具有中等组分不同网状结构功能梯度构件的三维动力特性分析

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂,因此其构件动力分析很难求得其解析解。该文建议一种新颖的功能梯度构件动力分析的细观元法。细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观结构之间的定量关系,它可揭示不同的材料组合具有不同的宏观性能的内在机制。此法可实现材料细观结构到构件宏观响应的直接过渡分析,而计算单元与自由度又等同一般常规有限元,却使得组成功能梯度材料构件的各种材料细观构造得到反映。通过细观元技术,对具有中等组分不同网状结构功能梯度构件进行三维动力特性分析,并给出其三维固有频率及振型的三维分布,特别是给出了不同网格结构功能梯度板件应力振型的平面等值线图差异。结果表明:不同细观网格结构对功能梯度材料结构三维动力响应有较明显影响。     

沿板平面变异功能梯度板件的三维动力特性

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂,因此其构件动力分析很难求得其解析解。文中建议一种新颖的功能梯度构件动力分析的细观元法。细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观结构之间的定量关系,它可揭示不同的材料组合具有不同的宏观性能的内在机制。目前功能梯度板件分析只能处理材料特性沿厚度方向梯度变化,而细观元法则直接从制备时给定的材料组分分布出发计算构件宏观三维动力特性,并给出了沿板平面方向材料特性梯度变化的功能梯度板件三维固有频率及振型的三维分布。     

复杂形状功能梯度板件的三维动力特性分析

从细观力学角度出发根据材料细观组分分布对具有不同复杂形状功能梯度材料构件进行三维动力特性分析,并相应给出其三维固有频率及其基频对应的位移振型和应力振型沿厚度方向的三维分布。结果发现对同样材料细观组分分布的不同功能梯度结构,其固有频率和相应的振型分布均有很大差异。此结果为建立专门的功能梯度板壳理论提供定量的资料依据。     

梯度功能材料的研究与展望

梯度功能材料是基于一种全新的材料设计概念合成的新型复合材料，本文叙述了梯度功能材料的概念和开发背景，着重介绍了梯度功能材料的研究内容和现状以及在航天、核能、电子、光学、生物医学等领域的应用前景，并展望了这种新材料今后的研究动向。     

梯度功能材料的研究

梯度功能材料是五年前由日本科学家提出的新概念和新思想,其两侧由不同性能的材料组成,以对付苛刻的使用环境;而中间部分的组成和结构又是连续变化的,使其内部界面消失,以减小和克服结合部位的性能不匹配因素。这类材料在航天事业和核工业中有看广阔的应用前景和极高的使用价值。本文着重介绍了梯度功能材料的设计思想、目前的研究现状、以及我们在这方面做的一些工作。并综述和比较了各类制备工艺技术。     

空隙、杂质及组分突变对功能梯度构件动力特性的影响

功能梯度材料具有复杂的细部结构, 其内部构造远比匀质材料复杂, 因此其构件动力分析很难求得其解析解。本文中提出了一种新颖的功能梯度构件动力分析的细观元法, 其目的在于建立材料的宏观性能与其组分材料性能及细观构造之间的定量关系, 以便揭示不同的材料组合及其变异所具有不同的宏观性能的内在机制。利用细观元法对含有空隙、 杂质及组分突变等情况下的功能梯度构件进行动力分析, 求得其三维固有频率及振型的三维分布。从而可知空隙、 杂质及组分突变均对功能梯度材料构件的宏观动力特性有很大的影响。      

梯度功能材料

梯度功能材料是一种新型的复合材料,其特点是界面的成分和组织连续变化,使材料的热应力大为缓和。本文叙述了梯度功能材料的进展以及在航天、核能源、生物医学工程、电子工程等领域的应用和制备方法。     

