Influence of random bridging on the elastic and elastoplastic properties of fiber-reinforced composites

Summary The overall elastic moduli and elastoplastic stress-strain relations of a fiber-reinforced composite containing either aligned or randomly oriented spheroidal voids are derived explicitly. The results are given in terms of the void shape and concentration, and for the elastic moduli the void shape is further pushed to the limit for cracked bodies. The present theory also corresponds to the condition of random bridging, with a longitudinal Young's modulus and axial shear modulus lying between those of full bridging and no bridging. Numerical results further indicate that both elastic and elastoplastic strength of the fiber-reinforced composite can be significantly weakened by the presence of both types of distribution, but the extent of stiffness or strength reduction is highly dependent upon the void shape and loading direction.     

Hybrid effective medium approximations for random elastic composites

Several popular effective medium approximations for elastic constants of random composites are reformulated in terms of a pair of canonical functions and their transform variables. This choice of reformulation enables easier comparisons of the results of all these methods with rigorous bounds. Furthermore, insight into the various methods gained by taking this point of view suggests a number of new effective medium approximations that, in some cases, are natural variants and/or combinations (i.e., hybrids) of the existing ones, and in other cases are new ones based in part on the bounds themselves. Numerical comparisons are given for several standard inclusion models — including spherical, needle, and penny-shaped inclusions — as well as the penetrable sphere model. Of the various alternatives considered, a new method called the split-step differential (SSD) scheme is one of the more useful ones, as it simplifies the differential scheme by replacing half of this scheme’s integration routines with a simple update formula for the bulk modulus.     

Electrical and elastic properties of conductor-polymer composites

Several series of conductor-polymer composites were prepared from metal, graphite and conducting ceramics as filler materials, and epoxy, silicone rubber, polyethylene and polypropylene as polymer matrix. Their percolation curves, pressure dependence of resistivity, and Young's modulus were examined for applications such as a pressure sensor.     

Modeling elastic properties and volume change in dental composites

A modeling approach was applied to study elastic properties and volume change in dental composites. Mechanics modeling results were compared with experimental data in model materials of known composition where the filler content was varied. Composite behavior was predicted based on polymer and filler properties in order to improve basic understanding. Model predictions agree well with data. The models were used to discuss effects of resin properties, filler volume fraction and microstructure (particle shape and filler size distribution).     

Alternating-current electrical properties of random metal-insulator composites

The complex a.c. impedance of three different random metal-insulator composites near their percolation threshold has been studied. These three metal-insulator systems include different shapes of nickel particles (filamentary and nodular shapes) in a matrix of polypropylene and silver particles in the matrix of potassium chloride. By using different metal-insulator structures and phases it is possible to elucidate the effect of different metal particle shapes and types of insulator phase on the electrical properties of these composites near their percolation threshold. Electrical properties, including d.c. conductivity, a.c. conductance, capacitance and dielectric loss tangent, of these metal-insulator composites as a function of metal volume fraction and frequency (5 Hz to 13 MHz) are presented. The results are correlated with structural characterization of these composites and are used to examine the applicability of different electrical transport models on these composite materials. The effect of different metal particle shapes on the percolation threshold and the power-law dependent percolation phenomenon is also discussed.     

Anomalies in the elastic and inelastic properties of ferromagnet-ferroelectric composites

We have studied the elastic and inelastic properties of composite materials of the Co _x (PZT)_{1 − x} system (x = 0.23–0.79) possessing a nonequilibrium nanogranular structure with an average grain size of ∼3 nm. The results of mechanical tests performed in a temperature range of 300–900 K revealed a significant increase in the level of mechanical losses (Q ⁻¹) above 750 K, which is caused by the thermoactivated migration of point defects. An additional heat treatment leads to grain coarsening and the appearance of a ferroelectric state in the dielectric matrix. The temperature dependences of Q ⁻¹ in annealed samples exhibit two maxima, one of which is due to the interaction of domain boundaries with lattice defects and the other is related to the motion of interfaces in the region of the ferroelectric phase transition.     

Jump conditions and boundary conditions for a multi-continuum theory for composite elastic materials

Summary The jump conditions for mass, momentum and energy across a propagating singularity surface are derived for a theory of mixtures developed for application to bonded composite materials. The jump conditions provide equations necessary for the study of shock and acceleration waves, and are also used to deduce the boundary conditions for the theory.

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Sprung- und Randbedingungen einer Kontinuumstheorie elastischer Verbundwerkstoffe

Zusammenfassung Die Sprungbedingungen für Masse, Impuls und Energie an einer sich ausbreitenden Singularitätenfläche einer, zur Anwendung auf Verbundwerkstoffen entwickelten Theorie von Gemischen werden abgeleitet. Die Sprungbedingungen liefern zur Untersuchung von Stoß und Beschleunigungswellen benötigte Gleichungen, und sie werden zur Herleitung der Randbedingungen verwendet.

