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Research Papers

Plastic Analysis of Metal Foam Core Sandwich Beam Transversely Loaded by a Flat Punch: Combined Local Denting and Overall Deformation

[+] Author and Article Information
Qing Hua Qin

State Key Laboratory for the Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics,  Xi’an Jiaotong University, Xi’an 710049, China

T. J. Wang1

State Key Laboratory for the Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics,  Xi’an Jiaotong University, Xi’an 710049, Chinawangtj@mail.xjtu.edu.cn

1

Corresponding author.

J. Appl. Mech 79(4), 041010 (May 09, 2012) (12 pages) doi:10.1115/1.4005561 History: Received February 15, 2011; Revised August 11, 2011; Posted January 30, 2012; Published May 09, 2012; Online May 09, 2012

The objective of this work is to investigate the quasi-static plastic behavior of a fully clamped metal foam core sandwich beam transversely loaded by a flat punch. A rigid-plastic beam-on-foundation model is extended to study the local denting deformation of a metal foam core sandwich beam. The effects of local denting and core strength on the overall deformation are incorporated in the analysis. Analytical solutions are derived for three different regimes of post-yield deformation mechanisms. Additionally, finite element results are obtained. Comparisons of the present analytical predictions with numerical, previous experimental, and analytical results are presented, respectively. It is shown that local denting has a significant effect on the finite deflection response of the metal foam core sandwich structure. The load-carrying and energy absorption capacities of sandwich beams may be overestimated if the effect of local denting is neglected in analysis. It is demonstrated that the present analytial model can reasonably predict the behaviors of post-yield deformation of sandwich beams. Moreover, the present analytical method can be extended to predict the low velocity/energy impact problems of sandwich structures.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of fully clamped metallic foam core sandwich beam transversely loaded by a flat punch

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Figure 2

Deformation laws of the materials: (a) face-sheets with σf being the yield strength, and (b) metal foam core with σc and ɛD being the yield strength and densification strain, respectively

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Figure 3

(a) Indentation of a fully clamped metal foam core sandwich beam, and (b) original and deformed cross-sections

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Figure 4

(a) Beam-on-foundation model for the indentation of a fully clamped metal foam core sandwich beam, (b) transverse displacement profile for the upper face-sheet transversely loaded by a flat punch, and (c) forces and moments on the upper face-sheet

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Figure 5

Overall deformation of the fully clamped metal foam core sandwich beam transversely loaded by a flat punch for the case of Pfyc  > Pi . (a) Transverse deflection profile, and (b) forces and moments.

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Figure 6

Local denting deformation w0 beneath the flat punch, overall deformation W0 and total deformation WT

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Figure 7

Comparisons of the present analytical predictions with the previous experimental and analytical results for a fully clamped metal foam core sandwich beam transversely loaded by a flat punch at midspan for the following cases: (a) 2a = 3.5 mm in Regime A, (b) 2a = 0 mm in Regime C, and (c) 2a = 18 mm in Regime C

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Figure 8

Finite deflection response in Regime A for fully clamped metal foam sandwich beams (σ¯=0.1, t/c = 0.1, and L/c = 5) transversely loaded by a roller (a¯→0). (a) Normalized total deflection versus normalized loading, and (b) normalized total deflection versus normalized plastic energy.

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Figure 9

Finite deflection response in Regime B for a fully clamped metal foam sandwich beam (σ¯=0.1, t/c = 0.3, and L/c = 3) transversely loaded by a flat roller (a¯→0). (a) Normalized total deflection versus normalized loading, and (b) normalized total deflection versus normalized plastic energy.

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Figure 10

Finite deflection response in Regime C for a fully clamped metal foam sandwich beam (σ¯=0.1, t/c = 0.1 and L/c = 30) transversely loaded by a roller (a¯→0). (a) Normalized overall deflection versus normalized loading, and (b) normalized overall deflection versus normalized plastic energy.

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