A comparative study of fiber-matrix interactions by using micromechanical models

The purpose of this study is to describe the interfacial interactions in terms of stress distributions on short fibers in fiber-matrix unit-cell models. The fiber and matrix are subjected to tensile loading. The study consists of three main parts. First, fiber-matrix cell segments are modeled using a 3D finite-element analysis (FEA) with ANSYS. Three different finite-element geometrical unit-cell models are generated in order to simulate the Cox analytical model: a fiber-matrix combination, a single fiber, and a single matrix element. The second part contains the results of 3D FE analyses, which are applied to the Cox formulations by using a computer program developed. In the last part, the analytical solutions for distributions of normal and shear stresses are investigated. Cox 2D linear elasticity solutions, together with finite-element ones, are presented in detail in graphs. The interfacial interactions between the fibers and matrix are also discussed considering the relative changes in the distributions of normal and shear stresses. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 505–520, July–August, 2008.     

The influence of imperfections on the creep behavior of woven polymer composites at elevated temperatures

The dynamic behavior of compression molded polymer/woven graphite fiber composites at elevated temperatures is investigated analytically. This is performed with the objective of predicting the initiation of catastrophic failure that may occur after prolonged usage of the material at these temperatures. Special attention is paid to the behavior of the voids present in them where the failure may occur. The polymer matrix is modeled as a 4-parameter model (Maxwell-Voigt combination) (Govindarajan et al., in: Advances in Computer-Aided Engineering, ASME, 1994) while the composite structure is modeled using the fiber undulation model (Ishikawa and Chou, J. Mater. Sci. 17, pp. 3211–3220, 1982). The relation between the polymer properties and the ambient temperature is modeled after Arhenius' relation (Govindarajan et al., 1994; Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1961). The multiple phases in the matrix are taken into account through Eshelby's theory (Proc. Royal Soc. London A 241, pp. 376–396, 1957) and its extension for multiple occurrences of the same phase (Tanden and Weng, Polymer Composites 5, pp. 327–333, 1984; Weng, Internat. J. Eng. Sci. 22 (7), pp. 845–856, 1984) which assumes an ellipsoidal shape for inclusions. The resulting elastic equations are transformed into the time domain using Laplace transformation and the correspondence principle (Govindarajan et al., 1994; Wang and Weng, ASME J. Appl. Mech, 1992). All the voids are considered to be prolate ellipsoids with the 1-axis being the axis of symmetry. The distribution of voids is assumed to be of a Gaussian form with respect to the aspect ratio. The response of the composite under creep condition (constant load) has been simulated. Relations between the applied stress and the stresses in the matrix/void phase are also supplied, so that the influence of the voids may be characterized. The model is then applied to simulate the behavior of an epoxy/woven graphite composite to obtain the numerical results.     

Investigation of the mechanical behavior of two-component granular composites in terms of structural models

A structural model is suggested for elastomers filled with particles of two fractions — with diameters exceeding 10 μm and submicronic ones. In each fraction, the particle diameter varies randomly, but between the fractions, the average particle diameter differs by several orders of magnitude. It is assumed that the small particles, together with the matrix, behave as a homogeneous medium relative to the large ones. By using this model, the mechanical behavior of composites based on elastomers filled with different volume contents of solid particles is investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 191–200, March–April, 2007.     

On a Representative Volume in the Micromechanics of Particulate Composites

A rectangle filled with closely packed spheres of random size and properties is considered as a micromechanical model of a two-phase particulate composite. A numerical simulation is used to determine the effective mechanical properties of the assembly and their scatter as a function of the number of spheres. It is shown that, in a system with relatively small number of particles (up to 300), the scatter of Young's modulus decreases with the system size. However, the rate of the scatter decrease becomes smaller with growing size of the system, so that the convergence to zero most likely takes place at infinity.     

Characterization of the classical domains by Caratheodory volume elements and Eisenman-Kobayashi volume elements

We give a sufficient and necessary condition that a domain is biholomorphic to the classical domain.     

Investigation of the dynamic characteristics of composites

The dynamic characteristics E and G and the damping capacity δ* of polymeric resins and composites based on glass, carbon, and boron fibers have been investigated. It is shown that the mechanical losses are correlated with the modulus of elasticity and the shear modulus of the resin and composites with different types of reinforcement. The vibrational strength of various structural materials is estimated.     

Analysis of elastomeric composites based on fiber-reinforced systems 3. Two-directional composites

Results of investigation of deformation of elastomeric composite materials with a two-directional reinforcement scheme are presented. The study is performed on the basis of a structural macroscopic theory. The matrix of the composites analyzed is of a poorly compressible material. The fibers of both reinforcing systems are simulated as compressible bodies. Dependences of the parameters of tensile and shear strains on the strain values for different geometries of fiber arrangement are obtained.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 479–492, May–June, 1999.     

Constitutive model of ferroelectric composites with a viscoelastic and dielectric relaxation matrix I

Based on micromechanics and Laplace transformation, a constitutive model of ferroelectric composites with a linear elastic and linear dielectric matrix is developed and extended to the ferroelectric composites with a viscoelastic and dielectric relaxation matrix. Thus, a constitutive model for ferroelectric composites with a viscoelastic and dielectric relaxation matrix has been set up Project supported by the National Natural Science Foundation of China (Grant No. 19891180).     

