Available online at www.sciencedirect.com Procedia Engineering 55 (2013) 45 – 50 6th International Conference on Cree ep, Fatigue and Creep-Fatigue Interaction [CF-6 6] Comparison of Creep Prooperties of Four Copper Alloys and d Creep Based Stress Analyysis of a Rocket Engine Combustio on Chamber A.K.Asraff∗, R.Aparnna, D.Kumaresan, R.Muthukumar Liquid Propulsion Systems Centre, IISRO, Valiamala, Thiruvananthapuram– 695 547, India Abstract Regeneratively cooled liquid rocket engine combustiion chambers are of double walled construction in which the ho ot inner wall will be usually fabricated out of a high therm mal conductive material like copper alloy. Such a material will be subjected to the creep phenomenon accompanied by high stresses exceeding the elastic limit. Creep constitutive modeling m uration, and creep based stress analysis of such chambers assumes significance in this context to evaluate the maximum du operties temperature and thrust levels to which the engine cann safely be operated. Comparison of high temperature creep pro of four copper alloys viz. NARloy-Z, Cu-8Cr-4Nbb Cu-4Cr-2Nb and Cu-Cr-Zr-Ti commonly used for thrust chamber fabrication is done based on results of creep tests at different stress and temperature levels. Published data of o creep o creep properties of the first three alloys is made use of whhereas tests are conducted for the fourth alloy for generation of data. The Norton and Exponential creep models are employed for representing the creep properties of the above materials m and the best material identified. The Least Square Fitt method is employed for evaluating the constants in the above models. m Finally finite element modeling and creep based stresss analysis of a cryogenic engine thrust chamber with inner walll of the chosen material is conducted using ANSYS code. R Results are presented in graphical and tabular forms and concclusions drawn. © 2013 Authors. Published by Elsevier Open access CC BY-NC-ND © 2013The The Authors. Published by Ltd. Elsevier Ltdd.under Selection and/orlicense. peer-review under responsibility of thee Indira Selection Centre and peer-review under responsibility Gandhi for Atomic Research of the Indira Gandhi Centre for Atomic Research. Keywords: Creep; copper alloy; rocket engine; thrust chambbe;, ANSYS 1. Introduction The thrust chamber of a rocket engine generaates propulsive thrust force for flight of the rocket by ejecction of combustion products at supersonic speeds. C Cryogenic rocket engines usually have regeneratively cooled double walled thrust chambers for extended duuration of operation, in which fuel will be circulated th hrough rectangular coolant channels milled on outer surrface of inner wall for enhanced cooling. The outer walll of the ∗ Corresponding author: E-mail address: akasraff@yahoo.com 1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research. doi:10.1016/j.proeng.2013.03.217 46 A.K. Asraff et al. / Procedia Engineering 55 (2013) 45 – 50 thrust chamber will usually be bonded to inner wall by processes such as brazing or electro-deposition. Inner wall is subjected to high thermal and pressure loads during operation of the engine due to which it will be in the elasto-plastic regime. This results in creep of the inner wall material. It is essential to characterize creep behaviour of this material in order to assess cyclic and sustained structural life of the chamber. 2. Creep characterization of Cu-Cr-Zr-Ti alloy Constant load creep rupture tests are conducted at Indira Gandhi Centre for Atomic Energy (IGCAR), Kalpakkam, Chennai for different stress and temperature levels. Stress levels are selected such that corresponding yield strength is exceeded at all temperatures during testing. Figure 1 gives details of specimen used for tests. Summary of test results is shown in table 1. Figure 2 gives creep curves at 873 K in which normalized creep strain is plotted against normalized rupture time. Normalized time Vs normalized strain ( 873.15K) 1.2 1 Normalized strain 0.8 0.6 0.4 0.2 0 0 0.2 Fig. 1.Creep test specimen. 