Effect of mineral fillers on properties of composite matrix material

The influence of mineral fillers on thermomechanical properties of matrix material of composites is investigated. Different methods to determine elastic properties and thermal expansion coefficients of composite materials have been considered and compared. Injection moulded polyester samples containing varying concentrations of talc filler are tested and properties such as Young 's modulus, thermal expansion coefficients, and volumetric shrinkage during cure are measured. Results obtained by theoretical models and from experiments are compared and discussed.To be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 435–445, July–August, 1995.     

Calculation of characteristics of the elastic and thermophysical properties of a multiphase composite containing composite or hollow spherical inclusions

Conclusion We generalized the self-consistent method of effective media to the case of a four-phase model consisting of a core, a shell, a binder, and the effective medium. We obtained analytic solutions for the elastic characteristics, coefficient of linear expansion, heat capacity, and thermal conductivity of a multiphase composite containing several types of composite (or hollow) spherical inclusions. In the special case of a composite containing inclusions of just one type, the solutions obtained for the bulk modulus of elasticity K, coefficient of linear expansion a, heat capacity c, and thermal conductivity agree (within the framework of the two-stage approach) with the values found using known solutions for a three-phase model [8]. The first stage entails calculation of the effective characteristics of a spherical composite inclusion, while the second stage involves calculating the analogous characteristics for the composite as a whole.The possibilities of the solutions that were found were illustrated in a calculation of the shear modulus of a composite containing spherical hollow inclusions. It was shown that by assuming a nonaxisymmetric Weibull distribution of the parameter (the ratio of the thickness of the wall of a particle to its radius) it is possible to reach better agreement between the calculations and the experimental data in [4] than when calculations are performed using only the mean value of .The solutions obtained here can be used to find optimum combinations of volume fractions of different types of fillers in multiphase composites.The work was sponsored at the University Iberoamericana in 1994 by the Mexican National Council of Science and Technology (CONACYT).Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 512–519, July–August, 1994.     

Thermal expansion of a polymer composite with an aggregating disperse filler

Conclusion The thermal deformation of HDPE with an aggregating disperse filler was experimentally studied in a wide range of temperatures. The effect of the filler on the characteristics of relaxation transitions in HDPE, determined from dilatometric tests, was analyzed. A method of calculating the effective thermal expansion coefficient of a composite with an aggregating filler was proposed. Satisfactory agreement between the calculated and experimental data was obtained. It was shown that the effect of aggregation results in a significant decrease in the thermal expansion coefficient of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 70–77, January–February, 1989.     

Singular approximation of the method of periodic components in statistical mechanics of composite materials

A quasi-periodic model is developed for random structures of composites, when the locations of inclusions are given in terms of random deviations from nodes of an ideal periodic lattice. Solution of the stochastic boundary problem of the theory of elasticity is examined for a quasi-periodic component by the method of periodic components, which is reduced to determination of the field of deviations from the known solution for a corresponding periodic composite. The solution is presented for the tensor of effective elastic properties of a quasi-periodic composite in singular approximation of the method of periodic components in terms of familiar solutions for tensors of the effective elastic properties of composites with periodic and chaotic structures and the parameters of the quasi-periodic structure: the coefficient of periodicity and the tensor of the anisotropy of inclusion disorder. A numerical calculation is performed for the effective transversally isotropic elastic properties of unidirectional fibrous composites with different degrees of fiber disorder.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 460–473, July–August, 1997.     

Effect of aggregation of a dispersed rigid filler on the elastic characteristics of a polymer composite

Conclusions We proposed a method for describing the effective elastic characteristics of a polymer composite with a rigid aggregating filler. An important feature of such a medium is the variable coupling of the inclusion phase in relation to its volume content. A change in the degree of coupling of the filler is accounted for by introducing an additional parameter. We examined a method of determining the coupling parameter from the results of statistical modeling of the geometry of the medium. Using the example of a calcite-HDPE composite, we showed that aggregation has a significant effect on the dependence of the elastic modulus on the volume content of filler; satisfactory agreement was obtained between the theoretical and experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 14–22, January–February, 1986.     

