Deformation and fracture in graphene nanosheets

Graphene nanosheets (GNSs) are flake-like materials composed of few-layer graphene sheets. GNSs are similar to multi-walled carbon nanotubes (CNTs) in graphene structures and in layer numbers. However, GNSs and CNTs behave very differently in deformation and fracture. In this study, natural graphite flakes were employed to make expanded graphite (EG), which is composed of partially connected GNSs. Both sonication and three-roll milling were used to separate the GNSs and to disperse them into an epoxy resin. By compacting EG, the GNSs inside were compressed and deformed. By breaking the GNS/epoxy composite, most GNSs on the cracked surfaces were fractured. Both SEM and TEM have been used for microscopic observations. The micrographs revealed that folding and wrinkling are the major modes of deformation, while tearing and peeling are the dominant modes of fracture. These modes are virtually non-existent in CNTs. The factors to cause the different behavior are discussed.     

Review on the fracture processes in nanocrystalline materials

An overview of experimental study, computer simulations and theoretical models of fracture of nanocrystalline materials is presented. The key experimentally detected facts on ductile and brittle fracture processes are discussed. Special attention is paid to computer simulations and theoretical models of nucleation and growth of nanocracks and nanopores in deformed nanocrystalline materials. Also, we discuss mechanisms for fracture suppression in such materials showing good ductility or superplasticity.     

Surface crystallographic structure insensitive growth of oriented graphene domains on Cu substrates

Cu-based chemical vapor deposition method can produce large-area graphene films, usually polycrystalline films with grain boundaries as the main defects. One way to reduce grain boundaries is to grow oriented graphene domains (OGDs), which can ultimately perfectly integrate. In contrast to previously reported methods of limiting OGD growth on Cu (1 1 1), we find that OGDs can grow on Cu substrates with a large surface crystallographic structure tolerance. Density functional theory calculations show that this is due to the single lowest energy state of graphene nucleation. The growth temperature is crucial. It must be high enough (1045 °C) to suppress mis-OGD nucleation, but not too high (1055 °C) to deteriorate OGD growth. Mis-OGD nucleation can also be caused by C impurity in Cu grains, which can be depleted by thermal pretreatment of the substrate in an oxidizing atmosphere. On the other hand, OGD growth is not sensitive to the atmosphere at growth stage within the range that we have tested.     

Grain boundary structure dependent fracture in nanocrystalline Au films

Nanocrystalline Au films were in situ strained in a high resolution transmission electron microscope, which demonstrated that the diffusion-assisted intergranular fracture was the dominant failure mode. Grain orientation with respect to grain boundaries (GBs) imposes important effect on the crack propagation and blunting. The low surface energy and high diffusion mobility of {111} planes lead to a notch-like crack. The stress concentration at the tip may help breaking {111} planes layer by layer and thus advance the crack. Cracks can be diverted from the preset path by GBs and grow into the grain interior, which has never been revealed by other experiments and molecular dynamics simulations.     

Effects of graphene nanoplatelets and graphene nanosheets on fracture toughness of epoxy nanocomposites

The effects of graphene nanoplatelets (GPLs) and graphene nanosheets (GNSs) on fracture toughness and tensile properties of epoxy resin have been studied. A new technique for synthesis of GPLs based on changing magnetic field is developed. The transmission‐electron microscopy and the Raman spectroscopy were employed to characterize the size and chemical structure of the synthesized graphene platelets. The critical stress intensity factor and tensile properties of epoxy matrix filled with GPL and GNS particles were measured. Influence of filler content, filler size and dispersion state was examined. It was found that the GPLs have greater impact on both fracture toughness and tensile strength of nanocomposites compared with the GNSs. For instance, fracture toughness increased by 39% using 0.5 wt% GPLs and 16% for 0.5 wt% GNSs.     

Thermoactivated fracture of graphene subjected to tensile strain

Graphene draws the attention of researchers due to its unique properties-in particular, record-high tensile strength. The time to fracture (TTF) of defect-free graphene strained by tension at a nonzero temperature has been studied by the method of molecular dynamics (MD). It is established that the time to thermoactivated fracture has a probabilistic character and obeys an exponential distribution. The mean TTF is proportional to the area of the graphene sheet and obeys the Arrhenius-Zhurkov law as a function of temperature and applied stress. The dependence of the activation energy for graphene fracture on the applied stress and sample area has been extrapolated to values of these parameters relevant for practical applications. The mechanism of graphene fracture has been analyzed.     

