1. Reference problem#

1.1. 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.

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

1.2. Material properties#

1.2.1. 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:

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

1.2.2. 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:

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

1.2.3. 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:

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.

1.2.4. 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:

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

1.2.5. 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:

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.

1.2.6. 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:

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

1.2.7. 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:

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, E5b*2
D	1.e-5
d_lat
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 \({\epsilon }_{\mathit{zz}}\).

1.2.8. 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:

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, E5b*2
D	1.e-5
d_lat
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

1.2.9. 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:

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, E5b*2
D	1.e-5
d_lat
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