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Influence of the loading rate on the indentation response of Ti-based metallic glass

  • J. Sort (a1), J. Fornell (a2), W. Li (a3), S. Suriñach (a1) and M.D. Baró (a2)...


The mechanical behavior of Ti-based metallic glass has been investigated by means of indentation experiments at different loading rates. Contrary to many crystalline materials, an increase of the loading rate causes a reduction of hardness, i.e., a mechanical softening. This effect is ascribed to deformation-induced creation of excess free volume, which is more pronounced for higher strain rates. The decrease of hardness is accompanied with an increase of the contact stiffness and a reduction of the reduced elastic modulus. Finite element simulations reveal that the mechanical response of this material can be described using the Mohr-Coulomb yield criterion. The changes in the nanoindentation curves with the increase of loading rate are well reproduced by decreasing the value of the Mohr-Coulomb cohesive stress. This result is consistent with the presumed enhancement of free volume.


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1.Bhushan, B.: Nanotribology and nanomechanics in nano/biotechnology. Philos. Trans. R. Soc. London, Ser. A 366, 1499 (2008).
2.Fischer-Cripps, A.C.: Nanoindentation, 1st ed. (Springer-Verlag Inc., New York, 2002).
3.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).
4.Mukhopadhyay, N.K. and Paufler, P.: Micro- and nanoindentationtechniques for mechanical characterisation of materials. Int. Mater. Rev. 51, 209 (2006).
5.Cheng, Y.T. and Cheng, C.M.: Scaling relationships in conical indentation of elastic-perfectly plastic solids. Int. J. Solids Struct. 36, 1231 (1999).
6.Schuh, C.A.: Nanoindentation studies of materials. Mater. Today 9, 32 (2006).
7.Lewandowski, J.J., Wang, W.H., and Greer, A.L.: Intrinsic plasticity or brittleness of metallic glasses. Philos. Mag. Lett. 85, 77 (2005).
8.Ramamurty, U., Jana, S., Kawamura, Y., and Chattopadhyay, K.: Hardness and plastic deformation in a bulk metallic glass. Acta Mater. 53, 705 (2005).
9.Schuh, C.A. and Nieh, T.G.: A survey of instrumented indentation studies on metallic glasses. J. Mater. Res. 19, 46 (2004).
10.Schuh, C.A., Lund, A.C., and Nieh, T.G.: New regime of homogeneous flow in the deformation map of metallic glasses: Elevated temperature nanoindentation experiments and mechanistic modeling. Acta Mater. 52, 5879 (2004).
11.Yang, B. and Nieh, T.G.: Effect of the nanoindentation rate on the shear band formation in an Au-based bulk metallic glass. Acta Mater. 55, 295 (2007).
12.Schuh, C.A., Argon, A.S., Nieh, T.G., and Wadsworth, J.: The transition from localized to homogeneous plasticity during nanoindentation of an amorphous metal. Philos. Mag. 83, 2585 (2003).
13.Spaepen, F.: Microscopic mechanism for steady-state inhomogeneous flow in metallic glasses. Acta Metall. 25, 407 (1977).
14.van Aken, B., de Hey, P., and Sietsma, J.: Structural relaxation and plastic flow in amorphous La50Al25Ni25. Mater. Sci. Eng., A 278, 247 (2000). Hey, P., Sietsma, J., and van Den Beukel, A.: Structural disordering in amorphous Pd40Ni40P20 induced by high temperature deformation. Acta Mater. 46, 5873 (1998).
16.van Steenberge, N., Sort, J., Concustell, A., Das, J., Scudino, S., Suriñach, S., Eckert, J., and Baró, M.D.: Dynamic softening and indentation size effect in a Zr-based bulk glass-forming alloy. Scr. Mater. 56, 605 (2007).
