Fracture analysis of a functionally graded interfacial zone between two dissimilar homogeneous materials

In this paper the plane elasticity problem for a functionally graded interfacial zone containing a crack between two dissimilar homogeneous materials has been considered. It is assumed that in the interfacial zone the reciprocal of the shear modulus is a linear function of the coordinate, while Possion’s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors are investigated. The numerical results show that the graded parameters, the thickness of interfacial zone, the crack size and location have significant effects on the stress intensity factors.     

Bending analysis of a functionally graded piezoelectric cantilever beam

A new analysis based on Airy stress function method is presented for a functionally graded piezoelectric material cantilever beam. Assuming that the mechanical and electric properties of the material have the same variations along the thickness direction, a two-dimensional plane elasticity solution is obtained for the coupling electroelastic fields of the beam under different loadings. This solution will be useful in analyzing FGPM beam with arbitrary variations of material properties. The influences of the functionally graded material properties on the structural response of the beam subjected to different loads are also studied through numerical examples.     

Thermal stresses around a circular inclusion with functionally graded interphase in a finite matrix

Based on the theory of the complex variable functions, the analysis of non-axisymmetric thermal stresses in a finite matrix containing a circular inclusion with functionally graded interphase is presented by means of the least square boundary collocation technique. The distribution of thermal stress for the functionally graded interphase layer with arbitrary radial material parameters is derived by using the method of piece-wise homogeneous layers when the finite matrix is subjected to uniform heat flow. The effects of matrix size, interphase thickness and compositional gradient on the interfacial thermal stress are discussed in detail. Numerical results show that the magnitude and distribution of interfacial thermal stress in the inclusion and matrix can be designed properly by controlling these parameters.     

The beam-mode stability of periodic functionally-graded-material shells conveying fluid

The characteristics of beam-mode stability of fluid-conveying shell systems are investigated in this paper for shells with clamped-free (cantilevered) boundary conditions. An FEM algorithm is developed to conduct the investigation. A periodic shell structure of functionally graded material (FGM), termed as PFGM shell here, is designed so as to enhance the stability for the shell system, and to eliminate the stress concentration problems that exist in periodic structures. Results show that by the introduction of periodic design the critical velocities can be raised over several desired ranges of the dimensionless fluid density β, and the stress concentration is effectively reduced in the PFGM shell. Finally, the effects of the geometric shape, material parameters and spring supports on the dynamical stability are probed.     

冲击相边界传播过程中梯度材料的形成

 采用一种基于简单混合物模型的本构，研究了不可逆相变材料中一维的冲击相边界的传播规律，发现在突加载荷并连续卸载的应力边界条件下，样品内部有梯度材料形成。分析了边界条件对材料梯度变化的影响，并且用基于特征线的数值方法计算了不同的边界条件下材料的梯度分布，从而提出利用冲击相边界的传播制备梯度材料的可能性。最后对这种方法的利弊做了探讨。     

功能梯度材料研究的现状与将来发展

功能梯度材料是近年来材料科学的研究热点之一,文章评述了ＦＧＭ的基本概念、制备技术、理论研究和应用情况等发展现状,同时对可能的发展进行了讨论,强调了对电磁性能研究的重要性。     

Electro-mechanical response of functionally graded beams with imperfectly integrated surface piezoelectric layers

The time-dependent behavior of a simply-supported functionally graded beam bonded with piezoelectric sensors and actuators is studied using the state-space method. The creep behavior of bonding adhesives between piezoelectric layers and beam is characterized by a Kelvin-Voigt viscoelastic model, which is practical in a high temperature circumstance. Both the host elastic functionally graded beam and the piezoelectric layers are orthotropic and in a state of plane stress, with the former being inhomogeneous along the thickness direction. A laminate model is employed to approximate the host beam. Moreover, the coupling effect between the elastic deformation and electric field in piezoelectric layers is considered. Results indicate that the viscoelastic property of interfacial adhesives has a significant effect on the function of bonded actuators and sensors with time elapsing.     

Studies on dry sliding wear behaviour of functionally graded graphite particle-filled glass-epoxy composites

The dry sliding wear characteristics of glass-epoxy (G-E), graphite-filled G-E and functionally graded graphite-filled G-E composites were investigated using pin-on-disc test rig. The specific wear rate was determined as a function of applied load, sliding velocity and sliding distance. The results revealed that the specific wear rate increases in all the tested composites with increasing wear parameter. But, the admirable wear resistance was obtained with functionally graded graphite-filled G-E composite. The scanning electron microscope studies of worn-out surfaces support the involved wear mechanisms and are well indicated in the worn-out surface features such as matrix wear, fibre exposure, fibre breakage, fibre and matrix deboning, microcracking, debris formation, fibre cracking and removal of fibres.     

