Investigation of isochronous stress-strain formulations for elevated temperature structural design

Transcription

1 Journal of Mechanical Science and Technology 26 (3) (212) 899~93 DOI 1.7/s Investigation of isochronous stress-strain formulations for elevated temperature structural design Gyeong-Hoi Koo * and Jong-Bum Kim Korea Atomic Energy Research Institute, Daedeok-daero , Yuseong-gu, Daejeon, Korea (Manuscript Received July 11, 211; Revised October 24, 211; Accepted October 26, 211) Abstract For elevated temperature design evaluations by the ASME-NH rules, the most important material data is the isochronous stress-strain curves, which can provide design creep information. The main purpose of this paper is to investigate appropriate formulations to be able to generate the isochronous stress-strain curves and implement it to the computer program which is coded the ASME-NH design evaluation procedures. To do this, formulations by the strain-time relationship are investigated in detail and the sensitivity studies for rapid initial transient creep contributions, slower and longer transient creep contribution, and secondary creep contributions are carried out for type 316 austenitic stainless steel. From the results of this study, it is found that the strain-time relationship formulations can well describe the isochronous stress-strain curves with the transient creep contributions. Keywords: Isochronous stress-strain curve; Strain-time relationship; ASME-NH; Creep; Transient creep; Secondary creep; Elevated temperature design Introduction After the Hukusima accident recently occurred in Japan, it is urged to develop a Gen-IV nuclear energy system which can greatly assure enhanced safety features like an inherent safety system. A Gen-IV system is now under development all over the world by the leadership of GIF (Generation IV International Forum) to further meet the needs for safety, sustainability, economics, and nuclear non-proliferation. Most Gen-IV systems have an operating temperature of over o C in elevated temperature services and a long life time of 6 years, which can invoke severe creep and creep rupture. Therefore, an elevated temperature structural design is one of big issues in terms of commercialization of the Gen- IV systems. A number of countries are making efforts to develop nuclear codes and standards such as ASME-NH [1], DDS [2], RCC-MR [3], R5 [4], etc., for the elevated temperature design of structures, systems and components. Among the nuclear codes and standards, the ASME-NH rules are principally based on the isochronous stress-strain (ISS) approach to calculate the inelastic strain and creepfatigue damages. However, the data of ISS on ASME-NH are graphically given by only curves for every 28 o C and specific This paper was recommended for publication in revised form by Associate Editor Kyeongsik Woo * Corresponding author. Tel.: address: ghkoo@kaeri.re.kr KSME & Springer 212 time points. This may result in inaccurate structural evaluations due to the problem of graphical determination of stress and strain values from ISS curves, especially for a design strain range less than 1%. To overcome the difficulties of ISS data management on ASME-NH rules, it is necessary to provide the ISS formulations to obtain the stress-strain values for any temperature and time point. Consequently, the formulations will be implemented into the SIE ASME-NH computer program [5], which implements the ASME-NH evaluation procedures for the elevated temperature structural design. Numerous studies have been done to generate isochronous stress-strain relationship using the approach of the Larson- Miller parameter [6-8] and the strain-time relationship [9-13]. Also, in the field of the time-dependent failure assessment diagram, the equivalent isochronous stress-strain method has been used [14]. In this paper, the formulations of the straintime relationship approach are reviewed and the methods of material parameter identifications are described in detail. In fact, this approach is known to consider transient creep contributions such as rapid initial creep behavior, and slower and longer transient creep behavior occurring in austenitic stainless steels. To investigate the transient creep contributions in ISS generations, this paper focuses on the sensitivity studies for each transient creep behavior by using the material properties proposed by Blackburn for type 316 austenitic stainless steels. The ISS curves by the strain-time approach are compared with those generated by the SIE ASME-NH computer program to verify the accuracy of the formulations.