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With 3 Figures     

Analysis of the effects of rigid and elastic boundary conditions in the elastic-plastic finite element analysis of rolling contact

The effects of boundary conditions and mesh refinement of finite element models of elasto-plastic 2-dimensional pure rolling contact are examined. The pure rolling of a cylinder is simulated by incrementally translating a semi-elliptical Hertzian pressure distribution over a finite element model of a semi-infinite half space. The half space is treated as an elastic-linear-kinematic-hardening-plastic (ELKP) material. The calculations evaluate the effects of rigid and elastic boundary conditions and two degrees of mesh refinement on the steady state residual stresses, the continuing cyclic plasticity, and the residual displacements. The results show that the boundary conditions influence the circumferential residual stresses and residual displacements, while they do not affect the axial residual stresses and the continuing cyclic plasticity. Careful choice of mesh refinement is shown to improve results and decrease computation time.List of symbols E elastic modulus - G shear modulus - _K kinematic tensile yield stress: - k _K kinematic shear yield strength - M plastic modulus - P normal contact load per unit length - p _o peak pressure - N number of cycles - w semi-contact width (macrocontact) - w semi-contact width (microcontact) - cyclic equivalent strain amplitude - _x circumferential stress - _z axial stress - _x ^R circumferential residual stress - _z ^R axial residual stress     

Defects in ceramic matrix composites and their impact on elastic properties

Defects created during the manufacture of an oxide/oxide and two non-oxide (SiC/SiNC and MI SiC/SiC) ceramic matrix composites (CMCs) were categorized as follows: (1) Intra-yarn defects such as dry fibers, (2) Inter-yarn defects such as those at crossover points, matrix voids, shrinkage cracks and interlaminar separation, and (3) Architectural defects such as layer misalignment. Their impact on elastic properties was analytically investigated using a stiffness averaging approach considering the defects to have volumetric and directional influences. In-plane tensile and shear moduli as well as the through-thickness compressive modulus were experimentally evaluated. Results of analytical model were around 7% on average from the mean value of the experimental data. It was observed that interlaminar separation drastically reduced the through-thickness modulus by about 63% for the SiC/SiNC, 40% for the MI SiC/SiC and around 32% for the oxide/oxide composites. Shrinkage cracks in oxide/oxide composite reduced the in-plane tensile and shear moduli by 14% and 8.8%, respectively.     

Micromorphic effects in a modelling of periodic multilayered elastic composites

The paper deals with the problems of modelling of multilayered periodic composites. The proposed models take into account certain micromorphic effects resulting from the periodic structure of the body. The governing equations describing motions and stresses of the nonhomogeneous elastic materials with microperiodic structure in the nonlinear as well as linear cases have been derived. As an example the time-harmonic vibrations of laminated medium consisting of alternating layers of two homogeneous, isotropic, linear-elastic materials have been discussed.     

The decomposed form and boundary conditions of elastic beams with free faces

Summary From the decomposition theorem of elastic beams, two classes of exact stress states are investigated for the equations of three dimensional elasticity governing elastic beams in bending deformations with free faces. One of these is the analogue of the Levy solution for elastic plates and is designated as the interior state. The other complementary class corresponds to a decaying state and is designated as the Papkovich-Fadle state. The appropriate boundary conditions have been established recently for the prescribed data at the end edge of beams to induce only an exponentially decaying elastostatic state. The present paper describes how these conditions may be used to determine the boundary conditions of these two states. The decomposition theorem of beams effectively allows us to split the prescribed edge-data correctly into two parts, one for the interior solution components and the other for the decaying solution components. An analytical solution of the decaying state is formulated to verify the validity of our boundary conditions. The results in turn show that the necessary conditions for the Papkovich-Fadle state are also sufficient conditions. The boundary conditions obtained for the interior state show that the interior solution determined by these conditions is the correct solution in the beam interior up to exponentially small terms. Moreover, with the separate consideration of the interior and decaying solution components, a relatively simple analytical solution is often practical and desirable, and the numerical computation process is essentially simplified. As an illustrative example, the present results are applied to the end-loaded cantilever beam.     

Effective elastic, piezoelectric and dielectric properties of braided fabric composites

Composites based upon 3D textile preforms have found broad structural application. This paper presents an analytical methodology for functional composites using piezoceramic fibers in a 3D braided preform. The effective elastic, piezoelectric and dielectric properties of 2-step braided composites with a polymeric matrix have been investigated. In the analytical approach, the effective properties of the braider and axial yarns of the unit cells are determined first using a 3D connectivity model. Then, the effective properties of the 2-step braided composite are predicted using an averaging technique. Results of a numerical example illustrating the variation of elastic, piezoelectric and dielectric constants with the braider yarn angle are provided. Textile preforming technique in general offers the potential of near net shape forming and 3D fiber placement. The present work provides the analytical basis for 3D piezoceramic textile composites.     

whole-field assessment of the effects of boundary conditions on the strain field in off-axis tensile testing of unidirectional composites

The objective of this paper is to present an experimental assessment of the effects of boundary conditions on the strain field in 10° off-axis tensile tests on unidirectional carbon/epoxy composites. It is shown experimentally by using a whole-field phase stepped grid technique that oblique tabbing of off-axis coupons results in a homogeneous strain field over the whole specimen, thus preventing premature failure near the tabs. A numerical sensitivity study reveals that the oblique angle is not very sensitive to the elastic moduli values. Therefore only estimates of the moduli are needed to derive the oblique angle. It is also shown by finite-element analysis that a 3° error on the oblique angle is acceptable in terms of stress concentrations near the tabs, but that a 7° error leads to significant stress concentrations for this material.     

