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Thermoviscoplastic Nonlinear Constitutive Relationships for Structural Analysis of High Temperature Metal Matrix Composites tHASA-Tfl*8729i) IHEEJSCVISCCEIASIIC NONLINEAB CONSTITUTIVE RELAltCNSHlPS FOE S1RUC20KAL ANALiSlS CF HIGH liKEEEAIUHB HETAL HATEIX CCKECSITES {NASA) 25 p HC A02/BF A01 CSCL 11D G3/2H HQ6-24756 Unclas 42913 Christos C. Chamis and Dale A. Hopkins Lewis Research Center Cleveland, Ohio Presented at the First Symposium on Testing Technology of Metal Matrix Composites sponsored by the American Society for Testing and Materials Nashville, Tennessee, November 18-20, 1985 / I Vi- -:*<r* 'j «.-•■* t'<-- -t/r ' plil'>"rSM^^i;:^TT^:V.V>'''V^i;Vv^ ■'fyZF*f*X-. i T5F 1 *»V' -..,>;•-•.-?,«■ . ■ v "**"-"- -"**'"" '■ w ' wv "-'""^ CONTENTS Page ABS1RACT ! INTRODUCTION ! EQUATION FORM/FEATURES 2 APPLICATION . . . 4 POSSIBLE EXTENSIONS/LIMITATIONS 7 CONCLUSIONS/REFERENCES 8 '"" " : "' ' ■ " ""■ y\ THERMOVISCOPLASTIC NONLINEAR CONSTITUTIVE RELATIONSHIPS FOR STRUCTURAL ANALYSIS OF HIGH TEMPERATURE METAL MATRIX COMPOSITES ChHstos C. Chamls* and DaTe A. Hopkins** National Aeronautics and Space Administration ^ Lewis Research Center Cleveland, Ohio 44135 SUMMARY A set of thermovlscoplastlc nonlinear constitutive relationships (TVP-NCR) T 1s presented. This set 1s unique and has been developed mainly for application ,] to high- temperature metal-matrix composites (HT-MMC) &nd is applicable to ther- i mal and mechanical properties. Formulation of the TVP-NCR 1s based at the .< mkromechanlcs level. The TVP-NCR are of simple form and readily Integrated into nonlinear composite structural analysis. Results show that this unique 4 § set of TVP-NCR Is computationally effective. It provides a direct means for ; £ predicting complex materials behavior at all levels of the composite Simula- j ,i tlon; that 1s, from the constituent materials, through the several levels of : *| composite mechanics, and up to the global response of complex HT-MMC structural \ -, components. \ INTRODUCTION High temperature metal matrix composites (HT-MMC) are emerging as mate- rials with potentially high payoffs In structural applications. Realization of these payoffs depends on the parallel and synergistic development of (1) a technology base for fabricating HT-MMC structures and components, (2) experi- mental techniques for measuring their thermal and mechanical characteristics, and (3) computational methodologies for predicting their nonlinear thermovlsco- plastlc (TVP) behavior 1n complex service environments. In fact, development of computational methodologies should precede the other two because the struc- tural integrity and durability of HT-MMC can be numerically assessed and the potential payoff for the specific application can be closely estimated. In this way, 1t 1s possible to minimize the costly and time consuming experimental effort that would otherwise be required m the absence of a predictive capability. Reteht research at NASA Lewis 1s directed towards the development of a computational capability to predict the nonlinear TVP behavior of HT-MMC. This capability 1s schematically depicted 1n figure 1. As can be seen in this figure the capability consists of several computational modules encompassing the material TVP behavior (bottom), composite mechanics (sides), and the finite element analysis of structural components (top). The TVP computational module consists of mathematical models which formally and explicitly relate the dependence of the constituent material properties on *Sen1or Research Engineer, Aerospace Structures/Composites. \ **Aerospace Structures Engineer. \ w-m-w^ ■^M^fffi w +*+mmm IfcL 1 . JfiKSfriCTI" i^twE'Jlnli IV St T S ' ? nd (3) t1me - These wth«nat1cal models are col- NCftJ !L"i !?M her T^° plast1c nonl1n "r constitutive relation ships (TVP. NCR). The objective of this report Is to present the ivp url aIIIIITJ* V part of the computational capability for HT-m? structures ° P ' d " * t1onIlVffec!?