Numerical Analysis of Structural Behavior Inside a Pressurized Water Reactor (PWR)

Abstract

The mechanisms of creep for zircaloy-4 have been studied for many years. The creep data published in the recent 35 years were collected and analyzed to identify different creep mechanisms (dislocation-glide creep, power-law and power-law breakdown creep and diffusional creep), based on the forms of the relationships between stress, temperature and strain rate. This identification allowed the activation energies and other associated creep parameters to be derived for each mechanism. The creep parameters were used to construct a deformation-mechanism map for zircaloy-4 that shows the conditions under which different mechanisms are dominant. This multi-mechanism creep model was implemented into the ABAQUS CREEP subroutine to study the effect of creep on the structure deformation and stress evolution. This subroutine allowed the finite-element analysis to select the most proper creep mechanism naturally based on the local stress and temperature, which improved the accuracy for structures with a complex geometry and stress distribution. The multiple-mechanism creep model was coupled with a wear model to study the in-pile relaxation of the contact force between the spacer grid and cladding, and the evolution of the wear profile before formation of a gap. These two processes occur at different time scales. Therefore, an effective-cycle technique was developed to couple the two mechanisms in a fashion that combined an acceptable level of both efficiency and accuracy. The simulations indicated that two stages exist during the relaxation of the contact force: partial slip and full slip. During partial slip, wear damage occurs at the edges of the contact region. Creep is the dominant relaxation mechanism during the partial-slip, and allows the wear scar to propagate across the entire contact, which causes a transformation from the partial slip to full slip. Once full-slip occurs, the contact forces are relatively low, and the creation of the wear scar becomes the dominant relaxation mechanism. In this regime, reducing the wear coefficient and the amplitude of excitation force delays the formation of a gap between the grid and cladding. The wear profile developed during full-slip occurs homogeneously. For a given initial interference, there is a master curve for the wear scar, which does not depend on the friction coefficient, the amplitude of the excitation pressure, or the wear coefficient. In addition to vibration, the coolant can also cause corrosion to the cladding. The reaction between water and zirconium on the cladding surface produces hydrogen in addition to the oxide. Hydrogen diffuses into the cladding and reacts with zirconium below the oxide layer to produce δ-hydride (ZrH1.66). δ-hydride formation is associated with a volumetric expansion of about 17%, which causes both misfit stress and geometrical deformation. Therefore, a multi-scale framework was developed to simulate hydrogen diffusion and hydride formation in the cladding. The hydride formation and growth were simulated by others using a phase-field model at the mesoscale. Then, the results of the phase-field model were used in a continuum-level finite-element analysis to study the effect of hydride on the structural behavior. The multiscale framework was first used to simulate an experiment for validation. Then, the framework was used to study the hydride formation in the cladding. Hydride forms a rim on the cladding outer surface with a maximum thickness of 0.12 mm. The hydride volume fraction distribution is plotted at different times.