how could we properly set rigid clamps' material to produce simple shear in bi-materials

[ruanqc]

Dear DAMASK team,
In spire of the simple shear of bi-materials case that using nonlocal constitutive law by Kords(2013) in his PhD thesis, I try to simulate a plastic deform metallic under simple shear condition by using damask 3.0.1 grid solver.

I want to simulate a simple shear of metallic material (blue region) with its top and bottom boundaries set as dislocation impenetrable boundaries.

I generate a bi-material-like geometry by setting one layer mesh on the top and bottom (red regions), these red regions are assigned another material property, which acts like rigid clamps and only under elastic deform.

I am not sure whether it is possible by this boundary can impose a simple shear to the interior plastic deform region? whether rigid clamps's material must define all the elastic modules, orientation etc. , material and loading inputs as follow,

Thank you and best regards, ruanqc

input1: shearXY.yaml
solver:
mechanical: spectral_basic
loadstep:

• boundary_conditions:
  mechanical:
  #shearXY
  dot_F: [[0, 1.0e-3, 0],
  [0, 0, 0],
  [0, 0, 0]]
  P: [[x, x, x],
  [x, x, x],
  [x, x, x]]
  discretization:
  t: 20.0
  N: 200
  f_out: 5

input2: material.yaml
homogenization:
SX:
N_constituents: 1
mechanical: {type: pass}
phase:
al:
lattice: cF
mechanical:
output: [F, P, F_e, F_p, L_p, O]
elastic: {type: Hooke, C_11: 112.9e+9, C_12: 66.4e+9, C_44: 27.9e+9}
plastic:
type: nonlocal
references:
- C. Kords,
On the role of dislocation transport in the constitutive description of crystal plasticity,
RWTH Aachen 2013,
http://publications.rwth-aachen.de/record/229993/files/4862.pdf
output: [rho_u_ed_pos , rho_u_ed_neg,gamma]
N_sl: [12]
b_sl: [2.86e-10]
V_at: 0.017e-27 # Omega
d_ed: [1.6e-9]
d_sc: [10.e-9]
i_sl: [60] # k_2 (lambda_0 in Tab. 7.1)
f_ed_mult: 0.1 # k_1
rho_u_ed_neg_0: [1.25e9] # 6e10 / (124)
rho_u_ed_pos_0: [1.25e9] # 6e10 / (124)
rho_u_sc_neg_0: [0.0] #[1.25e9] # 6e10 / (124)
rho_u_sc_pos_0: [0.0] #[1.25e9] # 6e10 / (124)
rho_d_ed_0: [0]
rho_d_sc_0: [0]
D_0: 7.e-29
Q_cl: 0.0 # no temperature dependency
Q_sol: 2.00272e-19 # 1.25 eV
c_sol: 1.5e-6 # correct unit?
f_sol: 0.572 # 2.0 # d_obst in multiples of b
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10 # w_k in multiple of b
p_sl: 1
q_sl: 1
nu_a: 50.e+9 # attack frequency
B: 1.e-2 # dislocation ciscocity
f_ed: 1.0 # k_3
h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Tab. 3.4
chi_GB: 0.0 # 0.0 full blocking at GB
chi_surface: 1.0 #1.0 # no blocking at surface
f_F: 0.0 # no line tension correction
sigma_rho_u: 0 # no random distribution
short_range_stress_correction: false
rho_significant: 1.e6

Fe:
lattice: cF
mechanical:
output: [F,F_e,O]
elastic: {type: Hooke, C_11: 232.2e+9, C_12: 136.4e+9, C_44: 117.0e+9}
#plastic:
#type: nonlocal
references:
- D.J. Dever,
Journal of Applied Physics 43(8):3293-3301, 1972,
https://doi.org/10.1063/1.1661710,

material:

• constituents:
  • phase: al
    O: [1.0, 0.0, 0.0, 0.0] #100
    v: 1.0
    homogenization: SX
• constituents:
  • phase: Fe
    O: [1.0, 0.0, 0.0, 0.0] #100
    v: 1.0
    homogenization: SX

geom_Al_Fe_Clamps.vti.txt

in order to upload the geom.vti file, i added .txt after it (should work after delete '.txt')

[eisenlohr]

The 'boundary conditions' specified for the grid solver are not truly applied at any boundary but prescribe the volume-averaged response. In other words, if you prescribe purely mechanical boundary conditions—as you do—the $\dot{\mathbf{F}}$ values apply a shape change to the corners of the simulated volume element but do not prevent any fluctuations in between.

The resulting shape change of the red layer in your geometry is then a function of the stiffness and strength assigned to it.

[ruanqc]

The 'boundary conditions' specified for the grid solver are not truly applied at any boundary but prescribe the volume-averaged response. In other words, if you prescribe purely mechanical boundary conditions—as you do—the F ˙ values apply a shape change to the corners of the simulated volume element but do not prevent any fluctuations in between.

The resulting shape change of the red layer in your geometry is then a function of the stiffness and strength assigned to it.

Thank you very much professor for your reply. If I understand right, the prescribed boundary condition is actually applied to the whole simulation domain( like all the red and blue meshes in this context). So if we want internal blue geometry undergoes simple shear in XY, and their top and bottom boundaries are impenetrable dislocation boundaries, WHETHER is it much properly to set red layer a soft elastic model so that minimum the correspond stress to the whole simulation domain when compared with the blue geometry, which is our intested in. Thank you

[eisenlohr]

The internal (blue) volume undergoes simple shear provided that the red volume is at least as stiff/strong as the blue one. If the red material were too soft, then most of the enforced deformation would be accommodated by it, causing the response of the interior blue part to become less well controlled.

The nonlocal model has two parameters

      chi_surface                !< transmissivity at free surface
      chi_GB                     !< transmissivity at grain boundary (identified by different texture)

that govern the transmissivity of dislocations through boundaries. For phase boundaries, the transmissivity is internally set to be always zero. Hence, if you were to define red as a different phase than blue, you would end up with impenetrable boundaries between both. (See line 1316 in phase_mechanical_plastic_nonlocal.f90.)

[ruanqc]

The internal (blue) volume undergoes simple shear provided that the red volume is at least as stiff/strong as the blue one. If the red material were too soft, then most of the enforced deformation would be accommodated by it, causing the response of the interior blue part to become less well controlled.

The nonlocal model has two parameters

      chi_surface                !< transmissivity at free surface
      chi_GB                     !< transmissivity at grain boundary (identified by different texture)

that govern the transmissivity of dislocations through boundaries. For phase boundaries, the transmissivity is internally set to be always zero. Hence, if you were to define red as a different phase than blue, you would end up with impenetrable boundaries between both. (See line 1316 in phase_mechanical_plastic_nonlocal.f90.)

I see, thank you agian for your help. ruanqc