PSI - Issue 14

Ritu. J. Singh et al. / Procedia Structural Integrity 14 (2019) 549–555

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Ritu .J. Singh/ Structural Integrity Procedia 00 (2018) 000–000

flow in the inner part of the cylinder. After removal of the internal pressure, residual compressive stresses are developed to a certain depth from the inner surface. These residual stresses serve to increase the load bearing capability in the subsequent loading and result in an increase in the fatigue lifetime of the component. Autofrettage process is also used in the formation of expansion joint where a mechanical joint is formed between the tube and the tubesheet/end fitting by plastic deformation of the tube and tubesheet achieved by the use of hydraulic pressure or mechanical rollers. These joints are commonly found in steam generator, heat exchanger, boiler and condenser. In the nuclear industry, rolled joints have also been used to join two dissimilar metals which cannot be welded due to the formation of brittle intermetallic compounds like in the case of connecting the zirconium alloy with stainless steel structural components. In pressurized heavy water reactors the pressure tube is rolled to the end fitting and calandria tube is rolled to stainless steel calandria side tube sheet. The expansion of tube-tubesheet joints has been a subject of both analytical and experimental studies. Several researchers like Bouzid, Mourad, and El Domiaty (2015), Lee et al. (2009), Tian, Huang, and Fu (2010), Huang and Xie (2011) have developed analytical models and proposed equations that give the adequate residual contact pressure. The finite elements have been extensively used to verify the analytical solutions and to propose modifications in analytical solutions. Residual stresses developed in a roll expanded joint between the Zr 2.5% Nb pressure tube and SS 403 end fitting is of critical importance w.r.t structural integrity of pressure tubes in a pressurized heavy water reactors. One of the important aspect w.r.t to development of residual stresses in the pressure tube is the anisotropy of the Zirconium material. Zirconium alloys have hexagonal close packed (hcp) crystal structure and exhibit highly anisotropic physical, mechanical and corrosion properties. This anisotropy is a result of the thermo mechanical processing route adopted for fabrication which leads to preferred orientation of grains. It is felt that effect of anisotropy on the residual stress in the roll expanded joint may be an important parameter and needs to be investigated. No work is reported so far where the effect of anisotropy on the residual stresses is investigated. Numerical simulation of mechanical roll expansion joint involves complexities like consideration of anisotropy (orthotropic), the dynamic aspects of the rolling process, and the existence of a three dimensional elastic-plastic state with accurate constitutive modeling. Therefore in order to have an understanding of the effect of anisotropy on residual stresses, a simplified autofrettage analysis is attempted. In this paper, a thick cylinder made from Zr 2.5% Nb is pressurized till elasto plastic interface is achieved and then unloaded to study effect of anisotropy on the development of residual stresses. Two material models are considered in the analysis i.e. isotropic and anisotropic behavior. Nomenclature a inner radius b outer radius � yield Stress p w internal pressure p wmax maximum pressure at which yielding start at the inner surface fourth order elasticity tensor stress tensor ϵ strain tensor 2. Residual stress in thick axisymmetric cylinder due to autofrettage under hydrostatic pressure Autofrettage of thick cylinders involves loading the cylinder with internal pressure till the cylinder undergoes plastic deformation and subsequent unloading. In order to verify the method used for numerical simulation of development of residual stresses, work done by Hu and Puttagunta (2012) was attempted. This problem served to understand methodology for obtaining residual stresses resulting after elastic unloading. Available analytical solutions by Gao (1992) were used to benchmark the methodology. After verification of the methodology, a thick cylinder made from Zr 2.5% Nb is loaded till elasto plastic interface is achieved and then unloaded to study the development of residual stresses. Two material models are considered for the analysis i.e. isotropic and anisotropic behaviour. 2.1. Mathematical model Commercial FE software ABAQUS is used for modeling the autofrettaged thick cylinder considering 1/4 th symmetry. A 2D plane stress idealization is considered. The cylinder is made from Zr 2.5% Nb with inner radius and outer radius as 60 mm & 90 mm respectively. A 8-node biquadratic plane stress quadrilateral with reduced integration is used to discretize the geometry. The meshed model is shown in Fig. 1a. Two material models are considered, i.e. isotropic and anisotropic elastic-plastic behavior. The stress and strain tensors at a material point are related by following equation, �� � ���� �� , where, σ is the stress tensor at a material point , ∈ is the strain tensor at a material point and ∁ is the fourth order elasticity stiffness tensor. For isotropic material,