三维多向编织复合材料有效弹性模量的细观计算力学分析

编织复合材料性能预报与材料优化设计研究是纺织复合材料研制开发的重要环节,本文在已建立的三维多向编程复合材料单胞几何模型的基础上,研究建立了含多相介质单元的有限元分析方法,结合实例预报了碳／环氧四向编织复合材料的有效性能并和实验结构进行了对比。     

Theoretical prediction of stiffness and strength of three-dimensional and four-directional braided composites

Based on unit cell model, the 3D 4-directional braided composites can be simplified as unidirectional composites with different local axial coordinate system and the compliance matrix of unidirectional composites can be defined utilizing the bridge model. The total stiffness matrix of braided composites can be obtained by the volume average stiffness of unidirectional composites with different local axial coordinate system and the engineering elastic constants of braided composites were computed further. Based on the iso-strain assumption and the bridge model, the stress distribution of fiber bundle and matrix of different unidirectional composites can be determined and the tensile strength of 3D 4-directional braided composites was predicted by means of the Hoffman＇s failure criterion for the fiber bundle and Mises＇ failure criterion for the matrix.     

树脂基三维编织复合材料粘弹性性能的有限元分析

根据材料的细观结构,采用APDL语言分别建立了纤维束和三维编织复合材料两级单胞的参数化几何模型;推导了Prony级数表示的树脂粘弹性本构方程,对模型进行了组分材料参数设置;对纤维束单胞模型进行扫掠式网格划分,对三维编织复合材料单胞模型进行线-面-体式网格划分;对两级单胞模型均施加合理的边界条件,使单胞边界上的位移满足周期性和连续性。以有限元模型为基础,计算了三维编织复合材料的粘弹性能,并给出了材料粘弹性效应随工艺参数变化的规律。计算结果表明:三维编织复合材料编织方向的粘弹性效应随编织角的增大而增强,随纤维体积比的增大而减弱。该结果与已有实验结论一致。     

Microstructure damage related to deformation properties of grain composites

Mathematical model of micro-heterogeneous medium with voids and shrinkage porosity is considered. Green’s tensor is used to obtain the formulas for macro modules of elasticity. Discrete and continuous probability distributions are used to describe random properties of microstructure elements. Convergence of the method is discussed. Sample calculations are provided.     

On the mechanics of braided composites in tension

An experimental investigation is reported on the uniaxial tensile behaviour of braided tubes, comprising glass fibres in an epoxy matrix. The failure mode switches from fibre fracture to neck propagation when the helix angle, defined as the angle between the fibre direction and the axis of the tube, exceeds about 45°. The observed neck geometry is used to deduce the evolution of deformation and damage within the matrix, and a work calculation is used to estimate the steady state neck propagation stress from a micromechanical model of braid deformation. A failure chart is constructed to show the effect of braid geometry on elastic modulus, yield strength, strain to failure and energy absorption of the braid.     

玄武岩纤维高延性水泥基复合材料的动态力学性能

利用玄武岩纤维和水泥基材料,通过一定配比融合制成了在静态拉伸试验中呈现多缝开裂、应变硬化、极限拉伸应变0.5%以上的玄武岩纤维高延性水泥基复合材料(basalt fiber engineered cementitious composites, BF-ECCs)。用分离式霍普金森压杆(split Hopkinson pressure bar, SHPB)装置对不同玄武岩纤维掺量的水泥基复合材料进行动态压缩和动态劈裂试验。结果表明:(1)在压、拉两种应力状态下,玄武岩纤维对水泥基复合材料的静态强度、动态强度均有增强,且高应变率下玄武岩纤维对抗压强度动态增幅较小,对劈裂强度动态增幅较大;(2) BF-ECC的抗压强度和劈裂强度均随应变率升高而显著提高,两者均可以采用动态增强因子(dynamic increase factor, DIF)反映动态强度的增幅,但劈裂强度的应变率敏感性强于抗压强度;(3)依据试验得到的普通水泥混凝土速率敏感性的CEB-FIP方程(2010)不适用于BF-ECCs。     

Manufacturing of Ti-alloy and Pd-alloy composites with superior thermal and mechanical properties

