracnonconstitutiveequationsummarizescompositemicromechanicstheoryandhasbeenusedto predictmaterialpropertiesfor aunidirectionalfiber-reinforcedlamina,basedon thecorrespondingpropertiesof theconstituentmaterials.

Theseequationshavebeenmodifiedto predictthelifetimestrengthfor asingleconstituentmaterialdueto "n" diverseeffectsor variables[5,6,7]. Theseeffectscouldincludevariablessuchashightemperature,creep,mechanicalfatigue,thermalfatigue,corrosion,strainrateeffects,andsoforth. Formostof thesevariables,strengthhasbeenobservedtodecreasewith anincreasein thevariable.Thisreportpresentstheresultsofwork to usethemodifiedmultifactorinteractionequationto accountfor thedegradationoflifetimestrengthduetothreevariables,hightemperature,mechanicalfatigueandcreep.Thereportalsopresentsanextensionof themodelto accountfor thermalfatigueeffects.Thegeneralformof thepostulatedmultifactorinteractionequationis

= fi [Ai U.mi] aii=l [Aiu - AioJ '

(1)

where A i, Aiu and Aio are the current, ultimate and reference values, respectively, of a

particular effect; ai is the value of an empirical constant for the i th product term in themodel; S and So are the current and reference values of material strength and n is thenumber of product terms in the model. Each term has the property that if the current value

equals the ultimate value, the current strength will be zero. Also, if the current value equalsthe reference value, the term equals one and strength is not affected by that variable.

This deterministic material strength degradation model may be calibrated by anappropriately curve-fitted least squares linear regression of experimental data [8], perhapssupplemented by expert opinion. Ideally, experimental data giving the relationship betweeneffects and strength is obtained. For example, data for just one effect could be plotted onlog-log paper. A good fit for the data may then be obtained by a linear regression analysis.This is illustrated schematically in Figure 1. The equation, for a single effect, is thenobtained by noting the linear relation between log S and log [(Au - Ao)/(Au - A)], asfollows:

log S=-a log[_-_-#]+log So

FAu - Ao]log S- log So = - a log [ _-o- A J

log --S- =-a log [-_--_-]So L _U" _ J

sSo =Lmuu Lm-J (2a)

2

_S_ =[ Au--A-1 a (2b)So [Au - AoJ

Equation (2a) is for a variable that lowers strength. Notice that if a variable raises strengththe exponent, a, in equation (2a) is negative.

Fig. 1

logs

log So

.3__, slope

• "'".<.%

,ogrAu-AflL-_J

Schematic of Data Illustrating the Effect of One Primitive Variable on Strength.

This general material strength degradation model, given by equation (1) may be

used to estimate the lifetime strength, S/So, of an aerospace propulsion system componentunder the influence of a number of diverse effects or primitive variables. The probabilistictreatment of this model includes randomizing the deterministic multifactor interactionequation, performing probabilistic analysis by simulation and generating probability densityfunction (p.d.f.) estimates for strength using the non-parametric method, maximumpenalized likelihood [9, 10]. Integration of the probability density function yields thecumulative distribution function (c.d.f.) from which probability statements regardingstrength may be made. This probabilistic material strength degradation model predicts therandom strength of an aerospace propulsion system component subjected to a number ofdiverse random effects.

The probabilistic constitutive model is embodied in two FORTRAN programs,PROMISS (_obabilistic Materi_al Strength Simulator) and PROMISC Pr(.__.QbabilisticMateri_al Strength Calibrator)[6]. PROMISS calculates the random strength of an aerospacepropulsion component due to as many as eighteen diverse random effects. Results arepresented in the form of probability density functions and cumulative distribution functionsof lifetime strength, S/So. PROMISC calculates the values of the empirical materialconstants, ai.

3.0 PROMISSAND PROMISCCOMPUTERPROGRAMS

PROMISSincludesarelativelysimple"timed"modelaswell asa"flexible" model.Thefixedmodelpostulatesaprobabilisticmultifactorinteractionequationthatconsidersthevariablesgivenin Table1 (seep. 5). Thegeneralformof thisconstitutiveequationisgivenin equation(1), whereintherearenown = 7 productterms,onefor eacheffectorprimitivevariablelistedabove.Notethatsincethismodelhassevenvariables,eachcontainingfourvaluesof thevariable,it hasatotalof twenty-eightvariables.Theflexiblemodelpostulatestheprobabilisticmultifactorinteractionequationthatconsidersup to asmanyasn= 18producttermsfor primitivevariables.Thesevariablesmaybeselectedtoutilizethetheoryandexperimentaldatacurrentlyavailablefor thespecificstrengthdegradationmechanismsof interest.Thespecificeffectsincludedin theflexiblemodelarelistedin Table2. Notethatin orderto providefor futureexpansionandcustomizationoftheflexiblemodel,six "other"effectshavebeenprovided.

Table2 VariablesAvailablein the"Flexible"Model.

