Showing papers in "Mechanics of Composite Materials in 2007"
TL;DR: In this article, the authors present a numerical approach for simulating the propagation of interlaminar cracks in composite structures, which can be considered analogous to interlaminar cracking.
Abstract: Analysing the collapse of skin-stiffened structures requires capturing the critical phenomenon of skin-stiffener separation, which can be considered analogous to interlaminar cracking. This paper presents the development of a numerical approach for simulating the propagation of interlaminar cracks in composite structures. A degradation methodology was introduced in MSC.Marc, which involved the modelling of a structure with shell layers connected by user-defined multiple-point constraints (MPCs). User subroutines were written that employ the virtual crack closure technique (VCCT) to determine the onset of crack growth and modify the properties of the user-defined MPCs to simulate crack propagation. Methodologies for the release of failing MPCs are presented and are discussed with reference to the VCCT assumption of self-similar crack growth. The numerical results obtained by using the release methodologies are then compared with experimental data for a double-cantilever beam specimen. Based on this comparison, recommendations for the future development of the degradation model are made, especially with reference to developing an approach for the collapse analysis of fuselage-representative structures.
43 citations
TL;DR: In this article, 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.
Abstract: 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.
42 citations
TL;DR: In this paper, the results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening, are presented, showing that it is possible to achieve a sufficient degree of moment redistribution if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models.
Abstract: The results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening, are presented. The internal flexural steel reinforcement was designed so that to allow steel yielding before the collapse of the beams. To prevent the shear failure, steel stirrups were used. The tests also included two nonstrengthened control beams; the other specimens were strengthened with different configurations of externally bonded carbon-fiber-reinforced polymer (CFRP) laminates. In order to prevent the premature failure from delamination of the CFRP strengthening, a wrapping was also applied. The experimental results obtained show that it is possible to achieve a sufficient degree of moment redistribution if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models.
36 citations
TL;DR: The use of a sandwich plate system composed of two steel plates with a solid polymer (polyurethane) core has been introduced as a refurbishment procedure for steel decks of bridges, the so-called orthotropic decks consisting of a deckplate with longitudinal stiffeners and transverse crossbeams as mentioned in this paper.
Abstract: The use of a sandwich plate system (SPS) composed of two steel plates with a solid polymer (polyurethane) core has been introduced as a refurbishment procedure for steel decks of bridges, the so-called orthotropic decks consisting of a deckplate with longitudinal stiffeners and transverse crossbeams. Unfortunately, a great many of existing steel bridges still have structural members that do not comply with the recommendations given in design codes, and therefore damages have developed in them. For a satisfactory refurbishment of the bridges, the SPS technique fulfils all necessary requirements. To this end, both experimental and calculative investigations were carried out at RWTH Aachen to demonstrate the reinforcing and stiffening effect and to prove the suitability of the SPS-overlay technique for general use. The practical applicability of a SPS has been tested successfully in a pilot project for a German motorway bridge under severe traffic.
29 citations
TL;DR: In this article, the stability and strength of concrete columns confined by carbon fiber reinforced polymer (FRP) jackets in which the fibers are oriented in the hoop direction was studied. And the theoretically predicted critical stress at the on set of in stability was compared with that obtained experimentally, and a good agreement between them was observed.
Abstract: External confinement by the wrapping of fiber-reinforced polymer (FRP) sheets is a very effective method for the strengthening and retrofit of round concrete columns. The stability and strength of concrete columns confined by carbon FRP jackets in which the fibers are oriented in the hoop direction was studied. Stability tests were conducted on hinged plain and confined concrete columns of different slenderness. The theoretically predicted critical stress at the on set of in stability was compared with that obtained experimentally, and a good agreement between them was observed.
27 citations
TL;DR: In this paper, an experimental investigation was carried out to estimate the cooperation between a steel bar reinforcement and round concrete cylinders confined by a carbon-epoxy composite, concerning the increase in the concrete compression strength due the composite wrapping.
Abstract: The paper presents results of an experimental investigations carried out to estimate the cooperation between a steel bar reinforcement and round concrete cylinders confined by a carbon-epoxy composite, concerning the increase in the concrete compression strength due the composite wrapping. The steel bar reinforcement with its yield stress considerably increases the bearing capacity of concrete. This also happens above the unconfined concrete strength of specimens. The onset of reinforcement yielding roughly coincides with reaching of the unconfined concrete strength at a compressive strain of ≈0.20%, and therefore it does not produce a change in the tangent modulus of the stress-strain relationships above the limit of linearity.
