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Finite Element Elastic Plastic Creep and Cyclic Life
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FINITE ELEMENT ELASTIC PLASTIC CREEP AND,CYCLIC LIFE ANALYSIS OF A COWL LIP. Vinod K Arya,University of Toledo,Toledo Ohio 43606. Matthew E Melis and Gary R Halford,National Aeronautics and Space Administration. Lewis Research Center,Cleveland Ohio 44135, Summary development of actively cooled leading edges fabricated from. specialized materials with innovative cooling concepts to. Results are presented of elastic elastic plastic and elastic enable the structure to withstand the severe environmental. plastic creep analyses of a test rig component of an actively conditions The details of different cooling concepts proposed. cooled cowl lip A cowl lip is part of the leading edge of an and studied under a NASA Lewis sponsored program called. engine inlet of proposed hypersonic aircraft and is subject to COLT Cowl Lip Technology Program were presented by. severe thermal loadings and gradients during flight Values Melis and Gladden. of stresses calculated by elastic analysis are well above the Under the severe thermal loadings and gradients experienced. yield strength of the cowl lip material Such values are highly by the component a propensity for significant inelastic. unrealistic and thus elastic stress analyses are inappropriate deformation of the material exists The intent of the present. The inelastic elastic plastic and elastic plastic creep analyses work was to perform linear elastic and nonlinear elastic. produce more reasonable and acceptable stress and Strain plastic and elastic plastic creep structural analyses of the cowl. distributions in the component Finally using the results from lip for a crossflow cooling concept and to assess potential. these analyses predictions are made for the cyclic crack durability to low cycle fatigue cracking In crossflow cooling. initiation life of a cowl lip A comparison of predicted cyclic the direction of coolant flow is perpendicular to that of the. lives shows the cyclic life prediction from the elastic plastic hot gas See Figure 1 A comparison of service lives. creep analysis to be the lowest and hence most realistic predicted from the outputs of the three structural analyses is. also presented The three dimensional finite element model. and steady state heat transfer results were obtained from. Introduction Reference 1 The imposed thermal loadings obtained from a. rig test of a cowl lip are shown in Figure 2 Measured gas. A significant research effort was launched recently at NASA and wall temperatures are shown for one complete cycle For. Lewis Research Center to develop state of the art technologies ease of calculations the leading edge metal temperature was. for hypersonic flight between Mach 3 and 25 At such high approximated by a simplified temperature cycle This sim. speeds the leading edges of hypersonic aircraft are subjected ulated thermal loading cycle shown in Figure 2 c was used. to high heat fluxes and thus high temperatures and severe in subsequent calculations Nonlinear variations in the material. thermal gradients To achieve high inlet aerodynamic constants with temperature were accounted for in the. performance not only must the high heating rates be tolerated computations The life assessment calculations for the cowl. but also distortions caused by thermal warping of the structure lip were performed by using data from the existing. must be minimized Consequently the need arises for the literature 2 Details of the finite element model and thermal. OR G AL CONTAINS,COLOR ILLUSTRATIONS, structural and life analyses of the cowl lip are presented in TABLE 1 MATERIAL CONSTANTS FOR COPPER.
the following sections, Young s modulus E ksi 18 504 0 3 164 Tb 0 0022 7 2. Coefficient of thermal expansion a 1 59x10 5 2 78x10 9 T. Poisson s ratio v 0 34,Analyses A sec 3 Ox 1024,Finite Element Model m 0 35. Activation energy i mole, A three dimensional finite element model of the cowl lip Lattice diffusion QL 2 Ox 105. Figure 1 was constructed by Melis and Gladden The Pipe diffusion Q 1 2x10. model consists of 3294 eight noded solid isoparametric X 1 8x10 5. elements and 4760 nodes The dimensions of the rig component Boltzmann s constant i mole K 8 314. are 6 by 1 5 by 0 25 in 15 2 by 3 8 by 0 6 cm The cowl aI ksi 6 895 MPa. b T is temperature in degrees Celsius, lip finite element model consists of the central 2 in 5 cm. portion of the component This small section was analyzed. to avoid the difficult to quantify constraining effects of the. ends A considerably large number of elements are required 0 75 sec and 2 25 and 3 sec to describe the temperature. to handle the severe thermal loadings imposed on the com distribution over the complete thermal loading cycle For the. ponent The severity of thermal loading together with the fine nonlinear elastic plastic analysis a combined isotropic and. grid finite element model makes the nonlinear structural kinematic hardening plasticity law was employed The tem. analyses computationally intensive However taking advantage perature and hardening effects were incorporated in the analysis. of the symmetry along the thickness reduces the computation through the input for the finite element program MARC. time appreciably To investigate the time dependent response of the cowl lip. a nonlinear combined elastic plastic creep stress analysis was. Heat Transfer Analysis performed The following creep law was used in the analysis. Reference 1 describes a boundary layer analysis conducted. to compute the film coefficients The authors used the. boundary layer heat transfer code STAN5 3 to estimate the. film coefficients on the hot gas side of the cowl lip Correlative. techniques 4 5 were employed to determine coefficients on the. coolant side The stagnation points and leading edge region. film coefficients were ascertained from a cylinder in. crossflow correlation Using the film coefficients determined. o exp X exp 2, by these procedures the authors performed a steady state heat kTk Q.
