Calculation of the moisture concentration field in a multilayered plate

Conclusion Thus, we have developed an algorithm and program to calculate fields of moisture concentration in a laminated plate for steady external temperatures and moisture contents. A test calculation and comparison of some of the findings with previous results demonstrated the accuracy of the program for solving a number of diffusion problems. For example, the program can be used to evaluate the life of the moisture-protective properties of polymer products, as well as to model moisture absorption in fiber composites.Curves of moisture concentration were calculated for a unidirectionally reinforced (with organic fibers) plastic at different relative humidities. We also calculated sorption curves and isotherms, which were shown to agree satisfactorily with previous empirical curves. It was shown that it is possible to approximately evaluate the sorption behavior of a unidirectionally reinforced fiber composite by means of a three-layer model and to analyze the stability of the result against an increase in the number of layers. For the two-component composite examined here, sorption behavior deviates from the classical behavior described by Fick's law — although the components of the composite obey this law.The algorithm and program that were developed make it possible to evaluate the kinetics of moisture absorption in complex composite systems and determine the distribution of moisture among and within the components.The study described here was conducted under grant 93.176 from the Latvian Science Council.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 502–511, July–August, 1994.     

Creep in unidirectionally reinforced polymer composites

Conclusions We have explored here the possibilities of predicting the permanent creep in unidirectionally reinforced polymer composite materials from the results of accelerated testing of their components. The mutually independent components of the viscoelastic compliance tensor under conditions of creep have been calculated with the aid of the Laplace transformation and an earlier verified variant of determining the mean elastic characteristics of a composite material, whereupon the originals of the sought functions have been obtained by a numerical inverse Laplace transformation. Experiments were performed with unidirectionally reinforced materials, a glass-plastic, an organoplastic, a carbon-plastic, and a boroplastic, all tested in tension in the direction of fiber reinforcement and in the transverse direction, also in longitudinal shear. The possibilities of predicting the creep in composite materials with the aid of functions characterizing the viscoelastic compliance of the binder and obtained by the method of temperature-time analogy have been confirmed twofold: by long-duration (up to 3 yr) control tests performed on the given materials and by control calculation of the creep in these composite materials from results of direct long-duration (up to 5 yr) tests performed on specimens of the binder.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 215–223, March–April, 1984.     

Effect of a uniaxial load on moisture absorption by an epoxy binder

Conclusion The above-developed method of studying the effect of uniaxial compressive and tensile loads on moisture absorption in polymers was tested on epoxy binder EDT-10. It was established experimentally for this material that tensile stresses up to 50 MPa significantly increase the equilibrium moisture content (up to 20% of the initial value). There is a corresponding increase in the rate of moisture absorption during the initial stage of the sorption process — up to 80% of the initial value. No changes in the diffusion coefficient were seen in this case. The application of compressive stresses of up to 40 MPa also had no effect on the kinetics of moisture absorption.Deceased.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 1, pp. 110–115, January–February, 1993.     

Structural approach to calculation of the effect of moisture on elastic characteristics of organoplastics

Data have been obtained for the structural calculation of the effect of moisture on the elastic characteristics of organoplastics from the properties of components. The distribution of moisture between the fiber and matrix — the components of a unidirectional composite — is considered. The elastic properties of the fiber are determined by an inverse calculation using the experimental dependences of the composite and matrix on moisture. The moisture effect on the properties of the materials is taken into account with influence functions, which differ by more than 25% for various characteristics. The results can be used for calculating the elastic properties of composites with various reinforcement schemes and at the nonequilibrium distribution of the moisture concentration in an actual environment.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 525–530, July–August, 1998.     

Contact problems for beams and plates with low shear stiffness

The low shear stiffness and strength of unidirectionally reinforced plates and beams predetermines the choice of calculation model in specific problems [4]. The contact problem is considered for a glass-reinforced plastic plate resting on a Winkler foundation; the deformation properties of the plate are described by the equations of an orthotropic material; the investigation is based on generalized applied theories of the Timoshenko and Ambartsumyan types [5–8], which permit the high shear compliance of thin-walled structures to be taken into account.L'vov Polytechnic Institute; Ivan Franko Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 4, pp. 715–720, July–August, 1970.     