2 9 G.-H. Koo and J.-B. Kim / Journal of Mechanical Science and Technology 26 (3) (212) 899~93 ε& s t = Strain ε T ε o ε = ε + & ε t T o Secondary Creep s t time can be calculated with the basic equations as follows: εep = εe + ε p (4) σ εe= E for σ σ p (5) σ σ p 1/ r ε p = K for σ > σ p (6) σ p = σ y C1 + C2T (7) Fig. 1. Simple method for strain-time relationship. 2. Formulation using strain-time relationship 2.1 Review of formulations For a basic strain-time relation, the total strain can be expressed analytically in the form: ε = ε + ε (1) o s t where ε is the total strain at time t, ε o is the intersection of the secondary creep rate tangent on the strain axis, and ε s is the secondary creep strain rate. As shown in Fig. 1, no time dependence of primary creep is taken into account in Eq. (1). Therefore, this simple method is not adequate to generate the isochronous stress-strain curves. To overcome the deficiency of the above simple model, Garofalo and his coworkers [9] introduced the strain-time relation during transient and secondary creep as follows: ε = εep + ε t 1 e +. (2) In the above equation, ε ep is the elastic-plastic strain at time t, ε t is the limiting magnitude transient creep strain, m is a constant relating to the rate of exhaustion of transient creep, and ε s is the secondary creep strain rate. In general, this model can accurately describe the creep behavior for metals and alloys in terms of slower and longer transient strain. However, this model can not describe a more rapidly accumulated timedependent initial transient strain than predicted by the Eq. (2). To consider the rapid initial transient strain contribution, Evans and Wilshire [1] introduced an additional term on the right side of Eq. (2) as follows: nt ε = εep + ε r 1 e + ε t 1 e +. (3) In fact, it is expected that the second term of Eq. (3) can be used to make a better fit to experimental strain-time data. The nt quantity of ( ε r 1 e + ε t 1 e + ) indicating a creep strain, ε c, is determined with the identified material parameters of ε r, n, ε t, m, and ε obtained from the creep test data. s where ε e and ε p present the true elastic and plastic strain respectively, σ p is the true stress at the proportional elastic limit, σ y is the yield stress, T is the temperature in o K, and C 1 and C 2 are constants. The parameters K and r in Eq. (6) are constants for a particular test and are determined from the tensile test results in terms of the following equation: p r p σ = σ + Kε (8) where σ is the true stress and ε p is the true plastic strain. The parameters K and r can be graphically obtained from the slop and intercept on plots of log( σ σ p ) against log( ε p ). In Eq. (5) through Eq. (8), parameters E, σ y, K, and r are expressed with temperature-dependent functions and can be obtained by the method of least squares using a linear temperature dependence. The time-dependent creep strain parameters in Eq. (3) can be determined from the equations as follows: ε r = C3 + C4σ (9) R2 R1σ = C5 R2 n ε ε t = C s 6 m D R2 R1σ = C7 R2 R4 R3σ s = C8 R4 m D (1) (11) (12) D ε (13) where C 3 through C 8 and R 1 through R 4 are parameters to be determined as functions of temperature, and D is the constant value. The parameters in Eq. (13) can be determined from the rewritten Eq. (13) by the stress-dependent exponential form as follows: ε s = Aexp( R3σ ) (14) where 2.2 Calculation procedures The time-independent elastic-plastic strain ε ep in Eq. (3) D A= Ao exp. (15)

3 G.-H. Koo and J.-B. Kim / Journal of Mechanical Science and Technology 26 (3) (212) 899~ Rapid initial transient creep strain ε r [1-e -nt ], % t = t = 1 h t = 3 h t = h t = h t = 1x1 3 h t = 3x1 3 h t = 1x1 4 h t = 3x1 4 h t = 1x1 5 h t = 3x1 5 h t = t = 1 hr t = 3 hr t = hr t = hr t = 1x1 3 hr t = 3x1 3 hr t = 1x1 4 hr t = 3x1 4 hr t = 1x1 5 hr t = 3x1 5 hr Fig. 3. Calculated isochronous stress-strain curves for. Fig. 2. Rapid initial transient creep contributions for. The parameters A and R 3 in Eq. (14) can be graphically determined from the slop and intercept on the high-stress linear plots of log( ε s ) against σ for each temperature. The constant value of D in Eq. (15) is determined from the slop of a log(a) against 1/T plot. Then, the parameters of C 8 and R 4 in Eq. (13) can be determined by taking the logarithm form as follows: D R σ ε C R (16) 3 log sexp = log( 8) + 4log. T R4 As shown in Eq. (16), R 4 is the slop on a plot of log[ ε s exp(-d/t)] against log[sinh(r 3σ /R 4 )] and log(c 8 ) is the intercept at log[sinh(r 3σ /R 4 )] =. However, the parameter R 4 is also included in the sinh function. Therefore, it is necessary to use the iterative trial and error method to find R 4 and C 8 parameters. The parameters included in Eq. (1) to Eq. (12) can also be obtained by the same procedures described above for a secondary creep strain rate. Fig. 4. Rapid initial transient creep contributions for 593 o C. 2.3 Sensitivity studies for austenitic stainless