11.1. Introduction

Since fuel element behavior during fast reactor transients can significantly affect accident energetics, an accurate and detailed model for the mechanical response of fuel elements is needed in safety assessments. During transients that lead to overheating of fuel and cladding, plastic straining of the cladding due to internal fission gas pressure and differential expansion between the fuel and cladding may result in cladding rupture and release of fission products to the primary coolant. In addition to the fundamental concern for cladding failure, fuel axial expansion can also have an important role due to the associated negative reactivity potential.

FPIN2 is a validated computer code that provides mathematical models that simulate fuel and cladding mechanical response and predict fuel element performance over a wide range of transients. It performs an analysis of metal fuel and cladding deformation, including the impact of fuel-cladding interactions, and estimates cladding failure locations and times.

FPIN2 has been incorporated into the SAS4A/SASSYS‑1 code system for mechanical analysis of individual fuel elements. In this implementation, SAS4A/SASSYS‑1 provides fuel and cladding temperatures, and FPIN2 performs the analysis of fuel element deformation and predicts the time and location of cladding failure. FPIN2 results are also used for the estimates of axial fuel expansion and the associated reactivity effects. In this chapter, FPIN2’s mechanical model, the SAS-FPIN2 coupling methodology, and the integrated SAS-FPIN2 model usage are presented.

11.1.1. Brief Description of FPIN2

The FPIN2 code has been developed to analyze the thermal-mechanical phenomena that control fuel element behavior during fast reactor transients. The early versions of the code were based on the characteristics of oxide and carbide ceramic fuels [11-1,11-2]. More recently, FPIN2 has been adapted for the analysis of metallic fuels [11-3,11-4]. The overall modeling for this metallic fuel version of the code was validated through comparison of FPIN2 calculations with the data from TREAT tests on EBR-II irradiated fuel, prototypic of the IFR concept [11-5,11-6]. The most recent version of the code integrated with SAS4A/SASSYS‑1 includes numerous model improvements that reflect the experience gained during these validation efforts.

A wide range of material behavior is modeled in the code that describes elastic, plastic, thermal, and swelling performance of fuel elements. Since the primary emphasis in FPIN2 is on the mechanical analysis of the fuel and cladding, in the standalone version of the code temperatures are calculated using a simple model based on pin-in-a-pipe geometry and single-phase flow. The mechanical model, on the other hand, is based on a rigorous force-displacement formulation and uses an implicit finite element method with linear shape functions. The finite element scheme used allows convenient modular coding in which different models for material behavior and improvements in specific algorithms are easily implemented. The equilibrium equations are derived form equations of virtual work. The elements are defined in an (r,z) mesh; however, axial symmetry and generalized plane strain are assumed so that the analysis is essentially one-dimensional. The elements are allowed to interact only at the radial boundaries (nodes), and the displacements within the elements are approximated by linear functions of the nodal displacements.

Additional models for metallic fuels such as models for fission gas generation and release, molten cavity formation, the large gas plenum, and fuel-cladding eutectic alloy formation are also provided in FPIN2 to complement the fuel element mechanics calculations. Internal pin pressure is determined from direct mass and volume balances in the central cavity and gas plenum. The molten fuel cavity in FPIN2 is located by the axial and radial extent to which the fuel has reached its solidus temperature and the elements inside the cavity boundary are dropped out of the stress-chain calculation. For cases where initial fuel melting occurs below the top axial segment, the plenum pressure calculation is decoupled from the molten cavity pressure calculation. Once melting reaches cavity-gas plenum interface, the two pressures are assumed to equilibrate and the plenum/cavity pressure-volume equations are solved together to give a common pin pressure and amount of molten fuel extruded into the plenum.

Checking rupture is predicted in the code by using the life fraction criterion. The life fraction change over a time step is determined from the change in rupture time for the instantaneous average cladding temperature and the hoop stress obtained form the thin-shell equations used in developing the life fraction correlations. The effect of low melting point eutectic formation between the fuel and the cladding is included in the calculations by considering only the thickness of unaffected cladding that is available to carry the load.

11.1.2. Overview

The finite element formulation that constitutes the basic structure of FPIN2’s mechanics calculation is described in Section 11.2. Although the models presented in Section 11.2 are primarily developed for oxide fuel, they provide a substantially robust structure that allows modifications to handle metallic fuels. The modifications and additions to the code for metal fuels are discussed separately in Section 11.3. Most of these models for metallic fuels reflect the experience gained during FPIN2 validation efforts through comparison with the data from TREAT tests.

Two modes of SAS-FPIN2 coupled operations are provided. In the stand-alone mode, independent FPIN2 input is used and FPIN2 is executed without interfacing to SAS4A/SASSYS‑1. In the interfaced mode, SAS4A/SASSYS‑1 calculated fuel and cladding temperatures are transferred to FPIN2, and FPIN2 results are used in the analysis of fuel behavior. The SAS-FPIN2 coupling methodology and the integrated SAS-FPIN2 model usage along with input and output descriptions are presented in Section 11.4.