^« e JH SCr1bed / e,re , deve1oped w1th an em P h "1s on computa- tional effectiveness and are unique m their following features- m SJIrir form - they are applicable to all constituent mateMal proper? es the£!l SKli?!' 1nclud1ft 9 strength), (2) evolutionary - they a?e e«ly extend/ modified to accommodate additional effects such as strain rat*^ m!fl? IS? tL rad Mj°: n il?L 1s T rph1c v?? y have >^ «^ ^a d t : < f _ This unique set of TVP-NCR consists Of products of terms with unknnur, exponents The exponents are determined fo° the specific material anS tine of tTp NcTeoualtJn 6 !^ 'V!*^'- th I" Product terms aVFr^ulr.ft.'XJ ° Ind"?Sf XI" E ac " unt for: 0> temperature dependence, (2) stress level T.t i?L Jh?" Pat J: Three ex P dn ** ts "*ed to be determined to complete y i5l!^J h1$ equa t 10n ' These "P^nts are determined from available expeM mental data or estimated from anticipated behavior of the particular prodScT The computational effectiveness of this unique set of TVP nch 1< ftu , lliafo , using the computational capability depicted schemat cal?y [f^ll i he St Sc Ihd l2Trl\° f d tUrb1 " 6 bUde ' made from f1ber relnfo ?ed superanoy HT-MMC and subject to representative mission loading conditions 1s determined The effectiveness of the TVP-NCR to represent the physlca behavior of th! 7&*llill* T PUtat1 ° nally assessed b * Perturbing the exponents and comparing the structural response of the blade to the unperturbed case. comparing i i i EQUATION FORM/FEATURES Is aI h follIX! C f ° rm S6leCted f ° r the TVP " NCR f ° r the co " st1 tuents of HT-MMC (1) Mechanical property (moduli, strength) P M Mo >" 1o J l> a m i F ' °o lA (1) (2> ^a r c1t Y rP Perty (expaf, ' 1ort coeff ^lents, thermal conductivity, heat P, 10 T" J [ Sf - m Sr - V- % (2) V n W-. v^: r ::*£'■■ **■ The notation used in equations (1) and (2) 1s as follows: PHj denotes the current property of Interest P 1s the corresponding property at reference conditions Tm Is the melting temperature T 1s the current temperature 1 1s the reference temperature at which P is determined Sp 1s the fracture stress determined at T conditions o the reference stress at which P 1s determined Sf Is an appropriately selected stress rate, for example, the stress rate at which penetration occurs during Impact o c Is the stress rate at which P 1s determined, and <j 1s the current stress rate The exponents n, m, and l are empirical parameters which are determined from available experimental data or estimated from the anticipated behavior of the particular product term. The first term on the right side of equation (1) represents the tempera- ture dependence, the second represents the stress dependence, and the third represents the rate dependence or the time dependence, In part. The other part of the time dependence 1s through the direct time Integration as will be described later. Equations (1) and (2) describe, then, material behavior 1n the temperature- stress- time space. Each term on the right side of equations (1) and (2) describes a mono tonic functional dependence of P/P from some Initial property value to a terminal or ultimate material state. The specific shape of the function