Fracture analysis of single-layer graphene sheets with edge crack under tension

In this study, the fracture of single-layered graphene sheets (SLGSs) with edge crack under simple tension is investigated using molecular dynamics simulations, and the variations in fracture strength of SLGSs with crack length, strain rate and temperature are analysed. It is found that the existing edge crack weakens mechanical properties of SLGSs. Fracture strength and strain decrease with the increase in crack length and temperature, but increase with the increase in strain rate. It is also shown that shorter initial cracks propagate faster than longer initial cracks, but shorter initial cracks begin propagating at higher axial strain at a certain temperature and strain rate. And cracks are found to propagate faster in higher strain rates.     

Mechanical properties of armchair silicene nanoribbons with edge cracks: a molecular dynamics study

Silicene has been proven to be a promising material with attractive electronic properties. During the synthesis of silicene, structural defects such as edge crack are likely to be generated and such defects in silicene have impacts on its properties. Herein, molecular dynamics simulations were performed to investigate the mechanical properties of the armchair silicene nanoribbons (ASiNRs) with edge cracks. Our results showed that the mechanical properties of the ASiNRs decrease because of the existence of edge crack. Both the pristine ASiNRs and the ASiNRs with edge cracks show brittle fracture behaviours. The crack length plays an important role in determining the critical strain and fracture strength of the ASiNRs. Moreover, we investigated the effects of strain rate and temperature on the mechanical properties of the ASiNRs with edge cracks. We observed that the increasing strain rate increases the critical strain and fracture strength while decreasing the Young’s modulus. Low-strain rates also changes the expanded directions of cracks in the ASiNRs. We also found that the increasing temperature could significantly decrease the mechanical properties of the ASiNRs with edge cracks.     

Molecular dynamics simulation studies of mechanical properties of different carbon nanotube systems

Various mechanical properties of single-walled carbon nanotubes (SWCNT) and double-walled carbon nanotubes (DWCNT) are evaluated using molecular dynamics (MD) simulations. A tensioning process was first performed on a SWCNT whose interaction is based on the Brenner’s ‘second generation’ potential under varying length–diameter ratios and strain rates, in order to understand the SWCNT’s behaviour under axial tension. The results showed an increase in the SWCNT’s ultimate tensile strength and a decrease in critical strain given the conditions of increasing strain rate and a decreasing length–diameter ratio. Comparison was done with previous studies on axial tensioning of SWCNT to validate the results obtained from the set-up, based on the general stress–strain relationship and key mechanical properties such as the strain at failure and the Young’s modulus. A DWCNT was then constructed, and Lennard-Jones ‘12-6’ potential was used to describe the energy present between the nanotube layers. Extraction of the inner tube in a DWCNT was performed using two inner wall tubings of different diameters to draw comparison to the energies needed to separate fully the outer and inner tubing. Finally, a bending test was performed on two DWCNTs with different intertube separations. Insights into the entire bending process were obtained through analyses of the variations in the strain energy characteristic of the surface atoms near the bending site, as the DWCNT is gradually bent until failure.     

Molecular dynamics simulation of crack growth in pure titanium under uniaxial tension

The analysis of crack growth in titanium was performed using molecular dynamics simulation with Embedded Atom Method potentials. The effect of temperature and strain rate on the mechanism of crack growth and the change of microstructure were discussed. After setting an initial crack, the specimen was subjected to uniaxial tension strain up to the total strain level of 0.2 with a constant strain rate. During the period, the shape and the microstructure of crack tip as well as the stress–strain curves were monitored. In the simulation, the gather of voids and stress concentration leading to the crack growth occurred, which are in agreement with experimental results observed by transmission electron microscopy. The transformation from HCP to BCC also occurred at crack tip. The remarkable effect of temperature and strain rate on the growth direction and rate of stacking fault of crack tip was observed. Moreover, initial crack greatly lowered the tension yield point of pure titanium. In the stage of deformation, simulation results showed that loading strain rate and temperature strongly influenced peak stress point, which was increased by the low temperature and high strain, whereas the initial slope of the stress strain curve was independent of loading strain rate.     

