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A constitutive theory and modeling on deviation of shear band inclination angles in bulk metallic glasses

Published online by Cambridge University Press:  31 January 2011

Ming Zhao  and
Mo Li
Ming Zhao
Affiliation:
Department of Advanced Materials and Nanotechnology, College of Engineering, Peking University, Beijing 100871, People’s Republic of China; and School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Mo Li*
Affiliation:
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
*
a) Address all correspondence to this author. e-mail: mo.li@mse.gatech.edu
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Abstract

A constitutive theory for metallic glasses is established that is based mainly on the Drucker-Prager model and a free-volume theory. The primary emphasis of this theory is on volume dilatation and its consequences on mechanical responses in metallic glasses that have been known from studies in both experiments and atomistic simulations. We also implemented the constitutive theory in a finite element modeling scheme and conducted numerical modeling of deformation of a metallic glass under plane-strain tension and compression. In particular, we focused our attention on the deviation of the shear band inclination angle, a commonly observed phenomenon for metallic glasses. We found very good qualitative agreement with available experimental data on shear band inclination angle and stress-strain relation. We also give a detailed discussion on different constitutive models, in particular the Coulomb-Mohr model, in the context of predicting the shear band inclination angle.

Keywords

AmorphousSimulationStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 8 , August 2009 , pp. 2688 - 2696
Copyright
Copyright © Materials Research Society 2009

