1. Reference problem#

1.1. Geometry#

Material point.

1.2. Properties of monocrystalline materials for modeling A#

Elastic behavior with:

Young’s module:

_images/Object_2.svg

Poisson’s ratio:

_images/Object_3.svg

Behavior mono-crystalline, with BCC24 sliding system.

Type of flow: MONO_VISC1 whose parameters are:

\(n=12\), \(K=15\mathit{MPa}\)

Isotropic work hardening type: MONO_ISOT1 ** whose parameters are:

_images/Object_5.svg _images/Object_6.svg _images/Object_7.svg

\(\text{H1}=0.1,\text{H2}=0.7,\text{H3=H4}=0.1\) (interaction between sliding systems)

No kinematic work hardening: \(C=d=0\)

1.3. Properties of monocrystalline materials for B modeling#

Young’s module: \(E=(236-\mathrm{0,0459}T)\text{GPa}\) Poisson’s Ratio \(\nu =0.35\)

\(\text{TEMP}=183K\) \(\text{D\_LAT}=\mathrm{0,01}\) \(\text{K\_BOLTZ}=8.62{10}^{\text{-5}}\) \(\text{GAMMA0}={10}^{\text{-6}}{s}^{\text{-1}}\) \(\text{TAU\_0}=363\text{MPa}\) \(\text{TAU\_F}=0\) \(\text{RHO\_MOB}={10}^{\text{6}}{\text{mm}}^{\text{-2}}\) \(\text{K\_F}=75\text{K\_SELF}=100\) \(\text{B}=2.48{10}^{\text{-7}}\text{mm}\) \(\text{N}=50\) \(\text{DELTAG0}=0.84\) \(\text{D}={10}^{\text{-5}}\text{mm}\) \(\text{GH}={10}^{\text{11}}\), \(\text{Y\_AT}=2{10}^{\text{-6}}\text{mm}\) \(\text{RHO\_IRRA}=1.e8\), \(\text{a\_irr}=\mathrm{0,1}\) The internal variables representing the dislocation density are initialized to \({\rho }_{0}={\mathrm{13,10}}^{\text{6}}{\mathit{mm}}^{\text{-2}}\),

The interaction matrix is constructed in both cases from the following values

\(\text{H1}=0.1024,\text{H2}=0.7,\text{H3=H4=H5=H6}=0.1\)

The family of sliding systems is cubic (\(\text{CC}\)).

1.4. Properties of homogenized polycrystal#

Behavior POLYCRISTAL homogenized (BZ method) with 30 phases, whose orientations are defined by:

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);

1.5. Boundary conditions and loads#

  • Face \(z=0\)

:

_images/Object_10.svg
  • Face \(y=0\)

:

_images/Object_11.svg
  • Face \(x=0\)

:

_images/Object_12.svg
  • Face \(z=1\)

:

_images/Object_13.svg

The load

_images/Object_14.svg

is increasing linearly from 0 for \(t=0\) to

_images/Object_15.svg

To reduce the calculation time, this one is carried up to \(t=20s\), i.e. an imposed deformation of \(\text{2 \%}\), in 2000 increments.