Mechanics of Composite Materials (v.43, #2)
Exact analytic solutions to the problem on plane buckling modes of rectangular orthotropic plates with free edges under biaxial loading
by V. N. Paimushin; T. V. Polyakova (pp. 97-112).
A two-dimensional linearized problem on plane buckling modes (BMs) of a rectangular plate with free edges, made of an elastic orthotropic material, underbiaxial tension-compression is considered. With the use of double trigonometric basis functions, displacement functions exactly satisfying all static boundary condition on plate edges are constructed. It is shown that the exact analytic solutions found describe only the pure shear BMs, and if the normal stress in one direction is assumed equal to zero, an analog of the solution given by the kinematic Timoshenko model can be obtained. Upon performing the limit passage to the zero harmonic in the displacement functions of one of the directions, the solution to the problem of biaxial compression can be obtained by equating the Poisson ratio to zero; in the case of uniaxial compression, this solution exactly agrees with that following from the classical Bernoulli-Euler model.
Keywords: linearized problem of stability; rectangular plate; biaxial tension-compression; shear and flexural buckling modes; free edges; trigonometric basis functions; exact analytic solutions; Bubnov method
Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites
by Yih-Cherng Chiang (pp. 113-126).
A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis.
Keywords: matrix cracking; debonding; Coulomb friction law; Poisson contraction
Investigation of the mechanical behavior of two-component granular composites in terms of structural models
by L. A. Golotina; L. L. Kozhevnikova; T. B. Koshkina (pp. 127-132).
A structural model is suggested for elastomers filled with particles of two fractions — with diameters exceeding 10 µm and submicronic ones. In each fraction, the particle diameter varies randomly, but between the fractions, the average particle diameter differs by several orders of magnitude. It is assumed that the small particles, together with the matrix, behave as a homogeneous medium relative to the large ones. By using this model, the mechanical behavior of composites based on elastomers filled with different volume contents of solid particles is investigated.
Keywords: two-component granular composite; structural cell; numerical experiment; constitutive relations
Numerical simulation of rheological processes in hardening plastics under stress control
by M. Klasztorny (pp. 133-140).
The paper concerns the simulation of rheological processes in hardening plastics (resins) under stress control. It is assumed that the resins work in the glassy state, under normal conditions, and the rheological processes are quasi-static and isothermal. The reduced stress levels do not exceed 30% of the instantaneous tensile strength. A resin is modelled as a homogeneous, isotropic, linearly viscoelastic material. The HWKK/H rheological model, developed recently by the author, is used. Short-term, medium-term, and long-term shear strain components are considered and described by one fractional and two normal exponential functions as the stress history (memory) functions. A novel algorithm for the numerical simulation of rheological processes in resins has been developed, which is unified for all stress history functions in the HWKK/H model. The algorithm employs the Boltzmann superposition principle, a virtual table for the classic creep process, and a high-rank Gaussian quadrature. The stress function is approximated with a stair case function. The constitutive equations governing the HWKK/H model are trans formed into an algebraic form suitable for algorithmization. The problem of quasi-exact calculation of the double-improper integral resulting from the fractional exponential function is solved effectively. The algorithm has been tested successfully on selected loading programs of unidirectional tension of epoxide.
Keywords: hardening plastics; HWKK/H model; rheological processes; stress control; numerical simulation
Buckling and the initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry
by N. P. Semenyuk; V. M. Trach (pp. 141-158).
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.
Keywords: stability; postbuckling behavior; composite materials; axial compression; torsion; external pressure; critical loads
Applied model of a round cylinder reinforced with systems of yarns at large tensile, inflation, and torsional deformations
by V. M. Akhundov (pp. 159-172).
Equations for a round cylinder weakly reinforced with systems of yarns and subjected to large tensile, inflation, and torsional deformations are presented. Since the degree of filling is small, the model of uniaxial stress state is assumed. The fibers are aligned with spirals on cylindrical surfaces and with radii in the transverse and meridional sections of the cylinder. The equations are obtained in the macroscopically unidimensional statement for the case of cylindrically symmetric strains. Numerical results are given for twisted hollow rubber cylinders reinforced with polymer yarns in the axial and radial directions.
Keywords: elastomeric matrix; polymeric fibers; applied model; large deformations; tension; inflation; torsion; deformation diagrams
The critical speed of a moving load on a prestressed plate resting on a prestressed half-plane
by S. D. Akbarov; C. Güler; E. Dincsoy (pp. 173-182).
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.
Keywords: critical speed; dynamical response; initial stress; layered half-plane; moving load
A system of steel-elastomer sandwich plates for strengthening orthotropic bridge decks
by M. Feldmann; G. Sedlacek; A. Geßler (pp. 183-190).
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.
Keywords: orthotropic steel bridge deck; elastomeric sandwich
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