Thermal deformation of unidirectionally reinforced hybrid composites. Report no. 1

Conclusion We conducted a dilatometric study of three types of hybrid unidirectionally reinforced composites (organic-glass-, organic-carbon-, and carbon-glass-fiber plastics), each of which was represented by several batches differing in the relative content of the two types of fibers. The tests were performed on a specially-designed laboratory prototype. It was shown that, for the materials studied, the coefficient of linear expansion can be controlled by means of hybridization — by combining several types of fibers with positive and negative values of the coefficient of linear expansion in one composite. Analytic expressions for the coefficient that were obtained by generalizing a three-phase model of a two-component composite with isotropic fibers to the case of a hybrid composite with anisotropic fibers satisfactorily describe the experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 229–236, March–April, 1989.     

Deformative characteristics of plastics reinforced with high-modulus anisotropic fibers

The independent elastic constants of plastics unidirectionally reinforced with transversely isotropic fibers have been determined. It has been assumed that the distribution of reinforcement in a transverse section of the plastic is regularly rectangular or hexagonal. To determine the transverse elastic modulus and the shear modulus in the plane of reinforcement, a constancy-of-plane-sections hypothesis was used. Values of deformative characteristics determined by the assumed calculational dependences have been compared with the experimental ones for plastics reinforced with graphite fibers.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 631–639, July–August, 1972.     

Thermal conductivity of organoplastics

The dependence of the thermal conductivity of a unidirectional reinforced organoplastic on the fiber volume fraction as well as thermal conductivity and structural porosity of the components was studied experimentally and using mathematical models. These results may be used to develop new methods for the manufacture of plastic items and the nondestructive thermal monitoring of the structural parameters of these items.Institute of Polymer Mechanics, Latvian Academy of Sciences, LV-1006 Riga, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 269–277, March–April, 1997.     

Dynamic compressive strength of epoxy composites

The strength of laminated and unidirectionally reinforced composite materials was investigated in conditions of dynamic uniaxial compression with a strain rate of 50–1000 sec^–1 using the split Hopkinson pressure bar method. It was shown that in conditions of dynamic compression, glass/epoxy, aramid/epoxy, and carbon/epoxy composites exhibit elastic-brittle behavior with anisotropy of the strength and elastic properties. The effect of the strain rate on the strength characteristics of fiberglass-reinforced plastics was demonstrated.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 776–782, November–December, 1995.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).     

Cutting of aramide fiber-reinforced plastics by Co2 laser

Comparative characteristics of aramide fiber reinforced plastics (AFRP) made by laser cutting or machining are presented. It is found that the strength of the specimens cut out by laser is 4–25% higher, while the moisture absorption is at least 2 times lower as compared to those cut out by machining. The deviation of the cutting edge size for AFRP 2 mm thick does not exceed 0.4 mm. Calculated and experimental data are given. The possibilities and conditions of cutting the AFRP up to 6 mm thick are determined.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 375–384, May–June, 1999.     

Effect of certain structural and technological parameters on the tensile strength and deformation of unidirectionally reinforced plastics

A model of the deformation and failure of unidirectionally reinforced plastics in short-time static tension with allowance for the effect of the properties of the components, the adhesion interaction between them, and the structure of the material is proposed as a basis for the selection and development of nondestructive methods of testing glass-reinforced plastic articles. It is shown that the proposed model is in qualitative agreement with the experimental data.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1042–1048, November–December, 1973.     