Some peculiarities of fracture of nanocrystalline nitride and boride films

Fracture surfaces including those through indentations on different nanocrystalline boride/nitride films were investigated by FE-SEM, conventional SEM, and AFM. TiB₂, TiN, Ti(B,N), AlN, and (Ti,Al)N films have been obtained by non-reactive r.f. magnetron sputtering. Deformation was realized by cleavage fracture and under a Vickers indentor. Two types of film fracture connected with homogeneous and inhomogeneous deformation are described and discussed. The analogy between the inhomogeneous deformation films image and the river pattern in the case of conventional ceramics is also pointed out.     

Atomistic and continuum modelling of temperature-dependent fracture of graphene

This paper presents a comprehensive molecular dynamics study on the effects of nanocracks (a row of vacancies) on the fracture strength of graphene sheets at various temperatures. Comparison of the strength given by molecular dynamics simulations with Griffith’s criterion and quantized fracture mechanics theory demonstrates that quantized fracture mechanics is more accurate compared to Griffith’s criterion. A numerical model based on kinetic analysis and quantized fracture mechanics theory is proposed. The model is computationally very efficient and it quite accurately predicts the fracture strength of graphene with defects at various temperatures. Critical stress intensity factors in mode I fracture reduce as temperature increases. Molecular dynamics simulations are used to calculate the critical values of $J$ integral ( $J_\mathrm{IC}$ ) of armchair graphene at various crack lengths. Results show that $J_\mathrm{IC}$ depends on the crack length. This length dependency of $J_\mathrm{IC}$ can be used to explain the deviation of the strength from Griffith’s criterion. The paper provides an in-depth understanding of fracture of graphene, and the findings are important in the design of graphene based nanomechanical systems and composite materials     

Nanoindentation and micro-mechanical fracture toughness of electrodeposited nanocrystalline Ni-W alloy films

Nanocrystalline nickel-tungsten alloys have great potential in the fabrication of components for microelectromechanical systems. Here the fracture toughness of Ni-12.7 at.%W alloy micro-cantilever beams was investigated. Micro-cantilevers were fabricated by UV lithography and electrodeposition and notched by focused ion beam machining. Load was applied using a nanoindenter and fracture toughness was calculated from the fracture load. Fracture toughness of the Ni-12.7 at.%W was in the range of 1.49-5.14 MPa √m. This is higher than the fracture toughness of Si (another important microelectromechanical systems material), but considerably lower than that of electrodeposited nickel and other nickel based alloys.     

Influence of grain boundary misorientation on intergranular fracture of nanocrystalline palladium

Atomistic simulations of tensile straining of three-dimensional nanocrystalline palladium samples at room temperature and at a constant strain rate of \(10^{8}\,\hbox {s}^{-1}\) were performed. Potential understating surface energies and therefore facilitating intergranular fracture was applied for modeling of interatomic interactions. Palladium samples subjected to uniaxial straining have demonstrated initiation of intergranular cracks which have occurred preferably at the high-angle grain boundaries oriented perpendicular to the direction of applied strain and independently of their tilt/twist character. Further propagation of cracks took place along the adjacent grain boundaries. No cases of intergranular fracture at low-angle grain boundaries, of both the general and special character, were found. Intergranular fracture was observed only in an insignificant number of special high-angle grain boundaries.     

A coupled quantum/continuum mechanics study of graphene fracture

A new technique is presented to study fracture in nanomaterials by coupling quantum mechanics (QM) and continuum mechanics (CM). A key new feature of this method is that broken bonds are identified by a sharp decrease in electron density at the bond midpoint in the QM model. As fracture occurs, the crack tip position and crack path are updated from the broken bonds in the QM model. At each step in the simulation, the QM model is centered on the crack tip to adaptively follow the path. This adaptivity makes it possible to trace paths with complicated geometries. The method is applied to study the propagation of cracks in graphene which are initially perpendicular to zigzag and armchair edges. The simulations demonstrate that the growth of zigzag cracks is self-similar whereas armchair cracks advance in an irregular manner. The critical stress intensity factors for graphene were found to be 4.21 MPa\({\sqrt {\rm m}}\) for zigzag cracks and 3.71 MPa\({\sqrt{\rm m}}\) for armchair cracks, which is about 10% of that for steel.     