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References

1Davis, L.A. and Yeow, Y.T.: Flow and fracture of a Ni-Fe metallic-glass. J. Mater. Sci. 15, 230 (1980).CrossRefGoogle Scholar
2Donovan, P.E.: Compressive deformation of amorphous Pd40Ni40P20. Mater. Sci. Eng. 98, 487 (1988).Google Scholar
3Donovan, P.E.: A yield criterion for Pd40Ni40P20 metallic-glass. Acta Metall. 37, 445 (1989).CrossRefGoogle Scholar
4Liu, C.T., Heatherly, L., Easton, D.S., Carmichael, C.A., Schneibel, J.H., Chen, C.H., Wright, J.L., Yoo, M.H., Horton, J.A., and Inoue, A.: Test environments and mechanical properties of Zr-base bulk amorphous alloys. Metall. Mater. Trans. A 29, 1811 (1998).CrossRefGoogle Scholar
5Lowhaphandu, P., Montgomery, S.L., and Lewandowski, J.J.: Effects of superimposed hydrostatic pressure on flow and fracture of a Zr-Ti-Ni-Cu-Be bulk amorphous alloy. Scr. Mater. 41, 19 (1999).CrossRefGoogle Scholar
6Flores, K.M. and Dauskardt, R.H.: Mean stress effects on flow localization and failure in a bulk metallic glass. Acta Mater. 49, 2527 (2001).CrossRefGoogle Scholar
7Flores, K.M. and Dauskardt, R.H.: Crack-tip plasticity in bulk metallic glasses. Mater. Sci. Eng., A 319, 511 (2001).CrossRefGoogle Scholar
8Vaidyanathan, R., Dao, M., Ravichandran, G., and Suresh, S.: Study of mechanical deformation in bulk metallic glass through instrumented indentation. Acta Mater. 49, 3781 (2001).CrossRefGoogle Scholar
9Wright, W.J., Saha, R., and Nix, W.D.: Deformation mechanisms of the Zr40Ti14Ni10Cu12Be24 bulk metallic glass. Mater. Trans. 42, 642 (2001).CrossRefGoogle Scholar
10Li, M., Eckert, J., Kecskes, L., and Lewandowski, J.: Mechanical properties of metallic glasses and applications—Introduction. J. Mater. Res. 22, 255 (2007).CrossRefGoogle Scholar
11Lund, A.C. and Schuh, C.A.: The Mohr-Coulomb criterion from unit shear processes in metallic glass. Intermetallics 12, 1159 (2004).CrossRefGoogle Scholar
12Lund, A.C. and Schuh, C.A.: Yield surface of a simulated metallic glass. Acta Mater. 51, 5399 (2003).CrossRefGoogle Scholar
13Zhang, Z.F., He, G., Eckert, J., and Schultz, L.: Fracture mechanisms in bulk metallic glassy materials. Phys. Rev. Lett. 91, 045505 (2003).CrossRefGoogle ScholarPubMed
14Zhao, M. and Li, M.: Unpublished results.Google Scholar
15Anand, L. and Su, C.: A theory for amorphous viscoplastic materials undergoing finite deformations, with application to metallic glasses. J. Mech. Phys. Solids 53, 1362 (2005).CrossRefGoogle Scholar
16Tandaiya, P., Narasimhan, R., and Ramamurty, U.: Mode I crack tip fields in amorphous materials with application to metallic glasses. Acta Mater. 55, 6541 (2007).CrossRefGoogle Scholar
17Li, Q.K. and Li, M.: Atomic scale characterization of shear bands in an amorphous metal. Appl. Phys. Lett. 88, 241903 (2006).CrossRefGoogle Scholar
18Li, Q.K. and Li, M.: Free volume evolution in metallic glasses subjected to mechanical deformation. Mater. Trans. 48, 1816 (2007).CrossRefGoogle Scholar
19Wakeda, M., Shibutani, Y., Ogata, S., and Park, J.: Relationship between local geometrical factors and mechanical properties for Cu-Zr amorphous alloys. Intermetallics 15, 139 (2007).CrossRefGoogle Scholar
20Yavari, A.R., Moulec, A. Le, Inoue, A., Nishiyama, N., Lupu, N., Matsubara, E., Botta, W.J., Vaughan, G., Michiel, M. Di, and Kvick, A.: Excess free volume in metallic glasses measured by x-ray diffraction. Acta Mater. 53, 1611 (2005).Google Scholar
21Flores, K.M., Suh, D., Dauskardt, R.H., Asoka-Kumar, P., Sterne, P.A., and Howell, R.H.: Characterization of free volume in a bulk metallic glass using positron annihilation spectroscopy. J. Mater. Res. 17, 1153 (2002).Google Scholar
22Heggen, M., Spaepen, F., and Feuerbacher, M.: Creation and annihilation of free volume during homogeneous flow of a metallic glass. J. Appl. Phys. 97, 033506 (2005).CrossRefGoogle Scholar
23Vallery, R.S., Liu, M., Gidley, D.W., Launey, M.E., and Kruzic, J.J.: Characterization of fatigue-induced free volume changes in a bulk metallic glass using positron annihilation spectroscopy. Appl. Phys. Lett. 91, 261908 (2007).CrossRefGoogle Scholar
24Eyring, H.: Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283 (1936).CrossRefGoogle Scholar
