Reference problem ===================== Geometry --------- .. image:: images/10000000000003E40000023E33C23B395C20F98C.png :width: 3.5661in :height: 2.4772in .. _RefImage_10000000000003E40000023E33C23B395C20F98C.png: A material point is defined, represented in the modeling A (:math:`\mathrm{3D}`) by a volume element :math:`\mathrm{MA1}`, containing the nodes :math:`\mathrm{P1}`, :math:`\mathrm{P2}`, :math:`\mathrm{P3}`, :math:`\mathrm{P4}`, :math:`\mathrm{P5}`, :math:`\mathrm{P6}`,,,, :math:`\mathrm{P7}` and :math:`\mathit{P8}`. Material properties ----------------------- .. csv-table:: "Elastic behavior with:", "Young's modulus: :math:`E\mathrm{=}145200\mathit{MPa}`" "", "Poisson's ratio: :math:`\nu \mathrm{=}0.3`" Benchmark calculation: behavior VISC_CIN1_CHAB ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is the reference solution used in models A and B. The material parameters are: CIN1_CHAB =_F (R_0=75.5 MPa R_I=85.27 MPa B=19.34, C_I=10.0 MPa K=1.0, W=0.0, G_0=36.68, A_I=1.0,), LEMAITRE =_F (N=10.0, UN_SUR_K =0.025 Mpa-1 UN_SUR_M =0.0,), Monocrystalline behavior type 1, with sliding system UNIAXIAL ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The parameters used here, in uniaxial, correspond to those used for VISC_CIN1_CHAB, just noting that :math:`Q\mathrm{=}{R}_{I}\mathrm{-}{R}_{0}`. So we need to get the same results as VISC_CIN1_CHAB. These behaviors are tested in :math:`\mathrm{3D}` (in modeling A) and in :math:`\mathrm{2D}` plane constraints (in modeling B). *Type of flow:** MONO_VISC1 **** whose parameters are: :math:`c\mathrm{=}10\mathit{MPa}`, :math:`n\mathrm{=}10`, :math:`K\mathrm{=}40\mathit{MPa}` *Isotropic work hardening type:** MONO_ISOT1 **** whose parameters are: :math:`{R}_{0}\mathrm{=}75.5\mathit{MPa}` :math:`b\mathrm{=}19.34` :math:`Q\mathrm{=}9.77\mathit{MPa}` :math:`h\mathrm{=}0` *Kinematic work hardening type:** MONO_CINE1 **** whose parameters are: :math:`d\mathrm{=}36.68` The family of sliding systems is: **UNIAXIAL** Two calculations are performed: one with implicit local integration, the other with explicit local integration. It is verified that these two calculations provide identical results (with the exception of time discretization). Monocrystalline type 2 behavior, comparable to type 1, with sliding system UNIAXIAL ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ The behavior of the mono-crystal is defined in such a way that one comes back to the behavior of type 1. So the results should match. The settings are: *Type of flow:** MONO_VISC2 **** whose parameters are: :math:`n\mathrm{=}10`, :math:`k=40\mathrm{MPa}`, :math:`c=10\mathrm{MPa}`, :math:`d=0`, :math:`a=0` *Isotropic work hardening type:** MONO_ISOT2 **** whose parameters are: :math:`{R}_{0}=75.5` :math:`{b}_{1}=19.34` :math:`{b}_{2}=0` :math:`{Q}_{1}=9.77\mathrm{MPa}` :math:`{Q}_{2}=0` *Kinematic work hardening type:** MONO_CINE2 **** whose parameters are: :math:`d=36.68` :math:`M=0` :math:`m=0` :math:`c=0` The family of sliding systems is: **UNIAXIAL** Two calculations are performed: one with implicit local integration, the other with explicit local integration. It is verified that these two calculations provide results identical to those of monocrystalline type 1 behavior. Monocrystalline type 2 behavior, complete test ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The parameters of the behavior of the mono-crystal of type 2 are all non-zero: *Type of flow:** MONO_VISC2 **** whose parameters are: :math:`n\mathrm{=}10`, :math:`k\mathrm{=}40\mathit{MPa}`, :math:`c\mathrm{=}10\mathit{MPa}`, :math:`d=0.1`, :math:`a=0.5` *Isotropic work hardening type:** MONO_ISOT2 **** whose parameters are: :math:`{R}_{0}\mathrm{=}75.5` :math:`{b}_{1}\mathrm{=}19.34` :math:`{b}_{2}=10` :math:`{Q}_{1}\mathrm{=}9.77\mathit{MPa}` :math:`{Q}_{2}=10` *Kinematic work hardening type:** MONO_CINE2 **** whose parameters are: :math:`d\mathrm{=}36.68` :math:`M=10` :math:`m=\mathrm{0,1}` :math:`c=10` The family of sliding systems is: **UNIAXIAL .