Showing papers in "Mechanics of Composite Materials in 1995"

Evaluation of porosity in composite aircraft structures

Abstract: The use of an analytical model for determining the moduli of elasticity of composite laminates made of woven or unidirectional plies with different porosity levels was described. The analysis of aircraft composite parts with different levels of voids (porosity) was based on a method which utilizes the results of state-of-the-art nondestructive testing methods (ultrasonic through transmission, loading, or pulse/echo) as the starting data for the analytical model. The porosity distribution over the volume of the material and correlations for the nondestructive testing methods were determined for epoxy-carbon laminates with standard and stiffened binders and corroborating experiments were conducted. It was shown that the moduli of elasticity of composite laminates decrease with an increase in the porosity levels. The type, thickness, and layup of the laminate are the basic factors that affect the decrease in the elastic properties of porous composite laminates.

Nondestructive evaluation of fatigue-induced changes in the structure of composites by an ultrasonic method using a laser

Abstract: Studies were conducted to nondestructively evaluate the damage to a glass-fiber-reinforced plastic during cyclic and static loading. The evaluation was made by an ultrasonic method employing a laser. In both the unloaded and loaded specimens, the ultrasound attenuation spectrum has a resonance peak attributable to the periodic nature of the structure of the composite. This peak is shifted to the low-frequency region during static loading, due to a decrease in the elastic modulus. The spectra obtained after cyclic loading have no resonance peaks, due to attenuation of the ultrasound over a broad range of frequencies by a large number of fatigue cracks. Additional static loading results in concentration of the cracks near the boundary between the glass fibers and the polymer matrix, which leads to the formation of a resonance peak in the high-frequency region of the spectrum.

Interlaminar failure and buckling of doubly-curved laminated composite shells

Abstract: A higher-order nonlinear shell theory of laminated axisymmetric structures is developed. The theory accounts for parabolic distribution of transverse shear strains and linear for normal strains through the thickness of the shell. The derived equations are employed into the analysis of the delamination initiation (via the strength criterion), propagation (the contact problem), and buckling (in the global or local sense). The space occupied by the shell is divided into four regions in order to obtain accurate description of the contact phenomena occurring between the delammated zones (the sublaminates). Various numerical examples have been solved to demonstrate the influence of the shallowness parameters on failure modes of delaminated spherical shells under external pressure.

Optimum stacking sequence of composite laminates for maximum strength

Abstract: 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.

A comparative study for the calculation of the temperature dependent shapes of unsymmetric laminates based on finite element analysis and extended classical lamination theory

Abstract: It is well known that the room-temperature shapes of unsymmetric laminates do not always conform to the predictions of classical lamination theory. Instead of being saddle shaped, as classical lamination theory predicts, the room-temperature shapes of unsymmetrically laminated composites are often cylindrical in nature. In addition, a second cylindrical shape can sometimes be obtained from the first by a simple snap-through action. Hyer examined the class of all square unsymmetric cross-ply laminates which can be fabricated from four layers, i.e., [0/0/0/90], [0/0/90/0], [0/90/0/90], [0/0/90/90], and developed an extended classical lamination theory to predict whether these laminates have a saddle shape or one or two cylindrical shapes. Finite element analysis (FEA) has just recently been used for the calculation of the room-temperature shapes of unsymmetric laminates because more sophisticated finite element codes are now available and the calculations can be made in an acceptable time. The hope is to get more accurate results for the shape and the stresses and forces that occur during the snap-through action. These results are needed for the development of active deformable composite structures based on unsymmetric laminates and incorporated shape memory alloy wires [1]. Results for different lay-ups are presented and compared.

Frequency response analysis of laminated composite beams

Abstract: The modeling of laminated composite beams has been derived systematically from the three-dimensional elasticity relations. The correctness of the solution found by using the present finite element model is verified by comparison with the results obtained by analytical solutions and other results presented in the literature. Numerical results indicate that the present technique can given accurate results for frequency response analysis for laminated composite beams. Loss factors of structures obtained by the method of complex eigenvalues and the direct frequency response method exhibit very good agreement. Optimum design of a laminated composite beam by the finite element method and the method of experiment planning has been successfully presented.