25Spaepen, F.: Microscopic mechanism for steady-state inhomoge-neous flow in metallic glasses. Acta Metall. 25, 407 (1977).CrossRefGoogle Scholar
26Li, Q.K. and Li, M.: Atomistic simulations of correlations between volumetric change and shear softening in amorphous metals. Phys. Rev. B: Condens. Matter 75, 094101 (2007).CrossRefGoogle Scholar
27Zhao, M. and Li, M.: Interpreting the change in shear band inclination angle in metallic glasses. Appl. Phys. Lett. 93, 241906 (2008).CrossRefGoogle Scholar
28Drucker, D.C. and Prager, W.: Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10, 157 (1952).CrossRefGoogle Scholar
29Steif, P.S., Spaepen, F., and Hutchinson, J.W.: Strain localization in amorphous metals. Acta Metall. 30, 447 (1982).CrossRefGoogle Scholar
30Huang, R., Suo, Z., Prevost, J.H., and Nix, W.D.: Inhomogeneous deformation in metallic glasses. J. Mech. Phys. Solids 50, 1011 (2002).CrossRefGoogle Scholar
31Gao, Y.F.: An implicit finite element method for simulating inho-mogeneous deformation and shear bands of amorphous alloys based on the free-volume model. Modell. Simul. Mater. Sci. Eng. 14, 1329 (2006).CrossRefGoogle Scholar
32Eshelby, J.D.: The continuum theory of lattice defects, in Solid State Physics, edited by Seitz, F. and Turnbull, D. (Academic Press, Inc., New York, 1956), p. 79.Google Scholar
33Chen, W.F.: Plasticity in Reinforced Concrete (McGraw-Hill, New York, 1982), p. 216.Google Scholar
34Bowden, P.B. and Jukes, J.A.: Plastic-flow of isotropic polymers. J. Mater. Sci. 7, 52 (1972).Google Scholar
35Hill, R.: On discontinuous plastic states, with special reference to localized necking in thin sheets. J. Mech. Phys. Solids 1, 19 (1952).CrossRefGoogle Scholar
36Guo, Y.Z. and Li, M.: Unpublished results.Google Scholar
37Li, Q.K. and Li, M.: Assessing the critical sizes for shear band formation in metallic glasses from molecular dynamics simulation. Appl. Phys. Lett. 91, 231905 (2007).CrossRefGoogle Scholar
38Davis, L.A.: Plastic instability in a metallic glass. Scr. Metall. 9, 339 (1975).CrossRefGoogle Scholar
39Kimura, H. and Masumoto, T.: Deformation and fracture of an amorphous Pd-Cu-Si alloy in V-notch bending tests. 1. Model mechanics of inhomogeneous plastic-flow in non-strain hardening solid. Acta Metall. 28, 1663 (1980).CrossRefGoogle Scholar
40Leamy, H.J., Chen, H.S., and Wang, T.T.: Plastic-flow and fracture of metallic glass. Metall. Trans. 3, 699 (1972).CrossRefGoogle Scholar
41Pampillo, C.A. and Polk, D.E.: Strength and fracture characteristics of Fe, Ni-Fe and Ni-base glasses at various temperatures. Acta Metall. 22, 741 (1974).CrossRefGoogle Scholar
42Davis, L.A. and Kavesh, S.: Deformation and fracture of an amorphous metallic alloy at high-pressure. J. Mater. Sci. 10, 453 (1975).Google Scholar
43Conner, R.D., Rosakis, A.J., Johnson, W.L., and Owen, D.M.: Fracture toughness determination for a beryllium-bearing bulk metallic glass. Scr. Mater. 37, 1373 (1997).CrossRefGoogle Scholar
44Bruck, H.A., Christman, T., Rosakis, A.J., and Johnson, W.L.: Quasi-static constitutive behavior of Zr41.25Ti13.75Ni10Cu12.5Be22.5 bulk amorphous-alloys. Scr. Metall. Mater. 30, 429 (1994).CrossRefGoogle Scholar
45Webb, T.W., Zhu, X.H., and Aifantis, E.C.: A simple method for calculating shear band angles for pressure sensitive plastic materials. Mech. Res. Commun. 24, 69 (1997).CrossRefGoogle Scholar
46Schuh, C.A., Hufnagel, T.C., and Ramamurty, U.: Overview No. 144—Mechanical behavior of amorphous alloys. Acta Mater. 55, 4067 (2007).Google Scholar
47Hsueh, C.H., Bei, H., Liu, C.T., Becher, P.F., and George, E.P.: Shear fracture of bulk metallic glasses with controlled applied normal stresses. Scr. Mater. 59, 111 (2008).CrossRefGoogle Scholar
48Kuroda, M. and Kuwabara, T.: Shear-band development in polycrystal-line metal with strength-differential effect and plastic volume expansion. Proc. R. Soc. London, Ser. A 458, 2243 (2002).CrossRefGoogle Scholar
49Thamburaja, P. and Ekambaram, R.: Coupled thermo-mechanical modelling of bulk-metallic glasses: Theory, finite-element simulations and experimental verification. J. Mech. Phys. Solids 55, 1236 (2007).CrossRefGoogle Scholar