Showing papers in "Journal of Composite Materials in 1969"
TL;DR: In this article, the limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions, and it is shown that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios.
Abstract: Limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions. The general class of problems treated involves the geometric configuration of any number of isotropic or orthotropic layers bonded together and subjected to cylindrical bending. In general it is found that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios, but converges to the exact solution as this ratio increases. The analysis presented is also valid in the study of sandwich plates under cylindrical bending.
1,194 citations
TL;DR: In this paper, the success of the lamination approximation is strongly dependent upon the assumption of physical volume averaging in real material systems combined with the assumption that real fibers are interconnected by a bonding substance.
Abstract: There are many technological applications for materials composed of short fibers interconnected by a bonding substance. In some naturally occurring cases, bone and teeth, the material is characterizable as oriented short fibers in a suitable matrix material. In the majority of cases, paper, leather, nonwoven fabrics and short fiber composites, the materials can be characterized as a random or nearly random arrangement of fibers in space. In this case the properties of an apparently homogeneous random or nearly random material can be treated as a laminated solid [1] [2]. In this approximation the homogeneous material is considered to be mathematically equivalent to a material composed of layers of oriented shortfiber material in which the percentage of fibers in each layer corresponds to the volume fraction of fibers of the particular orientation in the material being molded. Such a laminate for a random orientation of fibers is known as a &dquo;quasiisotropic&dquo; laminate [3] in laminated plate theory. Similar procedures [1] [2] [4] can be employed for the prediction of thermal expansion properties, transport properties, etc. The success of the lamination approximation is strongly dependent upon the assumption of physical volume averaging in real material systems combined with
773 citations
TL;DR: In this paper, a bending theory which includes transverse shear deformations was presented for laminated plates and closed form solutions were obtained for bending deflections, flexural vibration frequencies, and buck...
Abstract: A bending theory which includes transverse shear deformations is presented for laminated plates. Closed form solutions are obtained for bending deflections, flexural vibration frequencies, and buck...
443 citations
TL;DR: In this paper, the spatial orientation of the discontinuous fibers is intermediate between a truly random array in three dimensions and a random array of three dimensions in a continuous or discontinuous matrix.
Abstract: ’As discussed in [6], the magnitudes of the deformations involved here dictate the use of finite strains in the computations. Random or nearly random distributions of fibers, finite in length and arranged in either a continuous or discontinuous matrix, constitute many naturally occurring and synthetic materials. In the majority of cases, the spatial orientation of the discontinuous fibers is intermediate between a truly random array in three
268 citations
TL;DR: In this article, an analytical technique for determining the stress-strain response up to ultimate laminate failure for a laminated composite consisting of orthotropic lamina with nonlinear stressstrain behavior is presented.
Abstract: This paper presents an analytical technique for determining the stress-strain response up to ultimate laminate failure for a laminated composite consisting of orthotropic lamina with nonlinear stress-strain behavior. The procedure, which has been programmed for a digital computer, will produce a laminate stress-strain curve up to ultimate failure. The technique is restricted to the prediction of ultimate strength for plane anisotropic laminates with midplane symmetry sub jected to biaxial membrane loads. Comparisons are made between analytical predictions and experimental results. The basic concepts of ultimate and limit strength design as applied to an advanced com posite structure are discussed.
207 citations
TL;DR: In this paper, the anti-symmetric cross-ply and angle-ply laminates under transverse loading are analyzed and a closed form solution is obtained for special types of simp...
Abstract: Anti-symmetric cross-ply and angle-ply laminates under transverse loading are analyzed. By expanding the load in a double Fourier series a closed form solution is obtained for special types of simp...
140 citations
TL;DR: A theoretical analysis for determining the free vibra tional characteristics of thin-walled, circular cylindrical shells with layers of anisotropic elastic material arbitrarily laminated.
Abstract: A theoretical analysis is presented for determining the free vibra tional characteristics of thin-walled, circular cylindrical shells with layers of anisotropic elastic material arbitrarily laminat...
