Stress-strain fields and the effectiveness shear properties for three-phase composites with imperfect interface

Based on the 'average stress in the matrix' concept of Mori and Tanaka (:Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusion. Acta Metall. 21, 571-580) a micromechanical model is presented for the prediction of the elastic fields in coated inclusion composites with imperfect interfaces. The solutions of the effective elastic moduli for this kind of composite are also obtained. In two kinds of composites with coated particulates and fibers, respectively, the interface imperfections are takes to the assumption that the interface displacement discontinues are linearly related to interface tractions like a spring layer of vanishing thickness. The resulting effective shear modulus for each material and the stress fields in the composite are presented under a transverse shear loading situation.

边坡稳定性分析极限平衡法的简化条件

边坡稳定性分析极限平衡法在求解安全系数时,需要对条块间内力引入假定条件或某些平衡条件在求解时得不到满足.分析这些不同的假设条件对于计算结果的影响,建立一个满足极限平衡原理和合理性条件的数值优化模型.引入载荷系数,利用载荷系数与安全系数之间的单调关系,将模型的求解转化为求解一系列线性规划问题,算法中不存在数值收敛问题,且可以求出安全系数的全局最优解.通过对模型各个约束条件的变化来模拟引入的假定条件,以此探讨各种假定条件或静力平衡条件的缺失对计算结果影响及某些常用方法引入的假定条件可能带来的误差.

Investigation of the Mechanical Properties of Thin Films by Nanoindentation, Considering the Effects of Thickness and Different Coating-Substrate Combinations

In order to further investigate nanoindentation data of film-substrate systems and to learn more about the mechanical properties of nanometer film-substrate systems, two kinds of films on different substrate systems have been tested with a systematic variation in film thickness and substrate characteristics. The two kinds of films are aluminum and tungsten, which have been sputtered on to glass and silicon substrates, respectively. Indentation experiments were performed with a Nano Indent XP II with indenter displacements typically about two times the nominal film thicknesses. The resulting data are analyzed in terms of load-displacement curves and various comparative parameters, such as hardness, Young's modulus, unloading stiffness and elastic recovery. Hardness and Young's modulus are investigated when the substrate effects are considered. The results show how the composite hardness and Young's modulus are different for different substrates, different films and different film thicknesses. An assumption of constant Young's modulus is used for the film-substrate system, in which the film and substrate have similar Young's moduli. Composite hardness obtained by the Joslin and Oliver method is compared with the directly measured hardness obtained by the Oliver and Pharr method.

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

A new model for the energy release rate of fibre/matrix interfacial fracture

On the basis of the well-known shear-lag analysis of fibre/matrix interface stresses and the assumption of identical axial strains in the fibre and matrix, a new model for predicting the energy release rate of interfacial fracture of the fibre pull-out test model is attempted. The expressions for stresses in the fibre, matrix and interface are derived. The formula for interfacial debonding energy release rate is given. Numerical calculations are conducted and the results obtained are compared with those of the existing models.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Numerical Analyses of Discrete Gust Response for an Aircraft

Based on Navier-Stokes equations and structural and flight dynamic equations of motion, dynamic responses in vertical discrete gust flow perturbation are investigated for a supersonic transport model. A tightly coupled method was developed by subiterations between aerodynamic equations and dynamic equations of motion. First, under the assumption of rigid-body and single freedom of motion in the vertical plunging, the results of a direct-coupling method are compared with the results of quasi-steady model method. Then, gust responses for the one-minus-cosine gust profile arc analyzed with two freedoms of motion in plunging and pitching for the airplane configurations with and without the consideration of structural deformation.

Applicability Range of Stoneys Formula and Modified Formulas for a Film/Substrate Bilayer

In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

Deflections and Curvatures of a Film–Substrate Structure with the Presence of Gradient Stress in MEMS Applications

The close form solutions of deflections and curvatures for a film–substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film–substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film–substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film–substrate composite structure with the presence of gradient stress.

Shear Strength Measurements in LY-12 Aluminium Alloy During Shock Loading

Lateral stress of LY-12 alummium alloy under plate impact shock loading was measured. Based on the measured data, the Hugoniot relation and shear strength were obtained. The result has demonstrated that the shear strenath of the tested material increases remarkably with the increasing longitudinal stress. This means that the assumption of constant shear strength usually adopted in shock stress calculation is not suitable for the present material.

Planar Thermocapillary Migration of Two Bubbles in Microgravity Environment

A theoretical investigation is performed on the thermocapillary motion of two bubbles in arbitrary configuration in microgravity environment under the assumption that the surface tension is high enough to keep the bubbles spherical. The two bubbles are dr

Roll Waves in Overland Flow

Roll waves are frequently observed in overland flow, especially in rill flow, which has an important effect on the development of soil erosion. Using one-dimensional St. Venant equations, this paper investigates the dynamics of periodic roll waves based on Dressler’s and Brock’s work. Under the assumption that the average flow depth equals the uniform flow depth, expressions of the roll-wave speed and roll-wave profile were obtained. Testing with the results observed by Brock (1970) for wave properties shows that these expressions can approximately describe the characteristics of periodic permanent roll waves. Numerical solutions of roll waves under specific conditions are found, which show that when a roll wave appears, the shear stress of flow increases, and the soil erosion accelerates.

Squeeze-film Effects in MEMS Devices with Perforated Plates for Small Amplitude Vibration

Squeeze-film effects of perforated plates for small amplitude vibration are analyzed through modified Reynolds equation (MRE). The analytical analysis reckons in most important influential factors: compressibility of the air, border effects, and the resistance caused by vertical air flow passing through perforated holes. It is found that consideration of air compressibility is necessary for high operating frequency and small ratio of the plate width to the attenuation length. The analytical results presented in this paper agree with ANSYS simulation results better than that under the air incompressibility assumption. The analytical analysis can be used to estimate the squeeze-film effects causing damping and stiffness added to the system. Since the value of Reynolds number involved in this paper is low (< 1), inertial effects are neglected.

Application of Three-Dimensional Discrete Element Face-to-Face Contact Model with Fissure Water Pressure to Stability Analysis of Landslide in Panluo Iron Mine

Three-dimensional discrete element face-to-face contact model with fissure water pressure is established in this paper and the model is used to simulate three-stage process of landslide under fissure water pressure in the opencast mine, according to the actual state of landslide in Panluo iron mine where landslide happened in 1990 and was fathered in 1999. The calculation results show that fissure water pressure on the sliding surface is the main reason causing landslide and the local soft interlayer weakens the stability of slope. If the discrete element method adopts the same assumption as the limit equilibrium method, the results of two methods are in good agreement; while if the assumption is not adopted in the discrete element method, the critical phi numerically calculated is less than the one calculated by use of the limit equilibrium method for the same C. Thus, from an engineering point of view, the result from the discrete element model simulation is safer and has more widely application since the discrete element model takes into account the effect of rock mass structures.