A. EnvironmentalEffects

, Mechanical

a. Stress

b. Impactc. Other Mechanical Effect

. Thermal

a. Temperature Variationb. Thermal Shockc. Other Thermal Effect

3. Other Environmental Effects

a. Chemical Reactionb. Radiation Attackc. Other Environmental Effect

B° Time-Dependent Effects

1. Mechanical

a. Creepb. Mechanical Fatiguec. Other Mech. Time-Dependent. Effect

2. Thermal

a. Thermal Agingb. Thermal Fatiguec. Other Thermal Time-Dependent. Effect

, Other Time-Dependent Effects

a. Corrosionb. Seasonal Attack

c. Other Time-Dependent. Effect

4

Table1 VariablesAvailablein the"Fixed"Model.i thPrimitive Primitive

Variable VariableTlrpe

1 Stressdueto staticload2 Temperature3 Chemicalreaction4 Stressdueto impact5 Mechanicalfatigue6 Thermalfatigue7 Creep

Theconsiderablescatterof experimentaldataandthelackof anexactdescriptionoftheunderlyingphysicalprocessesfor thecombinedmechanismsof fatigue,creep,temperaturevariations,andsoon,makeit natural,if notnecessaryto considerprobabilisticmodelsfor astrengthdegradationmodel. Therefore,thefixedandflexiblemodelscorrespondingto equation(1)are"randomized",andyield the"randomlifetimematerialstrengthdueto anumberof diverserandomeffects." Notethatfor thefixedmodel,equation(1)hasthefollowing form:

S/So = f(Aiu, A1, AlO, al,..., Aiu, Ai, Aio, ai.....ATU,A7, A7o, aT) (3)

whereAi, Aiu andAio arethecurrent,ultimateandreferencevaluesof theithof seveneffectsorprimitivevariablesasgivenin Table1,andai is theith empiricalmaterialconstant.In general,this expressioncanbewrittenas,

S/So = f(Xi), i = 1..... 28, (4)

wheretheXi arethetwentyeightindependentvariablesin equation(3). Thus,thefixedmodelis "randomized"by assumingall the independentvariables,Xi, i = 1.....28, to berandomandstochasticallyindependent.Fortheflexiblemodel,equation(1)hasaformanalogousto equations(3)and(4),exceptthatthereareasmanyasseventy-twoindependentvariables.Applyingprobabilisticanalysisto eitherof theserandomizedequationsyieldsthedistributionof thedependentrandomvariable,lifetimematerialstrength,S/So.

Althoughanumberof methodsof probabilisticanalysisareavailable[9],simulationwaschosenfor PROMISS.Simulationutilizesatheoreticalsamplegeneratedby numericaltechniquesfor eachof theindependentrandomvariables.Onevaluefrom eachsampleissubstitutedinto thefunctionalrelationship,equation(3),andonerealizationof lifetimestrength,S/So,is calculated.Thiscalculationis repeatedfor eachvaluein thesetofsamples,yieldingadistributionof differentvaluesfor lifetime strength.

A probabilitydensityfunctionisgeneratedfrom thesedifferentvaluesof lifetimestrength,usinganon-parametricmethod,maximumpenalizedlikelihood. Maximumpenalizedlikelihoodgeneratesthep.d.f,estimateusingthemethodof maximumlikelihoodtogetherwith apenaltyfunctionto smoothit [10]. Finally,integrationof thegeneratedp.d.f, resultsin thecumulativedistributionfunction,from whichprobabilitiesof lifetimestrengthcanbedirectlyobserved.

5

where

In summary,PROMISSrandomizesthefollowingequation:

S _fi [Aiu-Ai] ai--- 'So i=l

Aiu-Ai] aiAiu - AioJ

(1)

is the ith effect; Ai, Aiu and Aio are random variables; ai is the i th empirical materialconstant and S/So is lifetime strength. There is a maximum of eighteen possible effects orprimitive variables that may be included in the model. For the flexible model option, theymay be chosen by the user from those in Table 2. For the fixed model option, the variablesof Table 1 are used. Within each primitive variable term, the current, ultimate and referencevalues as well as the empirical material constant, may be modeled as either deterministic(i.e., empirical, calculated by PROMISC), normal, lognormal, or Wiebull random

variables. Simulation is used to generate a set of realizations for lifetime random strength,S/So, from a set of realizations for primitive variables and empirical material constants.Maximum penalized likelihood is used to generate an estimate for the p.d.f, of lifetimestrength, from a set of realizations of lifetime strength. Integration of the p.d.f, yields thec.d.f. Plot files are produced to plot both the p.d.f, and the c.d.f. PROMISS alsoprovides information on lifetime strength, S/So. statistics (mean, variance, standarddeviation and coefficient of variation). A resident database is included in PROMISS and

may be used to provide user input for the empirical material constants.

PROMISC performs a multiple linear regression on actual experimental orsimulated experimental data for as many as eighteen effects or primitive variables, yieldingregression coefficients that are the empirical material constants, ai, required by PROMISS.It produces the linear regression of the log transformation of equation (1), the multifactorinteraction equation. When transformed it becomes

18

log S_ = Z -ai log [Aiu-__Aio_]i=l L Aiu - Ai J

(5)

or

18

log S = log So + Z -ai log[ Aio - Aio.]i=l L Aiu - Ai J '

(6)

6

where

is theitheffect,Ai, Aiu andAio areprimitivevariabledataandaiis the ithempiricalmaterialconstant,or thei thregressioncoefficientto bepredictedbyPROMISC. Also, logSois thelog transformedreferencevalueof strength,or theinterceptregressioncoefficientto bepredictedby PROMISC,andlog Sis the log transformedcurrentvalueof strength.Experimentaldatafor upto eighteenpossibleeffects,asgivenin Table2, maybeincluded.Thevariabledatamaybeeitheractualexperimentaldataor expertopinion,directlyreadfrom input,or simulateddatawhereexpertopinionis specifiedasthemeanandstandarddeviationof anormalor lognormaldistribution.Thesimulateddataoptionfor inputdatawasusedin theearlystagesof codedevelopmentto verify correctperformance.Theinputdata,whetheractualor simulated,is readin andassembledintoadatamatrix. Fromthisdatamatrix,acorrectedsumsof squaresandcrossproductsmatrix is computed.Fromthissumsof squaresandcrossproductsmatrix,andaleastsquaresmethodology,amultiplelinearregressionis performedto calculateestimatesfor theempiricalmaterialconstant,ai,andthereferencestrength,So. Thesearetheregressioncoefficients.

