Mechanics of Fiber Networks
Random fiber networks are assemblies of elastic elements connected in random configurations. They are used as models for a broad range of fibrous materials including biopolymer gels and synthetic nonwovens. Although the mechanics of networks made from the same type of fibers has been studied extensively, the behavior of composite systems of fibers with different properties has received less attention. In this work we numerically and theoretically study random networks of beams and springs of different mechanical properties. We observe that the overall network stiffness decreases on average as the variability of fiber stiffness increases, at constant mean fiber stiffness. Numerical results and analytical arguments show that for small variabilities in fiber stiffness the amount of network softening scales linearly with the variance of the fiber stiffness distribution. This result holds for any beam structure and is expected to apply to a broad range of materials including cellular solids.
Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work the mechanics of fiber networks with crimped fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of non-straight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the softening effect associated with the presence of crimp. The transition from the linear to the non-linear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically-relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.
We numerically investigate the propagation of small-amplitude elastic waves in random fiber networks. Our analysis reveals that the dynamic response of the system is not only controlled by its overall elasticity, but also by the local microstructure. In fact, we find that the longest fiber-segment plays a key role in dynamics when the network is excited with waves of short wavelength. In this case, the Bloch modes are highly non-affine as the longest segments oscillate close to their resonances. Based on this observation, we predict the low frequency dispersion curves of random fiber networks.
A discrete network model (DNM) to represent the mechanical behavior of the human amnion is proposed. The amnion is modeled as randomly distributed points interconnected with connector elements representing collagen crosslinks and fiber segments, respectively. This DNM is computationally efficient and allows simulations with large domains. A representative set of parameters has been selected to reproduce the uniaxial tension–stretch and kinematic responses of the amnion. Good agreement is found between the predicted and measured equibiaxial tension–stretch curves. Although the model represents the amnion phenomenologically, model parameters are physically motivated and their effect on the tension–stretch and in-plane kinematic responses is discussed. The model is used to investigate the local response in the near field of a circular hole, revealing that the kinematic response at the circular free boundaries leads to compaction and strong alignment of the network at the border of the defect.
We study the small strain elastic behavior of composite athermal fiber networks constructed by adding stiffer fibers to a cross-linked base network. We observe that if the base network is in the affine deformation regime, the composite behaves similar to a fiber-reinforced continuum. When the base network is in the nonaffine deformation regime, the stiffness of the composite increases by orders of magnitude upon the addition of a small fraction of stiff fibers. The increase is not gradual, but rather occurs in two steps. Of these, one is associated with the stiffness percolation of the network of added fibers. The other, which occurs at very small fractions of stiff fibers, is due to the percolation of perturbation zones, or “interphases,” induced in the base network by the stiff fibers, regions where the energy is stored mostly in the axial deformation mode. Their size controls the stiffening transition and depends on base network parameters and the length of added fibers. It is also shown that the perturbation field introduced in the base network by the presence of a stiff fiber is much longer ranged than in the case when the fiber is tied to a continuum of same modulus with the base network.
Systems composed of fibers are ubiquitous in the living and artificial systems, including cartilage, tendon, ligaments, paper, protective clothing, and packaging materials. Given the importance of fiber systems, their static behavior has been extensively studied and it has been shown that network deformation is nonaffine for compliant, low-density networks and affine for stiff, high-density networks. However, little is known about the dynamic response of fibrous systems. In this work, we investigate numerically the propagation of small-amplitude elastic waves in these materials and characterize their dynamic response as a function of network parameters.
Bonded random fiber networks are heterogeneous on multiple scales. This leads to a pronounced size effect on their mechanical behavior. In this study we quantify the size effect and determine the minimum model size required to eliminate the size effect for given set of system parameters. These include the net- work density, the fiber length and the fiber bending and axial stiffness. The results may guide the defi- nition of models and the selection of the size of representative volume elements in sequential multiscale models of fiber networks. To underline the origins of the size effect, we characterize the net- work heterogeneity by analyzing the geometry of the network (density distribution), the strain field and the strain energy distribution. The dependence of the heterogeneity on the scale of observation and sys- tem parameters is discussed.
The mechanical behavior of a three-dimensional cross-linked fiber network embedded in a matrix is studied in this work. The network is composed from linear elastic fibers which store energy only in the axial deformation mode, while the matrix is also isotropic and linear elastic. Such systems are encountered in a broad range of applications, from tissue to consumer products. As the matrix modulus increases, the network is constrained to deform more affinely. This leads to internal forces acting between the network and the matrix, which produce strong stress concentration at the network cross-links. This interaction increases the apparent modulus of the network and decreases the apparent modulus of the matrix. A model is developed to predict the effective modulus of the composite and its predictions are compared with numerical data for a variety of networks.
Biological as well as manmade materials with fibrous microstructures are ubiquitous in everyday life. At a certain length scale of observation, these materials appear in the form of a random network of cross-linked (connected) filaments. The computational effort required for investigating the mechanics of these structures by modeling the deformation of each fiber is very large. Therefore, a proper representation of their overall mechanical properties requires developing multiscale schemes capable of describing the behavior of the discrete system with a continuum model without loss of essential microstructural details. This article discusses two approaches developed for solving boundary value problems on large fiber-network domains using scale coupling techniques. We present first considerations related to sequential multiscale modeling, in particular linked to the scale of transition from a discrete to a continuum model of the network. Further, we review a method designed to construct a continuum model for the network structure, which takes into account the intrinsic spatial correlations of network properties. In both techniques, the geometrical and structural properties of network constituents at micro-scales are considered in estimating the macro-scale behavior of the structure subjected to external loads.
A soft tissue’s macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson’s ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.
Athermal random fiber networks are usually modeled by representing each fiber as a truss, a Euler-Bernoulli or a Timoshenko beam, and, in the case of cross-linked networks, each cross-link as a pinned, rotating, or welded joint. In this work we study the effect of these various modeling options on the dependence of the overall network stiffness on system parameters. We conclude that Timoshenko beams can be used for the entire range of density and beam stiffness parameters, while the Euler-Bernoulli model can be used only at relatively low network densities. In the high density-high bending stiffness range, strain energy is stored predominantly in the axial and shear deformation modes, while in the other extreme range of parameters, the energy is stored in the bending mode. The effect of the model size on the network stiffness is also discussed.
The deformation of dense random fiber networks is important in a variety of applications including biological and nonliving systems. In this paper it is shown that semiflexible fiber networks exhibit long-range power-law spatial correlations of the density and elastic properties. Hence, the stress and strain fields measured over finite patches of the network are characterized by similar spatial correlations. The scaling is observed over a range of scales bounded by a lower limit proportional to the segment length and an upper limit on the order of the fiber length. If the fiber bending stiffness is reduced below a threshold, correlations are lost. The issue of solving boundary value problems defined on large domains of random fiber networks is also addressed. Since the direct simulation of such systems is impractical, the network is mapped into an equivalent continuum with long-range correlated elastic moduli. A technique based on the stochastic finite element method is used to solve the resulting stochastic continuum problem. The method provides the moments of the distribution function of the solution (e.g., of the displacement field). It performs a large dimensionality reduction which is based on the scaling properties of the underlying elasticity of the material. Two examples are discussed in closure.
