Modelling flow and work hardening behaviour of cold worked Zr–2.5Nb pressure tube material in the temperature range of 30–600 ̊C

Abstract

Under a postulated accident scenario of loss of cooling medium in an Indian Pressurised Heavy Water Reactor (IPHWR), temperature of the pressure tubes can rise and lead to large deformations. In order to investigate the modes of deformation of pressure tube – calandria tube assembly, material property data defining the flow behaviour over a temperature range from room temperature (RT) to 800̊C are needed. It is of practical importance to formulate mathematical equations to describe the stress–strain relationships of a material for a variety of reasons, such as the analysis of forming operations and the assessment of component's performance in service. A number of constitutive relations of empirical nature have been proposed and they have been found very suitable to describe the behaviour of a material. Although these relations are of empirical nature, various metallurgical factors appear to decide applicability of each of these relations. For example, grain size influences mainly the friction stress while the strain hardening is governed by dislocation density. In a recent work, tensile deformation behaviour of pressure tube material of IPHWR has been carried out over a range of temperature and strain rates (Dureja et al., 2011). It has been found that the strength parameters (yield and ultimate tensile strength) vary along the length of the tube with higher strength at the trailing end as compared to the leading end. This stems from cooling of the billet during the extrusion process which results in the variation of microstructure, texture and dislocation density from the leading to the trailing end. In addition, the variation in metallurgical parameters is also expected to influence the work hardening behaviour, which is known to control the plastic instability (related to uniform strain).In the present investigation, the tensile flow and work-hardening behaviour of a cold worked Zr–2.5Nb pressure tube material of IPHWRs has been studied over the temperature range of 30–600̊C. The stress strain data have been analysed in terms of stress–strain relations proposed by Hollomon (1945), Voce (1948) and Ramberg–Osgood (RO) (Ramberg and Osgood, 1943). The relative efficacies of these relations has been examined by fitting the appropriate equation to the experimentally obtained true stress–true strain data. The quality of fit of these empirical relations is quantified using square root of co-efficient of determination, i.e. R value (in %). The results have been discussed in terms of the correlation coefficient and in error in the estimation of UTS and uniform strain. Of the various relations employed, the Voce's relation has been found to describe the stress–strain behaviour most precisely up to 300̊C. Hollomon's relation describes the strain–stress behaviour of the material over the entire temperature range but with over-estimation of UTS. RO relation does not fit well in the initial stage but satisfactorily models the uniform elongation regime till UTS for temperatures up to 500̊C.