Greenstreet, W.L.

Liu, K.C.

Pugh, C.E.

Greenstreet, W. L.

Liu, K. C.

Pugh, C. E.

UNT Digital Library

Information to "be presented at a Panel Discussion,ASME Pressure Vessel and Piping/Materials/NuclearConference, Miami Beach, Florida, June 2U-28, I97UOUTLINESTRUCTURAL DESIGN CRITERIA FOR LMFBR COMPONENTSAND INELASTIC MATERIAL BEHAVIOR*W. L. GreenstreetK. C. LiuC. E. PughOak Ridge National Laboratory-Oak Ridge, Tennessee 37830IO _. -- VJ «J5 0 =•<I l l s S = .*i i s i i i i ;" J" C - 3 " W S•a ffi 3-»-< « w au B » O l ( n ~£ n a x S «- t — O C*O<> ? " • - a S'S ?INTRODUCTION MASTERStructural design criteria being used in the design of Liquid Metal FastBreeder Reactor system components are basically those of Section III of theASME Boiler and Pressure Vessel Code and Code Case 1331. The latter appliesto Class 1 components for service at temperatures above those covered bySection III. These documents are currently supplemented by RDT StandardE15-2, "Eequirements for Nuclear Components (Supplement to ASME Boiler andPressure Vessel Code, Section III)," and RDT Standard F9-IT, "Requirements forNuclear Components at Elevated Temperatures (Supplement to ASME Elevated Tem-perature Code Case 1331)." The latter, F9-IT, is to be replaced by a moredefinitive set of documents now in preparation. These are RDT Standard F9-U,"Requirements for Design of Nuclear System Components at Elevated Tempera-tures (Supplement to ASME Code Case 1331)," and RDT Standard F9-5, "Guidelinesand Procedures for Design of Nuclear System Components at Elevated Tempera-tures."The ASME Code documents provide stress and strain limits for designevaluations, with structural behaviors being divided into the two categoriesof load-controlled and deformation-controlled. Linearly elastic materialmodels provide bases for design evaluations in the case of the first category.For the second, which includes considerations of ratchetting, the interactionof creep and fatigue, buckling, and structural instability, use of inelasticanalyses is recognized as necessary in some instances. To minimize needs for•Research sponsored by the U.S. Atomic Energy Commission under contractwith the Union Carbide Corporation.DISTRIBUTION OF THIS DOCUMENT 13 UNMMITm03-detailed inelastic analyses, means for evaluations on the basis of elastic andsimplified inelastic methods of analysis are given as possible alternatives.RDT Standard F9-IT modifies the Code Case limits and is more explicit concern-ing inelastic analyses; material behavior representation requirements appli-cable to types 30U and 316 stainless steel are given. The set of standardsin preparation (F9-I+ and F9-5) will provide guidelines for material behaviorrepresentations, or guidelines for inelastic analyses, to establish minimumquality levels for use with certain criteria. Materials in addition to stain-less steel are to be considered.As indicated, detailed considerations of inelastic behaviors of materialsand constitutive equations for appropriately describing these behaviors arevery important in the design of Liquid Metal Fast Breeder Reactor system com-ponents. This importance stems not only from the relatively high operatingtemperatures but also from the fact that large differential thermal strainsare induced due to the good heat transfer characteristics of the sodium coolant.Also important are the analysis methods used in predicting structural behavior.However, since finite-element methods currently are used in the majority ofdetailed inelastic analyses, separation of constitutive equations and analysismethods discussions can be made, within limits, without loss of generality.In this paper, we discuss particular aspects of inelastic behavior and con-stitutive equation development work.In the following sections, constitutive equations adopted for current usein describing inelastic behaviors of types 30U and 316 stainless steel inLiquid Metal Fast Breeder^Reactor applications are briefly outlined. Theseequations are for small deformation behavior and are based on the assumptionthat the total strain tensor can be expressed as the sum of elastic, plastic,and creep components. Constitutive equations appropriate to each componentwere identified and developed, primarily on the basis of existing, predominantly-uniaxial, test