Nonlinear deformation of Three-Component Composites

The model of nonlinear deformation of stochastic composites under microdamaging is developed for the case of threecomponent composite, when the microdamages are accumulated in the matrix. The composite is treated as isotropic matrix strengthened by two different types of spheroidal inclusions with transversally-isotropic symmetry of elastic properties. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic modules for the case of transversally-isotropic components are taken as basic relations. The fracture criterion is assumed to be given as the limit value of the intensity of average shear stresses occurring in the undamaged part of the material. The algorithm for determination of nonlinear deformative properties of such a material is constructed. The nonlinear stress-strain diagrams for three-component concrete for the case of uniaxial tension are obtained. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear deformation properties of materials with stochastically distributed anisotropic inclusions

In the present contribution, the problem of non-linear deformation of materials with stochastically distributed anisotropic inclusions is considered on the basis of the methods of mechanics of stochastically non-homogeneous media. The homogenization model of materials of stochastic structure with physically non-linear components is developed for the case of a matrix which is strengthened by unidirectional ellipsoidal inclusions. It is assumed that the matrix is isotropic, deforms non-linearly; inclusions are linear-elastic and have transversally-isotropic symmetry of physical and mechanical properties. Stochastic differential equations of physically non-linear elasticity theory form the underlying equations. Transformation of these equations into integral equations by using the Green's function and application of the method of conditional moments allow us to reduce the problem to a system of non-linear algebraic equations. This system of non-linear algebraic equations is solved by the Newton-Raphson method. On the analytical as well as the numerical basis, the algorithm for determination of the non-linear effective characteristics of such a material is introduced. The non-linear behavior of such a material is caused by the non-linear matrix deformations. On the basis of the numerical solution, the dependences of homogenized Poisson's coefficients on macro-strains and the non-linear stress-strain diagrams for a material with randomly distributed unidirectional ellipsoidal pores are predicted and discussed for different volume fractions of pores. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of the method of conditional moments to investigating the deformation properties of orthotropic composites with fiber microdamages

A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distributed quasi-spherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a fibrous composite with orthotropic components are used as the fundamental relations. The fracture criterion is given as a limit value of the intensity of average shear stresses occurring in the undamaged part of the material, which is assumed to be a random function of coordinates and is described by the Weibull distribution. Based on an analytical and numerical approach, the algorithm for determining the nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the fibers. By using a numerical solution, the nonlinear stress–strain diagrams for an orthotropic composite in uniaxial tension are obtained. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 17–30, January–February, 2009.     

Method suited for constructing deformation diagrams of composite materials on the basis of the statistical distribution of the strength of the reinforcing fibers

Starting from an analysis of the statistical accumulation of the defects during rupturing of the separate fibers in a composite material, a theoretical method suited for constructing deformation diagrams of composite materials and based on averaging of the stresses in the defect volumes of the material is proposed. The effect of two statistical distribution (Waybul's and uniform) laws of the strength of the original reinforcing fibers on the shape of the deformation diagrams of composite materials is analyzed.     

Mathematical simulation of failure processes of composite materials reinforced with brittle fibers

Conclusions 1. It is concluded on the basis of an analysis of experimental data and also from theoretical investigations with respect to stress redistribution upon the breaking of fibers that the successive breaking of a number of fibers, caused by the overload from the breaking of individual fibers, is one of the principal mechanisms according to which the complete failure of a material reinforced with brittle fibers takes place.2. A discrete model of a composite material has been worked out. A random fiber strength distribution over the surfaces of the cross sections of the composite material is produced on the computer by the application of Monte Carlo methods.3. A program was written for the computer which simulates the testing of composite materials, permitting the investigation of the statistical accumulation of damage in failure processes as well as the avalanchetype processes of the complete failure of a material.4. The effect of the statistical distribution of the strength of the reinforcing fibers, the ratio of properties, and the volume fractions of composites on the failure processes of composite materials is investigated. Deformation diagrams of a D-16 aluminum alloy-boron fiber composite material, constructed on the basis of an anlysis of the simulated process of fiber breaking in a composite, agree well with the experimental relations.5. The opinion is expressed that the development of cybernetic simulation of failure processes will permit giving an answer to a number of actual questions in the study of materials and the mechanics of failure.Baikov Institute of Metallurgy, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 800–808, September–October, 1976.     

