Effects of fiber aspect ratio evaluated by elastic analysis in discontinuous composites

An elastic stress analysis to investigate the effects of fiber aspect ratio in short fiber reinforced discontinuous composite materials has been done for different fiber volume fractions. In order to examine the elastic internal behavior, an evaluation of the load bearing capacity of discontinuous reinforcements is needed in advance. Accordingly, analytical derivation of composite mechanics has been carried out to predict fiber stresses and fiber/matrix interfacial shear stresses in discontinuous composites. The model is based on the theoretical development of conventional shear lag theory developed by Cox. However, the major shortcoming of the Cox model is due to the calculation without normal stress transfer from the end of fibers. In order to overcome the shortcoming, both of the normal and shear stress transfer mechanisms between the fiber and the matrix are accounted for with the stress concentration effects as well as material and geometrical properties. Results of predicted stresses concerning the various fiber aspect ratios are described by using the present model that is the closed form solution and compared with the Cox model and Taya model. It is found that the effect of fiber aspect ratio is significant to composite strengthening through load transfer from the matrix to the fiber, whereas the effect of fiber volume fraction is not so sensitive, relatively. It is also found that the present model has the capability to correctly predict the values of fiber stresses and fiber/matrix interfacial shear stresses.     

Analytical study on the elastic-plastic transition in short fiber reinforced composites

In discontinuous composites, the fiber end effects can be neglected when the length of fiber is much greater compared to the diameter. Thus, conventional shear lag theory is very useful for predicting composite properties deduced from each constituent. However, in the case of short fiber or whisker reinforced composites, the end effects cannot be neglected, and the composite properties are functions of material and geometrical parameters since the fiber end effects significantly influence the behavior of composites. For a good understanding of the behavior of short fiber or whisker reinforced composites, it is necessary to first understand the mechanism of stress transfer and it has well been modified before. However, the modification was limited to the basic elastic stress calculation of the fiber and matrix in a micromechanical model. Accordingly, the former modification of the shear lag model has been extended to predict the overall elastic composite behavior and elastic-plastic behavior of which result can predict the stress concentration in the matrix as well as the onset of matrix yielding. The extended modification results showed that it gives a good agreement with finite element analysis as well as with experimental data. It was also found that the local matrix yielding is initiated in the vincinity of the fiber ends which produces local plasticity and an elastic-elastic transition before the composite stress reaches matrix yield stress.     

含SMA约束层的复合材料矩形板的阻尼能力分析

研究由形状记忆合(shape memory alloy，简写为SMA)SMA约束层、SMA纤维混杂叠层材料构成的复合材料矩形板的阻尼性能。采用多胞模型和细观力学阻尼分析方法，分别预测叠层复合材料单层的弹性性能和阻尼性能，在叠层材料中计入横向剪切变形的影响。在导出矩形板的应变能和耗散能的基础上，根据最大应变能理论建立板的模态阻尼比的数学表达式。数值结果表明，文中提出的含有SMA约束层的SMA纤维叠层复合材料的集成阻尼设计方法，是一种有效的阻尼增强方案。     

碳纳米管增强聚合物复合材料的界面脱黏及应力分布

碳纳米管和复合材料基体间的界面力学行为是影响复合材料宏观力学性能的重要因素,为此本文利用有限单元法对单壁碳纳米管增强聚合物复合材料的界面脱黏、切应力分布及拔出载荷进行了数值模拟。建立了一个轴对称三圆柱壳模型,引入ABAQUS中的Cohesive单元模拟了单壁碳纳米管和聚合物基体之间的界面层,分析了单壁碳纳米管的长细比、界面强度以及热残余应力等因素对碳纳米管与聚合物基体间的界面切应力以及拔出载荷的影响。模拟结果表明：当单壁碳纳米管的长度变化为50~100 nm、与基体之间的界面强度为50~100 MPa、环境温度变化为100℃ 时,碳纳米管的长细比、界面强度以及由于热失配所引起的残余应力对单壁碳纳米管与聚合物基体间的界面切应力以及拔出载荷有着显著的影响。     

Ultimate strength prediction of continuous fiber-reinforced brittle matrix composites