The 2D elastic modulus (E2D) and strength (σ2D) of defective graphene sheets containing vacancies, epoxide, and hydroxyl functional groups are evaluated at 300 K by atomistic simulations. The fraction of vacancies is controlled in the range 0% to 5%, while the density of functional groups corresponds to O:C ratios in the range 0% to 25%. In-plane modulus and strength diagrams as functions of vacancy and functional group densities are generated using models with a single type of defect and with combinations of two types of defects (vacancies and functional groups). It is observed that in models containing only vacancies, the rate at which strength decreases with increasing the concentration of defects is largest, followed by models containing only epoxide groups and those with only hydroxyl groups. The effect on modulus of vacancies and epoxides present alone in the model is similar, and much stronger than that of hydroxyl groups. When the concentration of defects is large, the combined effect of the functional groups and vacancies cannot be obtained as the superposition of individual effects of the two types of defects. The elastic modulus deteriorates faster (slower) than predicted by superposition in systems containing vacancies and hydroxyl groups (vacancies and epoxide groups).
t is important from a fundamental standpoint and for practical applications to understand how the mechanical properties of graphene are influenced by defects. Here we report that the two-dimensional elastic modulus of graphene is maintained even at a high density of sp 3 -type defects. Moreover, the breaking strength of defective graphene is only B 14% smaller than its pristine counterpart in the sp 3 - defect regime. By contrast, we report a significant drop in the mechanical properties of graphene in the vacancy-defect regime. We also provide a mapping between the Raman spectra of defective graphene and its mechanical properties. This pro- vides a simple, yet non-destructive methodology to identify graphene samples that are still mechanically functional. By establishing a relationship between the type and density of defects and the mechanical properties of graphene, this work provides important basic information for the rational design of composites and other systems utilizing the high modulus and strength of graphene.
The creep behavior of epoxy–graphene platelet (GPL) nanocomposites with different weight fractions of filler is investigated by macroscopic testing and nanoindentation. No difference is observed at low stress and ambient temperature between neat epoxy and nanocomposites. At elevated stress and temperature the nanocomposite with the optimal weight fraction, 0.1 wt% GPLs, creeps significantly less than the unfilled polymer. This indicates that thermally activated processes controlling the creep rate are in part inhibited by the presence of GPLs. The phenomenon is qualitatively similar at the macroscale and in nanoindentation tests. The results are compared with the creep of epoxy–single-walled (SWNT) and multi-walled carbon nanotube (MWNT) composites and it is observed that creep in both these systems is similar to that in pure epoxy, that is, faster than creep in the epoxy–GPL system considered in this work.
Various aspects of the mechanical behavior of epoxy-based nanocomposites with graphene platelets (GPL) as additives are discussed in this article. The monotonic loading response indicates that at elevated temperatures, the elastic modulus and the yield stress are significantly improved in the composite as compared to neat epoxy. The activation energy for creep is smaller in neat epoxy, which indicates that the composite creeps less, especially at elevated temperatures and higher stresses. The composites also exhibit larger fracture toughness. When subjected to cyclic loading, fatigue crack growth rate is smaller in the composite relative to neat epoxy. This reduction is important by at least an order of magnitude at all stress intensity factor amplitudes. Optimal property improvements in the monotonic, cyclic, and fracture behaviors are obtained for very low filling fraction of approximately 0.1 wt. %. Similar differences in the mechanical behavior are observed when the composite is probed on the local scale by nanoindentation.
A coarse graining procedure aimed at reproducing both the chain structure and dynamics in melts of linear monodisperse polymers is presented. The reference system is a bead-spring-type representation of the melt. The level of coarse graining is selected equal to the number of beads in the entanglement segment, Ne. The coarse model is still discrete and contains blobs each representing Ne consecutive beads in the fine scale model. The mapping is defined by the following conditions: the probability of given state of the coarse system is equal to that of all fine system states compatible with the respective coarse state, the dissipation per coarse grained object is similar in the two systems, constraints to the motion of a representative chain exist in the fine phase space, and the coarse phase space is adjusted such to represent them. Specifically, the chain inner blobs are constrained to move along the backbone of the coarse grained chain, while the end blobs move in the three-dimensional embedding space. The end blobs continuously redefine the diffusion path for the inner blobs. The input parameters governing the dynamics of the coarse grained system are calibrated based on the fine scale model behavior. Although the coarse model cannot reproduce the whole thermodynamics of the fine system, it ensures that the pair and end-to-end distribution functions, the rate of relaxation of segmental and end-to-end vectors, the Rouse modes, and the diffusion dynamics are properly represented.
We performed pulsed-gradient spin-echo nuclear-magnetic-resonance NMR experiments on zinc oxide filled polyethylene. The molecular weights of the polyethylene samples ranged between 808 and 33 000 g/mol, and four different zinc oxide samples were used: 27-, 33-, 51-, and 2500-nm-diameter particles. The results of these experiments showed that the diffusion coefficients of the polyethylene chains did not change with nanofiller content, but a drastic change is observed in the NMR relaxation spectrum in spin-spin-relaxation experiments. At fixed zinc oxide content and polyethylene molecular weight (close to entanglement) , the system with the smallest zinc oxide showed the most rigid environment. At high polyethylene molecular weights, this effect was still observable but the difference between the three investigated systems was very small, suggesting that the system was dominated by entanglements.
The influence of the presence of a curved (convex) solid wall on the conformations of long, flexible polymer chains is studied in a dense polymer system and in the athermal limit by means of lattice Monte Carlo simulations. It is found that the chain conformation entropy drives a reduction of the density at the wall, similar to the flat wall case. The chain end density is higher next to the interface compared to the bulk polymer (segregation), with the difference increasing with chain length. The wall curvature does not significantly affect the segregation. The bonds are preferentially oriented in the direction tangential to the wall. The distance from the interface over which this effect is observed is about two bond lengths. Similar results are obtained when probing the preferential orientation of chain segments. In this case, the perturbed region has a thickness on the order of the considered probing chain segment length. This suggests that experimental results on the thickness of the ‘bonded layer’ next to a wall depend on the wavelength of the radiation employed for probing. The chains are ellipsoidal in the bulk and rotate close to the surface with the large semi-axis of the ellipsoid normal to the line connecting their center of mass with the filler center. Since there is no energetic interaction with the filler, no adsorption transition is observed, but the chains tend to wrap around the filler once the gyration radius becomes comparable to the filler radius.