transfer analysis for the cowl lip An instrumented rig. component was tested in the Hot Gas Test Facility at NASA. Lewis Research Center 6 Thermal loadings are displayed in In these equations u is the effective stress E is Young s. Figures 2 a and b modulus t is the time A n and m are material constants QL. and Qp are the activation energies for lattice and pipe. Structural Analyses diffusion respectively X is the constant to account for the. activation energy for pipe diffusion that must be included in. Linear elastic and nonlinear elastic plastic analyses were the temperature function 0 above a homologous temperature. performed by using the finite element program MARC 7 The of about 0 5 see Figure 3 k is Boltzmann s constant and. material of the cowl lip was copper The temperature Tk is the temperature in degrees Kelvin This form of the. dependence of Young s modulus E and the coefficient of creep law was obtained by using the experimental data of. instantaneous thermal expansion a taken from Freed and Barrett and Sherby 9 and Freed and Verrilli 8 and is shown in. Verrilli 8 are listed in table I The elastic Poisson s ratio v figures 3 and 4 respectively The material constants appearing. was assumed to be 0 34 for all temperatures in the creep law for copper are listed in table I. The structural response of the cowl lip was calculated by Elastic analysis Figures 5 and 6 depict respectively the. using an eight noded solid brick element This element was elastically calculated stress and total strain distributions along. compatible with the element used for the heat transfer analysis a cross section of the cowl lip at thermal steady state The. The steady state temperature values between 0 75 and total strain in this work does not include the thermal component. 2 25 sec in fig 2 c were obtained from Reference 1 A linear of strain Only a cross section of the component is shown in. interpolation technique was then employed to obtain the these figures Since the largest compressive stresses and total. transient temperature values in the periods between 0 and mechanical strains occur along the leading edge z direction. TABLE 11 COMPARISON OF HYSTERESIS LOOP CHARACTERISTICS. Analysis Effective stress Effective stess Total Elastic Plastic Creep Cycles. at maximum range mechan strain strain strain to,temperature ical range range range failure. ksi MPa Strain AEC pp AEPC N,ksi MPa range,Elastic 80 4 554 4 105 4 726 7 0 0062 0 0062 2300. Elastic 1 4 9 7 8 82 60 7 0085 0005 0 0080 1000, Elastic 1 3 9 0 8 7 60 0 0092 0005 0080 an 0007 800. aSt ress range between points A and B of hysteresis loop of figure 12. graphs showing these distributions are included in the dis effective stress and strain from the elastic plastic creep. cussion The magnitude of the largest stress predicted from analyses are calculated for the critical cowl lip location i e. the elastic analysis see Figure 5 is much higher than the yield where the total strain range is maximum In establishing these. strength values for the copper material This clearly indicates loops the algebraic signs of effective stress and strain are. the inappropriateness of an elastic stress analysis for this severe dictated by the signs of the maximum principal stress and. thermally driven problem The subsequently large imposed strain This is in accordance with the recommendations of. mechanical strains at these high temperatures are well above the Manson and Halford 0 for dealing with multiaxial stress. yield strain and hence are expected to result in significant inelastic strain states Critical location stress strain hysteresis loops for. flow necessitating a nonlinear inelastic stress strain analysis the first two complete loading cycles are presented in Figure 12. Elastic plastic analysis The stress and strain results of an Table II shows a comparison of hysteresis loop characteristics. elastic plastic analysis of the cowl lip problem are shown in stress range total strain range elastic strain range inelastic. Figures 7 and 8 These figures exhibit the stress and strain strain range plastic strain range and the approximate creep. distributions along the leading edge z direction The analysis strain range for the three different elastic elastic plastic and. shows the reduction of maximum compressive stress to a more elastic plastic creep structural analyses conducted The elastic. reasonable value of 28 5 ksi 196 5 MPa from about 80 4 analysis calculates the smallest total strain range whereas the. ksi 554 4 MPa obtained from the elastic analysis From elastic plastic creep analysis produces the largest Because the. Figure 8 the largest compressive strain occurring at the latter strain range is about 50 percent larger than the smallest. leading edge is greater than that obtained from the elastic the cowl lip structural geometry apparently offers only limited. analysis This indicates the existence of compressive plastic constraint to the inelastically deformed material at the leading. strains along the edge edge Hence the concept of total strain invariance suggested. Elastic