Metallic glasses (MGs) are often perceived as quintessential structural materials due to their superior mechanical properties such as high strength and large elastic limit. In practical applications, service conditions that introduce cyclic variations in stresses and strains are inevitably involved. The fatigue of MGs is thus a topic of research and practical interest. In this review, a brief introduction on MGs, their applications and challenges, is first provided. Next, experimental studies on fatigue behaviors of both macroscopic and nanoscale MGs are summarized. The range of topics covered include the stress-life behavior, fatigue-crack growth behavior, fatigue-fracture morphology, fatigue-failure mechanisms, as well as the effects of chemical composition, cycling frequency, loading condition, and sample size on the fatigue limits. Finally, recent progresses in simulation studies on the fatigue of MGs are discussed, with an emphasis placed on the atomic-level understanding of the fatigue mechanisms.

Carbon micro/nanolattice materials, defined as three-dimensional (3D) architected metamaterials made of micro/nanoscale carbon constituents, have demonstrated exceptional mechanical properties, including ultrahigh specific strength, stiffness, and extensive deformability through experiments and simulations. The ductility of these carbon micro/nanolattices is also important for robust performance. In this work, we present a novel design of using reversible snap-through instability to engineer energy dissipation in 3D graphene nanolattices. Inspired by the shell structure of flexible straws, we construct a type of graphene counterpart via topological design and demonstrate its associated snap-through instability through molecular dynamics (MD) simulations. One-dimensional (1D) straw-like carbon nanotube (SCNT) and 3D graphene nanolattices are constructed from a unit cell. These graphene nanolattices possess multiple stable states and are elastically reconfigurable. A theoretical model of the 1D bi-stable element chain is adopted to understand the collective deformation behavior of the nanolattice. Reversible pseudoplastic behavior with a finite hysteresis loop is predicted and further validated via MD. Enhanced by these novel energy dissipation mechanisms, the 3D graphene nanolattice shows good tolerance of crack-like flaws and is predicted to approach a specific energy dissipation of 233 kJ/kg in a loading cycle with no permanent damage (one order higher than the energy absorbed by carbon steel at failure, 16 kJ/kg). This study provides a novel mechanism for 3D carbon nanolattice to dissipate energy with no accumulative damage and improve resistance to fracture, broadening the promising application of 3D carbon in energy absorption and programmable materials.

Temperature- and stiffness-dependent edge forces offer new mechanisms of designing nanodevices driven by temperature and stiffness gradients. Here, we investigate the edge forces in a graphene nanolayer on a spring supported graphene substrate based on molecular dynamics (MD) simulations. The dependences of the edge forces on the temperature and stiffness of the substrate are discussed in detail. Special attention is paid to the effect of the out-of-plane deformation of the substrate on the constituent edge forces and the resultant edge force. The results show that the deformation may lead to a significant redistribution of the constituent edge forces but does not change the resultant edge force, suggesting that particular caution should be exercised in designing nanodevices based on sliding graphene layers to avoid potential edge damage.

Nanotwinned metals are a class of hierarchically structured materials that appear to transcend the limits of conventional material systems by exhibiting an exceptional combination of superior strength, ductility and resistance to fracture, fatigue, and wear. Recently, we reported a type of necklace dislocations in nanotwinned metals which become operative when the twin boundary (TB) spacing falls below a few nanometers. Here, we show that the presence of a cracklike defect as the dominant dislocation source could allow the same mechanism to operate at much larger twin spacings. This finding calls for further theoretical and experimental investigations of a new type of TB related dislocation mechanism which may play particularly important roles in crack-tip deformation in nanotwinned metals.

The low fracture toughness of graphene has raised sharp questions about its strength in the presence of crack-like flaws. Here, we discuss a number of recent studies that suggest some promising routes as well as open questions on the possibility of toughening graphene with controlled distributions of topological defects.

