A Unified Model to Describe the Anisotropic Viscoplastic Behavior of Zircaloy-4 Cladding Tubes

Abstract

This paper presents the constitutive equations of a unified viscoplastic model and its validation with experimental data. The mechanical tests were carried out in a temperature range of 20 to 400°C on both cold-worked stress-relieved and fully annealed Zircaloy-4 tubes. Although their geometry (14.3 by 1.2 mm) is different, the crystallographic texture was close to that expected in the cladding tubes. To characterize the anisotropy, mechanical tests were performed under both monotonic and cyclic uni- and bi-directional loadings, i.e., tension-compression, tension-torsion, and tension-internal pressure tests. The results obtained at ambient temperatures and the independence of the ratio Rp = εp θθ/εp zz. with respect to temperature would seem to indicate that the set of anisotropy coefficients does not depend on temperature. Zircaloy-4 material also has a slight supplementary hardening during out-of-phase cyclic loading. We propose to extend the formulation of a unified viscoplastic model, developed and identified elsewhere for other initially isotropic materials, to the case of Zircaloy-4. Generally speaking, anisotropy is introduced through fourth order tensors affecting the flow directions, the linear kinematical hardening components, as well as the dynamic and static recoveries of the forementioned hardening variables. The ability of the model to describe all the mechanical properties of the material is shown. The application of the model to simulate mechanical tests (tension, creep, and relaxation) performed on true CWSR Zircaloy-4 cladding tubes with low tin content is also presented.

In situ synchrotron X-ray diffraction study of hydrides in Zircaloy-4 during thermomechanical cycling

“…The Kearns factors [16] of the sheet used in the study were measured as f N =0.59, f L =0.05, and f T =0.31 in the normal, longitudinal/rolling, and transverse directions. These values are similar to those obtained in typical CWSR Zircaloy-4 nuclear fuel cladding tubes [17].…”

Failure of Hydrided Zircaloy-4 Under Equal-Biaxial and Plane-Strain Tensile Deformation

“…As described elsewhere [12], the sheet had strong crystallographic texture. Importantly, the Kearns factors [15] of this CWSR sheet (f N = 0.59, f R = 0.05, and f T = 0.31 in the normal, longitudinal/rolling, and transverse directions of the sheet, respectively) are similar to those reported for unirradiated CWSR Zircaloy-4 cladding tubes (0.58, 0.10, and 0.32, respectively) [16] if the hoop direction of the tube corresponds to the orientation transverse to the rolling direction of the sheet. Therefore, the texture of the Zircaloy-4 sheets used in this study is similar to the typical texture of Zircaloy-4 cladding tubes, i.e., the basal planes tend to align with their poles inclined approximately ± 30º away from the normal of the tube surface and oriented toward the transverse direction.…”

Mechanical Properties of Zircaloy-4 Cladding Tube by Advanced Expansion due to Compression (A-EDC) Test

“…This can be identi ed by the necking along tube z axis. In the previous studies, the parameter R values are found to be 1.3 tested in the axial direction 30) and 2.3 tested in the hoop direction 29) for unirradiated Zircaloy-4. On the contrary, it has been proved that the yield condition of irradiated nuclear fuel cladding is similar to those of isotropic materials, which illustrates that irradiation can reduce the anisotropic behavior of cladding tubes.…”