A new micromechanics-based scale transition model for the strain-rate sensitive behavior of nanocrystalline materials

An original two-step “three phase” elastic–viscoplastic scale transition model is developed based on the combined self-consistent and Mori–Tanaka schemes. A coated inclusion is embedded within a matrix, wherein the inclusion represents grain interiors and the coating of the inclusion mimics the effects of grain boundaries and triple junctions. The predominant behavior within the grain interiors is captured through dislocation glide, whereas grain boundary (GB) dislocation emission and absorption, as well as thermally assisted GB sliding, describe the deformation processes within the coating describing the GB affected zone. Furthermore, an imperfect interface is assumed between the inclusion and the coating to account for viscoplastic grain boundary sliding along a stick-slip mechanism. Results and discussion focus on the competitive roles of GB sliding, GB dislocation emission/absorption, dislocation sweep in grain cores and collective dislocation plasticity, and the origins of the pronounced strain rate sensitivity of fcc NC materials.     

Two-dimensional shear waves scattering by a large rigidity strip with interface crack

A two-dimensional problem of shear horizontal (SH) waves scattering by a finite width planar elastic (piezoelectric) inclusion partially debonded from its surrounding elastic matrix is investigated using the effective boundary conditions and singular integral equations technique. The case of large rigidity inclusions with blunted tips is considered, in which the upper face of the inclusion is perfectly bonded to the matrix. The debonding region is modeled as interface crack with non-contacting faces. Using the Green theorem the mixed boundary value problem is reduced to a system of the hypersingular integral equations. Numerical results of the scattering fields characteristics are presented. The effects of incidence direction, various material parameters of the strip on the scattering field are discussed and phenomenon of the non-specular reflection of SH waves is considered. The accuracy of the numerical results is confirmed by the use of analytical approximate problem solution of high-frequency SH waves scattering on a finite hard/soft inclusion.     

Thermo-elastic Greenʼs functions for an infinite bi-material of one-dimensional hexagonal quasi-crystals

This Letter is concerned with thermo-elastic fundamental solutions of an infinite space, which is composed of two half-infinite bodies of different one-dimensional hexagonal quasi-crystals. A point thermal source is embedded in a half-space. The interface can be either perfectly bonded or smoothly contacted. On the basis of the newly developed general solution, the temperature-induced elastic field in full space is explicitly presented in terms of elementary functions. The interactions among the temperature, phonon and phason fields are revealed. The present work can play an important role in constructing farther analytical solutions for crack, inclusion and dislocation problems.     

Micromechanical modelling of an arbitrary ellipsoidal multi-coated inclusion

The present work aims to provide a general framework to deal with an elementary heterogeneous problem, where the inhomogeneity consists of an n-layered inclusion composed of n concentric ellipsoids made of anisotropic elastic materials. The methodology is based on a combination of Green's function techniques with interface operators, illustrating the stress and strain jump conditions at the interfaces between two adjacent coatings, which are considered perfectly bonded. The model is validated in the case of double-coated spherical inclusions made of isotropic materials, where the obtained analytical results cover the exact solution of Hervé and Zaoui. The model can be applied, after adequate choice of scale-transition methods, to describe the overall behaviour of real composite materials with complex microstructures that are significantly influenced by the presence of interphase layers between constituents (fillers and matrix). Such composites are widely employed in automotive and aerospace industries. As a typical example one can consider a composite with an epoxy matrix reinforced by glass beads coated using a thin soft polymeric phase or syntactic foams particulate composites obtained by filling a polymeric matrix with hollow solid inclusions.     