Stress production in a model monodisperse polymeric material is investigated on multiple scales. The analysis is performed by means of equilibrium and non-equilibrium molecular dynamics. A family of mobile intrinsic coordinate systems is introduced, each system having one axis tied to the end-to-end vector of a generic chain segment of specified length. A similar mobile coordinate system tied to the large semiaxis of the ellipsoidal chains is defined on the chain scale. The atomic level stress is evaluated based on bonded and non-bondedinteratomic interactions, and averaged in the global coordinate system, to result in the global, system level stress, and in the various intrinsic systems, to result in intrinsic stresses. It is observed that the deviatoric intrinsic stress is scale independent, a bond, a chain segment and the chain scale intrinsic frame carrying the same stress. The hydrostatic component of the stress tensor scales with the segment length. This concept extends the previously introduced Intrinsic Stress Framework, scale linking the bond and chain scales. During melt deformation, the chain segments stretch and rotate. Chains shorter than the entanglement length mainly rotate during an elongational deformation of limited amplitude, their size remaining essentially constant. Longer chains distort and rotate. Two regimes are evidenced during the return to isotropy of the orientation on multiple scales. The faster mode is associated with the return to equilibrium of the internal structure of the generic chain, while the slower mode is associated with chain rotation in the global coordinate system. The intrinsic deviatoric stress carried by a chain changes during the first mode, and is essentially constant during the second. The physical picture of stress production defined on the scale of a bond (Kuhn segment) in the Intrinsic Stress Framework translates to the chain scale during this late relaxation regime: each rotating chain carries a constant deviatoric intrinsic stress, the preferential chain orientation leading to a non-zero global deviatoric stress.
Cyclotrimethylene trinitramine (RDX) crystalizes in the orthorhombic α-phase at the ambient pressure and temperature. In principle, the point defects commonly found in monatomic crystals, such as vacancies and interstitials, may exist in RDX as well. However, in molecular crystals one encounters additional point defects associated with the distortion of the molecules. A set of rotational defects are described in this article. These are molecules which are located in the proper positions in the crystal but are rotated relative to the molecules in the perfect crystal, and their ring is slightly puckered. The energetic barriers for defect formation and for their annealing back to the perfect crystal configuration are computed using an atomistic model. It is shown that the formation energy of rotational defects is smaller than the vacancy formation energy. Such defects are identified in the cores of dislocations in RDX and hence their concentration in the crystal is expected to increase during plastic deformation. The importance of such point defects is related to their role in phonon scattering and in dislocation-mediated plastic deformation.
The cyclotrimethylene trinitramine (RDX) molecule has four conformations denoted as Caaa, Caae, Caee, and Ceee, of which Caae is the conformer stabilized at room temperature in the α-RDX crystal subjected to atmospheric pressure. The barriers for transition between these conformers are evaluated using a molecular model both in vacuum and in the crystal. Apart from Caae, the only conformer stabilized in α-RDX is Caee and this occurs when the crystal is strained. The concentration of Caee depends on strain and temperature. The conformers interact elastically and electrostatically, which leads to their spatial clustering. Furthermore, the transition between Caae and Caee is a stochastic process characterized by temporal correlations. This is an effect of the field-mediated spatial interaction of conformers. It is observed that fluctuations in the intra-molecular effective temperature correlate with conformation transitions. The effect is quantified for both Caae-Caee and Caee-Caae transitions.
TWIP steels are materials with very high strength and exceptional strain hardening capability, parameters leading to large energy absorption before failure. However, TWIP steels also exhibit reduced (often negative) strain rate sensitivity (SRS) which limits the post-necking deformation. In this study we demonstrate for an austenitic TWIP steel with 18% Mn a strong dependence of the twinning rate on the strain rate, which results in negative strain hardening rate sensitivity (SHRS). The instantaneous component of SHRS is large and negative, while its transient is close to zero. The SRS is observed to decrease with strain, becoming negative for larger strains. Direct observations of the strain rate dependence of the twinning rate are made using electron microscopy and electron backscatter diffraction, which substantiate the proposed mechanism for the observed negative SHRS.
Al-SiC nanocomposites were prepared by high energy ball milling of mixtures of pure Al and 50-nm-diameter SiC nanoparticles, followed by spark plasma sintering. The final composites had grains of approximately 100 nm dimensions, with SiC particles located mostly at grain boundaries. The samples were tested in uniaxial compression by nano- and microindentation in order to establish the effect of the SiC volume fraction, stearic acid addition to the powder, and the milling time on the mechanical properties. The results are compared with those obtained for pure Al processed under similar conditions and for AA1050 aluminum. The yield stress of the nanocomposite with 1 vol pct SiC is more than ten times larger than that of AA1050. The largest increase is due to grain size reduction; nanocrystalline Al without SiC and processed by the same method has a yield stress seven times larger than AA1050. Adding 0.5 vol pct SiC increases the yield stress by an additional 47 pct, while the addition of 1 vol pct SiC leads to 50 pct increase relative to the nanocrystalline Al without SiC. Increasing the milling time and adding stearic acid to the powder during milling lead to relatively small increases of the flow stress. The hardness measured in nano- and microindentation experiments confirms these trends, although the numerical values of the gains are different. The stability of the microstructure was tested by annealing samples to 423 K and 523 K (150 °C and 250 °C) for 2 hours, in separate experiments. The heat treatment had no effect on the mechanical properties, except when treating the material with 1 vol pct SiC at 523 K (250 °C), which led to a reduction of the yield stress by 13 pct. The data suggest that the main strengthening mechanism is associated with grain size reduction, while the role of the SiC particles is mostly that of stabilizing the nanograins.
The mechanical properties of commercial dual phase (DP), transformation induced plasticity (TRIP), and high strength low alloy (HSLA-340) steel sheets are investigated and compared at various strain rates ranging from 0. 0017 to 0.17 s−1 at ambient temperature. TRIP steel outperforms the other two materials, having comparable ductility and twice as large strength relative to DP steel. TRIP has larger strength and much larger ductility than HSLA-340. The exceuent ductility of TRIP800 is due to its high strain hardening capability, which promotes stable plastic deformation. It is observed that the strain hardening rate in TRIP800 does not decrease to zero at failure, as common in most materials in which failure is preceded by necking.
A microstructural-based model, describing the plastic behavior of Al-30wt% Zn alloy, is proposed and the effect of solid solution decomposition, Orowan looping, twinning and grain refinement is analyzed. It is assumed that the plastic deformation process is dominated by strain-induced solute diffusion and dislocation motion. To capture the essential physics, a law describing the evolution of the mean free path of dislocations with plastic strain is proposed which reproduces the experimentally observed strain softening.
An experimental study is presented regarding the effect of pre-existing inhomogeneous solute distribution on the strain rate sensitivity of a non-heat treatable Al-Mg alloy (AA5182). Tests are performed with specimens heat treated to eliminate pre-existing solute structures within the material and with specimens equilibrated at room temperature. The rate sensitivity is significantly more pronounced in the equilibrated specimens, which indicates that solute structures that exist before the test play a role in determining the rate sensitivity of the material at low temperatures.
