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Journal Club for September 2016: Developments and challenges in miniaturized in situ experiments – Towards small-scale fracture mechanics

Small-scale mechanics, especially in situ in electron microscopes, is what I enjoy spending my time with. Within this monthly journal club topic on iMechanica, I would like to give a quick recapitulation of what happened in micromechanics, of course with special emphasis to in situ techniques, over the last years to set the stage. Subsequently, we should revisit some longstanding issues before turning towards recent developments in the field of fracture testing. To keep the amount of information focused, I will not touch on high temperature testing, and also provide mostly review papers for reference rather than referring to the original first works.

Over the last decade, a significant amount of effort was spent on examining the mechanical properties of small volumes. This was inspired by the seminal work of Mike Uchic and co-workers [1], who were the first to use a focused ion beam (FIB) to locally remove material to create small pillars to be loaded in compression. With this experimental achievement, they also encountered a novel size effect of the strength in small single crystal volumes that kept researchers interested for a couple years to follow [2-4].

To better understand the underlying mechanisms, different loading geometries and in situ testing setups were developed for the scanning electron microscope (SEM) [5], the transmission electron microscope (TEM) [5, 6], or the µLaue beam [7, 8] to gain insight into the deformation features evolving on the sample surface and the internal plastic deformation processes. These techniques, in conjunction with molecular dynamics and discrete dislocation dynamics simulations helped us to understand the dislocation processes governing strength and hardening in single crystals at small scales [2-4].

Nowadays, people use the established small-scale testing techniques to address the mechanical properties of various complex materials and specific microstructures, pretty much in the way it was initially devised by Uchic and co-workers. So if you want do small-scale mechanics, just go for it! All you need is a little piece of your exciting material of interest (it should tolerate vacuum and an electron beam, though), a FIB for milling your samples, and a possibility to load them. But nanoindenters are everywhere, and many labs have small loading devices that can operate in an SEM or TEM.

A word of caution while you FIB machine your first sample:
A permanent concern when FIB fabrication is involved touches on the material surface modification by the impinging Ga ions. Certainly, introducing knock on damage into an otherwise pristine material volume will be more dramatic than for a highly defective sample, so it depends on the situation, but should be a concern for anyone using a FIB.

There are certain ways to minimize, remove or avoid this damage. Reduction is possible by lowering the ion energy, or potentially using novel Xe or He based ion microscopes. Those, however, are not as common as their Ga based counterparts and have their own issues. Alternatively, thermal annealing at ~50% of the materials homologous temperature allows sufficient vacancy diffusion to heal the FIB damage [9], as shown exemplarily in Fig. 1 below. This of course requires that the microstructure of interest tolerates such heat treatment. Lastly, one could use alternative nanofabrication methods such as lithography, but these are not as flexible as an FIB and do not permit to address site-specific material properties such as, for example, individual grain boundaries or interfaces.


 
Fig. 1: HR TEM image of a FIB fabricated Cu pillar imaged along the [100] zone axis before (left) and after annealing (right). From [10].

Turning towards fracture experiments, there is a bunch of different geometries available, involving mostly notched pillars and beams as depicted in Fig. 2.


 
Fig. 2: Overview of the most common fracture testing geometries: (a) single end notched beam, (b) double clamped notched beam, (c) double cantilever beam, (d) pillar splitting. Taken from [11].

While these geometries again have their pros and cons for certain experiments (complexity, line of sight, notch accessibility, …), the more urgent question to address was whether there are some geometrical influences affecting the outcome of these tests. Recently, a very nice systematic comparison was performed for Si and the good news is that for all used geometries (Fig. 2) the fracture toughness of Si was pretty much the same [11]. Great, the geometries have been worked out, let us go ahead and break something!

At this point, maybe another word of caution is appropriate:
Looking into the literature published on small-scale fracture so far, most of the work has focused on low toughness materials such as semiconductors, hard coatings, glasses, and intermetallic components. Two good reasons for this might be that: (i) as long as plasticity is absent or limited to the very vicinity of the crack tip, the plastic zone around the crack tip should be contained within a reasonably large specimen, and classical fracture mechanics can be applied. (ii) We know from experience that for brittle materials such as glass, it is not very important how a surface defect or crack looks like, the stress concentration will make it shatter right there.

Now to extend this towards fracture of more ductile materials, it becomes an essential question that the crack should be as sharp as possible to closely mimic a native crack. One can use the well focussed Ga beam to introduce a notch, or leave some ligaments that will fracture first, thereby creating a native crack. This ligament will, however, prevent the in situ observation of the crack tip until they break. Also, one could use different ions for the notching to get sharper (or more blunt) notches or avoid material modification at the crack tip [12]. A recent comparison between Ga, Xe and He on CrN fracture beams is shown in Fig. 3. While these experiments still differ significantly in notch geometry and root radius, they demonstrate the additional flexibility offered by a combination of different ion sources to create largely unmodified samples with possibly sharp cracks.
 

