Al2O3—Ti系梯度功能材料残余热应力有限元分析

采用有限元方法对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线弹性分析，详细讨论了梯底层数目，梯度层厚度和成分梯度指数对应务大小和分布的影响，确定了各项最佳参数。非梯度功能材料与优化后的梯度功能材料的残余热应务对比结果显示；梯度功能材料缓和热应力的效果十分显著。     

Al_2O_3-Ti系梯度功能材料残余热应力的有限元分析

采用有限元方法（ＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄ）对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线弹性分析。详细讨论了梯度层数目、梯度层厚度和成分梯度指数对应力大小和分布的影响，确定了各项最佳参数。非梯度功能材料（ＮＦＧＭ）与优化后的梯度功能材料的残余热应力对比结果显示：梯度功能材料缓和热应力的效果十分显著。     

环氧树脂/聚氨酯梯度材料的残余热应力分析

采用有限元方(Finite Element Method)对环氧树脂/聚氨酯(EP/PU)梯度材料在制备过程中产生的残余热应力进行了分析.详细讨论了梯度层数目对应力大小的影响.研究结果表明:当体系中EP和PU组成相同时,梯度材料缓和热应力的效果比双层材料显著.且梯度材料的热应力缓和效果随梯度层数增加而增加.     

Al3O—Ti系梯度功能材料残余热应力的有限元分析

采用有限元方法对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线 性性分析。详细讨论了梯度层数目、梯度层厚度和成分梯度指数对应力大小和分布的影响，确定了各项最佳参数。非梯度功能材料与优化后的梯度功能材料的残余热絷力对此结果显示：梯度功能赫兹 热应力的效果十分显著。     

Y-TZP/LZAS微晶玻璃功能梯度涂层残余应力的有限元分析

设计了Y-TZP/LZAS微晶玻璃功能梯度涂层,使用有限元软件分析了成分分布指数、梯度层数目和梯度层厚度等参数对涂层/基体界面残余热应力的影响。结果表明:功能梯度材料的最佳成分梯度指数为m=1;涂层最佳层数为3-5层;涂层最佳厚度为1-1.5 mm;涂层表层主要分布为径向压应力;在涂层/基体界面的边缘区域应力集中较为严重;涂层/基体界面处的径向应力、轴向应力和剪切应力与成分分布指数、梯度层数目和梯度层厚度有密切的关系。用涂搪法制备了梯度涂层,用X射线衍射法(XRD)测试了涂层表面残余应力,验证了有限元结果的准确性。     

梯度功能材料物性值推定与热应力的分析

为推动梯度功能材料(FGM)的发展,本文论述了经验复合准则,微观力学的近似方法等推定物性值的一般方法,并进一步将模糊逻辑应用于FGM的物性值推定;另外,还对球形、无限长圆筒,无限大平板等形状的FGM中的热应力分布作了近似计算。     

梯度复合材料热应力影响因素正交有限元分析

为了分析梯度层厚度、梯度层组成相体积分数及组成相长径比三种因素对热应力的影响,建立了梯度复合材料的物理模型,并采用有限元分析方法计算了该模型冷却至室温的热应力,同时使用正交设计对各因素的重要程度进行了数量估计.结果表明:三种因素中梯度层厚度对热应力的影响最为显著,次之为组成相体积分数,而长径比的影响较小.     

Y-TZP/LZAS微晶玻璃功能梯度涂层残余应力分析

为了提高钢基体微晶玻璃涂层的韧性,设计了Y-TZP/LZAS微晶玻璃功能梯度涂层。运用有限元软件,分析了梯度层数目、梯度层厚度和层间3Y-TZP体积组分差等参数对涂层/基体界面残余热应力的影响。结果表明,涂层表层主要分布为径向压应力;在涂层/基体界面的边缘区域应力集中较为严重;涂层/基体界面处的径向应力、轴向应力和剪切应力以及梯度层数目、梯度层厚度和3Y-TZP体积组分差均有密切关系。最后通过涂搪法制备了梯度涂层,测试了涂层表面残余应力,并与有限元结果对比,以验证模拟的准确性。     

