Isotropic softening model for fuel cracking in BISON

In oxide nuclear fuel, the temperature gradient from the centerline to the radial edge of the pellet induces cracking due to thermal stress. We present a model that represents the effect of cracking as an isotropic softening of the material. The model considers a reduction of the elastic constants as a function of the number of cracks present in the fuel. This pragmatic approach aims to represent the average effect of cracking on the fuel stresses without attempting to explicitly describe the crack pattern or localization. Albeit simplistic, this approach has definite advantages in terms of computational expense and numerical convergence behavior for the mechanical analysis. It is also consistent with the uncertainties inherent in modeling the fuel cracking process, and suitable for engineering calculations aimed at representing the global fuel element behavior. The applied scaling of the elastic constants conserves the principal strain values and redistributes the principal stresses isotropically. Moreover, the model allows for the effect of an evolving number of cracks. In particular, an empirical correlation for the number of cracks as a function of the rod average linear heat rate is developed. Although the basic concept of the model was known, in this work we revisit and improve the original formulation, and implement the model in the BISON fuel performance code. Application in BISON is demonstrated through simulations of an idealized single fuel pellet irradiation and two integral fuel rod experiments. Results showcase the impact on calculated fuel stresses, the coupling to fuel creep, and the effect on cladding strains during pellet-cladding mechanical interaction.