Zhigang Suo

Mixed mode cracking in layered materials

Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Highly stretchable and tough hydrogels

Hydrogels are used as scaffolds for tissue engineering, vehicles for drug delivery, actuators for optics and fluidics, and model extracellular matrices for biological studies. The scope of hydrogel applications, however, is often severely limited by their mechanical behaviour. Most hydrogels do not exhibit high stretchability; for example, an alginate hydrogel ruptures when stretched to about 1.2 times its original length. Some synthetic elastic hydrogels have achieved stretches in the range 10–20, but these values are markedly reduced in samples containing notches. Most hydrogels are brittle, with fracture energies of about 10 J m−2 (ref. 8), as compared with ∼1,000 J m−2 for cartilage and ∼10,000 J m−2 for natural rubbers. Intense efforts are devoted to synthesizing hydrogels with improved mechanical properties; certain synthetic gels have reached fracture energies of 100–1,000 J m−2 (refs 11, 14, 17). Here we report the synthesis of hydrogels from polymers forming ionically and covalently crosslinked networks. Although such gels contain ∼90% water, they can be stretched beyond 20 times their initial length, and have fracture energies of ∼9,000 J m−2. Even for samples containing notches, a stretch of 17 is demonstrated. We attribute the gels’ toughness to the synergy of two mechanisms: crack bridging by the network of covalent crosslinks, and hysteresis by unzipping the network of ionic crosslinks. Furthermore, the network of covalent crosslinks preserves the memory of the initial state, so that much of the large deformation is removed on unloading. The unzipped ionic crosslinks cause internal damage, which heals by re-zipping. These gels may serve as model systems to explore mechanisms of deformation and energy dissipation, and expand the scope of hydrogel applications.

Fracture mechanics for piezoelectric ceramics

We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted—that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffiths energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r12±iϵand r12±iϵ, where ϵ. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.

Stretchable gold conductors on elastomeric substrates

Stripes of thin gold films are made on an elastomeric substrate with built-in compressive stress to form surface waves. Because these waves can be stretched flat they function as elastic electrical conductors. Surprisingly, we observe electrical continuity not only up to an external strain of ∼2% reached by stretching the films first flat (∼0.4%) and then to the fracture strain of free-standing gold films (∼1%), but up to ∼22%. Such large strains will permit making stretchable electric conductors that will be essential to three-dimensional electronic circuits.

Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

MECHANICS OF ROLLABLE AND FOLDABLE FILM-ON-FOIL ELECTRONICS

The mechanics of film-on-foil devices is presented in the context of thin-film transistors on steel and plastic foils. Provided the substrates are thin, such transistors function well after the foils are rolled to small radii of curvature. When a substrate with a lower elastic modulus is used, smaller radii of curvature can be achieved. Furthermore, when the transistors are placed in the neutral surface by sandwiching between a substrate and an encapsulation layer, even smaller radii of curvature can be attained. Transistor failure clearly shows when externally forced and thermally induced strains add to, or subtract from, each other.

Stretchable Interconnects for Elastic Electronic Surfaces

Elastic electronic surfaces will integrate stiff thin film devices onto compliant polymer substrates. These surfaces may be stretched once or many times, by up to tens of percent strain. One way to make such an elastic electronic surface is to distribute rigid subcircuit islands over the polymer surface, and then fabricate active devices on the islands. These islands need to be interconnected with stretchable metallization. We describe stretchable interconnects made of stripes of thin gold film patterned on elastomeric membranes. These membranes can be stretched by up to twice their initial length and maintain electrical conduction. We review the fabrication of these conductors, present their electrical and mechanical properties, and summarize our model for their extreme stretchability. Using such stretchable interconnects, we made the first elastic circuit, an inverter of thin film transistors. The circuit remains functional when stretched and relaxed by 12% strain.

Deformation mechanisms in nacre

Nacre (mother-of-pearl) from mollusc shells is a biologically formed lamellar ceramic. The inelastic deformation of this material has been experimentally examined, with a focus on understanding the underlying mechanisms. Slip along the lamellae tablet interface has been ascertained by testing in compression with the boundaries oriented at 45° to the loading axis. The steady-state shear resistance tss has been determined and inelastic strain shown to be as high as 8%. The inelastic deformation was realized by massive interlamellae shearing. Testing in tension parallel to the tablets indicates inelastic strain of about 1%, occurring at a steady-state stress, sss ∪ 110 MPa. The strain was associated with the formation of multiple dilatation bands at the intertablet boundaries accompanied by interlamellae sliding. Nano-asperities on the aragonite tablets and their interposing topology provide the resistance to interfacial sliding and establish the level of the stress needed to attain the inelastic strain. Detailed mechanisms and their significance for the design of robust ceramics are discussed.

Stretchable, Transparent, Ionic Conductors

Hydrogel Stretch A range of stretchable, conductive materials can be made either by making an electrical conductor more stretchable or by adding an electrical conductor to a stretchable material. Keplinger et al. (p. 984; see the Perspective by Rogers) have added to the possibilities of an alternative stretchable ionic conductor based on a hydrogel material used to make deformable devices that are fully transparent to light over the visible spectrum and that can withstand high voltages and high frequencies. Stretchable ionic gels are fabricated into transparent actuators and loudspeakers. [Also see Perspective by Rogers] Existing stretchable, transparent conductors are mostly electronic conductors. They limit the performance of interconnects, sensors, and actuators as components of stretchable electronics and soft machines. We describe a class of devices enabled by ionic conductors that are highly stretchable, fully transparent to light of all colors, and capable of operation at frequencies beyond 10 kilohertz and voltages above 10 kilovolts. We demonstrate a transparent actuator that can generate large strains and a transparent loudspeaker that produces sound over the entire audible range. The electromechanical transduction is achieved without electrochemical reaction. The ionic conductors have higher resistivity than many electronic conductors; however, when large stretchability and high transmittance are required, the ionic conductors have lower sheet resistance than all existing electronic conductors.

Sandwich test specimens for measuring interface crack toughness

Abstract A crack lying along one interface on an elastic sandwich structure is analyzed. When the thickness of the middle layer is small compared with the other length scales of the structure, a universal relation is found between the actual interface stress intensity factors at the crack tip and the apparent mode I and mode II stress intensity factors associated with the corresponding problem for the crack in the homogeneous material. Therefore, if the apparent stress intensity factors are known, for example calculated from the applied loads as if the structure was homogeneous, this information can be immediately converted into the interface stress intensity factors with the universal relation. This observation provides the theoretical basis for developing sandwich specimens for measuring interface crack toughness. The universal relation reveals the extent to which the asymmetry inherent to a bimaterial interface induces asymmetry in the near tip crack field. In particular, the result of the study can be used to infer whether stress intensity factors for a homogeneous body can be used with good approximation in place of the actual interface stress intensity factors. A proposal for simplifying the approach to interfacial fracture is made which plays down the role of the so-called oscillatory interface singularity stresses.