稳态温度场下轴对称梯度功能材料的热应力分析

本文基于热弹性理论及计算数学方法，对轴对称梯度功能材料内部各点的热应力进行了理论分析。提出了稳态温度场下，环状截面梯度功能柱体的温度分布与热应力计算公式。     

梯度功能材料的热应力研究现状与展望

回顾了近年来梯度功能材料热应力研究领域所取得的研究成果，并展望了ＦＧＭ热应力研究的发展趋势。     

梯度陶瓷喷嘴残余应力的有限元分析

为了提高喷嘴的抗冲蚀磨损能力,将梯度功能材料理论运用于喷嘴材料的设计中,改传统的均质喷嘴材料为非均质喷嘴材料,提出在梯度陶瓷喷嘴制备中将残余压应力引入喷嘴入口的设计目标.在组成分布指数一定的条件下,针对主要设计参数对梯度陶瓷喷嘴残余应力的影响进行有限元分析,探讨了梯度层厚度、临界梯度层材料组分差对SiC/(W,Ti)C单梯度陶瓷喷嘴残余热应力的影响规律,在组成分布指数取0.5时,优化SiC/(W,Ti)C梯度陶瓷喷嘴梯度层厚和临界梯度层材料组分差.结果表明,残余应力随梯度层厚h及临界梯度层SiC体积组分差的不同产生很大差异,合理设计梯度层厚h及临界梯度层SiC体积组分差可在喷嘴入口形成有效残余压应力,最佳梯度层厚为5mm,临界梯度层SiC组分差小于5%(体积分数).     

Finite element evaluation of mixed mode stress intensity factors in functionally graded materials

This paper is directed towards finite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks. Graded finite elements are developed where the elastic moduli are smooth functions of spatial co‐ordinates which are integrated into the element stiffness matrix. In particular, stress intensity factors for mode I and mixed‐mode two‐dimensional problems are evaluated and compared through three different approaches tailored for FGMs: path‐independent J^*_k‐integral, modified crack‐closure integral method, and displacement correlation technique. The accuracy of these methods is discussed based on comparison with available theoretical, experimental or numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

W/Cu功能梯度材料的制备及热循环应力分析

采用水煮溶解造孔剂法, 即先制备孔隙呈梯度分布的钨骨架、后渗铜的方法, 制备了W/ Cu 功能梯度材料, 并对钨铜在纵截面的分布进行了检测, 数据表明在纵截面上钨铜呈梯度分布。利用水淬法模拟其服役状况并用有限差分方法对产生的非稳态热应力进行了分析。结果表明, 热应力的最大值总是出现在两端, 由于富钨端相对密度较低, 裂纹总是在该端出现, 模拟结果与实验结果相一致。      

An extended element free Galerkin method for fracture analysis of functionally graded materials

An extended element free Galerkin method (XEFGM) has been adopted for fracture analysis of functionally graded materials (FGMs). Orthotropic enrichments functions are used along with the sub-triangle technique for enhancing the Gauss quadrature accuracy near the crack, and the incompatible interaction integral method is employed to calculate the stress intensity factors. Numerical simulations have proved that XEFGM provides more accurate results by less number of nodes (DOFs) in comparison with the unenriched EFGM and other conventional methods for several FGM problems with different crack locations and loadings. The results have been compared with the reference results, showing the reliability, stability, and efficiency of present XEFGM.

Received 9 June 2014 Accepted 17 September 2014.     

Transient thermal stress analysis of an edge crack in a functionally graded material

An edge crack in a strip of a functionally graded material (FGM) is studied under transient thermal loading conditions. The FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip. Thus the material is elastically homogeneous but thermally nonhomogeneous. This kind of FGMs include some ceramic/ceramic FGMs such as TiC/SiC, MoSi₂/Al₂O₃ and MoSi₂/SiC, and also some ceramic/metal FGMs such as zirconia/nickel and zirconia/steel. A multi-layered material model is used to solve the temperature field. By using the Laplace transform and an asymptotic analysis, an analytical first order temperature solution for short times is obtained. Thermal stress intensity factors (TSIFs) are calculated for a TiC/SiC FGM with various volume fraction profiles of the constituent materials. It is found that the TSIF could be reduced if the thermally shocked cracked edge of the FGM strip is pure TiC, whereas the TSIF is increased if the thermally shocked edge is pure SiC.     