Investigation of the state of water sorbed by an organic polymer by high-resolution1H nuclear magnetic resonance and differential thermal analysis

Conclusions The results of the experimental investigation of a moist organic composite by high-resolution NMR and DTA indicate a change in the structure of water, due to an interaction between the water molecules and the macromolecules when water is sorbed by the organic polymer. A part of the sorbed water molecules is strongly bound to the macromolecules; their mobility is very low and is not recorded by high-resolution NMR. As the moisture content of the composite increases, molecules of water appear, the mobility of which is intermediate between the strongly bound and free water molecules in the macrospace. This part of the molecules is represented in the NMR spectrum by a broadened and shifted line and a shift of the endothermic peak towards lower temperatures is observed on the thermal analysis diagrams. The weakly bound water can be detected in the composite starting at a moisture content of 5–8%.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 317–320, March–April, 1990.     

Influence of Modifiers on the Physicomechanical Properties of Sawdust-Polyethylene Composites

Polymer-wood composites based on recycled polyethylene (RPE) are investigated. Dispersed alder sawdust was utilized as a filler. To improve the compatibility between the nonpolar matrix and the polar wood fibers as a reinforcement, two types of modifiers were used, which differed in their chemical nature and mechanical interaction with the constituents of the composites. The modifiers of the first type (paraffin and OP) improved the dispersibility of sawdust (SD), and those of the second type (Exxelor 1015 and OREVAC) contained groups of maleic anhydride, which interacted with the OH-groups of SD. The effect of the modifiers on the moisture sorption by SD, the dispersibility of the filler in the matrix, and the strength characteristics (ultimate strengths and moduli in tension and bending) of dry and moist RPE–SD composites and on their moisture sorption is estimated. The best results were obtained for the composites modified with paraffin, which is due to the more efficient employment of the strength and rigidity of well-dispersed SD fibers. In their strength characteristics, the RPE-based composites investigated are comparable to composites based on low-density polyethylene.     

Prediction of the creep of polyester resin in the presence of randomly acting temperature and humidity factors

The possibility of using the theory of random processes to predict the temperature and moisture creep of polymeric materials in the presence of randomly acting temperature and humidity factors is considered. A procedure for estimating the long-term deformation under such conditions is described with reference to the uniaxial creep of PN-3 polyester resin using time—temperature and time—moisture superposition. The possible correlation of the ambient temperature and humidity is taken into account. The results of a computer calculation show that the theoretical and experimental data are in satisfactory agreement.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 219–226, March–April, 1973.     

Deformation and stress distribution in a layered plastic

The stress distribution over the unidirectionally reinforced layers is investigated in relation to the layer thickness ratio and the direction of loading of a two-way reinforced plastic. An expression is obtained for the modulus of elasticity of the layered plastic in an arbitrary direction relative to the directions of reinforcement. The effect of the geometry of the structure of the layered material on its deformation properties is experimentally illustrated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 563–570, May–June, 1972.     

A comparative analysis of moisture transport models as applied to an epoxy binder

The results of experimental and theoretical investigations into the kinetics of moisture sorption by a neat epoxy resin obtained from RAE Industries (Reapox 520, D523) are reported. The sorption process was realized in atmospheres with a constant relative humidity of 33, 53, 75, 84, and 97% and a temperature of 50°C. The results obtained showed that the diffusion behavior of epoxy resin did not obey Fick’s law under the experimental conditions considered. Consequently, the application of a non-Fickian diffusion model was necessary. For this purpose, two-phase moisture sorption models, a model with a time-dependent diffusivity, a two-phase material model, as well as relaxation and convection models of anomalous diffusion, were considered. The model parameters were obtained from the approximation of experimental sorption data. A comparative analysis of the sorption models was performed, and the specific features of their applications were estimated. The two-phase material model and the model with varying diffusivity were found to be the most suitable ones due to a good agreement between calculation results and experimental data and the rather small (three or four) number of parameters, which make them more flexible and physically more justified than the classical Fick’s model with its two parameters. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 555–570, July–August, 2007.     

