The transverse compression of PPTA fibers Part I Single fiber transverse compression testing

We report on the transverse compression testing of fine,highly anisotropic polymer fibers. Single KEVLAR 29 fibers were laid on a flat, stiff platen, and compressed by a second, stiff, parallel platen. Test output was a force-deflection curve, from which the effective transverse modulus, apparent strain at yield and the work required to compress the fibers were determined. The effects of specimen aspect ratio was examined experimentally and by finite element simulation for loaded fiber lengths of 1/4 to 7 fiber diameters, and a method proposed to deduce the plane strain response from short aspect ratio tests.     

Curvature effects in the buckling of symmetrically-laminated rectangular plates with transverse shear deformation

It is shown that the effect of stress discontinuities from ply-to-ply must be taken into account when curvature terms are included along with shear deformation in the buckling analysis of rectangular, symmetrically-laminated plates. Such ply-stress discontinuities lead to curvature terms in the governing equations which differ considerably from those derived for homogeneous plates. Critical buckling loads are determined for orthotropic laminates subjected to biaxial inplane loading and for cylindrical bending of anisotropic plates subjected to uniaxial compression loading. Simply-supported boundary conditions are considered in conjunction with the rectangular, orthotropic laminate, while simply-supported and clamped boundaries are considered for the case of cylindrical bending of anisotropic plates. Numerical results indicate that the curvature terms have little effect on critical buckling loads for the laminates investigated. The effect of transverse shear deformation is shown to depend on the degree of boundary constraint, laminate stacking geometry, and inplane load ratio.     

Effect of transverse shear deformation on free vibration of orthotropic conical shells

Summary The solutions for five displacements, in the form of a power series, are obtained for the five governing equations of free vibration of orthotropic conical shells including the transverse shear deformation. The convergence condition for the solutions is also determined. As an illustrative example, axisymmetric vibration of isotropic and orthotropic cones, with different geometric and material parameters and under two types of boundary conditions, are analyzed numerically to investigate the effect of the transverse shear deformation on the frequency parameters.     

Non-stationary boundary equations for plates with transverse shear deformation and elastic articulation of the boundary

Summary The existence of distributional solutions is investigated for the boundary integral equations associated with the bending motion of an elastic plate whose boundary is subjected to an elastic articulation.     

Enhanced transverse shear strain shell formulation applied to large elasto‐plastic deformation problems

In this work, a previously proposed Enhanced Assumed Strain (EAS) finite element formulation for thin shells is revised and extended to account for isotropic and anisotropic material non‐linearities. Transverse shear and membrane‐locking patterns are successfully removed from the displacement‐based formulation. The resultant EAS shell finite element does not rely on any other mixed formulation, since the enhanced strain field is designed to fulfil the null transverse shear strain subspace coming from the classical degenerated formulation. At the same time, a minimum number of enhanced variables is achieved, when compared with previous works in the field. Non‐linear effects are treated within a local reference frame affected by the rigid‐body part of the total deformation. Additive and multiplicative update procedures for the finite rotation degrees‐of‐freedom are implemented to correctly reproduce mid‐point configurations along the incremental deformation path, improving the overall convergence rate. The stress and strain tensors update in the local frame, together with an additive treatment of the EAS terms, lead to a straightforward implementation of non‐linear geometric and material relations. Accuracy of the implemented algorithms is shown in isotropic and anisotropic elasto‐plastic problems. Copyright © 2004 John Wiley & Sons, Ltd.     

The shear properties and deformation mechanisms of porous metal fiber sintered sheets

Porous metal fiber sintered sheets (MFSSs) are a type of layered transversely isotropic open cell materials with low relative density (i.e., volume fraction of fibers), high specific stiffness and strength, and controllable precision for functional and structural applications. Based on a non-contact optical full field strain measurement system, the in-plane and transverse shear properties of SMFFs with relative densities ranging from 15% to 34% are investigated. For the in-plane shear, the modulus and strength are found to depend linearly upon the relative density. The associated deformation is mainly due to fiber stretching, accompanied by the direction change of metal fibers. When the shear loading is applied in the transverse direction, the deformation of the material is mainly owing to fiber bending, followed by the separation failure of the fiber joints. Measured results show that the transverse shear modulus and strength have quartic and cubic dependence upon the relative density respectively and are much lower than their in-plane counterparts. Simple micromechanics models are proposed for the in-plane and transverse moduli and strengths of MFSSs in shear. The predicted relationships between the shear mechanical properties of MFSSs and their relative density are obtained and are in good agreement with the measured ones.     