steel To investigate the isochronous stress-strain characteristics by the strain-time relationship approach, the sensitivity studies for each term of Eq. (3) are carried out for type 316 stainless steels by using the material parameters proposed by Blackburn (1972). For investigations of rapid initial transient creep strain contributions by Evans and Wilshire [1], pure contributions by the term of ε r [1-exp(-nt)] are calculated in terms of stress and time for isothermal conditions of, 593 o C, and 649 o C respectively. Fig. 2 presents the pure contributions of the rapid initial transient creep at. As shown in the figure, we can see that there are no rapid initial transient creep strain contributions at. The term of ε r [1-exp(-nt)] is almost zero for all stress levels, thus sudden rapid increasing of creep strain does not occur during early transient time stage at this temperature. Fig. 3 reveals the calculated ISS curves for and there is no rapid initial transient creep behavior in curves. However, we can see that the rapid initial transient creep strain Fig. 5. Calculated isochronous stress-strain curves for 593 o C. is significantly affected at 593 o C as shown in Fig. 4 presenting the calculation results of pure contributions. For example at MPa, the creep strains rapidly increase at an early initial time and are exhausted at about hours. This is well indicated in the ISS curves shown in Fig. 5. For much higher temperature of 649 o C, the rapid initial transient creep strains also occur as shown in Fig. 6 but the quantities are less than those of 593 o C. Fig. 7 presents the calculated ISS curves for 649 o C. From this investigation, we can see that the type 316 austenitic stainless steels have severe rapid initial transient creep behavior at a specific temperature range. For the slower and longer transient creep strain contributions by Garofalo, the pure quantities of ε t [1-exp(-mt)] term in Eq. (3)

4 92 G.-H. Koo and J.-B. Kim / Journal of Mechanical Science and Technology 26 (3) (212) 899~ o C Rapid transient creep strain ε r [1 - e -nt ], % t = t = 1 h t = 3 h t = h t = h t = 1x1 3 h t = 3x1 3 h t = 1x1 4 h t = 3x1 4 h t = 1x1 5 h t = 3x1 5 h (a) For 482 o C Fig. 6. Rapid initial transient creep contributions for 649 o C. 649 o C t = Stress, ksi t = 1 hr t = 3 hr t = hr t = hr t = 1x1 3 hr t = 3x1 3 hr t = 1x1 4 hr t = 3x1 4 hr t = 1x1 5 hr t = 3x1 5 hr (b) For Fig. 7. Calculated isochronous stress-strain curves for 649 o C. are presented in Fig. 8 for each isothermal conditions. As shown in the figure, the slower and longer transient creep strains increase as temperatures increase. From Fig. 8(a) at 482 o C, the transient creep strain is not exhausted even in 3x1 5 hours at stresses below about 24 MPa. At over, the transient term is steadily exhausted at certain time point. For example, transient creep strain for 593 o C is exhausted at about 1x1 4 hours as shown in Fig. 8(c). However, the time points exhausted transient strain become shorten as temperatures increase. Finally, the pure contributions of the secondary creep strain term, ε s t in Eq. (3) are presented in Fig. 9 for each isothermal condition. As shown in figures, the secondary creep strains significantly increase as time and temperature increase. In fact, secondary creep strain dominates the time-dependent inelastic strain behavior over long periods of time, however, at lower temperatures less than, the secondary creep strain is less than the slower and longer transient creep strain during certain times as presented in Fig. 8. Fig. 1 presents the comparison results of the ISS curves by the strain-time relationship approach at 593 o F with the generated curves by the SIE ASME-NH computer program. As shown in figure, the overall shape of curves including the rapid initial transient creep behavior are in good agreement but the curves by the SIE ASME-NH database are not smoother than those by the formulations due to discrete data points used in calculations. 3. Conclusions (c) For 593 o C Fig. 8. Slower and longer transient creep contributions. In this paper, the formulations of the strain-time relationship were reviewed to investigate the characteristics of the isochronous stress-strain curves used in the elevated temperature design by ASME-NH rules. From the results of the sensitivity studies, it is found that the strain-time relationship approach can appropriately predict transient creep behavior such as rapid initial transient creep and slower and longer transient creep occurring in type 316 austenitic stainless steels. It is also expected that the formulation approach for ISS generations will result in more accurate elevated temperature structural evaluations by the ASME-NH rules. Therefore, the problem of graphical determination of ISS values will be resolved if the formulations of ISS curves can be provided in ASME-NH code rules. Acknowledgment This project has been carried out under the Nuclear R & D Program by MOST.