Three-dimensional static and dynamic analyses of the functionally graded cylinder bonded to the laminated plate under general loading

A graded finite element method code based on Rayleigh–Ritz energy formulation is developed and implemented to study the elastic behavior of a layered plate loaded by a solid isotropic cylinder and a functionally graded interlayer. The applied nonaxisymmetric loading to the inner cylinder induces a stress concentration in the flexible part of the joint. The effects of different thicknesses and power law exponents of functionally graded interlayer on the distribution of displacements and stresses are investigated, which verifies the ability of functionally graded material to control the stress and displacement waves. The time-dependent response of the structure is also obtained based on Newmark's time integration method.     

基于耦合扩展多尺度有限元方法的功能梯度材料热应力分析

以高效模拟功能梯度材料(FGM)微观非均质性对整体热力学性能的影响为研究目的,通过随机形态描述函数(RMDF)法和体积分数的指数分布建立FGM二维微结构,在此基础上,发展了FGM热应力分析的耦合扩展多尺度有限元方法(CEMsFEM)。该方法基于扩展多尺度有限元方法(EMsFEM)的基本思想,对温度场和位移场构造数值基函数,以把微观非均质材料性质带到宏观响应中。同时为了考虑泊松效应导致的不同方向间的耦合作用,在位移场数值基函数中增加了耦合附加项。通过数值基函数建立宏微观单元信息的映射关系,在宏观尺度求解有效方程,节约计算量。为了更好地考虑微观载荷的影响,把结构的真实响应分解为宏观响应和微观扰动,进一步推导出修正的宏观载荷向量。通过不同体积分数分布的FGM在不同载荷工况下的热应力分析算例验证了本文中方法的正确性和有效性,最后讨论了微结构的尺寸效应对结构热力学响应的影响。     

Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

Functionally graded material (FGM) bars in axial motion (hereafter called “FGM axial bars”) have great potential for applications in many engineering fields. Therefore, it is important to develop a reliable mathematical model that can provide very accurate dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. As an extension of our previous work, we present a spectral element model for a modified FGM axial bar model wherein nonuniform lateral contraction in the thickness direction is taken into account. We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the power law. The performance of the proposed spectral element model is validated through comparison with solutions from a conventional finite element model, and with the results from the previous FGM axial bar model. In addition, the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars are numerically investigated.     

Stochastic Finite element analysis of the free vibration of functionally graded material plates

The superior properties of functionally graded materials (FGM) are usually accompanied by randomness in their properties due to difficulties in tailoring the gradients during manufacturing processes. Using the stochastic finite element method (SFEM) proved to be a powerful tool in studying the sensitivity of the static response of FGM plates to uncertainties in their material properties. This tool is yet to be used in studying free vibration of FGM plates. The aim of this work is to use both a First Order Reliability Method (FORM) and the Second Order Reliability Method (SORM), combined with a nine-noded isoparametric Lagrangian element based on the third order shear deformation theory to investigate sensitivity of the fundamental frequency of FGM plates to material uncertainties. These include the effect of uncertainties on both the metal and ceramic constituents. The basic random variables include ceramic and metal Young’s modulus and Poisson’s ratio, their densities and ceramic volume fraction. The developed code utilizes MATLAB capabilities to derive the derivatives of the stiffness and mass matrices symbolically with a considerable reduction in calculation time. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using available data in the literature, in addition to comparisons with results of the well-established Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of FGM plates, when compared to the slower Monte Carlo simulation techniques.     

Numerical simulation of elastic plastic fatigue crack growth in functionally graded material using the extended finite element method

In the present work, the extended finite element method has been used to simulate the fatigue crack growth problems in functionally graded material in the presence of holes, inclusions, and minor cracks under plastic and plane stress conditions for both edge and center cracks. Both soft and hard inclusions have been implemented in the problems. The validity of linear elastic fracture mechanics theory is limited to the brittle materials. Therefore, the elastic plastic fracture mechanics theory needs to be utilized to characterize the plastic behavior of the material. A generalized Ramberg-Osgood material model has been used for modeling purposes.