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Journal Club for August 2016: Frontiers in Nanocrystalline Mechanical Behavior

Tim Rupert's picture


Nanocrystalline materials can be loosely defined as having an average crystallite or grain size that is less than 100 nm.  This small grain size means that the density of grain boundaries within the material is extremely high, leading to difficulty in dislocation movement (the principle carriers of plasticity in many engineering materials) and high yield strengths, as well as other improved properties like high wear and fatigue resistance.  Nanocrystalline materials have been implemented in a number of technological applications such as MEMS devices and protective coatings where relatively small amounts of material are needed, with current efforts often focused on scaling production up to bulk quantities.


This class of high strength materials serves as an interesting rallying point for materials scientists and mechanicians, as there has been significant progress in their development but important issues are still outstanding.  In this iMechanica Journal Club, I hope to stimulate a discussion by pointing out two important areas where innovation and further study is needed.  The first is what I call a “fundamental” problem associated with understanding and modeling basic deformation physics, while the second is a more “practical” issue that concerns the need for obtaining a beneficial combination of mechanical properties.  In each area, I will discuss the current strategies being pursued but also highlight what I feel are open challenges that our community can address.  I encourage readers to suggest and discuss other open opportunities in this field, as well introduce important examples from the literature.  I’ll do my best to introduce important literature works and present a balance view, but any one list is incomplete and we can do much better together.    


Fundamental Issue: Modeling Deformation Mechanisms

As mechanicians, we are at our most powerful when we can observe a broad trend in how a material behaves and suggest micro-mechanical models that can be used to predict the performance of new, hypothetical materials.  Such predictive laws then allow materials scientists to create better materials and enable new technologies.  One of the best known scaling laws connecting material microstructure to mechanical properties is the Hall-Petch relationship, which relates grain size to the yield strength of a material.  Starting as an empirical law based on observations of yielding in low carbon steel, the Hall-Petch relationship states that yield strength should be proportional to the inverse square root of grain size.  As grain size is reduced, and the density of grain boundaries increases, strength shoots up rapidly.  The physical explanation behind this scaling is less well understood, with competing theories suggesting a variety of mechanisms such as dislocation pile-up at boundaries, grain boundaries acting as dislocation sources, and the necessity of geometrically necessary dislocations to maintain compatibility between crystals.  A critical review of the Hall-Petch effect can be found in a recent paper by Cordero et al. [1].  Even with these challenges, Hall-Petch scaling highlights that dislocation interactions with grain boundaries are important and gives a predictive scaling law that can provide guidance for the discovery of high strength materials.


Hall-Petch predicts great strengths for nanocrystalline materials, but in truth the scaling law breaks down as grain size reaches this range.  Strengthening with decreasing grain size still occurs, but not with the exact same scaling with grain size predicted by Hall-Petch.  At extremely small grain sizes, usually ~10-15 nm [2], a complete shift is observed where either a plateau in strength is observed or even a weakening of the material with further grain refinement.  These new trends with grain size occur because new deformation physics begin to control plasticity.  Instead of the traditional pile-up of dislocations within grains, mechanisms that intimately involve the grain boundary emerge.  One example is the emission, pinning, and absorption of dislocations created at grain boundary sites [3].  Another mechanism is the rotation and sliding of grains past one another [4].  Finally, the boundaries themselves can also migrate under stress, transporting material and imparting a plastic strain [5].  For each of these mechanisms, new constitutive laws must be developed to describe plastic deformation and determine how properties connect to microstructure.  For example, Marisol Koslowski’s research group at Purdue University has been using a phase field dislocation dynamics approach to describe dislocation nucleation and slip within a nanoscale grain structure [6,7].  In this technique, the gamma surface (which describes stacking fault and other defect energies) is used to ensure that the correct balance of full and partial dislocation activity is present in different materials.  An example of such a simulation is shown in Figure 1, where dislocation activity can be observed to begin in one grain then spread throughout the microstructure.  This tells us that the dislocation nucleation events are not independent, but can be biased by plasticity in a neighboring crystal.  However, as mentioned previously, there are multiple deformation mechanisms that can be active in this grain size range.  Patric Gruber’s research team at the Karlsruhe Institute of Technology recently reported a synchrotron-based in situ compression experiment on nanocrystalline Ni with a 30 nm grain size [8].  Using this technique, they were able to estimate that their nanocrystalline sample’s overall deformation was comprised of 40% intragranular dislocation plasticity, 15% grain boundary migration, and 45% grain boundary mediated deformation such as grain rotation and sliding.  One of their summarizing plots is shown in Figure 2.  What stands out is that the different mechanisms are active at different applied strains.  As such, the numbers above can be a useful estimate but the relative contributions should be constantly evolving as more strain is applied.  To complicate matters even further, these grain boundary-mediated mechanisms can be strongly affected by seemingly minor alterations like impurity content.  An important recent paper that discusses this point comes from research led by Dan Gianola at the University of California Santa Barbara [9].  Using a combination of in situ nanoindentation within a transmission electron microscope and atom probe tomography, these researchers found that the mechanics and kinetics of boundary migration could be directly tied to the oxygen impurity content at an interface.  This means that any micro-mechanical model for nanocrystalline plasticity must be able to describe new physical mechanisms in a robust fashion, account for the relative contribution of the competing mechanisms, and also treat the complexities associated with other structural features beyond grain size.  This brings us to our first challenge/discussion point:


Challenge 1:

Develop micro-mechanical models that can simultaneously treat all possible mechanisms, while incorporating microstructural measures such as grain size, impurity content, texture, residual strain, etc.



Figure 1.  A nanocrystalline grain structure deformed at a strain rate of 1 x 106 s-1.  Yellow areas have been slipped by partial dislocations while grey areas have been slipped by full dislocations.  Taken from [6].



Figure 2.  (a,b) Important X-ray diffraction parameters during an in situ compression experiment, along with (c) a schematic representation of the active deformation mechanisms.  Taken from [8].




Practical Issue: Balancing Strength and Ductility

Nanocrystalline metals have extremely high strength, but this is almost always accompanied by a dramatic decrease in ductility.  In fact, a general trend is observed where strength and ductility of nanocrystalline metals are almost always mutually exclusive properties.  One can either have a strong yet seemingly brittle response, or a soft and ductile behavior.  Fracture surfaces from nanocrystalline materials show evidence of dimpled rupture, a signature that the nanometer-sized grains themselves are able to sustain plasticity.  However, this intrinsic ductility of each grain does not translate to macroscopic or extrinsic ductility.  Appreciable ductility is required of most structural materials, so that catastrophic failure is avoided.  A ductile response is also helpful for processing tasks, where shaping into a final form often requires plastic flow.


A number of novel strategies have been introduced in recent years to overcome this challenge.  One of the first to have success was the usage of nanotwinned microstructures.  Nanotwinned metals are typically comprised of grains with diameters of 500-1000 nm which contain twin boundaries with average spacings of 5-100 nm, as demonstrated by the work of Ke Lu’s research group at the Chinese Academy of Sciences [10,11] and shown in Figure 3(a).  This unique microstructure allows for both soft and hard modes of deformation, with slip parallel and perpendicular to the twin boundaries, respectively.  However, such a strategy is by definition limited to those materials which can sustain a large number of twin boundaries.  This is often tied to the stacking fault energy of the material, with lower values being better, which is why Cu was the initial model system.  A novel new strategy to overcome this limitation has been pursued by the research group of Xinghang Zhang of Texas A&M/Purdue, who have used templated layers of low stacking fault energy materials to seed a highly twinned film of Al (a high stacking fault energy material) [12].  Another type of strategy is the recent development of gradient nanostructured materials, where grain size changes smoothly from the nanometer scale on the surface of a component to the micron scale in the interior [13], as shown in Figure 3(b).  This type of microstructure has been found to induce a macroscopic strain gradient throughout the material, resulting in extra strain hardening and delayed failure [14].  A recent innovation has even coupled this concept with the idea of adding nanotwins, to make a material where there is a gradient of twin boundaries within the microstructure [15].  In a sense though, this is still balancing the strength and ductility of your overall material.  A soft coarse-grained interior is necessary, so the overall strength of these gradient materials is often below the nanostructured reference.  Finally, my research group at the University of California Irvine is pursuing a strategy of adding features called complexions at the grain boundaries that can easily absorb incoming dislocation and delay crack nucleation [16].  Complexions are thermodynamically-stable interfacial structures and they offer a way to tailor the level of structural order at a grain boundary in a controlled manner.  We recently were able to induce these features in a nanocrystalline Cu-Zr alloy, obtaining a material that was an order of magnitude more ductile than pure nanocrystalline Cu while also being stronger [17].  This was accomplished by adding structurally disordered or amorphous complexions to a nanocrystalline grain structure, as shown in Figure 3(c).  All of these examples rely on different physical principles but have achieved some success.  We come to our second challenge/discussion point:


