Research Papers

Fracture Behaviors of Bulk Metallic Glasses Under Complex Tensile Loading

[+] Author and Article Information
Li Yu

State Key Laboratory of Nonlinear Mechanics,
Institute of Mechanics
Chinese Academy of Sciences,
Beijing 100190, China;
School of Engineering Sciences,
University of Chinese Academy of Sciences,
Beijing 100049, China
e-mail: yuli@imech.ac.cn

Tzu-Chiang Wang

State Key Laboratory of Nonlinear Mechanics,
Institute of Mechanics
Chinese Academy of Sciences,
Beijing 100190, China;
School of Engineering Sciences,
University of Chinese Academy of Sciences,
Beijing 100049, China
e-mail: tcwang@imech.ac.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 28, 2017; final manuscript received October 25, 2017; published online November 13, 2017. Editor: Yonggang Huang.

J. Appl. Mech 85(1), 011003 (Nov 13, 2017) (6 pages) Paper No: JAM-17-1468; doi: 10.1115/1.4038286 History: Received August 28, 2017; Revised October 25, 2017

Up to now the theoretical analysis for fracture behaviors of bulk metallic glasses (BMGs) are limited to uniaxial loading. However, materials usually suffer complex stress conditions in engineering applications. Thus, to establish an analysis method that could describe fracture behaviors of BMGs under complex loading is rather important. In this paper, a universal formula for the fracture angle is proposed toward solving this problem. The ellipse criterion is used as an example to show how to predict fracture behaviors of BMGs subjected to complex loading according to this formula. In this case, both the fracture strength and fracture angle are found to be well consistent with experimental data.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Klement, W. , Willens, R. H. , and Duwez, P. O. L. , 1960, “ Non-Crystalline Structure in Solidified Gold-Silicon Alloys,” Nature, 187(4740), pp. 869–870. [CrossRef]
Johnson, W. L. , 1986, “ Thermodynamic and Kinetic Aspects of the Crystal to Glass Transformation in Metallic Materials,” Prog. Mater. Sci., 30(2), pp. 81–134. [CrossRef]
Greer, A. L. , 1995, “ Metallic Glasses,” Science, 267(5206), pp. 1947–1953. [CrossRef] [PubMed]
Inoue, A. , 2000, “ Stabilization of Metallic Supercooled Liquid and Bulk Amorphous Alloys,” Acta Mater., 48(1), pp. 279–306. [CrossRef]
Steif, P. S. , Spaepen, F. , and Hutchinson, J. W. , 1982, “ Strain Localization in Amorphous Metals,” Acta Metall., 30(2), pp. 447–455. [CrossRef]
Chen, H. , He, Y. , Shiflet, G. J. , and Poon, S. J. , 1994, “ Deformation-Induced Nanocrystal Formation in Shear Bands of Amorphous Alloys,” Nature, 367(6463), pp. 541–543. [CrossRef]
Hays, C. C. , Kim, C. P. , and Johnson, W. L. , 2000, “ Microstructure Controlled Shear Band Pattern Formation and Enhanced Plasticity of Bulk Metallic Glasses Containing In Situ Formed Ductile Phase Dendrite Dispersions,” Phys. Rev. Lett., 84(13), pp. 2901–2904. [CrossRef] [PubMed]
Xing, L. Q. , Li, Y. , Ramesh, K. T. , Li, J. , and Hufnagel, T. C. , 2001, “ Enhanced Plastic Strain in Zr-Based Bulk Amorphous Alloys,” Phys. Rev. B, 64(18), p. 180201. [CrossRef]
Schuh, C. A. , Hufnagel, T. C. , and Ramamurty, U. , 2007, “ Mechanical Behavior of Amorphous Alloys,” Acta Mater., 55(12), pp. 4067–4109. [CrossRef]
Flores, K. M. , and Dauskardt, R. H. , 1999, “ Local Heating Associated With Crack Tip Plasticity in Zr–Ti–Ni–Cu–Be Bulk Amorphous Metals,” J. Mater. Res., 14(3), pp. 638–643. [CrossRef]
Donovan, P. E. , 1988, “ Compressive Deformation of Amorphous Pd40Ni40P20,” Mater. Sci. Eng., 98, pp. 487–490. [CrossRef]
Liu, C. T. , Heatherly, L. , Horton, J. A. , Easton, D. S. , Carmichael, C. A. , Wright, J. L. , Schneibel, J. H. , Yoo, M. H. , Chen, C. H. , and Inoue, A. , 1998, “ Test Environments and Mechanical Properties of Zr-Base Bulk Amorphous Alloys,” Metall. Mater. Trans. A, 29(7), pp. 1811–1820. [CrossRef]
Zhang, Z. F. , He, G. , Eckert, J. , and Schultz, L. , 2003, “ Fracture Mechanisms in Bulk Metallic Glassy Materials,” Phys. Rev. Lett., 91(4), p. 045505. [CrossRef] [PubMed]
Flores, K. M. , and Dauskardt, R. H. , 2001, “ Mean Stress Effects on Flow Localization and Failure in a Bulk Metallic Glass,” Acta Mater., 49(13), pp. 2527–2537. [CrossRef]
Mukai, T. , Nieh, T. G. , Kawamura, Y. , Inoue, A. , and Higashi, K. , 2002, “ Effect of Strain Rate on Compressive Behavior of a Pd40Ni40P20 Bulk Metallic Glass,” Intermetallics, 10(11), pp. 1071–1077. [CrossRef]
Caris, J. , and Lewandowski, J. J. , 2010, “ Pressure Effects on Metallic Glasses,” Acta Mater., 58(3), pp. 1026–1036. [CrossRef]
Yu, M.-H. , 2002, “ Advances in Strength Theories for Materials Under Complex Stress State in the 20th Century,” ASME Appl. Mech. Rev., 55(3), pp. 169–218. [CrossRef]
Irgens, F. , 2008, Continuum Mechanics, Springer Science & Business Media, Berlin.
Zhang, Z. F. , and Eckert, J. , 2005, “ Unified Tensile Fracture Criterion,” Phys. Rev. Lett., 94(9), p. 094301. [CrossRef] [PubMed]
Chen, C. , Gao, M. , Wang, C. , Wang, W.-H. , and Wang, T.-C. , 2016, “ Fracture Behaviors Under Pure Shear Loading Bulk Metallic Glasses,” Sci. Rep., 6, p. 39522. [CrossRef] [PubMed]
Qu, R. , Eckert, J. , and Zhang, Z. , 2011, “ Tensile Fracture Criterion of Metallic Glass,” J. Appl. Phys., 109(8), p. 083544. [CrossRef]
Lowhaphandu, P. , Montgomery, S. , and Lewandowski, J. J. , 1999, “ Effects of Superimposed Hydrostatic Pressure on Flow and Fracture of a Zr–Ti–Ni–Cu–Be Bulk Amorphous Alloy,” Scr. Mater., 41(1), pp. 19–24. [CrossRef]
Lewandowski, J. J. , and Lowhaphandu, P. , 2002, “ Effects of Hydrostatic Pressure on the Flow and Fracture of a Bulk Amorphous Metal,” Philos. Mag. A, 82(17–18), pp. 3427–3441. [CrossRef]