The mechanical behavior of the commercial aluminum alloy AA5182-O is investigated at temperatures ranging from −120 to 150 °C and strain rates from 10−6 to 10−1 s−1. The strain rate sensitivity parameter is determined as a function of temperature and plastic strain, and the strain rate and temperature range in which dynamic strain aging leads to negative strain rate sensitivity is mapped. The effect of dynamic strain aging on ductility and strain hardening is investigated. The sensitivity of the measured quantities to the experimental method employed and their dependence on grain shape are discussed. The experimental data are compared with the predictions of a model constructed based on a recently proposed mechanism for dynamic strain ageing. The mechanism is based on the effect solute clustering at forest dislocations has on the strength of dislocation junctions. The model is shown to reproduce qualitatively the experimental trends.
A physically based constitutive model capturing the reduced strain-rate sensitivity of dilute solid solutions is developed. The decrease of the strain-rate sensitivity parameter is associated with the variation of the strength of dislocation junctions with the size of solute clusters forming on forest dislocations. It is shown that the strength of junctions formed by unclustered mobile dislocations and clustered forests increases with the size of the cluster and, therefore, with the aging time of forests. The formulation is calibrated based on results obtained from mesoscopic models of dislocation interactions in the presence of solute clusters at forest dislocations. The strength of junctions is evaluated for most geometries and an averaging procedure is used to predict the strain-rate sensitivity. Several features observed experimentally are reproduced by the model. Its limitations are discussed in closing. The data may also be used as input for discrete dislocation dynamics simulations.
A new mechanism is proposed for dynamic strain ageing and the negative strain-rate sensitivity (SRS) exhibited by dilute solid solutions containing mobile solute atoms. The mechanism is based on the strength variation of dislocation junctions due to the presence of solute clusters on forest dislocations. The strength of a Lomer–Cottrell lock in which the mobile dislocation is free of solute, while the forest dislocation is clustered, is studied by using an orientation-dependent line tension model. It is shown that the junction strength increases with the size of the cluster on the forest dislocation (binding energy of the forest dislocation to its cluster). The cluster forms by lattice diffusion and its size depends on the time lapsed from the formation of the respective dislocation segment. Therefore, the average size of clusters on new forest dislocations is smaller the larger the imposed strain rate. Consequently, the average strength of junctions decreases (after a transient) upon an increase of the strain rate, which leads to negative SRS. A model including the results of the mesoscopic analysis is developed to capture this mechanism. The model reproduces qualitatively a number of key features observed experimentally at the macroscopic scale. The new mechanism does not require solute diffusion to take place sufficiently fast for clustering of mobile dislocations to happen during their arrest time at obstacles, as assumed in previous models of the phenomenon.
Solute diffusion in an Al-rich binary Al–Mg alloy is studied by means of atomistic simulations. The activation energy for diffusion of Mg in the bulk is evaluated in the dilute solution limit for the nearest neighbor and the ring mechanisms. It is concluded that bulk diffusion at low and moderate temperatures must be assisted by vacancies. Further, diffusion of Mg along the core of edge, 60° and screw dislocations is studied. The activation energy for vacancy formation in the core and for vacancy-assisted Mg migration is evaluated for a large number of diffusion paths in the core region. It is observed that, similar to the bulk, Mg diffusion in absence of vacancies is energetically prohibitive. The paths of minimum activation energy are identified for vacancy-assisted diffusion, for all three types of dislocations. The lowest energy path is found in the core of the 60° dislocation, its activation energy being 60% of the activation energy in the bulk. Most diffusion paths have activation energies larger than 75% of the equivalent bulk quantity. This analysis is relevant for the discussion on the mechanism of dynamic strain aging in these alloys. The data presented here show that pipe diffusion, which is currently considered as the leading mechanism responsible for dynamic strain aging is too slow in absence of excess vacancies.
Clustering of Mg in Al–Mg binary alloys is studied by means of atomistic simulations. The phenomenon is analysed in the undistorted Al lattice, as well as in the presence of dislocations. In the undistorted lattice, Mg has a tendency to cluster in a coherent phase. The binding energy of this structure is rather low and it dissolves at room temperature, and only dynamic associations of doublets or triples of solute atoms are observed. Increasing the temperature above 100°C inhibits the formation of any solute short range order. The application of a homogeneous hydrostatic strain has no effect on clustering. In the presence of dislocations and at room temperature, Mg clusters at cores forming the coherent phase observed in the undistorted lattice at low temperatures. Clustering at the cores of all types of dislocations is discussed. It is shown that the size, shape and structure of the cluster cannot be predicted using elementary calculations based on the pressure field generated by the unclustered dislocation. Furthermore, the field of the clustered dislocation is observed to differ from that of the unclustered defect, even at distances as large as 20 Burgers vectors from the core. The variation of the stacking fault due to clustering is determined by simply monitoring the distance between partials, which is observed to decrease upon clustering.
A physically-based model for the deformation of Ti–6%–Al-4%V is proposed. The various deformation mechanisms active in this material over the whole range of temperatures of industrial interest are discussed, and a strategy by which the relevant strengthening effects are captured in the model is proposed. The flow stress contains a thermal and an athermal component. The thermally activated processes are modeled based on the Kocks–Mecking formalism, while the athermal processes are simulated using an internal state variable. The deformation of the α-and β-phases is captured separately. The model is calibrated based on experimental results obtained from tests performed in the temperature range (77–1400 K) and at strain rates between 10−3 and 10 s−1. The model predictions are extrapolated to strain rates as high as 2000 s−1. The experimental findings are presented in the companion paper.
This study investigates the plastic deformation of titanium alloy Ti–6%Al–4%V under low and moderate strain rates and various temperature conditions. Mechanical testing is performed in the temperature range 650–1340 K (710–1950 °F) and under constant strain rate loading ranging from 10−3 to 10 s−1. The test results are correlated with the evolution of the microstructure and compared to published data. The flow stress of this alloy is strongly dependent on both temperature and deformation rate, with the temperature effect becoming negligible in the upper part of the temperature range investigated. At temperatures above 800 K (980 °F) the flow stress decreases sharply with temperature. The effect of deformation rate on this transition is investigated and the possible mechanisms responsible for the behavior are discussed. Based on these experimental results, a physically-based constitutive law is developed in the sequel of this paper.
Concurrent Atomistic-Continuum Methods
A concurrent multiscale method for coupling discrete (atomistic) and continuum models at finite temperatures is presented. Motion of atoms is governed by an inter-atomic potential and is represented by molecular dynamics. A thermo-mechanical continuum defined by standard differential equations of conservation of momentum and heat transport is used. The coupling is performed by an interface region where the two models overlap. The phonon spectrum of the discrete region is divided into a low frequency part which is transferred to the continuum model as mechanical waves, and a high frequency component which is modeled in the continuum as diffusive heat transport. Seamless mechanical coupling is ensured by imposing weak compatibility of displacements in the interface region. The method is implemented in 1D and full bi-directional thermal and mechanical coupling is demonstrated in thermodynamic equilibrium and in non-equilibrium.