Prediction of creep of polymer concrete

Abstract: We studied the applicability of the phenomenological approach to the prediction of long-time creep of polymer concrete consisting of polyester binder with diabase filler and diabase aggregate. We discovered that the principles of temperature-time analogy, of moisture-time analogy, and of temperature-moisture-time analogy are applicable to the description of the diagrams of short-time creep and to the prediction of long-time creep of polymer concrete at different temperatures and constant moisture content of the material.

Hygromechanics of composites with unsymmetric structure

Abstract: An analytical method is presented for estimation of midplane strains and curvatures of a 3D general composite. By using the multilayer model based on the laminate analogy, the effect of an unsymmetric distribution of moisture content and material structure on swelling and wrap as well as the stability in compression of a densified technological pressing wooden composite board has been estimated for a real composite production process.

Analysis of a spherical crack on the interface of a two-phase composite

Abstract: Composite and partially homogeneous materials are nowadays the basis for the creation of the majority of advanced materials. In many cases, interfacial crack defects are the cause of the destruction of such materials. That is the reason for the investigation of the stress-strain (SSS) of the body containing an interfacial crack both from the point of view of the design of advanced materials and correctness of the mathematical description of physical processes occurring at and near the crack tip. At the present time, the problem of a plane straight interfacial crack in a compound infinite body has been studied extensively. Review of these results has been presented. Nevertheless, the solutions obtained do not take into account the thickness of the adhesive layer and local contact interaction of the crack edges. The presence of so-called oscillating singularities conflicts with physical reality. We consider an axially symmetric problem of the theory of elasticity for the determination of the SSS of a partially homogeneous two-layer spherical covering with an interface crack. The classical type of this problem, which assumes that the crack edges have no contact with each other, was considered in (3). This solution contains a rapidly oscillating singularity of the stressmore » at the crack tip. On the other hand, the model proposed by Comninou (4) assumes an overlapping of the crack surface near a crack tip of very small size, and was used to solve the problem of a spherical crack in the nonhomogeneous body consisting of an elastic sphere and an unbounded elastic medium (5). In this connection, it is assumed that the two sides of the crack are in frictionless contact. The contact zone is quite small, of the order of 10{sup {minus}4} of the crack length, and this fact reduces the effectiveness of the model. In this paper, we will show that a nonoscillatory model can also be used to solve the problem under consideration.« less

Mechanical properties of blends of liquid crystalline copolyesters with polyprophylene

Abstract: A significant effect of the addition of LCP on the mechanical properties and their anisotropy has been established. Already, if one considers the shape of curves of the stress-strain relationship it can be seen that curves typical for semicrystalline polymers (pure polypropylene) with clearly visible yield point and significant cold drawing leading to an anisotropic stiffening are changing into curves without yielding and with a brittle failure (LC-rich blends). Generally, the tensile elasticity modulus increases with increasing LCP content for both MD and TD. The maximum value of anisotropy of elastic properties was noted for a rather low content of LCP (c = 5%). On the contrary, the stress at yield decreases with increasing LCP content. The same was observed for the strain at yield but in both cases an important increase of anisotropy has taken place. Consequently, the total elongation during drawing (strain at break) showed a drastic decrease for blends with higher LCP content (about 60–80 times). The addition of the LCP to polypropylene has led to a stiffness increase (higher elasticity modulus) but simultaneously to a considerable plasticity decrease. As a confirmation of these observations, there served also the creep test where a decrease of the creep compliance (by two times) for LC-rich blends as compared with pure PP was noted. It also should be emphasized that, generally, a smaller effect of LCP content on the elastic deformation was noted than that on the time dependent effects (nonelastic creep deformation).

Prediction of creep of cured expoxy resin filled with marble flour

Abstract: 1. We discovered that the principles of TTA, CTA, TCTA are applicable to the description of series of diagrams of short-time creep of epoxy resin filled with marble flour, at different temperatures (20–60 °C) and with different concentrations of filler (c < 0.45). 2. It was experimentally established that the function of temperature-time reduction of filled resin does not depend on the degree of filling and coincides with the function of temperature-time reduction of unfilled binder; the function of concentration-time reduction does not depend on the temperature. 3. The applicability of the principles of analogy to the prediction of long-time creep of the filled polymer under consideration was experimentally established. 4. Modeling and calculation of the deformation properties of a composite on the basis of its structural components showed that near particles of filler there can be an interphase layer whose rigidity is greater than the rigidity of the matrix, and the pliability for all the time sections is proportional to the pliability of the matrix. 5. The results of evaluating the extension of the interphase layer correspond qualitatively to the results of the experiment for determining the thickness of the interphase layer by the method of viscosimetry.

