*Article* **Understanding the Plastic Deformation of Gradient Interstitial Free (IF) Steel under Uniaxial Loading Using a Dislocation-Based Multiscale Approach †**

**Hao Lyu 1,\* and Annie Ruimi <sup>2</sup>**


**Abstract:** Gradient interstitial free (IF) steels have been shown to exhibit a superior combination of strength and ductility due to their multiscale microstructures. The novelty of the work resides in the implementation of a modified slip transmission and a back-stress quantity induced by a long-range dislocation interaction in the dislocation-based multiscale model. This is an improvement over the model we previously proposed. Simulations are performed on IF specimens with gradient structures and with homogeneous structures. The macroscopic behavior of the samples under tension and compression is studied. The evolution of the microstructure such as dislocations, geometrically necessary dislocations (GNDs), and the effects of grain orientation is analyzed. Results show that with our enhanced model, the simulations can successfully reproduce the stress-strain curves obtained experimentally on gradient nano IF steel specimens under tension. The simulations also capture the tension-compression asymmetry (TCA) in specimens with homogeneous and gradient microstructures. The initial texture is found to have a significant effect on the TCA of specimens with gradient microstructures.

**Keywords:** multi-scale modeling; dislocations; gradient materials
