Development of Plasticity Model Using Non Associated Flow Rule for HCP Materials Including Zirconium for Nuclear Applications

Abstract

In this report (prepared in collaboration with Prof. Jeong Whan Yoon, Deakin University, Melbourne, Australia) a research effort was made to develop a non-associated flow rule for zirconium. Since Zr is a hexagonally close packed (HCP) material, it is impossible to describe its plastic response under arbitrary loading conditions with any associated flow rule (e.g. von Mises). As a result of strong tension-compression asymmetry of the yield stress and anisotropy, zirconium displays plastic behavior that requires a more sophisticated approach.Consequently, a new general asymmetric yield function has been developed which accommodates mathematically the four directional anisotropies along 0°, 45°, 90°, and biaxial, under tension and compression. Stress anisotropy has been completely decoupled from the r-value by using non-associated flow plasticity, where yield function and plastic potential have been treated separately to take care of stress and r-value directionalities, respectively. This theoretical development has been verified using Zr alloys at room temperature as an example as these materials have very strong SD (Strength Differential) effect. The proposed yield function reasonably well models the evolution of yield surfaces for a zirconium clock-rolled plate during in-plane and through-thickness compression. It has been found that this function can predict both tension and compression asymmetry mathematically without any numerical tolerance and shows the significant improvement compared to any reported functions.