Thermal-stress induced phenomena in two-component material:Part Ⅱ

The paper deals with analytical models of the elastic energy gradient Wsq representing an energy barrier. The energy barrier is a surface integral of the elastic energy density Wq. The elastic energy density is induced by thermal stresses acting in an isotropic spherical particle （q = p） with the radius R and in a cubic cell of an isotropic matrix （q = m）. The spherical particle and the matrix are components of a multi-particle-matrix system representing a model system applicable to a real two-component material of a precipitation-matrix type. The multi-particle-matrix system thus consists of periodically distributed isotropic spherical particles and an isotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with a central spherical particle in each of the cubic cells. The dimension d of the cubic cell then corresponds to an inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent micro- structural characteristics of a real two-component material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural charac- teristics. The thermal stresses originate during a cooling pro- cess as a consequence of the difference am - ap in thermal expansion coefficients between the matrix and the particle, am and ap, respectively. The energy barrier Wsq is used for the determination of the thermal-stress induced strengthening aq. The strengthening represents resistance against com- pressive or tensile mechanical loading for am - ap 〉 0 or am - ap 〈 0. respectively.     

DEM speedup： Stiffness effects on behavior of bulk material

A number of techniques exist for minimizing the computational cost of discrete element simulations （DEMs）. One such method is a reduction of particle stiffness, which allows for bigger time steps and therefore fewer iterations in a simulation. However, the limits and drawbacks of this approach are still unclear, and may lead to invalid results. This paper investigates the effect of a stiffness reduction on bulk behavior by examining three case studies. Two cases demonstrate that particle stiffness can be reduced without affecting the bulk material behavior, whereas the third test shows that a stiffness reduction influences the bulk behavior.     

固体表面开裂的周期图案：I. 现象与原理

温度与湿度非均匀变化引起固体表面大面积周期分布的裂纹. 从火星表面陨石坑的嵌套多边形缝隙到地球田地湖泊的干旱龟裂, 从火山熔浆之河凝固成的多边形玄武岩到冰川消蚀形成的晶莹剔透的周期冰雕, 都遵循一个简明的自然法则：最小能量原理. 介绍几个典型的自然现象, 并通过一个小实验浅析它们形成时所遵循的简明自然法则.     

采用压电机敏元件进行结构振动控制I：耦合系统动力分析

本文从机电耦合弹性体的理论出发，运用Ｈａｍｉｌｔｏｎ原理建立了一般压电耦合系统的动力分析模型，并给出了模态分析和有限元分析的耦合系统方程、作动方程及检测方程。该分析模型和计算公式可用于任意形状压电耦合系统的动力分析和振动控制设计。另外，导出的模态分析和有限元公式可用现有的商业软件求解。     

耐热梯度功能材料的热应力研究进展

介绍了梯度功能材料的概念和开发背景：回顾了近些年来在梯度功能材料热应力研究方面所取得的研究成果,并对梯度功能材料的发展趋势作一展望．着重论述了梯度功能材料在热应力分析领域的研究现状及其应用前景     

Void fraction and pressure drop during external upward two-phase crossflow in tube bundles – part I: Experimental investigation

The present paper is the part I of a broad study concerning void fraction and pressure drop for air-water upward external flow across tube bundles. Experimental results were obtained for liquid and gas superficial velocities ranging from 0.02 to 1.50 m/s and 0.20 to 10.00 m/s, respectively. Void fraction measurements were performed for bubbly flow using a capacitive probe. The test section consisted of a triangular tube bundle counting with 19 mm OD tube and transverse pitch of 24 mm. Initially, the paper describes the test facility and the data regression and experimental procedures. Then, the pressure drop and void fraction measurements are validated based on tests for single-phase flow and quiescent liquid conditions, respectively. Finally, the experimental data are presented and analyzed. In the second part of this study (Part II), a literature review on predictive methods for void fraction and pressure drop is presented. Additionally, these methods are compared with the database presented in Part I and new predictive methods for void fraction and frictional pressure drop are proposed.     

A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods

Based on the fundamental equations of the mechanics of solid continuum, the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix, imaginarily divided into identical cells with dimensions equal to inter-particle distances, containing a central spherical particle with or without a spherical envelope on the particle surface. Consequently, the multi-particle-（envelope）- matrix system, as a model system regarding the analytical modelling, is applicable to four types of multi-phase materials. As functions of the particle volume fraction v, the inter-particle distances dl, d2, d3 along three mutually per- pendicular axes, and the particle and envelope radii, R1 and R2, respectively, the thermal stresses within the cell, are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep- resented by the matrix, envelope and particle. Analytical-（experimental）-computational lifetime prediction methods for multi-phase materials are proposed, which can be used in engineering with appropriate values of parameters of real multi-phase materials.     