PROMISCincludesenhancementsof themultiplelinearregressionanalysistoscreendatafrom "outliers"andcollinearities;to determine"howwell" thedatafit theregression;to quantifytheimportanceandrelativeimportanceof eachfactorin themultifactorinteractionequation(1),aswell as,to checkassumptionsinherentin theuseofmultiplelinearregression.Furtherdetailsareprovidedin Reference6, Section6.0.

4.0 STRENGTHDEGRADATIONMODELSFORHIGH TEMPERATURE,MECHANICAL FATIGUEAND CREEP

FORINCONEL718

Themultifactorinteractionequationfor materialstrengthdegradation,givenbyequation(1),whenmodifiedfor hightemperature,fatigueandcreepbecomes,

_S_= [TM-To]-q rNu-_No.l-srto- tol-vSo [_---T] [Nu-NJ Ltu-tJ '

(7)

whereTMis theultimateor meltingtemperatureof thematerial,TOisareferenceor roomtemperature,T is thecurrenttemperature,Nu is theultimatenumberof cycles(for whichfatiguestrengthisvery small),No isareferencenumberof cycles(for whichfatiguestrengthisvery large),N is thecurrentnumberof cyclesthematerialhasundergone,tu istheultimatenumberof creephours(for whichrupturestrengthis very small),to isareferencenumberof creephours(for whichrupturestrengthis very large)andt is thecurrentnumberof creephours.Alsoq, sandv areempiricalmaterialparameters,oneforeachvariable,thatrepresenttheslopeof a straightline fit of thedataon log-logpaper.

Theappropriatevaluesfor ultimateandreferencequantitiesmustbeselectedpriortocalibrationof themultifactorinteractionequationfor Inconel718. For example,forInconel718themeltingtemperatureis TM= 2369 °F. Hence equation (7), for Inconel 718,becomes

_._._= [2369- 75]-q [101°- 0._]-S [10 6- 1.0] -vSO L2369-TJ [ 101°-NJ [ 106-t j "

(8)

The ultimate and reference quantities given in equation (8) become modelparameters or constraints for the multifactor interaction equation when modified for Inconel718. Figure 2 illustrates these model parameters graphically wherein each axis representsan effect or primitive variable. Note also an additional constraint in Figure 2, namely the

creep threshold temperature, Tc = 900 °F. Although this constraint is not explicitly builtinto the multifactor interaction equation, it may be taken into account indirectly. This isaccomplished by not including the creep effect whenever the current value of temperature,

T, is below 900 OF. Note that the empirical material parameters, q, s and v must bedetermined from actual experimental data.

TEMPERATURE (°F)

Fig. 2

TM,

T¢.

To.

tS 1.0

tu

CREEP (HOURS)

2369

900

75

No Nu

I I _ MECHANICAL FATIGUE (CYCLES)0.5 1010 v

Model Parameters for Inconel 718 for Temperature, Mechanical Fatigue and Creep.

5.0 STRENGTHDEGRADATIONMODELFORTHERMALFATIGUE

Thegeneralmodelfor thethermalfatigueeffectusesstress-life(o-N) dataobtainedfrom experimentalstrain-life(e-N)data.Totalstrainamplitudedata[14] andplasticstrainamplitudedata[12] wereusedto constructastrain-lifecurve.Theplasticportionof thecurvemayberepresentedbythefollowing powerlaw function:

= e_ (2NF) c (9)2

where Acrd2 is the plastic strain amplitude, 2NF is the reversals to failure. A power law

regression analysis of the data yields two thermal fatigue properties, namely, the fatigueductility coefficient, EF', and the fatigue ductility exponent, c. Regression statistics, such

as the coefficient of determination, R 2, may show that a power law representation of the

relationship between plastic strain amplitude and reversals to failure is satisfactory.

Stress amplitude, Act/2, can be calculated using the modulus of elasticity, E, andthe total and plastic strain amplitudes, AST/2 and Aep/2 respectively, from

When the resulting stress amplitude is plotted against plastic strain amplitude the cyclicstress-strain plot results. Again, a power law function may be satisfactory for expressingthe cyclic stress-strain relationship. The function is

!

.4___= K'{ Aep/n (11)2 _ 21'

where K' is the cyclic strength coefficient and n' is the cyclic strain hardening exponent,two additional thermal fatigue properties.

When the stress amplitude is plotted against reversals to failure, the stress-life plotresults. A power law function may represent a good fit to the data. This function is

A_ _ C'F (2NF) b (12)2

where _'F is the fatigue strength coefficient and b is the fatigue strength exponent. These

final two properties complete the set of thermal fatigue material properties.

With the ordinate now expressed in stress units (psi), a fourth effect can be addedto the multifactor interaction model depicted by equations (7) and (8). This effect will have

the form,

- -u,LNu-N J [ 105-NJ

where N'U = 105 is the ultimate number of thermal cycles (for which thermal fatiguestrength is very small), N'O = 0.5 is the selected reference number of thermal cycles (for

9

whichthermalfatiguestrengthis very large),N' is thecurrentnumberof thermal cycles thematerial has undergone and u is an empirical material constant found from a power lawregression of the data. Thus, equations (7) and (8) will have four terms, one for eacheffect,

IN_-_No.Is=[TM-To]-qrN,-.No?S[to-_J-v_ ' ,,-uSo /_M--T] I. Ntj-NJ [tu-tJ [NIj_N'J '

(13)

s - F2369- 75]-q[10'° - 0.5]-s[106-_1_0]-I105- 0.5]-uSo L2_--T] / 1010-N] 106 105_N'J '(14)

10

6.0 EXPERIMENTALMATERIAL DATA FORINCONEL718

Themultifactorinteractionequation,specific for Inconel 718, requires the collectionof experimental data to determine the empirical material constants, ai. A computerizedliterature search of Inconel 718, a nickel-base superalloy, was conducted to obtain existingexperimental data on various material properties. Data on high temperature tensile strength,mechanical fatigue strength and creep rupture strength properties were obtained forInconel 718 [14, 15, 16, 17].

