Simple RVE-type Simulation

Note

Read first: Simple Simulation

A polycrystal containing 20 grains, generated and meshed by Neper, is used:

The domain is a unit cube. Length units are assumed to be mm, thus, all pressure units assumed to be MPa for the simulation (including input parameters). An FCC material with Anisotropic Elasticity and the Base Model for plasticity is considered, with the following material parameters:

Single crystal elastic constants and plasticity parameters.

\(C_{11}\) [MPa]	\(C_{12}\) [MPa]	\(C_{44}\) [MPa]	\(m\) [-]	\(\dot{\gamma_0}\) [1/s]	\(h_0\) [MPa]	\(g_0\) [MPa]	\(g_s\) [MPa]
\(245.0 \times 10^3\)	\(155.0 \times 10^3\)	\(62.5 \times 10^3\)	0.05	1.0	200.0	210.0	330.0

As the domain is a cubic “(representative) volume element”, and if the aim is to apply uniform loading, it makes particular sense to define the loading in terms of strain rate, target strain and maximal strain increment instead of the standard velocity, target time and maximal time increment. The simulation described in Simple Simulation, can then be run using a simplified Configuration File (simulation.cfg) file, as described (and highlighted) below.

Specifying a Strain Rate (set_bc strainrate), etc.

• simulation.msh

• simulation.cfg

  ### FEPX Configuration File
  
  ## Material Parameters
  
      number_of_phases 1
  
      phase 1
  
        crystal_type FCC
  
        c11 245.0e3
        c12 155.0e3
        c44  62.5e3
  
        m 0.05d0
        gammadot_0 1.0d0
  
        hard_type isotropic
        h_0 200.0
        g_0 210.0
        g_s 330.0
  
  ## Boundary Conditions
  
      set_bc strainrate 33 0.001
      set_bc vel x0y0z0 x 0 y 0
      set_bc vel x1y0z0 y 0
  
  ## Steps
  
      number_of_steps 1
      target_strain33 0.01
      dstrain 0.001
  
  ## Printing Results
  
      print coo
      print ori
      print stress
      print strain
      print forces
  

Note

As the set_bc strainrate condition only act on the \(v_z\) components, additional set_bc vel conditions are still required to fix rigid-body motions.

Execution and simulation results are the same as in Simple Simulation. The deformed mesh is reproduced for completeness:

Strain field (\(\epsilon_{33}\)) at 1% axial strain (displacement field is exaggerated 10x for illustrative purposes).

Stress field (\(\sigma_{33}\)) at 1% axial strain (displacement field is exaggerated 10x for illustrative purposes).

Grip Boundary Conditions (grip)

Grip boundary conditions, which can be activated using the grip statement, are different in the sense that they fully constrain the reference and loading faces by prescribing zero velocities in the directions different from the loading direction. Different strain and stress field result, especially close to the reference and loading faces.

• simulation.msh

• simulation.cfg

  ### FEPX Configuration File
  
  ## Material Parameters
  
      number_of_phases 1
  
      phase 1
  
        crystal_type FCC
  
        c11 245.0e3
        c12 155.0e3
        c44  62.5e3
  
        m 0.05d0
        gammadot_0 1.0d0
  
        hard_type isotropic
        h_0 200.0
        g_0 210.0
        g_s 330.0
  
  ## Boundary Conditions
  
      set_bc strainrate 33 0.001 grip
  
  ## Steps
  
      number_of_steps 1
      target_strain33 0.01
      dstrain 0.001
  
  ## Printing Results
  
      print coo
      print ori
      print stress
      print strain
      print forces
  

Strain field (\(\epsilon_{33}\)) at 1% axial strain (displacement field is exaggerated 10x for illustrative purposes).

Stress field (\(\sigma_{33}\)) at 1% axial strain (displacement field is exaggerated 10x for illustrative purposes).