E modeling
==============

Behavioral law and material parameters
-------------------------------------------

The law of behavior tested 'LEMAITRE_IRRA', is documented in doc R5.03.08. This is a law of creep and enlargement behavior under irradiation for fuel assemblies. Values of the parameters used:


.. csv-table::

    "Settings", ":math:`T=0°C` "," :math:`T=500°C`"
    ":math:`E(T)` "," :math:`2.E5\mathit{MPa}` "," :math:`1.E5\mathit{MPa}`"
    ":math:`\nu (T)` "," :math:`0.` "," :math:`0.`"
    ":math:`\alpha (T)` "," :math:`1.E-5{K}^{-1}` "," :math:`2.E\mathrm{-}5{K}^{\mathrm{-}1}`"
    ":math:`N(T)` "," :math:`2.3364` "," :math:`2.3364`"
    ":math:`1\mathrm{/}K(T)` "," :math:`1.E-6{(\mathit{MPa})}^{-1}` "," :math:`1.E-6{(\mathit{MPa})}^{-1}`"
    ":math:`1\mathrm{/}M(T)` "," :math:`0.207060772` "," :math:`0.207060772`"
    ":math:`L` "," :math:`0.` "," :math:`0.`"
    ":math:`{\mathit{PHI}}_{}\mathit{ZERO}` ", "4.240281E+21", "4.240281E+21"
    ":math:`\mathit{BETA}` "," :math:`1.2` "," :math:`1.2`"
    ":math:`{\mathit{QSR}}_{K}` "," :math:`3321.093` "," :math:`3321.093`"


Finally, the last parameter GRAN_FO depends on both the temperature and the irradiation:

:math:`{\mathit{GRAN}}_{\mathit{FO}}(T,\mathit{IRRA})=(1.51E-14T+1.542E-11){\mathit{IRRA}}^{0.396}`

The irradiation values as a function of the times are as follows:


.. csv-table::

    "INST "," IRRA"
    ":math:`0` "," :math:`0`"
    ":math:`0.5` "," :math:`0`"
    ":math:`1` "," :math:`2`"



Results
---------


.. csv-table::

    "Result at order number :math:`i` ", "Name of the tested parameter", "Name of the tested parameter", "Reference type", "tolerance"
    "RESU_19 "," VMIS (MPa)", "AUTRE_ASTER ", "1000"," 0.10%"
    "RESU_19 "," TRACE (MPa)", "AUTRE_ASTER "," -1000", "0.10%"