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Journal Club Theme of Feb. 15 2008: Plasticity and Failure of Metallic Glasses
Metallic glasses, or called amorphous alloys, have unique physical and mechanical properties, particularly due to their non-crystalline atomic structure. Thin metallic glass ribbons have been discovered in 1960s, but the fabrication is restricted to a limited number of compositions and high cooling rate. In the past two decades, great progresses have been made and bulk samples covering a wide range of compositions can be routinely fabricated, as reviewed by W.L. Johnson (MRS Bulletin, 1999) and A. Inoue (Acta Mater., 2000). Although the yield strengths of metallic glasses are very high (e.g., several GPas), they have limited engineering applications because of their low ductility and intrinsic brittleness. To this end, a large set of research works aim at the fundamental understanding of the inelastic and failure mechanisms of metallic glasses, which will ultimately offer insights in the ductility enhancement methods and design of novel materials with combined high strength, ductility, and toughness.
1. International Symposia and Conferences
-- Series of International Bulk Metallic Glasses Conferences (current and past, see http://bmg2008.buaa.edu.cn/index.html)
-- TMS Symposia in Bulk Metallic Glasses
-- MRS Symposia in Bulk Metallic Glasses
2. Review Articles and Books
-- MRS Bulletin, August 2007 (edited by A.L. Greer and E. Ma)
-- Bulk Metallic Glasses, edited by M. Miller and P.K. Liaw, Springer, 2007
-- W.L. Johnson, MRS Bulletin, 24, 42-56, 1999
-- A. Inoue, Acta Mater. 48, 279-306, 2000 (http://dx.doi.org/10.1016/S1359-6454(99)00300-6).
-- C.A. Schuh, T.C. Hufnagel, U. Ramamurthy, Acta Mater. 55, 4067-4109, 2007 (http://dx.doi.org/10.1016/j.actamat.2007.01.052).
3. Research Topics
-- Processing kinetics and glass-forming ability
-- Atomic structure
-- Mechanical behavior
-- Other properties and applications
4. Current Understanding and Challenges in Mechanical Properties
The summary here only offers a very limited view, while a large set of literature is not covered. Keep in mind that one purpose of this journal club is to solicit your participation and input in this rapidly growing field. Your knowledge on literature and your ideas are sincerely welcome.
When deforming metallic glasses, the most important feature is the occurrence of strain localization, that is, the plastic strain field is localized into narrow bands. Since these bands usually follow the trajectories of principal shear stress, they are called shear bands. The shear band can catastrophically propagate through a monolithic metallic glass specimen in unconstrained conditions, so that little macroscopic plastic strain can be observed prior to the fracture failure. It is anticipated that the increase of the number and density of shear bands could enhance the ductility and toughness of amorphous alloys. Consequently, people have developed composite approach for ductility enhancement, such as the introduction nano- and micro-particles and/or phases.
From the mechanics point of view, shear bands can be modeled as a material instability. A constitutive law that may satisfy instability criterion will be able to predict shear bands. Examples include adiabatic shear bands in engineering alloys, dilatation-induced instability in geomaterials, among many others. The development of such a constitutive law clearly requires a connection to the atomistic mechanisms for the shear band initiation in metallic glasses. Along these lines, people have developed many theories, e.g., free-volume model (Spaepen), shear-transformation-zone model (Argon), etc. From the experimental point of view, measuring atomistic structure during deformation will offer invaluable insights into the deformation behavior. Great care is also needed in establishing the link between shear-banding behavior and material failure. For example, it remains unclear whether and how a shear band can transition into a crack.
Finally, an important point made by Greer and Ma (MRS Bulletin, Aug. 2007) is the observation that many of the thermodynamic, kinetic, elastic, and plastic properties of metallic glasses are remarkably correlated. Therefore, understanding the atomic structure and ordering/disordering process will be a key in understanding and manipulating the physical and mechanical properties of metallic glasses.