depends on the exponent as 1s shown In figure 2 for a fixed exponent and In figure 3 for a fixed T/T F ratio. By judicious selection of the exponent and the initial and terminal values, a variety of functional dependences can be simulated using equations (1) and (2). lhe form of equations (1) and (2) makes it convenient (provides direct feedback) to select the various parameters so that the functional dependence described Is consistent with the physical considerations. For example, 1t 1s well known that the melting temperature (1 H ) Is a fundamental parameter 1n metals and that the mechanical properties are "zero" at T(y|. Also, the stress at fracture for some reference condition 1s readily determined by simple experiments. In addition, the ultimate value of the stress rate may be determined from high velocity impact penetration tests. It can be seen from figure 2 that the P/P Increases/decreases very rapidly as the melt Ing temperature (or any terminal value) 1s approached. Furthermore, the form of the equations make It convenient to evaluate the exponents from available data since each term 1s "Isolated" from the others, that 1s, the other terms V can be taken at reference conditions and will be unity. The equations are computationally effective since each term requires simple substitution of values and one exponentiation. The form of the TVP-NCR selected has all the desirable features men- tioned 1n the introduction. These features can be conveniently summarized Into three groups: (1J physical, (2) fundamental, and (3) computational, as follows: (1) Physical - The constitutive relationships describe dependence on: tem- perature, time, stress, stress rate, and complete property degradation as the ultimate value 1s approached. (2) Fundamental - the constitutive relationships are: generic - they are applicable to all constituent material proper- ties (fig. 4) evolutionary - they are easily extended to Include additional dependence, for example cyclic (mechanical, thermal) isomorphic - they have the same form for all the properties unified - they are fully coupled from the initial to the terminal material state universal - they are equally applicable to any three constituents (fibers, matrix, interphase) nondimenslonal - they are normallzable with respect to reference and ultimate values. (3) Computational - the constitutive relationships are: ' computationally effective - they only require simple substitution * and exponentiation L< easily Integrated into nonlinear composite mechanics and struc- tural analysis codes - they can be fully Integrated using only a few programming statements i APPLICATION V The 1VP-NCR were Integrated into a special-purpose computer code for structural analysis of turbine blades fnade from HT-MMC (ref. 1). This code 1s depicted schematically in figure 1. The TVP-NCR describe the constituent material properties 1n the material space as shown at the bottom of the figure. Notfe that the cumulative time* temperature* <»rid stress at the cur- rent state are tracked through the Integrated computational process as shown 1n the figure. Once the current properties for the constituent materials have been determined, they are used In the various levels of composite mech- anics to generate the quantities required for the global structural analysis (ref. 1). 1 M MMMWMMMBPMi volume ratio of the fih<>r ui*c n * T k i * <uer/superai ioy hi~mmc. The »uL n ^ r % t :;^ Pendent PWrtlt.) are estimated or deduced fro"ot*er p >dt^;f t f ;=it t^?Mr r£ 9" If he S»L°? ^,'? C ?