Reference problem ===================== Geometry --------- Material point. Properties of monocrystalline materials for modeling A ---------------------------------------------------------------- +----------------------+-----------------------------------------------------------------------------------------------------------------------+ |Elastic behavior with:|Young's module: | + + + | | | + + .. image:: images/Object_2.svg + | | :width: 114 | + + :height: 21 + | | | + + + | | | + + + | | | +----------------------+-----------------------------------------------------------------------------------------------------------------------+ | |Poisson's ratio: | + + + | | | + + .. image:: images/Object_3.svg + | | :width: 114 | + + :height: 21 + | | | + + + | | | + + + | | | +----------------------+-----------------------------------------------------------------------------------------------------------------------+ **Behavior** **mono-crystalline, with BCC24 sliding system.** Type of flow: **MONO_VISC1** whose parameters are: :math:`n=12`, :math:`K=15\mathit{MPa}` Isotropic work hardening type: **MONO_ISOT1** ** whose parameters are: .. image:: images/Object_5.svg :width: 114 :height: 21 .. _RefImage_Object_5.svg: .. image:: images/Object_6.svg :width: 114 :height: 21 .. _RefImage_Object_6.svg: .. image:: images/Object_7.svg :width: 114 :height: 21 .. _RefImage_Object_7.svg: :math:`\text{H1}=0.1,\text{H2}=0.7,\text{H3=H4}=0.1` (interaction between sliding systems) No kinematic work hardening: :math:`C=d=0` Properties of monocrystalline materials for B modeling ---------------------------------------------------------------- .. csv-table:: "Young's module: :math:`E=(236-\mathrm{0,0459}T)\text{GPa}` Poisson's Ratio :math:`\nu =0.35`" ":math:`\text{TEMP}=183K` :math:`\text{D\_LAT}=\mathrm{0,01}` :math:`\text{K\_BOLTZ}=8.62{10}^{\text{-5}}` :math:`\text{GAMMA0}={10}^{\text{-6}}{s}^{\text{-1}}` :math:`\text{TAU\_0}=363\text{MPa}` :math:`\text{TAU\_F}=0` :math:`\text{RHO\_MOB}={10}^{\text{6}}{\text{mm}}^{\text{-2}}` :math:`\text{K\_F}=75\text{K\_SELF}=100` :math:`\text{B}=2.48{10}^{\text{-7}}\text{mm}` :math:`\text{N}=50` :math:`\text{DELTAG0}=0.84` :math:`\text{D}={10}^{\text{-5}}\text{mm}` :math:`\text{GH}={10}^{\text{11}}`, :math:`\text{Y\_AT}=2{10}^{\text{-6}}\text{mm}` :math:`\text{RHO\_IRRA}=1.e8`, :math:`\text{a\_irr}=\mathrm{0,1}` The internal variables representing the dislocation density are initialized to :math:`{\rho }_{0}={\mathrm{13,10}}^{\text{6}}{\mathit{mm}}^{\text{-2}}`," The interaction matrix is constructed in both cases from the following values :math:`\text{H1}=0.1024,\text{H2}=0.7,\text{H3=H4=H5=H6}=0.1` The family of sliding systems is cubic (:math:`\text{CC}`). Properties of homogenized polycrystal -------------------------------------- **Behavior** POLYCRISTAL **homogenized (BZ method) with 30 phases, whose orientations are defined by:** .. code-block:: text COMPORP = DEFI_COMPOR (POLYCRISTAL =( _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 84.0,349.0,233.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 348.0,24.0,172.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 327.0,126.0,335.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 235.0,7.0,184.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 72.0,338.0,73.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 136.0,285.0,103.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 96.0,128.0,46.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 253.0,265.0,288.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 329.0,184.0,274.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 164.0,169.0,107.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 220.0,26.0,179.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 79.0,14.0,203.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 251.0,342.0,329.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 226.0,217.0,337.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 51.0,290.0,315.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 124.0,67.0,241.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 228.0,163.0,9.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 274.0,56.0,275.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 203.0,25.0,99.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 118.0,190.0,269.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 225.0,50.0,295.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 45.0,129.0,310.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 248.0,21.0,292.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 218.0,247.0,150.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 196.0,299.0,81.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 152.0,64.0,148.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 33.0,292.0,311.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 43.0,207.0,8.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 318.0,51.0,34.0,),), _F (MONOCRISTAL = COMPORT, FRAC_VOL =0.033333, ANGL_REP =( 58.0,169.0,224.0,),),), LOCALISATION ='BZ', MU_LOCA =mu); Boundary conditions and loads ------------------------------------- +------------------------+---------------------------------------------------------------------------------------------------------+ | - Face :math:`z=0` |: | + + + | | | + + .. image:: images/Object_10.svg + | | :width: 114 | + + :height: 21 + | | | + + + | | | + + + | | | +------------------------+---------------------------------------------------------------------------------------------------------+ | - Face :math:`y=0` |: | + + + | | | + + .. image:: images/Object_11.svg + | | :width: 114 | + + :height: 21 + | | | + + + | | | + + + | | | +------------------------+---------------------------------------------------------------------------------------------------------+ | - Face :math:`x=0` |: | + + + | | | + + .. image:: images/Object_12.svg + | | :width: 114 | + + :height: 21 + | | | + + + | | | + + + | | | +------------------------+---------------------------------------------------------------------------------------------------------+ | - Face :math:`z=1` |: | + + + | | | + + .. image:: images/Object_13.svg + | | :width: 114 | + + :height: 21 + | | | + + + | | | + + + | | | +------------------------+---------------------------------------------------------------------------------------------------------+ The load .. image:: images/Object_14.svg :width: 114 :height: 21 .. _RefImage_Object_14.svg: is increasing linearly from 0 for :math:`t=0` to .. image:: images/Object_15.svg :width: 114 :height: 21 .. _RefImage_Object_15.svg: To reduce the calculation time, this one is carried up to :math:`t=20s`, i.e. an imposed deformation of :math:`\text{2 \%}`, in 2000 increments.