127 citations
TL;DR: In this article, a micromechanics analysis for the prediction of composite material properties, which are based upon the assumption of various idealized regular filament packings, indicate the significant in...
Abstract: Existing micromechanics analyses for the prediction of composite material properties, which are based upon the assumption of various idealized regular filament packings, indicate the significant in...
122 citations
TL;DR: In this paper, an experimental technique was developed to determine the condi tions for the onset of reinforcement unbonding in composite materials, based upon the continuous measurement of the d...
Abstract: An experimental technique was developed to determine the condi tions for the onset of reinforcement unbonding in composite materials. The technique is based upon the continuous measurement of the d...
111 citations
TL;DR: In this article, the energy formulation presented earlier is extended to include the analysis of plane anisotropic rectangular plates with nonuniform plate properties and non-uniform in-plane and distributed normal loadings.
Abstract: The energy formulation presented earlier is extended to include the analysis of plane anisotropic rectangular plates with non-uniform plate properties and non-uniform in-plane and distributed normal loadings. The formulation includes linear theory stability analysis, the calculation of natural frequencies and mode shapes, and analysis of displacement due to lateral loads. The extension presented in the present paper is formulated in a manner such that the non-uniform properties and loadings can be handled with no appreciable increase in difficulty over the formulations previously presented except for the evaluation of certain more general integrals. An easily automated method of evaluating these more general integrals is presented.
108 citations
TL;DR: In this paper, an approximate method of solution for the bending of unsymmetrically laminated plates was proposed, which, although approximate, yields solutions that compare favorably with those presented by Whitney.
Abstract: In a current article, Whitney [1] has presented exact solutions for certain problems of the bending of unsymmetrically laminated plates. This note considers an approximate method of solution for such plates which, although approximate, yields solutions that compare favorably with those presented by Whitney. Furthermore, since the approximate method reduces the problem to an equivalent anisotropic bending problem, the techniques that have been developed for the analysis of orthotropic and anisotropic plates can be directly utilized. It should be noted that the possibility of using the approximate analysis discussed herein was first suggested in [2] on the basis of experimental evidence. The present note presents an explanation of why this approximation does not introduce large errors, and presents numerical comparisons with Whitney’s exact solutions.
TL;DR: In this article, a plane elasticity solution for the end problem in a two-layer laminated strip is derived, which is obtained as a series of non-orthogonal eigenfunctions, each of which varies exponentially along the axis of the strip.
Abstract: A plane elasticity solution is derived for the end problem in a two- layer laminated strip. The laminae may have arbitrary elastic constants and an arbitrary thickness ratio. The solution is obtained as a series of non-orthogonal eigenfunctions, each of which varies exponentially along the axis of the strip. Each exponential coefficient is a complex root of an eigenvalue equation that results from the requirement of compatible displacements at the interface.The general solution obtained in this paper may be used to find the stress field in a two-layer laminated strip subjected to specified self- equilibrating end loading. It thus permits the determination of the stress concentration near the end which is usually neglected by invok ing St. Venant's Principle.
TL;DR: In this article, a modi-fied two-dimensional theory for fiber buckling is presented, which is in good agreement with the experimental data obtained from two epoxy matrix systems (AF-126 and BP-907).
Abstract: The compressive strength of fibrous composites is strongly de pendent upon the effectiveness of the matrix in supporting the fibers against buckling. Proper support of boron filaments by an epoxy matrix has resulted in average compressive fiber stresses of as high as 1,330,000 psi at failure. Experimental data obtained from two epoxy matrix systems (AF-126 and BP-907) is in good agreement with a modi fied two-dimensional theory for fiber buckling.
TL;DR: In this paper, a linear analysis is presented for determining the natural frequen cies of vibration of laminated anisotropic rectangular plates, where the plate may consist of an arbitrary number of thin orthotropic layers, the major material-symmetry axis of each layer oriented arbitrarily with respect to the longer plate edge.