Inconel 718 data for high-temperature tensile strength, mechanical fatigue strengthand creep rupture strength resulted from tests done on various hot and cold workedspecimens [14,16]. Tests were conducted on sheets of Inconel 718 and hot rolled bars ofthe superalloy.

Low cycle fatigue produces cumulative material damage and ultimate failure in acomponent by the cyclic application of strains that extend into the plastic range. Failure

typically occurs under 105 cycles. Low cycle fatigue is often produced mechanically, at agiven temperature. It is even more common to observe a machine part that undergoes lowcycle fatigue, producing cyclic strains due to a cyclic thermal field. These cyclictemperature changes produce thermal expansions and contractions that, if constrained,produce cyclic strains and stresses. These thermally induced stresses and strains will resultin fatigue failure just as those produced by external mechanical loading produce fatiguefailure.

Low cycle fatigue tests, comparing both mechanically strain cycled specimens atconstant elevated temperatures and thermally cycled constrained specimens, have beenconducted on stainless steel [11] and Inconel [12]. Results are typically ploaed as plasticstrain range versus cycles to failure. For stainless steel, these plots show that for equalvalues of plastic strain range the number of cycles to failure was much less for thethermally cycled specimens than for the mechanically cycled ones. To bring the thermalfatigue test results into coincidence with the isothermal mechanical fatigue test results [13],requires the multiplication of the strain, for any number of cycles to failure, by a factor ofapproximately 2.5. Inconel, however, responds to mechanically produced plastic strain inthe same manner as it responds to thermally produced plastic strain. Thus, the Inconel testresults provide a means for utilizing mechanically cycled data to build a thermal fatiguemodel for Inconel 718.

Inconel plastic strain data used for thermal fatigue was obtained by thermal

excursions about a mean temperature of 1300 °F [12]. Since Inconel responds tomechanically produced plastic strain in the same manner as it responds to thermallyproduced plastic strain, total strain data obtained from mechanically produced strain testswas used for the thermal fatigue model [ 14]. These data are given in Table 3 and displayedas the strain life curves shown in Figure 3. Using data for the modulus of elasticity for

Inconel 718 at 1300 °F, namely, E = 23 x 106 psi [14], the stress amplitude can becalculated from equation (10). Hence, stress amplitude is plotted against plastic strainamplitude to produce the cyclic stress-strain curve shown in Figure 4. Using the powerlaw regression techniques [18] indicated in equations (9), (11), and (12), and the data fromTable 4, the thermal fatigue material properties for Inconel 718 can be calculated. Thesematerial properties are displayed in Table 5 and indicated graphically, along with their

coefficient of determination, R 2, in Figures 5, 6, and 7. Although the values calculated for

the exponents, b, c, n', are close to the range for most metals, the values of the

11

coefficients,K' and(I'F ale extremely high. These high values may be due in part to thefollowing reasons:

(1) The thermal fatigue plastic strain data [12] was obtained from tests conducted onInconel rather than Inconel 718.

(2) The total strain data [14] used for the thermal fatigue model was obtained frommechanical fatigue tests conducted at room temperature rather than at a temperature of1300 °F, which was the mean temperature used for the thermal fatigue tests.

(3) The direct correlation found between the mechanical strain-cycled results underisothermal conditions and those obtained by thermally-cycling about a correspondingmean temperature was for the plastic strain and not the total strain component.

The Inconel 718 data selected was plotted in various forms, one of which was thesame as that used by the multifactor interaction equation in PROMISS and PROMISC. Thedata plotted in Figures 8 and 9 show the effect of temperature on yield strength forInconel 718. Figure 8 is the raw data and Figure 9 shows the data in the same form as that

used in the multifactor interaction equation. As expected, the yield strength of the materialdecreases as the temperature increases. Figures 10 and 11 display data for the effect ofmechanical fatigue cycles on fatigue strength for Inconel 718 for a given test temperature.As expected, the fatigue strength of the material decreases as the number of cyclesincreases. Figures 12 and 13 show data for the effect of creep time on rupture strength forInconel 718 for a given temperature. As expected, the rupture strength of the materialdecreases as the time increases. Figures 14 and 15 display data for the effect of thermal

fatigue cycles on stress amplitude at failure (i.e., thermal fatigue strength) for Inconel 718

for a mean thermal cycling temperature of 1300 °F. As expected, the thermal fatiguestrength of the material decreases as the number of cycles increases.

A linear regression of the data for temperature, mechanical fatigue, creep andthermal fatigue, produces a first estimate of the empirical material constants for theseeffects, namely, q, s, v and u. Figures 16, 17, 18, and 19 show the results of linearregression and indicate values for the four material constants.

iii

,.J

a.

<

zm

<

I--

.1

.01

.001

.0001

0 2

Fig. 3

A Total Strain Amplitude

0 Plastic Strain Amplitude

(Thermal Cycling, 1300°F)

.... ! .... !

10 3 10 4

CYCLES TO FAILURE, N

Strain - life Curve for INCONEL 718

12

¢.t

IaJ

I-_Ja.