23 citations
TL;DR: In this article, a theoretical-numerical hybrid method for determining the stresses distribution in composite laminates containing a circular hole and subjected to uniaxial tensile loading is presented.
Abstract: The paper presents a theoretical-numerical hybrid method for determining the stresses distribution in composite laminates containing a circular hole and subjected to uniaxial tensile loading. The method is based upon an appropriate corrective function allowing a simple and rapid evaluation of stress distributions in a generic plate of finite width with a hole based on the theoretical stresses distribution in an infinite plate with the same hole geometry and material. In order to verify the accuracy of the method proposed, various numerical and experimental tests have been performed by considering different laminate lay-ups; in particular, the experimental results have shown that a combined use of the method proposed and the well-know point-stress criterion leads to reliable strength predictions for GFRP or CFRP laminates with a circular hole.
19 citations
TL;DR: In this article, the strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated.
Abstract: The strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated. Two methods for calculating the shear force in the contact zone are considered, one of which takes into account the compliance of the zone and gives results agreeing rather well with experimental data for beams, regardless of the way the CFRP is fastened to concrete. The method of shear stresses is good for beams with in significant shear strains between CFRP and concrete. A method allowing for hardening of the contact zone is suggested. It is shown that the fracture mechanism of the zone depends on the way of fastening the CFRP and the depth the adhesive penetrates into concrete.
18 citations
TL;DR: In this paper, a detailed finite-element analysis of the stress-strain state in the load transfer zone of uneasily tensioned flat test specimens made of a high-strength unidirectional carbon fiber-epoxy composite is carried out with account of the elastoplastic behavior of a structural polyurethane adhesive.
Abstract: A detailed finite-element analysis of the stress-strain state in the load transfer zone of uneasily tensioned flat test specimens made of a high-strength unidirectional carbon fiber-epoxy composite is carried out with account of the elastoplastic behavior of a structural polyurethane adhesive. Various schemes of introduction of external loads into the specimens are considered. A numerical finite-element analysis of different configurations of specimen tabs allowed us to put forward a technique for significantly reducing the dangerous concentration of operating stresses.
15 citations
TL;DR: In this article, the authors used linear regression equations to describe the ultimate shear strength and modulus in relation to the density of expanded polystyrene (EPS) under short-term shear loading according to EN 12090.
Abstract: Data obtained in investigating the ultimate strength and deformability of expanded polystyrene under short-term shear loading according to EN 12090 are discussed. Linear regression equations are used for describing the ultimate shear strength and modulus in relation to the density of EPS. A correlation is found to exist between the ultimate strength of EPS and its density and specimen thickness. An empirical dependence between the shear modulus and density of EPS is established. The strains corresponding to the conditional limit of proportionality and to the ultimate shear strength of EPS in short-term loading are determined.
13 citations
TL;DR: In this article, a finite solution to the one-dimensional (along the radius) wave problem is derived for the shell, which differs from the solution for radial vibrations of a liquid.
Abstract: Free vibrations across the thickness of a closed spherical shell are studied. A finite solution to the one-dimensional (along the radius) wave problem is derived for the shell, which differs from the solution for radial vibrations of a liquid. The solution is used in constructing a model for joint vibrations of three spherical layers. An approximate version of their vibratory motion is suggested, which is based on a shell model with thin stiff layers enveloping a thick soft core layer. The solution to the dynamic problem of free vibrations of the soft core is obtained by the method of separation of variables. The elastic reactions of the thin face layers were taken as boundary conditions, which allowed us to reduce the dynamics of the three layers to a vibratory motion of the midlayer under mixed boundary conditions. A transcendental equation for eigenvalues of the problem on free vibrations is derived and analyzed. A graphic description of the effect of layer thickness and elastic properties on the spectrum of eigenvalues of the mixed boundary problem is represented. Relationships for the main eigenfrequency versus the stiffness of face layers and characteristic geometric parameters of the sandwich shell wall are obtained.
TL;DR: In this article, the authors investigated the dynamical response of a system consisting of a prestressed covering layer and a half-plane to a moving load applied to the free face of the covering layer.
