Reference problem
=====================


Geometry
---------

The geometry studied is a parallelepipedic plate 200 mm long, 60 mm wide and 7 mm thick.


.. image:: images/1000069E0000307900001DDE4B9F7E68CFCCA135.svg
    :width: 483
    :height: 297


.. _RefImage_1000069E0000307900001DDE4B9F7E68CFCCA135.svg:


.. csv-table::

    "Specimen thickness", "Width of
    The test tube", "Length of
    The test tube"
    ":math:`7\mathrm{mm}` "," :math:`60\mathrm{mm}` "," :math:`200\mathrm{mm}`"



Material properties
----------------------

The material under consideration is a forged austenitic stainless steel of type 316L (Z2 CND17 -12).

For non-linear thermal modeling, thermal conductivity and the product (density, density, heat capacity :math:`\rho c`) vary as a function of temperature. Their values are given in the table below:


.. csv-table::

    ":math:`T`
    Temperature (:math:`°C`)", ":math:`\lambda`
    Thermal conductivity
    (:math:`W/(\mathrm{mm}°C)`)", ":math:`\rho c`
    (:math:`J/{\mathrm{mm}}^{3}°C`)", ":math:`\beta`
    Enthalpy
    (:math:`J/{\mathrm{mm}}^{3}`)"
    "20", "14.0 E-3", "36.00 E-4", "0.0"
    "50", "14.4 E-3", "", ""
    "100", "15.2 E-3", "39.05 E-4", ""
    "150", "15.8 E-3", "", ""
    "200", "16.6 E-3", "41.63 E-4", ""
    "250", "17.3 E-3", "", ""
    "300", "17.9 E-3", "43.00 E-4", ""
    "350", "18.6 E-3", "", ""
    "400", "19.2 E-3", "43.90 E-4", ""
    "450", "19.9 E-3", "", ""
    "500", "20.6 E-3", "44.50 E-4", ""
    "550", "21.2-3", "", ""
    "600", "21.8 E-3", "44.95 E-4", ""
    "650", "22.4 E-3", "", ""
    "700", "23.1 E-3", "45.80 E-4", "2.979"
    "750", "23.7 E-3", "", ""
    "800", "24.3 E-3", "47.80 E-4", ""
    "900", "26.0 E-3", "49.00 E-4", ""
    "1000", "27.3 E-3", "49.90 E-4", ""
    "1200", "29.9 E-3", "50.40 E-4", ""
    "1370", "32.2 E-3", "50.40 E-4", "6.232"
    "1400", "48.9 E-3", "50.40 E-4", "8.184"
    "1450", "", "", "8.444"



.. image:: images/1000020100000218000001961DD38BEF53D8BA7C.png
    :width: 5.5937in
    :height: 4.2398in


.. _RefImage_1000020100000218000001961DD38BEF53D8BA7C.png:


.. image:: images/10000201000001E7000001882877297CCF18A9DE.png
    :width: 5.0835in
    :height: 4.0937in


.. _RefImage_10000201000001E7000001882877297CCF18A9DE.png:


.. image:: images/10000201000001E70000018868EFFABC0E317DF0.png
    :width: 5.0835in
    :height: 4.0937in


.. _RefImage_10000201000001E70000018868EFFABC0E317DF0.png:


Boundary conditions
----------------------

The welding parameters are shown in the table below:


.. csv-table::

    ":math:`I`
    (Intensity)", ":math:`U`
    (Voltage)", ":math:`V`
    (Workpiece speed)", "Electrode diameter"
    ":math:`\mathrm{200A}` "," :math:`\mathrm{13V}` "," :math:`14\mathrm{cm}/\mathrm{min}` "," :math:`3\mathrm{mm}`"


The upper surface of the plate is subjected to the action of a torch. This torch is placed in the center of the plate, :math:`15\mathrm{mm}` from the edge, and moves parallel to its length at a constant speed (:math:`\mathrm{14cm}/\mathrm{min}`) up to :math:`\mathrm{85.5mm}` from the edge corresponding to the flashlight's off position.


Initial conditions
--------------------

None.