data.To obtain more information on material behavior and to improve upon theformulations provided, either through extension or replacement, carefullycoordinated analytical and experimental studies are under way as a part of astructural design technology development program being carried out by the OakRidge National Laboratory. These studies are also described and summaries ofresults are given.KLASTIC-PLASTIC BEHAVIOR(Slide No.)A. Constitutive Equations Currently Used1. Based on classical kinematic hardening which isextended to cover nonisothexmal conditions2. Auxiliary rules to account for influence of deforma-tion history1 3. Experimental basis for initial selection: uniaxialmonotonic and cyclic stress-strain curvesB. Plasticity Studies1. Experimental studiesa. Initial and subsequent yield surfacest>. Stress-strain responses under arbitrary plasticloading histories2 2. Initial yield loci in stress-temperature space3 3. Subsequent yield surface behavior for a specimen sub-jected to nonradial plastic loadingsh. Observations from subsequent yield surface studiesa. Motion of surfaceb. Surface deforms in direction of loading; there isseme cross effectc. Surface does not pass through prestress pointd. Yield surface decreases in size when moved awayfrom origin; it increases in size when returnede. -Translation tensor increment and the plastic strainincrement are not necessarily colinearf. Normality condition is generally satisfiedh 5. Results of basic studies in thexmoplasticitya. Plastic loading at a given temperature causes yieldloci at lower temperatures to translateb. Essentially uniform translation occurs for smallplastic strains5 6. Stress-plastic strain response as function of direc-tion with respect to prestressing direction(Slide No.)7. Areas for constitutive equation improvement" a. History-dependent descriptions of subsequentyield surfacesb. Equations to describe motion of surfacesc. Improved representation of nonlinear stress-strain responseT3ME-DEPENDEHT BEHAVIOR6 A. Currently Used Constitutive Equations1. Mathematical description of uniaxial creep response underconstant stress and temperature conditions2. Equation-of-state-type formulation for combined stress3. Hardening rulesa. Classical strain-hardening ruleb. Auxiliary rulesB. Combined Stress Studies1. Thin-walled tubular specimens subjected to axial forceand torsional loadings7 2. Torsional creep strain vs axial creep strain correlation8 3. Effective creep strain vs time plotsC. Theory Development1. Identification of variables2. Potential function for creep3. State variable representationD. Creep Testing [1. Accurate specimen alignment and control and measure-ment of variables9 2. Influences of stress level on uniaxial creep response10 3. Comparison of uniaxial constant load creep curves fromtwo machines11 k. Constant load creep curves for specimens having samegrain size, E. General Observations1. High quality creep data are essential2. Constitutive equation development places stringentdemands on accuracy and reproducibillty of experimentalresultsSUMMAIffInelastic analyses of Liquid Metal Fast Breeder Reactor system components may,in some cases, be required to show satisfaction of applicable design criteria. Thus,appropriate mathematical descriptions of material behavior must be availablefor use in conducting meaningful analyses. Constitutive equations in currentuse as well as research and development work being carried out to derive Im-proved descriptions of inelastic responses were outlined. In the case ofelastic-plastic behavior, areas where improvements to existing formulations arerequired have been identified by testing thin-walled cylindrical specimensunder combined stress conditions. These tests were conducted primarily atroom temperature, and information on key behavioral features has been obtained.Temperature effect investigations, as needed for fuller understanding of defor-mation behavior and for improved constitutive equation formulation, have beeninitiated through examination of subsequent yield surfaces at various tempera-tures for a prestressed specimen.Both analytical and experimental studies of creep behavior also were dis-cussed. Improvements to existing theories and development of new theories arebeing addressed