Abstract: Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the dynamical response of a system consisting of a prestressed covering layer and a prestressed half-plane to a moving load applied to the free face of the covering layer is investigated. Two types (complete and incomplete) of contact conditions on the interface are considered. The subsonic state is considered, and numerical results for the critical speed of the moving load are presented. The influence of problem parameters on the critical speed is analyzed. In particular, it is established that the prestressing of the covering layer and half-plane increases the critical speed.
TL;DR: In this article, the mixed-mode I + II interlaminar fracture of multidirectional glass/epoxy laminates is investigated and the results were validated using the beam theory model.
Abstract: The mixed-mode I + II interlaminar fracture of multidirectional glass/epoxy laminates is investigated. Mixed-mode bending (MMB) tests were performed on specimens with delaminations in 0/θ-type interfaces, with θ varying from 0 to 90°. Preliminary three-dimensional finite-element analyses validated the beam theory model (BTM) used for analysing experimental data. The compliances measured are in a good agreement with BTM predictions. The total critical energy release rate Gc varies linearly with the mode II ratio GII/G, although some discrepancies are observed in the high-mode II results for the 0/45 and 0/90 specimens.
TL;DR: In this paper, the use of R-curves to study the fracture behavior of high-strength concrete and steel-fiber-reinforced concrete subjected to crack ing in a three-point bending configuration is presented.
Abstract: This paper addresses the use of R-curves to study the fracture behavior of high-strength concrete and steel-fiber-reinforced concrete subjected to crack ing in a three-point bending configuration. The R-curves are modeled through an effective approach based on the equations of linear-elastic fracture mechanics (LEFM), which relates the applied load to the fundamental displacements of notched-through beams loaded monotonically. It is initially shown that, for quasi-brittle materials, the R-curves responses can be evaluated in a quasi-analytical way, using the load-crack mouth opening, the load-load line displacement, or exclusively the displacement responses obtained experimentally. Afterward, the methodology is used to obtain the fracture responses of high-strength and fiber-reinforced concretes, up to the final stages of rupture.
TL;DR: The results obtained in an experimental investigation of deformability of expanded polystyrene (EPS) under short-term compression are presented in this paper, where the density of EPS varied from 13 to 28 kg/m3.
Abstract: The results obtained in an experimental investigation of deformability of expanded polystyrene (EPS) under short-term compression are presented. The density of EPS varied from 13 to 28 kg/m3. The method of design of experiments was used to determine the elastic modulus and the ultimate strain (corresponding to the end of quasi-linear deformability) under compression stresses operating perpendicularly and parallel to the faces of EPS products. A graphical interpretation of the models is also presented. Based on the experimental data obtained, it was concluded that the expanded polystyrene was homogeneous in mutually perpendicular planes with respect to its deformability in compression.
TL;DR: In this paper, the transient creep of a UD composite with a quadratic arrangement of elastic fibers of Quadratic cross section is investigated, and two types of basic and resolving governing equations of transient creep are deduced, which are based on static or kinematic assumptions.
Abstract: The transient creep of a UD composite with a quadratic arrangement of elastic fibers of quadratic cross section is investigated. The deformational properties of the composite are determined from the known properties of its constituents. A structural model of the UD composite is developed, whose minimal elementary cell contains four elements. The stress-strain state of the elements is assumed homogeneous. Two types of basic and resolving governing equations of transient creep are deduced, which are based on static or kinematic assumptions. In each of the cases, a formula for the longitudinal elastic shear modulus of the composite is found. The stationary solutions of creep equations allow one to obtain formulas of the steady-state creep of the composite in a form similar to Norton’s law. Numerical calculations are also performed, and a comparison of the results with data given in the literature bears witness to the efficiency of the models developed and the solutions obtained.
TL;DR: In this article, an elastic annular composite plate with a light filler lying on an elastic foundation is considered, and the reaction of foundation is described based on the Winkler model.
Abstract: Bending of an elastic annular composite plate with a light filler lying on an elastic foundation is considered. The plate is subjected to local loads. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of broken normal is accepted. The reaction of foundation is described based on the Winkler model. A system of equilibrium equations is constructed, and its exact solution in displacements is found. Numerical solutions for a metal-polymer sandwich plate are presented.
TL;DR: In this article, a linear softening cohesive zone model is used to predict the unnotched and open-hole compressive strength of glass-fibre epoxy/honey comb sand panels loaded in uniaxial compression.