The cellular transducer in damage-stimulated bone remodelling: a theoretical investigation using fracture mechanics

This paper reports on some theoretical work which used fracture mechanics concepts to draw conclusions about the nature of the so-called 'cellular transducer': the means by which bone cells detect the presence of damage and thus initiate remodelling and adaptation activities. Using analytical and numerical methods, we estimated the strains and displacements around cracks of the typical size, shape and orientation that normally occur in compact bone. We predicted that it is not possible for osteocytes or their processes to be fractured as a result of direct tensile strains, because the strains generated are much less than the expected failure strains of cellular material. We proposed a new failure mechanism by which osteocyte processes spanning the crack are cut by shearing motions between the crack faces. We predicted that failures of this type can occur. Failures begin to occur if crack lengths become greater than normal (100 microm), so this could act as a signal to initiate repair processes for individual cracks. Very large numbers of cell processes (greater than 1000) will fail if the crack length and/or applied stress reach dangerous levels (300 microm and 60 Mpa, respectively) at which point bone deposition may be required to prevent stress fractures. Similar results also occurred if we proposed a different mechanism of damage detection, involving cells' ability to detect the high levels of strain that occur near crack tips. This work, though based on theoretical mechanics considerations, suggests some biological experiments which might confirm our findings.     

Structural stability and buckling analysis of a series of carbon nanotorus using molecular dynamics simulations

Based on molecular dynamics (MD) simulations, the buckling analysis of a perfect carbon nanotorus is presented herein. First of all, the minimum length of single-walled carbon nanotubes (SWCNTs) with different radii is determined at which perfect toroidal CNTs can be formed without any ripple at the inner side of the rings. According to the results, by increasing the radius of SWCNT (r), the radius of its corresponding perfect nanotorus (R) increases. Also, for SWCNTs with various lengths, it is found that the buckling force and strain of related carbon nanotoruses increase by increasing R/r. In addition, as the perfect toroidal CNTs are arranged vertically in a column form in accordance with two different schemes, the effects of increasing the radius (R) and the number of carbon nanotoruses (the height of the column made by nanotoruses) on the buckling force and strain are investigated. Based on the results, as a fixed number of carbon nanotoruses with the same radius are arranged vertically in the column form, the buckling force and strain increase by increasing R/r. By contrast, increasing the height of the column made by carbon nanotoruses with similar radius leads to the reduction of buckling force and strain.     

Atomistic Simulations of Uniaxial Tensile Behaviors of Single-walled Carbon Nanotubes

Atomistic simulations, using the second-generation reactive empirical bond order (REBO) potential, are performed to investigate the uniaxial tensile behaviors of single-walled carbon nanotubes (SWCNTs). It is found that the effect of the nanotube diameters on the elastic modulus, the tensile strength and the stress vs. strain relation of SWCNTs is small yet noticeable. However, the effect of the degree of helicity is significant.     

Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure

The importance and priority of specific micro-structural and mechanical design parameters must be established to effectively engineer scaffolds (biomaterials) that mimic the extracellular matrix (ECM) environment of cells and have clinical applications as tissue substitutes. In this study, three-dimensional (3-D) matrices were prepared from type I collagen, the predominant compositional and structural component of connective tissue ECMs, and structural-mechanical relationships were studied. Polymerization conditions, including collagen concentration (0.3-3 mg/mL) and pH (6-9), were varied to obtain matrices of collagen fibrils with different microstructures. Confocal reflection microscopy was used to assess specific micro-structural features (e.g., diameter and length) and organization of component fibrils in 3-D. Microstructural analyses revealed that changes in collagen concentration affected fibril density while maintaining a relatively constant fibril diameter. On the other hand, both fibril length and diameter were affected by the pH of the polymerization reaction. Mechanically, all matrices exhibited a similar stress-strain curve with identifiable "toe," "linear," and "failure" regions. However the linear modulus and failure stress increased with collagen concentration and were correlated with an increase in fibril density. Additionally, both the linear modulus and failure stress showed an increase with pH, which was related to an increasedfibril length and a decreasedfibril diameter. The tensile mechanical properties of the collagen matrices also showed strain rate dependence. Such fundamental information regarding the 3-D microstructural-mechanical properties of the ECM and its component molecules are important to our overall understanding of cell-ECM interactions (e.g., mechanotransduction) and the development of novel strategies for tissue repair and replacement.     

