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Research Papers

A Micromechanical Bending Stage for Studying Mechanical Properties of Materials Using Nanoindenter

[+] Author and Article Information
Mohamed Elhebeary

Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: elhebea2@illinois.edu

M. Taher A. Saif

Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: saif@illinois.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 13, 2015; final manuscript received August 16, 2015; published online September 10, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(12), 121004 (Sep 10, 2015) (7 pages) Paper No: JAM-15-1365; doi: 10.1115/1.4031334 History: Received July 13, 2015; Revised August 16, 2015

An analytical and computational model of a novel bending stage is presented. The stage applies bending moments on micro/nanoscale beam specimens using a nanoindenter. In uniaxial tests, any flaw within the entire volume of the specimen may lead to fracture before material yields. The new stage minimizes the volume of material under a uniaxial state of stress in the specimen, but maximizes bending stress over a small volume such that high stresses can be reached within a small volume on the specimen without a premature failure by fracture. The analytical model of the stage accounts for the geometric nonlinearity of the sample, but assumes simplified boundary conditions. It predicts the deflection and stresses in the specimen beam upon loading. The numerical model of the stage and the specimen employing a finite element (FE) package tests the validity of the analytical model. Good agreement between analytical and numerical results shows that the assumptions in the analytical model are reasonable. Therefore, the analytical model can be used to optimize the design of the stage and the specimen. A design of the stage is presented that results in axial/bending stress < 2% in the sample. In order to test the feasibility of the proposed design, a 3D printed stage and a sample are fabricated using the Polyamide PA2200. Bending test is then carried out employing an indenter. Elastic modulus of PA2200 is extracted from the load-deflection data. The value matches closely with that reported in the literature.

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Figures

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Fig. 1

(a) Three-dimensional model of the bending stage, (b) four specimens connected to loading platform and supporting beams, (c) deformed specimens and supporting beams with the applied load, and (d) zoom in view of the specimen

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Fig. 2

Schematic representation for the proposed bending stage

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Fig. 3

Schematic representation for A1A2 segment of the sample beam

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Fig. 4

Schematic of the stage stiffness in the horizontal direction

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Fig. 5

(a) Vertical deflection versus applied load at the center of the loading platform, and (b) horizontal deflection of the supporting beams versus applied load at the center of the loading platform

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Fig. 6

Analytical model results of the uniaxial tension along the specimen at two different loads

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Fig. 7

Bending stress at 1 μm from the anchor of the sample predicted by FE analysis and the analytical model

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Fig. 8

(a) Schematic of the bending stage with fixed ends and (b) FE model result for deformed specimens upon loading

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Fig. 9

Vertical deflection of the loading platform predicted by FE analysis and the analytical model

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Fig. 10

Effect of the error in loading position on specimen stress at the anchors. The change of stress as a fraction of the stress due to concentric loading case is shown.

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Fig. 11

Three-dimensional printed bending stage before testing

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Fig. 12

(a) Test setup and (b) a zoom-in view of the bent specimen during loading

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Fig. 13

Modulus of elasticity of PA2200

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Fig. 14

Applied load on each specimen versus (a) vertical deflection and (b) horizontal deflection

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Fig. 15

Bending stress at the hinge versus applied load using the calculated modulus of elasticity

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