^ r t???"" "^"P""" to the outermost ply (Ply no'li at the nodal point Identified by the arrow 1n fitmre * (*«** ;« IX i ' of thJ JJJJl!J;.i he secondset was Performed to determine the sensitivity lift rt ructura ^ r ^Ponse to arbitrary perturbations of the 1VP-NCR exoon tlowl I?LL e t?nn *!* of * nal * s ? s ^onstrates the Importance of compu a £X . ? 2*!°" s1nce 1t P rov1d « an assessment of the accuracy of the data required to experimentally determine the parameters In the W-NCR f»hi 7 J e / esu J ts obtained from both structural analyse- are summarized in fo? thl wJ he 9 "J? 1 V f MableS (cru1se and ^sldual state) aTn"abe II cases ? ) I*?/ \ a V e L {C : uU V tate only) - The resu1t * are grouped 1n5o cases 1-7. case 1 1s the baseline case and has the "best" values for Ihl 'Z'Ztr^ th ? TVP ' NCR - Cases 2 ~ 7 constitute the sen 1t1v ty ana y es the£b^M obtain data for these exponents which 1s accurate to within 15 percent especially 1n these high temperature ranges. percent /*. k , lh M 9 ? test change (16 Percent) 1n the frequency occurs 1n cat* 3 (table I) where the perturbations in the exponents decrease ?he mechanLl properties and Increase the thermal properties of the matrix inT^*!<\ change (15 percent) 1h the ply stress occu n case 6 ?tab?e , u * perturbations in the exponents (1) Increase the "ber m a c 'p? p° t e prope e'fof h°e 6 f?LJ h h,ft r1X ' iM * 1°^^ < 2) decrease th/SSSl properties of the fiber but increase those of the matrix The residual <<■;.** Ply stresses for all case^re negligible for all pJactUal purposes '* The Integrated aralysls generates properties at all levels of the com- posite behavior simulation. Behavior of the longitudinal (fiber direction) modulus (En) of the constituents and ply are shown graphically 1n figures 7(a) and (b) for cases 1 and 6 throughout the mission duration. The modulus decreases Initially during the start-up and climb part of the mis- sion. The modulus levels off during the steady state (cruise) part of the mission. Finally, the modulus Increases during the landing and engine cut- off part of the mission. The significant point 1s that the TVP-NCR appear to represent the material behavior as would be Intuitively anticipated for this type of flight mission. The corresponding behavior for the transverse (perpendicular to fiber) modulus (E 2 2) 1s shown 1n figures 8(a) and (b) and for the 1n-p1ane shear modulus (G12) in figures 9(a) and (b). The behavior of these moduli 1s about the same as that for the longitudinal modulus (En). The behavior of the longitudinal thermal expansion coefficient (an) throughout the mission 1s shown In figures 10(a) and (b) for cases 1 and 6. This coefficient Initially Increases rapidly (during climb), levels off dur- ing cruise, and slowly decreases to about Its Initial value during landing. This type of behavior 1s to be expected since the thermal expansion coeffi- cients increase with increasing temperature. Note that even though an for the matrix for case 6 is about 30 percent smaller than for case 1, the coefficients for the ply and the interphase are about the same. This illu- strates, 1n part, the restraining Influence of the fibers in the HT-MMC behavior and in addition the Importance of having TVP-NCR defined at the mlcromechanics level. The corresponding behavior for the transverse thermal expansion coefficient (a 2 2) is shown in figures 11(a) \nd (b). The behavior of a22 is similar to that of an • The behavior of the three lowest natural frequencies of the airfoil throughout the flight mission is shown in figures 12(a) and (b) for cases 1 and 6. Note that each frequency behaves somewhat differently. This