Abstract: A linear analysis is presented for determining the natural frequen cies of vibration of laminated anisotropic rectangular plates. The plate may consist of an arbitrary number of thin orthotropic layers, the major material-symmetry axis of each layer oriented arbitrarily with respect to the longer plate edge. An approximate solution is obtained by the Rayleigh-Ritz energy method. Numerical results are presented for fully clamped boundary conditions and compared with experimental results for symmetrically and unsymmetrically laminated plates.
TL;DR: In this paper, a polyester resin reinforced with unidirectional R. A. E. carbon fibers or E-glass was subjected to torsional and flexural vibration.
Abstract: Specimens of polyester resin reinforced with unidirectional R. A. E. Type 1 (high modulus) carbon fibers or E-glass were subjected to torsional and flexural vibration. For both types of fibers the ...
TL;DR: In this article, the storage and loss moduli were measured for laminated glass fiber reinforced epoxy composite beams at frequencies up to 9400 Hz, with relatively insensitive storage moduli.
Abstract: Measurements of storage and loss moduli are reported for laminated glass fiber reinforced epoxy composite beams at frequencies up to 9400 Hz. The storage moduli were relatively insensitive and the ...
TL;DR: In this article, the Berger's approach for large deflections and a modified Reissner's variational principle are exploited to treat the nonlinear dynamic problem of plate deflection.
Abstract: In this work, the Berger's approach for large deflections and a modified Reissner's variational principle are exploited to treat the nonlinear dynamic problem of plates. A system of approximate equ...
TL;DR: In this article, a theoretical and experimental investigation was made of the integrated photoelastic effect in a transparent fiber glass reinforced epoxy resin, where vacuum impregnation techniques were developed to render the material transparent.
Abstract: A theoretical and experimental investigation was made of the integrated photoelastic effect in a transparent fiber glass reinforced epoxy resin. Vacuum impregnation techniques were developed to render the material transparent. The integrated effect of the isochro matics and isoclinics in the material when subjected to both uniaxial and biaxial stresses was observed and compared to the predicted data. Isochromatic data proved to be representable by a proposed orthotropic stress-optic law. Isoclinics were predictable, but at a given point in a stressed model the isoclinic angle depends on both the fiber orienta tion with respect to the principal stress directions and the ratio of principal stress magnitudes. Thus, the isoclinics do not directly give the principal stress directions. At this point, the anisotropic photo elasticity solution has not been determined.
TL;DR: In this article, a plane elasticity solution for the state of stress resulting from differential expansion in a composite made up of two rectangular strips bonded on an interface is presented, and it is found that the distribution of normal stress at the interface is quite sensitive to the modulus and thickness ratios of the laminae.
Abstract: A plane elasticity solution is presented for the state of stress resulting from differential expansion in a composite made up of two rectangular strips bonded on an interface. The stress field that has long been known to exist in the middle of such a laminated strip (to the St. Venant approximation) includes neither normal nor shear traction on the bonded interface. These stress components are shown to be significant only within a distance from each end equal to the total thickness, and their distribution is determined for a wide range of elastic moduli and strip dimensions.It is found that the distribution of normal stress at the interface is quite sensitive to the modulus and thickness ratios of the laminae. By making use of the form of this dependence, it may be possible to design bonded structures to withstand curing and/or temperature changes which would otherwise cause failure.
TL;DR: In this paper, a system comprised of approximately 50% by volume glass fibers in an epoxy resin matrix was used for measuring the orientation of short fibers during flow of short fiber composites.
Abstract: A method for characterizing the orientation of short fibers during flow of short fiber composites is described. A system comprised of approximately 50% by volume glass fibers in an epoxy resin matrix was used for this study. A glass rheometer was used to observe steel tracer fibers, which were incorporated into feed particles with the glass. By reacting the epoxy resin with a secondary amine, a product was obtained which did not react further during the measurements. The product also had a viscosity at room temperature similar to com mercial systems at processing temperatures; this made flow measure ments at room temperature possible. A technique of data reduction for the orientation measurements is described.Early results show that, at these high fiber loadings, plug flow with little change in orientation occurs above and below the constriction in the rheometer tube. At the constriction, particles are sheared into strands. If feed particles containing pre-oriented fibers are not used, a "log jam" results...
