Fracture toughness of brittle honeycombs

Superior fracture resistance and topology-induced intrinsic toughening mechanism in 3D shell-based lattice metamaterials

Lattice metamaterials have demonstrated remarkable mechanical properties at low densities. As these architected materials advance toward real-world applications, their tolerance for damage and defects becomes a limiting factor. However, a thorough understanding of the fracture resistance and fracture mechanisms in lattice metamaterials, particularly for the emerging shell-based lattices, has remained elusive. Here, using a combination of in situ fracture experiments and finite element simulations, we show that shell-based lattice metamaterials with Schwarz P minimal surface topology exhibit superior fracture resistance compared to conventional octet truss lattices, with average improvements in initiation toughness up to 150%. This superiority is attributed to the unique shell-based architecture that enables more efficient load transfer and higher energy dissipation through material damage, structural plasticity, and material plasticity. Our study reveals a topology-induced intrinsic toughening mechanism in shell-based lattices and highlights these architectures as a superior design route for creating lightweight and high-performance mechanical metamaterials.

Fracture toughness of fibrin gels as a function of protein volume fraction: Mechanical origins

The mechanical stability of blood clots necessary for their functions is provided by fibrin, a fibrous gel. Rupture of clots leads to life-threatening thrombotic embolization, which is little understood. Here, we combine experiments and simulations to determine the toughness of plasma clots as a function of fibrin content and correlate toughness with fibrin network structure characterized by confocal and scanning electron microscopy. We develop fibrin constitutive laws that scale with fibrin concentration and capture the force-stretch response of cracked clot specimens using only a few material parameters. Toughness is calculated from the path-independent J* integral that includes dissipative effects due to fluid flow and uses only the constitutive model and overall stretch at crack propagation as input. We show that internal fluid motion, which is not directly measurable, contributes significantly to clot toughness, with its effect increasing as fibrin content increases, because the reduced gel porosity at higher density results in greater expense of energy in fluid motion. Increasing fibrin content (1→10mg/mL) results in a significant increase in clot toughness (3→15 N/m) in accordance with a power law relation reminiscent of cellular solids and elastomeric gels. These results provide a basis for understanding and predicting the tendency for thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of the structural and mechanical integrity of blood clots. We determined that increasing the fibrin content in clots, as in some thrombi and fibrin-based anti-bleeding sealants, results in an increase in clot toughness. Toughness corresponds to the ability to resist rupturing in the presence of a defect. We couple bulk mechanical testing, microstructural measurements, and finite element modeling to capture the force-stretch response of fibrin clots and compute toughness. We show that increased fibrin content in clots reduces porosity and limits fluid motion and that fluid motion drastically alters the clot toughness. These results provide a fundamental understanding of blood clot rupture and could help in rational design of fibrin-containing biomaterials.

The toughness of mechanical metamaterials

Rapid progress in additive manufacturing methods has created a new class of ultralight mechanical metamaterials with extreme functional properties. Their application is ultimately limited by their tolerance to damage and defects, but an understanding of this sensitivity has remained elusive. Using metamaterial specimens consisting of millions of unit cells, we show that not only is the stress intensity factor, as used in conventional elastic fracture mechanics, insufficient to characterize fracture, but also that conventional fracture testing protocols are inadequate. Via a combination of numerical and asymptotic analysis, we extend the ideas of elastic fracture mechanics to truss-based metamaterials and develop a general test and design protocol. This framework can form the basis for fracture characterization in other discrete elastic-brittle solids where the notion of fracture toughness is known to break down.

Role of the Crystal Lattice Structure in Predicting Fracture Toughness

We examine the atomistic scale dependence of a material's resistance to failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a way incompatible with Griffith's relationship between fracture and free surface energy. Its value finds its origin in the matching between the continuum displacement field at the engineering scale, and the discrete nature of solids at the atomic scale. The generic asymptotic form taken by this field near the crack tip provides a solution for this matching, and subsequently a way to predict toughness from the atomistic parameters with application to graphene.

Insensitivity to Flaws Leads to Damage Tolerance in Brittle Architected Meta-Materials

Cellular solids are instrumental in creating lightweight, strong, and damage-tolerant engineering materials. By extending feature size down to the nanoscale, we simultaneously exploit the architecture and material size effects to substantially enhance structural integrity of architected meta-materials. We discovered that hollow-tube alumina nanolattices with 3D kagome geometry that contained pre-fabricated flaws always failed at the same load as the pristine specimens when the ratio of notch length (a) to sample width (w) is no greater than 1/3, with no correlation between failure occurring at or away from the notch. Samples with (a/w) > 0.3, and notch length-to-unit cell size ratios of (a/l) > 5.2, failed at a lower peak loads because of the higher sample compliance when fewer unit cells span the intact region. Finite element simulations show that the failure is governed by purely tensile loading for (a/w) < 0.3 for the same (a/l); bending begins to play a significant role in failure as (a/w) increases. This experimental and computational work demonstrates that the discrete-continuum duality of architected structural meta-materials may give rise to their damage tolerance and insensitivity of failure to the presence of flaws even when made entirely of intrinsically brittle materials.

Geometric control of failure behavior in perforated sheets

Adding perforations to a continuum sheet allows new modes of deformation, and thus modifies its elastic behavior. The failure behavior of such a perforated sheet is explored, using a model experimental system: a material containing a one-dimensional array of rectangular holes. In this model system, a transition in failure mode occurs as the spacing and aspect ratio of the holes are varied: rapid failure via a running crack is completely replaced by quasistatic failure, which proceeds via the breaking of struts at random positions in the array of holes. I demonstrate that this transition can be connected to the loss of stress enhancement, which occurs as the material geometry is modified.

The properties of foams and lattices

Man and nature both exploit the remarkable properties of cellular solids, by which we mean foams, meshes and microlattices. To the non-scientist, their image is that of soft, compliant, things: cushions, packaging and padding. To the food scientist they are familiar as bread, cake and desserts of the best kind: meringue, mousse and sponge. To those who study nature they are the structural materials of their subject: wood, coral, cancellous bone. And to the engineer they are of vast importance in building lightweight structures, for energy management, for thermal insulation, filtration and much more. When a solid is converted into a material with a foam-like structure, the single-valued properties of the solid are extended. By properties we mean stiffness, strength, thermal conductivity and diffusivity, electrical resistivity and so forth. And the extension is vast-the properties can be changed by a factor of 1000 or more. Perhaps the most important concept in analysing the mechanical behaviour is that of the distinction between a stretch- and a bending-dominated structure. The first is exceptionally stiff and strong for a given mass; the second is compliant and, although not strong, it absorbs energy well when compressed. This paper summarizes a little of the way in which the mechanical properties of cellular solids are analysed and illustrates the range of properties offered by alternative configurations.