Mechanical Behavior of Amorphous Alloys
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Acta Materialia 55 (2007) 4067–4109 www.elsevier.com/locate/actamat Overview No. 144 Mechanical behavior of amorphous alloys Christopher A. Schuh a,*, Todd C. Hufnagel b, Upadrasta Ramamurty c a Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, M.I.T., Cambridge, MA 02139, USA b Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, USA c Department of Materials Engineering, Indian Institute of Science, Bangalore-560 012, India Received 14 August 2006; received in revised form 29 January 2007; accepted 31 January 2007 Available online 19 April 2007 Abstract The mechanical properties of amorphous alloys have proven both scientifically unique and of potential practical interest, although the underlying deformation physics of these materials remain less firmly established as compared with crystalline alloys. In this article, we review recent advances in understanding the mechanical behavior of metallic glasses, with particular emphasis on the deformation and fracture mechanisms. Atomistic as well as continuum modeling and experimental work on elasticity, plastic flow and localization, frac- ture and fatigue are all discussed, and theoretical developments are connected, where possible, with macroscopic experimental responses. The role of glass structure on mechanical properties, and conversely, the effect of deformation upon glass structure, are also described. The mechanical properties of metallic glass-derivative materials – including in situ and ex situ composites, foams and nanocrystal- reinforced glasses – are reviewed as well. Finally, we identify a number of important unresolved issues for the field. Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Metallic glass; Amorphous metal; Mechanical properties 1. Introduction forming, glass structure, and the interesting and potentially valuable properties of amorphous metals [2–4]. Amorphous metallic alloys represent a relatively young One of the enduring attractions of amorphous alloys is class of materials, having been first reported in 1960 when their interesting (and impressive) suite of mechanical prop- Klement et al. performed their classic rapid-quenching erties. The mechanics of metallic glasses have proven to be experiments on Au–Si alloys [1]. Since that time, there of fundamental scientific interest for their contrast with has been remarkable progress in exploring alloy composi- conventional crystalline metals, and also occupy a unique tions for glass formers, seeking elemental combinations niche compared with other classes of engineering materials. with ever-lower critical cooling rates for the retention of For example, amorphous alloys generally exhibit elastic an amorphous structure. The so-called ‘‘bulk’’ glass-form- moduli on the same order as conventional engineering met- ing alloys represent particularly impressive success in this als, but have room-temperature strengths significantly in endeavor, with characteristic specimen sizes in excess of excess of those of polycrystals with comparable composi- 1 mm. These bulk glass formers – mostly complex alloys tion. And while they usually suffer a strong tendency for based on multicomponent mixtures – are now known to shear localization and macroscopically brittle failure at be numerous, and manifest intriguing properties due to ambient temperature, there is clear evidence that metallic their amorphous structures. There are several succinct glasses are capable of legitimate plastic shear flow at the and thorough recent reviews covering the science of glass microscale. The consequent promise of high strength with non-negligible toughness has inspired substantial research * Corresponding author. effort on the room-temperature properties of metallic E-mail address: [email protected] (C.A. Schuh). glasses. At the same time, the amorphous structure leads 1359-6454/$30.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.01.052 4068 C.A. Schuh et al. / Acta Materialia 55 (2007) 4067–4109 Nomenclature a crack length an coefficient of normal stress dependence A temperature-dependent constant ao parameter pertaining to the volume fraction of B bulk modulus deformable material 0 ct transverse wave speed ao modified version of ao for uniaxial loading C constraint factor ap coefficient of pressure dependence Cs constant pertaining to strength in the inhomoge- b ratio of the dilatation to the shear strain of an neous regime STZ D constant pertaining to strength in the inhomoge- c shear strain neous regime c_ shear strain rate E Young’s modulus cc critical strain for localization DFo free energy for STZ activation co characteristic strain of an STZ Gc fracture energy c_m strain rate in an