DOI: 10.1002/adem.201400423 Strain Gradient in Micro-Hardness Testing and Structural Relaxation in Metallic Glasses** By Yannick Champion* and Lo € ıcPerrie`re An analytical model is proposed to quantitatively describe the depth-dependence of Vickers micro- hardness in metallic glasses. The approach is based on a shear bands distribution-induced strain gradient during testing and was used to analyze thermal relaxation in the Zr 55 Cu 20 Al 10 Ni 10 Ti 5 , Ni 53 Nb 20 Zr 8 Ti 10 Co 6 Cu 3 , and Mg 65 Cu 12.5 Ni 12.5 MM 10 metallic glasses. It was shown that a decrease of the free volume leads systematically to a decrease of the alloy hardness. This analysis also gives an evaluation of the shear band thickness and the role of the elastic properties in the depth-dependence of the Vickers micro-hardness. 1. Introduction Indentation testing is providing with a preliminary insight of the mechanical properties of materials (strength, ductile/ fragile character, and toughness). [1,2] For example, it allows to follow easily the mechanical behavior evolutions during processing of a material and then gives a semi-quantitative guideline for its preparation and optimization. Among the various techniques, the Vickers indentation is probing at micrometer range length scale, which is well suited for investigations in materials science. For example, the strength s s is simply derived according to the Tabor rule: H ¼ 2.8  s s (0.15) n , with H, the Vickers hardness and n the work- hardening coefficient. A specific feature of indentation is the dependence of the measurement with the indent size or indent depth. [3] This is quantitatively explained for crystalline solids based on the dislocations theory. Ashby has proposed the general rule that a non-symmetric plastic deformation (as in indentation where deformation is confined) generates a strain gradient in the deformation zone. It results an extra hardening that Ashby described in terms of geometrically necessary dislocations (GND). [4] Using this approach, Nix and Gao [5] showed that the hardness measured follows the rule: H=H 0 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ h  =h p , with h* a constant depending on the materials and H 0 the hardness at infinite indent size. For non-crystalline solids, the rule is obviously different since dislocation are undefined. For metallic glasses, the deformation is localized in thin shear bands. This leads to absence of macroscopic plasticity when they are tested in tension or compression, but the plasticity is observed in indentation owing to the confined character of the testing. Similar to crystalline solids a depth-dependence of the hardness is observed, [6] but its follows a rule slightly different: H=H 0 ¼ 1 þ ffiffiffiffiffiffiffiffiffi h  =h p . [7] In this work, three different metallic glasses (Zr, Ni, and Mg based) were studied using Vickers micro-hardness testing at various loads to analyze the depth-dependence. In addition, experiments were performed after various thermal treatments in order to reveal the effect of structural relaxation on the glasses properties. A quantitative analytical description of the Vickers hardness variation with the indent size is then proposed based on strain gradient induced by the shear bands distribution and we show that this variation follows the relation: H=H 0 ¼ 1 þ ffiffiffiffiffiffiffiffiffi h  =h p . The modeling is used to analyze thermal relaxation effects on the hardness and the elastic properties of the Zr-, Ni-, and Mg-based metallic glass (MG) alloys. The role of shear bands in the strain gradient induced depth-dependence of the hardness is emphasized. As the mode of plastic deformation in MG, shear banding analysis is necessary for improving glass properties. 2. Experimental Section Three MG alloys having different mechanical and thermal properties have been investigated. A Zr-based MG (Zr 55 Cu 20 Al 10 Ni 10 Ti 5 , with glass transition T g ¼ 390 °C, strength of 1.7 GPa, elastic modulus 80 GPa) characterized by a high glass forming ability (GFA) was prepared by r.f. levitation melting and quenching in a copper crucible into cylinder form (diameter and length up to 10 and 30mm). [8] A Ni-based (Ni 53 Nb 20 Zr 8 Ti 10 Co 6 Cu 3 , T g ¼ 585 °C, strength about 2.7 GPa [*] Y. Champion, L. Perrière Institut de Chimie et des Mat  eriaux Paris-Est, CNRS-UPEC, 2 rue Henri Dunant 94320, Thiais Cedex, France E-mail: champion@icmpe.cnrs.fr [**] This work was supported by the ANR and the French MoD under the program ASTRID (2012–14) VMPB n° ANR-11- ASTR-03601. Arnold Soppo and Yvan Cotrebil are gratefully acknowledged for technical assistance. DOI: 10.1002/adem.201400423 © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 1 ADVANCED ENGINEERING MATERIALS 2014, FULL PAPER