A sequential multiscale modeling methodology is developed to study the diffusion of solute atoms in the vicinity of a dislocation core and the kinetics of the ensuing clustering process. The problem is set up in the continuum sense, taking into account the coupling between diffusion and deformation. Specifically, gradients of both strain and concentration drive diffusion, and the elastic constants are considered functions of the local solute concentration. These coupling parameters are calibrated from atomistic models. The problem is solved using a finite element formulation. Mg clustering at an edge dislocation in Al-5%Mg is studied, which is relevant for static and dynamic strain aging. The model is used to test the validity of the Cottrell-Bilby-Louat expression, broadly used to describe the kinetics of solute clustering at dislocation cores. It is concluded that the formula does not predict the variation in time of the concentration at every point within the cluster, the purpose for which it is customarily used. However, it properly describes the evolution of a global measure of the cluster size.
A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain where fine scale features need to be resolved, a continuum sub-domain which can adequately describe the macroscale deformation and an overlap interphase sub-domain that has a blended description of the two. The problem is formulated in terms of equilibrium equations with a blending between the continuum stress and the atomistic force in the interphase. Coupling between the continuum and the atomistics is established by imposing constraints between the continuum solution and the atomistic solution over the interphase sub-domain in a weak sense. Specifically, in the examples considered here, the atomistic domain is modeled by the aluminum embedded atom method (EAM) inter-atomic potential developed by Ercolessi and Adams [F. Ercolessi, J.B. Adams, Interatomic potentials from first-principles calculations: the force-matching method, Europhys. Lett. 26 (1994) 583] and the continuum domain is a linear elastic model consistent with the EAM potential. The formulation is subjected to patch tests to demonstrate its ability to represent the constant strain modes and the rigid body modes. Numerical examples are illustrated with comparisons to reference atomistic solution.
An adaptive method for the selection of models in a concurrent multiscale approach is presented. Different models from a hierarchy are chosen in different subdomains of the problem domain adaptively in an automated problem simulation. A concurrent atomistic to continuum (AtC) coupling method [27], based on a blend of the continuum stress and the atomistic force, is adopted for the problem formulation. Two error indicators are used for the hierarchy of models consisting of a linear elastic model, a nonlinear elastic model, and an embedded atom method (EAM) based atomistic model. A nonlinear indicator , which is based on the relative error in the energy between the nonlinear model and the linear model, is used to select or deselect the nonlinear model subdomain. An atomistic indicator is a stress-gradient-based criterion to predict dislocation nucleation, which was developed by Miller and Acharya [6]. A material-specific critical value associated with the dislocation nucleation criterion is used in selecting and deselecting the atomistic subdomain during an automated simulation. An adaptive strategy uses limit values of the two indicators to adaptively modify the subdomains of the three different models. Example results are illustrated to demonstrate the adaptive method.
The Composite Grid Atomistic Continuum Method, a method to couple continuum and atomistic models, is proposed in a three-dimensional setting. In this method, atomistic analysis is used only at places where it is needed in order to capture the intrinsically nonlinear/nonlocal behavior of the material at the atomic scale, while continuum analysis is used elsewhere for efficiency. The atomistic model is defined on a separate grid that overlaps the continuum in selected regions. The atomistic and the smallest scale continuum model are connected by appropriately defined operators. The continuum model provides boundary conditions to the discrete model while the atomistic model returns correcting eigenstrains. The adaptive selection of the spatial regions where the atomistic correction is needed is made based on error indicators developed to capture the nonlinearity and nonlocality modeling errors. The method is applied to represent dislocation nucleation from crack tips and nanoindentation in aluminum.
Simulations of nano-indentation in bcc molybdenum are performed using a coupled atomistic-continuum method and a multi-body interatomic potential which includes angular forces. The indenter is flat and rigid while the indented material is a single crystal having its ⦑100⦒ and ⦑111⦒ directions respectively parallel to the indentation direction, in separate simulations. Indentation is accommodated by elastic deformation of the surface, up to an indenter displacement of about 6 Å, and by nucleation of crystalline defects for deeper indents. When indented in the ⦑100⦒ direction, the crystal twins under the indenter, while indentation in the ⦑111⦒ direction produces dislocation nucleation from the stress concentration sites at the indenter edge. The critical loads for these events are computed and the nucleation mechanism is observed. The results are compared with available experimental data.
Testing at the Nanoscale
An atomic force microscope (AFM) was used to characterize the deformation behavior of amorphous Si (a-Si) nanostructures subjected to monotonic and cyclic loading. The sample geometry was specially designed (in the form of elbow) using finite element modeling for the purpose of these tests, and the samples were grown by glancing angle deposition. When deformed monotonically at room temperature, the a-Si specimens exhibited a nonlinear force–displacement response at forces larger than a critical force, a phenomenon not observed in bulk silicon. A fatigue testing methodology based on the use of the AFM was established. The fatigue life of the a-Si specimens was observed to increase by five orders of magnitude with a 50% reduction in the applied force amplitude. It was verified that this delayed failure is caused by progressive damage accumulation during cyclic loading. These results are compared with literature data obtained from micron-size specimens.
The article presents the basic principle of a nanodevice used to transport fluids through nanochannels. The nanochannel is defined by two parallel plates, one (or both of them) being covered by active thin films. The films deform under the action of an electric current passing in the film through the thickness direction. This leads to a local increase in film thickness, which forms a protrusion that narrows the channel. The propagation of such protrusions along the channel leads to the pumping effect. This motion is produced and controlled electronically. Here we focus on the mechanical actuation device as well as the ensuing coupled fluid and solid mechanics problem. We describe in detail the nature and function of the active films. Then, we provide an answer to the question: given a desired fluid flux, what is the magnitude and spatial distribution of the controlling current one has to supply to the actuators?
Mechanical testing was performed on a new class of nanostructures—amorphous Si slanted nanorods of rectangular cross section, fixed at one end to the substrate. These nanorods were grown spatially well separated on nano-pillars under the oblique angle physical vapor deposi- tion technique. Various samples with different dimensions and inclination angles were tested in bending using an atomic force microscope. The material response was elastic up to large stresses/deflections. The Young’s modulus was calculated from the slope of the experimentally observed stiffness versus the geometrical factor common to all the samples and was found to be (94.14 ± 10.21) GPa. No size effect of this parameter was observed within the accuracy of the present measurement.
