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The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

Analysis of curing stresses in resin matrix composite laminates involves a temperature range over which variation of elastic moduli is appreciable. A method based on total stress-strain-temperature relations is formulated and applied to determine the curing stresses in boron/epoxy composite lam inates. This method is shown to be preferable to the incremental method because the former requires the thermal strains and the stress-strain rela tions only at the final temperature of interest. The use of incremental constitutive equations is also discussed, and it is shown that proper care must be exercised to insure inclusion of interaction terms that have no counterparts in linear theories.

Elastic properties and stress concentration factors at a hole in boron-aluminium, fibreglass-epoxy, and boron-epoxy laminates have been investigated under both static and dynamic conditions. In laminates with low fibre-matrix moduli ratios, the dynamic Young's Modulus is practically the same as the static value. In laminates with high fibre-matrix moduli ratios, the dynamic modulus is noticeably lower than the static value. The stress wave velocity is the highest when the wave propagates along the fibre detection. The velocity decreases when the angle between the wave propagation direction and the fibre direction increases. In the static case, stress concentration factors in laminates are higher than those in isotropic materials. In the dynamic case, stress concentration factors in laminates are higher than the static value for small values of D/W, and lower for large values of D/W. The stress concentration factors in laminates increase with sol:E f E m and vary inversely with D W . In one composite material, the stress concentration factors increase generally in the order of ±20° angle-ply, 0°/90° cross-ply and uniaxial laminates.

An approximate elasticity solution is developed for the response of the finite-width, angle-ply composite laminate under uniform axial strain. The solution yields components of the displacement vector, strain tensor, and stress tensor in the form of sinusoidal-hyperbolic series. Results of the approximate solution are compared to numerical solutions of the exact equations for four-layer, symmetric laminate geometries. The nature of the boundary disturbance in the eight-layer laminate is also examined by the approximate solution.

An ultrasonic resonance technique for compressional and shear waves velocity measurements in thin composite laminates is described. The method utilizes a computer digitizing scheme and Fourier transform from time to frequency domain. Results showed an eight percent difference in compressional wave velocity across plies for specimens of two different fiber/resin systems. No difference was observed for specimens having different ply-orientations within a system. Shear wave velocity in one specimen was found to be 46% of the compressional wave velocity. The new technique could also be used for thickness measurements in thin-skin honeycomb structures.

Experimental and theoretical studies of edge effects in rectangular composite strips under tension are discussed. The objective of the study was to investigate the effect of various parameters, including reinforcement material, fiber orientation and the structure of the reinforcement, on the various quantities which are observed in the vicinity of free edges in multidirectionally reinforced laminates. Of particular interest was the confirmation of theoretical results related to differences in response of graphite- and boron-reinforced laminates. Experiments consisted of moire measurements of surface-displacement patterns which were compared with theoretical predictions, and examination of failure levels. The experiments were carried out on AVCO 5505 boron and Whitaker 5206 MODMOR II graphite-reinforced angle-ply laminates in which both stacking sequence and fiber orientation were varied parametrically. Moire techniques were developed which allowed observation of displacements on both the wide surface and along the narrow edge of 1 in.-wide × 16-ply-thick (.085 in.-.105 in.) laminates.

Design of composite laminates requires the determination of changes in stiffness and strength resulting from varying the ply orientation and total laminate thickness. Graphical determination can be made simple by use of laminate stiffnesses in conjunction with failure surface in a special strain space. A set of generalized graphs for all practical laminates of a given composite can now replace the current limitation of one set for each discrete laminate.

A new measurement geometry is proposed to determine the local galvanomagnetic coefficients in semiconductors and metals. The basis idea of the method is to measure the relative change of spreading resistance of a low resistivity ohmic point contact due to the magnetic field.

In previous papers (1, 2) we have analyzed the internal stresses in spherical particle composites for the cases where the particle is softer than the matrix (1), as in rubber particle filled polymers, or for the case where the particle is harder than the matrix as in ceramic filled glasses (2). Also, the analysis has been applied to porous composites such as foams in which case spherical voids simply replace the particles (2). A finite element analysis has been used for the calculation of internal stresses and for the prediction of elastic constants and strength of the composite with a suitable model geometry and proper boundary conditions. The results have been presented as a function of the volume fraction of particles or inter-particle spacing.