On Stability of a Thin‐Walled Shaft with Active Piezoelectric Fibers

The paper is concerned with the problem of active stabilisation of a rotating flexible shaft made of a composite material containing piezoelectric fibers being controllable by the applied electric field. Rotating shafts exhibit fluttertype instability while exceeding the critical angular velocity. The factor responsible for the loss of stability is internal friction present in the material of the shaft. In the case of a composite structure the internal friction is increased in comparison with steel shafts, and so is the susceptibility of the laminated shaft to self‐excitation. In the paper a method of stabilisation, i.e. shifting the critical threshold towards greater rotation speeds, possibly outside the operating range, is presented. The method is based on incorporation of piezoceramic fibers embedded into the host structure of the shaft. Such integral materials, reflecting the concept of a polymer matrix reinforced with active fibers, are known as Piezoelectric Fiber Composites (PFCs). The carried out examinations have proved that the method is efficient, however limited. It is shown that the critical rotation speed can be increased by several percents, but only within a certain range of structural parameters of the considered system.     

Comparison of Mechanical Properties and Effects in Micro- and Nanocomposites with Carbon Fillers (Carbon Microfibers,Graphite Microwhiskers,and Carbon Nanotubes)

The mechanical properties and effects in fibrous composite materials are compared. The materials are based on the same matrix (EPON-828 epoxy resin) and differ in the type of fibers: Thornel-300 carbon microfibers, graphite microwhiskers, carbon zigzag nanotubes, and carbon chiral nanotubes. Two material models are considered: a model of elastic medium (macrolevel model) and a model of elastic mixture (micro-nanolevel model). Mechanical constants of 40 materials (4 types + 10 modifications) are calculated and compared. The theoretical ultimate compression strength along the fibers is discussed. The effects accompanying the propagation of longitudinal waves in the fiber direction are investigated.     

Effect of surface treatment of carbon fibers on the strength properties of carbon fiber plastics

Conclusions The strength characteristics of composites based on carbon fibers having a coating of silicon carbide are in direct dependence on the coating thickness and on the porosity, which makes it possible to assume the possibility of increasing the degree of realization of the strength characteristics of fibers having a coating in a composite by increasing the degree of impregnation of the carbon cord with the binder. The latter finds confirmation also in the fact that at a small coating thickness on the carbon fiber (of the order of 5 nm) the porosity of the composite obtained is equal to the porosity of the material based on the carbon fiber without coating. Moreover, as is evident from Fig. 3c, the casing of silicon carbide does not form a continuous coatting over the whole perimeter of the cord. The presence of these prerequisites, and also the high resistance of carbon fibers having a silicon carbide coating to oxidation [9], open up wide prospects for creating new composite materials based on them.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 603–606, July–August, 1979.     

Computational modeling of shape memory fibers in conforming and non-conforming compound structures

In this work a material model for shape memory alloy (SMA) fibers is presented. A constitutive model is provided which aims for computational use. The presented model incorporates all relevant material nonlinear phenomena. It takes pseudoplasticity into account as well as pseudoelasticity and further the shape memory effect (SME). The constrained SME (CSME) and the two-way SME are covered by the presented material model. The constitutive model is implemented in a one-dimensional truss formulation and in a 3D-rebar element. Both formulations are used to model fiber composite structures. Those are described by the use of a non-conforming and a conforming mesh on the mesoscale. The numerical examples show the capability of the formulation. Different meshing strategies for the fiber–matrix compound are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure and properties of ceramic composites based on ZrO2

Monodisperse fine powders of high purity obtained by sol-gel method are used for production of high technical data ceramics. The fiber reinforcement is used for hardening of composite materials. It was of interest to study production possibility of reinforced composite material based on ZrO₂ obtained by sol-gel method with filler from fibers of partially stabilized zirconia. ZrO₂ powders were obtained by precipitation of its hydrated gel from aqueous zirconium oxychloride solution by ammonium hydroxide followed by thermal treatment. For composite reinforcement ceramic partially stabilized (8 mole Y₂O₃) ZrO₂ fibers 0.16–0.67 mm in length and 5–7 m in diameter were used. Content of the fibers in composite was 20 wt.%. From powders and their mixtures with fibers, the samples were pressed as disks, beams and cylinders, and anneal in air at 1100–1600°C temperature range. The investigation has shown that the fibers of partially stabilized zirconia change the composite structure, increase the content of tetragonal modification that promotes its hardening. Treatment temperature of precursor determines physical chemical properties of compositions with fibers. Their high specific surface and reaction ability provides a workability of forming and sintering processes into strong composite material. The ceramics was increased by 2.5–3 times as strength after fibrous filler introduction into ZrO₂ hydrogel matrix.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Presented at the Ninth International conference on the Mechanics of Composite Materials (Riga, October 1995). Institute of General and Inorganic Chemistry of the Academy Sciences of the Belarus. Minsk. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 418–427, May–June. 1996.     

