Fracture mechanics analysis on Smart-Cut~ technology.Part 2:Effect of bonding flaws

In Part 2 of the paper on the Smart-Cut process,the effects of bonding flaws characterized by the size andinternal pressure before and after splitting are studied byusing fracture mechanics models.It is found that the bon-ding flaws with large size are prone to cause severe devia-tion of defect growth,leading to a non-transferred area ofthin layer when splitting.In a practical Smart-Cut processwhere the internal pressure of bonding flaws is very small,large interfacial defects always promote defect grow...     

Fracture mechanics analysis on Smart-Cut technology. Part 1： Effects of stiffening wafer and defect interaction

In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator （SOI） wafers of high uniformity in thickness. Using integral transform and Cauchy singular integral equation methods, the mode-I and mode-II stress intensity factors, energy release rate, and crack opening displacements are derived in order to examine several important fracture mechanisms involved in the Smart-Cut process. The effects of defect interaction and stiffening wafer on defect growth are investigated. The numerical results indi- cate that a stiffener/handle wafer can effectively prevent the donor wafer from blistering and exfoliation, but it slows down the defect growth by decreasing the magnitudes of SIF＇s. Defect interaction also plays an important role in the splitting process of SOI wafers, but its contribution depends strongly on the size, interval and internal pressure of defects. Finally, an analytical formula is derived to estimate the implantation dose required for splitting a SOI wafer.     

COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE

The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared.     

Mechanical effects of circular liquid inclusions inside soft matrix: role of internal pressure change and surface tension

The mechanical effects of dilute liquid inclusions on the solid-liquid composite are explored,based on an analytical circular inclusion model incorporating the internal pressure change of the liquid and the surface tension of the interface.Several simple explicit dependences of the stress field and effective stiffness on the bulk modulus and the size of the liquid,the surface tension,and Poisson’s ratio of the matrix are derived.The results show that the stresses in the matrix are reduced,and the stiffness of the solid-liquid composite is enhanced with the consideration of either the surface tension or the internal pressure change.Particularly,the effective Young’s modulus predicted by the present model for either soft or stiff matrices agrees well with the known experimental data.In addition,according to the theoretical results,it is possible to stiffen a soft solid by pressured gas with the presence of the surface tension of the solid-gas interface.     

Application of particle splitting method for both hydrostatic and hydrodynamic cases in SPH

Smoothed particle hydrodynamics(SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse(mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process,conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.Smoothed particle hydrodynamics(SPH)method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems.However,in most simulations,uniform particle distributions are used and the multi-resolution,which can obviously improve the local accuracy and the overall computational efficiency,has seldom been applied.In this paper,a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems.The splitting algorithm is that,when a coarse(mother)particle enters the splitting region,it will be split into four daughter particles,which inherit the physical parameters of the mother particle.In the particle splitting process,conservations of mass,momentum and energy are ensured.Based on the error analysis,the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases.Finally,the scheme is validated by five basic cases,which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.     

A micromechanical model for effective conductivity in granular electrode structures

Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells （SOFC） and lithium-ion batteries （LIB）. For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB： the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete el- ement approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the con- nectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, es- pecially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of cal- endering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.     

SIZE EFFECT AND GEOMETRICAL EFFECT OF SOLIDS IN MICRO—INDENTATION TEST

Micro-indentation tests at scales of the order of sub-micron show that the measured hardness increases strongly with decreasing indent depth or indent size,which is frequently referred to as the size effect.At the same time,at micron or sub-micron scale,another effect,which is referred to as the geometrical size effects such as crystal grain size effect,thin flim thickness effect,etc.,also influences the measured material hardness.However,the trends are at odds with the size-independence implied by the conventional elastic-plastic theory.In the present research,the strain gradient plasticity theory(Fleck and Hutchinson)is used to model the composition effects(size effect and geometrical effect) for polycrystal material and metal thin film/ceramic substrate systems when materials undergo micro-indenting.The phenomena of the “pile-up“ and “sink-in“ apeared in the indentation test for the polycrystal materials are also discussed.Meanwhile,the micro-indentation experiments for the polycrystal Al and for the Ti/Si3N4 thin film/substrate system are carried out.By comparing the theoretical predictions with experimental measuremtns.the values and the variation trends of the micro-scale parameter included in the strain gradient plasticity theory are predicted.     

DEFORMATIONS AND STABILITY OF SPHERICAL CAPS UNDER CENTRALLY DISTRIBUTED PRESSURES

In this paper the deformations and stability in large axisymmetric deflection of spherical caps under centrally distributed pressures are investigated. The Newton-apline method for solving the nonlinear equations governing large axisymmetric deflection of spherical caps is presented. The buckling behavior is studied for a cap with fixed geometry when the size of the loaded radius is allowed to vary, and for a fixed loaded radius when the shell geometry is allowed to vary. The influence of the buckling modes on the criticalloads is analysed. Numerical results are given for v=0.3.     

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,     

Large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure

Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure.     

