Showing papers in "Journal of Composite Materials in 1970"
TL;DR: In this article, three-dimensional elasticity solutions for rectangular laminates with pinned edges are constructed for three dimensional elasticity problems, including a sandwich plate, and compared to the analogous results in classical laminated plate theory.
Abstract: In a continuing study, three-dimensional elasticity solutions are constructed for rectangular laminates with pinned edges. The lamination geometry treated consists of arbitrary numbers of layers which can be isotropic or orthotropic with material symmetry axes parallel to the plate axes. Several specific example problems are solved, including a sandwich plate, and compared to the analogous results in classical laminated plate theory.
1,730 citations
TL;DR: In this article, the response of a finite-width composite laminate under uniform axial strain is treated through the application of classical elasticity theory, and finite-difference solution techniques are employed to obtain solutions for stresses and displacements throughout the region.
Abstract: The response of a finite-width composite laminate under uniform axial strain is treated through the application of classical elasticity theory. Finite-difference solution techniques are employed to obtain solutions for stresses and displacements throughout the region. Results for material properties typical of a high modulus graphite-epoxy composite material system are presented which explain the mechanism of shear transfer within a symmetric laminate. In addition, results of this work are compared to those given in a recent approximate formulation.
1,048 citations
TL;DR: In this paper, a correlation exists between the Raman spectrum of the fiber surface and the shear strength of the graphite and carbon fibers, which is used for fiber characterization.
Abstract: Raman spectroscopy is used to characterize the fiber surface of graphite and carbon fibers. A correlation exists between the Raman spectrum of the fiber surface and the shear strength of the com po...
433 citations
TL;DR: The results of theoretical estimates for several thermal and thermoelastic constants of macroscopically isotropic composite materials are given in this paper, including elastic constants, thermal expansion coefficients, heat capacities (at constant volume and constant pressure), thermal conductivity, and related constants.
Abstract: The results of theoretical estimates are given for several thermal and thermoelastic constants of macroscopically isotropic composite materials. The composites considered consist of random mixtures of N isotropic constituents, at least ( N — 1) of which are presumed to be distributed in a particulate fashion, with the particles roughly spherical in shape. The results are based on "self-consistent" calcula tions, details of which are given in appendices.Equations (some of which are old, but are repeated for con venience) are given for the following quantities: elastic constants, thermal expansion coefficients, heat capacities (at constant volume and constant pressure), thermal conductivity, and, finally, Gruneisen and related constants.
253 citations
TL;DR: In this article, an analysis of interlaminar shear stresses is performed for a laminate under generalized plane stresses, where the laminate is modeled as a set of anisotropic layers separated by isotropic adhesive layers.
Abstract: An analysis of interlaminar shear stresses is performed for a lami nate under generalized plane stresses. The laminate is modeled as a set of anisotropic layers separated by isotropic adhesive layers. The corresponding equilibrium differential equations are developed and solved for laminates of infinite and finite width. In the first case, it is shown that the interlaminar shear stress is zero everywhere, while in the latter case, this stress attains finite maximum values at the edges of the strip. These results are important when interpreting strength data obtained from uniaxial tests.
245 citations
TL;DR: In this article, the exact solution of the problem of a pinned-end laminate composed of N layers, each of which possesses only a single plane of elastic symmetry, under cylindrical bending is investigated.
Abstract: Investigation of the success of classical lamination theory in predicting the response of composite laminates under static bending is extended by consideration of the influence of shear coupling. Specifically, we treat the exact solution of the problem of a pinned-end laminate composed of N layers, each of which possesses only a single plane of elastic symmetry, under cylindrical bending. Several example problems, involving unidirectional and angle-ply composites, are solved and the detailed results compared to corresponding approximate solutions. Some observations are offered in regard to the general range of validity of classical laminated plate theory.
245 citations
TL;DR: In this paper, numerical results for composite behavior beyond the elastic limit and up to first failure were obtained using finite element analysis, and examples representative of several actual material systems are presented.
