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


Geometry
---------


.. image:: images/10000000000006D00000045D038EA9C41E28FA82.png
    :width: 5.8193in
    :height: 3.722in


.. _RefImage_10000000000006D00000045D038EA9C41E28FA82.png:

The test piece in the shape of a diabolo, represented in (a), is fixed to the loading system (b) by six pins equivalent to joints.

The dimensions of the pieces are expressed in mm.

**Test tube:**


.. csv-table::

    "thickness :math:`B` variable", ":math:`\mathrm{6,36};\mathrm{6,39};\mathrm{6,44}\mathrm{mm}`"
    "overall width", ":math:`98\mathrm{mm}`"
    "distance between pin axes", ":math:`74\mathrm{mm}`"
    "width of the central part", ":math:`6\mathrm{mm}`"
    "overall height", ":math:`84\mathrm{mm}`"
    "distance between pin centers", ":math:`31\mathrm{mm}`"
    "center height :math:`W` "," :math:`30\mathrm{mm}`"
    "crack length :math:`a` "," :math:`\mathrm{15,}18` or :math:`21\mathrm{mm}`"
    "ligament :math:`b=W-a` "," :math:`\mathrm{15,}12` or :math:`9\mathrm{mm}`"
    "pin hole diameter", ":math:`8\mathrm{mm}`"


**Test tube holder:**


.. csv-table::

    "thickness", ":math:`25\mathrm{mm}`"
    "outside diameter", ":math:`190\mathrm{mm}`"
    "distance between the center of the room and the centers of the circular recesses", ":math:`\mathrm{40,3}\mathrm{mm}`"
    "radius of the recesses", ":math:`20\mathrm{mm}`"
    "diameter of the 2 holes where the loads are applied", ":math:`10\mathrm{mm}`"


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

**Test tube:**

The material is elastoplastic, of the Von Mises type, with isotropic work hardening, defined by a uniaxial tension curve.

Young's module: :math:`E=\mathrm{74,2}\mathrm{GPa}`

Poisson's ratio: :math:`\nu =\mathrm{0,32}`


.. csv-table::

    ":math:`E` tangent
    (:math:`\mathrm{GPa}`)", ":math:`\sigma ` uniaxial)
    (:math:`\mathrm{MPa}`)", ":math:`{\varepsilon }_{T}` uniaxial)
    (:math:`\text{\%}`)"
    "72.74", "334.6", "0.46"
    "50.69", "410.7", "0.61"
    "15.00", "431.6", "0.75"
    "4.75", "443.5", "1.00"
    "1.82", "480.0", "3.00"
    "0.80", "500.1", "5.50"
    "0.0017", "505.2", "300.0"


**Test tube holder:**

The material is isotropic linear elastic.

Young's module: :math:`E=206\mathrm{GPa}`

Poisson's ratio: :math:`\nu =\mathrm{0,3}`


Boundary conditions and loading
------------------------------------


.. image:: images/1000000000000610000006829FF771F8573396BC.png
    :width: 3.6173in
    :height: 3.9854in


.. _RefImage_1000000000000610000006829FF771F8573396BC.png:

The specimen holder has a fixed point :math:`\mathrm{UX}=\mathrm{UY}=0` at the lower attachment hole and is subject to a vertical point loading applied to the variable upper attachment hole :math:`\mathrm{UX}=0`, :math:`\mathrm{FY}=P`.

For crack length :math:`a/W=\mathrm{0,5}`:

:math:`P` varies from:

:math:`0N` to :math:`11772N` in 12 steps from :math:`981N`

:math:`11772N` to :math:`19620N` in 16 steps from :math:`\mathrm{490,5}N`

:math:`19620N` to :math:`23544N` in 20 steps from :math:`\mathrm{196,2}N`

:math:`23544N` to :math:`25114N` in 16 steps from :math:`\mathrm{98,1}N`