3D modeling of crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites

This work presents a time-domain hypersingular integral equation (TD-HIE) method for modeling 3D crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites (EMTE-CVP-MCs) under extended incremental loads rate through intricate theoretical analysis and numerical simulations. Using Green’s functions, the extended general incremental displacement rate solutions are obtained by time-domain boundary element method. Three-dimensional arbitrary crack growth problem in EMTE-CVP-MCs is reduced to solving a set of TD-HIEs coupled with boundary integral equations, in which the unknown functions are the extended incremental displacement discontinuities gradient. Then, the behavior of the extended incremental displacement discontinuities gradient around the crack front terminating at the interface is analyzed by the time-domain main-part analysis method of TD-HIE. Also, analytical solutions of the extended singular incremental stresses gradient and extended incremental integral near the crack fronts in EMTE-CVP-MCs are provided. In addition, a numerical method of the TD-HIE for a 3D crack subjected to extended incremental loads rate is put forward with the extended incremental displacement discontinuities gradient approximated by the product of time-domain basic density functions and polynomials. Finally, examples are presented to demonstrate the application of the proposed method.     

短纤维复合材料的本征应变边界积分方程计算模型

提出了短纤维复合材料的本征应变边界积分方程计算模型,并采用新发展的边界点法进行了求解．模型依据Eshelby等效夹杂物的概念并借助Eshelby张量,采用迭代方法来计算基体中各种性能短纤维的本征应变,其中所需的Eshelby张量不难通过解析或数值方法获得．由于未知量只出现在边界上,与已有的有限元和边界元模型相比,提出的计算模型可极大地减小异质体问题的求解规模,提高计算效率．通过数值算例计算了代表性体积单元上各种短纤维复合材料的整体弹性性能,验证了计算模型和求解方法的正确性和有效性．     

Bounds and estimates on the effective properties for nonlinear composites

In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle together with the bounds presented by Lukkassen, Persson and Wall in 1995. Moreover, we also present some examples where the bounds are so tight that they may be used as a good estimate of the effective behavior.     

Formation of a transition layer on the fillers of polymer composites

Based on a plane model of composites, the effect of a transition layer on the elastic modulus E_c of the composites is analyzed in the case where, under the action of a load, the transition layer is formed both on the side of matrix and filler. In evaluating E_c, it is assumed that the elastic modulus in the layer grows linearly from the elastic modulus of matrix to that of filler, but pores in the filler are impermeable to matrix macromolecules. Analytic relation ships are found which allow one to determine the volume fractions of the transition layer on the side of matrix and filler if the experimental elastic modulus of the composite is known. These relationships are used to find the magnitude of the layer in epoxy composites with various fillers and to evaluate its effect on the compressive elastic modulus of the composites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 693–700, September–October, 2006.     

Comparative micromechanical analysis of nonelastic behavior of unidirectional plastics with tetragonal and hexagonal structures

A mathematical model for determining the effective elastic properties and describing the processes of inelastic deformation and damage accumulation of unidirectional fiber-reinforced composites with tetragonal and hexagonal structures is developed. A comparative analysis of the effective elastic moduli of glass, boron, organic, and carbon unidirectional plastics shows that, if the fiber volume fraction does not exceed 0.5, the effective elastic properties calculated by the models presented give closely related results. The calculation results for nonlinear fields of deformation and failure are presented and the limiting strength surfaces of fibrous glass plastics with hexagonal and tetragonal structures are obtained for different transverse loading paths. It is found that the structure of a composite affects significantly its strength properties.Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Perm' State Technical University, Perm', Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 455–464, July–August, 2000.     

Optimization of properties of multicomponent isotropic composites

We suggest a method for the calculation of the extremal conductivity of composites under some natural assumptions concerning their microstructure. The method is based on the principle of consecutive assembling of binary mixtures by addition of infinitely small amounts of one of the initial compounds to the already-assembled isotropic composite. This process is assumed to produce an optimal isotropic binary mixture at each step, which is performed by the Hashin-Shtrikman procedure. We are seeking a suitable sequence of compounds to be added to the mixture in order to minimize its resultant conductivity. A solution is given to the corresponding optimization problems for both finite number and infinite number of initial compounds taken in prescribed concentrations. We also describe the microstructure of the optimal composites. The results can be used for the optimal design of elastic and heat-conducting constructions.Dedicated to G. LeitmannThe authors have accepted with pleasure the invitation to participate in the JOTA special issue dedicated to Professor G. Leitmann. The papers by Professor Leitmann are well known in the USSR. They have greatly influenced the formation of the authors' scientific viewpoints. The first author has learned much from Professor Leitmann in the course of his work in translating two books by Professor Leitmann published in the USSR; the second author has also benefited from these translations. Methods of optimization, whose development has been influenced so much by Professor Leitmann's contributions, have penetrated into a number of fields. Here, we apply these methods to a problem in the mechanics of composite materials.     

Constitutive models of ferroelectric composites with a viscoelastic and dielectric relaxation matrix (II)

Experimental analysis of ferroelectric composites with a viscoelastic and dielectric relaxation matrix is carried out, and the electromechanical coupling behavior of the ferroelectric composites is calculated by means of the constitutive model proposed in this paper. Comparisons between the experimental results and the calculations show that the constitutive model can reflect the electromechanical coupling behavior of the ferroelectric composites. The analysis indicates that the effect of viscoelasticity and dielectric relaxation of the matrix on the electromechanical coupling behavior of ferroelectric composites cannot be neglected.     

The metastable behavior of the three-dimensional stochastic Ising model I

The metastable behavior of the stochastic Ising model in a finite three-dimensional torus is studied in the limit as the temperature goes to zero. All metastable states are characterized and a hierarchic structure is found. For a large class of initial states, the logarithmic asymptotics of the hitting time of the states are studied with all spins +l or − 1. Project supported in part by the State Education Commission of China, the National Natural Science Foundation of China, the Tianyuan Foundation and the National 863 Project.