TL;DR: In this paper, the stability of unidirectional, equally spaced fibers in the plane of a composite plate is formulated by treating the fibers as beams and the matrix by the theory of generalized plane stress.
Abstract: The stability of unidirectional, equally spaced fibers in the plane of a composite plate is formulated by treating the fibers as beams and the matrix by the theory of generalized plane stress. Critical values of the axial load and the corresponding buckling modes are evaluated numer ically and shown graphically for various values of the parameters. Approximations leading to explicit expressions for the critical values are introduced, and restrictions on the applicability of the approximate results are determined. Experimental evidence of the occurrence of buckling modes of the type considered is presented.
TL;DR: In this article, an analytical investigation of gripping effects on the off-axis tensile test results for flat specimens is made, and the results support the findings of [1] in demonstrating that length/width ratio and type of constraint can significantly modify the intended uniform stress/strain fields in the subject test.
Abstract: An analytical investigation has been made of gripping effects on the off-axis tensile test results for flat specimens. It is an extension of the earlier work of Pagano and Halpin [1] and aims at establishing approxi mate bounds on the accuracy of the subject test. Considered are the cases of rigid clamping with and without end rotation for selected properties which are typical of glass, boron and graphite composites. Solutions of the corresponding mathematical models are effected numerically, utilizing a computerized finite-element approach.The results support the findings of [1] in demonstrating that length/width ratio and type of constraint can significantly modify the intended uniform stress/strain fields in the subject test. Despite this adverse effect, the analysis suggests that if strain measurements can be properly recorded, reasonably accurate test results should be obtain able for even small length/width specimens. Moreover, though the numerical results lack the generality of closed-form solution...
TL;DR: In this article, the authors studied the effect of the ratio of the space between inclusions and their diameter on the magnitude of stresses at the interface of a single inclusion in an infinite matrix during the transient period of curing.
Abstract: Shrinkage stresses produced during the curing of the matrix in a two-phase material were studied. Specimens representing a typical two-phase material made of unplasticized epoxy as inclusions and plasticized epoxy as the matrix were studied photoelastically.The magnitude of stresses at the interface of a single inclusion in an infinite matrix during the transient period of curing depended only on the constant elastic modulus of the inclusion and on the instantaneous value of the matrix elastic modulus and it was independent of the amount of shrinkage of the matrix. In the case of a square array of inclusions in close proximity, the stress-distribution depended on both elastic moduli and the amount of shrinkage. The influence of the ratio of the space between inclusions and their diameter on the magnitude of stresses was also studied, in the case of already set matrices.
TL;DR: In this paper, a theory based on flow across a selected control volume is developed to predict the Hugoniot of a shock moving along the longitudinal direction of a unidirectional fiber reinforced composite.
Abstract: : A theory based on flow across a selected control volume is developed to predict the Hugoniot of a shock moving along the longitudinal direction of a unidirectional fiber reinforced composite. From this theory the Hugoniot of a composite may be calculated from the equations of state of its constituents. The shear force along the matrix-fiber interface can also be computed. A sample calculation using polyethylene as matrix and beryllium as fiber has been made. The calculated shock Hugoniot is not far from linear. (Author)
TL;DR: In this paper, Wu et al. used the finite element method to demonstrate the effects of full clamping and free rigid rotation of the ends of the specimens. But in order to solve the problem only the centerline at the specimen ends was rigidly clamped.