由材料组分直接计算功能梯度复合材料开孔板宏观响应的跨尺度分析

建议一种新颖的功能梯度构件分析的细观元法, 给出了方法模型、基本算式及特点与功能。细观元法对构件的常规有限单元内部设置密集细观单元以反映材料组分梯度变化, 又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度, 再上机计算。此法可实现材料细观结构到构件宏观响应的直接过渡分析, 而计算单元与自由度又等同于常规有限元, 为解决功能梯度构件宏观、细观跨尺度分析提供了一种有效工具。本文中直接从制备时给定材料组分分布出发计算构件宏观响应, 给出了不同开孔形状与数量功能梯度板的力学量三维分布形态。      

功能梯度材料

介绍了功能梯度材料的提出，开发流程，研究现状，对于当前功能梯度材料的设计过程，制备方法，性能评价方法和实验手段进行了详细叙述，提出了功能梯度材料应进一步发展的方向。     

功能梯度材料最近的研究进展

本文综述了功能梯度材料最近的研究进展，包括这种材料的理论研究重点，制造工艺以及它的潜在应用。     

Modeling of functionally graded materials in dynamic analyses

In this investigation, functionally graded material is modeled in several different ways. Five models are presented, two of which simulate fiber phases and three simulate particle phases. For fibers, there is a model in which the detailed micro-structure is simulated and one in which the material is represented by layers such that the volume fraction of the fibers in each layer changes. For the particles, a model with layers is employed and two models with continuously changing material parameters are presented. Four different dynamic input loads are applied to the detailed micro-structure to examine its effect. The finite element method is employed to determine the effective stress.Then one of the dynamic loads which simulates a step function is applied to all models. It is observed that there are no significant differences in the effective stresses at particular points within the time domain. The amplitude of the wave for each model is quite similar. The phase of the wave shifts as time increases. Thus, in the space domain, differences are observed in the effective stress at a particular time. As may be expected, the stresses are rather high within the fibers in the detailed micro-structural model. It is concluded that a continuously changing material model is a good candidate for carrying out dynamic analyses of functionally graded material.     

基于正弦剪切变形理论的功能梯度材料三明治微梁的静动态特性

基于修正的偶应力理论和正弦剪切变形梁理论,研究了功能梯度材料三明治微梁的静态弯曲和自由振动行为。考虑两种不同类型的功能梯度材料三明治微梁,根据哈密顿变分原理建立其静动态力学行为的控制方程,应用Navier解法,得到了简支边界条件下弯曲变形和振动频率的解析解,同时,给出了固支等边界条件时的里兹法求解过程。数值算例表明,功能梯度三明治微梁的静动态力学行为具有明显的尺度效应,微梁的无量纲厚度、功能梯度指数、长厚比和结构形式等因素对其静动态响应有很大影响,相关结果和规律对功能梯度材料三明治微梁的结构设计和性能优化等实际工程应用具有一定的指导意义。      

Thermo-elasticity in shell structures made of functionally graded materials

An efficient low-order finite shell element is derived for the thermo-elastic analysis of shell structures made of functionally graded materials or multilayer composites. It is based on a one-way coupling between the thermal and the mechanical analysis. The thermal quantities are evaluated using a new iterative scheme that properly accounts for convection boundary conditions and large gradients of the thermal conductivity. The resulting non-constant temperature field with respect to the thickness direction gives nodal forces and couples, which are applied on a shear weak six-parameter shell formulation. Here, drill rotations are included, supplemented with a proper method for calculating effective elastic properties. Numerical results indicate theefficiency and accuracy of the proposed approach.     

Determination of dynamic effective properties in functionally graded materials

Summary This work is dedicated to the investigation of the dynamic effective properties in functionally graded materials resulting from an anti-plane shear wave. A micromechanics-based elastodynamic model is developed to predict the dynamic behavior of two-phase functionally graded materials, and the distribution of dynamic effective properties in the gradation direction is presented. Generally speaking, in functionally graded materials there exist two microstructurally distinct zones: a fiber-matrix zone and a transition zone. In the fiber-matrix zone, the dispersion relation for the effective wave number is derived using the effective medium method, and the dynamic effective properties for any macroscopic material points are determined in the corresponding microstructural representative volume element (RVE). In the transition zone, a transition function is introduced to make the wave fields continuous and differentiable. Numerical examples of the dynamic effective properties in the gradation direction under different parameters are presented graphically. The obtained results reveal that the distribution of dynamic effective properties in the gradation direction is dependent on the material properties of each phase, the incident frequency, and the gradation parameter of the materials. Comparisons between numerical solutions and experimental data are also made. At last, the results are discussed in detail.     

