A model to describe the anisotropic viscoplastic behaviour of Zircaloy-4 tubes

With the aid of multiaxial tests under monotonic and cyclic loadings (tension, torsion and internal pressure), the anisotropic viscoplastic properties of Zircaloy-4 tubes in two metallurgical states can be studied. The anisotropic behavior at a temperature of 350°C has been thoroughly quantified. The results obtained at room temperatures as well as the independence of the ratio RP = εσσP/εzzp with respect to the temperature would seem to indicate that the set of anisotropy coefficients do not depend on the temperature. However, the viscosity of this alloy possesses a clearly marked minimum in the neighborhood of 300°C, a behavior which is probably due to the dynamic strain aging frequently observed in solid insertion solutions. This material also presents a slight supplementary hardening during out-of-phase cyclic loading (tension-torsion with a 90° phase lag). It is proposed to extend the formulation of a viscoplastic model, developed and identified elsewhere for other initially isotropic materials, to the case of Zircaloy-4. Generally speaking, anisotropy is introduced into this model through fourth order tensors which affect the flow directions [M], the linear kinematical hardening components [N], as well as the dynamic and static recoveries, [q] and [R] respectively, of the forementioned hardening variables. The identification of this model is performed at 350°C. It is shown that the formulation is capable of describing the set of mechanical characteristics of this alloy.