,,¢

tDuJ

I---(D

350000 -

300000

250000

200000

150000

100000 , , , ,0.000 0.002 0.004 0.00 6 0.008

Fig. 4

PLASTIC STRAIN AMPLITUDE

Cyclic Stress-strain Curve for Inconel 718

Table 3 Thermal Fatigue Data for Inconel 718

Cycles to FailureNF

Total Strain Amplitude,

AET/2

Plastic Strain Amplitude,

Agpf2

350 0.021 0.007520 0.007840 0.004850 0.015910 0.016950 0.0051500 0.0111700 0.0112300 0.0023200 0.0103600 0.0023900 0.0105300 0.0016000 0.0017400 0.0079300 0.001

13

Table4 ThermalFatigueDataReducedfor ThermalFatigueMaterialProperties

ReversalstoFailure TotalStrain PlasticStrain Stress2NF Amplitude,AI3T/2 Amplitude,AI3p/2 Amplitude,AO/2

700 0.021 0.0079 302,012

1700 0.015 0.0044 244,437

1820 0.016 0.0042 271,878

3000 0.011 0.0030 183,964

3400 0.0109 0.0028 187,156

6400 0.01 0.0018 188,203

7800 0.01 0.0016 193,336

14800 0.0075 0.0010 148,511

*Thesevaluesuseplasticstrainamplituderegressionlinevalues.

Table5 ThermalFatigueMaterialPropertiesfor Inconel718

FatigueDuctility Coefficient,E'F

Fatigue Ductilty Exponent, c

Cyclic Strength Coefficient, K'

Cyclic Strain Hardening Exponent, n'

Fatigue Strength Coefficient, O'F

Fatigue Strength Exponent, b

0.6028

-0.66228

1.505 x 106 psi0.33492

1.270 x 106 psi-0.2218

14

"' -2.0a

-J -2.2n:i<

z -2.4,,:[n-)- -2.6

2_- -2.8(/)<..I

a. -3.0(3O" -3.2

2

R^2 = 0.970

• • _ y = - 011985 - 0.66228X

I

3 4 5

LOG REVERSALS TO FAILURE

Fig. 5 Regression of Equation (9) Data Yielding Fatigue Ductility Coefficient, e'F, andFatigue Ductility Exponent, c.

5.5

5.4

R^2 = 0.8345.3

_ 5.2

O

5.1 , , , ' ,"3.0 -2.8 -2.6 -2.4 -2.2 -2.0

LOG PLASTIC STRAIN AMPLITUDE

Fig. 6 Regression of Equation (11) Data Yielding Cyclic Strength Coefficient, K', andCyclic Strain Hardening Exponent, n'.

15

5.5A

(/)

I.Ua 5.4

..JO.=E< 5.3(/)(/)I.LIrrI--u) 5.2

0.-I

5.12

Fig. 7

= 6.1038 - 0.22181x R^2 = 0.834

I " I " I

3 4 5

LOG REVERSALS TO FAILURE

Regression of Equation (12) Yielding Fatigue Strength Coefficient, o'r: and FatigueStrength Exponent, b.

16

u)Q.

r.

o)

G)Im

rj)

"om

>-

180000

160000

140000

120000

100000

80000 I I I I

0 500 1000 1500 2000

T

Fig. 8 Effect of Temperature (°F) on Yield Strength for Inconel 718.(Linear Plot)

Fig. 9

5.3

Am

o"" 5.2-r-l--

Ziiirr

m 5.1t',,,,_1

_ 5.00.J

4.9 ,0.0 0.1 0.2 0.3 0.4 0.5

LOG (2369-75)/(2369-T)

Effect of Temperature (°F) on Yield Strength for Inconel 718.(Log-Log Plot)

17

140000 -

e,tv

r'-

L,,,

o_

14.

120000

100000

80000

a T=75OF

A T=1000OF

o T=1200OF

60000

Oe+O 2e+7 4e+7 6e+7 8e+7 1 e+8

N

Fig. 10 Effect of Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718.(Linear Plot)

Fig. 11

5.2

tO

v

-1-5.1

r,.-IzUJn,'I-

,,, 5.0

oF-

u.

0 4.90.,J

[] T=75°F

'= T=IOOO°F

o T=1200°F

4.80.000 0.001 0.002 0.003 0.004 0.005

LOG (10^ I0-0.5)/(I0 ^ 10-N)

Effect of Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718.(Log-Log Plot)

18

160000

v

f-

t_f-G)

o)

Q.

140000

120000

100000

80000

[] T=1000°F

& T=1200°F

600000 5000 10000 15000 20000 25000

t

Fig. 12 Effect of Creep Time (Hours) on Rupture Strength for Incone1718.(Linear Plot)

5.2

0.

5.1..r-l---Oziii

5.0I--

UJn-

4.9I-a.

n-

O 4.8o,.J

A T=1000°F

O T=1200°F

4.70.000 0.002 0.004 0.006 0.008 0.010

LOG (10^6-1.0)/(10^6-t)

Fig. 13 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718.(Log-Log Plot)

19

13.v

tllt_

I--

.Jgt.

t/)Or)UJreI-t/l

400000

300000

200000oO •

100000 , , ,0 2000 4000 6000

N

Thermal Cycling, 1300°F

Fig. 14 Effect of Thermal Fatigue (Cycles) on Thermal Fatigue Strength(i.e., Stress Amplitude at Failure) for Inconel 718

(Linear Plot)

I

8000

"I-I--(3Ziiiref-(n

W3

I--

U.