Abstract: The off-axis tension test is frequently used to characterize the strength behavior of fibrous composite materials. This test is, ideally, uniform tension applied along a single axis. Because this axis does not coincide with one of the principal axes of the material, i.e., since the fibers are neither parallel nor perpendicular to this loading axis, the state of stress or strain referred to the principal axes of the material includes biaxial tension and shear. Such combined stress information is needed to assess the interpolation formulas or failure theories that are based upon 0-degree and 90-degree test specimens. Recently Pagano and Halpin [1] have pointed out that the shear coupling compliance S16 causes a non-uniform state of stress and strain in such tensile specimens when the ends are clamped, and furthermore this non-uniformity cannot be eliminated by simply allowing the ends of the specimen to rotate. An analytical solution was presented in [1] which indicated the aforementioned effect. This solution was obtained by integrating the equations for the plane stress condition from the linear theory of elasticity, but in order to solve the problem only the centerline at the specimen ends was rigidly clamped. Rizzo [2] has presented numerical solutions utilizing the finite element method to indicate the effects of full clamping and free rigid rotation of the ends of the specimens. These results are consistent with the closed form solutions of reference [1] ] and also with the experimental data presented by Wu and Thomas [3]. In the present note, further numerical results are presented which indicate the accuracy of the closed form solution presented in [1], and these results are further used to design a reasonable off-axis tensile coupon.
TL;DR: In this paper, an experimental study of the uniaxial compressive stability of rectangular boron-epoxy laminated plates is presented, where the plates are clamped on the loaded edges and either clamped or simply supported on the sides.
Abstract: An experimental study of the uniaxial compressive stability of rectangular boron-epoxy laminated plates is presented. The plates are clamped on the loaded edges and either clamped or simply- supported on the sides. The buckling loads are determined by means of Southwell plots and are compared to analytical results obtained with a previously published method. Experimental results are presented for twenty composite plates and four metal plates. Good agreement between the experimental and analytical results is shown for both symmetrical and unsymmetrical plates, and for plates strongly aniso tropic as well as orthotropic and isotropic.
TL;DR: In this article, a general discussion of cylindrical bending in laminated plates displaying bending-extensional coupling is presented, including buckling and flexural vibrations in addition to conventional bending problems.
Abstract: Many rectangular laminated plates having a high length to width ratio can be analyzed as an infinite strip [1]. One-dimensional static bending under transverse load has been discussed to a limited extent in References 2 and 3. This note presents a general discussion of cylindrical bending in laminated plates displaying bending-extensional coupling. The analysis includes buckling and flexural vibrations in addition to conventional bending problems.
TL;DR: In this article, the electric permittivity of a composite can be expressed in terms of the average of the electric potential on the surface of a filler particle and the expression obtained is developed in powers of the volume fraction c of filler particles.
Abstract: The electric permittivity of a composite can be expressed in terms of the electric permittivity of the components and the average of the electric potential on the surface of a filler particle. The expression obtained is developed in powers of the volume fraction c of filler particles. Both the term linear in c and the term which is quadratic in c . are derived explicitly for two systems: (a) the particles are spheres; (b) the particles are circular cylinders perpendicular to the external field. Two methods are used. The first is an approximate treatment which is based on successive "reflections" of the perturbation caused by one particle off a second particle. The assumption is made that each reflection can be calculated as though the perturbation of the field is seen by the particle as a homogeneous field. This approach is worked out for cylinders and for spheres. The second method is carried through only for cylinders. It is based on the use of bipolar coordinates and is rigorous. The results obtained a...
TL;DR: In this article, the stability of unsymmetric cross-ply rectangular plates under uniform shear was investigated and the effect of coupling was ascertained by comparing coupled solutions to those obtained by neglecting the coupling coefficients in the governing equations.
Abstract: Recently solutions have been obtained [1, 2, 3] for the bending, vibrations, and buckling of laminated plates in which coupling between bending and stretch ing is important. However, buckling results were limited to unsymmetric angle- ply laminates under biaxial compression. Thus, there are no solutions available for the buckling of coupled laminates subjected to shear loading.This paper is concerned with the stability of unsymmetric cross-ply rectangular plates under uniform shear. These composites consist of an even number of layers all of the same thickness and elastic properties with the orthotropic axes of symmetry in each ply alternately oriented at 0° and 90° to the plate axes. Hinge- support boundary conditions are considered. The effect of coupling is ascertained by comparing coupled solutions to those obtained by neglecting the coupling coefficients in the governing equations. Applicability of the reduced bending stiffness approximation to shear buckling of cross-ply composites is also in vestig...