0.4 0.6 Normalized time 0.8 1 1.2 Fig.2. Creep curves at 873 K. Table 1. Summary of creep test results Sl. No. Temp, K Stress, MPa Life, h Elong, % RA, % SS rate /s 1 973 25 43.1 41 71 7.60E-07 within GL 2 923 52 16 18.2 82.4 1.67E-07 within GL 3 923 50 14 33.8 84.2 1.67E-07 within GL 4 923 50 20 23.8 81.9 1.67E-07 5 923 46 35 29.9 75.2 1.64E-07 within GL 6 923 25 242 39.2 71.5 2.20E-08 within GL 7 923 20 2677 5.50E-09 within GL 8 873 65 13 40.9 85.9 2.50E-08 within GL 9 873 65 9 50.7 87.4 6.20E-06 10 873 60 69 18.4 68.6 1.47E-07 within GL 11 873 55 100 19.3 74.3 1.74E-07 within GL 12 873 35 743 39 79.2 3.10E-08 within GL 13 873 25 2907 39.7 76 1.67E-09 within GL Remarks Repeated Repeated Fracture within GL within GL 47 A.K. Asraff et al. / Procedia Engineering 55 (2013) 45 – 50 3. Creep constitutive modelling The primary creep region for this material is found to be absent and tertiary creep is not considered. Hence the Norton and Exponential secondary creep models available in ANSYS FEA code (Version 11) [1] are chosen for constitutive modelling of the copper alloy owing to their simplicity. Creep strain rate by Norton model is given by: ε cr = C 1 σ ε C 2 e § −C ¨ © T 3 · ¸ ¹ (1) = creep strain rate cr Ȉ = stress C1,C2,C3 = Norton creep constants T = temperature (absolute) Creep strain rate by Exponential model is given by ε cr = C 4 e ε § σ · ¨¨ ¸¸ © c5 ¹ e § − c6 · ¨ ¸ © T ¹ (2) = creep strain increment cr ı C4,C5,C6 T = stress = Exponential creep constants = temperature (absolute) 3. Evaluation of creep constants by least square fit method The least squares fit method for multivariate polynomial functions is used for evaluation of the creep constant from test data. Logarithm of the above equations is taken to get an algebraic equation of the form: y = a + bx+ cz (3) The normal equations for the constants a, b and c are: aN + b¦ xi + c¦ zi = ¦ y i a¦ xi + b¦ xi2 + c¦ xi zi = ¦ xi y i a¦ yi + b¦ xi yi + c¦ yi zi = ¦ yi2 (4) These constants can be solved by Gaussian elimination. 4. Creep constants for other copper alloys Ref.2 gives the creep test results for Cu-8Cr-4Nb, Cu-4Cr-2Nb and NARloy-Z which are commonly used by NASA for thrust chamber fabrication. Comparison of the alloy chemistries for the four copper alloys is given in table 2. Based on least square fit method the Norton and Exponential creep constants are evaluated for the above alloys. Since it is difficult to compare the alloys based on the magnitudes of these creep constants alone, creep strains directly computed for a stress level of 60 MPa at 927 K for an operational duration of 7200 s are 48 A.K. Asraff et al. / Procedia Engineering 55 (2013) 45 – 50 compared instead. Details of the creep constants and computed creep strains are given in Tables 3 and 4. Units used for the above calculations are Kelvin, MN/m2 and seconds for temperature, stress and time respectively. Tables 3 and 4 indicate that Cu-Cr-Zr-Ti creeps by a small amount in comparison with other alloys. Maximum creep is found to be for NARloy-Z. From this it is evident that Cu-Cr-Zr-Ti is superior to the other three alloys. Table 2. Comparison of alloy chemistry (% by wt.) Alloy Ag Cr Nb Zr Ti Cu Cu-Cr-Zr-Ti - 0.5-0.7 - 0.02-0.05 0.02-0.05 Balance Cu-8Cr-4Nb - 6.5 3.6 - - Balance Cu-4Cr-2Nb - 3.8 5.5 - - Balance NARloy-Z 3 - - 0.5 - Balance Table 3. Comparison of creep characteristics for Norton model. Material C2 C1 C3 Stress Temp Time MPa K s Creep strain Cu-Cr-Zr-Ti 8.09E-06 2.72 12843 60.77 927 7200 0.00051276 Cu-8Cr-4Nb 4.13E-03 4.7323 25387 60.77 927 7200 0.0013507 Cu-4Cr-2Nb 4.54E-02 5.6154 29738 60.77 927 7200 0.00510879 NARloy-Z 1.35E+02 4.7008 31224 60.77 927 7200 0.07158153 Table 4. Comparison of creep characteristics for Exponential model. Stress Temp MPa K 13912.73 60.77 7.85 30054.398 6.87234 34844.99 5.00605 40466.079 Material C4 C5 C6 Cu-Cr-Zr-Ti 2.03E-02 12.56168 Cu-8Cr-4Nb 6.89E+04 Cu-4Cr-2Nb 1.42E+07 NARloy-Z 1.09E+10 Time s Creep strain 927 7200 0.0055907 60.77 927 7200 0.0094931 60.77 927 7200 0.0334668 60.77 927 7200 1.6223291 5. Finite element modeling and stress analysis of thrust chamber Figure 3 shows the