Abstract: Cohesive-zone models have been successfully applied to predicting the damage from notches in engineering materials loaded intension. They have also been used to determine the growth of fibre microbuckling from a hole in a composite laminate under compression. The usual strategy is to replace the in elastic deformation associated with plasticity or microbuckling with a line crack and to assume some form of stress-displacement bridging law across the crack faces. This paper examines recent published experimental data for notched glass-fibre epoxy/honey comb sand wich panels loaded in uniaxial compression. A plastic fibre kinking analysis and a linear softening cohesive-zone model are used for the prediction of the unnotched and open-hole compressive strength and the theoretical results are found to be in a good agreement with experimental data.
TL;DR: In this paper, a non-associated flow rule with different values of Poisson ratio intension and compression is proposed to describe the deformation behavior of non-reinforced thermoplastics.
Abstract: The tightening of industrial safety standards for structures generates a need for refined computational methods, which, among other things, must be able to describe the yield surface and the deformation behaviour of non-reinforced thermoplastics. To describe the plastic behaviour of materials, a potential formulation is suggested. This formulation contains a number of known potentials as special cases. The parameters of the model, which are obtained from test data, are restricted by the convexity condition for the potential. The new model allows one to take into account effects of the second order, for instance, the unequal behaviour under tension and compression, the plastic compressibility, and the Poynting-Swift effect. For each particular choice of the parameters, the Poisson ratio in tension is computed. If the restrictions imposed on the Poisson ratio do not hold, the application of a non-associated flow rule is necessary. A simple non-associated flow rule with different values of Poisson ratio intension and compression is proposed.
TL;DR: In this article, the effect of water on the mechanical properties of both chemically treated and untreated composites based on a recycled low-density polyethylene and linen yarn production waste is analyzed.
Abstract: The effect of water on the mechanical properties (tensile modulus, ultimate tensile strength, tensile strain, and specific work at break) of both chemically treated and untreated composites based on a recycled low-density polyethylene and linen yarn production waste is analyzed. It is found that three water sorption-desorption cycles change the tensile properties of both the materials irreversibly. This effect is considered as the result of partial fracture of the fiber-matrix interface.
TL;DR: In this article, a fast simulation procedure for axially loaded ribbed composite structures is suggested based on the response surface methodology (RSM), which is used to assess material degradation in terms of stiffness reduction in the skin-stringer zone.
Abstract: A fast simulation procedure for axially loaded ribbed composite structures is suggested based on the response surface methodology (RSM). The assessment of material degradation in terms of stiffness reduction in the skin-stringer zone is carried out to ensure the design reliability, thus acquiring a fast simulation procedure for an efficient and reliable analysis of the behaviour of axially loaded ribbed composite panels in their postbuckling state.
TL;DR: In this article, the authors explore an alternative approach and obtain the plastic potential of a cross-ply glass/epoxy laminate under uniaxial tensile loading at different angles to the material orthotropy axes.
Abstract: The plasticity theory has been successfully used for describing the nonlinear deformation of laminated composite materials under a monotonically increasing loading. Generally, several tests are needed to determine the parameters of the plastic potential for a laminate. We explore an alternative approach and obtain the plastic potential by using theoretical considerations based on a laminate analysis. The model is shown to provide an accurate prediction for the response of a cross-ply glass/epoxy laminate under uniaxial tensile loading at different angles to the material orthotropy axes.
TL;DR: In this article, the multicriteria optimization of the structure and geometry of a laminated anisotropic composite plate subjected to thermal and shear loading is considered, and the domain of allowable solutions and the Pareto-optimal subregion are found.
Abstract: The multicriteria optimization of the structure and geometry of a laminated anisotropic composite plate subjected to thermal and shear loading is considered. From the known properties of the monolayer and given values of variable structural parameters, the thermoelastic properties of the layered composite are determined. The optimization criteria — the critical shear load and the longitudinal thermal stresses — depend on two variable design parameters of composite properties and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subregion are found.
TL;DR: A survey of various methods for determining the complex elasticity and shear moduli from the resonant frequencies of flexural and torsional vibrations of rectangular rods cut out from a plate of an orthotropic composite is presented in this article.