** The tests are non-regression. Calculation with single-crystal type 1 behavior and orthotropic elasticity ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The orthotropy parameters in fact correspond to isotropy: .. code-block:: text ELAS_ORTH =_F (E_L = 145200.0, E_T = 145200.0, E_N = 14520.0, NU_LT = 0. , NU_LN = 0. , NU_TN = 0. , G_LT = 72600. , G_LN = 72600. , G_TN=72600), The results must therefore correspond to the reference calculation. Two calculations are performed: one with implicit local integration, the other with explicit integration. Calculation with the single-crystal type 1 behavior and the sliding systems of ZIRCONIUM ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Five calculations are carried out with this family of sliding systems: 1. a non-regression calculation with the family defined in the code 2. a comparative calculation to the first, by providing a table containing the interaction matrix 3. a calculation comparative to the previous ones, with a polycrystal comprising a single grain, 4. a comparative calculation with the previous ones, by providing five families defined from a table containing sliding systems. All of these systems correspond to the Zirconium family. This tests the possibility of defining different material coefficients according to the sliding systems in question, 5. a calculation identical to the previous one, with a polycrystal comprising a single grain. Kocks-Rauch behavior: mono-crystalline, with BCC24 sliding system ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The behavior of the single crystal is defined by the flow: **MONO_DD_KR** ** whose parameters are: .. code-block:: text K = 8.62E-5, TAUR = 498. , TAU0 = 132. , GAMMA0 = 1.E6, DELTAG0 = 0.768, BSD = 2.514E-5, GCB = 31.822, KDCS = 22.9, P = 0.335, Q = 1.12, H1 = 0.25, H2 = 0.25, H3 = 0.25, H4 = 0.25 Three calculations are performed with this behavior: 1. An implicit MONOCRISTAL calculation 2. An explicit MONOCRISTAL calculation 3. An explicit POLYCRISTAL calculation, with only one phase These three calculations should lead to the same results. Boundary conditions and loads ------------------------------------- .. csv-table:: "Knot :math:`\mathit{P4}` ", ": :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}0`" "Knot :math:`\mathit{P8}` ", ": :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0`" "Nodes :math:`\mathit{P2}` and :math:`\mathit{P6}` ", ": :math:`\mathit{DX}\mathrm{=}0`" "Nodes :math:`\mathit{P1}`, :math:`\mathit{P3}`, :math:`\mathit{P5}` and :math:`\mathit{P7}` ", ": either :math:`\mathit{FX}\mathrm{=}25` or :math:`\mathit{DX}\mathrm{=}0.001`" The imposed force load is increasing from :math:`\mathit{FX}\mathrm{=}0` to :math:`\mathit{FX}\mathrm{=}25\mathrm{\times }0.755N`, in an increment, which leads to a uniaxial stress state of :math:`75.5\mathit{MPa}` (linearity limit) The load then increases to :math:`\mathit{FX}\mathrm{=}25\mathrm{\times }0.955N` in :math:`n` increments. The reference calculation is obtained with :math:`n\mathrm{=}100`. Monocrystalline calculations are done with :math:`n\mathrm{=}20`. With respect to behaviors MONO_VISC2 and MONO_DD_KR, loading is an imposed displacement varying from 0, at the initial moment, to 0.001 at time 2, in :math:`m` increments. For implicit resolutions, :math:`m\mathrm{=}20`, and for explicit resolutions, :math:`m\mathrm{=}100`. For modeling B, the load is an imposed displacement varying from 0, at the initial instant, to 0.001 at time 3, in 20 increments.