Abstract
As the characteristic scale of products and production processes decreases, the plasticity phenomena observed start to deviate from those evidenced at the macroscale. The current research aims at investigating this gap using a lower-order gradient enhanced approach both using phenomenological continuum level as well as crystal plasticity models. In the phenomenological approach, a physically based hardening model relates the flow stress to the density of dislocations where it is assumed that the sources of immobile dislocations are both statistically stored (SSDs) as well as geometrically necessary dislocations (GNDs). In the crystal plasticity model, the evolution of the critical resolved shear stress is also defined based on the total number of dislocations. The GNDs are similarly incorporated in the hardening based on projecting the plastic strain gradients through the Burgers tensor on slip systems. A rate-independent formulation is considered that eliminates any artificial inhomogeneous hardening behavior due to numerical stabilization. The behavior of both models is compared in simulations focusing on the effect of structurally imposed gradients versus the inherent gradients arising in crystal plasticity simulations.
Highlights
In metals, the primary mechanism of inelastic deformation is plastic slip due to dislocation movement along glide planes
It is possible to directly relate the geometrically necessary dislocations (GNDs) to a hardening function that is based on dislocation densities to start with, such as the one proposed by Bergström [11], thereby circumventing the use of an arbitrary length scale parameter
This hardening function is originally developed considering the evolution of statistically stored dislocations (SSDs), in this study this formulation is enriched by introducing GNDs that evolve with the plastic strain gradients in order to determine the flow stress of the material
Summary
The primary mechanism of inelastic deformation is plastic slip due to dislocation movement along glide planes. It is possible to directly relate the GNDs to a hardening function that is based on dislocation densities to start with, such as the one proposed by Bergström [11], thereby circumventing the use of an arbitrary length scale parameter This hardening function is originally developed considering the evolution of SSDs, in this study this formulation is enriched by introducing GNDs that evolve with the plastic strain gradients in order to determine the flow stress of the material.
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