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Yielding and intrinsic plasticity of Ti-Zr-Ni-Cu-Be bulk metallic glass. (English) Zbl 1272.74088

Summary: Bulk metallic glass with composition Ti\(_{40}\)Zr\(_{25}\)Ni\(_{8}\)Cu\(_{9}\)Be\(_{18}\) exhibits considerably high compressive yield stress, significant plasticity (with a concomitant vein-like fracture morphology) and relatively low density. Yielding and intrinsic plasticity of this alloy are discussed in terms of its thermal and elastic properties. An influence of normal stresses acting on the shear plane is evidenced by: (i) the fracture angle (\(<45^\circ \)) and (ii) finite-element simulations of nanoindentation curves, which require the use of a specific yield criterion, sensitive to local normal stresses acting on the shear plane, to properly match the experimental data. The ratio between hardness and compressive yield strength (constraint factor) is analyzed in terms of several models and is best adjusted using a modified expanding cavity model incorporating a pressure-sensitivity index defined by the Drucker-Prager yield criterion. Furthermore, comparative results from compression tests and nanoindentation reveal that deformation also causes strain softening, a phenomenon which is accompanied with the occurrence of serrated plastic flow and results in a so-called indentation size effect (ISE). A new approach to model the ISE of this metallic glass using the free volume concept is presented.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74M25 Micromechanics of solids
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[1] Ai, K.; Dai, L. H.: A new modified expanding cavity model for characterizing the spherical indentation behaviour of bulk metallic Glass with pile-up, Scripta mater. 56, 761-764 (2007)
[2] Al-Rub, R. K. A.; Voyiadjis, G. Z.: Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro-and nano-indentation experiments, Int. J. Plasticity 20, 1139-1182 (2004)
[3] Anand, L.; Su, C.: A theory for amorphous viscoplastic materials undergoing finite deformations, with application to metallic glasses, J. mech. Phys. solids 53, 1362-1396 (2005) · Zbl 1120.74361 · doi:10.1016/j.jmps.2004.12.006
[4] Argon, A. S.: Plastic deformation in metallic glasses, Acta metall. 27, 47-58 (1979)
[5] Ashby, M. F.; Greer, A. L.: Metallic glasses as structural materials, Scripta mater. 54, 321-326 (2006)
[6] Concustell, A.; Sort, J.; Alcalá, G.; Mato, S.; Gebert, A.; Eckert, J.; Baró, M. D.: Plastic deformation and mechanical softening of pd40 cu30 ni10 P20 bulk metallic Glass during nanoindentation, J. mater. Res. 20, 2719-2725 (2005)
[7] Daniel, B. S. S.; Reger-Leonhard, A.; Heilmaier, M.; Eckert, J.; Schultz, L.: Thermal relaxation and high temperature creep of zr55 cu30 al10 ni5 bulk metallic Glass, Mech. time-depend. Mat. 6, 193-206 (2002)
[8] Dao, M.; Chollacoop, N.; Van Vliet, K. J.; Venkatesh, T. A.; Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation, Acta mater. 49, 3899-3918 (2001)
[9] De Hey, P.; Sietsma, J.; Den Beukel, A. Van: Structural disordering in amorphous pd40 ni40 P20 induced by high temperature deformation, Acta mater. 46, 5873-5882 (1998)
[10] Duan, G.; Wiest, A.; Lind, M. L.; Kahl, A.; Johnson, W. L.: Lightweight ti-based bulk metallic glasses excluding late transition metals, Scripta mater. 58, 465-468 (2008)
[11] Fischer-Cripps, A. C.: Nanoindentation, (2002)
[12] Fischer-Cripps, A. C.: Significance of a local temperature rise in nanoindentation testing, J. mater. Sci. 39, 5849-5851 (2004)
[13] Flores, K. M.; Dauskardt, R. H.: Mean stress effects on flow localization and failure in a bulk metallic Glass, Acta mater. 49, 2527-2537 (2001)
[14] Gao, Y. F.; Yang, B.; Nieh, T. G.: Thermomechanical instability analysis of inhomogeneous deformation in amorphous alloys, Acta mater. 55, 2319-2327 (2007)
[15] Gerberich, W. W.; Tymiak, N. I.; Grunlan, J. C.; Horstemeyer, M. F.; Baskes, M. I.: Interpretations of indentation size effects, J. appl. Mech. 69, 433-442 (2002) · Zbl 1110.74454 · doi:10.1115/1.1469004
[16] Guo, F.; Wang, H. -J.; Poon, S. J.; Shiflet, G. J.: Ductile titanium-based glassy alloy ingots, Appl. phys. Lett. 86, 091907 (2005)