Influence of interfacial microcracks on the elastic properties of composites

A model is established to quantify the influence of interfacial microcracks on the elastic properties of a particulate composite using a combination of theoretical and finite element analysis. A unique way to construct physical models which could accommodate both crack size and crack density is proposed. Based on energy principles, the influence of a dilute concentration of interfacial microcracks is first studied. The case of a finite concentration of microcracks is solved subsequently by combining the dilute concentration solutions and the differential scheme. Both cases agreed well with existing composite theories for the limiting condition of complete decohesion. The final model predicts the effective elastic properties as functions of both crack size and microcrack density.     

Combining self-consistent and numerical methods for the calculation of elastic fields and effective properties of 3D-matrix composites with periodic and random microstructures

The work is devoted to the calculation of static elastic fields in 3D-composite materials consisting of a homogeneous host medium (matrix) and an array of isolated heterogeneous inclusions. A self-consistent effective field method allows reducing this problem to the problem for a typical cell of the composite that contains a finite number of the inclusions. The volume integral equations for strain and stress fields in a heterogeneous medium are used. Discretization of these equations is performed by the radial Gaussian functions centered at a system of approximating nodes. Such functions allow calculating the elements of the matrix of the discretized problem in explicit analytical form. For a regular grid of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and matrix-vector products with such matrices may be calculated by the fast fourier transform technique. The latter accelerates significantly the iterative procedure. First, the method is applied to the calculation of elastic fields in a homogeneous medium with a spherical heterogeneous inclusion and then, to composites with periodic and random sets of spherical inclusions. Simple cubic and FCC lattices of the inclusions which material is stiffer or softer than the material of the matrix are considered. The calculations are performed for cells that contain various numbers of the inclusions, and the predicted effective constants of the composites are compared with the numerical solutions of other authors. Finally, a composite material with a random set of spherical inclusions is considered. It is shown that the consideration of a composite cell that contains a dozen of randomly distributed inclusions allows predicting the composite effective elastic constants with sufficient accuracy.     

Time‐dependent absorbing boundary conditions for elastic wave propagation

This paper develops a finite element scheme to generate the spatial‐ and time‐dependent absorbing boundary conditions for unbounded elastic‐wave problems. This scheme first calculates the spatial‐ and time‐dependent wave speed over the cosine of the direction angle using the Higdon's one‐way first‐order boundary operator, and then this operator is used again along the absorbing boundary in order to simulate the behaviour of unbounded problems. Different from other methods, the estimation of the wave speed and directions is not necessary in this method, since the wave speed over the cosine of the direction angle is calculated automatically. Two‐ and three‐dimensional numerical simulations indicate that the accuracy of this scheme is acceptable if the finite element analysis is appropriately arranged. Moreover, only the displacements along absorbing boundary nodes need to be set in this method, so the standard finite element method can still be used. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑纤维随机分布的复合材料热残余应力分析及其对横向力学性能的影响

建立了考虑纤维随机分布并包含界面的复合材料微观力学数值模型,模拟玻璃纤维/环氧复合材料固化过程中的热残余应力。通过与纤维周期性分布模型的计算结果进行对比,发现纤维分布形式会对复合材料的热残余应力产生重要影响,纤维随机分布情况下的最大热残余应力明显大于纤维周期性分布的情况下。研究了含热残余应力的复合材料在横向拉伸与压缩载荷下的损伤和破坏过程,结果表明:热残余应力的存在显著影响了复合材料的损伤起始位置和扩展路径,削弱了复合材料的横向拉伸和压缩强度。在横向拉伸载荷下,考虑热残余应力后,复合材料的强度有所下降,断裂应变显著降低;在横向压缩载荷下,考虑热残余应力后,复合材料的强度略有下降,但失效应变基本保持不变。由于热残余应力的影响,复合材料的横向拉伸和压缩强度分别下降了10.5%和5.2%。      

任意边界条件弹性杆结构扭转振动特性分析

采用改进傅里叶级数方法建立了任意边界条件弹性杆扭转振动特性预报模型。针对传统傅里叶级数在扭振边界处存在的位移导数不连续问题,通过改进傅里叶级数的方法改善解的收敛性和准确性。弹性杆结构扭振微分方程与任意边界条件方程进行联合求解,得到弹性杆扭振问题的特征矩阵方程。数值算例分析结果充分验证了本文模型的可行性与正确性。