The deformation and fracture behavior of an electrodeposited nanocrystalline Ni under compression

A bulk and dense nanocrystalline Ni with an average grain size of 19 nm and a thickness of 5.4 mm was fabricated by an electro-deposition technique. The nc Ni had a preferable (2 0 0) growth texture along the depositing direction. Under compression test, the nc Ni exhibited a high strength of 2920 MPa and an accepted good ductility of 16%. A novel fracture character, i.e., the triple-junction shaped micro-cracks with the size varying from few to several tens of micrometers which run through the holistic fracture body of the nc Ni, was observed. The reason for the formation of such cracks is attributed to GB activities, which leads to the formation of nano-sized void, and the subsequent formation of micro-crack.     

Dynamic and static fracture analyses of graphene sheets and carbon nanotubes

Dynamic and static fracture properties of Graphene Sheets (GSs) and Carbon nanotubes (CNTs) with different sizes are investigated based on an empirical inter-atomic potential function that can simulate nonlinear large deflections of nanostructures. Dynamic fracture of GSs and CNTs are studied based on wave propagation analysis in these nanostructures in a wide range of strain-rates. It is shown that wave propagation velocity is independent from strain-rate while dependent on the nanostructure size and approaches to 2.2 × 10⁴ m/s for long GSs. Also, fracture strain shows extensive changes versus strain-rate, which has not been reported before. Fracture stress is determined as 115 GPa for GSs and 122 GPa for CNTs which are independent from the strain-rate; in contrast to the fracture strain. Moreover, fracture strain drops at extremely high strain-rates for GSs and CNTs. These features are considered as capability of carbon nanostructures for reinforcing nanocomposites especially under impact loadings up to high strain-rates.     

The effect of annealing on deformation and fracture of a nanocrystalline fcc metal

The tensile deformation and fracture behavior of electrodeposited nanocrystalline Ni–15% Fe alloy samples after annealing for 90 min at 250, 400 and 500 °C temperatures were investigated. The structure of the samples was studied using TEM and XRD techniques and the fracture surfaces were investigated employing SEM. The results of this study indicated that annealing at 250 °C modified grain size distribution slightly but resulted in a significant increase in the initial strain hardening rate. While the average grain size in the 400 °C sample was increased to 59 nm, its yield strength was comparable to the as-deposited alloy with a 9 nm grain size. The plastic tensile elongation of all annealed samples was lowered significantly to less than 1% from approximately 6% in the as-deposited state. These results are discussed in terms of the inhomogeneity of plastic deformation and the evolution of internal stresses in nanocrystalline materials.     

A temperature insensitive quartz microbalance

Mass deposition onto a microbalance is generally accompanied by a temperature change. By measuring a single frequency only, it is not possible to separate the frequency change due to mass change from that due to temperature change. In the temperature insensitive microbalance technique, measurements of two frequencies, the fundamental mode and third overtone frequencies of an SC-cut resonator, yield two equations with two unknowns. This allows the separation of mass change effects from temperature change effects. Dual mode excitation can be used for highly accurate resonator self-temperature sensing over wide temperature ranges. SC-cut resonators are also thermal transient compensated. These unique properties allowed the development of a temperature compensated microbalance that is highly sensitive to mass changes, which can be used in rapidly changing thermal environments, over wide temperature ranges, and which requires neither temperature control nor a thermometer other than the resonator. To demonstrate the performance of this microbalance, SC-cut resonators were coated with thin polymethylmethacrylate (PMMA) photoresist films then placed into a UV-ozone cleaning chamber that initially was at about 20 degrees C. When the UV lamp was turned on, the UV-ozone removed PMMA from the surfaces while the chamber temperature rose to about 60 degrees C. The frequency changes due to mass changes could be accurately determined, independently of the frequency changes due to temperature changes.