Abstract: Composite material behavior is divisible into three distinct re gimes, linear elastic response up to the elastic limit, inelastic be havior beyond the elastic limit and up to that point at which first failure occurs locally, and subsequent crack propagation and total composite failure. The first regime has been thoroughly explored in previous investigations, while the second is the main topic of the present paper. The third is briefly discussed and is a subject under investigation.Utilizing a finite element analysis, numerical results are obtained for composite behavior beyond the elastic limit and up to first failure. Examples representative of several actual material systems are presented and discussed in detail.Results indicate that extensive local yielding and redistribution of stresses can occur in a composite with very little indication of such behavior being apparent by observation of the total stress- strain response of the composite alone. Thus, the establishment and interpretation of design crit...
148 citations
TL;DR: In this article, a real variable integral formula of the Somigliana type is derived for linear anisotropic elasticity, which relates an elastic displace field to boundary traction and displacement vectors; all refer to an arbitrary equilibrated stress state present in an orthotropic body of arbitrary shape and connectivity.
Abstract: Using a fundamental solution to the appropriate field equations of linear anisotropic elasticity, a real variable integral formula of the Somigliana type is derived. The formula relates an elastic displace ment field to boundary traction and displacement vectors; all refer to an arbitrary equilibrated stress state present in an orthotropic body of arbitrary shape and connectivity. A fundamental relation between boundary traction and displacement is then derived which is a mechanism for determining (numerically in practice) that part of such boundary data not initially given from a knowledge of that part which is given. Once all boundary quantities are known, the field solution is given by the integral formula and its first derivatives. Finally, the body may be composite; i.e., it may contain inclusions or inhomogeneities which may be isotropic or rigid as special cases. Numerical techniques are indicated and several problems are solved for illustration.
141 citations
TL;DR: In this paper, the effect of boundary conditions on the bending, vibrations, and buckling of unsymmetrically laminated rectangular plates is investigated, and the applicability of the reduced-bending stiffness approximation is also explored.
Abstract: The effect of boundary conditions on the bending, vibrations, and buckling of unsymmetrically laminated rectangular plates is in vestigated. Five sets of boundary conditions corresponding to various clamped and simply-supported edges are treated. The effect of in- plane boundary conditions is shown to be a function of fiber orienta tion within the laminate. Numerical results also show that the effects of bending-extensional coupling can be severe for all the boundary conditions considered. The applicability of the reduced-bending- stiffness approximation is also explored.
129 citations
TL;DR: In this paper, a procedure is outlined to determine the proper geometry of anisotropic and laminated cylinders such that elastic stress gradients can be reduced to a predetermined limit, which consists of combining a modified plane strain elasticity solu tion with shell theory.
Abstract: The stress field within a highly anisotropic cylinder, even under simple loading conditions, is far from uniform. Thus, like other verbage which has its origins in the stress analysis of isotropic bodies, the terminology "thin-walled cylinder" must be redefined for aniso tropic materials, and is a strong function of elastic moduli. This places a severe burden on the experimentalist who must employ such specimens to characterize composite materials under biaxial states of stress. In this work, a procedure is outlined to determine the proper geometry of anisotropic and laminated cylinders such that elastic stress gradients can be reduced to a predetermined limit. The ap proach consists of combining a modified plane strain elasticity solu tion with shell theory. Parametric studies on materials possessing high and low degrees of anisotropy indicate general guidelines for proper tube geometry for precise characterization under simulated laboratory loading and clamping conditions.
103 citations
TL;DR: In this paper, the Halpin-Tsai equations are used to estimate the longitudinal shear modulus of fiber reinforced composites, and a simple but approximately precise formula to interpolate the existing exact machine calculations available in the current literature is presented.