梯度厚板热应力分层计算方法的改进

为了使功能梯度材料厚板的分层计算具有更快的收敛速度和更好的精度,而采用每层热力系数与梯度材料厚度变化为指数函数的分层方法,来平滑均匀分层法引起材料热力系数的跳跃,使热力系数更逼近实际,并将该方法命名为指数函数有限分层法.通过算例表明,在精度为0.1的情况下,均匀分层法的分层层数是指数函数分层法的分层层数的2倍多,并且随着精度的提高,分层层数相差的倍数就越大.     

Magnetically assisted gas-solid fluidization in a tapered vessel： Part I. Magnetization-LAST mode

This article presents further experimental results of the Magnetization-LAST mode in magnetically assisted gas-fluidized tapered beds, including external transverse magnetic field control of solid phase movement, central channel formation, spout depth and the pressure drop across the bed. Phase diagrams similar to those recently reported for the Magnetization-FIRST mode were also developed. Dimensional analysis based on ＂pressure transform＂ of the initial set of variables and involving the magnetic granular Bond number pertinent to particle aggregate formation was applied to develop the scaling relationships.     

The PELskin project—part I: fluid–structure interaction for a row of flexible flaps: a reference study in oscillating channel flow

Previous studies of flexible flaps attached to the aft part of a cylinder have demonstrated a favourable effect on the drag and lift force fluctuation. This observation is thought to be linked to the excitation of travelling waves along the flaps and as a consequence of that, periodic shedding of the von Kármán vortices is altered in phase. A more general case of such interaction is studied herein for a limited row of flaps in an oscillating flow; representative of the cylinder case since the transversal flow in the wake-region shows oscillating character. This reference case is chosen to qualify recently developed numerical methods for the simulation of fluid–structure interaction in the context of the EU funded ‘PELskin’ project. The simulation of the two-way coupled dynamics of the flexible elements is achieved via a structure model for the flap motion, which was implemented and coupled to two different fluid solvers via the immersed boundary method. The results show the waving behaviour observed at the tips of the flexible elements in interaction with the fluid flow and the formation of vortices in the gaps between the flaps. In addition, formation of vortices upstream of the leading and downstream of the trailing flap is seen, which interact with the formation of the shear-layer on top of the row. This leads to a phase shift in the wave-type motion along the row that resembles the observation in the cylinder case.     

Analytical modelling of thermal stresses in anisotropic composites

This paper represents a continuation of the author's previous work which deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid elastic continuum. This continuum consists of anisotropic spherical particles which are periodically distributed in an anisotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with central particles. This multi-particle–matrix system represents a model system which is applicable to two-component materials of the precipitate–matrix type. The thermal stresses, which originate due to different thermal expansion coefficients of components of the model system, are determined within the cubic cell. The analytical modelling results from fundamental equations of continuum mechanics for solid elastic continuum (Cauchy's, compatibility and equilibrium equations, Hooke's law). This paper presents suitable mathematical procedures which are applied to the fundamental equations. These mathematical procedures lead to such final formulae for the thermal stresses which are relatively simple in comparison with the final formulae presented in the author's previous work which are extremely extensive. Using these new final formulae, the numerical determination of the thermal stresses in real two-component materials with anisotropic components is not time-consuming.     

Thermal stresses in two- and three-component anisotropic materials

This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists of anisotropic spherical particles periodically distributed in an anisotropic infinite matrix. The particles are or are not embedded in an anisotropic spherical envelope, and the infinite matrix is imaginarily divided into identical cubic cells with central particles. The thermal stresses are thus investigated within the cubic cell. This mulfi-particle-（envelope）-matrix system based on the cell model is applicable to two- and three-component materials of precipitate-matrix and precipitate-envelope-matrix types, respectively. Finally, an analysis of the determination of the thermal stresses in the multi-par- ticle-（envelope）-matrix system which consists of isotropic as well as uniaxial- and/or triaxial-anisotropic components is presented. Additionally, the thermal-stress induced elastic energy density for the anisotropic components is also derived. These analytical models which are valid for isotropic, anisotropic and isotropic-anisotropic multi-particle- （envelope）-matrix systems represent the determination of important material characteristics. This analytical determination includes： （1） the determination of a critical particle radius which defines a limit state regarding the crack initiation in an elastic, elastic-plastic and plastic components; （2） the determination of dimensions and a shape of a crack propagated in a ceramic components; （3） the determination of an energy barrier and micro-/macro-strengthening in a component; and （4） analytical-（experimental）-computational methods of the lifetime prediction. The determination of the thermal stresses in the anisotropic components presented in this paper can be used to determine these material characteristics of real two- and three-component materials with anisotropic components or with anisotropic and isotropic components.     

Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

Damage in a viscoplastic material part I: Cavity growth

The exact velocity, stress and strain rate fields around a spheroidal cavity in an infinite linear viscoplastic compressible matrix are derived analytically by the ‘three function approach’. The perturbation of the velocity field due to the cavity is the superposition of three independent modes, inducing homothetic growth, pure distortion and both volume and shape changes, respectively. This solution is then used to investigate the velocity field around a spheroidal cavity in a nonlinear viscous compressible material by means of a variational principle. The behaviour of such damaged linear and nonlinear materials will be discussed in a forthcoming companion paper.The importance of the reference strain, while studying void growth in a compressible material, is emphasized. If the axial strain is chosen as a reference, void growth is found to be enhanced at low triaxiality ratios, but lowered at high triaxiality ratios in a compressible matrix relative to an incompressible one. Finally, the transition from a power law to a linear law with intercept, at increasing strain rates, is shown to reduce damage growth rate.     

Microdamage of a nonlinear elastic material in combined stress state

The structural theory of short-term damage is used to study the coupled processes of deformation and microdamage of a physically nonlinear material in a combined stress state. The basis for the analysis is the stochastic elasticity equations for a physically nonlinear porous medium. Damage in a microvolume of the material is assumed to occur in accordance with the Huber-Mises failure criterion. The balance equation for damaged microvolumes is derived and added to the macrostress-macrostrain relations to produce a closed-form system of equations. It describes the coupled processes of nonlinear deformation and microdamage of the porous material. Algorithms are developed for calculating the dependence of microdamage on macrostresses and macrostrains and plotting stress-strain curves for a homogeneous material under either biaxial normal loading or combined normal and tangential loading. The plots are analyzed depending on the type of stress state __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 30–39, November 2006.     

Stochastic analysis of a thermoelastic problem in functionally graded plates with uncertain material properties

The statistics (i.e., mean and variance) of temperature and thermal stress are analytically obtained in functionally graded material (FGM) plates with uncertainties in the thermal conductivity and coefficient of linear thermal expansion. These FGM plates are assumed to have arbitrary nonhomogeneous thermal and mechanical properties through the entire thickness of plate and are subjected to deterministic convective heating. The stochastic temperature and thermal stress fields are analysed by assuming the FGM plate is multilayered with distinct, random thermal conductivity and coefficient of linear thermal expansion in each layer. Vodicka’s method, which is a type of integral transform method, and a perturbation method are employed to obtain the analytical solutions for the statistics. The autocorrelation coefficients of each random property and cross-correlation coefficients between different random properties are expressed in exponential function forms as a non-homogeneous Markov random field of discrete space. Numerical calculations are performed for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304), which have the largest dispersion of the random properties at the place where the volume fractions of the two constituent materials are both 0.5. The effects of the spatial change in material composition, thermal boundary condition and correlation coefficients on the standard deviations of the temperature and thermal stress are discussed.     

Axisymmetric static and dynamics snap-through phenomena in a thermally postbuckled temperature-dependent FGM circular plate

Thermal postbuckling analysis and the axisymmetric static and dynamic snap-through phenomena due to static/sudden uniform lateral pressure in a thermally postbuckled functionally graded material circular plate are performed in this research. Plate is formulated using the first order shear deformation plate theory. Thermo-mechanical properties of the plate are assumed to be temperature dependent where dependency is described according to the higher order Touloukian representation. Two types of temperature loading are considered. Uniform temperature rise and heat conduction across the thickness direction. The one dimensional heat conduction equation in the thickness direction is obtained and discreted via the central finite difference method. The obtained system of equations is nonlinear since the thermal conductivity itself is a function of the unknown nodal temperatures. Using the von-Kármán assumptions, the governing equations of the plate are obtained in a matrix representation with the aid of the conventional Ritz method whose shape functions are developed using the Gram-Schmidt process. At first thermal postbuckling analysis is performed which is a nonlinear problem with respect to both temperature and displacements. Afterwards, response of the bulged thermally postbuckled plate is obtained under the static and dynamic uniform pressure. Snap-through phenomenon may be observed in both static and dynamic loading cases, due to the immovability of the edge of the plate and the initial deflection caused by postbuckling deflection. To capture the snapping phenomenon and trace the path beyond the limit loads, cylindrical arch-length technique is used. In dynamic snap-through analysis, the effect of structural damping is also included. Numerical results of this study reveal that the structure is sensitive to the initial deflection caused by thermal postbuckling load. Increasing the temperature prior to mechanical loads enhances the snap-through intensity and also increases both the upper and lower limit loads. As shown, dynamic snap-through loads are lower than the static ones, however dynamic snap-through intensity is more than the static snap-though intensity. Furthermore, structural damping enhances the dynamic buckling loads of the plate and decreases the dynamic postbuckling deflection of the plate.     

Stress and fabric in granular material

It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading conditions.