Analysis of stress field in a single anisotropic diamond/square shaped inclusion using the volume integral equation method and the numerical equivalent inclusion method

A volume integral equation method (VIEM) is used to study elastostatic problems in an unbounded elastic solid containing a single diamond/square shaped inclusion subject to uniform tensile stress at infinity. The inclusion is assumed to be a long parallel diamond/square cylinder composed of isotropic or anisotropic elastic materials and perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinder. A detailed analysis of the stress field at the interface between the isotropic matrix and the single isotropic/orthotropic diamond/square shaped inclusion is carried out. The effects of a single isotropic/orthotropic diamond/square shaped inclusion on the stress field at the interface between the matrix and the inclusion are investigated in detail. The accuracy of the volume integral equation method for the interfacial stress field is validated and compared by the numerical equivalent inclusion method (NEIM) and the finite element method (FEM) using ADINA. Through detailed analysis of plane elastostatic problems using the parallel volume integral equation method (PVIEM) in an unbounded isotropic matrix with multiple isotropic diamond shaped inclusions under uniform remote tensile loading, it is demonstrated that the volume integral equation method can also be applied to solve general two- and three-dimensional elastostatic problems involving multiple isotropic/anisotropic inclusions whose shape and number are arbitrary.     

Dislocation model of an asymmetric weak zone for problems of interaction between crack-like defects

An adhesively bonded asymmetric weak zone is proposed as a model for studying the problem of interaction between crack-like defects in an elastic medium. The opening of the weak zone is prescribed by a two-parameter basis function, i.e. by a special dislocation which automatically accounts for the asymmetry and other expected physical features of the stress–strain field near the tips of the weak zone. The adhesive forces corresponding to the prescribed opening are then calculated from the solution of the particular problem. The application of the model is demonstrated on the problem of a long interface crack subjected to wedge opening forces which is separated from a short collinear interface weak zone by a small unbroken strong microstructural feature (a small obstacle). Two key questions pertaining to limiting situations are addressed: (i) when does the weak zone become the nucleus of a cohesive crack on its own without linking with the pre-existing long crack; and (ii) when does it force the rupture of the obstacle and coalesce with the long crack.     

Dislocation mechanism of hollow fiber sliding during ceramic nanocomposite fracture

A dislocation model is proposed for describing the sliding of hollow fibers (and, in particular, carbon nanotubes) as a mechanism of elastic energy relaxation near cracks in ceramic nanocomposites. In this model, the sliding of a hollow cylindrical fiber occurs through the formation of a prismatic circular dislocation loop gliding along the boundary between the fiber and the matrix. The energy characteristics of this process are calculated, and the critical stress required for the barrierless nucleation and glide of such a loop is determined. It is shown that the critical stress increases with the ratio between the shear moduli of the matrix and the fiber and (over a wide range of changes in this ratio) with the fiber wall thickness.     

Elastic-energy relaxation in heterostructures with strained nanoinclusions

Elastic-energy relaxation in systems with nanoinclusions is considered. The relaxation is related to the formation of the following dislocation loops: a single misfit dislocation loop or a group of such loops on the matrix-nanoinclusion interface and/or a satellite dislocation loop near the inclusion. The critical inclusion sizes beginning from which misfit dislocation loops and satellite dislocation loops can nucleate are determined for various models of relaxation processes. The dependences of the satellite-dislocation-loop diameter on the inclusion size are calculated and compared with experimental data.     

Subsurface deformation studies of aluminium during wear and its theoretical understanding using molecular dynamics

Adopting the bonded interface technique for wear experiments under vacuum, this paper reports the nature of the localised shear bands that appear at the different deformation zones of the subsurface of aluminium under different sliding conditions. The plastic deformations are mapped under both low load/low sliding velocities as well as high load and high sliding velocities. A monotonic change in local plastic strain as a function of depth at low sliding velocities give way to a discontinuity separating two different zones with differing plastic behaviour for high sliding speed wear test. Besides shear bands, bonded interface also reveals the presence of kinks particularly in the samples subjected to wear test with high sliding velocities. A molecular dynamic simulation of the wear process successfully replicated the experimental observation, thus allowing us to discuss the mechanism of subsurface deformation during the wear process in the absence of any significant oxide layer for aluminium under sliding condition.     

Shielding effect of a nano-circular inclusion acting on semi-infinite wedge cracks

The model of a screw dislocation near a semi-infinite wedge crack tip inside a nano-circular inclusion is proposed to investigate the shielding effect of nano inclusions acting on cracks. Utilizing the complex function method, the closed-form solutions of the stress fields in the matrix and the inclusion region are derived. The stress intensity factor, the image force, as well as the critical loads for dislocation emission are discussed in detail. The results show that the nano inclusion not only enhances the shielding effect exerted by the dislocation, but also provides a shielding effect itself. Moreover, dislocations may be trapped in the nano inclusion even if the matrix is softer than the inclusion. This helps the dislocation shield crack, and reduces the dislocation density within the matrix.     

Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

Shear-induced adhesive failure of a rigid slab in contact with a thin confined film

A rigid-glass prism (square or rectangular base, rectangular cross-section) is sheared off a thin film of silicone elastomer bonded to a glass plate by applying a tangential force at various distances above the prism/elastomer interface. At a given tangential force, the prism starts to slide on the elastomeric film. As the sliding velocity, thus the frictional force, is progressively increased, an elastic instability develops at the interface that results in the formation of numerous bubbles. These bubbles, the lateral dimension of which is comparable to the thickness of the film, move across the interface with speeds 1000 times faster than the overall sliding speed of the glass prism against the PDMS film. It is found that the glass prism continues to slide on the elastomeric film as long as the applied shear stress is less than a critical value. During sliding, however, a normal stress is developed at the interface that decays from the front (i.e. where the force is applied) to the rear end of the prism. When the normal stress reaches a critical value, the prism comes off the film. The critical shear stress of fracture increases with the modulus of the film, but decreases with the thickness following a square root relationship, as is the case with the removal of rigid punches from thin elastomeric films by normal pull-off forces.     

Thermoelastic behavior of a thermoelectric thin-film attached to an infinite elastic substrate

Abstract

This paper examines the thermoelectric behaviour of a thermoelectric thin film bonded to an elastic substrate. A calculation model for thermoelectric thin films is developed based on the singular integral equation method. The interface shear stress is found to exhibit singular behaviour at the ends of the films. Numerical results for the thermal stress distribution in the film and the film/substrate interface are obtained. Effects of film thickness and the substrate to film stiffness ratio on the stress of the film and the stress intensity factor of the interface are identified. The effects of interface electricity conductivity and the elastic–plastic deformation of the film are discussed.     

Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity

A theoretical model is proposed for elastic stress relaxation of a buried strained cylindrical inhomogeneity, which assumes the edge misfit dislocation dipole formation in the soft matrix at some distance from the interface. The critical radius of the inhomogeneity for the formation of the edge misfit dislocation dipole is given and the influence of various parameters on the critical radius is evaluated. The result indicates that the critical radius decreases with increasing misfit strain and core radius of the misfit dislocation. It is also found that, compared to the edge misfit dislocation dipole formation in the interface, the critical radius of the inhomogeneity decreases when the location of an edge misfit dislocation dipole formation is in the soft matrix at some distance from the interface.     

Influence of imperfectly bonded micropolar elastic half-space with non-homogeneous viscoelastic layer on propagation behavior of shear wave

A mathematical model is developed in which the effect of imperfect bonding between the constituents of layer and half-space on the phase velocity and damped velocity of SH-wave is discussed. The model consists of a micropolar elastic half-space bonded imperfectly with a heterogeneous viscoelastic layer. The dispersion equation and damping equation of SH-wave propagation in the said model is obtained in the closed form analytically. The effects of imperfect bonding, internal friction, heterogeneity, micropolarity, and complex interface stiffness parameters highlighted through numerical computation and graphical demonstrations. Standard Love-wave equation and dispersion equation as well as damping equation for perfectly bonded micropolar half-space with heterogeneous viscoelastic layer is obtained as a special case of the problem. Through comparative study of homogeneity with heterogeneity in the layer; imperfect bonding of layer and half-space with their welded (perfect) contact; and presence of micropolarity in half-space with its absence in half-space are compared meticulously.     