Vibrations of axially compressed laminated orthotropic cylindrical shells,including transverse shear deformation

Summary The free vibrations, buckling and the effect of initial prestress upon the frequency spectrum of orthotropic composite cylindrical shells are examined in the context of a theory that includes transverse shear deformation. Results obtained are compared with the predictions of refined Love-type theory and simplified Donnell-type theory that do not consider shear deformation.The calculated examples indicate that transverse shear deformation can be significant not only for short composite shells but even for longer shells possessing low shear moduli.

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Schwingungen axial gedrückter, laminierter, orthotroper zylindrischer Schalen einschließlich Querschubverformung

Zusammenfassung Es werden die freien Schwingungen, das Beulen und der Einfluß einer Anfangsvorspannung auf das Frequenzspektrum orthotroper, kompositer, zylindrischer Schalen im Rahmen einer Theorie, die die Querschubverformung mitberücksichtigt, untersucht. Die erhaltenen Resultate werden mit den Vorhersagen der verbesserten Loveschen Theorie und der vereinfachten Donnellschen Theorie, welche keine Querschubverformung in Betrach ziehen, verglichen.Die durchgerechneten Beispiele zeigen, daß die Querschubverformung nicht nur für kurze, komposite Schalen sondern sogar für längere Schalen mit niederem Schubmodul Bedeutung gewinnen kann.

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Nomenclature a radius of reference surface of cylindrical shell - A _i amplitudes of displacements - A _ij elastic area - B _ij elastic statical moment - D _ij elastic moment of inertia - E _ij elastic stiffness modulus - h shell thickness - k ₄₄,k ₅₅ shear correction factors - l length of cylindrical shell - L _ij functional operator - m number of half-waves in axial direction - M ,M ,M axial, circumferential and twisting moments, respectively - n number of circumferential waves - N ⁰ axial compression force - N ,N ,N axial, circumferential and shear forces, respectively - Q ,Q transverse shear forces - R ₀,R ₁,R ₂ inertia terms - t time - T matrix defined in Eq. (25) - u, v, w displacements in axial, circumferential and radial directions, respectively - U _i time-independent displacement or rotation - nondimensional axial wave parameter - , , axial, circumferential and shear strains, respectively - radial coordinate, taken positive inward - polar angle - , , curvature changes - circular frequency - nondimensional axial coordinate - density - , , , , stress components - , rotations of normal to undeformed midsurface With 6 Figures     

Damping optimization of symmetrically laminated plates with transverse shear deformation using lamination parameters

This paper deals with the damping characteristics of symmetrically laminated plates with transverse shear deformation. First, the effect of laminate configuration on the damping characteristics is investigated for cantilevered laminated plates based on the Reissner–Mindlin’s first-order shear deformation theory. To examine the effect of laminate configuration, the concept of specific damping capacity is introduced and the damping characteristics are represented on the lamination parameter plane, where the damped stiffness invariants in transverse shear are newly proposed in this paper. Next, the optimal laminate configurations for the cantilevered laminated plates with maximal damping are determined taking into account the transverse shear effect by using differential evolution in which lamination parameters are used as intermediate design variables. The relation between the laminate configurations and the damping characteristics is discussed based on the concept of lamination parameters.     

On the spatial behaviour of the transient and steady-state solutions in thin plates with transverse shear deformation

This paper studies the spatial behaviour of the transient and steady-state solutions in the problem of bending of a plane elastic plate. When the transient solutions are discussed a bounded or unbounded plane plate of an arbitrary regular form is considered. Then an appropriate time-weighted line-integral measure is introduced and, for each fixed t∈[0,T], it is shown that it vanishes at distances from the support of the given data on the time interval [0,T] greater than ct, where c is a characteristic material constant. Moreover, for distances to the support lower than ct, it is established a spatial decay estimate of Saint-Venant-type. For the harmonic vibrations the case of an elastic plate whose middle surface is like a (semi-infinite) strip is considered for which the lateral sides are clamped. Then a cross-sectional line-integral measure is associated with the amplitude of the vibration and the spatial estimate is established for describing the spatial behaviour of the amplitude, provided that the frequency of the harmonic vibration is lower than a critical frequency.     