Abstract: A survey of various methods for determining the complex elasticity and shear moduli from the resonant frequencies of flexural and torsional vibrations of rectangular rods cut out from a plate of an orthotropic composite is presented. The errors in the computed values of dynamic shear moduli caused by inaccuracies in the experimental determination of resonance frequencies are examined. A new variant of the resonance method is developed, which permits one to find three complex shear moduli of a composite from the resonant frequencies and the damping of torsional vibrations of three rods oriented along three symmetry axes of the material. For computing the moduli in the case of an overdetermined system, an algorithm of nonlinear optimization based on the least-squares method is recommended. From the results obtained it follows that, for determining the interlaminar shear moduli with a necessary accuracy, the rods must be sufficiently thick. It is shown that a good agreement alone between calculated and experimental frequencies of flexural and torsional vibrations of rods does not ensure a reliable determination of the moduli of interlaminar shear if experiments are carried out on wide test specimens cut out from a thin plate. Recommendations are given for the choice of geometrical sizes of test specimens for resonance experiments.
TL;DR: In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied.
Abstract: The ultrasonic nondestructive evaluation of composite cylinders requires a thorough understanding of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied. The frequency equations obtained for free cylinders and the effect of increased fiber volume fraction (increased anisotropy) on the dispersion characteristics of the rod are explored. The numerical results reveal a number of previously unnoticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves propagating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques.
TL;DR: A postbuckling analysis for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments is presented in this article.
Abstract: A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments. The material properties are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear-deformation shell theory with the von Karman-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. The boundary-layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling region, and the initial geometric imperfections of the shell, is extended to the case of shear-deformable anisotropic laminated cylindrical shells under lateral or hydrostatic pressure in thermal environments. The singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The results obtained show that the variation in temperature, layer setting, and the geometric parameters of such shells have a significant influence on their buckling load and postbuckling behavior.
TL;DR: In this paper, the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is investigated, and it is shown that at a great number of layers and appropriate reinforcing angles the shells can be considered orthotropic.
Abstract: A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections. This fact is important from the practical point of view.
TL;DR: In this article, an isotropic medium containing a system of foreign transverse rectilinear inclusions is considered, and the boundary value problem on equilibrium of the periodic system of cracks under the action of external tensile forces is reduced to a singular integral equation, from the solution of which the stress in tensity factors are found.
Abstract: An isotropic medium containing a system of foreign transverse rectilinear inclusions is considered. Such a medium can be interpreted as an infinite plate strengthened with a regular system of ribs (stringers) whose cross section is a very narrow rectangle. The medium is weakened by a periodic system of rectilinear cracks. The action of the stringers is re placed by unknown equivalent concentrated forces at the points of their connection with the medium. The boundary-value problem on equilibrium of the periodic system of cracks under the action of external tensile forces is reduced to a singular integral equation, from the solution of which the stress in tensity factors are found. The condition of limiting state of equilibrium of the cracks is formulated based on a criterion of brittle fracture. The stress state in the case where crack faces come into a partial contact is also considered.
TL;DR: In this paper, the limiting state of a multilayer eccentric ring made of a nonlinearly elastic material and subjected to a uniform external pressure is investigated, and the topicality and importance of the problem are connected with the search for reserves of savings in materials, with a simultaneous in crease in the load-carrying capacity of structures.
Abstract: The limiting state of a multilayer eccentric ring made of a nonlinearly elastic material and subjected to a uniform external pressure is investigated. The topicality and importance of the problem are connected with the search for reserves of savings in materials, with a simultaneous in crease in the load-carrying capacity of structures. Since rings often must have walls of varying thickness, their critical buckling force is determined as a function of a parameter considering this fact. In solving the problem, the geometric nonlinearity is also taken into account.
TL;DR: In this paper, the adhesive strength as a function of filler concentration has a maximum, which is more or less pronounced depending on the nature of filler and particle geometry, and the possible reasons for the phenomenon observed are discussed.
Abstract: The concentration dependences of adhesive strength are investigated for fiber/dispersedly filled epoxy matrix systems. The measurements were carried out using an improved model of adhesiometer under normal conditions at a constant rate of loading. It is shown that the adhesive strength as a function of filler concentration has a maximum, which is more or less pronounced. The location of the maximum depends on the nature of filler and particle geometry. The increase in the adhesive strength at the maximum reaches 20–30% in comparison with that for the unfilled epoxy matrix. Since the interfacial strength between steel wire and all the mineral powders investigated is zero, the growth in the adhesive strength upon introduction of a finely divided filler in polymer binders is rather un expected. The possible reasons for the phenomenon observed are discussed.