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.For Pt. 1, see [1].Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 200–214, March–April, 1997.     

Generalized self-consistent method: Modeling and computation of effective elastic properties of composites with composite or hollow inclusions

A new approach to the generalized self-consistent method [1,2] has been developed for problems of the statistical mechanics of composites with composite or hollow inclusions. The approach can reduce the problem of predicting the effective elastic properties of composites to a simpler averaged problem of a single, composite, or hollow inclusion with inhomogeneous elastic surrounding in a homogeneous effective elastic medium. The problem of predicting the effective elastic properties of composites with unidirectional hollow fibers or hollow spherical inclusions are studied by using the new approach.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 173–183, March–April, 1998.     

Optimum stacking sequence of composite laminates for maximum strength

A method is presented for maximum strength optimum design of symmetric composite laminates subjected to in-plane and transverse loadings. The finite element method based on shear deformation theory is used for the analysis of composite laminates. Ply orientation angles are chosen as design variables. The quadratic failure criterion which is meant to predict fracture, is used as an object function for optimum stacking sequence design of a laminated plate. The Broydon-Fletcher-Goldfarb-Shanno optimization technique is employed to solve the optimization problem effectively. Numerical results are given for various loading conditions, boundary conditions, and aspect ratios. The results show that the quadratic failure criterion such as Tsai-Hill theory is effective for the optimum structural design of composite laminates.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 393–404, May–June, 1995.     

Thermal deformation of a composite reinforced with hybrid cloth strips

Conclusion We tested (for mechanical and thermal effects) composites reinforced with hybrid cloth COS and VAI strips; five alternate schemes of material, which differred in terms of the content of VAI layers and layers reinforced with COS, were tested. The elasticity characteristics, tension diagrams, and CLTE of the composites were determined. It was established experimentally that variation in the relative content of the above-indicated layers makes it possible to regulate the thermal expansion of the composite in the longitudinal direction of the reinforcing strips Objectively over significant ranges; in this case, the elastic modulus varies negligibly, while the specific elastic modulus remains virtually unchanged,An alternate scheme for determining the elasticity characteristics and CLTE of laminar polymeric materials reinforced with hybrid cloth strips on the basis of component properties is developed. The model according to which the structural organization of the composite is subdivided into several levels is primarily a computational model. The stress-strain state of the repeating structural elements is evaluated by methods of the strength of materials. The proposed algorithm for computing the physicomechanical characteristics of laminar composites is implemented in the form of a computer program. The experimental elasticity characteristics and CLTE obtained for composites with a different content of COS and VAI layers are compared with those calculated in accordance with the method developed (the computed values correspond to the experimental with an accuracy acceptable for engineering applications).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 392–401, May–June, 1988.     

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].Perm State Technical University, Perm, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 785–796, November–December, 1999.     

Generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures

The feasibility of using a generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures has been examined. Using this method, the problem is reduced to solution of simpler special averaged problems for composites with single inclusions and corresponding transition layers in the medium examined. The dimensions of the transition layers are defined by correlation radii of the composite random structure of the composite, while the heterogeneous elastic properties of the transition layers take account of the probabilities for variation of the size and configuration of the inclusions using averaged special indicator functions. Results are given for a numerical calculation of the averaged indicator functions and analysis of the effect of the micropores in the matrix-fiber interface region on the effective elastic properties of unidirectional fiberglass—epoxy using the generalized self-consistent method and compared with experimental data and reported solutions.Perm State Technical University. Translated from Mekhanika Kompozitmykh Materialov, Vol. 33, No. 3, pp. 289–299, May–June, 1997.     

