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.     

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.     

Deformation and Damaging of Composites with Transversally-isotropic Components under Compressive Loading

In the present paper, the problem of deformation and damage of composites with a porous isotropic matrix and transversally-isotropic unidirectional fibers under compressive loading is considered when microdamages are accumulated in the fiber. Fractured micro-volumes are modelled by a system of randomly distributed quasi spherical pores. The Shleicher-Nadai fracture criterion is used as a condition for the origin of micro-pores (micro-damage) based on the assumption of a rigid material. The limit value of the strength of the material is assumed as a stochastic function of coordinates. By using a numerical procedure, the solution of the above problem is found. The nonlinear stress-strain diagrams for a transversally-isotropic composite are obtained for the case of uniaxial compression-tension along the fibers. The nonlinearity of the deformations of the composite is caused by accumulation of micro-damages in the matrix. The influence of the physical-mechanical properties of materials, of the volume concentration, of the porosity of components, of the geometrical parameters of the structure, and of the character of the scatter of the strength in the material on the micro-damage of the material and, as a consequence, the influence on the macro-stress-macro-strain diagram is analyzed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of the deformation properties of a polymeric composite with a granular-fibrous filler

Conclusion A variant of calculation of the characteristics of the deformation properties of a hybrid composite containing a complex disperse filler in the form of granular particles and short fibers was proposed. The effect of aggregation of the granular filler, the statistical distributions of the fibers by lengths and orientation in the material, and the anisotropy of the fibers are taken into consideration in the calculation. The statistical distribution of the orientation of the fibers is given by a function proportional to the distance from the center to the surface of a triaxial ellipsoid in the corresponding direction. The uniform random distribution of the fibers in bulk and in the plane is a special case of this distribution. The results of the analysis of the effect of the parameters of the statistical distributions of the length and orientation of short fibers on the elasticity characteristics of a composite are reported. The dependence of the creep of the composite on the ratio of the concentration of the components of the complex filler was determined, and the efficiency of partial replacement of a granular filler by a short-fiber filler to inhibit creep of the composite was demonstrated. The possibilities of predicting the long-term creep were experimentally confirmed on the example of LDPE filled with ground limestone and short glass fibers.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 898–909, September–October, 1987.     

Analysis of Elastomeric Composites Based on Fiber Systems. 4. 3D Composites

The elastic properties of 3D elastomeric composite materials under large deformations are considered. The investigation is based on the structural macroscopic theory of stiff and soft composites. The results of micro- and macromechanical analyses of composite materials with compressible and poorly compressible matrices are presented. The character of interaction between the fibers of various reinforcing systems in these matrices is revealed. The deformation characteristics of the composites in tension and shear are presented as functions of their orientation and loading parameters. The evolution of the configuration of a composite material with a compressible matrix during loading is traced.     

Strength and deformability of reinforced polymers in tension normal to the fibers

The strength and deformability of reinforced polymers in tension across the fibers is investigated. It is assumed that the polymer deforms as an ideal elastoplastic body. Relations are obtained for the nature of the deformation of the polymer between the fibers and the strength and deformability of the composite with allowance for the structural distribution of the components. Theoretical stress-strain diagrams are presented for composites with different reinforcement densities and resin elasticities. The theoretical values of the strength and deformation of reinforced polymers with the load applied across the fibers are compared with the results of experiments on model specimens of epoxy-Thiokol polymers.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 682–687, July–August, 1970.     

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.     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.     

Evolution of the Fiber Density in Biological Tissues

An important challenge in the field of biomechanics is to understand and to model the properties of fibrous tissues. We consider a matrix-fiber composite for which the matrix microstructure and its mechanical properties are taken to be constant. The initial fiber distribution is assumed to be unstructured and the mechanical properties of the fibers evolve during deformation. Further we assume that the fiber creation rate is constant while the fiber degeneration is stretch-dependent. In particular, this study investigates the change of the fiber orientation density when a sudden simple shear is applied to the material. The fiber orientation density depends on the current deformation, the history of the deformation, and the deformation state of the fibers at the time of their creation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Realization of the mechanical properties of fibers in high-modulus polymer composites

The effect of scatter in the strength and deformation properties of the high-modulus fibers, the degree of twist, and the presence of pores in the polymeric matrix on the degree of realization of the potential possibilities of these fibers in composite materials is briefly considered.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1123–1125, November–December, 1972.     