On the influence of the shear deformation and boundary conditions on the transverse vibration of multi-walled carbon nanotubes

The vibrational properties of multi-walled carbon nanotubes (MWCNTs) are studied, especially the influence of the shear deformation and the boundary conditions on the non-coaxial frequencies. A high order continuum beam model is proposed, which can be applied to study the transverse vibrations of MWCNTs, including those that could have initial deformations due to defects or external actions. Using the model it was found that the non-coaxial intertube frequencies are independent of the shear deformation and the boundary conditions. This result is important considering that the concentric structure of MWCNTs is a crucial geometrical characteristic and a non-coaxial vibration would affect their electronic and optical properties.     

Control of mechanical deformation of a laminate by electrical load to piezoelectric actuator considering the effects of damping and transverse shear

In this paper, we treat the control of dynamic deformation of a laminate by applying electrical load to piezoelectric actuators. Dynamic behavior of the laminate is analyzed considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all edges simply supported and to be subjected to unavoidable mechanical load and to electrical loads to piezoelectric actuators. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. The following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) transient deflection due to loads varying arbitrarily with time. Moreover, the methods to control the deflection due to mechanical load by applying electrical voltage to the piezoelectric actuator are shown.     

A BEM solution to transverse shear loading of beams

In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of beams of arbitrary simply or multiply connected constant cross section. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson’s ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses at any interior point is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ‘exact’ elastic beam theory is remarkable.     

Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, , of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, , of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Nanoindentation contribution to mechanical characterization of vegetal fibers

Nanoindentation tests were performed on flax fibers or stems sections in order to study the influence of the maturity of the fibers and the one of the location of the fibers within a bundle on their mechanical properties. The first results evidence the interest of this technique to approach differences into mechanical properties of plant fibers and highlight some questions linked to the specific structure of fibers.     

Effect of fiber,matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites

The effect of fiber, matrix and interface properties on the in-plane shear response of carbon-fiber reinforced epoxy laminates was studied by means of a combination of experiments and numerical simulations. Two cross-ply laminates with the same epoxy matrix and different carbon fibers (high-strength and high-modulus) were tested in shear until failure according to ASTM standard D7078, and the progressive development of damage was assessed by optical microscopy in samples tested up to different strains. The composite behavior was also simulated through computational micromechanics, which was able to account for the effect of the constituent properties (fiber, matrix and interface) on the macroscopic shear response. The influence of matrix, fiber and interface properties on each region and on the overall composite behavior was assessed from the experimental results and the numerical simulations. After the initial elastic region, the shear behavior presented two different regions, the first one controlled by matrix yielding and the second one by the elastic deformation of the fibers. It was found that in-plane shear behavior of cross-ply laminates was controlled by the matrix yield strength and the interface strength and was independent of the fiber properties.     

Sound transmission loss characteristics of unbounded orthotropic sandwich panels in bending vibration considering transverse shear deformation

A theoretical study on the sound transmission loss (STL) characteristics of unbounded orthotropic sandwich panels considering the transverse shear deformation is presented. With the transverse shear deformation taken into account, the governing equation of bending vibration for unbounded orthotropic sandwich panels is derived and implemented to the sound transmission problem. The expressions for impedance and transmission coefficient are also derived. The accuracy of the theoretical predictions is checked against available experimental data. The influence of several key parameters on the sound insulation properties of the orthotropic sandwich panel is then systematically studied, including shear rigidity of the core, face sheet thickness, and core thickness. Numerical analysis shows that shear rigidity has evident effect on coincidence critical frequency and STL property, and should not be neglected when predicting STL. Increasing face sheet thickness can move coincidence critical frequency to lower frequency region and improve STL, which is much more effective than increasing the core thickness.