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Journal Club for December 2022:  Order or disorder in microstructures and microarchitectures: Which is better for mechanical performance?

Francois Barthelat's picture

 

Order versus disorder in microstructures and material architectures: which is better for mechanical performance? Traditional engineering materials have random microstructures: In a typical metal the size, shape and orientation of the grains can be somewhat manipulated but it is still characterized by wide statistical distributions. Rubbers and hydrogels can be described as random networks. Engineering cellular materials such as polyurethane foams or biological cellular materials such as cork or trabecular bone display large spatial variations in terms of cell size and interconnectivity. Progress in fabrication (self-assembly, polymer chemistry, material processing, microfabrication, additive manufacturing…) have enabled a much greater control over the microstructure of materials, which can now be made with highly ordered, spatially periodic “architectures”. However, setting aside fabrication constraints and capabilities, are perfectly periodic architectures always desirable over random and stochastic microstructures for mechanical performance? As illustrated by the examples below, there is no clear and universal answer.

Metallurgy: Perfect, single crystals have low yield strength and are not desirable for most applications. “Disordered” features such as point defects, alloying, line defects, grain boundary and polycrystalline structures form the basis of strengthening in metallurgy. There have been significant efforts however, notably by David Embury and co-workers, to induce well-ordered 3D “architectures” in metals, using a variety of processing methods to create highly controlled multilayers and gradients at the mesoscale [1-3]. These ordered structures enable spatially distributed wear resistance, control of instabilities and fracture, or new combinations of high strength and ductility in metals. Second phase particles distributed along well-controlled sinusoidal patterns can also be used to guide and “engineer” the path of cracks, while also increasing overall toughness [4]. Yet there are also many examples where disorder is beneficial in metallurgy: Inclusions spaced randomly in front of a crack in a ductile material produce more toughness than regularly spaced inclusions because of increased crack pinning [5] and crack meandering [6]. Taken to the extreme, creating disorder in metals leads to metallic glasses, whose absence of crystalline structure and dislocations produces extremely high strength (at the expense of ductility [7]). In high-entropy alloys [8, 9], several deformation and fracture mechanisms occur simultaneously or in specific sequences (solid-solution strengthening, mechanical twinning, martensite formation, recrystallization), resulting in unusually high combinations of strength and toughness [10].

Dense architectured materials: High order and periodic material architecture can be achieved using identical building blocks [11, 12]. In topologically interlocked materials (TIMs), regular arrays of blocks are interlocked to form panels mechanically constrained by an external ligament [13, 14]. Individual building blocks are relatively stiff and hard, but their collective sliding can lead to large deformation and energy absorption, frictional sliding, progressive interlocking (“geometric hardening”) and delocalization of deformations [15, 16]. Random arrangements of these same blocks would lead to poor materials: We recently assembled millimeter-size building blocks or “grains” of into fully dense granular crystals with FCC or BCC structures. Well-ordered force lines, flat-on-flat contacts between grains and controlled collective deformation mechanisms resulted in granular crystals 10-20 times stiffer and stronger than randomly packed grains [17]. Yet, a recent study [18] showed that when some irregularities are introduced in the tiling of TIMs, load transfer between some of the blocks is enhanced, which results in improvements in overall strength and toughness.

Low-density architected materials: Traditional cellular materials such as trabecular bone, cork or solid foams have a stochastic structure with high spatial variations in cell size, shape and connectivity [19]. In lattice materials, this randomness is eliminated.  These materials can be modelled and optimized using small unit cell representative elements [20], leading to materials with very high specific stiffnesses [21], strengths [22] or energy absorption capabilities [23] that outperform random cellular materials. Periodic architected materials also enabled negative Poisson’s ratio [24] or programmable instabilities [25]. In this context, imperfections and defects are perceived as a hindrance which decreases mechanical performance [26-29]. Yet, defects in the lattice can also lead to major improvements in properties. For example, disruptions in a perfect lattice can be engineered to increase properties: “macroscale” grain boundaries, precipitates and phases result in increased robustness and damage-tolerance [30, 31], in ways which are reminiscent of strengthening methods in metals. Unusual behavior such as negative Poisson’s effect does not require perfectly periodic lattices, it can also be achieved in stochastic cellular materials and disordered networks  [19, 32]. Disorder in metamaterials and composite materials seems to be making a comeback, and it is now engineered to achieve attractive material responses [33-35].