is expected since each frequency is influenced differently by the centrifugal force. The second and third frequencies decrease during climb, increase during the early part of cruise, remain constant during the major portion of the cruise, and increase gradually to about their initial value during land- ing and engine cut-off. On the other hand* the first frequency increases sharply during climb (due to centrifugal force stiffening), levels off during cruise, increas&S sMghtly during landing (cooling but speed retained) and gradually decreases to approximately its initial value (zero- speed) . The coupled behavior of these three frequencies throughout the flight mission further demonstrates the computational effectiveness of the TVP-NCR to represent the physics of the HT-MMC from the constituent materials level to the component global structural response. The longitudinal stress (on) behavior throughout the mission in the constituents and 1h the ply is shown in figures 13(a) and (b) for cases 1 and 6. The stress 1h the fiber Increases very rapidly during climb, decreases gradually during cruise, decreases rapidly during landing, and decreases gradually to a small residual compressive stress at engine cut off. Ihe ply stress exhibits the same behavior as the fiber stress but 1s much lower 1n magnitude. The stress in the matrix increases (compressively) very rapidly 1 W*i * •P"^ mmmmm during climb, remains compressive during cruise and decreases gradually to a residual tensile value during landing and engine cut-off. The corresponding behavior for the transverse stress (o 2 2) 1s shown 1n figures 14(a) and (b) and that for the IntralarMnar shear stress (o 12 ) 1n figures 15(a) and (b). Note there are three different regions (A f B, and C) for the matrix and two different regions (B and C) for the Interphase 1n which c 2 2 ahd 12 are computed. These regions correspond to the 1ntra- lamlftar regions shown 1n figure 4. The Interesting points to note are: (1) the matrix in the different regions 1s subjected to both tensile and compres- sive transverse stresses which can be of substantial magnitude, (2) the interphase can be subjected to relatively high transverse tensile stresses which may cause Interfaclal damage, (3) the fiber 1s subjected to very high transverse tensile stresses which could cause fiber splitting, and (4) the transverse ply stress 1s relatively small compared to the stress distribution 1n the constituents. Collectively, the effectiveness of the 1 constituents at the ml anks) level. Determl possible because the 1 and the formulation 1s gradual decrease Indie the material thermovls creep. local stress behavior demonstrates the computational VP-NCR to predict the Instantaneous behavior of the cromechanlcs level as well as at the ply (macromech- natlon of the stress behavior 1n the constituents 1s VP-NiJR are referred to the constituent material space based at the composite mlcromechanlcs level. Ihe ated for all the stresses during cruise 1s caused by coplastlc behavior and may be thought of as a form of POSSIBLE EXUNSiONS/i. IMITATIONS The 1VP-NCR can be extended to Include thermal cycle and mechanical cycle effects, diffusion, other material degradation effects, as well as time directly. Though terms for these factors are easily added since they will be of similar form, 1t 1s not necessarily clear which of these will contribute to Independent material behavior. In the direct time Integration analysis, the effects of temperature are directly accounted for. Any ratchettlng, for example, wilt be part of the residual