Isolated three-dimensional nanostructures were grown on templated or flat substrates by oblique angle deposition with or without substrate rotation where the physical shadowing effect dominates and controls the structures. The mechanical and electromechanical properties of Si springs and Co coated Si springs were measured by atomic force microscopy. The electrical property of β -phase W nanorods were measured by scanning tunneling microscopy. Examples of measurements of the elastic property of springs, electromechanical actuation, field emission of electrons, and field ionization of argon gas are presented. Potential applications and improvements of growth of uniform nanostructures are discussed.
Slanted nano-columns and square nano-springs made of amorphous silicon (a-Si) were fabricated on bare Si and patterned substrates by oblique angle deposition with a back–forth substrate swing rotation mode. Scanning electron microscopy was used to characterize the grown nanostructures. The tilt angle of slanted nano-rods is determined by the incident angle of deposition flux and the azimuthal swing rotation angle of a substrate. The controlled substrate rotation affects the uniformity and the shape of the nanostructures. On the patterned substrate, the broadening of the size of individual nano-columns is greatly reduced and the nano-columns are not connected as they grow. A simple model based on decomposing the deposition flux is used to describe the effect of substrate rotation on tilt angle, uniformity, and the top-end shape of nanostructures. The feasibility of fabricating separated and well aligned nanostructures by our swing rotation method provides an effective and controllable way to fabricate nano-devices.
The residual stress in thin films is a major limiting factor for obtaining high quality films. We present a strategy for stress reduction in sputter depositedfilms by using a nanostructured compliant layer obtained by the oblique angle deposition technique, sandwiched between the film and the substrate. The technique is all in situ, does not require any lithography steps, and the nanostructured layer is made from the same material as the depositedthin film. By using this approach we were able to reduce stress values by approximately one order of magnitude in sputter depositedtungstenfilms. These lower stress thin films also exhibit stronger adhesion to the substrate, which retards delamination buckling. This technique allows the growth of much thicker films and has enhanced structural stability. A model is developed to explain the stress relief mechanism and the stronger adhesion associated with the presence of the nanostructured compliant layer.
The mechanical properties of benzocyclobutene film are investigated at the nanoscale by nano-indentation using atomic force microscopy(AFM). The force versus indentation depth data were collected with two different AFM tips of radii ∼ 20 and ∼ 380 nm . A strong size effect of the plastic flow stress was observed as the radius of the indenter tip was reduced. More important, the material exhibited pronounced strain rate sensitivity when probed at the nanoscale, while it was rate insensitive at larger scales. These two size effects were quantified by analytic and finite element modeling.
We demonstrated a nanoscale electromechanical actuator operation using an isolated nanoscale spring. The four-turn Si nanosprings were grown using the oblique angle deposition technique with substrate rotation, and were rendered conductive by coating with a 10-nm-thick Co layer using chemical vapor deposition. The electromechanical actuation of a nanospring was performed by passing through a dc current using a conductive atomic force microscope(AFM) tip. The electromagnetic force leads to spring compression, which is measured with the same AFM tip. The spring constant was determined from these measurements and was consistent with that obtained from a finite element analysis.
The elastic response, including the spring constant, of individual Si helical-shape submicron springs, was measured using a tip-cantilever assembly attached to a conventional atomic force microscope. The isolated, four-turn Si springs were fabricated using oblique angle deposition with substrate rotation, also known as the glancing angle deposition, on a templated Si substrate. The response of the structures was modeled using finite elements, and it was shown that the conventional formulae for the spring constant required modifications before they could be used for the loading scheme used in the present experiment.
The transformation of dislocation cores from the shuffle to the glide set of {111} glide planes in Si is examined in this work. The transformation is thermally activated and is favored by a resolved shear stress which applies no force on the original perfect shuffle dislocation. A resolved shear stress driving dislocation motion in the glide plane is not observed to promote the transition. The stress-dependent activation energy for the described shuffle-glide transformation mechanism is evaluated using a statistical analysis. It is observed that the transformation is not associated with an intermediate metastable state, as has been previously suggested in the literature.
Nucleation of dislocation loops from sharp corners playing the role of stress concentrators located on the surface of Si1−xGex strained layers is studied. The surface is of {100} type and the concentrator is oriented such as to increase the applied resolved shear stress in one of the {111} glide planes. The mean stress in the structure is controlled through the boundary conditions, independent of the Ge concentration. Shuffle dislocations are considered throughout, as appropriate for low temperature-high stress conditions. The effect of Ge atoms located in the glide plane, in the vicinity of the glide plane and at larger distances is studied separately. It is observed that Ge located in the glide plane leads to the reduction of the activation energy for dislocationnucleation. The activation volume in presence of Ge is identical to that in pure Si. Ge located in {111} planes three interplanar distances away from the active glide plane has little effect on nucleation parameters. The far-field Ge contributes through the compressive normal stress it produces and leads to a slight reduction of the activation energy for shuffle dislocationnucleation.
The nucleation of dislocations from sharp corners acting as stress concentration sites on a silicon (100) surface is studied by a combination of atomistic and continuum modeling. Ledges of various heights, similar to those found in microelectronic devices, are considered. In this work we focus on the effect of ledge height and of ledge-ledge elastic interaction on the activation energy for dislocationnucleation. The activation energy decreases slightly with increasing the height of the ledge and has a more pronounced, nonmonotonic variation with the distance between stress concentration sites. The effect of introducing a radius of curvature at the root of the ledge is also studied. It is concluded that even a small radius of curvature renders the nucleation process similar to that from a flat surface of same crystallographic orientation.
The functional form of non-local elasticity kernels is studied within the context of the integral formalism. The study is limited to linear isotropic elasticity. The kernels are derived analytically based on the discrete structure of the material at the atomic scale. Atomistic simulations are used to validate the results. Materials in which the interatomic interactions are represented by pair, as well as embedded atom-type potentials are considered. The derived kernels have a range which extends up to the cut-off radius of the interatomic potential, are positive at the origin, and become negative approximately one atomic distance away, thus departing from the commonly assumed Gaussian functional form. The functional form of the potential and the radial distribution function of interacting neighbors about a representative atom fully define their shape. This new continuum model involves two material length scales that are both derived from atomistics for a Morse solid and for Al. Two applications are considered in closure. It is shown that in strained superlattices, the non-local model predicts maximum stresses that are much larger than those obtained within the local theory. This observation has implications for defect nucleation in these structures. Furthermore, the new non-local model improves upon the Gaussian one by predicting a more realistic wave dispersion relationship, with essentially zero group velocity at the boundary of the Brillouin zone.