Dynamic testing of discontinuous fibre reinforced composite materials

The work reported is part of a larger study of the mechanics of discontinuous fibre reinforced composite materials—particularly those with interfacial slip. The materials used were models composed of aligned stub steel rods of 0·4 mm diameter and 25 mm length as fibres and a proprietary silicone rubber as matrix. The specimens, which were of low volume fraction (～7·5%), were in the form of square section rods and had either bonded or unbonded matrix/fibre interfaces. The tests conducted consisted of simple strain controlled tensile tests at 0·83 Hz and 0·083 Hz and the use of the specimens as the spring/damper element in a single degree of freedom system resonating near 20 Hz. In the latter tests, the damping in the system extraneous to the specimen was quite high and, in the case of the bonded specimens, a correction had to be made. Both the damping and stiffness of all the specimens were broadly dependent upon the amplitude of oscillation. In all cases in the single degree of freedom system tests, softening resonances were exhibited, but in the case of the bonded specimens this was due to the nature of the matrix while for the unbonded specimens reduction in stiffness with increase in amplitude was due to sliding at the interface. The specimens had been designed to investigate this latter effect, which also occasioned a substantial increase in damping and led to flat-topped resonance curves characteristic of a system containing friction. The tests further exhibited the rate sensitivity of the properties of the unbonded interface specimens which showed higher stiffness and lower damping in the resonance tests than in those at lower frequencies. It was concluded that a discontinuous fibre composite developed for its damping properties would be most effectively achieved in a composite where there was a good bond at the interface and the matrix damping increased greatly with increase in shear or rate of deformation.     

(001) silicon surfacial grain boundaries obtained by direct wafer bonding process: accurate control of the structure before bonding

Ultra-thin (001) silicon films bonded onto (001) silicon wafers, which form ‘surfacial grain boundaries’, are analysed by transmission electron microscopy and X-ray diffraction. The aim of this study is to find a way of controlling precisely, before direct wafer bonding, the structure of the Si/Si (001) interface. Two kinds of dislocation networks are found at the bonded interface. A square array of screw dislocations accommodates the twist between the two crystals, whereas a linear network of mixed dislocations accommodates the tilt resulting from the residual vicinality of the initial surfaces. A theoretical study shows that knowing and choosing before bonding the characteristics of these interfacial dislocations depend on the control of the ‘twist’ angle during the hydrophobic molecular bonding process. Recently, a new bonding method allows us to obtain an accuracy of ±?0.005° for the ‘twist’ angle from patterned grooves without any crystallographic measurement. The precision of this technique is compared with three different measurement of the disorientation between the two grains taken after bonding. The first one is deduced from the periodicity of the dislocation networks located at the interface. The second one is calculated from large angle convergent beam electron diffraction patterns. The last one is obtained by synchrotron X-ray diffraction. The possibility of choosing precisely the characteristics of the Si (001) ‘surfacial grain boundaries’ before direct wafer bonding process is then discussed in light of an experimental study.     

Stress analysis of multiple anisotropic elliptical inclusions in composites

A volume integral equation method is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple anisotropic elliptical inclusions subject to uniform remote tension or remote in-plane shear. This method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central elliptical inclusion is carried out for square and hexagonal packing of anisotropic inclusions. The effects of the number of anisotropic inclusions and various inclusion volume fractions on the stress field at the interface between the isotropic matrix and the central elliptical cylindrical inclusion are investigated in detail. The stress field at the interface between the isotropic matrix and the central elliptical inclusion is also compared with that between the isotropic matrix and the central circular inclusion.     

In源流量与Ⅲ族流量之比对InGaN/GaN多量子阱性质的影响

利用x射线三轴晶衍射和光致发光谱研究了生长参数In源流量与Ⅲ族流量之比对InGaN/GaN多量子阱结构缺陷(如位错密度和界面粗糙度)和光致发光的影响.通过对（0002）对称和（1012）非对称联动扫描的每一个卫星峰的ω扫描，分别测量出了多量子阱的螺位错和刃位错平均密度，而界面粗糙度则由（0002）对称衍射的卫星峰半高全宽随级数的变化得出.试验发现多量子阱中的位错密度特别是刃位错密度和界面粗糙度随In源流量与Ⅲ族源流量比值的增加而增加，导致室温下光致发光性质的降低，从而也证明了刃位错在InGaN/GaN 关键词： x射线三轴晶衍射 界面粗糙度 位错 InGaN/GaN多量子阱