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National Institute for Materials Science

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[MULTISCALE AND FUNCTIONALLY GRADED MATERIALS (FGM IX 2006) (pp.3-253)](https://mdr.nims.go.jp/datasets/baf8c580-f999-4c7b-b9d1-34c699ccd0d4)

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Sheet1 BookTitle_j BookTitle_e Volume/Issue Issueddate Page Title_j Title_e AuthorList_j AuthorList_e Abstract Language MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 3-8 気孔傾斜構造型窒化シリコンセラミックスの作成 Fabrication of Silicon Nitride Ceramics with Pore Gradient Structure Zhang Lian-meng, Chen Fei, Shen Qiang and Yan Fa-qiang Zhang Lian-meng, Chen Fei, Shen Qiang and Yan Fa-qiang  In the present study, Si3N4 ceramics with pore gradient structure were prepared by spark plasma sintering (SPS) technique. Silicon nitride ceramics with different controlled porosities were prepared by using ZrP2O7 as a binder material and heat treated at 1100 deg.C in a pressureless nitrogen atmosphere. Si3N4 ceramics with controlled porosity of 34-47% were obtained. The distribution of porous structure was homogenous. Fully dense Si3N4 ceramics could be sintered at 1400 - 1600 deg.C by using MgO and alumina Al2O3 as the sintering aids. Pore gradient structure was formed by laminating the Si3N4 porous ceramics and powder mixture was used to obtain fully dense ceramics, and then sintering at 1400 -1600 deg.C. Microstructure of sintered samples was observed by scanning electronic microscope (SEM) and the change of phase compositions was analyzed by X-ray diffraction (XRD). The results showed that these samples exhibited a good porous graded structure with a highly porous layer and a dense surface layer. The major phase of the Si3N4 ceramics was still alfa phase. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 9-15 衝撃負荷下の気泡材料の挙動への特性傾斜の影響 Influence of Property Gradient on the Behavior of Cellular Materials Subjected to Impact Loading H.Zeng, I.Nasri, S.Pattofatto, H.Zhao H.Zeng, I.Nasri, S.Pattofatto, H.Zhao  Recent manufacturing advances offer the possibility of introducing controlled porosity gradients in metallic-based cellular materials (foam, hollow, spheres), which are promising structural materials used in applications involving lightweight structures, impact energy absorption, acoustical wave attenuation, etc. However, the influence of such porosity gradients on the overall mechanical properties of these cellular materials still lacks understanding. This paper presents a study of such porosity gradient influence using numerical simulation. Basic material behavior of a given sphere size is experimentally characterized using a recently developed testing device - a 60 mm diameter nylon Hopkinson bar system, which provides an interesting solution for both the impedance match and reasonable specimen size. Numerical results using realistic material constants permit the determination of optimized porosity gradient influence on various properties such as impact resistance, thermal diffusion, etc. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 16-21 直交異方性FGMコーティングの埋め込み亀裂のための混合モード応力拡大係数 Mixed-Mode Stress Intensity Factors for an Embedded Crack in an Orthotropic FGM Coating  S.Dag, K.A.Ilhan, F.Erdogan S.Dag, K.A.Ilhan, F.Erdogan  Analytical and computational methods are developed to examine mixed-mode fracture behavior of an orthotropic FGM coating bonded to a homogeneous substrate through a layer of a bond-coat. The coating is assumed to contain an embedded crack perpendicular to the direction of the material property gradation. First, an analytical solution is developed considering a perturbation problem. Using Fourier transform, the problem is reduced to a system of singular integral equations which are solved by means of an expansion-collocation technique. Then, finite element method is utilized to investigate the same problem using the displacement correlation technique (DCT). By using the developed finite element method, mixed-mode stress intensity factors are also evaluated for an FGM coating-bond coat-substrate structure that is subjected to thermal stresses. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 22-27 Ni/Al203粉末混合物の焼結応力および速度 Sintering Stress and Viscosity of Ni/Al2O3 Powder Mixtures Kazunari Shinagawa Kazunari Shinagawa  Sinter-forging tests of Ni/Al203 powder compacts with mixing ratios ranging from 0/100 to 100/0 are performed to reveal the influence of mixing different types of powder on the sintering properties. The sintering stress and the viscosity are evaluated from the data of strain-time curves with different loads at an elevated temperature. The sintering stress as well as the viscosity of pure Ni powder compact is lower than that of pure Al2O3. The increase in viscosity of the powder mixtures by adding Al2O3 into Ni is large compared with that in sintering stress within small amounts of addition, which corresponds to the retard of the sintering rate. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 28-32 衝撃下にある機能傾斜バリアの熱弾性応答 Thermoelastic Response of Functionally Graded Barriers Subjected to Shocks C.A.Vieira Carneiro, F.A.Rochinha, L.M.S.Alves Borges C.A.Vieira Carneiro, F.A.Rochinha, L.M.S.Alves Borges  The development of Functionally Grade Materials (FGMs) for energy-absorbing applications requires understanding of stress waves propagation in these structures in order to optimize their resistance to failure. The advantage of using these materials is that they are able to withstand high temperature gradient environments while maintaining their structural integrity with superior resistance to interfacial failure. In this present work, it presents a model to solve the coupled thermomechanical problem subjected to thermal solicitations. A staggered algorithm, which does not upset the unconditional stability property characteristic of fully implicit schemes, is employed. Numerical simulations are presented involving one-dimensional configurations with FGM materials subjected to thermal shocks. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 33-38 FGMの応力回復および動態分析 Stress Recovery and Dynamic Analysis of Functionally Graded Materials Rivania H.Paulino, Juan S. Romero and Fernando C.M.Menandro Rivania H.Paulino, Juan S. Romero and Fernando C.M.Menandro  A macroelement recovery technique for the strain field of a functionally graded material (FGM), based on the residual dynamic equilibrium equation for elasticity, is proposed. The derivatives are recovered by solving a local variational problem, using the superconvergence points. The basic idea is to utilize post-processing to achieve a more accurate approximation of the stresses while considering the dynamic nature of the problem. The development includes dynamic modeling of FGM and can be applied to direct and inverse problems. A numerical simulation is presented to better demonstrate the proposed methodology. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 39-44 ３次元分岐亀裂および高分子結晶に関するHp汎用有限要素法 Hp Generalized Finite Elements for Three-Dimensional Branched Cracks and Polycrystals  C.A.Duarte, L.G.Reno, A.Simone and E.Van der Giessen C.A.Duarte, L.G.Reno, A.Simone and E.Van der Giessen  Branched discontinuities appear in problems like crack propagation in brittle materials, stress corrosion cracks, high velocity impact and modeling of polycrystalline grains. The analysis of this class of problems using the classical finite element method (FEM) encounters several difficulties. The singularities at crack fronts and triple joints of polycrystalline grains require strongly refined finite element meshes that must fit the discontinuity surfaces while keeping the aspect ratio of the elements within acceptable bounds. These requirements are not always feasible, specially in three-dimensional simulations, or may require a large number of finite elements. The authors have recently proposed a generalized FEM(GFEM) able to model arbitrary polycrystalline structures [4] using only the grain topology and a background GFEM discrimination that can accommodate grain boundaries joints arbitrarily located in the mesh. This paper presents extensions of the generalized FEM presented in [4] that is able to handle arbitrary three-dimensional branched discontinuities and polycrystalline grains while delivering high convergence rates. In the GFEM presented in [4], the mesh can be refined independently of the discontinuity topology. This combined with the proposed high-order GFEM approximations, provides a very flexible and robust method that can deliver highly accurate solutions. Some of the capabilities of the method are demonstrated in the solution of three-dimensional branched cracks and in a study of the effect of grain morphology on anelasticity of polycrystals. A series of simulations are carried out on a wide range of grain morphologies in several arrangements of grains. Theoretical analysis and numerical experiments show that the method delivers optimal convergence rates. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 45-50 セラミック粒子強化金属マトリックス複合材の動的圧縮特性の数値シミュレーション Numerical Simulations of the Dynamic Compressive Properties of Ceramic Particle Reinforced Metal Matrix Composites. J.T.Zhang, L.S.Liu, P.C.Zhai, M.Zhang, Q.J.Zhang J.T.Zhang, L.S.Liu, P.C.Zhai, M.Zhang, Q.J.Zhang  A multi-particle 2D plane strain model was used to investigate the dynamic compressive properties of ceramic particle reinforced metal matrix composites (MMCs) in this paper. Ceramic particles were simulated as circles with different diameters, which were randomly and discretely embedded in the matrix. The constitutive relationship of ceramic material was characterized by Johnson-Holmquist (JH-2) damage model. The matrix was assumed to be power-law strain hardening material, coupled with power-law strain rate hardening. The ceramic/metal interface was assumed to be perfect. The predicted stress-strain curves by the numerical models agreed well with those of experiments and unit cell analysis formulae developed by Bao and Lin [3]. The effects of overall strain rates and ceramic volume fraction on the dynamic behavior of the composites had been investigated by this numerical model. The effect of particles' distribution on the particles' damage was also discussed. The results show that the distribution and volume fraction of the particles have obvious effect on the particles' damage. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 51-56 粒子ポリマー複合材FGMにおける動的混合モード亀裂成長 Dynamic Mixed-Mode Crack Growth in a Particulate Polymer Composite FGM M.S.Kirugulige, H.V.Tippur M.S.Kirugulige, H.V.Tippur  Functionally graded epoxy beams with monotonically varying volume fraction of reinforcement are subjected to mixed-mode loading by eccentric impact relative to the crack plane. The optical method of Coherent Gradient Sensing (CGS) along with high-speed photography is used to map transient crack tip deformations before and after crack initiation. Two configurations, one with crack on the stiff side and the second with crack on the compliant side, are examined experimentally. Differences in both pre- and post-crack initiation behaviors are reported in terms of initiation time, crack path, crack velocity and stress intensity factor histories. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 57-62 Face-Offsetting法を用いた形状記憶合金微細構造における固ー固相転移の模擬 Simulating Solid-Solid Phase Transition in Shape-Memory Alloy Microstructure by Face-Offsetting Method Ravi S.Bellur Ramaswamy, Eliot Fried, Xiangmin Jiao, Daniel A. Tortorelli Ravi S.Bellur Ramaswamy, Eliot Fried, Xiangmin Jiao, Daniel A. Tortorelli  Advances in the understanding of martensitic transformations (diffusionless, solid-solid phase transformations) have been instrumental to the recent discovery of new low hysteresis alloys. However, some key fundamental issues must be better understood to design still better alloys. Restricting attention to antiplane shear, we use finite element analysis to model the shape-memory alloy microstructure within the Abeyaratne-Knowles continuum thermomechanical framework and use an interface kinetic relation of the kind proposed by Rosakis and Tsai. Geometric singularities and topological changes associated with microstructural evolution pose significant numerical challenges. We address such challenges with a recently developed front-tracking scheme called the face-offsetting method (FOM) to explicitly model phase interfaces. Initial results demonstrate the effectiveness of FOM in resolving needle-like twinned microstructures. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 63-68 ZrO2多孔質傾斜機能防熱材の熱分析 Thermal Analysis of ZrO2 Porous Functionally Graded Thermal Protection Materials Qiwen Liu, Qiang Shen, Lianmeng Zhang Qiwen Liu, Qiang Shen, Lianmeng Zhang  The temperature field of two types of porous graded ZrO2 subjected to thermal shock loading is analyzed in this paper using the finite-element method. The numerical simulation results indicate that the structure of ZrO2 with an un-symmetric porous microstructure is superior to symmetric one and that, ignoring the influence of temperature dependent properties, the effects if thermo-mechanical coupling can be ignored if the imposed heat flux density is less than 4 WM/M**2. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 69-75 傾斜機能直交異方性材料特性の扁平殻のためのMLPG(Meshless Local Petrov-Galerkin)法 Meshless Local Petrov-Galerkin Method for Shallow Shells with Functionally Graded and Orthotropic Material Properties J.Sladek, V.Sladek, Ch.Zhang J.Sladek, V.Sladek, Ch.Zhang  A meshless local Petrov-Galerkin(MLPG) formulation is presented for analysis of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness. Shear deformation of shells described by the Reissner theory is considered. Analyses of shells under static and dynamic loads are given here. For transient elastodynamic case the Laplace-transform is used to eliminate the time dependence of the field variables. A weak formulation with a unit test function transforms the set of the governing equations into local integral equations on local subdomains in the plane domain of the shell. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 76-81 傾斜機能固体電解質型燃料電池における亀裂成長のシミュレーション Simulation of Crack Growth in Functionally Graded Solid Oxide Fuel Cells under Thermal Loads Jeong-Ho Kim Jeong-Ho Kim  This paper addresses finite element simulation of mixed-mode crack growth in functionally graded solid oxide fuel cells under steady-state thermal loads. The crack growth simulation is performed by means of a re-meshing algorithm in conjunction with the finite element method. In each step of simulation, stress intensity factors are calculated using interaction integrals, and are utilized for the determination of the crack growth direction. A fracture criterion is tailored for FGMs using the local homogenization of asymptotic crack-tip fields in FGMs. Crack trajectories and mixed-mode stress intensity factors (SIFs) obtained by the numerical simulation are presented. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 82-87 金属－セラミックFGMのための弾性ー塑性モデルのキャリブレーション On the calibration of elastic-plastic models for metal-ceramic functionally graded materials Massimiliano Bocciarelli, Gabriella Bolzon, Giulio Maier Massimiliano Bocciarelli, Gabriella Bolzon, Giulio Maier  The mechanics performances of industrial components for advanced engineering applications can be greatly enhanced by a coating with ad-hoc designed metal-ceramic functionally graded materials (FGMs). The continuously varying properties of FGMs can be related to the spatial distribution of their components by a modified rule of mixture; their mechanical behavior is here described by an elastic-plastic model, in which the volume fraction of the material components governs the transition from Huber-Mises theory, typical of the metallic phase, toward a Drucker-Prager constitutive model more suitable to describe the behavior of ceramics. The present communication presents an inverse analysis procedure for the calibration of parameters involved in such elastic-plastic model. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 88-93 傾斜機能圧電変換器の数値設計および解析的設計 Numerical and Analytical Design of Functionally Graded piezoelectric Transducers Wilfredo Montealegre, Rubio, Flavio Buiochi, Julio C Adamowski, Emilio Carlos Nelli Silva Wilfredo Montealegre, Rubio, Flavio Buiochi, Julio C Adamowski, Emilio Carlos Nelli Silva  This paper presents analytical and finite element methods to model broadband transducers with a graded piezoelectric parameter. The application of FGM concept to piezoelectric transducer design allows the design of composite transducers without interface between materials (e.g. piezoelectric ceramic and backing material), due to the continuous change of property values. Thus, large improvements can be achieved in their performance characteristics, mainly generating short-time waveform ultrasonic pulses. Nevertheless, recent research on functionally graded piezoelectric transducers shows lack of studies that compare numerical models of FGM piezoelectric material gradation, specially, in ultrasonic applications. In addition, results using FGM piezoelectric transducers are compared with non-FGM piezoelectric transducers. We concluded that the developed modeling techniques are accurate, providing a useful tool for designing FGM piezoelectric transducers. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 94-99 相互作用積分を用いたFGMの熱応力拡大係数の評価 Evaluation of Thermal Stress Intensity Factors in Functionally Graded Materials by means of Interaction Integrals Jeong-Ho Kim, Amit KC Jeong-Ho Kim, Amit KC  Interaction integrals are developed to evaluate mixed-mode stress intensity factors in functionally graded materials under steady-state thermal loading. A non-equilibrium formulation is developed in an equivalent domain integral from that is naturally suitable to the finite element method. Graded material properties are integrated into the element stiffness matrix using the direct Gaussian formulation. The type of material gradation considered includes continuum functions, e.g. an exponential function. This study presents a few thermal fracture problems and assesses the accuracy of the present method compared with available semi-analytical and/or numerical solutions. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 100-105 様々な熱条件下でのマルチスケール解析方式による破壊挙動シミュレーション Fracture behavior simulation using multi-scale analysis scheme under various thermal conditions Juwhan Kim, Yun Mook Lim, Kunwhi Kim Juwhan Kim, Yun Mook Lim, Kunwhi Kim  A series of fracture simulations are performed and presented. A two dimensional configuration with a notch is assembled via the popular Lennard-Jones (LJ) potential, and the configuration is subjected to displacement controlled tension tests. Five sets of analyses are performed at different temperatures, where the specimens share the same initial geometry and particle number and strain rate is fixed at the same value. Results show qualitatively that a heightened temperature may induce relation of crack propagation, and consequently an increase in material toughness. Peak stress response is shown to increase with ambient temperature, and the trend coincides with what is commonly observed in actual toughness tests. What is also shown is local heating around crack tips. The local temperature variance is observed to concentrate behind the crack tip, i.e., deferred heat transfer. The localized heating appears more pronounced in the lower ambient temperature cases, while the effect becomes less susceptible in the higher ambient temperature cases. The phenomenon may be related to higher mobiles states of particles induced by increased internal energy. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 106-114 セラミック／金属傾斜装甲への通常弾道衝撃の1次元解析モデル One dimension analytical model of normal ballistic impact on ceramic/metal gradient armor Lisheng Liu, Qingjie Zhang, Pengcheng Zhai,Dongfeng Cao Lisheng Liu, Qingjie Zhang, Pengcheng Zhai,Dongfeng Cao  An analytical model of normal ballistic impact on the ceramic/metal gradient armor, which is based on modified Alekseevskii-Tate equations, has been developed. The process of gradient armor impacted by the long rod can be divided into four stages in this model. First stage is projectile's mass erosion or flowing phase, mushrooming phase and rigid phase; second one is the formation of comminuted ceramic canoed; third one is the penetration of gradient layer and last one is the penetration of metal back-up plate. The equations of third stage have been advanced by assuming the behavior of gradient layer as rigid-plastic and considering the effect of strain rate on the dynamic yield strength. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 115-120 3次元FGMの応力拡大係数の数値解析 Numerical Analysis of Stress Intensity Factore in Three-Dimensional Functionally Graded Materials Li-Cheng Guo, Linzhi Wu, Hongjun Yu Li-Cheng Guo, Linzhi Wu, Hongjun Yu  In this paper, a finite element method based on nonhomogeneous elements is used to study crack problems in three-dimensional (3D) functionally graded materials (FGMs). Since the actual material properties at each integral point are employed in the integration during formation of the element stiffness matrix, each element can have nonhomogeneous material properties. By this method, the number of elements is reduced and the meshing effort for the structure is simplified. Therefore, the modeling process for numerical simulation of fracture behavior in 3D FGMs is greatly simplified. The crack front characteristics of Mode-I edge penetrable crack in 3D FGM specimens are studied under uniform tension loading. The influence of material nonhomogeneity constant and geometric parameters on the stress intensity factors (SIFs) of the 3D FGM specimens are investigated. