# Mechanics of Composite Materials (v.45, #2)

Exact analytical and numerical solutions of stability problems for a straight composite bar subjected to axial compression and torsion by V. N. Paimushin; V. A. Ivanov; S. A. Lukankin; N. V. Polyakova; V. A. Firsov; S. A. Kholmogorov

*(113-136)*. Based on linearized equations of the theory of elastic stability of straight composite bars with a low shear rigidity, which are constructed using the consistent geometrically nonlinear equations of elasticity theory for small deformations and arbitrary displacements and a kinematic model of Timoshenko type, exact analytical solutions of nonclassical stability problems are obtained for a bar subjected to axial compression and torsion for various modes of end fixation. It is shown that the problem of direct determination of the critical parameter of the compressive load at a given torque parameter leads to transcendental characteristic equations that are solvable only if bar ends have cylindrical hinges. At the same time, we succeeded in obtaining solutions to these equations in terms of wave formation parameters of the bar; these parameters, in turn, enabled us to find the parameter of the critical load at any boundary conditions. Also, an algorithm for numerical solution of the problems stated is proposed, which is based on reducing the problems to systems of integroalgebraic equations with Volterra-type operators and on solving these equations by the method of mechanical quadratures (finite sums). It is demonstrated that such numerical solutions exist only for certain ranges of parameters of the bar and of the parameter of torque. In the general case, they can not be obtained by the numerical method used. It is also shown that the well-known solutions of the stability problem for a bar subjected to torsion or to compression with torsion are in correct.

**Keywords:**straight bar; compression and torsion; Timoshenko model; exact analytical solutions; numerical solutions; experiment

Effect of long-term exposure to water on the viscoelastic properties of an epoxy-based composition by K. Aniskevich; R. Krastev; Yu. Hristova

*(137-144)*. For modeling the effect of volume change on the viscoelastic properties of a polymer, an equation underlying the concept of free volume is used. The parameters of the moisture–time reduction function, characterizing changes in the viscoelastic properties of an epoxy-based composition, are determined from tests results. To verify the approach suggested, results of long-term (up to one year) tests on stress relaxation under compression in an epoxy composition (COMFLOOR), both in the initial state and after a long-term (up to one year) exposure to water, are used. A satisfactory agreement between the reduction functions based on predictions and determined experimentally is found to exist.

**Keywords:**polymer; viscoelasticity; exposure to water; stress relaxation; reduction function

A model for predicting the multiscale crack growth due to an impact in heterogeneous viscoelastic solids by F. V. Souza; D. H. Allen

*(145-152)*. A two-scale model for predicting the multiple crack growth in viscoelastic solids due to an impact is presented. The cracks are considered only at the local scale through the use of a micromechanical viscoelastic cohesive zone model. The multiscale model has been implemented in a finite-element code. In order to minimize the computation time, the local finite-element meshes are solved in parallel by multiple processors. An example problem is given in order to demonstrate the capabilities of the model.

**Keywords:**multiscale model; heterogeneous viscoelastic media; dynamic/impact loading; fracture

Multicriteria optimization of a composite cylindrical shell subjected to longitudinal thermal stresses and buckling under the action of torque by G. Teters

*(153-158)*. The multicriteria optimization of the structure and geometry of a multilayer cylindrical shell under the action of external torque and longitudinal thermal stresses is considered. From known monolayer properties of the composite and given values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined. The criteria to be optimized — the critical external torque and thermal stresses — depend on two variable parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found.

**Keywords:**composite cylindrical shell; external torque; thermal stresses; multicriteria optimization

A variational principle in a geometrically nonlinear theory of heterogeneous viscoelastic shells by R. Yu. Amenzadeh

*(159-164)*. The use of the hereditary theory for shells heterogeneous across their thickness is considered. A variational method is formulated for calculating thin anisotropic shells made of a material whose deformation behavior can be described by relations of the linear theory of viscoelasticity. In order to transform the corresponding functional into a form suitable for shells, some assumptions related to concepts of the theory of thin shells are introduced. In the capacity of Euler equations, physical relations, nonlinear equilibrium equations, and nonlinear boundary conditions are derived. The state equations are deduced for a multilayered shell.

**Keywords:**multilayer shell; tensors of instantaneous compliance; creep operators

Measuring and modeling the thermal conductivities of three-dimensionally woven fabric composites by J. Schuster; D. Heider; K. Sharp; M. Glowania

*(165-174)*. The effect of a three-dimensional fiber reinforcement on the out-of-plane thermal conductivity of composite materials is investigated. Composite preforms with different fibers in the thickness direction were fabricated. After in fusion by using a vacuum-assisted resin transfer molding process, their through-thickness thermal conductivities were evaluated. The measured thermal conductivities showed a significant increase compared with those of a typical laminated composite. Although the through-thickness thermal conductivity of the samples increased with through-thickness fiber volume fraction, its values did not match those predicted by the simple rule of mixtures. By using finite-element models to better under stand the behavior of the composite material, improvements in an existing analytical model were performed to predict the effective thermal conductivity as a function of material properties and in-contact thermal properties of the composite.