Stability of aneurysm solutions in a fluid-filled elastic membrane tube

When a hyperelastic membrane tube is inflatedby an internal pressure, a localized bulge will form when thepressure reaches a critical value. As inflation continues thebulge will grow until it reaches a maximum size after whichit will then propagate in both directions to form a hat-likeprofile. The stability of such bulging solutions has recentlybeen studied by neglecting the inertia of the inflating fluidand it was shown that such bulging solutions are unstableunder pressure control. In this paper we extend this recentstudy by assuming that the inflation is by an inviscid fluidwhose inertia we take into account in the stability analysis.This reflects more closely the situation of aneurysm forma-tion in human arteries which motivates the current series ofstudies. It is shown that fluid inertia would significantly re-duce the growth rate of the unstable mode and thus it has astrong stabilizing effect.     

Mechanically induced phase transformation of zinc sulfide

Molecular dynamics(MD) simulations of the consecutive compression-decompression cycles of hexagonal zinc sulfide(wurtzite) nanoparticles predict an irreversible phase transformation to the cubic polymorph.The phase transformation commences at the contact area between the particle and the indenter and proceeds with the number of compression cycles.Dislocations are visible for a particle size above 5 nm.Results from wet grinding and dry powder compression experiments on a commercial wurtzite pigment agree qualitatively with MD simulation predictions.X-ray diffraction patterns reveal that the amount of cubic polymorph in the compressed samples increases with pressure applied to the powder.In comparison with powder compression,wet milling leads to a more pronounced phase transformation.This occurs because the particles are exposed to a large number of stress events by collision with the grinding media,which leads to the formation of defects and new surface crystallites by particle fracture.According to the MD simulations,phase transformation is expected to occur preferentially in surface crystallites because they experience the highest mechanical load.Because of the phase transformation,the wet ground and compressed samples exhibit a lower photoluminescence intensity than the feed material.In comparison with powder compression,milling reduces the photoluminescence intensity more substantially.This occurs because a higher defect concentration is formed.The defects contribute to the phase transformation and photoluminescence quenching.     

Lattice Boltzmann study of the interaction between a single solid particle and a thin liquid film

The isothermal single-component multi-phase lattice Boltzmann method(LBM) combined with the particle motion model is used to simulate the detailed process of liquid film rupture induced by a single spherical particle.The entire process of the liquid film rupture can be divided into two stages.In Stage 1,the particle contacts with the liquid film and moves into it due to the interfacial force and finally penetrates the liquid film.Then in Stage 2,the upper and lower liquid surfaces of the thin film are driven by the capillary force and approach to each other along the surface of the particle,resulting in a complete rupture.It is found that a hydrophobic particle with a contact angle of 106.7° shows the shortest rupture duration when the liquid film thickness is less than the particle radius.When the thickness of the liquid film is greater than the immersed depth of the particle at equilibrium,the time of liquid film rupture caused by a hydrophobic particle will be increased.On the other hand,a moderately hydrophilic particle can form a bridge in the middle of the liquid film to enhance the stability of the thin liquid film.     

THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD

The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.     

Computation of pressure drop for dilute gas-solid suspension across thin and thick orifices

The present work deals with the computation of the gas-solid two-phase flow pressure drop across thin and thick orifices for a vertically downward flow configuration at the higher limits of a dilute phase flow situation(0.01≤αs,in≤0.10).The Eulerian-Eulerian(two-fluid)model has been used in conjunction with the kinetic theory of granular flow with a four-way coupling approach.The validation of the solution process has been performed by comparing the computational result with the existing experimental data.It is observed that the two-phase flow pressure drop across the orifice increases with an increase in the thickness of the orifice,and the effect is more prominent at higher solid loading.The pressure drop is found to increase with an increase in the solid volume fraction.An increase in the Reynolds number or the area ratio increases the pressure drop.An increase in the size of the particles reduces the pressure drop across the orifice at both small and relatively large solid volume fractions.Finally,a two-phase multiplier has been proposed in terms of the relevant parameters,which can be useful to evaluate the gas-solid two-phase flow pressure drop across the orifice and can subsequently help to improve the system performance.     

Mathematical problems in the integral-transformation method of dynamic crack

In the investigation on fracture mechanics, the potential function was introduced,and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied.After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility. A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.     

The singular perturbation method applied to the nonlinear stability problem of a shallow spherical shell (II)

In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author’s previous paper[11].     

A wavelet approach for active-passive vibration control of laminated plates

As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors,this paper proposes a hybrid activepassive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers.Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory,this waveletbased control method has the ability to automatically filter out noise-like signal in the feedback control loop,hence reducing the risk of residual coupling effects which are usually the source of spillover instability.Moreover,the existence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process.A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control process.Numerical results demonstrate the efficiency of the proposed approach.     

FORMATION OF MICRO-POROUS SPHERICAL PARTICLES OF CALCIUM SILICATE （XONOTLITE）IN DYNAMIC HYDROTHERMAL PROCESS

Stiming during hydrothermal synthesis plays an important role in the formation of porous spherical xonotlite particles.The size of spherical particles formed during dynamic hydrothermal process is related to the size of minimum vortices in the reaction slurry,which is determined by stirring speed.The kinetics of growth of xonotlite particless is de-termined by measuring the apparent viscosity of the reactant slurry at various reaction time and reaction temperatures.It is found that the growth of particles follows the contracting-volume equation.and the activation energies for nucleation and growth are 104 and 123 kJ-mol,respectively.