Biological materials: Order or disorder? It is tempting to turn to natural material for answers, but things are not too clear there either. The Journal Club of last month (Nov 2022) discussed nice examples of biological membranes with crystalline order. Biological material indeed display a broad array of microstructures, many of them spatially periodic [36]. For example, a collagen fibril, which is the main structural building block in biology, is made of rope-like molecules (tropocollagen) which have identical length of about 300 nm. These molecules are parallel to the axis of the fibril with a uniform overlap (the “D-bands” of collagen fibrils) and a 3D arrangement with high crystalline order [37]. This arrangement is critical for a uniform shear-lag type of load transfer within individual fibrils [38], and the length and overlap between molecules is optimum for load transfer [39]. The near perfect order of a collagen fibril is therefore critical to its performance and function, and minute deviations or defects can have profound consequences [40]. At the next length scale, high order also creates high mechanical performance as in unidirectional collagen fibrils in tendon [41], crossply [42] or Bouligand fibrillar structures in fish scales [43]. Another famous example of a biological material with a periodic microstructure is nacre, which can be described as a three-dimensional brick and mortar architecture. A key mechanism in nacre is the massive sliding of the bricks on one another under tensile load, which generates ductility and powerful toughening mechanisms. We recently demonstrated that any small deviations from the perfect periodicity of a “brick wall” is detrimental to strength, to energy absorption and to fracture toughness [44, 45]. The explanation is simple: a perfect brick wall has a homogenous strength distribution. Introducing local variations of strength creates weaker regions, whose failure and coalescence governs tensile strength and ductility. More spatial variations make the weaker regions (the “weakest links”) even weaker, which further decreases overall performance. Achieving nacre-like spatial periodicity in synthetic material with micron-size microstructures is not currently possible [46-48], which is probably why these materials cannot duplicate the massive and collective sliding of the bricks in natural nacre. Perfectly periodic nacre-like brick walls can however be fabricated at larger length scales, enabling collective tablet sliding and high toughness [49-51]. These examples highlight the importance of order in collagenous materials and nacre. Yet, disorder is also found in many strong and tough biological materials [52]. The same collagen fibrils assemble in random networks to form skin, a remarkably tough and damage tolerant material. The random network of collagen fibrils in skin enables large deformations and a key mechanism where collagen fibrils are “recruited” to align along the direction of loading, generating stiffening and strengthening along that direction. It is the random and “loose” microstructure of skin that enable this dynamic adaptation to mechanical loads [53]. Other examples of disordered biological materials include mussel adhesives, hedgehog quills, oyster cement [52]. In these materials, disorder at the atomic scales, nanoscale or microscale promotes compliance, isotropic behavior, resilience, and adaptability to changing loading conditions. Adaptation mechanisms in random biological materials have in fact recently inspired virtual “growth rules”, which have produced cellular materials with unusual graded properties and mechanical robustness against damage [35]. Bone is a complex hierarchical material which displays highly periodic features together with random microstructures [52]. Is this an outcome of growth or is bone trying to get the best of both order and disorder?

So, order versus disorder in microstructures and material architectures: which is better for mechanical performance? The list of papers referenced here is by no means comprehensive, but it illustrates the conflicting answers found in the literature. Is disorder beneficial only for certain mechanisms or certain properties? Or only in particular circumstances? Or only if it introduced under strict rules? Answers to these questions seem critical for the design and optimization of materials and structures.

 

References

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Comments

Ruobing Bai's picture

 Dear Francois,

Thank you for bringing up this timely and interesting topic to the journal club discussion. I fully enjoyed your discussions and appreciate your comprehensive literature review. I have a question to initiate some brainstorming to hopefully help establish the relationship between structure order and mechanical properties:

What do you think are the key parameters (across length scales) that will play roles in determining a material's macroscopic properties (e.g., strength, toughness, etc.)? I can begin with parameters such as: average particle (or rod) size, average particle-particle distance (or unit cell size), standard deviations of these length scales, individual material properties (of particles and matrices), interfacial properties, and fractions of materials in a composite. The challenge here is a HUGE parameter space. Could you shed light on some dominant factors among these? I am particularly interested in the effect on fracture properties (toughness and fatigue-resistance).

Thank you in advance.

Best,

Ruobing 

Francois Barthelat's picture

Dear Ruobing

Thanks for your comments, I am glad you found the post interesting. Regarding your question on which key parameters are needed in models: I think it all depends on what mechanism(s) you are trying to capture in your model, and what level of accuracy / complexity you need from your model. Sometimes you do not need many parameters to capture the properties of complex materials. For example, solid foams have complex 3D architectures, but mechanics on a simpler cubic unit cell (see Gibson and Ashby) can produce good predictions for stiffness or strength.

To capture the effect of order vs. disorder in models, parameters that properly capture order/disorder are also needed (see references 18, 34, 44, 45 above). Some reports referenced above suggest that properties would be highest for perfectly periodic structures, while other reports suggest that a controlled amount of irregularities or disorder in the material is desirable.

Francois

Dear Francois,

Thank you very much for bringing attention to this very timely and important topic of whether disorder or order is desired in the case of mechanical performance of a microstructured or heterogeneous material. This question is also of great importance for other performance characteristics of the material, such as transport and optical properties. A crucial point that is not fully appreciated by many scientific communities is that there is no single type of disordered material. Indeed, there is a spectrum of disorder/order across length scales that spans, for example, from fully uncorrelated disordered systems to correlated disordered systems, then to ordered (periodic) systems with disorder (e.g., defects such as positional randomness, vacancies or dislocations) and finally all the way up to perfectly periodic systems. For instance, one can have exotic states of matter that are intermediate between uncorrelated disorder and perfect order that are isotropic and outperform periodic materials in their photonic and phononic properties; see Refs. 33, 34 and references therein. Quasicrystals of course provide another example of a state of matter with a high degree of order, but with prohibited crystallographic symmetries and long-range orientational order. How does the performance characteristics of a microstructured material depend on the degree of disorder/order across length scales? To answer this broader question requires us to quantify this disorder/order spectrum, which is a highly challenging task. An initial step in this direction was recently undertaken to characterize two-phase media [R1]. However, we are in the infancy of identifying sensitive order metrics and correlating them with material performance. Thus, this is a very fertile topic for future research.

R1: S. Torquato, M. Skolnick, and J. Kim, Local order metrics for two-phase media across length scales, Journal of Physics A: Mathematical and Theoretical, 55 274003 (2022).

Best regards,

Salvatore

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