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Research Papers

Elastic and Plastic Response of Perforated Metal Sheets With Different Porosity Architectures

[+] Author and Article Information
Hamed Khatam, Marek-Jerzy Pindera

Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904-4742

Linfeng Chen

 Gilsanz Murray Steficek LLP, New York, NY 10001

J. Eng. Mater. Technol 131(3), 031015 (Jun 04, 2009) (14 pages) doi:10.1115/1.3086405 History: Received October 12, 2008; Revised January 15, 2009; Published June 04, 2009

The effects of porosity architecture and volume fraction on the homogenized elastic moduli and elastic-plastic response of perforated thin metal sheets are investigated under three fundamental loading modes using an efficient homogenization theory. Steel and aluminum sheets weakened by circular, hexagonal, square, and slotted holes arranged in square and hexagonal arrays subjected to inplane normal and shear loading are considered with porosity volume fractions in the range 0.1–0.6. Substantial variations are observed in the homogenized elastic moduli with porosity shape and array type. The differences are rooted in the stress transfer mechanism around traction-free porosities whose shape and distribution play major roles in altering the local stress fields and thus the homogenized response in the elastic-plastic domain. This response is characterized by four parameters that define different stages of micro- and macrolevel yielding. The variations in these parameters due to porosity architecture and loading direction provide useful data for design purposes under monotonic and cyclic loading.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Hexagonal array of circular holes showing a highlighted unit cell (left) and discretization of the unit cell using quadrilateral subvolumes (right). (b) Mapping of the reference square subvolume in the η−ξ coordinate system onto the corresponding quadrilateral subvolume in the actual microstructure defined in the y2−y3 coordinate system (after Ref. 20).

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Figure 2

(a) Homogenized modulus E22∗/Em versus pore content: FVDAM versus elasticity results (4). (b) σ¯22−ε¯22 response: FVDAM versus experimental data (31).

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Figure 3

Unit cells of the investigated porous architectures (with a porosity volume fraction of 0.40 except for round end slots with 0.41)

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Figure 4

Homogenized elastic moduli of perforated steel plates with different architectures as a function of the porosity volume fraction: (a) E22∗/Em, (b) E33∗/Em, (c) G23∗/Gm, and (d) υ23∗

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Figure 5

Comparison of local σ22 stress distributions in five unit cells with a 0.40 porosity volume fraction subjected to loading by σ¯22≠0

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Figure 6

Comparison of local σ33 stress distributions in three unit cells with a 0.40 porosity volume fraction subjected to loading by σ¯33≠0

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Figure 7

Comparison of local σ23 stress distributions in five unit cells with a 0.40 porosity volume fraction subjected to loading by σ¯23≠0

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Figure 8

Macroscopic stress-strain response of perforated plates with circular holes in a square array under uniaxial loading by σ¯22≠0 (a) and σ¯23≠0 (b) as a function of the porosity volume fraction. Note that the letters A,…,D in Fig. 8 denote σyA,…,σyD

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Figure 9

Macroscopic stress-strain response of perforated plates with circular holes in a hexagonal array under uniaxial loading by σ¯22≠0 (a), σ¯33≠0 (b) and σ¯23≠0 (c) as a function of the porosity volume fraction

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Figure 10

Comparison of the macroscopic stress-strain response of the five steel sheet configurations containing 0.40 porosity fraction under uniaxial loading by (a) σ¯22≠0, (b) σ¯33≠0, and (c) σ¯23≠0

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Figure 11

Effective plastic strain distributions in unit cells with circular holes in square (a) and hexagonal (b) arrays containing 0.40 porosity fraction under uniaxial loading by σ¯22≠0

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Figure 12

Yield parameters for circular holes in hexagonal arrays as a function of porosity volume fraction under uniaxial loading by (a) σ¯22≠0 and (b) σ¯33≠0

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Figure 13

Yield parameters for circular and square holes in square arrays as a function of porosity volume fraction under uniaxial loading by σ¯22≠0: (a) circular holes and (b) square holes

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Figure 14

Yield parameters for hexagonal (a) and slotted (b) holes in hexagonal arrays as a function of porosity volume fraction under uniaxial loading by σ¯22≠0 and σ¯33≠0

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Figure 15

Comparison of the asymptotic yield parameters of the five perforated steel configurations as a function of the porosity volume fraction under uniaxial loading by (a) σ¯22≠0, (b) σ¯33≠0, and (c) σ¯23≠0

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