Session: 03-03-01: Integrated Computational Materials Engineering (ICME)

Paper Number: 94854

94854 - A Dislocation-Based Crystal Plasticity Finite Element Simulation for the Micropillar Compression 

Micropillar compression test provides a way to quantify a variety of material properties and mechanical behavior of low volume materials. It can also be used to investigate the relationship between complicated dislocation patterning, deformation modes, and strengthening mechanisms in metals. It is challenging to precisely capture the plastic deformation process of the microstructure and extract the derivation of the microstructure-material constants relationship. It is well established that the plastic slip process of metallic materials is accompanied by the production, movement, storage, interactions, and annihilation of dislocations. The material modeling related to physical processes in low-length scales is the underlying task to predict the plastic flow of metals and alloys.

The statistically stored dislocation (SSD) dislocations evolve over dislocation reactions with the non-vanishing Burgers vector and all immobile SSDs are generated by the reactions of mobile SSDs. External plastic deformation is primarily controlled by mobile SSDs, while strain hardening is caused by the buildup of immobile SSDs. The mobile dislocations interact with other dislocations and barriers as they shift to accommodate the imposed strain. To connect material behavior in different length scales between macroscale and microscale, some widely utilized flow rules in crystal plasticity are introduced as follows: a. power-law model, b. Arrhenius type model, c. mixed power law, and d. Orowan type model. The dislocation mobility in the flow rules can be characterized in terms of thermally activated motion and drag-dominant motion. Dislocations should be able to overcome both short- and long-range obstacles during plastic deformation. The stress field of dense immobile dislocations and forest dislocations is thought to produce short-range obstacles. The aid of thermal activation energy facilitates the motion of dislocations resulting in overcoming the short-range barrier. Two types of thermal activation energy address the shape of the activation barrier such as double exponent form, and hyperbolic sine form due to skewing of the activation barrier. Dislocations originated from heterogeneous plastic deformation, on the contrary, cause long-range barriers. The strain gradient by geometrically necessary dislocation (GND) densities or dislocation pileups near grain boundaries is responsible for long-range interactions stress fields. The strain gradient effect can be expressed in terms of energetic and dissipative gradient effects.

A new crystal plasticity model based on the dislocation mechanism is developed to study the mechanical behavior of face-centered cubic single crystals under heterogeneous inelastic deformation through a crystal plasticity finite element method. The main feature of this work is generalized constitutive relations that incorporate the thermally activated and drag mechanisms to cover different kinetics of viscoplastic flow in metals at a variety of ranges of stresses and strain rates. The constitutive laws are founded upon integrating continuum description of crystal plasticity framework with dislocation densities which is relevant to the geometrically necessary dislocation densities and the statistically stored dislocation densities. The model describes the plastic flow and the yielding of face-centered cubic single-crystal employing evolution laws of dislocation densities with mechanism-based material parameters passed from experiments or small-scale computational models. The geometrically necessary dislocation densities evolve on account of the curl of the plastic deformation gradient where its associated closure failure of the Burgers circuit exists. A minimization scheme termed -norm is utilized to secure the physical values of the geometrically necessary dislocation densities on slip systems. The evolution equations of statistically stored dislocation densities describe the complex interactions between two distinct dislocation populations, mobile, and immobile statistically stored dislocation dislocations, relying on generation, annihilation, interactions, trapping, and recovery. The experiments of a micropillar compression for the copper single crystal are compared to the computational results obtained using the formulation. The physics-based model clarifies the complex microstructural evolution of dislocation densities in metals and alloys, allowing for more accurate prediction.

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Presenting Author: George Z Voyiadjis Louisiana State University

Presenting Author Biography: Dr. George Z. Voyiadjis is the Boyd Professor at the Louisiana State University, in the Department of Civil and Environmental Engineering. This is the highest professorial rank awarded by the Louisiana State University System. He is also the holder of the Freeport-MacMoRan Endowed Chair in Engineering. He is currently the Chair of the Department of Civil and Environmental Engineering. He currently also serves since 2012 as the Director of the Louisiana State University Center for GeoInformatics (LSU C4G; http://c4gnet.lsu.edu/c4g/ ).<br/>He is a Distinguished Member of the American Society of Civil Engineers, Fellow of the American Society of Mechanical Engineers, the Society of Engineering Science, the American Academy of Mechanics, the Engineering Mechanics Institute of ASCE, and Associate Fellow of the American Institute of Aeronautics and Astronautics. He was recently elected as a Senior Member of National Academy of Inventors.

Authors:

George Z Voyiadjis Louisiana State University
Juyoung Jeong Louisiana State University