Effect of frequency of free level fluctuations and hold time on the thermal ratcheting behavior A. Mishra a, * , P. Chellapandi a , R. Suresh Kumar a , G. Sasikala b a Reactor Design Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, India b Metallurgy & Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, India article info Article history: Received 6 February 2014 Received in revised form 19 March 2015 Accepted 24 March 2015 Available online 1 April 2015 Keywords: Thermal ratcheting Level fluctuation Visco-plastic Ratcheting strain with hold time abstract Investigation of cyclic strain accumulation behavior of a thin cylindrical shell (SS 316L) due to thermal ratcheting, in the framework of time independent (Model-1) and dependent formulations (Model-2) is carried out. The effect of frequency of free level fluctuations by varying cycle time (CT) is compared for Model-1 and Model-2. Contribution of strain due to high frequency and low frequency level fluctuations is quantified. Further, the contribution of ratcheting strain with hold time is evaluated to highlight the effect of free level hold on radial deformation of the cylinder. Improvement in predicting ratcheting strain is observed using semi-implicit plasticity integration method. Implicit plastic increment formu- lation is derived using Newton's method. Validation of code for Model-1 is done by comparing the results with the existing experimental results. Strain controlled cyclic characteristics and uniaxial monotonic loading at different strain rate is analyzed to validate the code for Model-2. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction Components and structures operating at high temperature conditions as in nuclear application have to be designed as per nuclear design codes for their safe functioning. The phenomenon of inelastic material behavior due to thermal loading, as in the main vessel of pool type nuclear reactors results into thermal ratcheting. It is a critical phenomenon, which should be considered while designing a reactor main vessel to limit the radial deformation within acceptable values as per design codes [1e3]. However, these codes discuss the basic elastic approach to evaluate such type of deformation, which involves higher safety margins to take care of several possible uncertainties due to inelastic material deformation behavior. Many researchers [4e8] have studied ratcheting phe- nomenon for various steels under uniaxial and multiaxial loading cases. These studies have shown that different materials exhibit different ratcheting behavior (hardening/softening). The cyclic hardening behavior of austenitic steels employing nonlinear constitutive model has been analyzed in detail and provided a good insight of ratcheting phenomenon [9e11]. As discussed by Bari and Hassan [12], kinematic hardening rules considering Chaboche model can be suitably used to predict nonlinearity due to yield surface translation in multi-axial ratcheting. Portier and co-authors [13] studied ratcheting behavior of SS 316 following five sets of constitutive models. They performed several tests to generate an experimental database for mechanical behavior under uniaxial and multiaxial loadings. Investigation of different type of models for damage evaluation is of high importance for the nuclear industries to achieve high reliability and safety levels during operational life. Ratcheting studies by Bree [14], under the combination of both primary and secondary stresses, neglected the Bauchinger effect. Roche et al. [15] later provided insight of combined hardening behavior in ratcheting phenomenon for nuclear components. Moreover, the effect of employing different kinematic hardening rule for predicting thermal ratcheting due to moving temperature front shows importance of material model selection [16]. Ratchet- ing following inelastic analysis route for different combination of loads [17] is explained in DDS (Demonstration plant Design Stan- dard). Japanese LMR (Liquid Metal Reactor) design code DDS [18] implemented methods to evaluate ratcheting strain considering combinations of primary and secondary stresses with imposition of secondary membrane and bending stresses. Igari [19] discussed time independent analysis of thermal ratcheting due to moving temperature front, implementing different hardening rules super- posing creep effect independently. Time independent progressive deformation and the effect of loading method on the progressive * Corresponding author. Tel.: þ91 44 27480500x21176. E-mail address: ashutoshjssate@gmail.com (A. Mishra). Contents lists available at ScienceDirect International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp http://dx.doi.org/10.1016/j.ijpvp.2015.03.004 0308-0161/© 2015 Elsevier Ltd. All rights reserved. International Journal of Pressure Vessels and Piping 129-130 (2015) 1e11