ITER 718合金螺栓断裂原因分析及工艺改进

通过化学成分检测、金相组织分析、氢含量的测定、断口的宏微观观察、大直径高强螺栓的原型件拉伸试验以及有限元分析等手段从材料、结构、制造工艺三个方面上探究了ITER 磁体支撑718 螺栓低强度断裂的原因。材料分析结果表明,国产718 螺栓材料的性能满足要求。工艺分析结果表明,螺栓低强度断裂的主要原因为滚压螺纹后的热处理导致螺纹根部脆性。结构分析结果表明,由于应力集中的影响,718 螺栓的强度低于原材料强度,而且随着螺栓直径的增大而降低。基于以上分析结论,提出了能显著提高718 螺栓强度的新工艺。通过原型件的拉伸试验,新工艺螺栓可以有效地提高螺栓的强度160MPa,达到1230MPa。     

亚表面异质缺陷对功能梯度材料表面温度场的影响

基于双曲型热传导方程,采用镜像法和波函数展开法,求解了含亚表面异质圆柱缺陷的半无限功能梯度材料的表面温度场,给出了功能梯度材料中热波散射的一般解.分析了亚表面异质圆柱缺陷的几何参数(如埋藏深度)和热物理参数(如导热系数、热扩散长度、热扩散率及热弛豫时间等)对功能梯度材料表面温度场的影响.温度波由调制的超短脉冲激光在功能梯度材料表面激发,异质圆柱缺陷表面的边界条件为导热边界.研究结果可望为功能梯度材料的红外热波无损检测、导热反问题提供计算方法和参考数据.     

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通过化学成分检测、金相组织分析、氢含量的测定、断口的宏微观观察、大直径高强螺栓的原型件拉伸试验以及有限元分析等手段从材料、结构、制造工艺三个方面上探究了ITER磁体支撑718螺栓低强度断裂的原因。材料分析结果表明,国产718螺栓材料的性能满足要求。工艺分析结果表明,螺栓低强度断裂的主要原因为滚压螺纹后的热处理导致螺纹根部脆性。结构分析结果表明,由于应力集中的影响,718螺栓的强度低于原材料强度,而且随着螺栓直径的增大而降低。基于以上分析结论,提出了能显著提高718螺栓强度的新工艺。通过原型件的拉伸试验,新工艺螺栓可以有效地提高螺栓的强度160MPa,达到1230MPa。     

Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis

The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin–Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori–Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.     

运用功能梯度结构降低大功率激光系统中镜面热变形的数值分析

提出一种运用功能梯度结构以有效降低大功率激光系统中镜子温度和镜面热变形以及减缓热应力的新方法。讨论了环形分布和高斯分布2种类型的激光源。有限元分析结果表明,通过这种方法可使硅镜和铜镜的表面热变形成倍降低,并且还能同时显著降低镜体温度。讨论了代表热学和力学性质的函数表达式的斜率对镜面热变形的影响,研究表明：功能梯度结构的热物理对镜面形变产生重大影响,而力学性质对镜面形变的影响非常小。该结论可为具有该功能梯度结构的镜子优化设计和制造提供参考。     

Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

In this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson's ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.     

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

Based on the Mindlin's first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton's principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.     

Fracture investigation of V-notch made of tungsten-copper functionally graded materials

The fracture of V-notches with end holes made of tungsten-copper functionally graded material under mode I has been studied in this paper. The averaged strain energy density over a well-defined control volume was employed to predict the fracture loads. A numerical approach was used to determine the outer boundary of the control volume. Mechanical properties such as elasticity modulus, Poisson’s ratio, fracture toughness K_Ic, and ultimate tensile stress have been considered to obey the power law function through the specimen width.     

Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity

Using three-dimensional (3-D) nonlocal elasticity theory of Eringen, this paper presents closed-form solutions for in-plane and out-of-plane free vibration of simply supported functionally graded (FG) rectangular micro/nanoplates. Elasticity modulus and mass density of FG material are assumed to vary exponentially through the thickness of micro/nanoplate, whereas Poisson's ratio is considered to be constant. By employing appropriate displacement fields for the in-plane and out-of-plane modes that satisfy boundary conditions of the plate, ordinary differential equations of free vibration are obtained. Boundary conditions on the lateral surfaces are imposed on the analytical solutions of the equations to yield the natural frequencies of FG micro/nanoplate. The natural frequencies of FG micro/nanoplate are obtained for different values of nonlocal parameter and gradient index of material properties. The results of this investigation can be used as a benchmark for the future numerical, semi-analytical and analytical studies on the free vibration of FG micro/nanoplates.     

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.     

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针对不同体积分布指数p的W/Cu连续功能梯度材料的偏滤器第一壁结构,采用有限元软件计算了8MW.m?2稳态运行热加载以及等离子体破裂条件下1GW.m?2热流冲击下的力学响应。相同稳态加载条件下,W/Cu连续功能梯度材料的最优分布指数与分层梯度材料存在较大差异,其最优等效应力比分层梯度材料要小26%,表现出更优异的性能。在热冲击响应过程中,连续梯度W/Cu材料塑性损伤随p值不同也存在较大变化,其最优p值与其稳态运行时热应力最优p值存在一定差异,从第一壁应用条件考虑,应综合选取,最佳p值在1.2附近。综合来看,连续梯度W/Cu材料具有更连续变化的热物理属性及力学性能,在聚变堆第一壁结构设计中具有更大的应用潜力。