Periodic RVE-type Simulation

Note

A periodic polycrystal containing 40 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 periodic “(representative) volume element”, the loading is defined in terms of strain rate, target strain and maximal strain increment. Minimal changes (compared to Simple Simulation and Periodic RVE-type Simulation) is made to the Configuration File (simulation.cfg) file, as described (and highlighted) below. However, in the current implementation, all components of the strain rate must be specified, and the shear components must be zero. Rigid-body motions are fixed automatically.

The example below shows plane tension-compression of the polycrystal.

simulation.msh

simulation.cfg

### FEPX Configuration File

## Material Parameters

    number_of_phases 1

    phase 1
    
      crystal_type BCC

      c11 236.9e3
      c12 140.6e3
      c44 116.0e3

      m 0.020d0
      gammadot_0 1.0d0

      hard_type isotropic
      h_0 391.90d0
      g_0 200.0d0
      g_s0 335.0d0
      n 1.0d0

## Boundary Conditions

    set_bc strainrate 11 1e-2 periodic
    set_bc strainrate 22 0 periodic
    set_bc strainrate 33 -1e-2 periodic
    set_bc strainrate 12 0 periodic
    set_bc strainrate 13 0 periodic
    set_bc strainrate 23 0 periodic  

## Deformation History

    number_of_steps 1
    target_strain11 0.01
    dstrain 0.001
    
## Printing Results

    print coo
    
    print disp
    print forces
    
    print strain
    print strain-eq
    print strain-el
    print strain-el-eq
    print strain-pl
    print strain-pl-eq
    
    print stress
    print stress-eq
    
    print work
    print work-pl

    print ori
    
    print slip
    print sliprate
    print crss