5 G.-H. Koo and J.-B. Kim / Journal of Mechanical Science and Technology 26 (3) (212) 899~ (a) For 482 o C t = t = 1 h t = 3 h t = h t = h t = 1x1 3 h t = 3x1 3 h t = 1x1 4 h t = 3x1 4 h t = 1x1 5 h t = 3x1 5 h 482 o C (b) For t = t = 1 h t = 3 h t = h t = h t = 1x1 3 h t = 3x1 3 h t = 1x1 4 h t = 3x1 4 h t = 1x1 5 h t = 3x1 5 h t = t = 1 h t = 3 h t = h t = h t = 1x1 3 h t = 3x1 3 h t = 1x1 4 h t = 3x1 4 h t = 1x1 5 h t = 3x1 5 h 593 o C (c) For 593 o C Fig. 9. Secondary creep strain contributions : Strain-Time Approach : SIE ASME-NH Database 593 o C t = t = 1 hr t = 3 hr t = hr t = hr t = 1x1 3 hr t = 3x1 3 hr t = 1x1 4 hr t = 3x1 4 hr t = 1x1 5 hr t = 3x1 5 hr Fig. 1. Comparison isochronous stress-strain curves with SIE ASME- NH data. References [1] ASME B&PV Section III Division 1-Subsection NH: Class 1 Components in Elevated Temperature Service, ASME, New York (21). [2] Elevated temperature structural design guide for class 1 components of prototype fast breeder reactor, PNC N , PNC (1984). [3] RCC-MR Design and construction rules for mechanical components of FBR nuclear islands, AFCEN, Paris (7). [4] An assessment procedure for the high temperature response of structures: Assessment procedure R5, British Energy Generation Ltd, UK (3). [5] G. H. Koo and J. H. Lee, Development of an ASME-NH program for nuclear component design at elevated temperatures, Int J of Pres Ves Piping, 85 (8) [6] R. W. Swindeman, Isochronous stress versus strain curves for normalized-and-tempered 2(1/4)Cr-1Mo steel, ASME Pressure Vessel and Piping Conference, Orlando, Florida (1997). [7] R. W. Swindeman and M. J. Swindeman, A comparison of creep models for nickel base alloys for advanced energy system, Int J Pres Ves Piping, 85 (8) [8] R. Matera, High temperature time dependent allowable stress and isochronous curves of an austenitic MN-Cr steel, J of Nuclear Materials, (1988) [9] L. D. Blackburn, The generation of isochronous stress-strain curves, ASME, New York (1972) [1] W. J. Evans and B. Wilshire, Transient and steady-state creep behavior of nickel, zinc, and iron, trans. TMS-AIME, 242 (1968) 131. [11] R. W. Evans and B. Wilshire, Creeps of metals and alloys, Chapter 6, Int. Inst. Met. London (1985). [12] F. Garofalo, C. Richmond, W. F. Domis and F. von Gemmingen, Strain-time, rate-stress, and rate-temperature relations during large deformations in creep, Joint International Conference on Creep, Inst. Mech. Eng., London (1963) [13] K. Maruyama and H. Oikawa, Comments on exponential descriptions of normal creep curves by S. G. R. Brown, R.W. Evans and B. Wilshire, Metallurgica, 21 (1987) [14] F. Xuan, S. Tu and Z. Wang, A modified time-dependent failure assessment diagram for cracks in mismatched welds at high temperatures, fatigue & fracture of material and structures, 29 (2) (6) Gyeong-Hoi Koo received his Ph.D degree from KAIST in Dr. Koo is working for Korea Atomic Energy Research Institute since 1989 as a principal researcher in nuclear mechanical engineering. He is a chairman of the ASME BPV III Korea International Working Group Committee and the Korea ASME Mirror Committee. He is an adjunct professor at division of electronics and control engineering in Hanbat National University since 7.