**Keywords:**textile composites; thermal properties; modeling; finite-element analysis

Polytetramethylene glycol-modified polycyanurate matrices reinforced with nanoclays: synthesis and thermomechanical performance by G. I. Anthoulis; E. Kontou; A. Fainleib; I. Bei

*(175-182)*. The outstanding improvement in the physical properties of cyanate esters (CEs) compared with those of competitor resins, such as epoxies, has attracted appreciable attention recently. Cyanate esters undergo thermal polycyclotrimerization to give polycyanurates (PCNs). However, like most thermo setting resins, the main draw back of CEs is brittleness. To over come this disadvan tage, CEs can be toughened by the introduction of polytetramethylene glycol (PTMG), a hydroxyl-terminated polyether. How ever, PTMG has a detrimental impact on Young’s modulus. To simultaneously enhance both the ductility and the stiffness of CE, we added PTMG and an organoclay (mont morillonite, MMT) to it. A series of PCN/PTMG/MMT nanocomposites with a constant PTMG weight ratio was pre pared, and the resulting nanophase morphology, i.e., the degree of filler dispersion and distribution in the composite and the thermomechanical properties, in terms of glass-transition behaviour, Young’s modulus, tensile strength, and elongation at break, were examined using the scanning elec tron micros copy (SEM), a dynamic mechanical analysis (DMA), and stress–strain measurements, re spectively. It was found that, at a content of MMT below 2 wt.%, MMT nanoparticles were distributed uniformly in the matrix, suggesting a lower degree of agglomeration for these materials. In the glassy state, the significant increase in the storage modulus revealed a great stiffening effect of MMT due to its high Young’s modulus. The modification with PTMG led to a 233% greater elongation at break compared with that of neat PCN. The nanocomposites exhibited an invariably higher Young’s modulus than PCN/PTMG for all the volume factors of organoclay examined, with the 2 wt.% material displaying the most pronounced in crease in the modulus, in agreement with micros copy results.

**Keywords:**polycyanurate; organoclay; thermomechanical properties

Stress distribution in an infinite elastic body with a covered periodically curved fiber by R. Kosker; D. M. Dikbas

*(183-198)*. Within the frame work of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of elasticity theory, a method is developed for determining the stress distribution in unidirectional fibrous composites with periodically curved fibers. The distribution of the normal and shear stresses acting on interfaces for the case where there exists a bond covering cylinder of constant thickness between the fiber and matrix is considered. The concentration of fibers in the composite is assumed to be low, and the interaction between them is neglected. Numerous numerical results related to the stress distribution in the body considered are obtained, and the influence of geometrical nonlinearity on this distribution is analyzed.

**Keywords:**fibrous composite; covering material; geometrical nonlinearity; normal stresses

Polyetheretherketone (PEEK) nanocomposites for extreme mechanical and tribological loads by N. Knör; A. Gebhard; F. Haupert; A. K. Schlarb

*(199-206)*. Nano-zinc sulfide (ZnS)- and nano-titanium dioxide (TiO

_{2})-reinforced polyetheretherketone (PEEK) composites for use under extreme mechanical and tribological loads were developed and investigated systematically. The nanocomposites were manufactured with particle concentrations of 1 to 15 vol.% by using an optimized twin-screw extrud er technology. A simultaneous increase in the strength and elastic modulus of PEEK and an improvement in the tribological properties of PEEK/ZnS compounds were observed. Also, the specific wear rate decreased with increasing ZnS content, reaching its minimum at 3 vol.%. This minimum corresponded to a 60% reduction in the wear rate com pared with that of the neat PEEK. A wear map was re corded for the 3 vol.% composite, which depicted the in fluence of the sliding speed and the normal force on the wear rate over a wide range of parameters.**Keywords:**nanocomposite; stiffness; strength; wear rate; abrasion resistance

Analytical and numerical techniques for predicting the interfacial stresses of wavy carbon nanotube/polymer composites by K. Yazdchi; M. Salehi; M. M. Shokrieh

*(207-212)*. By introducing a new simplified 3D representative volume element for wavy carbon nanotubes, an analytical model is developed to study the stress transfer in single-walled carbon nanotube-reinforced polymer composites. Based on the pull-out modeling technique, the effects of waviness, aspect ratio, and Poisson ratio on the axial and interfacial shear stresses are analyzed in detail. The results of the present analytical model are in a good agreement with corresponding results for straight nanotubes.

**Keywords:**carbon nanotubes; interfacial stresses; nanocomposites; fiber waviness