Multicriteria optimization of a composite cylindrical shell subjected to thermal and dynamic actions

Multicriteria optimization of the structure and geometry of a laminated anisotropic composite shell subjected to thermal and dynamic actions is considered. From the known properties of monolayers and the given values of variable structural and geometric parameters, the thermoelastic properties of the layered anisotropic composite are determined. The criteria to be optimized—the natural frequency and the thermal stresses—depend on two variable design parameters, stochastic properties of the composite, and temperature. In the space of the optimization criteria, the domain of allowable solutions and the Pareto-optimal region are found.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 753–760, November–December, 2004.     

Minimum weight design of sandwich and laminated composite structures

Conclusions The illustrative examples presented above show that the proposed optimum design method based on planning of experiments is an efficient method for the minimum weight design of sandwich and laminated composite plates. Vibration and damping constraints can be modeled using simple mathematical expressions. These expressions are obtained using the finite element solution in the experiment points. Reference points in the search domain are determined from plans of experiment. The advantage of the proposed method is its minimum computational effort for repeated finite element solutions. The major advantage of the method is the possibility of using the data not only from the computer solution, but also the data obtained experimentally in the reference points. In this case, simple mathematical models represent both theoretical and experimental data.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 51–64, January–February, 1995.     

Multi-objective optimization of composite structures. A review

Studies performed on the optimization of composite structures by coworkers of the Institute of Polymers Mechanics of the Latvian Academy of Sciences in recent years are reviewed. The possibility of controlling the geometry and anisotropy of laminar composite structures will make it possible to design articles that best satisfy the requirements established for them. Conflicting requirements such as maximum bearing capacity, minimum weight and/or cost, prescribed thermal conductivity and thermal expansion, etc. usually exist for optimal design. This results in the multi-objective compromise optimization of structures. Numerical methods have been developed for solution of problems of multi-objective optimization of composite structures; parameters of the structure of the reinforcement and the geometry of the design are assigned as controlling parameters. Programs designed to run on personal computers have been compiled for multi-objective optimization of the properties of composite materials, plates, and shells. Solutions are obtained for both linear and nonlinear models. The programs make it possible to establish the Pareto compromise region and special multicriterial solutions. The problem of the multi-objective optimization of the elastic moduli of a spatially reinforced fiberglass with stochastic stiffness parameters has been solved.The region of permissible solutions and the Pareto region have been found for the elastic moduli. The dimensions of the scatter ellipse have been determined for a multidimensional Gaussian probability distribution where correlation between the composite's properties being optimized are accounted for. Two types of problems involving the optimization of a laminar rectangular composite plate are considered: the plate is considered elastic and anisotropic in the first case, and viscoelastic properties are accounted for in the second. The angle of reinforcement and the relative amount of fibers in the longitudinal direction are controlling parameters. The optimized properties are the critical stresses, thermal conductivity, and thermal expansion. The properties of a plate are determined by the properties of the components in the composite, eight of which are stochastic. The region of multi-objective compromise solutions is presented, and the parameters of the scatter ellipses of the properties are given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 363–376, May–June, 1996. Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga.     

Determination of in-plane shear characteristics of composite materials with [±45°] layup

The shear characteristics of a composite with a [±45°] layer layup are measured experimentally by different methods. Investigations were conducted on flat and tubular specimens. The strength and shear modulus were determined by the rail method, the losipescu method, and by applying torsion to thin-wall tubes; only the shear modulus was determined by applying torsion to square plates. Determination of the shear modulus yields quantitatively comparable results, and, at the same time, the scatter of the shear-strength values of the specimens is significant. Maximum strength is achieved on the tubular specimens. The cause of the lower strength values of the flat specimens can be explained by secondary stresses and strains in their effective sections. The influence exerted by the geometry of the specimens on their strength is investigated for specimens tested by the rail and losipescu methods. It is shown that it is possible to increase the strength appreciably by varying the specimen's geometry.Institute of Polymer Mechanics. Latvian Academy of Sciences, Riga, Latvia. AERPAC Company. Netherlands. Translated from Mekhanika Kompozitmykh Materialov, Vol. 32, No. 2, pp. 256–264, March–April, 1996.     