simultaneously. Accuracy and reproducibility of experimentalresults on creep behavior are difficult to achieve; some of the factors con-tributing to lack of reproducibility are discussed. Additional concentratedefforts are required to realize results which are compatible with detailedidentifications of deformation behavior characteristics necessary for con-stitutive equation derivation.ORNL-DWG 73-3740IOftNL-OWO 7 I - 3 4 I MTYPE 304 STAINLESS STEEL. ANNEALEO (HEAT 8043813) TYPE304 STAINLESS STEEL,ANNEAL£D (HEAT 9T2796)ROOM TEMPERATURE TEMPERATURE MO0»FSTRAIN RATE 0.005/min STRAIN RATE 0.005/mlnSTRAIN RANGE* 0.9% STRAIN RANGE 1.0%UIO8)403020to-to-to-30-40 -.1 I I ICYCLE NO: 1 TO JO. 15, 20. 30iii1IBf— 30SO1///Mfs* -r/1i t__ <—r/ /w\'f«i0.«1if-0.4 -0.2 O 0.2STRAIN (%)0.4I I I ICYCLE NO: I TO 10,20-10-20- 3 0- 4 0* * Cyclic stress-strain curves for type 30U stainless steelat room temperature and llOO'F.i t t - - " f - T ' fJ — ' : " " ' * * ' ; " v •*»•*•"- '- • '•••• '• ait*ORNL-OWG 73-114578 tOAXIAL STRESS (1000 psi) / V3~-6 -4 -2 I i I IAXIAL STRESS (1000psi)/-/3~10Experimentally determined initial yield loci in stress-temperature space (type 30»t stainless steel).SLIDE NO. 2ORNL-DWG 73-12152TYPE 304 S/S, ANNEALED (9T2796)ROOM TEMPERATURESPECIMEN, C-6LOADING PATH4 . PRESTRESS15 20 25 30AXIAL STRESS, ksiA*INITIAL YIELD SURFACEMISES* YIELO CONDITION2w-28JLINITIAL a SUBSEQUENT YIELO SURFACESInitial and subsequent yield loci for tubular specimensubjected to axial force and torsional moment loadings.SLIDE NO. 3<M»«l-0W6 74-5741 RTYPE 304 SS, ANNEALEDHEAT NO. 9T2796SPECIMEN C-IOLOADING PATHPRESTRESSFIRST PRESTRESS AT 26O*C-ACCIDENTAL PRESTRESSAT 177* CAXIAL STRESSFIRST SUBSEQUENTYiELO SURFACETHIRO PRESTRESSAT 260*C15 20AXIAL STRESSA^HtfSECOND PREST^ESSAT ZfiO'CSubsequent yield surfaces at'selected temperature levels.SLIDE HO. kOftNL-OWO 74-57405«5-rTYPE 304 S/S, ANNEALED (9T2796)ROOM TEMPERATURESPECIMEN* C-8LOAOINS PATHPRESTRESSC-8(EXTENSION)20 25 SOAXIAL STRESS, MA'SC-9C - 8 ~ INITIAL YIELO SURFACE-VON MISES' YIELO CONDITION-25JLINITIAL AND FIRST SUBSEQUENT YlgLD SURFACES.ep, EFFECTIVE PLASTIC STRAINEFFECTIVE STRESS-EFFECTIVE PLASTIC STRAINCORRELATIONS.Stress-plastic-strain curves for tubular specimens subjectedto radial and nonradial loading histories. -ORNL DWG. 72-12261 RTIME-DEPENDENT (CREEP) BEHAVIORI. Constant-uniaxial-stress creep equation:Write:#9 _ 3 i(a,t,T) ,ij *\ _ ij •3. For strain-hardening law:3+ A2(a,T) [l-e-'a('.T)tJ +em(a,T)t.2. Multiaxial constitutive equations:e§ = X ay .DefineSLIDE NO. 6ORNL DWC 72-10046100008000a.•z 6000iTORSIONAI2000CORRELATION COEFFICIENT ' 0.9999en • 0.9196e,,'O03655(STRAINJ/• y/sy304 STEMPI/TAINLESSMEN No. 1'RATURE */UISESTRESCtSTEEL (H-304-IBtlOO'FSLOPE *1 SLOPE't.9TZ?96)i0.062491.149932000 3000 4000 5000 6000 7000AXIAL STRAIN, «„ t/i in./in)8000 9000Torsional creep strain vs tensile creep strain tinder combined tensionand torsion (a = 10,628 psi, T = 6lll psi; test duration = 1000 hr).ORNL- DWG 74-6270CDI IEQUIVALENT STRESS, S=H 5,000 psi400 600TIME(hr)800 1000Effective creep strain vs time for a constant equivalentstress of 15 ksi (type 30U stainless steel).140967ii0t—130.(I 'L-Rf1 t,< 7?P55-X)0« 1J7\ \I/I//FRP57//25.CRPI50-1 • • —400100 pi. — •r——i^22.5(P162800DOpsi2(- - — 'J.000,psi'1S.0C0psi<200 (600TIME (hr)— RE/L 1 FO fORNL-OWC 73-10666Ml V— STRAIN-CYCLED AT 1 % A«PRIOR TO CREEP TESTING«0 CYCLE.——_ • — • •.S)RP51RP;Q"FRP582000L — —_ •20.000FRP542400 2800Uniaxi&l creep curves for type 304 stainless steel at 1100°F.SLIDE NO. 9ORNL-DWG 74-62684.503.75TYPE 304 SS (HT.9T2796)1100°F20?000psi(FULL LOAD TRAIN DATA) "BWR-5BWR-14 -BWC-10500 1000 1500 2000 2500 3000 3500 4000TIME (hr)Constant load uniaxial creep curves from two creep machines.3.75 I-<OLLU§ LJ53.002.251.500.7520,000 psi(FULL LOAD TRAIN DATA) BWR-J4 -XBWC-10BWC-5B500 1000 1500 2000 2500 3000 3500TIME (hr)Constant load uniaxial creep curves from two creep machines.4000CO15ORNL-DWG 74-626912OHa.UJUJa:o? 9Q:6TYPE 304 SS (HT 9T2796)1100°F _25,000 psi(FULL LOAD TRAIN DATA)150 300 450 600 750 900 1050TIME (hr)Constant load creep curves for specimens having same grain size.

Structural design criteria for LMFBR components and inelastic material behavior

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