Constitutive equations for a modified Zr-2.5wt.%Nb pressure tube material

Abstract

Abstract The anistropic mechanical behavior of a modified Zr-2.5wt.%Nb pressure tube material has been studied. Based upon the stress-strain relationships in the three principal orthogonal directions of the tube, namely axial, circumferential and radial directions, a series of constitutive equations in the form of power law and Ramberg-Osgood equations have been established. The use of the Ramberg-Osgood equation is more advantageous owing to the fact that a single equation can be used to describe the behavior of a material in the elastic region, the transition region, and the fully developed plastic region, while the power law equation can only be used to describe material behavior in the fully developed plastic region. A better Ramberg-Osgood curve fit is obtained when the parameters are calculated from ln-ln plots as compared with the three parameters method. To further demonstrate the effectiveness of the ln-ln plot method, it was used to obtain the parameters of the Ramberg-Osgood equations for CANDU reactor Zircaloy-2 calandria tubes (a calandria tube is placed concentric to the pressure tube in the nuclear reactor; the gap between these two tubes is maintained by spacers) and standard Zr-2.5Nb pressure tubes, in tension. However, it was found that there are instances where a single Ramberg-Osgood equation cannot adequately describe the full range of deformation when the material showed complicated strain hardening behavior. In such cases, two Ramberg-Osgood equations are used to describe the material behavior. In addition to the establishment of constitutive equations, an attempt has been made to explain the deformation mechanisms responsible for the highly anistropic behavior of modified Zr-2.5Nb pressure tube material based upon previous work of various researches on single crystal, textured polycrystalline zirconium, Zircaloy-2 and Zircaloy-4.