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

Abstract: 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 cσ, 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.

Minimum weight design of sandwich and laminated composite structures

Abstract: 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.

Rectangular anisotropic (orthotropic) plates on a tensionless elastic foundation

Abstract: The behavior of anisotropic (orthotropic) elastic plates of rectangular shape on a tensionless Winkler foundation is analyzed. The tensionless character of the foundation is taken into account by using an auxiliary function. The displacement function of the plate is approximated by using the eigenfunctions of the completely free beam. The difference between the free-end boundary conditions of the plate and the beam is compensated for by considering a differential operator in addition to the governing equation of the plate. Using Galerkin's method, the problem is reduced to the solution of a system of algebraic equations. The governing equations of the plate are derived under action of external uniformly distributed load, concentrated load, and moments. However, the influence of the mechanical properties on the configurations of the contact region and on the distribution of the displacements is investigated for concentrated load and moments for various values of the mechanical properties characterizing the anisotropy of the plate material. Considered problems are solved within the framework of Kirchhoff-Love hypothesis.

Effect of temperature on the creep of a thermotropic liquid crystalline polymer

Abstract: Thermotropic liquid crystalline polymers (LCP) are a relatively new class of materials; they are currently being intensively investigated. Many articles have been published concerning their rheological, dielectric, thermal, and mechanical properties, processing, and morphology. New areas of their potential applications continue to emerge. The LCP have good physical and mechanical properties as well as a satisfactory dimensional stability and chemical resistance. They show ease of processing thanks to their low melt viscosity. In fabricated products, these properties are highly anisotropic which is associated with the sensitivity of stiff molecules to flow fields causing a molecular orientation in the longitudinal direction.

The effect of interphase on residual thermal stresses. 1. Single fiber composite materials

Abstract: The residual thermal stresses in the constituents of a fiber-reinforced epoxy have been predicted using a concentric three-cylindrical (fiber-interphase-matrix) assemblage analysis. The interphase has been treated as a region with a variable Young's modulus — a direct consequence of the changes in the microstructure of the matrix near the fiber surface. The Navier equations of elasticity have been solved in series form solutions for each type of property variation. A parametric study is used to demonstrate the fact that changes in the interphase properties can drastically affect the residual stresses in the interphase.

New mathematical model for nonuniform deformation of composites

Abstract: A new mathematical model is suggested for nonuniform deformation of composite materials valid for arbitrary external load gradients. As a basis stochastic equations are suggested for the statics of an elastic microinhomogeneous two-component material with volumetric forces differing from zero. Expressions are obtained for all coefficients in terms of elastic constants of the components and geometric parameters of the structure.

Numerical analysis method for studying local forms of stability loss of bearing layers of three-layered shells using mixed forms

Abstract: A revised formulation of linearized stability problems of three-layered shells with a sofi filler has been presented. The form of stability loss of the rigid layers is mixed in the shells when the moment precritical stress-strain state (SSS) is reached and is localized in the principal moment SSS zones. If the filler thickness is much greater than the thickness of the rigid layers, the size of the bulges and thickness of the filler have the same order of magnitude. Thus, a very fine grid must be used for a numerical solution of the stability loss equations, which poses considerable computational difficulties. A numerical analysis method is proposed for the local forms of mixed mode stability loss of the rigid layers of a three-layered shell. Using this method, the solution of equations for the precritical SSS by the finite element scheme is found but an analytical solution of reduced stability loss equations is presented for estimating the critical load. This solution is an asymptotic approximation for local modes of stability loss implemented into design.