A model to predict ultimate strength of continuous fiber-reinforced brittle matirix composites has been developed. A statistical theory for the strength of the uniaxially fiber-reinforced brittle matrix composite is presented. Material of matrix is assumed to be homogeneous and isotropic, so that the strength of material is anywhere constant, whilst that of fiber is considered to show Weibull statistical distribution. The theory may be utilized to optimize the biaxial and multidirectional tensile strength properties of laminated materials. The composite strength is estimated by assuming no interacting matrix cracks. The frictional shear stress caused by bridging fibers is involved in the strength computation. The predicted strength is compared to experimental results with LAS-Glass/Nicalon fiber composite.     

Evaluation of elastic modulus for unidirectionally aligned short fiber composites

An analytical approach of to reinforcement for of short fiber reinforced composites has been extended to include the estimation of elastic modulus. The model is based on the theoretical development of shear lag theory developed by Cox for unidirectionally Aligned aligned Short short Fiber fiber Compositescomposites. Thus, the evolution of conventional models is described in detail along with the effect on the modulus of various parameters. Results are shown with experimental data as well as the comparison of other theories. It is found that the present model agrees well with experimental data and resolves some of the discrepancies among the previous models. It is also found that the present model is very accurate yet relatively simple to predict Young’s modulus of discontinuous composites and has the capability to correctly predict the effects of fiber aspect ratio, fiber volume fraction, and fiber/matrix modulus ratio. This paper was recommended for publication in revised form by Associate Editor Chongdu Cho Hong Gun Kim received a B.S. and M.S. degree in Mechanical Engineering from Hanyang University in 1979 and 1984. He then went on to receive his Ph.D. degrees from University of Massachusetts in 1992, respectively. Dr. Kim is currently a Professor at the Department of Mechanical & Automotive Engineering at Jeonju University in jeonju, Korea. He is currently serving as an Editor of the KSAE and KSMTE. Dr. Kim’s research interests are in the area of fuel cell, FEM analysis, mechanical design, and composite mechanics. Lee Ku Kwac received a B.S. degree in Precision Mechanical Engineering from Chosun University in 1999. He then went on to receive his M.S. and Ph.D. degrees from Chosun University in 2001 and 2005, respectively. Dr. Kwac currently a Professor at the Department of Mechanical & Automotive Engineering at Jeonju University in jeonju, Korea. Dr. Kwac’s research interests are in the area of fuel cell, nano-mechanism, and micro-machining.     

间断式纤维增强热塑性基复合材料应力应变场分析

用有限元法通过引入一个单胞模型和适当的边界条件，分析了间断式纤维增强复合材料在外部载荷作用下复合材料内部应力－应变场的变化规律，比较了基体在弹性和弹塑性条件下纤维、纤维与基体界面应力分布的特点。     

Novel contact probing method using single fiber optical trapping probe

A novel contact probing method for microdevices with high aspect ratio or biological samples is proposed. In this technique, a dielectric microsphere is optically trapped by an optical fiber and used as a touch probe. In the simulations, the finite difference time domain (FDTD) method and Maxwell stress theory are applied to obtain a suitable shape for the tip of the optical fiber. The results show that it is possible to trap the microsphere by using a single optical fiber. In experiments, single fiber optical trapping is successfully demonstrated by considering the simulation results. In order to use the trapped microsphere in the touch probe, the intensity of the reentered beam that is reflected from the surface of the microsphere is monitored. When the probe is in contact with the surface of the object, the intensity of the beam changes and this change is used as the contact signal. Because the probe is trapped optically and the trapping force is very small, this system can be used in a low invasive method.     

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded orthotropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.     