Pure titanium and titanium alloys have superior heat and corrosion resistance in addition to specific mechanical strength. Their specific gravity is approximately three-fifths of steel. Such thermal and mechanical properties make them useful for aerospace, nuclear and chemical equipment and structural components. The palladium alloys were selected because of their oxidation resistance, ductility, relatively high melting points, and lower cost as compared to gold-based alloys. The Pd---Cu---Co system of alloys, 30Pd---59Cu---10Co---1Si and 30Pd---57Cu---10Co---3Ti are developed in this work. The microstructures and reactions are examined for composites made with Ti---6Al---4V and the Pd alloys. The Ti---6Al---4V/30Pd---59Cu---10Co---1Si composites possessed strengths of 56 to 768 MPa from 293 to 1073 K while those for the Ti---6Al---4V/---30Pd---57Cu---10Co---3Ti composites are 53 to 75 MPa from 293 to 1073 K. Optical microscope and electron microprobe analyzes are used to study the details of the composite microstructure. Reported are also their thermal and mechanical properties.     

Experimental and analytical characterization of multidimensionally braided graphite/epoxy composites

This paper presents results of an investigation of a novel, through-the-thickness fiber-reinforced composite material. The generic name for this composite technology is multidimensional (X-D) braiding. X-D braided composites consist of a net-shaped, densely braided fiber skeleton which is rigidized with a structural epoxy-resin system. This material is an alternative to the conventional laminated composite and has the potential for being more resistant to delamination and matrix cracking. This paper describes results of the mechanical characterization of one graphite fiber system which was braided into panels in which two braid parameters could be investigated. The variables investigated included the effect of edge condition and braid pattern on the tensile, compressive and flexural properties of the braided panels. These properties were obtained in the braid direction only. The cutting of the specimen edges substantially reduced both tensile and flexural strengths and moduli. Of the three braid patterns investigated, 1×1, 3×1, and 1×1×1/2 F, the 3×1 braid pattern showed superior tensile performance, while the 1×1×1/2 F braid pattern exhibited superior flexural properties. The development of an analytical method for modeling the tensile performance of the multidimensionally (X-D) braided composite is also presented. The fiber geometry in X-D braids was modeled based on the braid parameters used in the construction of these composites. By the nature of the symmetry of the resulting braided structure, an analytical model based on classical lamination theory was used to determine the extensional stiffness in the three principal geometric directions of a braided composite. These analytical results are shown to compare favorably with those obtained experimentally. Finally, to further validate the ability of this material to contain damage, multidimensionally braided and conventionally laminated panels were impacted and the resulting damage was nondestructively determined. The multidimensionally braided material was shown to reduce the area of damage caused by impact by a factor of three for the energy levels tested.     

Effect of transverse cracks on the mechanical properties of angle-ply composites laminates

A modified shear lag analysis, taking into account the notion of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in [±θ_n/90_m]_S angle-ply laminated composites. Effects of number of 90° layers and number of ±θ layers on the laminate stiffness have also been studied. The present results represent well the dependence of the degradation of mechanical properties on the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of uncracked outer ±θ layers in the laminate.     

Effective mechanical properties of unidirectional composites in the presence of imperfect interface

In this paper, the equivalent inclusion method is implemented to estimate the effective mechanical properties of unidirectional composites in the presence of an imperfect interface. For this purpose, a representative volume element containing three constituents, a matrix, and interface layer, and a fiber component, is considered. A periodic eigenstrain defined in terms of Fourier series is then employed to homogenize non-dilute multi-phase composites. In order to take into account the interphase imperfection effects on mechanical properties of composites, a stiffness parameter in terms of a matrix and interphase elastic modulus is introduced. Consistency conditions are also modified accordingly in such a way that only the part of the fiber lateral stiffness is to be effective in estimating the equivalent composite mechanical properties. Employing the modified consistency equations together with the energy equivalence relation leads to a set of linear equations that are consequently used to estimate the average values of eigenstrain in non-homogeneous phases. It is shown that for composites with both soft and hard reinforcements, largest stiffness parameter that indicates complete fiber–matrix interfacial debonding causes the same equivalent lateral properties.     