Cohesive modeling of dynamic fracture in functionally graded materials

The dynamic fracture of functionally graded materials (FGMs) is modeled using an explicit cohesive volumetric finite element scheme that incorporates spatially varying constitutive and failure properties. The cohesive element response is described by a rate-independent bilinear cohesive failure model between the cohesive traction acting along the cohesive zone and the associated crack opening displacement. A detailed convergence analysis is conducted to quantify the effect of the material gradient on the ability of the numerical scheme to capture elastodynamic wave propagation. To validate the numerical scheme, we simulate dynamic fracture experiments performed on model FGM compact tension specimens made of a polyester resin with varying amounts of plasticizer. The cohesive finite element scheme is then used in a parametric study of mode I dynamic failure of a Ti/TiB FGM, with special emphasis on the effect of the material gradient on the initiation, propagation and arrest of the crack.     

On the dynamic energy release rate in functionally graded materials

By using the effective shear modulus and mass density, the influence of functional gradient on dynamic energy release rate is discussed under the condition of constant velocity of crack propagation.     

Transient thermo-mechanical analysis of dynamic curving cracks in functionally graded materials

Mixed-mode dynamic crack growth behavior along an arbitrarily smoothly varying path in functionally graded materials (FGMs) under transient thermo-mechanical loading is studied. An asymptotic analysis in conjunction with displacement potentials is used to develop transient thermo-mechanical stress fields around the propagating crack-tip. Asymptotic temperature field equations are derived for exponentially varying thermal properties, and later, these equations are used to derive transient thermo-mechanical stress fields for a curving crack in FGMs. The effect of the transient parameters (loading rate, crack-tip acceleration, and temperature change) and temperature gradient on the maximum principal stress and circumferential stress associated with the propagating crack-tip is discussed. Finally, using the minimum strain energy density criterion, the effect of temperature gradient, crack-tip speeds, and T-stress on crack growth directions is determined and discussed.     

Uncertainty quantification in non-linear dynamic response of functionally graded materials plate

This study deals with the stochastic non-linear dynamic response of functionally graded materials (FGMs) plate with uncertain system properties subjected to time-dependent uniformly distributed transverse load in thermal environments. System properties, such as material properties of each constituent's material, volume fraction index, and transverse load, are taken as uncorrelated random input variables. Material properties are assumed as temperature dependent (TD). The formulation is based on higher-order shear deformation theory (HSDT) with von-Karman non-linear strain kinematics using modified C° continuity. A Newton–Raphson-based non-linear finite element method along with a first-order perturbation technique (FOPT) and Monte Carlo sampling (MCS) is outlined to examine the second-order statistics (mean, standard deviation (SD), and probability density function (PDF)) of the non-linear dynamic response of the FGM plate. The governing dynamic equation is solved by Newmark's time integration scheme. The effects of volume fraction index, load parameters, plate thickness ratios, and temperature changes with random system properties are examined through parametric studies. The present outlined approach is validated with the results available in the literature and by MCS.     

Higher-order theory for functionally graded materials

This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.     

Characterisation methods for functionally graded materials

In this paper the characterisation of functionally graded materials is elucidated by several different methods. These methods described here are used for the quantitative analysis of materials with a local dependence of microstructure parameters. Using X-ray microscopy (computed tomography) for 3D-measurements and optical microscopy on polished sections for 1D and 2D measurements on the same sample, a ceramic filter consisting of sintered spherical particles, various mathematical evaluation methods are described and compared.