B modeling
==============




Characteristics of modeling
-----------------------------------

We use a AXIS model.

In this case, the coefficient :math:`{K}_{D}` is chosen depending on the temperature and on :math:`{\sigma }_{0}`.


.. csv-table::

    "T (°C)", "0 MPa ", "100 MPa ", "200 ", "200 MPa"
    "900", "14,355", "14,855", "15,355"
    "1000", "14.5", "15", "15.5"
    "1025", "14.5363", "15.0363", "15.5363", "15.5363"
    "1050", "14.5725", "15.0725", "15.5725", "15.5725"


**Table** 4.1-1 **: K_D of B** modeling

The discretization in time is quite fine:


.. code-block:: text

    (JUSQU_A = 2, NOMBRE = 10),

    (JUSQU_A = 2., NOMBRE = 10),

    (JUSQU_A = 20., NOMBRE = 10),

    (JUSQU_A = 200., NOMBRE = 10),

    (JUSQU_A = 2000., NOMBRE = 10),

    (JUSQU_A = 20000., NOMBRE = 10),

    (JUSQU_A = 200,000., NOMBRE = 10),

    (JUSQU_A = 1000000., NOMBRE = 30),

    (JUSQU_A = 1600000., NOMBRE = 30),

    (JUSQU_A = 1700000., NOMBRE = 40),

    (JUSQU_A = 1800000., NOMBRE = 40),

    (JUSQU_A = 1900000., NOMBRE = 40),

    (JUSQU_A = 2000000., NOMBRE = 40),

    (JUSQU_A = 2100000., NOMBRE = 40),

    (JUSQU_A = 2200000., NOMBRE = 40),

    (JUSQU_A = 2300000., NOMBRE = 40),

    (JUSQU_A = 2400000., NOMBRE = 40),

    (JUSQU_A = 2500000., NOMBRE = 40),




Characteristics of the mesh
----------------------------

It is chosen to represent the cylindrical test piece by a quadrangle with 8 knots in axisymmetry.

Number of knots: 8

Number of stitches: 1 (QUAD8)


.. image:: images/10000201000001BD0000022CAEC440B46B4E3C28.png
    :width: 2.3744in
    :height: 2.0681in


.. _RefImage_10000201000001BD0000022CAEC440B46B4E3C28.png:

Image 4.2-1: Modeling B mesh



Tested sizes and results
------------------------------

Evolution of the constraint, :math:`{\sigma }_{0}`, as a function of time. This value is tested at various times:


.. csv-table::

    "**Instant**", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "1000000", "'ANALYTIQUE'", "75.97849999999999997", "0.5"
    "1600000", "'ANALYTIQUE'", "55.54209999999999998", "10.0"


**Table** 4.3-1 **: B** modeling results**

Evolution of the damage variable, :math:`D` as a function of time. This value is tested at various times depending on the modeling:


.. csv-table::

    "**Instant**", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "1000000", "'ANALYTIQUE'", "0.110134", "1.0"
    "1600000", "'ANALYTIQUE'", "0.28131600000000001", "10.0"


**Table** 4.3-2 **: B modeling results**

Evolution of the viscoplastic isotropic work hardening variable, :math:`r`, as a function of time. This value is tested at various times:


.. csv-table::

    "**Instant**", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "1000000", "'ANALYTIQUE'", "2.747799999999999999E-3", "0.5"
    "1600000", "'ANALYTIQUE'", "2.79276E-3", "0.5"


**Table** 4.3-3 **: B modeling results**

Evolution of the viscoplastic isotropic work hardening variable, :math:`p`, as a function of time. This value is tested at various times:


.. csv-table::

    "**Instant**", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    "1000000", "'ANALYTIQUE'", "2.7607899999999999E-3", "0.5"
    "1600000", "'ANALYTIQUE'", "2.814779999999999998E-3", "0.5"


**Table** 4.3-4 **: B** modeling results**