Abstract
The role of pre-existing mobile and immobile dislocation densities on the evolution of geometrical necessary dislocation densities (GNDs) during cyclic fatigue in shear is studied using a continuum dislocation-based model incorporated in a crystal plasticity finite element scheme. Clusters with different immobile dislocation densities are implemented in a homogeneous medium containing a certain mobile dislocation density. It is found that whether GND walls are formed around the initial immobile cluster (or not) strongly depends on the absolute values of initial mobile dislocation density and on the ratio between mobile and immobile densities. The results are discussed in terms of the apparent GND densities experimentally obtained using Laue micro-diffraction.
Highlights
Coupling 3D dislocation dynamics with a 3D finite element methods (FEM) allows to simulate the crystal lattice rotation induced by plastic deformation, using the polar decomposition of the elastic deformation gradient [8], as it has been shown for the 3D cell structures formed after monotonic uniaxial tensile loading [9,10,11,12,13]
Dislocation-based rate equations have been implemented in a crystal plasticity FEM (CPFEM) scheme to reproduce dislocation structures during cyclic fatigue starting from a perfect single crystal [15]
The reason behind is that the dislocations in the forming geometrical necessary dislocation densities (GNDs) wall increase the threshold stress t1th, which during reverse loading prevents part of the GNDs to move to their original position
Summary
This computational method is based on the decomposition of the deformation gradient F into an elastic and plastic part: F = Fe ⋅ Fp. The plastic deformation gradient evolves based on the activity of all the slip systems of the FCC crystal [23]:. A=1 where ma and na are the slip direction and slip plane normal of the slip system α. In dislocation-based models, the plastic strain rate g a p is given by Orowan’s law:. Where ra m is the mobile dislocation density on the slip system α, b is the Burgers vector and va is the dislocation velocity. In this work the DAMASK subroutine is used [24], which allows implementing user-defined rate equations for the dislocation densities
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