Stochastic multi-objective optimization of a viscoelastic composite plate

Abstract: A layered viscoelastic rectangular plate fiber-reinforced in three directions and compressed in one direction has been studied. Two plate properties, namely, the critical compressive stress σcr and the coefficient of linear thermal expansion αxx, were analyzed by varying two parameters of the reinforcement geometry. The properties of the plate are determined by the properties of the composite components, eight of which are considered stochastic. The problem was solved for two variants: αxx → min or αxx → max. The calculations were carried out for three time intervals: t = 0, 27 days, and ∞. For t = 0, the region of t≂ real plate properties is determined with isolines for design parameters. Multi-objective compromise solutions are given for all three times t for each of the two variants along with the parameters of the property scatter ellipses.

Analysis of stress relaxation processes in conveyor belts

Abstract: 1. When optimizing the composition of a layered composite in the form of conveyor belt as to its strength characteristics, an additional parameter, i.e., a time factor, should be taken into consideration. By the application of linear viscoelasticity methods, it is possible to predict the belt behavior under the determined stress-time conditions. Boundary relaxation stresses σi for a given type of belt and conveyor should be specified together with other performance parameters. 2. For all types of conveyor belts tested, the largest relaxation changes occur at the initial stage of start-up and during the steady motion of the belt (up to approx. 1 h). Later stresses in conveyor belts vary very slowly. 3. Rubber conveyor belts do not have worse relaxation characteristics than the PVC type ones. Four-layer rubber belts are characterized by the highest stress stability within the belt operation load range. 4. Well-known methods used for analysis of stress relaxation processes in polymer composites can find application to computations of stress relaxation characteristics of conveyor belts.

Compression of an infinite composite material along a finite cylindrical crack

Abstract: The approaches of classic fracture mechanics cannot be used in studying the compression of a material with forces directed along cracks. This is because within the framework of linear fracture mechanics, the forces acting along cracks do not affect the fracture process since they do not affect the stress intensity parameter or magnitude of crack propagation included in formulation of fracture criteria of the Griffith-Irwin or KRT type. The results of many experimental and theoretical studies show that the losses of the stability of a composite material in compression along a crack can be considered the onset of fracture. For this reason, the criterion in the three-dimensional linearized theory of stability of deformable bodies is used as the criterion of the onset of fracture, where the onset of fracture is characterized by local loss of stability in the vicinity of a defect of a crack type.

Elastic characteristics of ferrocement reinforced with woven meshes

Abstract: Applying structural mechanics methods for composite materials, we have worked out a procedure for predicting the elasticity modulus, the shear modulus, and Poisson's ratio for ferrocement taking into account the elastic properties of the components, the wire diameter, the mesh size, and the distance between the meshes. The results make it possible to exploit the potential of such reinforcement to the fullest.

Self-reinforcement of liquid-crystal polymers at static and dynamic loading

Abstract: The self-reinforcement effect of a solid uniaxially oriented SVM-K liquid-crystal polyamide and a copolyester of hydroxybenzoic and hydroxynaphthoic acids has been investigated by tensile-strength, stress-relaxation, and dynamic methods. The samples were prepared by spinning from lyotropic solution (SVM-K) and from a thermotropic melt (polyester). The tensile-strength and stress-relaxation tests were performed on complex fibers and the dynamic test on single fibers. The set of stress-strain curves, changing from a convex shape with two linear sections (at room temperature) to a concave shape (at high temperatures) is shown for both materials in Fig. 1. There is a pronounced difference between the deformation mechanisms at low and high strains in the stability of rigidity. At high temperatures the rigidity becomes less than the initial one during deformation and the current modulus at high strains has the same value within large ranges of temperatures and strains (Fig. 2). A low-deformation transition of another physical parameter than the yield-stress has been found. The stress-strain diagram for both investigated polymers has been generalized by using the constant value of the current modulus for the normalization of the stress value (Fig. 3). The stress-relaxation phenomena are shown to be anomalous. At high temperatures the stress-relaxation intensity decreases with increasing deformation, i.e., after deformation the polymer is characterized by a stability of rigidity which is higher than the initial value (Fig. 4). The dynamic modulus appears to increase with increasing deformation rate (Fig. 5). Due to these peculiarities the liquid-crystal polymers must be considered not only as normal high-modulus reinforcements for composite materials but also as materials, self-reinforcing under loading.

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

Abstract: There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.