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Research Papers

Modeling Strain Localization Using a Plane Stress Two-Particle Model and the Influence of Grain Level Matrix Inhomogeneity

[+] Author and Article Information
Xiaohua Hu, David S. Wilkinson

Department of Materials Science and Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canada

Mukesh Jain

Department of Mechanical Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canada

Raja K. Mishra

 General Motors Research and Development Center, Mail Code 480-106-212, 30500 Mound Road, Warren, MI 48090-9055

J. Eng. Mater. Technol 130(2), 021002 (Mar 12, 2008) (10 pages) doi:10.1115/1.2840959 History: Received July 13, 2007; Revised November 21, 2007; Published March 12, 2008

The role of dilute small particles on the development of strain localization under uniaxial tension has been studied by finite element analysis using a plane stress model with two small hard particles embedded in Al matrix. The influence of particle alignment and interparticle spacing in a homogeneous and inhomogeneous matrix are investigated. When the matrix material is a homogeneous continuum, there are small localization strains when close packed and aligned along the loading direction. In the case of an inhomogeneous matrix with grains of different strengths represented by their Taylor factors, the location of localization band is insensitive to the interparticle spacing, but mainly determined by grain-level inhomogeneity. This is because the particles are dilute and small compared with the matrix grains. The particles, however, can decrease the localization strains when they straddle the localization band.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The illustration of the two particle square unit-cell model; LD denotes loading direction and TD denotes the transverse direction in a tensile sample of thin sheet

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Figure 2

Experimental flow curve and Holloman fitting of the data using parameters in Table 1

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Figure 3

The grain structure in the cell model: (a) the geometry drawn in ABAQUS/CAE and (b) the meshed model where the color contour shows the Rg distribution

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Figure 4

An example of σ¯11-ε¯11 curve and ε¯22-ε¯11 curves where the points of critical strains (εin and εps) are indicated

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Figure 5

The σ11(×106MPa) stress fields of the cropped regions around the two round particles at initial deformation for models of different alignment angle α of particles

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Figure 6

The σ11(×106MPa) stress fields of the cropped regions around one single particle at initial deformation when ε11=0.06

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Figure 7

The equivalent strain distribution when the model enters global in-plane plane strain state for models of different alignment angles of particles

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Figure 8

Simulation results with different alignment angle α: (a) global stress-strain curves for α=0–90 and (b) εin and εps as a function of α for one and two particle models

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Figure 9

The σ11(×106MPa) stress fields of the cropped regions around the two round particles at initial deformation when ε11=0.06 and their interaction pattern with respect to normalized interparticle spacing R

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Figure 10

The equivalent strain distribution when the model enters global in-plane plane strain state for models of different normalized interparticle spacing R

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Figure 11

Simulation results with different normalized interparticle spacing R: (a) global stress-strain curves for R=0.2–2 and (b) εin and εps as a function of R for the two particle models

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Figure 12

The equivalent strain distribution showing the band patterns after localization for models of different normalized interparticle spacings R where the matrix is inhomogeneous

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Figure 13

Simulation results with different normalized interparticle spacings R: (a) global stress-strain curves for R=0.2–2 and (b) εin and εps as a function of R for the two particle models when the matrix is inhomogeneous

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Figure 14

The equivalent strain distribution showing the band patterns after localization for models of different d where the matrix is inhomogeneous. d is the distance between the center of the connection line of the two particles and the center of the whole model.

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Figure 15

Simulation results with different d: (a) global stress-strain curves for d=2μm, 7μm, and 12μm, where R=0.2 and (b) εin and εps as a function of d for the two particle models when the matrix is inhomogeneous. For comparison, the results of R=0.6 are also shown in (b). d is the distance between the center of the connection line of the two particles and the center of the whole model.

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Figure 16

The Taylor factor distribution of the model with the Taylor factor of each integration point (or element) is an average of (a) 1 orientation and (b) 100 orientations randomly assigned from a sample of 4000 grains

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Figure 17

(a) The σ¯11-ε¯11 curve of the models with the Taylor factor of each element is an average of n orientations and (b) the variation of critical strain (εin,εps) values with n

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