Asymptotic homogenization of three-dimensional thermoelectric composites

Thermoelectric composites are promising for high efficiency energy conversion between thermal flows and electric conduction, though their effective behaviors remain poorly understood due to nonlinear thermoelectric coupling. In this paper, we develop an asymptotic homogenization theory to analyze the effective behavior of three-dimensional (3D) thermoelectric composites, built on the observation that the equations governing microscopic field fluctuations in the composite are actually linear instead of nonlinear after separation of length scales. A set of solutions similar to Green's function method are used to construct the unit cell problem, and appropriate interfacial continuity conditions and boundary conditions are derived. The homogenized governing equations are then developed for thermoelectric composites, and they are further reduced for a special case wherein the heat flow and electric conduction in the composite remains one-dimensional (1D) at macroscopic scale, even though the composite itself is 3D in general. The general homogenization theory is implemented using finite element method, and a key constant in the constructed solutions is determined using the reformulated eigenvalue problem. The algorithm is validated, and is applied for a number of case studies for the effective behavior of thermoelectric composites.     

填充硅橡胶的泡沫铝复合材料的力学性能

用渗流法向开孔泡沫铝-硅合金和泡沫纯铝中充填硅橡胶获得含硅橡胶的泡沫材料, 在材料试验机和SHPB上对含硅橡胶的复合材料进行动态与准静态压缩实验。实验结果表明：含硅橡胶的泡沫复合材料只有弹性段和塑性段两个阶段,具有更高的应变率敏感性,其应力-应变曲线抖动幅度比较大。     

考虑损伤界面的多相复合材料总体平均力学性能的预测

在广义自洽有限元迭代法￣［１］的基础上研究了损伤界面对多相复合材料的总体平均横向力学性能的影响。给出了对于不同体分比和损伤界面性质的典型复合材料的数值结果。数值分析表明损伤界面的厚度及其损伤程度对复合材料总体平均横向平面应变体积模量和剪切模量有显著影响。本文还计算了损伤界面区域的局部应力场。     

Compressive response and failure of braided textile composites: Part 2—computations

In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.     

三维编织复合材料渐进损伤的非线性模型及强度分析

建立了考虑周期性位移边界条件的细观体胞模型,对三维编织复合材料的渐进损伤过程进行数值模拟。采用Eshelby-Mori—Tanaka方法计算含损伤裂纹的材料的剐度矩阵,并将有限元网格尺寸和单元裂纹尺寸引入损伤演化方程,有效地降低了模拟结果对有限元网格的依赖程度。通过计算得到了材料应力应变的非线性关系和失效时的极限强度,并分析了材料的破坏机理。结果表明,大编织角材料的破坏模式主要是基体失效与纤维横向拉剪破坏,模拟计算结果与文献中的实验值吻合较好。     

Compressive response and failure of braided textile composites: Part 1—experiments

Experimental results obtained by examining the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) are reported in this paper. These experiments were motivated by a need to examine the failure of 2DTBC in a state of stress that would be similar to what is experienced by the walls of a tubular member under compressive crush loads. Results obtained from a series of biaxial tests that were conducted with different proportional displacement loading ratio combinations of compression and tension are reported. In all cases, the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite. Full field surface displacement data is acquired concurrently during all biaxial and some uniaxial tests using the technique of digital speckle photography. Digital images of the specimen surface that is illuminated with a He-Ne laser are acquired at discrete time intervals during the loading history using a high-resolution digital camera. These images are stored and analyzed to obtain the incremental inplane surface displacement field, Δu(x,y) and Δv(x,y). From these, the incremental inplane surface strains Δε_x, Δε_y and Δγ_xy are obtained by numerical differentiation. The present paper, which is the first in a two part series, is devoted to the biaxial experimental results pertaining to 2DTBC failure.     

Harmonic waves in three-dimensional elastic composites

For a periodic elastic composite which consists of a matrix and fibers with finite dimensions (i.e. a three-dimensional problem), here are given estimates for eigenfrequencies and eigenfunctions. Calculations are based on a new quotient which has been proposed by Nemat-Nasser. The periodic character of the eigenfrequencies is pointed out, and illustrative examples are given.