configuration of the rocket engine whereas figure 4 gives the details of its combustion chamber. Finite element modelling and stress analysis of the chamber are carried out using ANSYS. Details of the chamber cross section are given in figure 5 whereas figure 6 shows the axisymmetric model. Full length of the chamber is not considered for the sake of simplicity. Analysis of the chamber has been conducted for nominal thrust condition of 94.5 kN as well as uprated thrust levels of 111% and 126% of nominal. Thermal loading is taken as the same in all these cases. Maximum temperature of 927K is experienced at the throat. Material, geometric, creep and contact nonlinearities are invoked in the analysis. Details of cyclic thermo structural analysis of the chamber are given in Ref.3 and 4. Analysis is done using both Norton and Exponential creep models for a total steady state thrusting duration of 7200 seconds (which is 10 times the nominal operating duration of 720 seconds). Inner surface of inner wall at throat is studied in detail since it is the most critical location. Deformed shape of the chamber at peak loads is shown in figure 7. Cyclic stress strain graph at middle of inner wall inner surface at throat is given in figure 8. Salient load step points are shown in the above figure (0: no load condition, 1: low coolant pressure, 2: full coolant pressure + chamber pressure, 3: full coolant pressure + chamber pressure + thermal loads, 4: above loads acting for a duration of 49 A.K. Asraff et al. / Procedia Engineering 55 (2013) 45 – 50 7200 seconds). Results show that the effect of o creep is not significant even with 126% uprated thru ust, the maximum creep strain being less than 0.1%. Fig. 3. Configuration of cryogenic engine. e Fig. 4. Configuration of thrust chamber . Fig. 5. Cross section of thrust chamber Fig. 6. Finite Element model of chamber. Cyclic stress strain graph at throat inner wall in thrust chamber, 26% uprated 2 100 80 Stress (N/sq.mm) 60 40 0 20 4 0 -0.008 -0.006 -0.004 -0.002 0 0.002 -20 1 -40 -60 3 Fig. 7. Deformed shape of chamber. -80 Strain Fig.8. Cyclic stress strain graph at throat . 0.004 50 A.K. Asraff et al. / Procedia Engineering 55 (2013) 45 – 50 6. Conclusions Creep rupture tests are performed for a Cu-Cr-Zr-Ti alloy at different temperature and stress levels exceeding the material yield strength. This alloy is used by ISRO for fabrication of its cryogenic rocket engine thrust chambers. Creep constitutive properties of the same are evaluated using least square fit technique employing two models. Comparison of creep properties of this alloy with three other copper alloys used by NASA for their thrust chambers is done. The study shows that Cu-Cr-Zr-Ti alloy is superior to all the others. Finally elasto plastic cyclic stress analysis of a thrust chamber is performed using these properties with ANSYS finite element analysis code. Analysis shows that the effect of creep is not significant for an operational duration of 7200 seconds (10 times the nominal thrust duration of the engine) even for 126% uprated thrust level. Both creep models gave similar results. Acknowledgment The authors wish to thank Director, LPSC for granting permission to publish this paper. Thanks are also due to Dr. M.D.Mathew and his brilliant team at Mechanical Metallurgy Division of IGCAR for extending support for creep testing of copper specimens. References [1] [2] [3] [4] Anonymous, ANSYS- Engineering analysis system, Users Manual. ANSYS Inc, USA, (2009). David L.Ellis & Gary M.Michal, Mechanical and Thermal Properties of two Cu-Cr-Nb alloys and NARloy-Z, NASA CR 198529, (1996), National Aeronautical & Space Administration, USA. A.K.Asraff, S.Sunil, R.Muthukumar, T.J.Ramanathan, Stress analysis and life prediction of a rocket engine thrust chamber considering low cycle fatigue, creep and thermal ratcheting, Transactions of the Indian Institute of Metals, Vol. 63, (2010), pp 601606. Aparna, Creep modelling and stress analysis of a double walled cryogenic rocket thrust chamber, M.Tech dissertation, Mahatma Gandhi University, Kerala, 2011.
