Technical Brief

Effect of Material Frame Rotation on the Hardening of an Anisotropic Material in Simple Shear Tests

[+] Author and Article Information
Kelin Chen, Martin Scales

Research Center for Mechanics of Solids,
Structures and Materials,
The University of Texas at Austin,
WRW 110,
Austin, TX 78712

Stelios Kyriakides

Research Center for Mechanics of Solids,
Structures and Materials,
The University of Texas at Austin,
WRW 110,
Austin, TX 78712
e-mail: skk@mail.utexas.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 9, 2018; final manuscript received August 21, 2018; published online September 21, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(12), 124501 (Sep 21, 2018) (5 pages) Paper No: JAM-18-1391; doi: 10.1115/1.4041320 History: Received July 09, 2018; Revised August 21, 2018

The shear stress–strain response of an aluminum alloy is measured to a shear strain of the order of one using a pure torsion experiment on a thin-walled tube. The material exhibits plastic anisotropy that is established through a separate set of biaxial experiments on the same tube stock. The results are used to calibrate Hill's quadratic anisotropic yield function. It is shown that because in simple shear the material axes rotate during deformation, this anisotropy progressively reduces the material tangent modulus. A parametric study demonstrates that the stress–strain response extracted from a simple shear test can be influenced significantly by the anisotropy parameters. It is thus concluded that the material axes rotation inherent to simple shear tests must be included in the analysis of such experiments when the material exhibits anisotropy.

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Fig. 3

Measured shear stress–plastic shear strain (τ−γp) response for the Al-6061-T6 tube analyzed

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Fig. 2

Material element under simple shear; shown are the initial and rotated material axes

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Fig. 1

Tubular test specimen loaded in pure torsion generating simple shear in the thin-walled test section (dimensions in inches; 1 in = 25.4 mm)

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Fig. 4

The material and reference frame equivalent stress–equivalent plastic strain responses extracted from the measured τ−γp response. Included are the calibrated Hill-48 anisotropy constants.

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Fig. 5

Comparison of the Reference Frame equivalent stress–equivalent plastic strain response with the von Mises and Hosford responses when the anisotropy is neglected

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Fig. 6

Effect of anisotropy constants on the material and reference frame equivalent stress–equivalent plastic strain responses: (a) vary S12, (b) vary S2, and (c) vary S3

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Fig. 7

Effect of anisotropy constants on the material and reference frame equivalent stress–equivalent plastic strain responses; three different combinations of Sij



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