High strain rate response of rabbit femur bones

Strain rate dependence of the mechanical response of hard tissues has led to a keen interest in their dynamic properties. The current study attempts to understand the high strain rate characteristics of rabbit femur bones. The testing was conducted using a split-Hopkinson pressure bar equipped with a high speed imaging system to capture the fracture patterns. The bones were also characterized under quasi-static compression to enable comparison with the high strain rate results. The quasi-static compressive moduli of the epiphyseal and diaphyseal regions were measured to be in the range of 2–3 and 5–7 GPa, respectively. Under high strain rate loading conditions the modulus is observed to increase with strain rate and attains values as high as 15 GPa for epiphyseal and 30 GPa for diaphyseal regions of the femur. The strength at high strain rate was measured to be about twice the quasi-static strength value. A large number of small cracks initiated on the specimen surface close to the incident bar. Coalescence of crack branches leading to fewer large cracks resulted in specimen fragmentation. In comparison, the quasi-static failure was due to shear cracking.     

Can the theory of critical distances predict the failure of shape memory alloys?

Components made from shape memory alloys (SMAs) such as nitinol often fail from stress concentrations and defects such as notches and cracks. It is shown here for the first time that these failures can be predicted using the theory of critical distances (TCDs), a method which has previously been used to study fracture and fatigue in other materials. The TCD uses the stress at a certain distance ahead of the notch to predict the failure of the material due to the stress concentration. The critical distance is believed to be a material property which is related to the microstructure of the material. The TCD is simply applied to a linear model of the material without the need to model the complication of its non-linear behaviour. The non-linear behaviour of the material at fracture is represented in the critical stress. The effect of notches and short cracks on the fracture of SMA NiTi was studied by analysing experimental data from the literature. Using a finite element model with elastic material behaviour, it is shown that the TCD can predict the effect of crack length and notch geometry on the critical stress and stress intensity for fracture, with prediction errors of less than 5%. The value of the critical distance obtained for this material was L?=?90?μm; this may be related to its grain size. The effects of short cracks on stress intensity were studied. It was shown that the same value of the critical distance (L?=?90?μm) could estimate the experimental data for both notches and short cracks.     

Increasing amperometric biosensor sensitivity by length fractionated single-walled carbon nanotubes

In this work the sensitivity-increasing effect of single-walled carbon nanotubes (SWCNTs) in amperometric biosensors, depending on their average length distribution, was studied. For this purpose the SWCNTs were oxidatively shortened and subsequently length separated by size exclusion chromatography. Transmission electron micrographs of different fractions of SWCNTs were collected. Diaphorase "wired" to an osmium redox polymer was blended with the shortened SWCNTs of different lengths. Depending on the average length of the SWCNTs the sensitivity of the amperometric biosensor model system towards oxidation of 1,4-dihydronicotinamide adenine dinucleotide (NADH) was increased by a factor of five. The best performance was achieved with SWCNTs of medium length. The linear range for NADH detection was between 5muM and 7mM, the maximum sensitivity was 47nAmuM(-1)cm(-2), and the detection limit was 1muM. The biosensor exhibited excellent electrocatalytic properties. Even at relatively high NADH concentrations the oxidative current was limited by the diffusion rate of NADH.     

Stress intensity variations in bone microcracks during the repair process

Microscopic cracks form and grow in compact bone in vivo due to cyclic loading. Their growth can cause stress fractures and has been implicated in the processes of remodelling and adaptation. These cracks are repaired by the actions of BMUs which are mobile resorption cavities. In this work, we studied the interaction between cracks and BMUs by making finite element models representing different stages in the repair process. The tendency of the crack to grow was measured by its stress intensity factor, K. We found that K changes in a complex manner during the repair process, both decreasing and increasing depending on the size of the crack and the type of loading applied. For loading conditions similar to those that exist in vivo, the presence of the BMU can cause K to rise significantly, in some cases by more than 20%, implying a substantial increase in crack growth rate. This information is important for our general understanding of the complexities of the repair process, and especially for the development of theoretical models to simulate damage and repair in bone.     