Linear free vibration analysis of cross-ply laminated cylindrical helical springs

A linear free vibration analysis of symmetric cross-ply laminated cylindrical helical springs is performed based on the first-order shear deformation theory. Considering the rotary inertia, the shear and axial deformation effects, governing equations of symmetric laminated helical springs made of a linear, homogeneous, and orthotropic material are presented in a straightforward manner based on the classical beam theory. The free vibration equations consisting of 12 scalar ordinary differential equations are solved by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy. The soundness of the present results are verified with the reported values which were obtained theoretically and experimentally. After presenting the non-dimensional graphical forms of the free vibrational characteristics of (0°/90°/90°/0°) laminated helical spring made of graphite-epoxy material (AS4/3501-6) with fixed–fixed ends, a non-dimensional parametric study is worked out to examine the effects of the number of active turns, the shear modulus in the 1–2 plane (G₁₂), the ratio of the cylinder diameter to the thickness (D/d), and Young's moduli ratio in 1 and 2 directions (E₁/E₂) on the first six natural frequencies of a uniaxial composite helical spring with clamped-free, clamped-simple, and clamped–clamped ends.     

碳纤维增强树脂基复合材料切削机理研究

碳纤维增强树脂基复合材料（Carbon fiber reinforced plastic,CFRP）在细观尺度上由纤维、树脂及界面不同相组成,在宏观尺度上呈层叠特征,具有非均质性和各向异性。CFRP切削过程的实质是在切削力、热共同作用下同时去除高强度纤维和低强度树脂的复杂过程,极易出现加工损伤。抑制加工损伤的前提是准确揭示CFRP切削机理,而揭示其切削机理的关键是分析材料去除过程。由于纤维是复合材料内部承受主要载荷的组成相,材料的去除过程主要由纤维的断裂过程决定。因此,通过分析切削过程中纤维的受力状态,以双参数弹性地基梁理论为基础,建立了虑及纤维所受法向及切向约束,且兼虑树脂及界面温变特性的单纤维切削模型,可准确表征纤维实际受力状态,实现纤维断裂过程的准确求解。研究发现：切削深度和纤维角度影响纤维变形深度,即切深越大,纤维变形深度越大,更易产生加工损伤;随着纤维角度增加,纤维变形深度减小。同时,为解决单纤维切削模型难以直接验证的难题,利用其求解得到宏观切削力理论值,通过与试验值对比,间接验证了单纤维切削模型的正确性。同时与未考虑被切削纤维所受切向约束和树脂及界面温变特性时相比,同时考虑这两个因素可使CFRP宏观切削力计算精度平均提升20%。所建立的单纤维切削模型不仅能够从细观尺度准确揭示CFRP去除机理,而且可为后续有关损伤抑制的研究提供理论依据。     

Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates

This paper presents analytical solutions of deflection and stress for orthotropic plates using a two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor. Additional features of the theory are that it has strong similarity with classical plate theory in many aspects, and the number of involved variables is only two as against three in case of other shear deformation theories. The Levy-type solution procedure in conjunction with the state space concept is used to determine the closed-form solutions for orthotropic rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are performed to verify the validity of the present results. Finally, the effects of thickness ratio, modulus ratio and aspect ratio on the deflection and stress of orthotropic plates are investigated and discussed.     

应用扰动广义微分求积法的复合材料层合板剪切屈曲分析与优化

广义微分求积(GDQ)法求解复合材料层合板剪切屈曲时存在计算精度差、计算振荡不收敛问题,研究发现该现象源于载荷矩阵存在奇异,为此,提出扰动GDQ法,通过扰动主对角线权重系数以改善载荷矩阵的奇异性来消除计算振荡。数值算例验证了扰动策略的有效性,实现复合材料层合板剪切屈曲问题的高效稳定求解。在此基础上,结合直接搜索模拟退火算法,开展了含剪切载荷的复合材料层合板铺层顺序优化。结果表明：剪切工况时对称复合材料层合板的优化铺层不受铺层数和铺设形式影响,优化铺层角随长宽比增大而趋于60°;而剪切与轴压组合工况下较小的剪切力能改善层合板屈曲性能,随着剪切力的增大,优化屈曲性能逐渐降低,优化铺层趋同于剪切工况。研究结果为复合材料层合板的剪切屈曲性能设计提供了参考。     