Unique Solvability of the Inverse Problem with a Time-Dependent Boundary Condition for a Sorption Model

A mixed initial boundary-value problem is considered for nonequilibrium sorption dynamics with inner-diffusion kinetics. The problem allows for convection and longitudinal diffusion and has a time-dependent boundary condition. This condition contains the time derivative of a solution component and constitutes the balance equation for the absorbed mixture near the output boundary of the sorption region—inside the diffusion barrier. Bounds on the solution of the direct problem are obtained: nonnegativity of the solution and its first time derivatives, and boundedness of the solution by known functions. The inverse problem of estimating the nonlinear system parameter—the sorption isotherm—is considered and a uniqueness theorem is proved.     

Elastic and Sorption Characteristics of an Epoxy Binder in a Composite During Its Moistening

Results of an experimental investigation into the elastic and sorption characteristics of a model composite material (CM) — epoxy resin filled with LiF crystals — during its moistening are presented. Properties of the binder in the CM with different filler contents (v _f = 0, 0.05, 0.11, 0.23, 0.28, 0.33, 0.38, and 0.46) were evaluated indirectly by using known micromechanical models of CMs. It was revealed that, for the CM in a conditionally initial state, the elastic modulus of the binder in it and the filler microstrain (change in the interplanar distance in the crystals, measured by the X-ray method) as functions of filler content had the same character. The elastic modulus of the binder in the CM with a low filler content was equal to that for the binder in a block; the elastic modulus of the binder in the CM decreased with increasing filler content. The maximum (corresponding to water saturation of the CM) stresses in the binder and the filler microstresses as functions of filler content were of the same character. Moreover, the absolute values of maximum stresses in the binder and of filler microstresses coincided for high and low contents of the filler. At v _f = 0.2–0. 3, the filler microstrains exceeded the stresses in the binder. The effect of moisture on the epoxy binder in the CM with a high filler content was not entirely reversible: the elastic characteristics of the binder increased, the diffusivity decreased, and the ultimate water content increased after a moistening-drying cycle.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 499–511, July–August, 2005.     

Adjustment of Residual Stresses in Unsymmetric Fiber-Reinforced Composites Using Genetic Algorithms

During the manufacturing process of multilayered fiber-reinforced composites with variable fiber orientations, residual stresses build up in these composites due to the directional expansion of single unidirectionally reinforced layers. Depending on the laminate lay-up, the inhomogeneous residual stresses, which are caused by thermal effects, moisture absorption, and chemical shrinkage, can lead to large multistable out-of-plane deformations. Instead of avoiding these curvatures, they can be advantageously used for technical applications following the near-net-shape technology. In order to adjust the deformations to the technical requirements, genetic algorithms in combination with a nonlinear calculation method have been developed, which can purposefully adapt the laminate lay-up depending on the loading and process parameters.     

Various methods of determining the natural frequencies and damping of composite cantilever plates. 3. The Ritz method

The Ritz method was used to determine the frequencies and forms of free vibrations of rectangular cantilever plates made of anisotropic laminated composites. Orthogonal Jacobi and Legendre polynomials were used as coordinate functions. The results of the calculations are in good agreement with the published experimental and calculated data of other authors for plates made of boron and carbon fiber reinforced plastics with different angles of reinforcement of unidirectional layers and different sequence of placing the layers, and also of isotropic plates. The dissipative characteristics in vibrations were determined on the basis of the concept of complex moduli. The solution of the frequency equation with complex coefficients yields a complex frequency; the loss factors are determined from the ratio of the imaginary component of the complex frequency to the real component. For plates of unidirectionally reinforced carbon fiber plastic with different relative length a detailed analysis of the influence of the angle of reinforcement on the interaction and frequency transformation and on the loss factor was carried out. The article shows that the loss factor of a plate depends substantially on the type of vibration mode: bending or torsional. It also examines the asymptotics of the loss factors of plates when their length is increased, and it notes that the binomial model of deformation leads to a noticeable error in the calculation of the loss factor of long plates when the angle of reinforcement lies in the range 20°<<70°.For Communication 2, see [1].Institute of Engineering Science of the Russian Academy of Sciences, St. Petersburg, Russia. St. Petersburg State University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 215–225, March–April, 1997.