The behaviour of roots encountering cracks in soil

Summary Experimental methods are described for observing the behaviour of roots encountering cracks in soil. The proportions of roots which enter a second soil block after crossing a crack of known width were measured. Soil strength was measured with a penetrometer.Results are presented for the proportions of seminal roots of wheat and primary lateral roots of pea which enter moulded soil of various strengths after crossing cracks. Results are also presented for the proportions of seminal roots of pea, rape and safflower which enter undisturbed soil after crossing cracks.It was found that, in all cases, the proportion of roots penetrating the second soil block decreased with increasing crack width and increasing soil strength. Also, a smaller proportion of thinner roots penetrated the second soil block than thicker roots under similar conditions. Root diameter in the cracks was influenced by both crack width and soil strength, and an empirical equation is presented to describe this effect.     

Stress intensity factors for a vertical surface crack in polyethylene subject to rolling and sliding contact.

Pitting wear is a dominant form of polyethylene surface damage in total knee replacements, and may originate from surface cracks that propagate under repeated tribological contact. In the present study, stress intensity factors, KI and KII, were calculated for a surface crack in a polyethylene-CoCr-bone system in the presence of rolling or sliding contact pressures. Variations in crack length and load location were studied to determine probable crack propagation mechanisms and modes. The crack tip experienced a wide range of mixed-mode conditions that varied as a function of crack length, load location, and sliding friction. Positive KI values were observed for shorter cracks in rolling contact and for all crack lengths when the sliding load moved away from the crack. KII was greatest when the load was directly adjacent to the crack (g/a = +/- 1), where coincidental Mode I stresses were predominantly compressive. Sliding friction substantially increased both KImax and KIImax. The effective Mode I stress intensity factors, Keff, were greatest at g/a = +/- 1, illustrating the significance of high shear stresses generated by loads adjacent to surface cracks. Keff trends suggest mechanisms for surface pitting by which surface cracks propagate along their original plane under repeated reciprocating rolling or sliding, and turn in the direction of sliding under unidirectional sliding contact.     

Singularity solution of Lanir's osmoelasticity: verification of discontinuity simulations in soft tissues

The literature characterizes cartilaginous tissues as osmoviscoelastic. Understanding the damage and failure of these tissues is essential for designing treatments. To determine tissue strength and local stresses, experimental studies—both clinical and animal—are generally supported by computational studies. Verification methods for computational studies of ionized porous media including cracks are hardly available. This study provides a method for verification and shows its performance. For this purpose, shear loading of a finite crack is addressed analytically and through a commercial finite element code. Impulsive shear loading by two-edge dislocation of a crack was considered in a 2D plane strain model for an ionized porous medium. To derive the analytical solution, the system of equation is decoupled by stress functions. The shear stress distribution at the plane of the crack is derived using Fourier and Laplace transformations. The analytical solution for the shear stress distribution is compared with computer simulations in ABAQUS version 6.4-5. Decoupling of the equations makes it possible to solve some boundary value problems in porous media taking chemical effects into account. The numerical calculations underestimate the shear stress at the crack-tips. Mesh refinement increases accuracy, but is still low in the neighborhood of the crack-tips.     

Single-walled carbon nanotubes induce cytotoxicity and DNA damage via reactive oxygen species in human hepatocarcinoma cells

Carbon nanotubes (CNTs) are gradually used in various areas including drug delivery, nanomedicine, biosensors, and electronics. The current study aimed to explore the DNA damage and cytotoxicity due to single-walled carbon nanotubes (SWCNTs) on human hepatocarcinoma cells (HepG2). Cellular proliferative assay showed the SWCNTs to exhibit a significant cell death in a dose- and time-dependent manner. However, SWCNTs induced significant intracellular reactive oxygen species (ROS) production and elevated lipid peroxidation, catalase, and superoxide dismutase in the HepG2 cells. SWCNTs also induced significant decrease in GSH and increase caspase-3 activity in HepG2 cells. DNA fragmentation analysis using the alkaline single-cell gel electrophoresis showed that the SWCNTs cause genotoxicity in a dose- and time-dependent manner. Therefore, the study points towards the capability of the SWCNTs to induce oxidative stress resulting cytotoxicity and genomic instability. This study warrants more careful assessment of SWCNTs before their industrial applications.     

