Abstract—Purpose of the present study is to predict thermal ratchetting deformation of thin cylindrical shell, in the framework of unified Chaboche visco-plastic constitutive model. Strain controlled cyclic characteristics and uniaxial monotonic loading at different strain rate is analyzed for SS316 L. Thermal ratchet load of 550 ºC is applied cyclically along the axis of the cylinder to predict the deformation pattern accounting strain rate dependence of the material operating at high temperature condition as in Prototype Fast Breeder Reactor (PFBR). The effect of axial temperature variation is simulated by cyclically varying the heat transfer properties at the interacting surfaces of cylindrical shell. To achieve comparable accuracy and better convergence, semi-implicit plasticity integration approach is implemented in UMAT code. Cyclic hardening and strain rate dependence of material is compared by the experimental results. Index Terms—Progressive deformation, thermal ratchetting, visco-plastic, chaboche model. I. INTRODUCTION Ratchetting deformation due to sodium free level variation is one of the critical phenomena in reactor assembly of the Prototype Fast Breeder Reactor (PFBR). Axial temperature variation due to Sodium free level, during normal operations and other operating conditions depend upon the temperatures of hot and cold pools. During normal operation, the upper cylindrical portion of the inner vessel in the vicinity of hot pool sodium free level is highly affected by level variations. Cyclic loading, induced by level variations in PFBR main vessel shown in Fig.1, result into complex material behavior leading to progressive deformation. It was reported that speed of level variation affects the deformation pattern [1]. Unified visco-plastic constitutive theory for time dependent formulation is considered to investigate deformation behavior of smooth cylindrical portion of main vessel of PFBR. Cylinder of dimension 500 mm outside diameter (OD) and thickness of 1 mm is considered for the analysis. Since progressive deformation in austenitic stainless steel structure includes plastic straining with cyclic hardening property, it is essential to involve sophisticated constitutive model to simulate inelastic behavior. Classical ratchetting model by J. Bree [2], discussed the evolution of ratchetting phenomenon due to primary and secondary load combination however thermal ratchetting in reactor components can occur by secondary stresses alone. There are various literatures Manuscript received June 16, 2013; revised July 30, 2013. Ashutosh Mishra is with DGFS PhD Fellow in Reactor Design Group at Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, India (e-mail: ashutoshjssate@gmail.com). available on thermal ratcheting for high temperature reactor components [3]. Visco-plastic constitutive model is implemented in user defined subroutine with semi-implicit integration technique for plasticity calculation. Transient thermal loading of 550 °C is achieved by FILM subroutine. Fig. 1. Typical sodium free level variations in PFBR main vessel. II. CONSTITUTIVE EQUATIONS In this section, a constitutive model is shown describing temperature dependent ratchetting of material. The main equations of unified visco-plastic theory considered for the present analysis are reproduced here as below: In e T ij ij ij ij        (1) 1 e ij ijkl kl D     (2) 3 2 n y ij ij In ij ij ij F S K S        (3) T ij ij ij CT      (4) 1.5( )( ) y ij ij ij ij F S S R       (5) where ij  , In ij  , e ij  , T ij  and In ij   are total strain inelastic strain elastic strain, thermal strain and rate of inelastic strain respectively; T ij   is the thermal strain rate and ijkl D is the matrix of elasticity; K and n are material parameters representing the viscous characteristics. ij C is the coefficient Time Dependent Ratchetting of Thin Cylindrical Shell Due to Axial Temperature Variation Using Visco-Plastic Model Ashutosh Mishra, R. Suresh Kumar, and P. Chellapandi IACSIT International Journal of Engineering and Technology, Vol. 6, No. 3, June 2014 234 DOI: 10.7763/IJET.2014.V6.703