Document Type : Research Paper

Authors

1 University of Mohagheh Ardabili

2 Un. of Mohaghegh Ardabili

Abstract

In this paper the ratcheting behavior of carbon steel(ASTM A106B) and stainless steel(304L) elbows is studied under steady internal pressure and in-plane external moments at frequencies typical of seismic excitations. The finite element analysis with the nonlinear isotropic/kinematic (combined) hardening model has been used to evaluate ratcheting behavior of the elbows. Material parameters have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The rate of ratcheting depends significantly on the magnitudes of the internal pressure, dynamic bending moment and material constants for combined hardening model. The results show that the maximum ratcheting is occurred in the hoop direction at crown. Also, the results show that initially, the calculated rate of ratcheting is large and then decreases with the increasing of cycles. Also, the results obtained by using the Combined hardening model gives acceptable adaptation in comparison with the other hardening models(AF and Chaboche hardening models); however this model gives over estimated values comparing with the experimental data.

Graphical Abstract

Evaluation of combined hardening model in ratcheting behavior of pressurized piping elbows subjected to in-plane moments

Keywords

Main Subjects

[1]        J. L. Chaboche, “Time-independent constitutive theories for cyclic plasticity”, Int. J. of Plasticity, Vol. 2, No. 2, pp.149-188, (1986).
[2]        J. L. Chaboche, “On some modifications of kinematic hardening to improve the description of ratcheting effects”. International Journal of Plasticity, Vol. 7, No. 7, pp. 661–678, (1991).
[3]        J. L. Chaboche, “Modeling of ratcheting: evaluation of various approaches”. European Journal of Mechanics, A/Solids, Vol. 13, No. 13, pp. 501–518, (1994).
[4]        J. L. Chaboche , “A review of some plasticity and viscoplasticity constitutive theories”, Int. J. of Plasticity, Vol. 24, No. 10, pp. 1642–1963, (2008).
[5]        N. Ohno, and J. D. Wang, “Kinematic hardening rules with critical state of dynamic recovery, part I: formulations and basic features for ratcheting behavior”. International Journal of Plasticity, Vol. 9, No. 3, pp. 375–390, (1993a).
[6]       N. Ohno, and J. D. Wang , “Kinematic hardening rules with critical state of dynamic recovery, Part II: application to experiments of ratcheting behavior”. International Journal of Plasticity, Vol. 9, No. 3, pp. 391–403, (1993b).
[7]        N. Ohno, “Constitutive modeling of cyclic plasticity with emphasis on ratcheting”. International Journal of Mechanics and Sciences, Vol. 40, No. 2-3, pp. 251–261, (1998).
[8]       T. Hassan, and S. Kyriakides, “Ratcheting in cyclic plasticity, part I: uniaxial behavior”, International Journal of Plasticity, Vol. 8, No. 1, pp. 91–116, (1992).
[9]        T. Hassan, E. Corona, and S. Kyriakides, “Ratcheting in cyclic plasticity, Part II: multiaxial behavior”, International Journal of Plasticity, Vol. 8, No. 2, pp. 117-146, (1992).
[10]    T. Hassan, and S. Kyriakides, “Ratcheting of cyclically hardening and softening materials, Part I: uniaxial behavior”, International Journal of Plasticity, Vol. 10, No. 2, pp. 149–184, (1994a).
[11]    T. Hassan, and S. Kyriakides, “Ratcheting of cyclically hardening and softening materials, Part II: multiaxial behavior”. International Journal of Plasticity, Vol. 10, No. 2, pp. 185-212, (1994b).
[12]    M. Abdel Karim, and N. Ohno, “Kinematic hardening model suitable for ratcheting with steady-state”, International Journal of Plasticity, Vol. 16, No. 3, pp. 225-240, (2000).
[13]    S. Bari, and T. Hassan, “Anatomy of coupled constitutive model for ratcheting simulation”, International Journal of Plasticity, Vol. 16, No. 3-4, pp. 381-409, (2000).
[14]    S. Bari, and T. Hassan, “Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation”, International Journal of Plasticity, Vol. 17, No. 7, pp. 885-905, (2001).
[15]    S. Bari, and T. Hassan, “An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation”, International Journal of Plasticity, Vol. 18, No. 7, pp. 873–894, (2002).
