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


Geometry
---------

The geometry of the C modeling is that of a 10-grain aggregate generated by a Python procedure based on Voronoi cells. Edge cutting planes are defined to impose boundary conditions.


.. image:: images/10000000000004F90000027712DF9B4A647D3410.png
    :width: 6.2043in
    :height: 3.0563in


.. _RefImage_10000000000004F90000027712DF9B4A647D3410.png:

The other models are carried out on hardware points (SIMU_POINT_MAT).


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


Modeling B: single crystal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the single-crystal elasto-visco-plastic model with implicit integration, by comparison with model MONOCRISTAL on a hardware point.

The material coefficients are:


.. csv-table::

    "E", "208000"
    "NAKED", "0.3"
    "G", "80000"
    "N", "10"
    "K", "25"
    "C", "14363"
    "R_0", "66,62"
    "Q", "11,43"
    "B", "2,1"
    "D", "494"


The Mfront files defining the behavior are:

MonoCrystal_ CFC .mfront


C modeling: single crystal on an aggregate of 10 grains
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the single-crystal elasto-visco-plastic model with implicit integration, and complete definition of the family of sliding systems and the interaction matrix, compared to model MONOCRISTAL on a 10-grain aggregate.

The material coefficients are:


.. csv-table::

    "E", "210000"
    "NAKED", "0.3"
    "G", "80769.23"
    "N", "12"
    "K", "5"
    "C", "0"
    "R_0", "250"
    "Q", "55"
    "B", "12"
    "D", "0"


The Mfront files defining the behavior are:

MonoCrystal_ CFC .mfront


Modeling D: polycrystal homogenized on 30 grains
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the polycrystalline elasto-visco-plastic model with explicit integration, by comparison with model POLYCRISTAL on a hardware point with 30 grains. The material coefficients are:


.. csv-table::

    "E", "145200"
    "NAKED", "0.3"
    "G", "55846.15"
    "N", "10"
    "K", "40"
    "C", "0"
    "R_0", "75.5"
    "Q", "9.77"
    "B", "19.34"
    "D", "0"


The Mfront files defining the behavior are:

Polycrystal_mc.mfront

Polycrystal_Orientation.mfront

The "Polycrystal_Orientation.mfront" file defines 30 Euler angle triplets in degrees.


E modeling: single crystal DD_CFC
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the monocrystalline model DD_CFC on a hardware point, in comparison with MONO_DD_CFC. The material coefficients are:


.. csv-table::

    "E", "208000"
    "NAKED", "0.3"
    "G", "80000"
    "TAU_F ", "105"
    "Y", "2.5E-7"
    "N", "5"
    "GAMMA_0 ", "1.E-3"
    "A", "0.13"
    "B", "0.005"
    "RHOREF ", "1.E6"
    "ALPHA ", "0.35"
    "BETA ", "2,54E-7"
    "G", "80000"


The initial dislocation density is 1.E6. The analytical solution is contained in the file mfron03e.30. The Mfront files defining the behavior are:

MonoCrystal DDCFC .mfront

MonoCrystal_ DD_CFC_InteractionMatrix .mfront


F modeling: homogenized polycrystal of type DD_CFC on 30 grains
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the homogenized polycrystalline model DD_CFC on a hardware point with 30 grains, in comparison with POLYCRISTAL. The material coefficients are:


.. csv-table::

    "E", "208000"
    "NAKED", "0.3"
    "G", "80000"
    "TAU_F ", "80"
    "Y", "2.5E-7"
    "N", "20"
    "GAMMA_0 ", "1.E-3"
    "A", "0.13"
    "B", "0.005"
    "RHOREF ", "1.E6"
    "ALPHA ", "0.35"
    "BETA ", "2,54E-7"
    "G", "80000"


The initial dislocation density is 1.E5. The Mfront files defining the behavior are:

PolyCrystal DDCFC .mfront

MonoCrystal_ DD_CFC_InteractionMatrix .mfront

The "Polycrystal_Orientation.mfront" file defines 30 Euler angle triplets in degrees.