Micromechanical Analysis of Inelastic Deformation of Unidirectional Fibrous Composites under Multiaxial and Shear Loadings

An algorithm is proposed for numerically solving nonlinear 3D problems of micromechanics of a unidirectionally reinforced composite with a regular structure. For the matrix, equations of the deformation theory of plasticity and relations of reduced rigidity in its failure zones are used, whereas the fibers are elastic and indestructible. According to the method of local approximation, fields of microstresses and microstrains are determined in a structural fragment containing nine periodic cells. Boundary conditions of the fragment correspond to an arbitrary combination of longitudinal, transverse, and shear microstresses occurring in the central part of the fragment. The solution to the nonlinear 3D problem is sought by the method of superposition with an iterational refinement based on the successive solution of an antiplane problem and a problem on a generalized plain strain state of the structural segment. Special features of the iteration procedure are considered. The calculated deformation diagrams and ultimate strengths of a unidirectional glass-epoxy composite are presented for several loading trajectories.     

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.     

Deformation of composites with arbitrarily oriented orthotropic fibers under matrix microdamages

In the present work, a model of nonlinear deformation of stochastic composites under microdamaging is developed for the case of a composite with orthotropic inclusions, when microdefects are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by triaxial arbitrarily oriented ellipsoidal inclusions with orthotropic symmetry of the elastic properties. It is assumed that the process of loading leads to accumulation of damage in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic modules in the case of orthotropic components are taken as basic relations. The fracture criterion is specified as the limiting value of the intensity of average shear stresses acting in the intact part of the material. On the basis of the analytic and numerical approach, we propose an algorithm for the determination of nonlinear deformation properties of the investigated material. The nonlinearity of composite deformations is caused by the finiteness of deformations. By using the numerical solution, the nonlinear stress–strain diagrams are predicted and discussed for an orthotropic composite material for various cases of orientation of inclusions in the matrix.     

Calculation of the Ultimate State of Reinforced Plastics and Unoriented Polymers in Asymmetric High-Cycle Tension–Compression

The fatigue failure of reinforced plastics and unoriented polymers under a joint action of static and high-cycle loadings is considered. The fatigue failure strength is estimated from stress range diagrams with a static tensile component. The models of ultimate state are constructed based on the hypothesis of existence of a unified ultimate diagram invariant with respect to the number of cycles to failure. The unified diagram is given by a transcendental power function whose exponent characterizes the sensitivity of the material to the stress-cycle asymmetry. The models of ultimate state make it possible to span practically all forms of ultimate diagrams of composite and polymer materials, including concave, rectilinear, S-shaped, and convex ones.     

Effect of stress ratio on the fatigue strength of organic plastics

Conclusions Experimental fatigue curves of a unidirectional organic plastic are obtained for a number of asymmetry factors and diagrams of the limiting cycle stresses are constructed for a load in the direction of the fibers and across the fibers, and for in-plane shear of a layer. The simplest methods of approximating the calculated diagrams are tested. It is shown that the method of layer-by-layer analysis of fatigue failure makes it possible to construct limiting-stress diagrams for a laminar oblique-ply composite with an accuracy acceptable for engineering calculations, proceeding from the same analysis as for an individual layer.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 421–429, May–June, 1991.     

Modelling the material behaviour of magnetorheological fluids under shear deformation

In recent years the interest in materials with specific adjustable properties has increased due to higher requirements on the material performance. Here a smart composite material is to be developed, whose stiffness can be varied subjected to a magnetic field. To realise this aim a magnetorheological fluid (MRF) embedded in a polymeric matrix material is considered. To model the material behaviour of the composite a homogenisation method will be applied. Amongst others this requires the knowledge of the multiaxial material behaviour of each constituent. The modelling of the material behaviour of MRF under shear deformation, which is the aim of this work, represents the first step in this process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deformation of orthotropic composites with unidirectional ellipsoidal inclusions under matrix microdamages

In the present paper, a model of deformation of stochastic composites under microdamaging is developed for the case of orthotropic composite, when the microdamages are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by three-axial ellipsoidal inclusions with orthotropic symmetry of elastic properties. It is assumed that the loading process leads to accumulation of damages in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a composite with orthotropic components are taken as the 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. Based on the analytical and numerical approach, an algorithm for the determination of nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the matrix. Using the numerical solution, nonlinear stress-strain diagrams for the orthotropic composite in the case of biaxial extension are obtained. Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 121–130, January–March, 2008.     

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.     

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.     

Calculation and Experimental Study of a Two-Way Reinforced Rubber-Cord Composite in Tension

A rubber-cord composite, reinforced in two directions with fibers of polyamide cord, under large tensile deformations is investigated based on calculations of a rubber-cord composite material and on tensile tests of specimens made of the casing of a diagonal truck tire. A method of the experimental tensile testing of rubber-cord composite specimens is described. The calculations are based on the carcass theory of composite materials. The calculated and experimental parameters of the macroscopic strains of the rubber tire cord and of its structure in a deformed configuration are given. The manifestation of edge effects in relation to the reinforcement angle is described.