Abstract: It has been suggested [1] that it is often advantageous for design purposes to be able to rapidly calculate accurate estimates for the elastic moduli of fibre reinforced composites, and that a simple but approximately precise formula to interpolate the existing exact machine calculations available in the current literature is to be desired. The Halpin-Tsai equations, presented in [1], aim to satisfy this need, and the expression for estimating the longitudinal shear modulus is given as:
TL;DR: Elastic properties for reinforced composite material with hollow spherical inclusions embedded in the matrix were determined for the case of reinforced composite materials as mentioned in this paper, where the inclusions were embedded in a hollow spherical sphere.
Abstract: Elastic properties determined for reinforced composite material with hollow spherical inclusions embedded in matrix
TL;DR: The behavior of polyester resin reinforced with hard-drawn steel wires and with fully-softened wires of the same steel has been studied in compression tests on free-standing cylinders in which the wires are parallel with the direction of the applied load as discussed by the authors.
Abstract: The behaviour of polyester resin reinforced with hard-drawn steel wires and with fully-softened wires of the same steel has been studied in compression tests on free-standing cylinders in which the wires are parallel with the direction of the applied load. Despite the predictions of various theories of the compressive strength of composites, the two materials behave dissimilarly, and their strengths fall well below values predicted by models based on treatments of the fibres as col umns on an elastic foundation. Fibres appear to buckle into helical shapes rather than into the planar forms usually postulated, and it is likely that the lower elastic energy required for this deformation could be the factor responsible for the disagreement between theory and experiment.
TL;DR: In this paper, a unique elasticity finite element program has been implemented which can deal with the general three-dimensional nature of axisym metric composite bodies, which is used to analytically predict the response of unidirectional composite tube specimens to uniaxial tension/compression.
Abstract: To gain needed insight into the effects of thickness to diameter ratio (t/Di), length to diameter ratio (l/Di ), and helical angle (α) on the response of laminated tubes in material characterization tests, a unique new elasticity finite element program has been implemented which can deal with the general three-dimensional nature of axisym metric composite bodies The program, which is utilized here to analytically predict the response of unidirectional composite tube specimens to uniaxial tension/compression, differs from the usual finite element formulations in that it accounts for general anisotropy In particular, it deals with all shear coupling terms and all six com ponents of stress The effects of different gripping methods are also considered Similar studies of torsion and internal pressurization tests will be reported in subsequent notesThis first phase of the study shows that while the response of axial and hoop wrapped tubes (α = 0°, 90°) is essentially indepen dent of length and thickness ra
TL;DR: In this paper, Timoshenko beam theory was used to account quantitatively for the dependence of ex perimental resonant frequencies on mode of vibration, length/thickness ratio, and the ratio of Young's modulus/shear modulus of the com posite beam.
Abstract: The resonant frequencies of unidirectional graphite epoxy com posite beams were found to deviate markedly from classical beam theory predictions at higher modes of vibration. Timoshenko beam theory was used to account quantitatively for the dependence of ex perimental resonant frequencies on mode of vibration, length/thickness ratio, and the ratio of Young's modulus/shear modulus of the com posite beam. By using reasonable values for the longitudinal-trans verse shear moduli, the longitudinal Young's modulus of anisotropic composite beams under vibration agreed well with values determined by static tests and became independent of mode of vibration and L/t. The vibrating beam test method was employed for the deter mination of E11, E22, and G12.
TL;DR: In this paper, the requirements on the boundary conditions of the assumed series in a Ritz solution for anisotropic plates are discussed for classical and elastically restrained boundary conditions, and extensive numerical results are presented to illus trate the solution method for series satisfying only the geometrical boundary conditions.
Abstract: The requirements on the boundary conditions of the assumed series in a Ritz solution for anisotropic plates is discussed for classical and elastically restrained boundary conditions. A convenient method is indicated for handling elastically restrained boundary conditions which satisfies the natural boundary conditions for orthotropic or iso tropic plates and which utilizes the integration formulas given in a previous paper. Extensive numerical results are presented to illus trate the solution method for series satisfying only the geometrical boundary conditions and for series satisfying both natural and geo metrical boundary conditions.