Continuum mechanics of metallic glasses
A few years ago, at a Gordon Conference, Bill Nix told me some phenomena of metallic glasses. Our conversation plus a lot of hard work of Rui Huang led to a joint paper:
R. Huang, Z. Suo, J.H. Prévost, W.D. Nix, "Inhomogeneous deformation in metallic glasses", Journal of the Mechanics and Physics of Solids 50, 1011-1027 (2002).
The paper attempted to address an ubiquitous phenomenon in metallic glass: the formation shear bands during deformation. We would like to have a theory that can evolve shear bands. To do that, we invoked an internal variable, the density of free volume, and prescribed a kinetic model to evolve the internal variable. The theory thus acquired a length scale. After publishing the paper, we have not returned to the problem. There must be other ways to introduce internal variables and length scales.
At the MRS Fall Meeting, possibly in 2006, I heard a talk by Frans Spaepen. He showed an experimental observation that a nanoscale pillar of a metallic glass deforms substantially without forming shear bands. This size effect seems to be a good point to pick up the mechanics of metallic glasses again.
Zhigang: Thanks. Indeed
Zhigang: Thanks.
Indeed there are a number of continuum plasticity theories that can predict shear bands. My understanding your work in JMPS 2002 is a multiaxial generalization of Spaepen's model, together with a diffusion term added to the free volume evolution equation. Thus a length scale is introduced, although the physics of it is not explained. Recently, Falk and Langer published a number of papers that may lead to a different version of length-dependent constitutive model. Nevertheless, in order to explain the size effect experiments, perhaps a length-dependent model will have some insights. On the other hand, when the pillar compression tests do not show shear band, it might be related to other reasons, e.g., not stiff enough to trigger material instability.
It's no doubt that the size effect is a good line for the mechanics study of metallic glass. But to materials scientists, they are pushing for realistic applications of these materials, so ductility enhancement is of primary interest to them.
Yanfei, I enjoyed
Yanfei,
I enjoyed reading your post as well as the articles you suggested....certainly, metallic glasses offer an interesting venue to study size-effects. In a recent work we found that (as far elasticity is concerned), amorphous materials exhibit much stronger size-effects than crystalline materials due to large non-affine deformations (Maranganti and Sharma, 2007). In particular, I am somewhat reminded of a discussion we had on the first journal club issue ever on imechanica.
One thing I have always been curious about is the following: what is the technological interest in amorphous materials? While I can understand interest in them from a fundamental science perspective, I am not quite clear on their applications. Do you have any insights on this?
BMG applications
The technological applications of metallic glasses are the first question this research field faces. There have been some applications in golf club and cell phones. As for structural applications, perhaps it is not that useful for its brittleness. That's also why people are working on ductility enhancement.
Recently there are a number of novel metallic glass composites that display potentials along this line, although these works are under hot debate.
For the size effect in elasticity, I don't know much about it, and would expect it's related to the glass structure. The shear banding behavior is also a thermo-mechanical process, so that glass transition, fragility, etc. are typically involved.
Shear Banding in BMGs?
Shear Banding in BMGs? In metals we characterize shear bands as macroscopic bands running through a few grains and we call them Macro-Shear bands. The origin of these bands has confused everybody till now without a clue. Some say the formation of SBs are totally non-crystallographic, some resort to the belief that the formation of Macro-SBs must originate from micro-scopic shear bands, and all these micro-scopic SBs are linked head-on to form a Macro-SB. Formation of Micro-SBs can only be explained crystallographically through the use of plastic instability criterion d(S)/d(E) = 0. So, the origins of SBs are to some extent crystallographic.
Now coming back to BMGs: I am just curious how does shear bands form in a disordered continuua? If SB formation is assumed to have some crystallographic origin (at microscopic length scale), then there must be some way to explain SB formation in BMGs. Does any stress/strain induced ordering occur in BMGs before failure? Like nanoscopic domains of ordering.