A theoretical model is developed to investigate the mechanical behavior of closely packed carbon nanoscrolls (CNSs), the so-called CNS crystals, subjected to uniaxial lateral compression/decompression. Molecular dynamics simulations are performed to verify the model predictions. It is shown that the compression behavior of a CNS crystal can exhibit strong hysteresis that may be tuned by an applied electric field. The present study demonstrates the potential of CNSs for applications in energy-absorbing materials as well as nanodevices, such as artificial muscles, where reversible and controllable volumetric deformations are desired.

An efficient numerical method is developed to analyze the mechanical responses of tensegrity structures subjected to various actuations that lead to large and highly nonlinear (e.g., hardening or softening) deformations. The proposed method, whose accuracy and efficacy are demonstrated through a number of representative examples, holds promise for applications in design, analysis, and safety evaluations of large-scale tensegrity structures.

Molecular dynamics simulations are performed to investigate the effect of surface energy on equilibrium configurations and self-collapse of carbon nanotube bundles. It is shown that large and reversible volumetric deformation of such bundles can be achieved by tuning the surface energy of the system through an applied electric field. The dependence of the bundle volume on surface energy, bundle radius, and nanotube radius is discussed via a dimensional analysis and determined quantitatively using the simulation results. The study demonstrates potential of carbon nanotubes for applications in nanodevices where large, reversible, and controllable volumetric deformations are desired.

Load-bearing biological materials such as bone, teeth, and nacre have acquired some interesting mechanical properties through evolution, one of which is the tolerance of cracklike flaws incurred during tissue function, growth, repair, and remodeling. While numerous studies in the literature have addressed flaw tolerance in elastic structures, so far there has been little investigation of this issue in time-dependent, viscoelastic systems, in spite of its importance to biological materials. In this paper, we investigate flaw tolerance in a viscoelastic strip under tension and derive the conditions under which a pre-existing center crack, irrespective of its size, will not grow before the material fails under uniform rupture. The analysis is based on the Griffith and cohesive zone models of crack growth in a viscoelastic material, taking into account the effects of the loading rate along with the fracture energy, Young’s modulus, and theoretical strength of material.

Mechanical stresses and failure are believed to be a major cause for the limited cycle life of lithium-ion batteries employing high capacity Si electrodes. Recent experiments have shown that patterned Si thin film electrodes on substrate exhibit improved cycling stability and substantial sliding at the film/substrate interface. To facilitate experimental studies of stress evolution in such systems, we have developed a modified Stoney equation which accounts for the effect of interfacial sliding on the relationship between curvature and stress in patterned thin films on substrate.

Carbon nanotubes (CNTs) constitute a prominent example of nanomaterials. In most studies on mechanical properties, the effort was concentrated on CNTs with relatively small aspect ratio of length to diameters. In contrast, CNTs with aspect ratios of several hundred can be produced with today’s experimental techniques. We report atomistic-continuum studies of single-wall carbon nanotubes with very large aspect ratios subject to compressive loading. It was recently shown that these long tubes display significantly different mechanical behavior than tubes with smaller aspect ratios (Buehler, M. J., Kong, Y., and Guo, H., 2004, ASME J. Eng. Mater. Technol. 126 , pp. 245–249). We distinguish three different classes of mechanical response to compressive loading. While the deformation mechanism is characterized by buckling of thin shells in nanotubes with small aspect ratios, it is replaced by a rodlike buckling mode above a critical aspect ratio, analogous to the Euler theory in continuum mechanics. For very large aspect ratios, a nanotube is found to behave like a wire that can be deformed in a very flexible manner to various shapes. In this paper, we focus on the properties of such wirelike CNTs. Using atomistic simulations carried out over a several-nanoseconds time span, we observe that wirelike CNTs behave similarly to flexible macromolecules. Our modeling reveals that they can form thermodynamically stable self-folded structures, where different parts of the CNTs attract each other through weak van der Waals (vdW) forces. This self-folded CNT represents a novel structure not described in the literature. There exists a critical length for self-folding of CNTs that depends on the elastic properties of the tube. We observe that CNTs fold below a critical temperature and unfold above another critical temperature. Surprisingly, we observe that self-folded CNTs with very large aspect ratios never unfold until they evaporate. The folding-unfolding transition can be explained by entropic driving forces that dominate over the elastic energy at elevated temperature. These mechanisms are reminiscent of the dynamics of biomolecules, such as proteins. The different stable states of CNTs are finally summarized in a schematic phase diagram of CNTs.