TL;DR: In this article, elastic fields in bimaterial plate under uniform compressive and anti-plane shear loadings were used to find stress distribution and induced interfacial shear stresses.
Abstract: Elastic fields in bimaterial plate under uniform compressive and anti-plane shear loadings, finding stress distribution and induced interfacial shear stresses
TL;DR: In this article, a simply supported cross-ply laminated plate infinite in length was analyzed and the first two mode shapes were compared to classical plate theory up to moderate wavelengths for various wavelengths.
Abstract: Vibration of a simply supported cross-ply laminated plate infinite in length is analyzed. Existence of plane strain conditions allow an exact solution of the field equations. Curves of variation of exact natural frequencies versus wavelength for several cases of a two-ply laminated plate are calculated. The first two mode shapes are plotted for various wavelengths and compared to classical plate theory. Flex ural vibration appears to be well approximated by classical theory up to moderate wavelengths. Extensional vibration is approximated mar ginally only for very long wavelengths.
TL;DR: In this paper, a cylindrical test sample is placed between two silver plates that are maintained at constant temperatures by liquids with different boiling points, and saturated vapor from the liquid with the higher boiling point condenses on the lower plate and transfers energy to the sample.
Abstract: Thermal conductivity measurements were made with a Colora Thermoconductometer, which is described in detail by Schrbder [10]. A cylindrical test sample is placed between two silver plates that are maintained at constant temperatures by liquids with different boiling points. Saturated vapor from the liquid with the higher boiling point condenses on the lower silver plate and transfers energy to the sample. The liquid with the lower boiling point evaporates from the upper silver plate, and the generated vapor is condensed and collected in a graduated container.
TL;DR: Elastic-plastic shear cracks propagation in two-phase composite materials using dislocation model, determining critical fracture strength as mentioned in this paper, is used to determine fracture strength of composite materials.
Abstract: Elastic-plastic shear cracks propagation in two phase composite materials using dislocation model, determining critical fracture strength
TL;DR: In this paper, a model for nonplate/shell geometries, such as plate and cylinder structures, is proposed, which requires a consideration of interlaminar shear ef-
Abstract: Recent advances with the new high-performance fibers, such as boron and graphite, have precipitated a dramatic upsurge of effort in the field of filamentreinforced composites. The structural configurations of interest have thus far been treated primarily by classical plate and shell theories. Considerably less attention has been accorded the formulation of models for nonplate/shell geometries, e.g., thick plates and cylinders which require a consideration of interlaminar shear ef-
TL;DR: In this article, it was shown that the optimum filament orientation differs from the principal stress direction and depends on the normal strength parallel and perpendicular to the filament X and Y and the shear strength T as well as on applied stresses.
Abstract: Of considerable concern to the designer is the orientation of the filaments in a filamentary composite for a specified combination of normal and shear stresses. Using Hill’s yield criterion for transversely isotropic materials in a state of plane stress, Sandhu [ 1 recently determined the filament orientation yielding maximum strength for the applied stresses shown in Figure 1. From a study of the computed data, he concluded that if the composite shear strength is less than the transverse normal strength, the filaments should be oriented in the principal stress direction. However, if the converse is true, the optimum filament orientation differs from the principal stress direction and depends on the normal strengths parallel and perpendicular to the filaments X and Y and the shear strength T as well as on the applied stresses. In this note, these results will be obtained analytically rather than empirically. For reference, Hill’s criterion as expressed by Tsai [2] for filamentary composites is,
TL;DR: In this paper, a procedure for calculating the pressure, densities, internal energies and particle velocities behind a plane shock in an infinite composite consisting of alternate layers of two materials or of parallel fibers imbedded in a matrix is presented.