17.Yang, F., Geng, K., Liaw, P.K., Fan, G., and Choo, H.: Deformation in a Zr57Ti5Cu20Ni8Al10 bulk metallic glass during nanoindentation. Acta Mater. 55, 321 (2007).
18.Schuh, C.A. and Lund, A.C.: Atomistic basis for the plastic yield criterion of metallic glass. Nat. Mater. 2, 449 (2003).
19.Vaidyanathan, R., Dao, M., Ravichandran, G., and Suresh, S.: Study of mechanical deformation in bulk metallic glass through instrumented indentation. Acta Mater. 49, 3781 (2001).
20.Lund, A.C. and Schuh, C.A.: The Mohr-Coulomb criterion from unit shear processes in metallic glass. Intermetallics 12, 1159 (2004).
21.Ogata, S., Shimizu, F., Li, J., Wakeda, M., and Shibutani, Y.: Atomistic simulation of shear localization in Cu-Zr bulk metallic glass. Intermetallics 14, 1033 (2006).
22.Fornell, J., Concustell, A., Suriñach, S., Li, W., Cuadrado, N., Gebert, A., Baró, M.D., and Sort, J.: Yielding and intrinsic plasticity of Ti-Zr-Ni-Cu-Be bulk metallic glass. Int. J. Plast. (2009 DOI: 10.1016/j.ijplas.2008.11.002).
23.Lewandowski, J.J. and Greer, A.L.: Temperature rise at shear bands in metallic glasses. Nat. Mater. 5, 15 (2006).
24.Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity., J. Mech. Phys. Solids 46, 411 (1998).
25.Strader, J.H., Shim, S., Bei, H., Oliver, W.C., and Pharr, G.M.: An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, 5285 (2006).
26.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).
27.Wei, B.C., Zhang, T.H., Zhang, L.C., Xing, D.M., Li, W.H., and Liu, Y.: Plastic deformation in Ce-based bulk metallic glasses during depth-sensing indentation. Mater. Sci. Eng., A 449–451, 962 (2007).
28.Liu, L. and Chan, K.C.: Plastic deformation of Zr-based bulk metallic glasses during nanoindentation. Mater. Lett. 59, 3090 (2005).
29.Mukai, T., Nieh, T.G., Kawamura, Y., Inoue, A., and Higashi, K.: Effect of strain rate on compressive behavior of a Pd40Ni40P20 bulk metallic glass. Intermetallics 10, 1071 (2002).
30.Hufnagel, T.C., Jiao, T., Li, Y., Xing, L.Q., and Ramesh, K.T.: Deformation and failure of Zr57Ti5Cu20Ni8Al10 bulk metallic glass under quasi-static and dynamic compression. J. Mater. Res. 17, 1441 (2002).
31.Concustell, A., Sort, J., Greer, A.L., and Baró, M.D.: Anelastic deformation of a Pd40Cu30Ni10P20 bulk metallic glass during nanoindentation. Appl. Phys. Lett. 88, 171911 (2006).
32.Lee, Y.H., Kim, J.Y., Nahm, S.H., and Kwon, D.: Loading rate effect on inelastic deformation in a Zr-based bulk metallic glass. Mater. Sci. Eng., A 449–451, 185 (2007).
33.Jiang, W.H., Fan, G.J., Liu, F.X., Wang, G.Y., Choo, H., and Liaw, P.K.: Rate dependence of shear banding and serrated flows in a bulk metallic glass. J. Mater. Res. 21, 2164 (2006).
34.Narasimhan, R.: Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model. Mech. Mater. 36, 633 (2004).
35.Anand, 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).
36.Zhao, J.: Applicability of the Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock. Int.J. Rock Mech. Min. Sci. 37, 1115 (2000).
37.Ott, R.T., Sansoz, F., Jiao, T., Warner, D., Fan, C., Molinari, J.F., Ramesh, K. T., and Hufnagel, T.C.: Yield criteria and strain-rate behavior of Zr57.4Cu16.4Ni8.2Ta8Al10 metallic glass-matrix composites. Metall. Mater. Trans. A 37, 3251 (2006).


Influence of the loading rate on the indentation response of Ti-based metallic glass

  • J. Sort (a1), J. Fornell (a2), W. Li (a3), S. Suriñach (a1) and M.D. Baró (a2)...


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