displacements. Also, residual thermal stresses and other stresses are known and constitute a part of the cumulative stress history. On the other hand, vibratory stress effects are not accounted for 1n the direct time Integration of the structural analysis. Though these effects can be accounted for through the stress rate, vibratory stress effects may Indeed contribute to Independent behavior. Diffusion or any other material degrada tlon can be Incorporated once the type of degradation has been defined. Other extensions will become self evident as HT-MMC start being extensively applied 1n environments where limited o no property data are available. Some limitations of the 1VP-NCR described herein are that they: (1) must be used at the current Instant of time, (2) must be used with a direct time Integration nonlinear composite structural analysis, (3) cannot be verified experimentally at all levels of the composite mechanics analysis and at the very high temperatures, and (4) do not Incorporate Initial tangent unloading or possible shakedown 1n the classical plasticity sense. Whether (3) and (4) are serious limitations 1s yet to be determined. At this stage I ^.-^< of the development 1t 1s prudent to say that these TVP-NCR must be used judiciously in design studies relying mainly on sensitivity analyses and other Judgment factors that are appropriate for the specific case CONCLUSIONS /tvp Uppw!! 6 kJVI thermov *scoplast1c nonlinear constitutive relationships (TVP-NCR) for high-temperature metal-matrix composites (HT-MMC) has been cabtlT.n^ 5 prese i; te ?- n™ 5 S6t of 7VP " NCR 1s of ^P le form? Is appli- cable to all thermomechanlcal properties, 1s fully coupled, 1s readily 1nte- SfeSilI! !nnnr!Mi^!!; P0S H te struc * u ^l analyses , and 1s computationally effective. Applicability and computational efficiency were demonstrated through an application to a HT-MMC turbine blade structural anal? Is Sen- sitivity analyses Indicated that substantial perturbations 1n the TVP-NCR exponents have rather minimal effect on the global and local response of the structure These TVP-NCR make it possible to trace the history of Hl-MMC mirrn^h]n5 0ft, T er, J S K f !: om fabr ] cat1on th ™"9h service and from the composite micromechanlcs to global composite structural response. The TVP-NCR are suitable for preliminary designs and parametric studies. They should be tal lj Tr flT d 1n 6 J eSi9n a PP l1cat1 <™ since they have not been experlmen- REFERENCE 1. Wins, D.A., "Nonlinear Analysis of H1gh-7emperature Multl layered Fiber Composite Structures," NASA TM-83754, National Aeronautics and Space Administration, Washington, D.C., 1984. ■>, 7 TABLE I. - EXPONENT PERTURBATION EFFECTS ON STRUCTURAL RESPONSE Case Constituent Property Change Exponent Structural response Percent freq. Cruise conditions Residual Cruise/ res. N M L Displ. Unt't Freq. Displ. Unt't Freq. 1 Fiber Matrix F a R R R R 0.3 .6 .8 .2 0.6 .1 2.8 .1 0.1 .05 .1 .05 0.015 -0.22 3650 0.00016 -0.04 4380 0/0 2 Fiber Matrix R R I D 0.3 .6 .4 .1 0.6 .1 2.0 .05 0.1 .05 .1 .05 0.015 -0.16 3840 0.00016 -0.03 4550 +S/+4 3 Fiber Matrix Pt R R D I 0.3 .6 1.2 .6 0.6 .1 4.0 0.2 0.1 .05 0.1 0.05 0.017 -0.31 4230 0.00012 -0.05 4650 +16/+6 4 Fiber Matrix ft I R R 0.1 .2 .8 .2 0.2 .05 2.8 .1 0.1 .05 .1 .05 0.014 -0.20 3470 0.00010 -0.04 4370 -5/~ 5 Fiber Matrix % % I R R 0.5 1.0 .8 .2 1.0 .2 2.8 .1 0.1 .05 .1 .05 0.016 -0.23 4050 0.00020 -0.02 4540 +11/+4 6 Fiber Matrix ? * I D I 0.1 .2 1.2 .6 0.2 .05 4.0 .2 0.1 .05 .1 .05 0.015 -0.29 3660 0.00021 -0.06 4580 ~/ + 6 7 Fiber Matrix ft D I I 0.5 1.0 .4 .1 1.0 .2 2.0 .05 0.1 .05 .1 .05 0.0J !: > -0.17 4040 0.00018 -0.02 4350 +11/+6 P M - Mech. Prop. Pj - Thermal Prop. R - Reference I - Increase D - Decrease Units: Displ. - In: Unt't - Deg: Freq., Hz « t i i .i-ri IV \ / 'J "»*■ TABLE II. - EXPONENT PERTURBATION EFFECTS ON PLY STRESSES B > Case Constituent Property Chanqe Exponent. Ply stresses Percent tot n Cruise conditions Residual N M L atii °*22 o*12 a m ot 2 2 **12 Cruise/ res. 1 Fiber i* R 0.3 0.6 0.1 P T R .6 .1 .05 29.2 8.4 -13.7 0.4 -0.6 • Matrix s? R R .8 .2 2.8 .1 .1 .05 2 Fiber E* R 0.3 0.6 0.1 P T R .6 .1 .05 27.6 10.2 -13.6 0.5 -0.4 ~ -5 Matrix PM pt I .4 .1 2.0 .05 .1 .05 3 Fiber &* R 0.3 0.6 0.1 P T R .6 .1 .05 32.1 6.0 -13.7 0.5 -0.7 *. +10 Matrix PM pt I 1.2 0.6 4.0 0.2 0.1 0.05 4 Fiber ft I 0.1 0.2 0.1 p T .2 .05 .05 30.8 . 7.1 -13.9 1.9 -1.8 ~ +5 Matrix f? R R .8 .2 2.8 .1 .1 .05 5 Fiber S* D 0.5 1.0 0.1 P T I 1.0 .2 .05 33.2 10.4 -16.1 5.2 -1.4 -2.8 +14 Matrix Pt R R .8 .2 2.8 .1 .1 .05 6 Fiber E* I 0.1 0.2 0.1 P T D .2 .05 .05 33.7 4.5 -13.7 1.4 -1.4 -0.2 +15 Matrix p M pt I 1.2 .6 4,0 .2 .1 .05 7 Fiber 5« 0.5 1.0 0.1 Pt I 1.0 .2 .05 26.7 11.1 -13.7 0.1 - -0.2 -9 Matrix o PM p t I D .4 .1 2.0 .05 .1 .05 P M - Mech. Prop Pj - Thermal Prop R - Reference I - Increase D - Decrease w w y y , « ! w. - , w^" -V 4 TO GLOBAL STRUCTURAL ANALYSIS LAMINATE f LAMINATE THEORY COMPOSITE MICROMECHANICS V THEORY ^ COMPONENT CONSTITUENTS V FROM GLOBAL STRUCTURAL ANALYSIS LAMINA"' ( THEORY { NONLINEAR MATERIAL n MODEL LAMINATE PLY > COMPOSITE * MICROMECHANICS >' THEORY MATERIAL PROPERTIES P * P(0, T. t) Fig. 1. "Integrated nonlinear composite structural analysis. Fig ; , 2 ;. * Thermoviscoplastic nonlinear constitutive relationships - typical behavior for a given exponent. y up**.. mj>- ^^ -2 -1 1 EXPONENT, n 3 Fig. 3. -Thermoviscoplastic nonlinear constitutive relationships typical behavior for given T/T F ratio. SUBREGIONS OF INTRALAMINAR NONUNIFORMS -^ MATRIX INTERPHASE FIBER **2 Fig. 4. -Typical interconstituent regions for composite micromechanics. J, W-L5ThO^Fe-25Cr-4A|.lY v f ■ 0. 50 \ g * 0.01 in. 9 • [±45L Fig. 5. - Finiie-element model for hollow turbine blade airfoil of high temperature metal matrix composite. -J — I I i r^i 20 40 60 J 1— |J — i l2j 2 40 60 120 80 40- 20 13 120 OS a. 80 40 r 40 60 J L 2 40 60 TIME, t, mir, 8000 r 6000 4000 2000 3 J — I L (a) a. 8000 6000 4000 2000 20 40 60 i r J L 40 (b) -J i 60 Fig. 6. -Flight mission profile for turbine blade structural analysis. Node6 ; Ply 4. ■" -j? •.-*•■ »i i i «a ~w* 60 40 20 i o o o 5 60 i O F FIBER M MATRIX D INTERPHASE L PLY CASE1 J I I L 20 40 60 V 40 20 v CASE1 T M J L J I I 2 40 60 CASE 6 I L 20 CASE 6 (a) J I I 40 60 J L ^- J I L 2 40 60 (b) TIME, t, min Fig. 7. - Longitudinal modulus behavior during flight mission. Node 6* ply 4. >j ^™^r^" a 60 40 ■5 20 CASE1 " F FIBER M MATRIX D INTERPHASE L PLY J I ' i 3 :d a o UJ 60 </* QC LU > V* Z < 0£ 40 20 20 CASE1 40 J L 40 60 J i 60 CASE 6 TIME, t, min Fig. 8. - Transverse modulus behavior during flight mission. Node 6- ply 4. * 1«T F FIBER M MATRIX D INTERPHASE L PLY 25 r- CASE1 CASE 6 F F 20 "" _j D D 15 - Y~~\- ^^T 10 5 ^ /^~~k /^ M *v> Ol s CM - 1 J i t 1 ■ i i i i i (a) i i t o 20 40 60 C ) 20 40 j — i — j 60 =5 U 3 o 25 p — S CASE1 CASE 6 OS i 20 15 10 ^_ 1 i — F_ D ^~~m \ , j L D t=-j Y~~t m i — ' /^~lb 5 1 »— ** J 1 r^A 1 i i \ , J 1 1 A 1 I (b) | 2 40 60 2 40 — — i i 60 TIME, t, mi n Fi L?' I ln ! raIaminar she * r modulus behavior during flight mission Node 6; ply 4. s^aBCTEsrsrarsmEEiS , I.?.. ~? -■-—*. J* o z o z 0£ s 4- £ 2 F FIBER M MATRIX D INTERPHASE L PLY CASE 1 I i i I t 20 CASE1 40 60 7 J L^J L 40 60 6 4h 2- CASE6 I'll jja 20 40 60 CASE 6 TIME, t, min Fig. 10. - Longitudinal thermal expansion coefficient behavior during flight mission. Node 6; ply 4. "'--* *--* : : SSTST: c © o z o z < 2 LU (/> Of LU > 00 z < 0£ F FIBER M MATRIX INTERPHASE L PLY rCASEl 6- * I I I I I 1 20 40 60 8h 6 4 2 CASE1 / V M >=%^_ D i — L F J 1 I I 60 CASE 6 4 - 2 J L 20 r CASE 6 40 (a). 