Abstract: A procedure for calculating the pressure, densities, internal energies and particle velocities behind a plane shock in an infinite composite consisting of alternate layers of two materials or of parallel fibers imbedded in a matrix is presented. The direction of shock propagation is assumed to be parallel to the layers or fibers. Cal culated values of the shock parameters are given for a hypothetical aluminum polymethylmethacrylate composite. Shock speeds in the composite which are lower than the sonic velocity of one of the constituents are found to be possible.
TL;DR: In this article, a closed-form solution for the problem of laminated plates subjected to simple bending by the application of the nonlinear von Karman equations of heterogeneous anisotropic plates is presented.
Abstract: A closed-form solution is presented for the problem of laminated plates subjected to simple bending by the application of the nonlinear von Karman equations of heterogeneous anisotropic plates. The...
TL;DR: In this paper, an experimental investigation was conducted to study the fracture properties of laminated composites under uni-axial tension, and it was found that the distribution of breaking strength of a composite...
Abstract: An experimental investigation was conducted to study the fracture properties of laminated composites under uni-axial tension. It was found that the distribution of breaking strength of a composite ...
TL;DR: Natural vibration frequencies and mode shapes for laminated orthotropic shells of revolution using finite element method as discussed by the authors were used to estimate the vibration frequency and mode shape of a laminated shell of revolution.
Abstract: Natural vibration frequencies and mode shapes for laminated orthotropic shells of revolution using finite element method
TL;DR: In this article, the mechanism by which the lift off phenomenon occurs is discussed in detail and the effect of shear coupling can be severe, as shown by Halpin and Pagano.
Abstract: Because of the end-constraint problem introduced by tensile specimens, which has been discussed by Pagano and Halpin [1], there is increasing interest in beam bending experiments as a means of characterizing off-axis unidirectional composites. This method of characterization is also inadequate as shear coupling causes the beam to twist and physically lift off of the supports. Such behavior has been demonstrated experimentally by Halpin [2] as shown in Figure 1. This note discusses in detail the mechanism by which the lift off phenomenon occurs. Experimental data shows that the effect of shear coupling can be severe. Consider a rectangular homogeneous plate which lies in the region a/~ G x ~ a/2, b/2 G y G b/2. If the plate is subjected to the uniform bending moment Mx = Mo = constant, the plate deflection w is of the form [3]
TL;DR: In this paper, a partial differential equation is derived that describes the motion of a transversely isotropic Timoshenko beam under initial stress, initial displacement, and transverse loading.
Abstract: A partial differential equation is derived that describes the motion of a transversely isotropic Timoshenko beam under initial stress, initial displacement, and transverse loading. Suitable specializations of this equation permits one to investigate buckling behavior, vibrational be havior as affected by initial stress, and wave propagation behavior in initially stressed infinite beams. Each separate topic provides important results for designing structures with high values of the ratio of longi tudinal modulus to longitudinal-transverse shear modulus which are common among advanced composites. The buckling investigation pre dicts moderate decreases in the buckling coefficient for simply sup ported beams but predicts very large decreases for clamped beams. The vibration investigation shows that initial tension and compression have practically no effect on the thickness shear frequencies for all modes. The wave propagation investigation shows (a) the extreme sensitivity of the thickness shear cutoff freque...
TL;DR: In this article, a numerical finite-element analysis has been performed on thin-wall laminated cylindrical tubes to characterize tube responses to axial tension/compression, torsion and internal pressurization.
Abstract: The use of thin-wall laminated cylindrical tubes is currently of considerable interest for the material property characterization of hard composites. In view of this interest, a numerical finite-element analysis has been reported in Reference [ 1 ] which characterizes tube responses to axial tension/compression, torsion and internal pressurization as a function of the tube geometry, material, ply orientation and end constraints. In brief, it was found that for infinitely long tubes an accurate prediction of tube behavior can be obtained from the closed form solution of Sherrer [2]. However, this solution doesn’t easily lend itself to the determination of elastic moduli from test data. Moreover, the numerical calculations associated