功能梯度材料热应力研究进展

梯度功能材料的热应力问题贯穿梯度功能材料设计、制备、性能评价及应用整个研究领域,其中,热传导问题是热应力研究基础。介绍了梯度功能材料的概念及热传导和热应力问题的研究背景,重点分析了梯度功能材料热传导和热应力问题在数学模型、物性参数模型、解析方法、数值方法等方面的国内外研究进展,并展望进一步研究方向。     

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。     

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。     

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。     

圆板状SiC/C功能梯度材料残余热应力特征有限元分析

功能梯度材料残余热应力的大小及分布对其性能有效发挥及长期稳定使用有着较大的负面影响,为了尽可能充分发挥材料性能,增加材料的使用寿命,需尽可能减小残余应力以及使其合理分布.本文采用ANSYS有限元分析软件对不同叠层工艺参数的等离子体第一壁候选材料--SiC/C功能梯度材料(FGM)的残余热应力进行了数值模拟,获得了使热应力有效缓和的较适宜的工艺参数,对实际研发制备目标材料也可提供一些理论参照.相关结果表明,适量增加梯度叠层数及中间梯度层厚度可逐步有效缓和残余热应力,同时,针对本文今后应用的仍以炭材料为主体的炭基陶瓷保护层复合SiC/C FGM而言,纯SiC层厚度应取较小值,而叠层成分分布指数应取0.8～1.0为宜.     

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。     

Al－Fe系梯度功能材料断口特征及其多尺度分形研究

研究了Ａｌ－Ｆｅ系梯度功能材料的试样不同部位的断口特征；基于离散分形布朗随机场模型，对试样断口进行多尺度分形研究，结果表明断口的分形参数Ｈ值也呈梯度分布，它反映了该材料的韧性呈梯度分布。     

梯度功能材料稳态温度场下的热应力分析

采用一种新的显微数字散斑相关方法，对微薄层梯度材料在恒温热载荷情况下的应变场进行了实验研究，并与双材料恒温下的应变场进行了比较与分析，从而为优化设计和制备梯度功能材料提供了一种可行的实验方法和有意义的结果。     

A coupling extended multiscale finite element method for dynamic analysis of heterogeneous saturated porous media

A coupling extended multiscale finite element method (CEMsFEM) is developed for the dynamic analysis of heterogeneous saturated porous media. The coupling numerical base functions are constructed by a unified method with an equivalent stiffness matrix. To improve the computational accuracy, an additional coupling term that could reflect the interaction of the deformations among different directions is introduced into the numerical base functions. In addition, a kind of multi‐node coarse element is adopted to describe the complex high‐order deformation on the boundary of the coarse element for the two‐dimensional dynamic problem. The coarse element tests show that the coupling numerical base functions could not only take account of the interaction of the solid skeleton and the pore fluid but also consider the effect of the inertial force in the dynamic problems. On the other hand, based on the static balance condition of the coarse element, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the CEMsFEM. Both one‐dimensional and two‐dimensional numerical examples of the heterogeneous saturated porous media are carried out, and the results verify the validity and the efficiency of the CEMsFEM by comparing with the conventional finite element method. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

复杂边界条件功能梯度板三维分析的半解析方法

推导出适应功能梯度材料构件分析的半解析方法基本算式,并针对功能梯度构件的材料参数随空间坐标变化的特点,将材料参数纳入到力学方程中进行整体积分计算,从而编制统一程序计算不同边界条件下的板件问题.该法适应性强而又简洁高效,且不同于一般的半解析法,可采用一维离散,给出三维分析结果,是一种解决功能梯度构件力学性能分析的有效数值方法.文中用半解析法分析几种具有不同复杂边界条件的功能梯度板,给出了板件的力学量三维分布形态.     

Thermal post-buckling analysis of functionally graded material elliptical plates based on high-order shear deformation theory

Thermal post-buckling analysis is first presented for functionally graded elliptical plates based on high-order shear deformation theory in different thermal environments. Material properties are assumed to be temperature-dependent and graded in the thickness direction. Ritz method is employed to determine the central deflection-temperature curves, the validity of which can be confirmed by comparison with related researchers' results; it is worth noting that the forms of approximate solutions are well chosen in consideration of both simplicity and accuracy. Influences played by different supported boundaries, thermal environmental conditions, ratio of major to minor axis, and volume fraction index are discussed in detail.     

多孔功能梯度梁的热-力耦合屈曲行为

采用经典欧拉梁理论和高阶三角剪切变形理论,研究了多孔功能梯度梁的热-力耦合屈曲行为。分析中考虑了材料物性与温度的相关性,采用含孔隙率的Voight混合模型描述了多孔功能梯度的材料属性。利用迭代算法求解结构在均匀、线性和非线性温升(考虑热传导效应)下的热-力耦合屈曲临界温度,讨论了材料非均匀参数、孔隙率和长细比等参数对屈曲临界温度的影响。ABAQUS数值模拟结果和文献对比结果验证了理论的可靠性,同时表明高阶剪切变形理论较经典欧拉梁理论精确。结果表明,功能梯度材料梁的热屈曲分析必须考虑物性与温度的相关性,否则可能高估热屈曲临界温度10%~30%;随着孔隙率增大,材料的等效弹性模量减少,即结构刚度有所弱化,但屈曲临界温度反而大大增高。     

Nonlocal static analysis of a functionally graded material curved nanobeam

This article is concerned with the analytical solution for a curved nanobeam based on nonlocal elasticity. The structure is made of functionally graded (FG) material, and its property varies in accordance with a power law function through the thickness. To obtain the displacement function, the static differential equations for a curved FG beam are combined with the nonlocal Eringen stress equations. By using the direct method for solving the nonlocal force–strain and moment–curvature relations covering the distributed loads, the explicit expressions of nonlocal strains are achieved. The strain-displacement relations are also employed to find displacement field. Numerical examples with different types of boundary conditions are carried out in order to investigate the effects of nonlocal parameters, the nonhomogeneity index, and geometric characteristics.     

A robust,four-node,quadrilateral element for stress analysis of functionally graded plates through higher-order theories

ABSTRACT

A hybrid-mixed, four-node, quadrilateral element for the three-dimensional (3D) stress analysis of functionally graded (FG) plates using the method of sampling surfaces (SaS) is developed. The SaS formulation is based on choosing an inside the plate body N, not equally spaced SaS parallel to the middle surface, in order to introduce the displacements of these surfaces as basic plate variables. Such a choice of unknowns, with the consequent use of Lagrange polynomials of the degree N ? 1 in the assumed distributions of displacements, strains, and mechanical properties through the thickness leads to a robust FG plate formulation. All SaS are located at Chebyshev polynomial nodes that permit one to minimize uniformly the error due to the Lagrange interpolation. To avoid shear locking and spurious zero-energy modes, the assumed natural strain method is employed. The proposed four-node quadrilateral element passes 3D patch tests for FG plates and exhibits a superior performance in the case of coarse distorted meshes. It can be useful for the 3D stress analysis of thin and thick metal/ceramic plates because the SaS formulation gives an opportunity to obtain the solutions with a prescribed accuracy, which asymptotically approach the 3D exact solutions of elasticity as the number of SaS tends to infinity.