.. _section-A9.1: Appendix 9.1: Main Assumptions ============================== The main assumptions associated with the MFUEL models are given as follows: **Fuel Constituent Redistribution** - Phase changes are assumed to occur rapidly compared with migration of alloy constituents. - When a non-zero diffusion current is computed, U and Zr atoms switch places and Pu is immobile. - Enthalpy of solution is negligible. - Kinetic reactions terminate and equilibrium is assumed when a solubility limit is reached. - Axial Zr migration is assumed to be negligible. **Fuel Clad Chemical Interaction** - Lanthanides can collectively be treated as diffusion in a single-phase medium due to their low solubility in metal fuel. - Lanthanide diffusion into the cladding does not start until fuel-cladding soft contact. - The brittle layer from lanthanide interaction does not bear any load. - Eutectic formation of cladding is assumed to occur at any fuel cladding contact condition if the fuel surface temperature exceeds the eutectic temperature. - The eutectic interaction layer in the cladding does not bear any load. - Slow eutectic threshold temperatures vary as a function Pu content (e.g., 715 °C for U-10Zr) and is set to 1080 °C as constant for the rapid eutectic formation. **Fission Gas Behavior and Fuel Swelling** - Fission gas bubbles and interconnected porosity are modeled in six discrete groups. - Bubbles are divided in to three groups based on constant atom number per bubble to model the observed bubble size distribution, bubble size evolution and their interactions. - Bubbles nucleate uniformly in fuel matrix. It is assumed that phase boundaries are effective nucleation sites which are distributed uniformly. - Gas swelling threshold for interconnected open porosity initiation is 10%. - Fission yield of assumed to be 0.25 gas atoms/fission. - Equilibrium bubble volume is assumed to behave based on the Van Der Waals EOS. - The bubble shape correction factor is assumed to be different for spherical and ellipsoidal bubbles. :math:`\alpha + \zeta + \delta` phase forms ellipsoidal bubbles whereas single :math:`\gamma` and :math:`\beta + \zeta + \gamma` phases form spherical bubbles. - Nonequilibrium bubble behavior depends on the phases present, hydrostatic stress, bubble pressure, and fuel creep. **Plenum Pressure** - Plenum gas pressure is assumed to behave as an ideal gas assuming there is mechanical equilibrium between open porosity and plenum volume. - Plenum gas volume accounts for the upper plenum and interconnected porosity in the fuel **Mechanical Analysis** - Plane strain is assumed for the computation of axial displacements, i.e., the area-averaged axial displacements are used to determine the axial displacement of a fuel axial node. - Thin shell theory is assumed to compute cladding stresses. It is assumed that shear stresses are negligible in both the fuel and cladding. - Fuel creep is assumed to be sufficiently high to avoid fuel stress gradients. - All strain components are accounted for while computing the Fuel Clad Mechanical Interaction. Mostly fuel porosity sintering is the dominating balancing strain, which is assumed to be isotropic. - When cracked fuel contacts with the cladding, it is assumed that axial growth is constrained by the cladding during the steady state. - When the fuel is fully swollen, hard contact initiates such that fuel expansion can take place at the expense of porosity sintering which is assumed to be isotropic. - Once eutectic forms between fuel and cladding, fuel clad mechanical interaction is assumed to be negligible. Note that at eutectic temperatures, fuel is fully single gamma phase which is very soft and porous. - Upon eutectic formation, the default model assumes aggregated axial expansion without pore sintering consistent with experimental observation. Also a conservative option is provided for the users to allow for limited pore sintering in radial direction. - Axial pressure due to fuel mass is accounted for. - It is assumed that fuel swelling strain is isotropic. However, it is assumed that axial cracking in the fuel can lead to anisotropic fuel axial growth. - It is assumed pore sintering/hot pressing occurs only to the open porosity bubble populations and is isotropic. - It is assumed that cladding creep strain depends on the Von Mises or deviatoric stress. **In-Pin Sodium** - It is assumed that sodium does not infiltrate beyond 60% of the fuel radius, and only in the :math:`\alpha + \zeta + \delta` phase region. For fuel nodes beyond 60% of the fuel radius, it is assumed that sodium infiltration fills 30-60% of the available/open porosity, depending on the burnup level. **Corrosion due to Clad/Sodium Coolant Interactions** - It is assumed that sodium corrosion has a constant corrosion rate for a given temperature (no time/depth dependence). **Clad Failure Models** - It is assumed that D9 CDF models do not apply to steady-state (pre-transient) characterization. - In mechanistic clad creep rupture model, the grain boundary cavities are divided in to three groups based on their sizes to model the observed behavior, interaction between cavities, and growth/coalescence behavior. - It is assumed that, for the mechanistic clad creep rupture models, when the cavitated grain boundary area reaches 30%, failure occurs.