Studying Grain Boundary Strengthening by Dislocation-Based Strain Gradient Crystal Plasticity Coupled with a Multi-Phase-Field Model.

Waseem Amin,Napat Vajragupta,Alexander Hartmaier,Muhammad Adil Ali

doi:10.3390/ma12182977

Abstract

One ambitious objective of Integrated Computational Materials Engineering (ICME) is to shorten the materials development cycle by using computational materials simulation techniques at different length scales. In this regard, the most important aspects are the prediction of the microstructural evolution during material processing and the understanding of the contributions of microstructural features to the mechanical response of the materials. One possible solution to such a challenge is to apply the Phase Field (PF) method because it can predict the microstructural evolution under the influence of different internal or external stimuli, including deformation. To accomplish this, it is necessary to take into account plasticity or, specifically, non-homogeneous plastic deformation, which is particularly important for investigating the size effects in materials emerging at the micron length scale. In this work, we present quasi-2D simulations of plastic deformation in a face centred cubic system using a finite strain formulation. Our model consists of dislocation-based strain gradient crystal plasticity implemented into a PF code. We apply this model to study the influence of grain size on the mechanical behavior of polycrystals, which includes dislocation storage and annihilation. Furthermore, the initial state of the material before deformation is also considered. The results show that a dislocation-based strain gradient crystal plasticity model can capture the Hall-Petch effect in many aspects. The model reproduced the correct functional dependence of the flow stress of the polycrystal on grain size without assigning any special properties to the grain boundaries. However, the predicted Hall-Petch coefficients are significantly smaller than those found typically in experiments. In any case, we found a good qualitative agreement between our findings and experimental results.

Highlights

The properties of engineering materials are size-dependent if the microstructural length scale falls into an order of a few microns to less than a micron [1,2]
In order to investigate the influence of the grain size, first of all we evaluated the distributions of ρGND, ρSSD and ρtotal in all Representative Volume Elements (RVE) at 5% total strain, and we applied the volume averaged homogenization scheme to investigate the evolution of these quantities with respect to the plastic deformation
By decreasing the grain diameter, ρGND increases and tends to concentrate along the grain boundaries. Such observed concentration of ρGND along the grain boundaries is consistent with the large strain gradients in these regions of strain incompatibility between neighboring grains

Summary

Introduction

The properties of engineering materials are size-dependent if the microstructural length scale falls into an order of a few microns to less than a micron [1,2]. Within the domain of metallic materials, the main plastic deformation mechanism is dislocation slip This deformation mechanism depends on the density and evolution of the dislocations, crystal structures, and crystallographic orientations, and on the localization of deformation as a result of the gradients of the grain morphology and the distribution of grain sizes [11]. The grain size effect is the manifestation of the fact that a polycrystal with larger grains experiences larger strain incompatibility during plastic deformation. This generates higher internal stresses in the microstructure which leads to lowering of yield strength and as the grain size is reduced, an opposite phenomenon is observed [3,4]. This is associated with the state of the material, e.g., its initial dislocation density, which determines the strength of a material [15]

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