注塑成型短玻纤增强复合材料各向异性弹性常数预测方法

针对注塑成型短玻纤增强复合材料,研究二阶纤维取向张量与纤维取向角度之间的连续函数关系,建立纤维均质化RVE模型。基于Taguchi正交试验设计方法,利用DIGIMAT软件对短玻纤增强复合材料RVE模型进行仿真试验,定量分析纤维质量分数（A）、纤维长径比（B）和纤维取向张量（C）对短玻纤增强复合材料力学性能的影响规律。考虑注塑成型过程中的纤维分层效应,提出了夹芯分层模型并进行铺层设计。基于灰箱理论和反求工程,选取纤维长径比、表层厚度比和芯层厚度比、表层纤维取向张量、纤维取向矢量旋转角四个影响因素,反演预测短玻纤增强复合材料PA66（GF50）正交各向异性弹性常数,与材料拉伸弹性模量E₃₃、泊松比u₃₁和泊松比u₃₂的试验结果对比,相对误差分别为0.80%、0.29%和1.35%。     

Deflections and free vibrations of laminated plates—Levy-type solutions

This study is concerned with the static deflections and natural frequencies of isotropic, orthotropic/laminated composite plates using a Levy-type solution. Mindlin plate theory is applied in conjunction with the state-space concept to find such solutions. A state-space formulation of such plates is composed of variables having physical meanings, such as moments, shear forces, displacements and rotations. The influences of aspect ratio, ratio, fiber orientation angle, laminate-layer arrangement and ratio of moduli have been investigated. Some numerical results from the present analyses are compared with published results and good agreement is found.     

压电智能梁的拉伸—弯曲耦合模型

利用力平衡原理,建立了单面粘贴有压电致动器的梁结构的拉伸—弯曲耦合模型,在分析过程中,考虑了梁与致动器之间粘贴层的影响。通过分析可得,粘贴层切应力的分布与致动器端部附近的应变分布有相似的特征,随着粘贴层的切变模量的增加或其厚度的减小,切应力在靠近压电致动器端部区域迅速增大。     

表面粘贴式MEMS应变传感器的应变传递分析

表面粘贴式MEMS应变传感器已被广泛运用于航空航天、汽车工业及土木工程等领域的应变测量和监测中。但由于粘接层的影响,结构的应变并不能全部准确、有效地传递到MEMS应变传感器上,造成传感器的测量值与结构的真实应变之间存在一定误差。为了分析表面粘贴式MEMS应变传感器的应变传递机理,基于剪滞理论建立了MEMS应变传感器的力学分析模型,推导出基体和MEMS应变传感器基底上的应变分布、粘接层中的剪力分布及表征MEMS应变传感器应变传递效果的应变传递率,并与有限元数值模拟结果进行了比较。特别地,具体分析了粘接层及MEMS应变传感器基底的几何参数和物理特性参数对应变传递率的影响。结果表明,金属类粘接材料的应变传递率明显高于有机胶的应变传递率,且粘接层厚度越薄,应变传递效果越好。此外,在制造MEMS应变传感器时,采用厚度较薄的Si或Si C基底能保证较高的应变传递率。     

短纤维增强金属基复合材料界面微塑性变形区的研究

建立了包括金属基复合材料增强体短纤维体积比、长径比、热残余应力、外载作用及短纤维相互扰动应力等的微塑性变形区细观力学模型,分析了外载、热残余应力、短纤维长径比等对微塑性变形区尺寸范围的影响,并结合不同短纤维长径比的复合材料微屈服试验,分析了材料微塑性变形区与微屈服强度的关系。结果表明,材料微屈服强度受微塑性变形区的尺寸范围、位错密度等多种因素的综合影响。     

Hygrothermal effects on the postbuckling of shear deformable laminated plates

The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.     

高长径比粉末冶金零件成形过程的数值模拟

针对粉末冶金法生产高长径比产品尺寸变形大和产品精度低等问题,提出分段成形控制工艺。通过ABAQUS进行数值分析,采用更新的Lagrange方式和大变形弹塑性理论从Mises应力、节点位移、径向最远端密度分布方面进行对比,结果表明,该方法可有效提高密度分布均匀性,显著减小零件双向成形腰部尺寸偏小问题。与现有高长径比产品生产工艺进行对比,节省原材料并简化后续加工工艺。