[16]    X. Chen, B. Gao, and G. Chen, “Multiaxial ratcheting of pressurized elbows subjected to reversed in-plane bending”, J. Pres. Eq. Syst., Vol. 3, No. 3, pp. 38-44, (2005).
[17]    X. Chen, B. Gao, and G. Chen, “Ratcheting study of pressurized elbows subjected to reversed in-plane bending”, J. of Pressure Vessel Technology, Vol. 128, No. 4, pp. 525-532, (2006).
[18]    X. Chen, R. Jiao, and K. S. Kim, “Simulation of ratcheting strain to a high number of cycles under multiaxial loading”, International Journal of Solids and Structures, Vol. 40, No. 26, pp. 7449-7461, (2003).
[19]    X. Chen, and R. Jiao, “Modified kinematic hardening rule for multiaxial ratcheting prediction”, International Journal of Plasticity, Vol. 20, No. 4-5, pp. 871-898, (2004).
[20]    X. Chen, R. Jiao, and S.K. Kwang,  “On the Ohno–Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel”, Int. J. of Plasticity, Vol. 21, No. 1, pp. 161-184, (2005).
[21]    X. Chen, Xu. Chen, D. Yu, and B. Gao, “Recent progresses in experimental investigation and finite element analysis of ratcheting in pressurized piping”, Int. J. of Pressure Vessels and Piping , Vol. 101, No. 1, pp. 113–142, (2013).
[22]    W. F. English, “Piping and fitting dynamic reliability program-fourth semi-annual progress report” Nov. 1986- Apr.1987,GE Nuclear Energy, NEDC- 31542, (1988).
[23]    S. Ranganath, H. Hwang, and S. W. Tagart, “Piping and fitting dynamic reliability program”. EPRI Nuclear Power Division, (1989).
[24]    K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Techniques for the investigation of the ratcheting behavior of piping components under internal pressure and simulated seismic loading”, BSSM J. strain, Vol. 28, No. 2, pp. 53-90, (1992).
[25]    K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Single frequency seismic loading tests on pressurized branch pipe intersections machined from solid”, J. of strain Analysis, Vol. 28, No. 3, pp. 197-207, (1993).
[26]    K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Stress Limits for Pressurized Piping Branch Junctions Under In-Plane Run pipe Simulated Seismic Loadings”. ASME J. Pressure Vessel Tec, Vol. 116, No. 2, pp. 150–160, (1994).
[27]    K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Cumulative damage assessment  at  pressurized piping branch junctions under in- plane run pipe simulated seismic bending”, Int. J. pres. ves. piping, Vol. 63, No. 2, pp. 119–128, (1995).
[28]    K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Response and cyclic strain accumulation of pressurized piping elbows under dynamic in plane bending”, J. of strain analysis, Vol. 31, No. 2, pp. 135–151, (1996).
[29]    K. Yahiaoui, D. N. Moreton, and  D. G. Moffat, “Response and cyclic strain accumulation of pressurized piping elbows under dynamic out-of- plane bending”, J. of strain analysis, Vol. 311, No. 2, pp. 153–166, (1996).
[30]    T. Hassan, T. Lakhdar, and K. Shree,  “Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models”, Int. J. of Plasticity, Vol. 24, No. 10, pp. 1863-1889, (2008).
[31]    T. Igaria, M. Kobayashi, F. Yoshida, and S. Imatani, Inoue, T., “Inelastic analysis of new thermal ratcheting due to a moving temperature front”, International Journal of Plasticity, Vol. 18, No. 9, pp. 1191-1217, (2002).
[32]    X. Feaugas, and C. Gaudin, “Ratcheting
 
 
 process in the stainless steel AISI 316L at 300 K: An experimental investigation”. International Journal of Plasticity, Vol. 20, No. 4, pp. 643-662, (2004).
[33]    P. J. Armstrong, and C. O. Frederick, “A mathematical representation of the multi axial Bauschinger effect”. CEGB Report RD/B/N 731, Central Electricity Generating Board. The report is reproduced as a paper: 2007, Materials at High Temperatures, Vol. 24, No. 1, pp. 1-26, (1966).
[34]    J. L. Chaboche, “Constitutive equations for cyclic plasticity and cyclic viscoplasticity”. Int. J. of Plasticity, Vol. 5, No. 3, pp. 247-302, (1989).
[35] S. J. Zakavi, M. Zehsaz, and M. R. Eslami,  “The ratcheting behavior of pressurized plain pipework subjected to cyclic bending moment with the combined hardening model”, Nuclear Engineering and Design, Vol. 240, No. 4, pp. 726-737, (2010).
 
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