,.J

reI,U

I---

(30-J

5°5 "

5o4'

5.3

5.2

5.10.00

l

l • Thermal Cycling, 1300°F

O • •

i i i i

0.01 0.02 0.03 0.04

LOG(10,5-0.5)/(10 ^ 5-N')

Fig. 15 Effect of Thermal Fatigue (Cycles) on Thermal Fatigue Strength(i.e., Stress Amplitude at Failure) for Inconel 718.

(Log-Log Plot)

20

5.3

5.2

5.1

q1.1,1

s°t4.9

0.0

(90_1

I I I I I

0.1 0.2 0.3 0.4 0.5

LOG (2369-75)/(2369-T)

Fig. 16 Effect of Temperature (°F) on Yield Strength for Incone1718.(Log-Log Plot with Linear Regression)

Fig. 17

5.2

tnQ.

-r5.1

(9Zu,In-

,,, 5.0

I,-<

_ 4.90.J

y = 5.0349 19.954x (75°F) m

&

o

T=75°F

T=1000°F

T=1200°F

y = 5.0139 14.342x (1000°F)

y = 4.9778 28.072x

4.80.000 0.001 0.002 0,003 0.004 0.005

LOG (10^ 10-0.5)/(10^ 10-N)

Effect of Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718.(Log-Log Plot with Linear Regression)

(1200°F)

21

A

(nIx

2:i-oZiiin-I-(/)

uJn-::)I-n=)rr

0..I

4.7

0.000

&

O

- 10.922x

y = 5.0021 50.520x

o

0.002 0.004

• T=1000°F

0 T=1200°F

Fig. 18

0.006 0.008 0.010

LOG (10^6-1.0)/(10^6-t)

Effect of Creep Time (Hours) on Rupture Strength for Inconel 718.(Log-Log Plot with Linear Regression)

Ixv

-!-I-OZiiin-i-(n

iii

0i-.,<tl

.J<=E

i!1-rI-

00..I

5.5

5.4

5.3

5.2

5.1

0.00

Fig. 19

• Thermal Cycling, 1300°F

4 _______y = 5.4077 - 7.8371X

• ee i O, , , i

0.01 0.02 0.03 0.04

LOG(10 ^6-0.5)/(10 ^5-N')

Effect of Thermal Fatigue (Cycles) on Fatigue Strength for Inconel 781.(Log-Log Plot with Linear Regression)

22

7.0 PROBABILISTIC LIFETIME STRENGTH SENSITIVITY STUDYINCLUDING SOME SYNERGISTIC EFFECTS

Using the model given in equation (8), probabilistic lifetime strength was computedusing PROMISS. Three effects were included in this study, high temperature, mechanicalfatigue and creep. Using the experimental data of Figures 16, 17 and 18 and regressionanalysis, empirical material constants for these effects, namely, q, s and v were calculated,thus calibrating the model. NASA Lewis Research Center expert opinion and engineeringjudgment supplied other input values. Typical sets of input values for a PROMISS modelrepresented by equation (8) are given in Tables 6, 7 and 8. For example, Table 6 gives

program input data for a current temperature of 75 °F and a current value of mechanical

fatigue cycles of 200 (log 200 = 2.3). Note that the creep effect is not applicable (N/A) for

low current values of temperature such as 75 °F. The sensitivity study demonstrates the

effect of the three variables, high temperature, mechanical fatigue, and creep, onprobabilistic lifetime strength. Some of the important input values for this study are givenin Table 9. The results of this study, in the form of cumulative distribution functions, aregiven in Figures 20 to 22, one figure for each effect. For example, Figure 21 shows theeffect of mechanical fatigue cycles on lifetime strength. Note that the c.d.f, shifts to theleft, indicating a lowering of lifetime strength for increasing mechanical fatigue cycles. Inthis manner PROMISS results display the sensitivity of lifetime strength to any effect orvariable.

The values of the empirical material constants used to calibrate the model and usedas input to the PROMISS program are given as mean values in these tables. Theseconstants were calculated individually for each effect, high temperature, mechanical fatigueand creep. Also, inherent in the model given by equation (8) is the assumption that thevariables are independent and that there are no synergistic effects.

Table 6 Sensitivity study input to PROMISS for Incone1718: Temperature = 75 °F.

Effect Variable Units Distribution Mean Standard Deviation

Symbol T_e ('Value) (% of Mean)

Temperature

Mechanical

Fatigue

Creep

TM o F Normal 2369.0 71.07 3.0T o F Normal 75.0 2.25 3.0

TO o F Normal 75.0 2.25 3.0

q N/A Normal 0.4432 0.01329 3.0

NU log of cycle Normal 10.0 1.0 10.0N log of cycle Normal 2.3 0.35 10.0NO log of cycle Normal - 0.3 - 0.03 10.0s N/A Normal 19.95 0.5985 3.0

tu hours Lognormal N/A N/A N/At hours Lognormal N/A N/A N/AtO hours Lognormal N/A N/A N/Av N/A Normal N/A N/A N/A

23

Table7 Sensitivitystudyinputto PROMISSfor Inconel718: Temperature= 1000°F.

Effect Variable Units Distribution MeanSp'nbol T_pe

Temperature

MechanicalFatigue

Creep

StandardDeviation(Value)(%of Mean)

TM oF Normal 2369.0 71.07 3.0T oF Normal 1000.0 30.0 3.0TO oF Normal 75.0 2.25 3.0q N/A Normal 0.4432 0.01329 3.0

NU logof cycle Normal 10.0 1.0 10.0N logof cycle Normal 2.3 0.35 10.0NO logof cycle Normal - 0.3 - 0.03 10.0s N/A Normal 14.34 0.4302 3.0

tu hours Lognormal 1.0x 106 5.0 x 104 5.0t hours Lognormal 100.0 3.0 3.0tO hours Lognormal 1.0 0.03 3.0v N/A Normal 10.92 0.3276 3.0

Table8 Sensitivitystudyinputto PROMISSfor Inconel718: Temperature= 1200°F.

