Strain-Gradient Crystal Plasticity Finite Element Modeling of Slip Band Formation in α-Zirconium

Omid Sedaghat,Hamidreza Abdolvand

doi:10.3390/cryst11111382

Omid Sedaghat, Hamidreza Abdolvand

Open Access

https://doi.org/10.3390/cryst11111382

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Journal: Crystals	Publication Date: Nov 12, 2021
Citations: 3	License type: CC BY 4.0

Affiliation: Western University

Abstract

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of GNDs, while Method II has unlimited solutions, where an optimization technique is used to determine GND densities. The performance of each method for capturing the formation of slip bands based on the calculated GND maps is critically analyzed. First, the model parameters are identified using single crystal simulations. This is followed by importing the as-measured microstructure for a deformed α-zirconium specimen into the finite element solver to compare the numerical results obtained from the models to those measured experimentally using the high angular resolution electron backscatter diffraction technique. It is shown that both methods are capable of modeling the formation of slip bands that are parallel to those observed experimentally. Formation of such bands is observed in both GND maps and plastic shear strain maps without pre-determining the slip band domain. Further, there is a negligible difference between the calculated grain-scale stresses and elastic lattice rotations from the two methods, where the modeling results are close to the measured ones. However, the magnitudes and distributions of calculated GND densities from the two methods are very different.

Highlights

A significant number of crystal plasticity studies have focused on modeling deformation via slip, which is controlled by the movement of dislocations on a particular plane known as the slip plane and in a particular direction known as the slip direction
This paper focuses on examining the methods available in the literature for calculating geometrically necessary dislocation (GND) densities in the lower-order crystal plasticity framework by providing a direct comparison between the results of each method to those measured experimentally
The crystal plasticity finite element (CPFE) results for GND densities are presented and compared to those measured via via high angular resolution electron back scatter diffraction (HR-EBSD)

Summary

Introduction

The strength of the obstacles interacting with dislocations determines the resistance of a slip system to the movement of the dislocations and the consequent material hardening These obstacles can be categorized into short-range and long-range barriers [8]. When conventional crystal plasticity models are used, the difference between these two obstacles is generally ignored and the critical resolved shear stress (CRSS) for the movement of the dislocations does not depend on the deformation state in the neighboring points. Incorporation of the plastic strain gradient in crystal plasticity constitutive equations makes the model response dependent on the neighboring elements—this is generally investigated in the non-local crystal plasticity approach [11,12,13,14,15]. This paper focuses on examining the methods available in the literature for calculating GND densities in the lower-order crystal plasticity framework by providing a direct comparison between the results of each method to those measured experimentally

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Results

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Conclusion