plastic creep analysis To study the effects of time by for highly constrained thermally dominated. on stress and strain distributions in the cowl lip a time loading problems should not be used for the limited geometric. dependent creep analysis was also performed The results are and thermal constraint found in the current problem. displayed in Figures 9 and 10 These figures show that the The difference in inelastic strain range between the elastic. maximum compressive stresses and total strains still occur at plastic and the elastic plastic creep results can be attributed. the leading edge The magnitude of maximum stress decreases to creep deformation the creep strain range listed in the table. whereas the magnitude of total strain increases This increase is defined simply as this difference The large inelastic strain. in strain magnitude implies the existence of compressive creep range is dominated in this instance by time independent. strains along the leading edge During the steady state of plasticity Furthermore because of the very large strain range. thermal loading i e between 0 75 and 2 25 sec no further the loops of figure 12 exhibit a high degree of symmetry about. redistribution of stress due to creep is observed This is made the zero stress axis This gives rise to remarkably well. clear by comparing figures 9 and 11 which show the stress balanced hysteresis loops that exhibit little of the unbalanced. distributions in the cowl lip at 0 75 and 2 25 see respectively. Life Analysis,Effective stress Ui 0 2 2 02 03 2 03. The stress strain results from the structural analyses were. used in estimating the cyclic crack initiation life of the cowl effective strain u 2 2 2 3 2 u3 t1. lip The thermomechanical fatigue TMF hysteresis loops of. characteristics CP and PCtypet hysteresis loops normally cycle fatigue criterion for failure Other failure modes such. associated with thermomechanical cycling at much smaller as thermal ratcheting could further degrade cyclic durability. strain ranges 12 Consequently the hysteresis loops are. composed of inelastic strain ranges of the balanced PP and. CC types The CC portion of the inelastic strain range is Conclusions. imposed quite naturally near the very highest temperature. whereas the PP strain range is imposed over the entire Elastic elastic plastic and elastic plastic creep analyses for. spectrum of temperatures from lowest to highest the cowl lip were performed A purely elastic stress strain. Because of the large inelastic strains imposed at the critical analysis for the problem is found inappropriate since it. location a strain based high temperature life prediction calculates values of maximum stresses along the leading edge. approach was sought Ideally the most accurate approach that are much larger than the yield strength of the copper used. would be to generate TMF data for the alloy in question to manufacture the cowl lip The elastic plastic or elastic. Unfortunately TMF data are virtually impossible to generate plastic creep analyses are found to produce more reasonable. in the laboratory under the high loading and heating rates and hence acceptable values of stresses This clearly indicates. encountered in the current problem Thus approximations the necessity for performing inelastic analyses for severely. have been necessary to establish a relation between strain range loaded structural components. and cyclic crack initiation life that would be applicable for use The estimations for cyclic crack initiation life of the cowl. in predicting life for the current problem lip were made by using the results from the elastic elastic. Isothermal strain controlled low cycle fatigue results have plastic and elastic plastic creep analyses The lowest expected. been reported by Conway Stentz and Berling 2 for annealed life of 800 cycles is obtained by using the results from the. oxygen free high conductivity OFHC copper at 1000 F most realistic elastic plastic creep analysis Use of an elastic. 538 C for a nonoxidizing argon atmosphere These results analysis gives an expected life of 2300 cycles about a factor. are shown in Figure 13 At the strain range of current interest of 3 higher than that obtained from the elastic plastic creep. approximately 0 009 the frequency of loading is about analysis. 0 1 Hz This frequency is slightly lower and thus more. degrading than that of the cowl lip TMF cycle 0 33 Hz. nonoxidizing gaseous hydrogen environment Because of the References. relative temperature insensitivity of the tensile ductility of. OFHC copper and dilute alloys of copper such as zirconium 1 M E Melis and H J Gladden Thermostructural Analysis With. copper variations measured at NASA Lewis range from 81 Experimental Verification in a High Heat Flux Facility of a Simulated. Cowl Lip in29th Structures Structural Dynamics and Materials. to 89 percent reduction of area over the temperature range. Conference Part 1 AIAA New York 1988 pp 106 115, of concern low cycle fatigue resistance is also expected 14 2 J B Conway R H Stentz and J T Berling High Temperature Low.