Fig. 3: Notched CrN beams and fracture surfaces produced by different ions: Ga, Xe and He from top to bottom. Scale bar length is 500 nm. Taken from [12].

Another possibility to introduce exactly positioned and very sharp cracks, at least into nanoscale samples, is to sputter the material with the focused electron beam of a TEM [13]. This might sound a funny idea, but if we intend to test the material in situ in the TEM to have access to quantities such as the crack tip opening or local dislocation processes near the crack tip, then why not make use of the sub-nm beam to introduce a notch right where you want it (Fig. 4, bottom left) [13]? Notably, the in situ TEM experiment shown below was performed several years ago and I leave it to the interested reader to identify the experimental issues we identified and improved since.


 
Fig. 4: Still images i-vi and details extracted from an in situ TEM loading sequence of an austenitic steel sample. The corresponding load-displacement data is shown color-coded in the center. The crack was introduced with the focused electron beam of the TEM. Length of the scale bar is 100 nm. Taken from [13].

Any evaluation of such experiments poses a severe challenge, as classical fracture mechanics concepts, even energy based ones, do not necessary hold anymore. The way we choose out of this in order to address even more complicated situations that involve multiple elastic-plastic materials and residual stresses was to pair such miniaturized fracture experiments with informed finite element computations that allow us to assess the configurational driving forces for the propagation of the crack tip [14, 15]. Fig. 5 shows an in situ SEM fracture experiment of a W-Cu-W trilayer system on Si containing residual stresses, and the corresponding local crack driving forces determined from the finite element calculations.

 


Fig. 5: In-situ SEM fracture experiment on a W-Cu-W trilayer system (left) and corresponding local crack driving forces (right). Taken from [15].

In summary, I hope I could highlight some recent developments, address ongoing concerns, but also possible solutions, on our way to establishing best practices for miniaturized fracture experiments.

Looking forward to your comments and questions, and hopefully a lively discussion!

References:
[1]    Uchic MD, Dimiduk DM, Florando JN, Nix WD. Sample Dimensions Influence Strength and Crystal Plasticity. Science 2004;305:986.
[2]    Uchic MD, Shade PA, Dimiduk D. Plasticity of Micrometer-Scale Single Crystals in Compression. Ann. Rev. Mater. Res. 2009;39:361.
[3]    Greer JR and De Hosson JTM. Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect. Prog. Mater. Sci. 2011;56:654.
[4]    Kraft O, Gruber PA, Mönig R, Weygand D. Plasticity in Confined Dimensions. Ann. Rev. Mater. Res. 2010;40:293.
[5]    Legros M, Gianola DS, Motz C. Quantitative In Situ Mechanical Testing in Electron Microscopes. MRS Bull. 2010;35:354.
[6]    Legros M. In situ mechanical TEM: Seeing and measuring under stress with electrons. Comptes Rendus Physique 2014;15:224.
[7]    Maaß R, Van Petegem S, Borca CN, Van Swygenhoven H. In situ Laue diffraction of metallic micropillars. Mater. Sci. Eng. A 2009;524:40.
[8]    Kirchlechner C, Keckes J, Micha J-S, Dehm G. In Situ µLaue: Instrumental Setup for the Deformation of Micron Sized Samples. Adv. Eng. Mater. 2011;13:937.
[9]    Lee S, Jeong J, Kim Y, Han SM, Kiener D, Oh SH. FIB-induced dislocations in Al submicron pillars: Annihilation by thermal annealing and effects on deformation   behavior. Acta Mater. 2016;110:283.
[10]    Kiener D, Zhang Z, Sturm S, Cazottes S, Imrich PJ, Kirchlechner C, et al. Advanced nanomechanics in the TEM: effects of thermal annealing on FIB prepared Cu samples. Phil. Mag. A 2012;92:3269.
[11]    Jaya BN, Kirchlechner C, Dehm G. Can microscale fracture tests provide reliable fracture toughness values? A case study in silicon. J. Mater. Res. 2015;30:686.
[12]    Best JP, Zechner J, Shorubalko I, Oboňa JV, Wehrs J, Morstein M, et al. A comparison of three different notching ions for small-scale fracture toughness measurement. Scripta Mater. 2016;112:71.
[13]    Hintsala E, Kiener D, Jackson J, Gerberich WW. In-Situ Measurements of Free-Standing, Ultra-Thin Film Cracking in Bending. Experim. Mech. 2015;55:1681.
[14]    Kolednik O, Predan J, Fischer FD, Fratzl P. Bioinspired Design Criteria for Damage-Resistant Materials with Periodically Varying Microstructure. Adv. Funct. Mater. 2011;21:3634.
[15]    Treml R, Kozic D, Schöngrundner R, Kolednik O, Gänser HP, Brunner R, et al. Miniaturized fracture experiments to determine the toughness of individual films in a multilayer system. Extreme Mechanics Letters 2016; online.

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