Introduction

In this study the MKS was used to predict total strain fields in a 2-phase composite where each phase was assigned properties from distinct orientation of $\alpha$-Ti single crystals. The properties from especially “soft” and “hard” orientations were used in order to simulate the worst case scenario in a fully polycrystalline simulation.

Parameters

  • 2 phase microstructures with isotropic phases
  • Both phases exhibit elastic, perfectly plastic behavior
  • 0.814% applied strain amplitude
  • Periodic boundary conditions
    • uniaxial tension
    • contraction allowed on transverse sides of MVE (BCs for plasticity)

Phase 1 Parameters:

  • Young’s Modulus: 115 GPa
  • Poisson’s Ratio: 0.3
  • Yield Strength: 800 MPa

Phase 2 Parameters:

  • Young’s Modulus: 145 GPa
  • Poisson’s Ratio: 0.3
  • Yield Strength: 1200 MPa

The following image shows the stress strain plots for each phase (with their associated material parameters)

Calibration Set:

  • 399 realistic $\alpha$-Ti microstructures generated in DREAM.3D by Matthew Priddy
  • Phases randomly assigned to grains in DREAM.3D microstructure
  • Volume fraction varied between 5% and 95%

Validation Sets:

  • 400 realistic $\alpha$-Ti microstructures generated in DREAM.3D by Matthew Priddy
  • Phases randomly assigned to grains in DREAM.3D microstructure
  • Volume fraction varied between 5% and 95%

Results

When only first order terms were used in the MKS procedure the following errors resulted:

  • Mean Error: 2.49%
  • Average Maximum Error: 21.65%
  • Absolute Maximum Error: 44.28%

where:

  • Mean % Error: mean error per voxel in all microstructures
  • Average Maximum % Error: max error per microstructure
  • Absolute Maximum % Error: max error in any microstructure

The following image shows a slice of the microstructure, the FE strain field and the MKS prediction of the strain field given the original microstructure:

References

  • M. Groeber,M. Jackson, Integrating materials and manufacturing innovation, vol. 3, p. 5, 2014.
  • S.R. Kalidindi, S.R. Niezgoda, G. Landi, S. Vachhani, T. Fast A Novel Framework for Building Materials Knowledge Systems CMC 17 (2010) 103-125
  • T. Fast, S.R. Kalidindi Formulation and calibration of higher-order elastic localization relationships using the MKS approach Acta Mat. 59 (2011) 4595-4605