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Research Papers

An Assessment of the Evolving Microstructural Model of Inelasticity Coupled With Dislocation- and Disclination-Based Incompatibilities

[+] Author and Article Information
A. A. Adedoyin

CCS-7 Division,
Los Alamos National Laboratory,
Los Alamos, NM 87544
e-mail: aadedoyin@lanl.gov

K. Enakoutsa

Department of Mathematics,
California State University,
Northridge, CA 91330
e-mail: koffi.enakoutsa@csun.edu

D. J. Bammann

Department of Mechanical Engineering,
Mississippi State University,
Mississippi State, MS 39762
e-mail: douglas.bamann@msstate.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received April 2, 2018; final manuscript received April 16, 2019; published online May 28, 2019. Assoc. Editor: Vadim V. Silberschmidt.

This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government’s contributions.

J. Eng. Mater. Technol 141(4), 041009 (May 28, 2019) (20 pages) Paper No: MATS-18-1094; doi: 10.1115/1.4043627 History: Received April 02, 2018; Accepted April 22, 2019

The evolving microstructural model of inelasticity (EMMI) previously developed as an improvement over the Bammann–Chiesa–Johnson (BCJ) material model is well known to describe the macroscopic nonlinear behavior of polycrystalline metals subjected to rapid external loads such as those encountered during high-rate events possibly near shock regime. The improved model accounts for deformation mechanisms such as thermally activated dislocation motion, generation, annihilation, and drag. It also accounts for the effects of material texture, recrystallization and grain growth and void nucleation, growth, and coalescence. The material incompatibilities, previously disregard in the aforementioned model, manifest themselves as structural misorientation where ductile failure often initiates are currently being considered. To proceed, the representation of material incompatibility is introduced into the EMMI model by incorporating the distribution of the geometrically necessary defects such as dislocations and disclination. To assess the newly proposed formulation, classical elastic solutions of benchmarks problems including far-field stress applied to the boundary of body containing a defect, e.g., voids, cracks, and dislocations, are used to compute the plastic velocity gradient for various states of the material in terms of assumed values of the internal state variables. The full-field state of the inelastic flow is then computed, and the spatial dependence of the dislocations and disclination density is determined. The predicted results shows good agreement with finding of dislocation theory.

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Figures

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Fig. 1

Finite strain decomposition of the deformation gradient F = Fe Fp

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Fig. 2

Volterra’s defects: (a) reference cylinder with defect line ξ0 and cut surface S, (b) and (c) edge dislocations, (d) screw dislocation with Burgers vector b, (e) and (f) twist disclinations, and (g) wedge disclination with Frank vector w, Clayton et al. [1]

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Fig. 3

Cauchy stress for the case of the plate with a circular hole: (left) “2,2” component of the stress and (right) stress triaxiality

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Fig. 4

(Left) Circular hole in the infinite plate and (right) elliptical hole in the infinite plate

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Fig. 5

Evolution of the structure tensor (A) as a function of the time showing the predicted texture of the material after 20% of deformation for the case of a plain strain compression test

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Fig. 6

Distribution of the disclination density tensor component “1,1” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 7

Distribution of the disclination density tensor component “1,2” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 8

Distribution of the disclination density tensor component “1,3” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 9

Distribution of the disclination density tensor component “2,1” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 10

Distribution of the disclination density tensor component “2,2” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 11

Distribution of the disclination density tensor component “2,3” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 12

Distribution of the disclination density tensor component “3,1” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 13

Distribution of the disclination density tensor component “3,2” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 14

Distribution of the disclination density tensor component “3,3” in the plate for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 15

Distribution of the GNDs tensor component “1,1” for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 16

Distribution of the GNDs tensor component “1,2” for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 17

Distribution of the GNDs tensor component “1,3” for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 18

Distribution of the GNDs tensor component “2,1” for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 19

Distribution of the GNDs tensor component “2,2” for the case of the plate with a circular hole and different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 20

Distribution of the component “2,3” of the GNDs tensor in the plate for the case of the plate with a circular hole at different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 21

Distribution of the component “3,1” of the GNDs tensor in the plate for the case of the plate with a circular hole at different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 22

Distribution of the component “3,2” of the GNDs tensor in the plate for the case of the plate with a circular hole at different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 23

Distribution of the component “3,3” of the GNDs tensor in the plate for the case of the plate with a circular hole at different angles of orientation of the material texture: 0, 20, 40, and 60 deg

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Fig. 24

Distribution of the components of the disclination density tensor in the plate for the case of the plate with an elliptic hole

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Fig. 25

Distribution of the components of the dislocation density tensor in the plate for the case of the plate with an elliptic hole

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Fig. 26

Cauchy stress for the case of the plate with elliptic hole: (left) “2,2” component of the stress and (right) stress triaxiality

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