to be insensitive to temperature over the range of current Cycle Fatigue of Copper Base Alloys in Argon Part I Preliminary. interest Thus the fatigue curve of Figure 13 serves as a Results for 12 Alloys at 1000 F 538 C NASA CR 121259 1973. reasonable approximation to the TMF resistance of the cowl 3 M E Crawford and W M Kays STAN5 A Program for Numerical. Computation of Two Dimensional Internal and External Boundary Layer. lip problem at hand Respective total strain ranges of 0 0062. Flows NASA CR 2742 1976, 0 0085 and 0 0092 for the elastic elastic plastic and elastic 4 R C Hendricks et al Bulk Expansion Factors and Density Fluctuations. plastic creep analyses correspond to cyclic crack initiation lives in Heat and Mass Transfer in XV International Congress on. of 2300 1000 and 800 Since the elastic plastic creep analysis Refrigeration 1979 Paper B1 1 19. is judged to give the most realistic structural analysis results 5 W M Rohsenow and H Y Choi Heat Mass and Momentum Transfer. Prentice Hall Englewood Cliffs NJ 1961, the corresponding life of 800 cycles to failure is also judged. 6 M E Melis et al A Unique Interdisciplinary Research Effort to Support. to be the most realistic estimate of expected lifetime Note that Cowl Lip Technology Development for Hypersonic Applications. for the present problem use of an elastic analysis to obtain NASA TP 2876 1989. the total strain range i e using the concept of total strain 7 MARC General Purpose Finite Element Program MARC Analysis. invariance 1 I would have resulted in a life prediction of about Research Corporation Palo Alto CA 1983. 8 A D Freed and M J Verrilli A Viscoplastic Theory Applied to. a factor of 3 too high i e unconservative It should be noted. Copper NASA TM 100831 1988, that the predicted life of 800 cycles is based solely on a low 9 C R Barrett and O D Sherby Steady State Creep Characteristics of. Polycrystalline Copper in the Temperature Range of 480 C to 950 C. Trans AIME 230 1322 1327 1964, 10 S S Manson and G R Halford Treatment of Multiaxial Creep Fatigue. Me CP PC CC and PP terminology for describing the hysteresis loops by Strainrange Partitioning in 1976 ASME MPC Symposium on. derives from the strainrange partitioning life prediction method of Manson Creep Fatigue Interaction R M Curran Ed ASME New York 1976. Halford and Hirschberg 13 The letter P refers to time independent plasticity pp 299 322. and C to time dependent thermally activated creep deformation the first ii S S Manson Thermal Stress and Low Cycle Fatigue McGraw Hill. letter refers to the tensile and the second to the compressive inelastic strains 1966. 12 G R Halford Low Cycle Thermal Fatigue in Thermal Stresses II 14 G R Halford M H Hirschberg and S S Manson Temperature Effects. R B Hetnarski Ed Elsevier 1987 pp 329 428 on the Strainrange Partitioning Approach for Creep Fatigue Analysis. 13 S S Manson G R Halford and M H Hirschberg Creep Fatigue in Fatigue at Elevated Temperatures ASTM STP 520 A E Carden. Analysis by Strain Range Partitioning in Design for Elevated A J McEvily and C H Wells Eds American Society for Testing. Temperature Environment S Y Zamrik Ed ASME New York and Materials Philadelphia PA 1973 pp 658 667. 1971 pp 12 28,Figure 1 Cowl lip finite element model.
1600 3000 800 1500,F 2500 I 1250,I 2000 1000,800 J 1500 100 750. lOOI Lo 200 LD,0 5 1 0 1 5 2 0 0 1 2 3 4 5,TIME SEC TIME SEC. a MEASURED HOT GAS TEMPERATURES FOR THREE TESTS b MEASURED TRANSIENT LEADING EDGE THERMOCOUPLE. IN HOT GAS FACILITY DATA,0 75 1 50 2 25 3 00 3 75, C SIMULATED THERMAL RESPONSE USED IN STRUCTURAL ANALYSES. Figure 2 Measured and approximated temperature distributions. o MONOTONIC,LATTICE DIFFUSION,PIPE DIFFUSION,1001 I 11111111 I 11111111. 0 2 6 8 1 0 100 101 102,HOMOLOGOUS TEMPERATURE T TM TENSILE FLOW STRESS.