[17] Heggen, M.; Spaepen, F.; Feuerbacher, M. J.: Creation and annihilation of free volume during homogeneous flow of a metallic Glass, J. appl. Phys. 97, 033506 (2005)
[18] Huang, Y.; Qu, S.; Hwang, K. C.; Li, M.; Gao, H.: A conventional theory of mechanism-based strain gradient plasticity, Int. J. Plasticity 20, 753-782 (2004) · Zbl 1254.74019
[19] Huang, Y.; Zhang, F.; Hwang, K. C.; Nix, W. D.; Pharr, G. M.; Feng, G.: A model of size effects in nano-indentation, J. mech. Phys. solids 54, 1668-1686 (2006) · Zbl 1120.74658 · doi:10.1016/j.jmps.2006.02.002
[20] Jana, S.; Ramamurty, U.; Chattopadhyay, K.; Kawamura, Y.: Subsurface deformation during vickers indentation of bulk metallic glasses, Mater. sci. Eng. A 375 – 377, 1191-1195 (2004)
[21] Jiang, W. H.; Fan, G. J.; Liu, F. X.; Wang, G. Y.; Choo, H.; Liaw, P. K.: Spaciotemporally inhomogeneous plastic flow of a bulk-metallic Glass, Int. J. Plasticity 24, 1-16 (2008) · Zbl 1290.74006
[22] Johnson, K. L.: Correlation of indentation experiments, J. mech. Phys. solids 18, 115-126 (1970)
[23] Johnson, W. L.; Samwer, K.: A universal criterion for plastic yielding of metallic glasses with a (T/tg)2/3 temperature dependence, Phys. rev. Lett. 95, 195501 (2005)
[24] Kanungo, B. P.; Glade, S. C.; Asoka-Kumar, P.; Flores, K. M.: Characterization of free volume changes associated with shear band formation in zr- and cu-based bulk metallic glasses, Intermetallics 12, 1073-1080 (2004)
[25] Keryvin, V.: Indentation of bulk metallic glasses: relationships between shear bands observed around the prints and hardness, Acta mater. 55, 2565-2578 (2007)
[26] Kim, Y. C.; Kim, W. T.; Kim, D. H.: A development of ti-based bulk metallic Glass, Mater. sci. Eng. A 375 – 377, 127-135 (2004)
[27] Kim, K. B.; Zhang, X. F.; Yi, S.; Lee, M. H.; Das, J.; Eckert, J.: Effect of local chemistry, structure and length scale of heterogeneities on the mechanical properties of a ti45cu40ni7.5zr5sn2.5 bulk metallic Glass, Philos. mag. Lett. 88, 75-81 (2008)
[28] Kusy, M.; Kühn, U.; Concustell, A.; Gebert, A.; Das, J.; Eckert, J.; Schultz, L.; Baró, M. D.: Fracture surface morphology of compressed bulk metallic Glass-matrix-composites and bulk metallic Glass, Intermetallics 14, 982-986 (2006)
[29] Lam, D. C. C.; Chong, A. C. M.: Model and experiments on strain gradient hardening in metallic Glass, Mater. sci. Eng. A 318, 313-319 (2001)
[30] Lele, S.P., Anand, L., 2008. A large-deformation strain-gradient theory for isotropic viscoplastic materials. Int. J. Plasticity, doi:10.1016/j.ijplas.2008.04.003. · Zbl 1277.74009
[31] Lewandowski, J. J.; Greer, A. L.: Temperature rise at shear bands in metallic glasses, Nat. mater. 5, 15-18 (2006)
[32] Lewandowski, J. J.; Lowhaphandu, P.: Effects of hydrostatic pressure on the flow and fracture of a bulk amorphous metal, Philos. mag. A 82, 3427-3441 (2002)
[33] Lewandowski, J. J.; Wang, W. H.; Greer, A. L.: Intrinsic plasticity or brittleness of metallic glasses, Phil. mag. Lett. 85, 77-87 (2005)
[34] Lewandowski, J. J.; Shazly, M.; Nouri, A. S.: Intrinsic and extrinsic toughening of metallic glasses, Scripta mater. 54, 337-341 (2006)
[35] Li, H.; Ghosh, A.; Han, Y. N.; Bradt, R. C.: The frictional component of the indentation size effect in low load microhardness testing, J. mater. Res. 8, 1028-1032 (1993)
[36] Lockett, F. J.: Indentation of a rigid plastic material by a conical indenter, J. mech. Phys. solids 11, 345-355 (1963)
[37] Lund, A. C.; Schuh, C. A.: Yield surface of a simulated metallic Glass, Acta mater. 51, 5399-5411 (2003)
[38] Lund, A. C.; Schuh, C. A.: The mohr – Coulomb criterion from unit shear processes in metallic Glass, Intermetallics 12, 1159-1165 (2004)
[39] Ma, C.; Ishihara, S.; Soejima, H.; Nishiyama, N.; Inoue, A.: Formation of new ti-based metallic glassy alloys, Mater. trans. 45, 1802-1806 (2004)
[40] Manika, I.; Maniks, J.: Size effects in micro- and nanoscale indentation, Acta mater. 54, 2049-2056 (2006)
[41] Mukhopadhyay, N. K.; Paufler, P.: Micro- and nanoindentation techniques for mechanical characterisation of materials, Int. mater. Rev. 51, 209-245 (2006)