Computation of the Coupled Dynamics of Fibers in a Spray

The PUR-fiber-spray molding technology is a manufacturing process which produces polyurethane-based (PUR) composites by spraying the matrix together with reinforcing fibers in a tool form or on a substrate. Thereby chopped fibers are laterally (sidewise) injected in the polyurethane-air spray cone for wetting before the entire composite is spread on the substrate, where it starts curing. To investigate and compute the fiber orientation and density distribution in the final composites manufactured by this process, a new approach simplifying the multiply coupled interaction of the three phases is presented in this paper. Hereby it is presumed that the final position and orientation of a fiber on a substrate results from its dynamics and coupled interactions with air, PUR-droplets and other fibers within the spray cone. Thus, a model of the process is built, that computes the transient behavior of the air-liquid droplets mixture by the CFD code ANSYS Fluent and its influence on the dynamics of the fibers by an extra code called FIDYST. For this multiphase problem two approaches are presented for the droplet-fiber coupling using a concept called “homogenization” of the liquid phase (droplets in the continuous phase). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting ‘nanocomposite’ is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.     

Deformation and strength of hybrid composites reinforced with unidirectional fibers. 1. Numerical models

The hybrid composite consists of n(n > 2) jointly working phases. We define the thermomechanical characteristics and strength of composites by filling and reinforcing materials thermomechanical characteristics and strength basing on the suggestion that thin and strong fibre reinforced composite is quasiuniform, and there is a continuous contact between the filling medium and reinforcing fibers. The development of a mathematical model of the design under consideration has been based on following assumptions: 1) for irreversible processes, the classical thermodynamic postulates are valid, and they are introduced as functions of state of internal energy and entropy; 2) for a solitary volume of materials, internal energy is assumed to be proportional to the volume fraction of the j-th phase v_j; 3) for the material pressure limit conditions just before the essential damage, it is suggested that: a) the whole composite as well as the components are steady, i.e. Drukker's postulate is valid; b) the deformation law associated with the corresponding strength surface is valid, and c) small values of increases in plastic deformation play the leading role. The strength of unidirectionally reinforced hybrid monolayers is predicted by using a linear programming code.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 186–192, March–April, 1995.The studies were carried out with financial support of the International Scientific Fund founded by G. Soros.     

Creep of Heat-Resistant Composites of an Oxide-Fiber/Ni-Matrix Family

A creep model of a composite with a creeping matrix and initially continuous elastic brittle fibers is developed. The model accounts for the fiber fragmentation in the stage of unsteady creep of the composite, which ends with a steady-state creep, where a minimum possible average length of the fiber is achieved. The model makes it possible to analyze the creep rate of the composite in relation to such parameters of its structure as the statistic characteristics of the fiber strength, the creep characteristics of the matrix, and the strength of the fiber-matrix interface, the latter being of fundamental importance. A comparison between the calculation results and the experimental ones obtained on composites with a Ni-matrix and monocrystalline and eutectic oxide fibers as well as on sapphire fiber/TiAl-matrix composites shows that the model is applicable to the computer simulation of the creep behavior of heat-resistant composites and to the optimization of the structure of such composites. By combining the experimental data with calculation results, it is possible to evaluate the heat resistance of composites and the potential of oxide-fiber/Ni-matrix composites. The composite specimens obtained and tested to date reveal their high creep resistance up to a temperature of 1150°C. The maximum operating temperature of the composites can be considerably raised by strengthening the fiber-matrix interface.     

