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Research Papers

An Eccentric Ellipse Failure Criterion for Amorphous Materials

[+] Author and Article Information
Bin Ding

Applied Mechanics Laboratory,
Department of Engineering Mechanics,
Centre for Advanced Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Xiaoyan Li

Applied Mechanics Laboratory,
Department of Engineering Mechanics,
Centre for Advanced Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: xiaoyanlithu@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 19, 2017; final manuscript received May 31, 2017; published online June 14, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(8), 081005 (Jun 14, 2017) (7 pages) Paper No: JAM-17-1265; doi: 10.1115/1.4036943 History: Received May 19, 2017; Revised May 31, 2017

We proposed an eccentric ellipse criterion to describe the failure of amorphous materials under a combination of normal stress σ and shear stress τ. This criterion can reflect a tension–compression strength asymmetry, and unify four previous failure criteria in the σ–τ stress space, including von Mises criterion, Drucker–Prager criterion, Christensen criterion, and ellipse criterion. We examined the validity of the eccentric ellipse criterion in the tensile-shear failure regimes using the results from our atomistic simulations for two typical amorphous CuZr and LiSi, and recent tension–torsion experiments on metallic glasses. The predictions from the eccentric ellipse criterion agree well with these results from atomistic simulations and experiments. It indicates that this eccentric ellipse criterion is essential for the tensile-shear failure of amorphous materials.

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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of the eccentric ellipse failure criterion in the σ–τ stress space

Grahic Jump Location
Fig. 2

Variations of (a) tensile fracture angle θT and (b) uniaxial tensile strength σT with the ratio α = τ0/σ0 for different ζ

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Fig. 3

Variations of (a) compressive fracture angle θC and (b) uniaxial compressive strength σC with the ratio α = τ0/σ0 for different ζ

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Fig. 4

(a) Schematic illustration of initial atomic configuration of simulated sample under a combination of normal stress σy and shear stress τxy. (b) and (c) Radial distribution functions of amorphous CuZr and LiSi samples.

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Fig. 5

Uniaxial tensile/compressive stress–strain curves of amorphous (a) CuZr and (b) LiSi. Shear stress–strain (τxyεxy) curves of amorphous (c) CuZr and (d) LiSi under different tensile stress σy.

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Fig. 6

Comparison between MD simulation results and predictions from eccentric ellipse criterion. MD data and fitting curves of (a) CuZr and (c) LiSi. Dashed circle represents the Mohr's circle with the uniaxial tension. Line segment on the horizontal axis reflects the range of uniaxial tensile strength from MD simulations. Von Mises shear strain contours of amorphous (b) CuZr and (d) LiSi at uniaxial tensile strain εy = 0.2.

Grahic Jump Location
Fig. 7

Comparison between experimental data of metallic glass Zr41Ti14Cu12.5Ni10Be22.5 [26] and predictions from the eccentric ellipse criterion, Mohr–Coulomb criterion, and von Mises criterion

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