amorphous matrix surrounding DGs activation free enthalpy to initiate deformation a forming shear band h indentation depth c_s characteristic strain rate of shear banding H hardness ct surface tension k Boltzmann constant d shear band thickness ky shear resistance or shear flow stress di plastic zone size around an indentation Kc fracture toughness e_ uniaxial strain rate KIc mode I fracture toughness j thermal conductivity DK stress intensity factor kc critical wavelength of an instability m Paris law exponent l, l(T) shear modulus, temperature-dependent shear n stress sensitivity modulus N number of fatigue loading cycles m Poisson’s ratio p hydrostatic pressure mo attempt frequency for an STZ P load r uniaxial stress Q activation energy r0 yield stress in uniaxial tension or compression c r distance ahead of a propagating shear front r0 yield stress in uniaxial compression rp plastic zone size r1,r2,r3 principal stresses s_ diffusion jump rate rn normal stress acting on the shear plane S stress amplitude ry yield strength T temperature ru uniaxial tensile strength TDB ductile-to-brittle transition temperature rm yield or flow stress of the amorphous matrix of a Tg glass transition temperature composite To reference temperature for excess free volume rp yield or flow stress of a reinforcement phase in a DT temperature increase above ambient composite u_ shear displacement rate s shear stress Du shear displacement, as on a shear band so athermal shear stress * Du critical shear displacement for fracture sy effective yield stress vf average free volume assigned to each atom h angle of the shear plane with respect to the uni- v* critical volume required for deformation axial loading axis v mean free volume v fraction of plastic work converted into heat V activation volume n geometrical constant of order unity Vp volume fraction of the reinforcement particles f pressure gradient ahead of the crack tip a coefficient of normal stress or pressure depen- Xo characteristic volume of an STZ dence (see also ap and an) Xs characteristic volume for a critical shear acte volume coefficient of thermal expansion event to high-temperature rheological properties well known in The availability of more and larger amorphous alloy other glassy systems, including oxides and amorphous specimens, combined with the intriguing collection of prop- polymers: stable Newtonian flow at low stresses enables erties outlined above, has led to a rapid proliferation of superplastic-like deformation that may be useful in research on the mechanical properties of metallic glasses shape-forming operations. over the past decade or so. Entirely new classes of metal C.A. Schuh et al. / Acta Materialia 55 (2007) 4067–4109 4069 glass-based materials have also been developed – including foams, composites and nanocrystal-reinforced alloys – whose mechanical properties are just beginning to be stud- ied seriously. There are a number of recent papers which outline the mechanical properties of metallic glasses in broad strokes, which tabulate and compare the properties among glasses of different and varied compositions, or which review some specific properties in detail [2–7].On the other hand, the fundamental principles and mecha- nisms that underpin the mechanical properties of amor- phous metals have not yet been holistically synthesized with the accumulation of new data over the past decade or so. Fig. 1. Two-dimensional schematics of the atomistic deformation mech- Our purpose in this article is to present an overview of anisms proposed for amorphous metals, including (a) a shear transfor- the mechanical properties of metallic glasses with a specific mation zone (STZ), after Argon [40], and (b) a local atomic jump, after Spaepen [39]. focus upon fundamentals and mechanisms of deformation and fracture. This synthesis follows in the vein of the classic review articles of Pampillo (1975) [8] and Argon (1993) [9]; transformation zone’’ (STZ) [12,16–22]. The STZ is essen- while many of the concepts laid out in these earlier reviews tially a local cluster of atoms that undergoes an inelastic remain equally valid today, we incorporate here what we shear distortion from one relatively low energy configura- view as the most important refinements, revisions and tion to a second such configuration, crossing an activated recent advances in understanding the deformation of configuration of higher energy and volume. Since the origi- metallic glasses and their derivatives. Beginning from an nal analog model of Argon et al. [10,23], more sophisti- atomistic picture of deformation mechanisms in amor- cated computer models have been employed to study phous metal, we proceed to review elastic, plastic and frac- glass deformation in both two and three