Effect

Temperature

Mechanical

Fatigue

Creep

Variable Units Distribution Mean Standard Deviation

S_mabol T_Te (Value) (% of Mean)

TM ° F Normal 2369.0 71.07 3.0T o F Normal 1200.0 36.00 3.0

TO ° F Normal 75.0 2.25 3.0

q N/A Normal 0.4432 0.01329 3.0

NU logofcycle Normal 10.0 1.0 10.0N log of cycle Normal 2.3 0.35 10.0NO log of cycle Normal - 0.3 - 0.03 10.0s N/A Normal 28.07 0.8421 3.0

tU hours Lognormal 1.0 x 106 5.0 x 104 5.0t hours Lognormal 100.0 3.0 3.0tO hours Lognormal 1.0 0.03 3.0v N/A Normal 50.52 1.5156 3.0

24

Table9 Sensitivitystudyof probabilisticmaterialstrengthdegradationmodelusingPROMISS.

Temp. Mech.Fatigue Creep(oF) (Cycles) (Hours)75 200 N/A

1000 200 1001200 200 100

1000 100 1001000 200 1001000 300 100

1000 200 101000 200 1001000 200 190

1200°F

oF

0.8

1000OF

0.6

_ 0.4

0.2

0.0 ...... ,|

0.000 0.005 0.010 0.015 0.020 0.025

LIFETIME STRENGTH, S/SO

Fig. 20 Comparison of Various Levels of Uncertainty of Temperature (°F) on ProbableStrength for Inconel 781 for 200 Cycles of Fatigue and 100 Hours of Creep.

25

m,./

<

Oeeel

1°t e"f /"300OF

o-_7 ,_ ,C(--_OOOF/_ .....0.6

0.4

0.2

0.0

0.005 0.010 0.01 5 0.020 0.025 0.030 0.035 0.040

Fig. 21

LIFETIME STRENGTH, S/SO

Comparison of Various Levels of Uncertainty of Mechanical Fatigue (Cycles) onProbable Strength for Inconel 718 for 1000°F and 100 Hours of Creep.

0.8'

I-•_ 0.6O3<rnO 0.4'

el

0.2'

0.0

Fig. 22

1.0- 10, 100, 190

" _ i , =

0.008 0.012 0.016 0.020I

0.024

LIFETIME STRENGTH, S/SO

Comparison of Various Levels of Uncertainty of Creep Time (Hours) on ProbableStrength for Inconel 718 for 1000°F and 200 Cycles of Fatigue.

26

An attemptto takeintoaccountsynergisticeffectsincludedappropriatemodificationsto inputdata.Forexample,it hasalreadybeenmentionedthatcreepeffectsarenotapplicableatlow temperaturevalues.Hence,theinputvaluesin Table6 havebeenmodifiedsuchthatcreepis notapplicableat thiscurrenttemperature.Notealsoin Tables6,7 and8thatthevalueof theempiricalmaterialconstants,s andv, changeaccordingtothecurrenttemperaturevalue. Forexample,thecreepconstant,v, is 10.92at atemperatureof 1000oF,but increasesto 50.52at 1200°F Thesevaluesof thecreepconstantarecomputedfrom linearregressionasshownin Figure18. Theincreasedvalueof theconstantat 1200°F isexpected.Themechanicalfatigueconstant,s, alsochangesastemperaturechanges.As Figure17indicates,however,thedatashowalowerconstantat1000°F thanat 75°F. For 1200°F theconstanthasdefinitelyincreased.Thesevaluesoftheempiricalmaterialconstantfor mechanicalfatiguearebasedupononly fouractualtestpoints. Thusfor mechanicalfatigue,confidencewouldbeincreasedif a few moreactualexperimentaldatapointswereavailable.

Simultaneouscalibration of the model for all three effects together to build a"combined"or synergisticmodelto betterrepresenttheinterdependenceof effectsmaybeadvantageous.In addition,thesubsequentstatisticaltestingof eachindividualeffect,usinga synergisticmodelwill assurethatit will alsomodelindividualeffectsaccurately.

8.0 CONCLUSIONS

A probabilisticmaterialbehaviordegradationmodel,applicableto aerospacematerials,hasbeenpostulatedfor predictingtherandomlifetime strengthof structuralcomponentsfor aerospacepropulsionsystemssubjectedto anumberof effectsorvariables.Themodeltakestheformof arandomizedmultifactorinteractionequationandcontainsempiricalmaterialconstants,ai. Datais availablefrom theopenliteraturefor anumberof nickel-basesuperalloys,especiallyInconel718, principallyforthreeindividualeffectsnamely,hightemperature,mechanicalfatigueandcreep.Linearregressionof thisdata,togetherwith expertopinion,hasresultedin estimatesfor theempiricalmaterialconstantsthroughwhichthemodeliscalibrated.Extensionof themodelfor afourtheffect,thermalfatigue,hasbeenoutlined.

Thus,ageneralcomputationalsimulationstructureisprovidedfor describingthescatterin lifetime strengthin termsof probablevaluesfor anumberof diverseeffectsorvariables.Thesensitivityof randomlifetimestrengthto eachvariablecanbeascertained.Probabilitystatementsallow improvedjudgmentstobemaderegardingthelikelihoodoflifetimestrengthandhencestructuralfailureof aerospacepropulsionsystemcomponents.