Recent studies on hard and tough biological materials have led to a concept called flaw tolerance which is defined as a state of material in which pre-existing cracks do not propagate even as the material is stretched to failure near its limiting strength. In this process, the material around the crack fails not by crack propagation, but by uniform rupture at the limiting strength. At the failure point, the classical singular stress field is replaced by a uniform stress distribution with no stress concentration near the crack tip. This concept provides an important analogy between the known phenomena and concepts in fracture mechanics, such as notch insensitivity, fracture size effects and large scale yielding or bridging, and new studies on failure mechanisms in nanostructures and biological systems. In this paper, we discuss the essential concept for the model problem of an interior center crack and two symmetric edge cracks in a thin strip under tension. A simple analysis based on the Griffith model and the Dugdale-Barenblatt model is used to show that flaw tolerance is achieved when the dimensionless number Λ ft = Γ E ∕ ( S 2 H ) is on the order of 1, where Γ is the fracture energy, E is the Young’s modulus, S is the strength, and H is the characteristic size of the material. The concept of flaw tolerance emphasizes the capability of a material to tolerate cracklike flaws of all sizes.

We report atomistic studies of single-wall carbon nanotubes with very large aspect ratios subject to compressive loading. These long tubes display significantly different mechanical behavior than tubes with smaller aspect ratios. We distinguish three different classes of mechanical response to compressive loading. While the deformation mechanism is characterized by buckling of thin shells in nanotubes with small aspect ratios, it is replaced by a rod-like buckling mode above a critical aspect ratio, analogous to the Euler theory in continuum mechanics. For very large aspect ratios, a nanotube is found to behave like a flexible macromolecule which tends to fold due to vdW interactions between different parts of the carbon nanotube. This suggests a shell-rod-wire transition of the mechanical behavior of carbon nanotubes with increasing aspect ratios. While continuum mechanics concepts can be used to describe the first two types of deformation, statistical methods will be necessary to describe the dynamics of wire-like long tubes.

Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the stiffening effect of carbon nanotubes is quantitatively investigated by micromechanics methods. Especially, the effects of the extensively observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight nanotubes. Then, a novel micromechanics model is developed to consider the waviness or curviness effect of nanotubes, which are assumed to have a helical shape. Finally, the influence of nanotube agglomeration on the effective stiffness is analyzed. Analytical expressions are derived for the effective elastic stiffness of carbon nanotube-reinforced composites with the effects of waviness and agglomeration. It is found that these two mechanisms may reduce the stiffening effect of nanotubes significantly. The present study not only provides the relationship between the effective properties and the morphology of carbon nanotube-reinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites.

The structural reliability of piezoelectric ceramics in smart sensors and actuators is hindered by the lack of an appropriate fracture mechanics model. Recent experimental observations of their cracking behavior under combined electrical and mechanical loads contradict predictions made by the linear theory. Evidently, a fracture criterion suitable for piezoelectrics must account for material nonlinearity. Because these materials are typically mechanically brittle, we expect electrical ductility to be the dominant effect. By adopting a multiscale viewpoint, we identify a region of electrical nonlinearity near the crack tip in which the mechanical response of the material remains linear. The equilibrium equations for a fully anisotropic solid have closed-form solutions if the material’s behavior is assumed to be entirely linear outside of the plane of the crack. This approximation is equivalent to Dugdale’s model of the plastic zone in cracked metal sheets. The energy release rate derived using this load for specimens with cracks perpendicular to the poling direction. A remarkable feature of our model is that the energy release rate is strictly independent of the form of the nonlinear electrical constitutive relation. In fact, the material may even experience domain switching in the Dugdale zone without affecting the fracture criterion determined by our formulation.

