A dislocation-based model for deformation and size effect in multi-phase steels

• A multi-scale modeling method is proposed and applied on multi-phase material.
• The GND dislocation density is implemented into the mean free path of mobile dislocations to capture the size effect.
• The mechanical behavior, dislocation density and texture evolution of different DP steels are predicted.
• The model predicts grain size effects.

In this work, we investigate the mechanical behavior of multi-phase steels using a continuum dislocation dynamic model (CDD) coupled with a viscoplastic self-consistent (VPSC) model that accounts for both the effect of dislocations evolution inside the grain as well as grain–grain interactions. Because the conventional viscoplasticity theory does not capture the grain size effect, we introduce an intrinsic length scale within the concepts of geometrically necessary dislocations (GND) by means of the Nye's dislocation tensor. The effect of the GND density is implemented into the model for the mean free path of dislocations and is shown to contribute to strain hardening. As a validation of this multiscale model, we investigate the mechanical behavior of various dual phase steels. The stress-strain response obtained from this approach is compared to experimental data found in the literature and reveal good agreement between experimental results and predictions. The model also predicts the evolution of dislocation densities in each phase and suggests the connection between underlying deformation mechanisms and macroscopic material hardening. The relation between flow stress and grain size is also investigated. The model predictions follow the Hall–Petch relation of strength versus grain size for grains larger than one micron meter but deviates from this relation for grains in the order of tens of nanometers.