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.     

Thermoelasticity problems in the mechanics of composite materials with large-scale deformation of the filler

A problem is posed and a method of solution developed for a class of thermoelasticity problems in the mechanics of composite materials with large-scale structural deformations, in which in the continuum approximation the composite material is modelled by a homogeneous orthotropic body with curvilinear orthotropy. As an application the authors establish the foundations of a theory of buckling for planar structural elements subjected to constant thermal fields.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 16–25, 1989.     

Taking account of heat transfer in locally heated thermoelastic plates made out of composite materials

Conclusions The proposed approach to the determination of the thermal stress state of thin plates made out of composite materials permits taking into account the effect of the coefficient of heat transfer from a region of local heating outside of it. The significant effect of heat transfer from the heating zone on the temperature field and the stresses indicates the necessity of taking it into account in connection with calculations on the strength of composite plates subjected to local heating.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1027–1030, November–December, 1979.     

Aging of polymer composite materials exposed to the conditions in outer space

A comprehensive investigation is made of glass, carbon, organic fiber-reinforced plastics, and epoxy-based hybrid composite materials employed in Salyut-type spacecraft which remained in space for up to 1501 1501 days. In particular, the properties, aging mechanism, and strain-strength variations in these materials due to exposure to the conditions in outer space were studied. After a series of tests were performed in space the standard strain and strength parameters as well as the mass, density, and thickness changes in the composite materials were estimated. Electron-microscopic and dynamic-mechanical analyses were performed, and the thermal expansion was estimated for a wide range of temperatures. The principal, dominant process occurring due to the continuous presence in outer space was found to be post-curing of the resin materials, which in turn affected the mechanical characteristics of the composite materials. After 456–1501 days in space the room-temperature strength of the composite materials (except for organic plastics) did not decrease, while at high temperatures it even increased. The post-curing and restructuring of some composite materials lowered their dynamic shear moduli in the glassy state of the resin. Due to consolidation of the surface layer of hybrid composite materials irradiated and subjected to thermal cycles, failure during bending varied from transverse fracture to delamination. The negative effect of the post-curing process was expressed as higher internal tension in the hybrid composite materials with different linear thermal expansion coefficients. The magnitude of this effect depended on the amplitude of the thermal cycles. The unprotected surface of the composites bombarded by atomic oxygen, microparticles, and space garbage were subjected to pickling and microerosion, the maximum effect occurring at the initial stage of exposure. Desorption of moisture and low-molecular products during the first 100–200 days of thermal cycling in the vacuum of near-earth orbit must be considered when estimating the total mass loss of composite materials. Data from microscopic, dynamic-mechanical, and other types of analyses revealed that the outer-space factors improved the supermolecular order of the resin volume, while the subsurface layer structure of the composite materials had loosened. Microcracks formed in the plastic's surface during 1501 days in outer space did not, in general, affect the mechanical parameters of the composite materials. Most of the observed effects of exposure to conditions in outer space were less pronounced for plastics protected by aluminum foil or other plastic coatings. The data obtained can be used for designing external elements of spacecraft by selecting materials with specified and predictable properties for long-term service.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 457–467, July–August, 1993.In conclusion we thank I. G. Zhigun and R. P. Shlits for assisting in determining the mechanical properties of PCM as well as the crew of the Salyut-6 and Salyut-7 space stations for setting up, monitoring, and delivering samples to earth.     

Elastic characteristics of ferrocement reinforced by hexagonal grids

The methods of the structural mechanics of composite materials are used to develop a method for predicting the elastic modulus and shear modulus of ferrocement reinforced with hexagonal woven and stamped grids. The method takes into account the elastic properties of the components and the geometry of the reinforcement.Riga Technical University, LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 182–186, March–April, 1997.