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


.. _Ref482175678:


Geometry
---------

Each test is carried out on a smooth cylindrical test piece. For obvious reasons of symmetries, an axisymmetric 2D modeling of a quarter of the structure is sufficient.


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    :height: 4.4374in


.. _RefImage_10000000000002AB000001BC1F39A487FF1FBC28.png:


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

The behavior of the material studied is described by a Von Mises elasto-plastic law with linear isotropic work hardening, 'VMIS_ISOT_LINE'. The deformations used in the behavior relationship are linearized deformations.


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    :width: 249
    :height: 182


.. _RefImage_1000214E000069BB00004D4F16B6534DE5FFFC59.svg:

Poisson's ratio does not depend on temperature, :math:`\nu =\mathrm{0,3}`.

The values of the Young's modulus :math:`E`, the tangent modulus :math:`{E}_{t}` and the elastic limit are given in the following table:


.. csv-table::

    "**Temperature** :math:`[°C]` ", "**—150**", "**—100**", "**—50**", "**—50**"
    ":math:`E[\mathrm{MPa}]` ", "200000", "200000", "200000"
    ":math:`\mathrm{Et}[\mathrm{MPa}]` ", "2000", "2000", "2000"
    ":math:`{\sigma }_{Y}[\mathrm{MPa}]` ", "750", "700", "700", "650"



Boundary conditions and loads
-------------------------------------

With reference to the figure in §1.1, the limit and load conditions are as follows:

On segment :math:`\mathrm{BC}` (:math:`Y={L}_{0}`), displacement imposed in the direction :math:`\mathrm{OY}`:


+-------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|:math:`T[°C]`|**Displacement (** :math:`l-{l}_{0}` **) at break for a reference length** :math:`{l}_{0}` **of** :math:`203.5\mathrm{mm}` :math:`[\mathrm{mm}]` The results for each temperature are in ascending order                                                                                    |
+-------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|**-50**      |10.68                                                                                                                                                                                                   |28.78|30.31|31.66|32,53|33,90|34.38|35.82|36.69|37.09|37.37|37.49|38.45|39.77|44,39|
+-------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|**-100**     |20,57                                                                                                                                                                                                   |21.68|23,32|24,37|24.66|25.59|25.84|27.51|28.44|29.30|29.68|30.16|30.18|30,20|30.95|
+-------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|**-150**     |11.33                                                                                                                                                                                                   |14.70|14.79|14.90|18.62|18.87|19.00|19.37|19.61|20,07|21,19|22.79|23,28|24.17|24,41|
+-------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

On segment :math:`\mathrm{OA}` (:math:`Y=0`) blocked movements following the direction :math:`\mathrm{OY}`.

On segment :math:`\mathrm{OB}` (:math:`X=0`) blocked movements following the direction :math:`\mathrm{OX}`.


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

Zero stresses and deformations.