Challenge 2:

Optimize these new strategies for strong yet ductile nanocrystalline materials, or even develop new avenues that are more promising.



Figure 3.  (a) An example of a nanotwinned Cu specimen taken from [10].  (b) Gradient nanostructured materials, such as that reported on in [14], have a gradient from nanoscale grains to a micron-sized grains.  (c) An example of a disordered complexion in nanocrystalline Cu-Zr, taken from [17].




The challenges and papers presented above represent only a small example of the possible research directions for the field of nanocrystalline mechanical behavior, but they are instructive for highlighting the interdisciplinary nature of this area.  Solid mechanicians will be essential for creating new micro-mechanical models to explain the new deformation physics observed in these materials.  Materials scientists can then hypothesize about which new materials may have improved properties and brainstorm new material design concepts.  Those focused on materials processing can then bring these new types of microstructures to life.  To push this area forward, please read the text above but also become an active participant.  In the comments below, feel free to suggest other excellent papers in this area, identify additional challenges and focus areas, or perhaps even help us isolate what the rate limiting steps will be for future innovation (characterization, processing, property measurement, etc.).






1.Cordero, Z. C., Knight, B. E. and Schuh, C. A. "Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals." Int. Mater. Rev., 1-18, (2016).

2.Trelewicz, J. R. and Schuh, C. A. "The Hall-Petch breakdown in nanocrystalline metals: A crossover to glass-like deformation." Acta Mater. 55, 5948-5958, (2007).

3.Brandl, C., Derlet, P. M. and Van Swygenhoven, H. "Dislocation mediated plasticity in nanocrystalline Al: the strongest size." Modell. Simul. Mater. Sci. Eng. 19, (2011).

4.Wang, Y. B., Li, B. Q., Sui, M. L. and Mao, S. X. "Deformation-induced grain rotation and growth in nanocrystalline Ni." Appl. Phys. Lett. 92, 011903, (2008).

5.Legros, M., Gianola, D. S. and Hemker, K. J. "In situ TEM observations of fast grain-boundary motion in stressed nanocrystalline aluminum films." Acta Mater. 56, 3380-3393, (2008).

6.Cao, L. and Koslowski, M. "Rate-limited plastic deformation in nanocrystalline Ni." J. Appl. Phys. 117, 244301, (2015).

7.Cao, L., Hunter, A., Beyerlein, I. J. and Koslowski, M. "The role of partial mediated slip during quasi-static deformation of 3D nanocrystalline metals." Journal of the Mechanics and Physics of Solids 78, 415-426, (2015).

8.Lohmiller, J. et al. "Untangling dislocation and grain boundary mediated plasticity in nanocrystalline nickel." Acta Mater. 65, 295-307, (2014).

9.He, M.-R. et al. "Linking stress-driven microstructural evolution in nanocrystalline aluminium with grain boundary doping of oxygen." Nature Communications 7, 11225, (2016).

10.Lu, L., Chen, X., Huang, X. and Lu, K. "Revealing the Maximum Strength in Nanotwinned Copper." Science 323, 607-610, (2009).