The effect of non-locality on the Peierls stress of a dislocation, predicted within the framework of the Peierls–Nabarro model, is investigated. Both the integral formulation of non-local elasticity and the gradient elasticity model are considered. A modification of the non-local kernel of the integral formulation is proposed and its effect on the dislocation core shape and size, and on the Peierls stress are discussed. The new kernel is longer ranged and physically meaningful, improving therefore upon the existing Gaussian-like non-locality kernels. As in the original Peierls–Nabarro model, lattice trapping cannot be captured in the purely continuum non-local formulation and therefore, a semi-discrete framework is used. The constitutive law of the elastic continuum and that of the glide plane are considered both local and non-local in separate models. The major effect is obtained upon rendering non-local the constitutive law of the continuum, while non-locality in the rebound force law of the glide plane has a marginal effect. The Peierls stress is seen to increase with increasing the intrinsic length scale of the non-local formulation, while the core size decreases accordingly. The solution becomes unstable at intrinsic length scales larger than a critical value. Modifications of the rebound force law entail significant changes in the core configuration and critical stress. The discussion provides insight into the issue of internal length scale selection in non-local elasticity models.
Biaxial compression experiments were carried out to investigate the mechanism of feather crack nucleation in columnar freshwater ice. The tests were performed with a strain rate of 10−3 s−1 at −10°C. It is shown that the nucleation of feather cracks corresponds to a transition when the last of the remaining ligaments bonding the two grains fractures and the grain boundary transforms into a traction-transmitting frictional crack. This is in contrast to the nucleation of wing cracks, proposed earlier, where the nucleation was due to the onset of viscous sliding of grains. In addition to the mechanism, the nucleation stress for feather cracks was measured for different confinement ratios. A fracture-mechanics-based model for the nucleation process is presented by V. Gupta and R. C. Picu [Nucleation of feather cracks in columnar freshwater ice: Theoretical modeling, manuscript in preparation].
The stress singularity at the point of intersection of a grain triple junction line with the free surface has been numerically evaluated in single-phase polycrystals of cubic and hexagonal grains. The angle spanned by the grain boundaries, the orientation of the crystal axes within each grain and the position of the triple junction line with respect to the free surface were taken as variables, and their effect on the singularity exponent γ (defined by σ ∞ rγ−1) determined. In general, the configurations possessing geometrical and material symmetries were associated with stronger singularities and almost all triple junction geometries were characterized by two singularity exponents, each corresponding to the symmetric and the antisymmetric fields. Thus, such a singular point is associated with a fixed mixed mode. Interestingly, the values obtained were somewhat different and stronger when compared with those obtained for the corresponding two-dimensional plane stress and strain configurations.
Under across-column uniaxial and biaxial compression loading of columnar ice polycrystals in the brittle regime, a set of cracks that split the columnar grains has been observed. However, both the mechanism responsible for their nucleation and a quantitative description of the stress associated with such events have remained unresolved in the literature. In this paper, we first show that the nucleation of such cracks is consistent with the sliding of grain facets along the column axes, and then describe a fracture mechanics-based model that correctly predicts their nucleation stress.
The axisymmetric problem of the elastic stress singularity at the vertex of a conical inclusion bonded into a conical notch is analyzed. The shear stress is assumed to vanish along the interface while the normal stress is fully transmitted. This corresponds to the low load-low deformation regime of high temperature materials, when the grain boundaries and the interfaces of second phase particles may slide viscously. The stress and displacement fields are expressed in terms of spherical harmonic functions and the singularity exponent is obtained from the solution of the eigenproblem defined by the boundary conditions. Supersingularities of the stress field close to the vertex were found for certain configurations. In all analyzed cases, only real singularities were obtained.
Stress singularities at grain triple junctions due to freely sliding grain boundaries in idealized two-dimensional single-phase polycrystals have been analyzed. The shear stress is assumed to be completely relaxed along the grain boundaries while the normal stress is allowed to be fully transmitted. The singularity exponent was found to be independent of the elastic constants of the grains, and for some triple junction configurations, super-singularities (i.e., stronger than the standard −0.5 as found at the tip of a crack in homogeneous material) were obtained. Interestingly, for most geometrical configurations, the solution structure indicates a fixed mode near the triple junction, irrespective of the far-field load combination.
The crack-tip stress-field singularity of a crack lying along a grain boundary and impinging on a grain triple junction is investigated. The three grains forming the triple junction are considered to be made from the same anisotropic material, albeit with different orientations of the principal material axes. The analysis is limited to elastic plane-strain deformation and is carried out using the Eshelby-Stroh formalism for anisotropic elasticity. The effect of the anisotropy on the level of the singularity is investigated for both transversely cubic and orthotropic grains.
Biaxial compression experiments were carried out to investigate the mechanisms of crack nucleation in columnar freshwater ice. For strain rates higher than 10−3 s−1 at — 10°Cm, it is observed that crack nucleation is preceded by grain boundary sliding which results in local decohesion pockets spread intermittently along the boundary facets. The experimental results are shown to support the crack nucleation model presented in the companion paper.
The phenomenon of crack nucleation from grain triple junctions is investigated in columnar freshwater ice at rates of loading where the dislocation pile-up process is inhibited. Two mechanisms are explored. First, crack nucleation due to elastic anisotropy-induced singular stress field at the triple junction is investigated. To this end, both the singularity exponent and the energy release values associated with crack nucleation are provided for random orientations of the grain boundaries and material axes of the grains. The computed energy release rate values fall much short of those required for nucleation. Next, by assuming a linear viscous response for the boundary, the stress concentrations due to grain boundary sliding are computed, and the resulting energy release rate values are shown to be sufficiently high to overcome the barrier for crack nucleation. Experimental evidence for grain boundary sliding-induced boundary decohesions at — 10°C are presented in the companion paper. At such temperatures, sliding is activated even though the strain rate of loading invokes an overall brittle response from the polycrystal.
A particular case of indentation-induced damage in ice where the micro-cracked zone directly beneath the indenter takes the shape of an isosceles triangle, and the overall failure characterized by an unstable propagation of an apex crack, is considered. Both the failure criterion and the related size effect are derived and compared to the results of both the laboratory and basin studies on freshwater ice in the literature. Although the above failure mode is typical in low velocity indentation experiments with nominal strain rates between 0.2 and 0.34 s−1 and with the indenter width-ice sheet thickness ratio measuring less than 5, the derived scaling law is applicable to other experimental conditions too, as long as the above deformation profile is maintained. Applicability of the scaling law to saline ice is also discussed.