9.0 ACKNOWLEDGMENTS

TheauthorsgratefullyacknowledgethemanyhelpfulconversationswithDr.ChristosC. Chamisandthesupportof NASA LewisResearchCenter.AlsoacknowledgedareMr. PaulVanVeen,UndergraduateResearchAssistant,of TheUniversityof TexasatSanAntonio.

27

10.0 REFERENCES

1. Chamis, C. C., "Simplified CompositeMicromechanicsEquationsfor Strength,FractureToughness,ImpactResistanceandEnvironmentalEffects," NASA TM 83696,Jan. 1984.

2. Hopkins, D. A., "Nonlinear Analysis for High-TemperatureMultilayered FiberCompositeStructures,"NASA TM 83754,Aug. 1984.

3. Chamis, C. C. and Hopkins, D., "Thermoviscoplastic Nonlinear ConstitutiveRelationshipsfor StructuralAnalysis of High TemperatureMetal Matrix Composites,"NASA TM 87291,Nov. 1985.

4. Hopkins,D. andChamis,C. C., "A Unique Set of MicromechanicsEquationsforHighTemperatureMetalMatrix Composites,"NASA TM 87154,Nov. 1985.

5. Boyce,L. andChamis,C. C., "ProbabilisticConstitutiveRelationshipsfor MaterialStrengthDegradationModels,"Proceedings of the 30th Structures. Structural Dynamicsand Materials Conference, Mobile, AL, April 1989, pp. 1832 - 1839.

6. Probabilistic Lifetime Strength of Aerospace Materials Via Computational Simulatignby L. Boyce, J. Keating, T. Lovelace, and C. Bast, Final Technical Report, NASA TM187178, NASA Lewis Research Center, Cleveland, Ohio, Aug. 1991.

7. Computational Simulation of coupled Material De_m'adation Processes for ProbabilisticLifetime Strength of Aero_pa_¢ Materi_l,s, L. Boyce, C. Bast, Final Technical Report,NASA TM 1887234, NASA Lewis Research Center, Cleveland, Ohio, Mar. 1992.

8. Ross, S. M., Introduction to Probability and Statistics for Engineers and Scientists,Wiley, New York, 1987, p. 278.

9. Siddall, J. N., "A Comparison of Several Methods of Probabilistic Modeling,"Proceedings of the Computers in En_neering Conference, ASME, Vol. 4, 1982, pp. 231-238.

10. Scott, D.W., "Nonparametric Probability Density Estimation by OptimizationTheoretic Techniques," NASA CR-147763, April 1976.

11. Manson, S.S., Thermal Stress and Low-cycle Fatigue, McGraw-Hill Book Co.,N.Y., 1966. p. 256.

12. Swindelman, R. W. and Douglas, D.A., "The Failure of Structural Metals Subjectedto Strain-Cycling Conditions," Journal of Basic Engineering. ASME transactions, 81,Series D, 1959, pp. 203 -212.

13. Collins, J. A., Failure of Materials in Mechanical Design, Wiley-IntersciencePublication, John Wiley & Sons, N.Y., 1981, pp. 391 - 393.

14. INCONEL 718 Allgy 71_, Inco Alloys International, Inc., Huntington, WV, 1986,pp. 8-13.

28

15. Cullen, T. M. andFreeman,J. W., The Mechanical Properties of INCONEL 718

Sheet Alloy at 800°F 1000°F and 1200OF, NASA CR 268, National Aeronautics andSpace Administration, Washington, DC, 1985, pp. 20-34.

16. Barker, J. F., Ross, E.W. and Radavich, J. F., "Long Time Stability of INCONEL

718," Journal of Metals, Jan. 1970, Vol. 22, p. 32.

17. Sims, C. T., Stoloff, N.S. and Hagel, W.C., Superalloys II, Wiley, New York,

1987, pp. 581-585, 590-595.

18. Bannantine, J.A., et. al., Fundamentals of Metal Fatigue Analysis, PrenticeHall,Englewook Cliffs, N.J., 1990, pp. 63 - 66.

29

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REPORT DOCUMENTATION PAGE OMBNo. 0704-0188

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

November 1992

4. TITLE AND SUBTITLE

Computational Simulation of Probabilistic Lifetime Strength for Aerospace

Materials Subjected to High Temperature, Mechanical Fatigue, Creep

and Thermal Fatigue

6. AUTHORIS)

Lola Boyce, Callie C. Bast, and Greg A. Trimble

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

University of Michigan

Department of Mechanical Engineering

Ann Arbor, Michigan 48109

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

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

Final Contractor Report

5. FUNDING NUMBERS

WU-590-21-11

G-NAG3-867

8. PERFORMING ORGANIZATIONREPORT NUMBER

E-7415

10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

NASA CR-190794

11. SUPPLEMENTARY NOTES

Project Manager, e.G. Chamis, (216) 433-3552.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 39

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

This report presents the results of a fourth year effort of a research program conducted for NASA-LeRC by The

University of Texas at San Antonio (UTSA). The research included on-going development of methodology that

provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic

material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated

for strength degradation of structural components of aerospace propulsion systems subjected to a number of

effects or primitive variables. These primitive variables may include high temperature, fatigue or creep, tn most

cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation

equation has been randomized and is included in the computer program, PROMISS. Also included in the

research is the development of methodology to calibrate the above-described constitutive equation using actual

experimental materials data together with regression analysis of that data, thereby predicting values for the

empirical material constants for each effect or primitive variable. This regression methodology is included in the

computer program, PROMISe. Actual experimental materials data were obtained from industry and the open

literature for materials typically for applications in aerospace propulsion system components. Material data for

lnconel 718 has been analyzed using the developed methodology.

14. SUBJECT TERMS

Degradation; Temperature effects; Cyclic loads; Creep; Computer programs; Data

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