11.Lu, L., Shen, Y. F., Chen, X. H., Qian, L. H. and Lu, K. "Ultrahigh strength and high electrical conductivity in copper." Science 304, 422-426, (2004).

12.Bufford, D. et al. "Formation Mechanisms of High-density Growth Twins in Aluminum with High Stacking-Fault Energy." Materials Research Letters 1, 51-60, (2013).

13.Lu, K. "Making strong nanomaterials ductile with gradients." Science 345, 1455-1456, (2014).

14.Wu, X., Jiang, P., Chen, L., Yuan, F. and Zhu, Y. T. "Extraordinary strain hardening by gradient structure." Proc. Natl. Acad. Sci. USA 111, 7197-7201, (2014).

15.Wei, Y. et al. "Evading the strength–ductility trade-off dilemma in steel through gradient hierarchical nanotwins." Nature Communications 5, 3580, (2014).

16.Pan, Z. and Rupert, T. J. "Amorphous intergranular films as toughening structural features." Acta Mater. 89, 205-214, (2015).

17.Khalajhedayati, A., Pan, Z. and Rupert, T. J. "Manipulating the interfacial structure of nanomaterials to achieve a unique combination of strength and ductility." Nature Communications 7, 10802, (2016).




Shailendra's picture

Hi Tim, 

A wonderful, succinct introduction to the richness of the plasticity mechanisms in nanocrystalline materials and very thought-provoking challenges that are sure to bring up tremendous opportunities in designing novel, scalable microstructures. Thank you for setting up this problem on iMechanics Journal Club!

From a mechanics perspective, there are useful mechanism-based models that can be integrated into continuum plasticity (depending upon length-scales of interest). One question that arises is - how disparate are the time scales and length scales over which different mechanisms persist? Also, an interesting challenge is to be able to extract competitive versus cooperative nature of these mechanisms through high-resolution simulations and/or experiments and develop a reasonable coarse-grained description. 

It would be useful if shed some light on these.




Tim Rupert's picture

Hi Shailendra,

These are wonderful questions!  Thank you for bringing them up.  First, the question of disparate time and length scales might have to be addressed by different techniques.  Length scales come into play in the example shown above in Figure 1, which nicely shows how events in a single grain can bias future events in the surrounding microstructure.  This is perhaps a place where these types of mesoscale models (phase field dislocation dynamics in this case) can let us build from an atomic understanding to one that affects a larger microstructure.  Timescales are also tricky, as their is evidence that any one mechanisms can be extremely sensitive to strain rate.  In Ref. [1] below, Christian Brandl, Peter Derlet and Helena Van Swygenhoven report on an excellent study of strain rate effects on dislocation nucleation and propagation.  The one thing I always recall from this paper is that the cross-slip of dislocations can be very different depending on the strain rate!  Grain rotation and sliding should be very rate sensitive as well, since atomic shuffling is needed.


You also bring up a great point about competitive vs. cooperative mechanisms.  We tend to think of deformation mechanisms as competitive, with the easiest to activate dominating, and in fact my discussion above probably sounded like it was from this perspective.  However, there are a number of cases where they must be cooperative.  Erik Bitzek had a very nice paper a few years back, Ref. [2] below, where he used atomistics to study the stress and strain in individual nanograins as they plastically deformed.  He found that a single dislocation can result in 2-3% shear strain, a rather violent deformation compared to the usual view of what a single dislocation can do.  Such a shear would have to be accomodated by some ammount of grain boundary sliding, if only to maintain compatibility between the neighboring grains


1.Brandl, C., Derlet, P. M. and Van Swygenhoven, H. "Strain rates in molecular dynamics simulations of nanocrystalline metals." Philos. Mag. 89, 3465-3475, (2009).

2.Bitzek, E., Derlet, P. M., Anderson, P. M. and Van Swygenhoven, H. "The stress-strain response of nanocrystalline metals: A statistical analysis of atomistic simulations." Acta Mater. 56, 4846-4857, (2008).


Thanks again for the comments and I hope others can shed further light on these excellent questions...




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