G modeling: single crystal DD_CFC_IRRA
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the model DD_CFC_IRRA on a hardware point, in comparison with the behavior MONO_DD_CFC_IRRA. The material coefficients are:


.. csv-table::

    "E", "208000"
    "NAKED", "0.3"
    "G", "80000"
    "TAU_F ", "80"
    "Y", "2.5E-7"
    "N", "20"
    "GAMMA_0 ", "1.E-3"
    "A", "0.13"
    "B", "0.005"
    "RHOREF ", "1.E6"
    "ALPHA ", "0.35"
    "BETA ", "2,54E-7"
    "G", "80000"
    "ome_void", "1000,"
    "PHI_LOOP ", "5,9E-6"
    "ALP_VOID ", "0"
    "ALP_LOOP ", "0,1"
    "ome_sat", "0"
    "PHI_SAT ", "4, E-2"
    "XI_IRRA ", "10"
    "DZ_IRRA ", "1, E7"


The initial internal variables are:

RHO_0 =1, E5

RHO_LOOPS =7, 4E13

PHI_VOIDS =1.e-3

The Mfront files defining the behavior are:

Mono DDCFC_Irra .mfront

MonoCrystal_ DD_CFC_InteractionMatrix .mfront


H modeling: single crystal DD_CC
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the DD_CCsur model at a hardware point, by comparison with the MONO_DD_CC behavior of the ssnd110b test. The material coefficients are:


.. csv-table::

    "E (GPa)", "236-0.0459* TEMP"
    "NAKED", "0.35"
    "G", "80000"
    "B", "2,48e-7"
    "GH", "1.e11"
    "DeltaG0", "0.84"
    "TAU_0 (MPa)", "363"
    "TAU_F ", "0"
    "gamma0", "1, e-6"
    "n", "50"
    "rho_ini", "1, E5*b**2"
    "D", "1.e-5"
    "d_lat", "1000."
    "y_at", "2.e-6"
    "K_f", "30,"
    "K_self", "100"
    "k_boltz", "8.62E-5"
    "epsi_1", "3e-4"
    "G", "80000"
    "a_self", "0.1024"
    "a_coli", "0.7"
    "a_ncol", "0,1"


The simulation temperature is 50 K.

The initial dislocation density is 1.E5 (multiplied by BETA **2).

The Mfront files defining the behavior are:

MonoCrystal DDCC .mfront

MonoCrystal_ DD_CC_InteractionMatrix .mfront

MonoCrystal_ DD_CC_SlidingSystems .mfront

The monocrystal is defined according to the -1,4,9 orientation. It is subject to an imposed deformation :math:`{\epsilon }_{\mathit{zz}}`.


Modeling I: single crystal DD_CC_IRRA
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate model DD_CC_IRRA on a hardware point, by comparison with the MONO_DD_CC_IRRA behavior of the ssnd110d test. The material coefficients are:


.. csv-table::

    "E (GPa)", "236-0.0459* TEMP"
    "NAKED", "0.35"
    "G", "80000"
    "B", "2,48e-7"
    "GH", "1.e11"
    "DeltaG0", "0.84"
    "TAU_0 (MPa)", "363"
    "TAU_F ", "20"
    "gamma0", "1, e-3"
    "n", "20"
    "rho_ini", "1, E5*b**2"
    "D", "1.e-5"
    "d_lat", "1000."
    "y_at", "1.e-6"
    "K_f", "30,"
    "K_self", "100"
    "k_boltz", "8.62E-5"
    "epsi_1", "1e-5"
    "G", "80000"
    "a_irr", "0.3"
    "xi_irr", "4"
    "a_self", "0.1024"
    "a_coli", "0.7"
    "a_ncol", "0,1"


The simulation temperature is 250 K.

The monocrystal is subjected to a tensile force imposed according to the orientation 1,5,9

The initial dislocation density is 1.E5 (multiplied by BETA **2). The Mfront files defining the behavior are:

Mono DDCC_Irra .mfront

MonoCrystal_ DD_CC_InteractionMatrix .mfront

MonoCrystal_ DD_CC_SlidingSystems .mfront

K modeling: homogenized polycrystal DD_CC
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This modeling makes it possible to validate the homogenized polycrystalline model DD_CCsur a hardware point with 30 grains, by comparison with the POLYCRISTALdu ssnv194D test behavior. The material coefficients are:


.. csv-table::

    "E (GPa)", "236-0.0459* TEMP"
    "NAKED", "0.35"
    "G", "80000"
    "B", "2,48e-7"
    "GH", "1.e11"
    "DeltaG0", "0.84"
    "TAU_0 (MPa)", "363"
    "TAU_F ", "0"
    "gamma0", "1, e-6"
    "n", "50"
    "rho_ini", "1, E5*b**2"
    "D", "1.e-5"
    "d_lat", "1000."
    "y_at", "2.e-6"
    "K_f", "30,"
    "K_self", "100"
    "k_boltz", "8.62E-5"
    "epsi_1", "3e-4"
    "G", "80000"
    "a_self", "0.1024"
    "a_coli", "0.7"
    "a_ncol", "0,1"


The Mfront files defining the behavior are:

PolyCrystal DDCC .mfront

PolyCrystal_ DD_CC_SlidingSystems .mfront

MonoCrystal_ DD_CC_InteractionMatrix .mfront