Abstract
In monolithic UMo fuels, the interaction between the Al cladding and large gas bubble volumetric swelling causes both elastic-plastic and creep deformation. In this work, a phase-field model of gas bubble evolution in polycrystalline UMo under elastic-plastic deformation was developed for studying the dynamic interaction between evolving gas bubble/voids and deformation. A crystal plasticity model, which assumes that the plastic strain rate is proportional to resolved shear stresses of dislocation slip systems on their slip planes, was used to describe plastic deformation in polycrystalline UMo. Xe diffusion and gas bubble evolution are driven by the minimization of chemical and deformation energies in the phase-field model, while evolving gas bubble structure was used to update the mechanical properties in the crystal plasticity model. With the developed model, we simulated the effect of gas bubble structures (different volume fractions and internal gas pressures) on stress-strain curves and the effect of local stresses on gas bubble evolution. The results show that 1) the effective Young’s modulus and yield stress decrease with the increase of gas bubble volume fraction; 2) the hardening coefficient increases with the increase of gas bubble volume fraction, especially for gas bubbles with higher internal pressure; and 3) the pressure dependence of Xe thermodynamic and kinetic properties in addition to the local stress state determine gas bubble growth or shrinkage. The simulated results can serve as a guide to improve material property models for macroscale fuel performance modeling.
Highlights
The results demonstrate that 1) a tensile stress state leads to gas bubble growth, while a compressive stress states causes a slight shrink of gas bubbles; 2) a vacancy rich environment promotes gas bubble growth under a tensile stress state while it prevents gas bubble from shrinking under a compressive stress state
In this work we developed a phase-field model of gas bubble evolution in polycrystalline UMo under elastic-plastic deformation
We simulated the effect of gas bubble structures on stress-strain curves and the effect of local stress fields on gas bubble evolution
Summary
We leverage the existing computational capability of gas bubble evolution and crystal plasticity to develop a phase-field model of gas bubble evolution in polycrystalline UMo fuels under elastic-plastic deformation to study the effect of gas bubble structures, such as volume fraction and internal pressures, on mechanical properties as well as the effect of local stress on gas bubble evolution. The KKS model (Kim et al, 1999) is used to describe the gas bubble evolution in polycrystalline UMo. The total free energy G of the system is formulated as a functional of the order parameter field χ(r, t) and concentration field cXe(r, t) as. We use iteration and FFT to solve Eqs 25, 27 and let the obtained stresses and displacements satisfy the given boundary condition. With a known strength hardening law such as Eq 30, the shear strain rate c_ s(r) can be obtained from Eq 15
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