60 i i i U». TIME, t, min 40 60 Fig. 11. -Transverse thermal expansion coefficient behavior during flight mission. CASEl - 1 1st MODE 2 2nd MODE 3 3rd MODE J 1 60 CASE 6 20 CASE 6 J L 40 (a) 60 — L ^p — i — ' ' i 2 40 60 TIME, t, min Fig. 12. -Turbine airfoil frequencies behavior during flight mission. V im&trgm MMtfMi 111* Iri fe ) 120 n F FIBER M MATRIX D INTERPHASE L PLY CASE 6 4/> UJ Z o CASE 6 60 TIME, t, min Fig. 13. - Longitudinal stress variation during flight mission. Node 6; Ply 4. i ill i g gg^a-i* ^*w 1 FIDER 2 MATRIX (A) 3 MATRIX (B) 4 MATRIX (C) 5 INTERPHASE <B) 6 INTERPHASE (C) 7 PLY D UJ 200 ]caseT~ 6^ W 100 • 7n > 4-i \ r- •inn - 2- 1 5 J 1 1 L 3 I I 1 I 1 TIME, t, min Fig. 14. -Transverse stress variation during flight mission. Node 6; ply 4. ! * •zvmzzr LMUL JL.-l*ll-JHLh-: 1 FIBER 2 MATRIX (A) 3 MATRIX (B) 4 MATRIX (C) 5 INTERPHASE (B) 6 INTERPHASE (C) 7 PLY 60 TIME, t, min Fig. 15. - Intralaminar shear stress variation during flight mission. Node 6; ply 4. 1. Report No. NASA TM-87291 2. Government Accession No. 3. Recipient's Catalog No. 4. Title and Subtitle 5. Report Date Thernrtovlscoplastlc Nonlinear Constitutive Relation- ships for Structural Analysis of High Temperature Metal Matrix Composites 6. Performing Organization Code 505-63-11 7. Authors) Chrlstos C. Chamls and Oale A. Hopkins 6. Performing Organization Report No. E-2998 10. Work Unit No. 9. Performing Organization Name and Address National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135 11. Contract or Grant No. 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington* O.C. 20546 13. Type of Report and Period Covered Technical Memorandum 14. Sponsoring Agency Code 15. Supplementary Notes Presented at the First Symposium on Testing Technology of Metal Matrix Composites, sponsored by the American Society for Testing and Materials, Nashville, Tennessee, November 18-20, 1985. 16. Abstract A set of thermov1scoplast1c nonlinear constitutive relationships (1VP-NCR) 1s presented. This set Is unique and has been developed mainly for application to high- temperature metal-matrix composites (HT-MMC) and Is applicable to thermal and mechanical properties. Formulation of the TVP-NCR 1s based at the micro- mechanics level. The TVP-NCR are of simple form and readily Integrated Into non- linear composite structural analysis. Results show that this unique set of TVP-NCR 1s computationally effective. It provides a direct means for predicting complex materials behavior at all levels of the composite simulation; that 1s, from the constituent materials, through the several levels of composite mech- anics, and up to the global response of complex HT-MMC structural components. 17. Key Words (Suggested by Author(s)) Fiber composites; Metal matrix; Thermovisco- plastic behavior; Composite mechanics; Structural analysis; Stress analysis; Turbine blades; Thermal properties; Mechanical properties; Micro stresses; Vibration frequencies. 19. Security Classif. (of this report) Unclassified 18. Distribution Statement Unclassified - unlimited STAR Category 24 20. Security Classif. (of this page) Unclatss1f1jed- 21. No. of pages 22. 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