[42] Narasimhan, R.: Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model, Mech. mater. 36, 633-645 (2004)
[43] Nix, W. D.; Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity, J. mech. Phys. sol. 46, 411-425 (1998) · Zbl 0977.74557 · doi:10.1016/S0022-5096(97)00086-0
[44] Ogata, S.; Shimizu, F.; Li, J.; Wakeda, M.; Shibutani, Y.: Atomistic simulation of shear localization in cu – zr bulk metallic Glass, Intermetallic 14, 1033-1037 (2006)
[45] Oliver, W. C.; Pharr, G. M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. mater. Res. 7, 1564-1583 (1992)
[46] Park, J. M.; Chang, H. J.; Han, K. H.; Kim, W. T.; Kim, D. H.: Enhancement of plasticity in ti-rich ti – zr – be – cu – ni bulk metallic glasses, Scripta mater. 53, 1-6 (2005)
[47] Patnaik, M. N. M.; Narasimhan, R.; Ramamurty, U.: Spherical indentation response of metallic glasses, Acta mater. 52, 3335-3345 (2004)
[48] Schuh, C. A.; Lund, A. C.: Atomistic basis for the plastic yield criterion of metallic Glass, Nature mater. 2, 449-452 (2003)
[49] Schuh, C. A.; Nieh, T. G.: A survey of instrumented indentation studies on metallic glasses, J. mater. Res. 19, 46-57 (2004)
[50] Schuh, C. A.; Lund, A. L.; 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, 5879-5891 (2004)
[51] Schuh, C. A.; Hufnagel, T. C.; Ramamurty, U.: Overview no. 144 – mechanical behaviour of amorphous alloys, Acta mater. 55, 4067-4109 (2007)
[52] Spaepen, F.: Microscopic mechanism for steady-state inhomogeneous flow in metallic glasses, Acta metall. 25, 407-415 (1977)
[53] Telford, M.: The case for bulk metallic glasses, Mater. today 7, 36-43 (2004)
[54] Vaidyanathan, R.; Dao, M.; Ravichandran, G.; Suresh, S.: Study of mechanical deformation in bulk metallic Glass through instrumented indentation, Acta. mater. 49, 3781-3789 (2001)
[55] Van Aken, B.; De Hey, P.; Sietsma, J.: Structural relaxation and plastic flow in amorphous la50 al25 ni25, Mater. sci. Eng. A 278, 247-254 (2000)
[56] Van Steenberge, N.; Sort, J.; Concustell, A.; Das, J.; Scudino, S.; Suriñach, S.; Eckert, J.; Baró, M. D.: Dynamic softening and indentation size effect in a zr-based bulk Glass-forming alloy, Scripta mater. 56, 605-608 (2007)
[57] Wang, W. H.: Correlations between elastic moduli and properties in bulk metallic glasses, J. appl. Phys. 99, 093506 (2006)
[58] Wang, W. -H.; Wang, R. J.; Li, F. Y.; Zhao, D. Q.; Pan, M. X.: Elastic constants and their pressure dependence of zr41ti14cu12.5ni9be22.5c1 bulk metallic Glass, Appl. phys. Lett. 74, 1803-1805 (1999)
[59] Xi, X. K.; Zhao, D. Q.; Pan, M. X.; Wang, W. H.; Wu, Y.; Lewandowski, J. J.: Fracture of brittle metallic glasses: brittleness or plasticity, Phys. rev. Lett. 94, 125510 (2005)
[60] Yang, B.; Nieh, T. G.: Effect of the nanoindentation rate on the shear band formation in an au-based bulk metallic Glass, Acta mater. 55, 295-300 (2007)
[61] Yang, B.; Liu, C. T.; Nieh, T. G.: Unified equation for the strength of bulk metallic glasses, Appl. phys. Lett. 88, 221911 (2006)
[62] Yavari, A. R.; Lewandowski, J. J.; Eckert, J.: Mechanical properties of bulk metallic glasses, MRS bull. 32, 635-638 (2007)
[63] Zhang, Z. F.; Eckert, J.; Schultz, L.: Difference in compressive and tensile fracture mechanisms of zr59 cu20 al1 0Ni8 ti3 bulk metallic Glass, Acta mater. 51, 1167-1179 (2003)
[64] Zhang, Z. F.; He, G.; Eckert, J.; Schultz, L.: Fracture mechanisms in bulk metallic glassy materials, Phys. rev. Lett. 91, 045505 (2003)
[65] Zhang, B.; Pan, M. X.; Zhao, D. Q.; Wang, W. H.: ”Soft” bulk metallic glasses based on cerium, Appl. phys. Lett. 85, 61-63 (2004)
[66] Zhang, H. W.; Jing, X.; Subhash, G.; Kecskes, L. J.; Dowding, R. J.: Investigation of shear band evolution in amorphous alloys beneath a vickers indentation, Acta mater. 53, 3849-3859 (2005)
[67] Zhang, H. W.; Subhash, G.; Jing, X. N.; Kecskes, L. J.; Dowding, R. J.: Evaluation of hardness-yield strength relationships for bulk metallic glasses, Phil. mag. Lett. 86, 333-345 (2006)
[68] Zhang, J.; Park, J. M.; Kim, D. H.; Kim, H. S.: Effect of strain rate on compressive behaviour of ti45 zr16 ni9 cu10 be20 bulk metallic Glass, Mater. sci. Eng. A, 290-294 (2007)
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