Three-dimensional slightly nonplanar cracks are studied via a perturbation method valid to the first-order accuracy in the deviation of the crack shape from a perfectly planar reference crack. The Bueckner-Rice crack-face weight functions are used in the perturbation analysis to establish a relationship, within first-order accuracy, between the apparent and local stress intensity factors for the nonplanar crack. Perturbation solutions for a cosine wavy crack with arbitrary wavelengths are used to examine the effects of three T -stress components, T xx , T XZ , T ZZ , on the stability of a mode 1 planar crack in the x-z plane with front lying along the z -axis. A condition for the mode 1 crack to be stable against three-dimensional wavy perturbations of wavelengths λ x and λ z is determined as T xx + T zz g < 0 where g is negative, with a very small magnitude, for 0 < λ x / λ z < 1 / 3 and positive for 1 / 3 < λ x / λ z < ∞ ; this suggests that when T xx = 0, a compressive stress T zz may cause crack deflection with large wavelengths parallel to the crack front and a tensile stress T zz may cause deflection with small wavelengths parallel to the front. For comparable T -stress values, it is shown that a negative T xx always enhances the stability of a mode 1 planar crack and a negative T zz ensures the stability of a mode 1 crack against perturbations parallel to the crack front. The shear component T xz , while not affecting the mode 1 path stability, induces a mode 3 stress intensity factor once crack deflection occurs, and thus promotes the formation of en echelon-type cracking patterns.

This paper has two goals. First, it is aimed at providing a fundamental understanding of the oscillatory behavior of an interface crack between two dissimilar materials from the viewpoint of the interface mismatch that results from the cracking. Second, we extend the Bueckner-Rice weight function method to facilitate the interface crack analysis. Using properties of the surface Green’s functions of a homogeneous solid and solutions obtained from weight function formulae, a mismatch analysis is carried out which indicates that the local mismatch near the crack tip results in the oscillatory near-tip field while the mismatch on the global scale leads to the corresponding stress intensity factors. For an oscillatory interface crack field, it is shown that, other than a few extra material constants, the interface weight function analysis is completely parallel to the well-developed homogeneous theory so that knowledge of one crack solution for a given bimaterial geometry is sufficient for determination of solutions under any other loading conditions.

A first-order perturbation analysis is presented for the configuration of an initially straight crack front which is trapped against forward advance by contact with an array of obstacles (i.e., regions of higher fracture toughness than their surroundings). The problem is important to the micromechanics of crack advance in brittle, locally heterogeneous solids. The formulation is based on a linear perturbation result for the stress intensity factor distribution along the front of a half-plane crack when the location of that front differs moderately from a straight line. The trapping solutions for a periodic array of blocking rectangular obstacles are given using an analogy to the plane stress Dugdale/BCS elastic-plastic crack model. For a periodic array of obstacles with a given spacing and size in the direction parallel to the crack front, the obstacle shape may affect the limit load at which the crack breaks through the array. When such effects are examined within the range of validity of the linear perturbation theory, it is found that obstacles whose cross-sections fully envelop a critical reference area give the maximum limit load while others are broken through at lower load levels. We also formulate a numerical procedure using the FFT technique and adopting a “viscoplastic” crack growth model which, in an appropriate limit, simulates crack growth at a critical stress intensity factor. This is applied to show how a crack front begins to surround and penetrate into various arrays of round obstacles (with a toughness ratio of 2) as the applied load is gradually increased. The limitations of the first-order analysis restrict its validity to obstacles only slightly tougher than the surrounding elastic medium. Recently, Fares (1988) analyzed the crack trapping problem by a Boundary Element Method (BEM) with results indicating that the first-order linear analysis is acceptable when the fracture of toughness of the obstacles differs by a moderate amount from that of their surroundings (e.g., the toughness ratio can be as large as 2 for circular obstacles spaced by 2 diameters). However, the first-order theory is not only quantitatively inaccurate, but can make qualitatively wrong predictions when applied to very tough obstacles.