Dynamic mechanical characterization of CNT–PP nanocomposites

In this study, molecular dynamic simulations were used to carry out a dynamic mechanical analysis of polymer nanocomposites (PNC) containing polypropylene (PP) and various volume fractions of single walled carbon nanotubes (SWCNTs). After assembling the composite unit cell, relaxation studies were performed by loading the specimen to a predetermined strain under quasistatic loading and then sustaining the strain while allowing the material to relax. Nano level readjustments of the polymer chains took place during this process, reducing the overall stress levels in the specimen. Free volumes and small voids permitted chain mobility around the carbon nanotubes. By fitting a standard relaxation curve, the nano relaxation parameters of the PNCs were deduced. Relaxation studies were also conducted at different equilibrium temperatures. Using the time temperature transformation relation, a master curve was generated for the nanocomposite with 1.0 % SWCNTs in order to obtain results over an extended period of time.     

Do microcracks decrease or increase fatigue resistance in cortical bone?

Fatigue of cortical bone produces microcracks; it has been hypothesized that these cracks are analogous to those occurring in engineered composite materials and constitute a similar mechanism for fatigue resistance. However, the numbers of these linear microcracks increase substantially with age, suggesting that they contribute to increased fracture incidence among the elderly. To test these opposing hypotheses, we fatigued 20 beams of femoral cortical bone from elderly men and women in load-controlled four point bending having initial strain ranges of 3000 or 5000 microstrain. Loading was stopped at fracture or 10(6) cycles, whichever occurred first, and microcrack density and length were measured in the loaded region and in a control region that was not loaded. We studied the dependence of fatigue life and induced microdamage on initial microdamage, cortical region, subject gender and age, and several other variables. When the effect of modulus variability was controlled, longer fatigue life was associated with higher rather than lower initial crack density, particularly in the medial cortex. The increase in crack density following fatigue loading was greater in specimens from older individuals and those initially having longer microcracks. Crack density increased as much in specimens fatigued short of the failure point as in those that fractured, and microcracks were, on average, shorter in specimens with greater numbers of resorption spaces, a measure of remodeling rate.     

Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence

Residual stress due to shrinkage of polymethylmethacrylate bone cement after polymerisation is possibly one factor capable of initiating cracks in the mantle of cemented hip replacements. No relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed which allows direct observation of damage in the cement layer on the femoral side of total hip replacement. The model contains medial and lateral cement layers between a bony surface and a metal stem; the tubular nature of the cement mantle is ignored. Five specimens were prepared and examined for cracking using manual tracing of stained cracks, observed by transmission microscopy; cracks were located and measured using image analysis. A mathematical approach for the prediction of residual stress due to shrinkage was developed which uses the thermal history of the material to predict when stress-locking occurs, and estimates subsequent thermal stress. The residual stress distribution of the cement layer in the physical model was then calculated using finite element analysis. Results show maximum tensile stresses normal to the observed crack directions, suggesting a link between residual stress and pre-load cracking. The residual stress predicted depends strongly on the definition of the reference temperature for stress-locking. The highest residual stresses (4-7 MPa) are predicted for shrinkage from maximum temperature; in this case, magnitudes are sufficiently high to initiate cracks when the influence of stress raisers such as pores or interdigitation at the bone/cement interface are taken into account (up to 24 MPa when calculating stress around a pore according to the method of Harrigan and Harris (J. Biomech. 24(11) (1991) 1047-1058). We conclude that the damage accumulation failure scenario begins before weight-bearing due to cracking induced by residual stress around pores or stress raisers.     

Analysis of Internal Crack Healing Mechanism under Rolling Deformation

A new experimental method, called the ‘hole filling method’, is proposed to simulate the healing of internal cracks in rolled workpieces. Based on the experimental results, the evolution in the microstructure, in terms of diffusion, nucleation and recrystallisation were used to analyze the crack healing mechanism. We also validated the phenomenon of segmented healing. Internal crack healing involves plastic deformation, heat transfer and an increase in the free energy introduced by the cracks. It is proposed that internal cracks heal better under high plastic deformation followed by slow cooling after rolling. Crack healing is controlled by diffusion of atoms from the matrix to the crack surface, and also by the nucleation and growth of ferrite grain on the crack surface. The diffusion mechanism is used to explain the source of material needed for crack healing. The recrystallisation mechanism is used to explain grain nucleation and growth, accompanied by atomic migration to the crack surface.