Fracture Model for a Thin Layer of a Fibrous Composite

A model for a flat isolated layer of a unidirectional fibrous composite with a regular structure is constructed to investigate the possible variants of its failure development. An integrodifferential equation for determining the forces in fibers is obtained. Primary attention is focused on examining the failure process after the rupture of one fiber. This causes a drastic redistribution of stresses, which can lead to a failure of adjacent fibers owing to the increased load on them, to an interfacial shear fracture, and to the matrix cracking. It is shown that the development of layer failure is determined by the strength of fibers, the crack resistance of the matrix in axial tension and transverse shear, and also by the adhesion strength of the matrix-fiber interface. The sufficient conditions of applicability of the brittle fracture model are formulated.     

The shear modulus of a composite material with a transversely isotropic matrix and a fibre

A relation is proposed for determining of the shear modulus of a fibrous composite material with a transversely isotropic matrix and a fibre as a function of the elastic constants of the matrix and the fibre as well as the volume fraction of each of them in the composite material. The isotropy planes of the matrix and fibre coincide and are perpendicular to the fibre axis. Two boundary value problems are solved in order to obtain the required relation: the problem of the longitudinal shear of a transversely isotropic solid cylinder that simulates the fibrous composite material and the problem of the combined longitudinal shear of a hollow and solid cylinder that simulate the matrix material and the fibre material respectively. Calculations using the proposed formula are compared with the available experimental data.     

Influence of fiber structure modification on the mechanical properties of flax fiber-epoxy composites

The mechanical characteristics of flax fibers were optimized by using the NaOH treatment process to improve the properties of composite materials. Shrinkage of the fibers during this treatment had a significant effect on the structure and, as a result, on the mechanical properties of the fibers and the composites based on them. Due to the higher mechanical strength and stiffness of flax fibers after NaOH treatment under isometric conditions, the strength and stiffness of composites in general increase. Further, NaOH treatment leads to a rougher surface morphology, as shown, e.g., for jute fibers, compared with the surface of untreated fibers without improved fiber/matrix adhesion.     

Structural macroscopic theory of stiff and soft composites. Invariant description

A structural macroscopic theory of stiff and soft composites, which generalizes the theory in [1] constructed with application of a model of one-dimensional stressed state of reinforcing fibers in the current configuration of a composite is presented. The theory combines the micro- and macromechanics of composite materials. The two trends in the mechanics of composites are based on the idea of a field of macroscopic displacements and the concept of macroscopic stresses of the composite material when changes in the metrics of the matrix and reinforcing fibers in the current state of a composite medium are taken into consideration. The fibers of the reinforcing systems and matrix are analyzed on the basis of a general 3D model of deformation. No limits on the stiffness of the materials of the structural components are imposed. The analysis of the composite medium, on the macromechanical level, includes a definition of macrodisplacement and macrodeformation fields, as well as parametric structural fields in the current configuration. On the micromechanical level, the fields of macroscopic stresses in the medium, together with the fields of microscopic strains and stresses in the structural components, are defined on the basis of information obtained from the analysis of the field of the macroscopic displacements. With the corresponding interpretation of the field of macroscopic displacements, the structural macroscopic theory is applied to composite media with fibrous, laminated, and matrix structures.     

Micromechanical modelling and two-scale simulation of epoxy/glass composites with interphases and interfaces

Composite systems consisting of glass fibres and epoxy matrix with interphases and interfaces will be considered in the modelling approach. The interphase forms the transition zone between the epoxy matrix and the glass fibre. The interface is the layer between the glass fibre and the surrounding interphase. The macroscopic strength of the composite material is intrinsically related to the bond strength of the polymeric/solid interface and the micromechanical characteristics of the three phases (epoxy, glass and interphase). Homogenization is an appropriate methodology to link these two scales to predict the overall physical behaviour of the composite. The nonlinear behaviour of amorphous polymers, cohesive interface elements and the elastic behaviour of glass fibres as part of the considered composite material are presented, as well as a representative example to show the necessity of taking interface influences into account. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the natural Fiber (Maize) Composite material

This work is focused on the compressive behavior in the elastic region of a composite material made out of stalk-based maize fiber and unsaturated polyester resin polymer as matrix with methyl ethyl ketone peroxide as a catalyst and Cobalt Octoate as a promoter [1]. Deformation and fracture behavior are investigated by using Extended Finite Element Method (XFEM). XFEM enables the accurate approximation of solutions with jumps, discontinuities or general high gradients across interfaces between the fibers and the matrix [2], [3]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)