Grahic Jump Location
Fig. 1

Illustration of the critical fracture lines and critical Mohr circle of the M–C criterion and ellipse criterion in the case of tensile loading. The ellipse is tangent to the straight line at point B according to the uniaxial tensile experimental data. The τ0M−C, τ0Ellipse, σ0M-C, σ0Ellipse, θTM−C, and θTEllipse in the plot denote the critical shear fracture stresses, critical fracture normal stresses, and fracture angles predicted by the M–C criterion and ellipse criterion, respectively.

Grahic Jump Location
Fig. 2

The stress state and shear plane of cylindrical specimen: (a) the stress state and shear plane are shown and (b) the shear plane and fracture angle are shown in the x1-x2 plane

Grahic Jump Location
Fig. 3

The critical Mohr circles for different loading modes and the critical fracture lines of the ellipse criterion: (a) ρ=−0.5, (b) ρ=0, (c) ρ=ρcr, and (d) ρ=0.9

Grahic Jump Location
Fig. 4

The variation of fracture angle and critical stresses with respect to the proportionality coefficient ρ. (a) Variation of the fracture angle with the proportionality coefficient ρ. The points denote the fracture angle of the loading pattern shown in the Figs. 3(a)3(d). (b) The shear stress and normal stress on the fracture plane. The points denote the results of fracture stress while ρ=ρcr.

Grahic Jump Location
Fig. 5

Fracture behaviors of BMGs based on τM and σM: (a) variation of σM and τM with ρ and (b) τM versus σM. The points denote the results of fracture stress while ρ=ρcr.

Grahic Jump Location
Fig. 6

Variation of the shear fracture stress with respect to the normal stress acting on the fracture plane. The critical fracture lines of the two criteria as well as the tangent point B for Mohr's circle are plotted for comparisons.

Grahic Jump Location
Fig. 7

Comparisons between the theoretical calculation results and experimental points (a) fracture angle versus confining pressure, (b) axial fracture stress σ1 versus confining pressure, (c) shear stress on the fracture plane versus confining pressure, and (d) τM versus σM




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In