.. _section-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 SASSYS/SAS4A code system for
mechanical analysis of individual fuel elements. In this implementation,
SASSYS/SAS4A 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.

.. _section-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
SASSYS/SAS4A 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.

.. _section-11.1.2:

Overview
~~~~~~~~

The finite element formulation that constitutes the basic structure of
FPIN2's mechanics calculation is described in :numref:`section-11.2`. Although the
models presented in :numref:`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 :numref:`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 SASSYS/SAS4A. In the interfaced mode,
SASSYS/SAS4A 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 :numref:`section-11.4`.