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Plastic-strain gradient induced internal stress and geometrically necessary dislocation density in grain boundary regions

Anxin Ma, Ruhr-Universität Bochum, Bochum, Germany

Alexander Hartmaier, Ruhr-Universität Bochum, Bochum, Germany

Time & Place
  • Date: 12.07.2012
  • Time:
  • Place: 8th European Solid Mechanics Conference ESMC 2012 Graz, Austria

Abstract

In this paper the passing stress and the internal stress of geometrically necessary dislocation densities are formulated within a nonlocal constitutive model. The passing stress mainly depends on the forest GND density and the Taylor hardening coefficient. The internal stress relies on the gradient of the GND density and an average pileup length. The intrinsic length scale, magnitude of Burgers vector b, has been introduced to the isotropic hardening by τp∝ √b. The intrinsic length scale, average GND pileup length L, has been introduced to the kinematic hardening by SGND ∝ L2.

The short range isotropic hardening and the long range kinematic hardening caused by a geometrically necessary dislocation density have been considered within nonlocal constitutive models. With respect to simple shear of single and polycrystals, adopting a weak coupling algorithm between the stress equilibrium and the plastic strain gradient evolution, the influence of numerical noise and local orientation perturbation on the GND density distribution have been investigated.

It was found that the lower order nonlocal model, which only considers the isotropic hardening of the GND density, tends to predict unrealistic GND patterns when numerical noise exists. However, the higher order nonlocal model, which considers the isotopic and the kinematic hardening of GND density at the same time, predicts reasonable GND density distributions in the presence of numerical noises. The lower order and the higher order nonlocal constitutive models predicted very different GND patterns under a orientation perturbation.

With the help of the higher order nonlocal model, the intrinsic features of grain boundaries including grain boundary induced internal stress and GND density distributions have been investigated with respect to rigid boundaries, grain boundaries with different misorientations and grain size variations. For polycrystals under large deformations, the influence of the higher order boundary condition has also be investigated.

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