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 121-128 セラミック／金属傾斜装甲の構成部品の特性の衝撃耐性特性への影響 The effect of ceramic/metal gradient armor's components characteristic on its impact-resistant characteristic Lisheng Liu, Qingjie Zhang, Pengcheng Zhai, Dongfeng Cao Lisheng Liu, Qingjie Zhang, Pengcheng Zhai, Dongfeng Cao  The effect of ceramic/metal gradient armor's components characteristic on its impact-resistant characteristic has been investigated by a new modified Alekseevskii-Tate equation. The following researching work is done by the former model[1]; the effect of ceramic layer on the impact-resistant characteristic, the effect of gradient layer on the impact-resistant characteristic and the effect of metal layer on the impact-resistant characteristic. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 129-134 FGMの熱弾塑性応力についての解析モデル Analytical Model for Thermal Elastoplastic Stress of Functionally Graded Materials P.C.Zhai, G.Chen, L.S.Liu, C.Fang, Q.J.Zhang P.C.Zhai, G.Chen, L.S.Liu, C.Fang, Q.J.Zhang  A modification analytical model is presented for the thermal elastoplastic stress of functionally graded materials subjected to thermal loading. The presented model follows the analytical scheme presented by Y.L.Shen and S.Suresh. In the present model, the functionally graded materials are considered as multilayered materials. Each layer consists of metal and ceramic with different volume fraction. The ceramic layer and the FGM interlayers are considered as elastic brittle materials. The metal layer is considered as elastic-perfectly plastic ductile materials. Closed-form solutions for different characteristic temperature for thermal loading are presented as a function of the structure geometries and the thermomechanical properties of the materials. A main advance of the present model is that the possibility of the initial and spread of plasticity from the two sides of the ductile layers taken into account. Comparing the analytical results with the results from the finite element analysis, the thermal stresses and deformation from the present model are in good agreement with the numerical ones. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 135-140 界面と交差した表面亀裂をもつ機能傾斜二層ストリップの破壊解析 Fracture Analysis of a Functionally Graded Two-Layer Strip with a Surface Crack Intersecting the Interface Li-Cheng Guo, Naotake Noda Li-Cheng Guo, Naotake Noda  The crack problem for a functionally graded two-layer strip under an in-plane load is investigated. The functionally graded layer is assumed to contain a surface crack intersecting the interface. An auxiliary function related to two layers is used. By using integral transform methods, the singular integral equation is obtained. The parameter influences on the stress intensity factors (SIFs) are studied. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 141-146 異粒子形状微粒子複合材の効果的な熱伝導性 Effective Thermal Conductivity of Particulate Composites with Different Particle Configurations M.Zhang, P.C.Zhai, Y.Li, J.T.Zhang, Q.J.Zhang M.Zhang, P.C.Zhai, Y.Li, J.T.Zhang, Q.J.Zhang  A new micromechanical method, called the Weighted Residual Self-Consistent Scheme (WRSCS), is developed to study the effective thermal conductivity of particulate composites. WRSCS provides us with a new approach to the approximation of effective thermal conductivity of particulate composites with arbitrary phase geometry based on the thermal conduction theory of two-phase materials within the framework of SCS. FE analyses of a generalized multi-inclusion model and GSCS model are also carried out in the prediction of the effective thermal conductivity at different inclusion volume fractions. Results show that the effective thermal conductivity depends not only on the properties and volume fractions of its constituents, but also on the geometric shape of the particulate. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 147-152 厚壁FGMパイプの弾塑性応力解析 Elasto-plastic stress analysis of thick-walled FGM pipes Fabio Figueiredo, Lavinia Borges, Fernando Rochina Fabio Figueiredo, Lavinia Borges, Fernando Rochina  The paper is concerned with quasi-static deformation process of elastic-plastic FGM structures. It is assumed that the structures undergo small strain and the material properties of the graded layer are modeled by the modified rule of mixtures approximation. The elastic domain for ductile phases is defined through the Von Mises yield criterion. The mathematical problem consists of a variational equation that represents the equilibrium of the body and a variational inequality expressing the plastic strain rate evolution. An iterative method for solving this nonlinear system, combining a finite element approximation and an incremental-iterative of tubes with abrupt transition to different configurations obtained using smooth transitions containing FGM layers between the two dissimilar materials are provided. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 153-158 傾斜機能材料の確率論的破壊解析ーPart 1:不確実性および確率論的解析法 Probabilisic Fracture Analysis of Functionally Graded Materials-Part I: Uncertainty and Probabilistic Analysis Method Junho Song, Tam H.Nguyen, Glaucio H.Paulino Junho Song, Tam H.Nguyen, Glaucio H.Paulino  The uncertainties in material properties including Young's modulus and fracture toughness are considered. The limit state function for a crack initiation event is defined in terms of the J-integral for FGMs. The First-Order-Reliability-Method (FORM) is used in conjunction with a finite element code that computes the J-integral with high accuracy. A two-step probabilistic analysis procedure is proposed to investigate the effects of the uncertainties in the spatial distribution of Young's modulus on the probability of crack initiation in FGMs. First, we investigate the effects of the uncertainties in the shape of the spatial distribution by considering the slope and the location of the inflection point of a spatial distribution profile as random quantities. Second, we investigate the effects of the spatial fluctuations of Young's modulus by making use of a discredited random field. The companion paper (Part II) implements this method into a finite element fracture analysis code and presents numerical examples. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 159-164 傾斜機能材料の確率論的破壊解析ーPart II:実行および数値例 Probabilistic Fracture Analysis of Functionally Graded Materials - Part II : Implementation and Numerical Examples Tam H.Nguyen, Junho Song, Glaucio H.Paulino Tam H.Nguyen, Junho Song, Glaucio H.Paulino  Probabilistic fracture analysis are performed for investigating uncertain fracture response of Functionally Graded Material (FGM) structures. The First-Order-Reliability-Method (FORM) is implemented into an existing Finite Element code for FGM (FE-FGM), which was previously developed at the University of Illinois at Urbana-Champaign. The computational simulation will be used in order to estimate the probability of crack initiation with uncertainties in the material properties only. The two-step probability analysis method proposed in the companion paper (Part I) is illustrated by a numerical example of a composite strip with an edge crack. First, the reliability index of a crack initiation event is estimated as we vary the mean and standard deviation of the slope and the location of the inflection point of the spatial profile of Young's modules. Secondly, the reliability index is estimated as we vary the standard deviation and the correlation length of the random field that characterize the random spatial fluctuation of Young's modulus. Also investigated is the relative importance of the uncertainties in the toughness compared to those in Young's modulus. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 165-170 プレストレスコンポジットメディア内の局所リカバリーのためのHi-Fi漸近理論 A Hi Fidelity Asymptotic Theory For Local Field Recovery Inside Pre-Stressed Composite Media Timothy Breitzman, Robert Lipton and Endel Iarve Timothy Breitzman, Robert Lipton and Endel Iarve  We introduce a new mathematically rigorous high fidelity asymptotic theory for recovering the local field behavior inside complex composite architectures. The theory applies to zones containing strong spatial variance of local material properties. The method is used to recover the local field across ply interfaces for a pre-stressed multi-ply fiber reinforced composite. The results are shown to be in good agreement with direct numerical simulations for realistic fiber sizes and fiber-matrix elastic properties. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 171-177 マルチスケールシミュレーションにおけるモデル間の遷移：傾斜材料および粒状材料 Transition between the models in multiscale simulations: Continua and granular materials Sinisa Dj. Mesarovic, Jaganmohan Padbidri Sinisa Dj. Mesarovic, Jaganmohan Padbidri  We consider two-scale problems: the fine-scale and the coarse-scale. The coarse model is taken to be a continuum. The key question in this class of problems is related to the simulation of the fine-scale cell: How are the coarse-scale fields to be passed onto the fine scale? Often used periodic boundary conditions, have important drawbacks. The mathematical conditions that answer this question are called minimal boundary conditions (MBC). MBC are imposed on a fine-scale computational cell as a constraint derived from the coarse-scale model. They are minimal in the sense that nothing but the desired constraint is imposed-in contrast to periodic boundary conditions. Owing to their integral nature, the MBC can be applied to any shape of the fine-scale computational cell. The application to fine-scale continuum models has been discussed earlier, Mesarovic and Padnidri. In this paper, we discuss application of MBC to fine-scale discrete models with local interactions-granular materials. The key to this application is the equivalent representation of kinematics of granular flow using the Delaunay network. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 178-183 効果的な特性の効果性について Are Effective Properties Effective? Ru Han, Marc S. Ingber, Shin-Chun Hsiao Ru Han, Marc S. Ingber, Shin-Chun Hsiao  The effective module (effective Young's modulus, effective Poisson's ratio, effective shear modulus, and effective bulk modulus) of dispersed-phase-reinforced composite materials are determined at the mesoscopic level using three-dimensional parallel boundary element simulations. By comparing the mesoscopic BEM results and the macroscopic results based on effective properties, limitations in the effective property approach have been examined. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 184-189 中心亀裂を有する有限周期的多層の微細構造の影響 Microstructural Effects in Finite Periodic Multilayers with a Centred Crack Linfeng Chen, Marek-Jerzy Pindera Linfeng Chen, Marek-Jerzy Pindera  The effect of microstructural refinement of a multilayer comprised of periodically alternating hard and soft layer pairs on the stress intensity factors and crack-opening displacements of a single centered crack within the layered structure is studied using an exact elasticity solution. The results indicate that the crack-opening displacements converge to the corresponding ones in the fully homogenized configuration with increasing microstructural refinement. In contrast, the stress intensity factors asymptotically converge to values that depend on the layer stiffness. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 190-195 傾斜機能材料の微細構造のランダム性の分析に用いられる微小機構的方法の概観 An Overview of Micromechanics-Based Techniques for the Analysis of Microstructural Randomness in Functionally Graded Materials Fernando J.Ferrante, Lori L, Graham Brady, Katherine Acton, and Sanjay R. Arwade Fernando J.Ferrante, Lori L, Graham Brady, Katherine Acton, and Sanjay R. Arwade  A review of current research efforts to develop micromechanics-based techniques for the study of microstructural randomness of functionally graded materials is presented, along with a framework developed by the authors of this paper that includes stochastic simulation of statistically inhomogeneous samples and a windowing technique coupled with a micromechanical homogenization technique. The methodology is illustrated through the analysis of one sample coupled with finite element modeling. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 196-202 高密度粒子複合材の脱濡れ損傷のマルチスケールモデリング Multiscale Modeling of Dewetting Damage in Highly Filled Particulate Composites P.H.Geubelle, H.M.Inglis, J.D.Kramer, J.J.Patel, N.C.Kumar, H.Tan P.H.Geubelle, H.M.Inglis, J.D.Kramer, J.J.Patel, N.C.Kumar, H.Tan  Particle debonding or dewetting constitutes one of the key damage processes in highly filled particulate composites such as solid propellant and other energetic materials. To analyze this failure process, we have developed a multiscale finite element framework that combines, at the microscale, a nonlinear description of the binder response with a cohesive model of the damage process taking place in a representative periodic unit cell (PUC). To relate micro-scale damage to the macroscopic constitutive response of the material, we employ the mathematical theory of homogenization (MTH). After a description of the numerical scheme, we present the results of the damage response of a highly filled particulate composite subjected to a uniaxial macroscopic strain, and show the direct correlation between the complex damage processes taking place in the PUC and the nonlinear macroscopic constitutive response. We also present a detailed study of the PUC size and a comparison between the finite element MTH-based study and a micromechanics model of the dewetting process. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 203-208 周期的に不均一な材料を局所的に正確に均質化する方法 A Locally-Exact Homogenization Approach for Periodic Heterogeneous Materials Anthony S. Drago, Marek-Jerzy Pindera Anthony S. Drago, Marek-Jerzy Pindera  Elements of the homogenization theory are utilized to develop a new micromechanics approach for unit cells of periodic heterogeneous materials based on locally-exact elasticity solutions. Closed-form expressions for the homogenized moduli of unidirectionally-reinforced heterogeneous materials are obtained in terms of Hill's strain concentration matrices valid under arbitrary combined loading, which yield the homogenized Hook's law. Results for simple unit cells with off-set fibers, which require the use of periodic boundary conditions, are compared with corresponding finite-element results demonstrating excellent correlation. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 209-215 弾性マンモグラフィー：乳房組織における弾性特性の復元 Elasto-Mammography: Elastic Property Reconstruction in Breast Tissues Z.G.Wang, Y.Liu, G.Wang, L.Z.Sun Z.G.Wang, Y.Liu, G.Wang, L.Z.Sun  Mammography is the primary method for screening and detecting breast cancers. However, it frequently fails to detect small tumors and is not quite specific in terms of tumor benignity and malignancy. The objective of this paper is to develop a new imaging modality called elasto-mammography that generates the modulus elastograms based on conventional mammographys. A new elastic reconstruction method is described based on elastography and mammography for breast tissues. Elastic distribution can be reconstructed through the measurement of displacement provided by mammographic projection. It is shown that the proposed elasto-mammography provides higher sensitivity and specificity than the conventional mammography in its own for breast cancer diagnosis. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 216-221 傾斜機能複合材料の損傷開始と成長の計算微小機構 Computational Micromechanics of Damage Initiation and Growth in Functionally Graded Composites Leon Mishnaevsky Jr., Dietmar Gross Leon Mishnaevsky Jr., Dietmar Gross  The purpose of this work is to investigate the effect of microstructures of functionally graded particle reinforced composites on the strength and damage resistance in the materials. In order to study the microstructure-strength and microstructure-damage resistance relationships of graded composites with metal matrix and ceramic inclusions, a series of numerical mesomechanical experiments has been carried out. The tensile stress-strain curves, fraction of failed particles versus applied strain curves, and stress and damage distributions at different stages of loading were determined for different generic graded microstructures and compared. It was shown that the flow stress and stiffness of composites increase and failure strain decreases with decreasing property gradient. The damage growth in particles in graded composites initiates within particles, which are located in the transition zone between the zone of high particle density and the particle-free regions. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 222-229 n-層FGMシリンダーとしての光学ファイバーの解決法および応用 Solutions for Optical Fibers as n-plies FGM Cylinders and Applications Massimiliano Fraldi, Luciano Nunziante Massimiliano Fraldi, Luciano Nunziante  In the framework of heterogeneous materials, the purpose of the present work is to furnish a general approach to the construction of exact elastic solutions for FGM cylinders made of a central core and n arbitrary cylindrical hollow homogeneous and isotropic phases. The hypothesis of axi-symmetric boundary conditions is here assumed in order to analyze a class of elastic problems characterized by non-decaying selected mechanical quantities, and in particular the axial strains epsilon33 in the radial direction, with chi3 being the axis of the laminated cylinder. Example applications are finally illustrated, with reference to the problem of interpreting strain measurements obtained by using optical fiber sensors. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 230-235 傾斜機能複合材の効果的な弾性：粒子相互作用をもつマイクロ工学構造 Effective Elasticity of Functionally Graded Composites: A Micromechanics Framework with Particle Interactions H.M.Yin, G.H.Paulino, L.Z.Sun H.M.Yin, G.H.Paulino, L.Z.Sun  The present paper aims to develop a micromechanics-based effective elastic model of functionally graded composites. At the macroscopic scale, effective material properties of the composites are uniform in the same graded layer while gradually changing along the grading direction. Microstructurally, infinite particles are randomly dispersed in the matrix with gradual transitions. Particles are assumed to be spherical and nonintersecting. They are perfectly bonded with the matrix. A micromechanical framework is proposed to investigate effective mechanical properties along the grading direction. Within the context of the representative volume element (RVE), the effect of pair-wise interactions between particles is taken into account for the local stress and strain fields by using the modified Green's function method. Homogenization of the local field renders relations between the averaged strain, strain gradient and external loading. The effective elastic modulus tensor of the functionally graded composites is further constructed by numerical integration. The model prediction is compared with available experimental data. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 236-241 傾斜機能材料のためのパラメーター有限体積理論 Parametric Finite-Volume Theory for Functionally Graded Materials Marcio.A.A. Cavalcante, Severino P.C. Marques, M-J Pindera Marcio.A.A. Cavalcante, Severino P.C. Marques, M-J Pindera  A parametric formulation of the finite-volume theory for functionally graded materials is presented based on a mapping of a square reference subcell onto a quadrilateral subcell in the actual discredited microstructure. This formulation significantly advances the capability and utility of the theory, enabling modeling of curved boundaries of functionally graded structural components, as well as inclusions employed for grading purposes, without the disadvantage of stress concentrations at the corners of rectangular subcells used in the standard version. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 242-247 局在的な傾斜構造を有する複数の含有物の単位胞のFVDAM（Finite-Volume Direct Averaging Micromechanics）解析 FVDAM Analysis of Multi-Inclusion Unit Cells with Locally Graded Architectures Yogesh Bansal and Marek-Jerzy Pindera Yogesh Bansal and Marek-Jerzy Pindera  The extensive and unique modeling capability of the Finite-Volume Direct Averaging Micromechanics (FVDAM) model is employed to investigate the response of macroscopically periodic heterogeneous materials with locally graded architectures. Both spatially and dimensionally graded unit cells reinforced by stiff fibers and weakened by porosities are examined and their response compared with regular square and hexagonal arrays in the elastic and plastic regions. English MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) MULTISCALE AND FUNCTIONALLY GRADED MATERIALS(FGM IX 2006) 30 2006-10-18 248-253 混合モデル負荷下の傾斜機能材料における亀裂開始角度 Crack Initiation Angles in Functionally Graded Materials under Mixed Model Loading Alpay Oral, Jorge L. Abanto-Bueno, John Lambros, Gunay Anlas Alpay Oral, Jorge L. Abanto-Bueno, John Lambros, Gunay Anlas  In this study, quasi-static crack initiation under mixed mode loading in planar (2-D) functionally graded materials is presented. First, crack initiation in the homogeneous material which forms the basis of our FGM -polyethylene- is studied. The Generalized Maximum Tangential Stress Criterion (GMTS) is applied through use of finite elements to determine crack initiation angles in a cracked 2-D functionally graded material. The effects of crack length, T-stress, inherent length scale rc and mode fixity are discussed. Computational results of crack initiation angles are compared to experimental results obtained using functionally graded polyethylene. Stress Intensity factors for a center cracked FGM are calculated. English