Figure 3 Apparent activation energies for creep of copper Figure 4 Stress dependence of creep rate temperature function i O. 25 0 11 9 1 32 14 5 27 7 40 9 54 1 67 2 80 4,STRESS ksi. I I I II I I I I, 172 0 82 0 9 1 100 0 191 0 282 0 373 0 463 3 554 3. STRESS MPa, Figure 5 Elastic analysis of cowl lip stress in z direction. pp I I 150,940 835 729 624 519 413 308,TOTAL STRAIN xlOO. Figure 6 Elastic analysis of cowl lip total strain in z direction. 12 1 6 27 476 5 32 11 1 169 22 7 28 5,STRESS ksi,I I I I I I I I I I I I I I I.
83 4 43 2 3 3 36 7 76 5 116 5 156 5 196 5, Figure 7 Elastic plastic analysis of cowl lip stress in c direction. 1 030 904 779 653 528 402 276 151,TOTAL STRAIN xlOO. Figure 8 Elastic plastic analysis of cowl lip total strain in z direction. 11 6 7 52 3 44 636 4 71 8 79 12 9 19 0,STRESS kzi,I I I I I I I I I I I I I I I. 80 0 51 9 23 7 4 4 32 5 60 6 88 9 131 0,STRESS MPa. Figure 9 Elastic plastic creep analysis of cowl lip stress in z direction at 0 75 sec. 1 079 957 835 713 590 468 346 163,TOTAL STRAIN xlOO.
Figure 10 Elastic plastic creep analysis of cowl lip total strain in z direction at 0 75 sec. 11 6 7 52 3 44 636 4 71 8 79 12 9 19 0,STRESS ksi,I I I I I I I I I I I I I. 80 0 51 9 23 7 4 4 32 5 60 6 88 9 131 0,STRESS MPa. Figure 11 Elastic plastic creep analysis of cowl lip stress in z direction at 2 25 sec. CRI1ICAL LOCAIION,S u U U U U U U,10 2 103 104,8 I I I I CYCLES 10 FAILURE. 10 8 6 4 2 0 2 4 6 8 10003, EFFECTIVE STRAIN Figure 13 Number of cycles to failure N1 low cycle fatigue data obtained. Figure I2 Hystersis loops for cowl lip elastic plastic creep analysis strain in argon at 1000 F 538 C with strain rate of 2 x l0 sec I for. range Ae 0 0092 annealed oxygen free high conductivity copper. Nallonal Report Documentation Page,Space Adm nstratoo.
1 Report No 2 Government Accession No 3 Recipient s Catalog No. NASA TM 102342,4 Title and Subtitle 5 Report Date, Finite Element Elastic Plastic Creep and Cyclic Life Analysis April 1990. of a Cowl Lip,6 Performing Organization Code,7 Author s. B Performing Organization Report No, Vinod K Arya Matthew E Melis and Gary R Halford E 5050. 10 Work Unit No,9 Performing Organization Name and Address. 11 Contract or Grant No,National Aeronautics and Space Administration.
Lewis Research Center,Cleveland Ohio 44135 3191,13 Type of Report and Period Covered. 12 Sponsoring Agency Name and Address Technical Memorandum. National Aeronautics and Space Administration,14 Sponsoring Agency Code. Washington D C 20546 0001,15 Supplementary Notes, Vinod K Arya University of Toledo Toledo Ohio 43606 Matthew E Melis and Gary R Halford NASA. Lewis Research Center Cleveland Ohio 44135,16 Abstract. Results are presented of elastic elastic plastic and elastic plastic creep analyses of a test rig component of an. actively cooled cowl lip A cowl lip is part of the leading edge of an engine inlet of proposed hypersonic aircraft. and is subject to severe thermal loadings and gradients during flight Values of stresses calculated by elastic. analysis are well above the yield strength of the cowl lip material Such values are highly unrealistic and thus. elastic stress analyses are inappropriate The inelastic elastic plastic and elastic plastic creep analyses produce. more reasonable and acceptable stress and strain distributions in the component Finally using the results from. these analyses predictions are made for the cyclic crack initiation life of a cowl lip A comparison of predicted. cyclic lives shows the cyclic life prediction from the elastic plastic creep analysis to be the lowest and hence. most realistic, 17 Key Words Suggested by Author s 18 Distribution Statement.
Finite element analysis Cyclic life analysis Creep Unclassified Unlimited. Fatigue metal Structural analysis Subject Category 39. 19 Security Classif of this report 20 Secu rity Classif of this page 21 No of pages 22 Price. Unclassified Unclassified 11 A03,NASA UflM lbZb OCT86. For sale by the National Technical Information Service Springfield Virginia 22161. National Aeronautics and,Space Administration,Lewis Research Center. FOURTH CLASS MAIL,ADDRESS CORRECTION REQUESTED,Cleveland Ohio 44135 MAt. Official Business,Penalty for Private Use 300,iaF ees Pj.


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