A mechanism for crack nucleation in saline ice is presented, by considering a planar array of hexagonal grains containing the brine pockets as a model of poly crystalline saline ice. It is shown through a thermodynamic analysis that important local stresses arise associated with the internal pressure which builds up inside a brine pocket due to a drop in the temperature. As the temperature drops, the water inside the brine freezes, and because of the variation in the water density on freezing, this results in a buildup of pressure inside the pocket. For typical field conditions, assuming elastic behavior for the matrix, pressures as high as 7 MPa are estimated. Next, using a finite element method, the stress concentration at a grain triple junction is determined under the influence of the stress field associated with a nearby brine pocket. The resulting stress state is used to determine the condition for crack nucleation. The analysis is restricted to only elastic deformation regimes with isotropic grains, albeit with elastic constants corresponding to extreme values in a single freshwater ice crystal. The mechanism discussed here provides an explanation for the widely observed brine channels in sea ice. In addition, the effect of the externally applied stress is also considered, and the resulting stress singularities at the grain triple junctions analyzed by an asymptotic method as well as by a numerical solution. Both the strength and an approximate energy criteria suggest crack nucleation from the brine pocket surface towards the grain triple junction. The results are shown to be consistent with the experimental observations.
testing testing testing
The shear-induced volumetric strain (SIS) of a set of model CuZr metallic glasses is studied for various deformation conditions characterized by different strain rates, temperatures and applied hydrostatic stress states. The various systems considered are obtained by quenching from the melt at different cooling rates. During shear deformation at constant pressure, the material reaches a steady state in which the sample volume remains constant. It is observed that the density of the glass during steady state deformation depends on temperature, pressure and shear strain rate, and is independent of the initial state of the sample. The SIS vanishes as the temperature of the shear test reaches the glass transition temperature. The SIS can become negative under compressive pressure since the instantaneous bulk modulus is lowered by the shear flow. The results suggest that the magnitude of the SIS is related to the difference in density between samples quenched with given finite rate and a fictitious sample quenched infinitely fast.
Sticky ends are unpaired nucleotides at the ends of DNA molecules that can associate to link DNA segments. Self-assembly of DNA molecules via sticky ends is currently used to grow DNA structures with desired architectures. The sticky end links are the weakest parts of such structures. In this work, the strength of sticky end links is studied by computational means. The number of basepairs in the sticky end and the sequence are varied, and the response to tension along the axis of the molecule is evaluated using a full atomistic model. It is observed that, generally, increasing the number of basepairs in the sticky end increases the strength, but the central factor controlling this parameter is the basepair sequence. The sticky ends are divided into two classes of low and high strength. The second class has strength comparable with that of a double stranded molecule with one nick in one of the strands. The strength of the first class is roughly half that of the strong sticky ends. For all strong sticky ends tested, the enhanced stability is associated with the formation of an unusually stable complex composed from two basepairs and two flanking bases of certain sequence. This complex rotates and aligns with the direction of the force allowing significant deformation and providing enhanced strength. This is similar to a mechanism recently suggested to enhance the mechanical stability of an RNA kissing loop from the Moloney murine leukemia virus. The model is tested against experimental structural data for sticky ends and against published simulation results for the stretch of double stranded DNA. The results provide guidance for the design of DNA self-assembled structures and indicate the types of sticky ends desirable if maximizing the strength and stability of these structures is targeted.
Several non-Schmid effects of plasticity in Si are discussed in this article. The contribution of shear strain applied in the direction of the Burgers vector and normal to it in the glide plane, and of strain applied normal to the glide plane to defining the Peierls stress are analyzed. The analysis is performed using a combination of atomistic simulations and the Peierls–Nabarro model based on generalized stacking faults. It is shown that a shear strain acting in the direction of the Burgers vector decreases the Peierls stress and the effect is due to the reduction of the shear modulus. Bonding across the glide plane has the most important contribution to the Peierls stress, but the elastic non-linearity of the surrounding material contributes to reducing the instability threshold. A shear strain acting perpendicular to the Burgers vector has no effect on the Peierls stress. A compressive strain normal to the glide plane reduces the Peierls stress for shuffle dislocations and has a weak increasing effect on the critical stress of glide-set dislocations.
One of the crucial factors that affects the performance of solid electrolyte - lithium-ion batteries is the electrode/electrolyte contact characteristics. Better contact implies greater ion transfer efficiency, leading to improved charge/discharge characteristics, and higher-power densities. In this study, the authors investigate the contact characteristics, viz. wettability, of germanium nanorod thin films initially by water, followed by polyethylene oxide (PEO)/water solution and PEO melt. The authors demonstrate that the electrode surface is hydrophilic, and considerably wettable, as evidenced by the contact angle for PEO/water solution and PEO melt, which are both below 25-. Electron microscopy was used to investigate the electrode/electrolyte contact area, and our results showed that PEO melt efficiently penetrates the inter-rod space, which is a further indication of considerable increase in the contact area.
Mechanical properties of porous methyl silsesquioxane samples with dielectric constant 2.4 and 2.0 and a recently developed nanoclustering silica film samples with dielectric constants 2.3 and 2.0 were evaluated using an atomic force microscope based nanoindentation. It was found that the Young’s modulus and the hardness decrease while the fracture toughness increases with a decrease in the dielectric constant in the same type of material. Moreover, the Young’s modulus and the hardness of the nanoclustering silica films were observed to be at least twice and fracture toughness values ~1.3–1.5 higher than those for methyl silsesquioxane films with similar dielectric constants. The high resolution topographic imaging capability of atomic force microscope was shown to be particularly useful in the measurement of cracks generated by the ultra-low indentation loads, and the evaluation of the fracture toughness of the nanoscale volumes of materials.
The classical approach to linking lattice dynamics properties to continuum equations of motion, the "method of long waves," is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the first part of the article, the derivation is made within the harmonic approximation for the perfect lattice response. Higher order terms are included in the continuum equation of motion to account for non-linear dispersion effects. Wave propagation coefficients as well as fourth order dispersion coefficients are obtained. In the second part, the lattice anharmonicity is considered and nonlinear macroscopic equations of motion are obtained within the local approximation. Both continuum solutions are particularized to the one-dimensional case and are compared with the lattice response in order to establish the accuracy of the approximation.
The relative role of the residual strain and dimensional scaling on heat transport in nanostructures is investigated by molecular dynamics simulations of a model Lennard-Jones solid. It is observed that tensile (compressive) strains lead to a reduction (enhancement) of the lattice thermal conductivity. A nonhydrostatic strain induces thermal conductivityanisotropy in the material. This effect is due to the variation with strain of the stiffness tensor and lattice anharmonicity, and therefore of the phonon group velocity and phonon mean free path. The effect due to the lattice anharmonicity variation appears to be dominant. The size effect was studied separately in unstrained thin films. Phononscattering on surfaces leads to a drastic reduction of the thermal conductivity effect which is much more important than that due to strain in the bulk. It is suggested that strain may be used to tailor the phonon mean free path which offers an indirect method to control the size effect.
The sublimation of a CdTe{111} surface at 600oC has been studied by highresolution transmission electron microscopy in the profile-image geometry. The sublimation involves the simultaneous desorption of Cd and Te atoms of the outermost layer and occurs by a kink-step propagation mechanism. The rate of sublimation is found to be independent of the presence of twins in the film. Further, the surface relaxation in this system is investigated. It is found that the relaxation affects only the outermost atomic layer, which finds its equilibrium position at a {111} interplanar spacing 13 1% larger than the corresponding bulk value. Surface relaxation measurements have been performed at both room temperature and 600oC with similar results.