The basic building block of a filamentary-composite laminate is a ply or a lamina consisting of a larger number of stiff filaments (e.g. glass) embedded in a compatible material (e.g. epoxy). The laminate or multi-directional composite is considered to comprise a number of perfectly bonded laminas with different fibre orientations. The deformation response of a laminate to an applied force is calculated by means of its material constants. One of the common methods of determining these constants is by means of a micro-macro mechanical analysis in which the characteristics of the composite are found in terms of the constituent material properties, geometry, and volume percentage of fibre content. Numerous papers have been published to investigate the micro-macro mechanical approach. Some of these works are based on the mechanics of materials approach and on the variational principle of minimum potential energy, as well as on the classical theory of elasticity.

Bilinear stress-strain relation of symmetric, [0/90] composite laminates is shown to be associated with gradual, not complete, degradation of 90° layers. Difference between the complete failure model and gradual failure model is discussed, complemented by pertinent experimental evidences. Experimental data on glass/epoxy and graphite/epoxy cross-ply laminates are compared with the theoretical predictions. The effect of strain biaxiality on failure of 90° layers is shown to be negligible when the laminate is subjected only to a uniaxial tension.

In the limit of low frequencies the displacement u(x, t) in a one-dimensional composite can be written in the form of an operator acting on a slowly varying envelope function, U(x, t): u(x, t) = [1 + v1(x)∂/∂x + …] U(x, t). U(x, t) itself describes the overall long wavelength displacement field. It satisfies a wave equation with constant, i.e., x-independent, coefficients, obtainable from the dispersion relation ω = ω(k) of the lowest band of eigenmodes: (∂2/∂t2 − c¯2∂2/∂x2 − β∂4/∂x4 + …) U(x, t) = 0. Information about the local strain, on the microscale of the composite laminae, is contained in the function v1(x), explicitly expressible in terms of the periodic stiffness function, η(x), of the composite. Appropriate Green’s functions are constructed in terms of Airy functions. Among applications of this method is the structure of the so-called head of a propagating pulse.

Definition of the influence of interlaminar stresses on the failure characteristics of composite laminates may require the development of novel experimental characterization procedures. The so-called free edge problem in laminate elasticity offers a cnovenient mechanism to accomplish this purpose because of the high interlaminar stresses in the neighbourhood of a free boundary. The detailed design of a laminate specimen which can exhibit catastrophic delamination induced by interlaminar tension is presented, along with a preliminary failure hypothesis to characterize this mode of rupture and the associated experimental demonstration of the phenomena.

The model studied in this paper is that of a composite structure represented by two elastic rods, of uniform cross section, which are bonded together along their generators. The rods are semi-infinite in length and are suddenly loaded by a pressure step applied over the end of the structure. The resulting elastic waves which are generated in each of the rods cause a dynamic bond shearing stress which is proportional to the difference between the two rod displacements. An integral solution is obtained for the bond stress and is evaluated numerically. The bond stress is composed of a static and a dynamic part and it is found that the peak bond stress, which occurs at the loaded end, is dominated by the static stress. Results are shown graphically for a particular rod configuration as well as the parametric dependence of the peak bond stress on the rod composite-stiffness ratio. Several limiting cases for the stiffness parameter and elastic wave-speed ratio parameter are investigated analytically and some asymptotic formulas are given which describe the small and large time behavior of the dynamic-bond stress.

Based upon considerations relating to the nature of the inter laminar stresses in composite laminates, an approach is presented to predict the detailed stacking sequence of specific layer orientations which leads to optimum protection against delamination under uniaxial static and fatigue loadings. In particular, it is argued that the interlaminar normal stress, as well as the interlaminar shear stress, is instrumental in precipitating delamination and subsequent strength degradation. Correlation with existing experimental evidence of the stacking sequence phenomenon is presented.

The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.

In a series of three papers [1,2,3], the range of applicability of classical laminated plate theory (CPT) in describing the response of composite laminates under static bending has been examined. Briefly, exact solutions within the framework of linear elasticity theory were developed and compared to the respective solutions governed by CPT [4,5,6]. Numerical data calculated based on simple harmonic load distributions have indicated rather wide discrepancy between the two solutions for laminates having low span-to-depth ratios. At high aspect ratios however, the CPT solution is in good agreement with the elasticity solution.

A simplified scheme is presented for discussing and calculating estimates of the third-order elastic constants of quasi-isotropic material based on single-crystal data. The difference between the Voigt and Reuss averages at the third order is shown to depend solely on the second-order single-crystal anisotropy. Only the two smaller constants are affected in this way. Chang's data for niobium are used to compare the methods.

For a simplified model of a laminated medium consisting of alternating layers of elastic and viscoelastic materials, the dispersion and attenuation characteristics for “plane,” longitudinal waves propagating in the direction of the layering are obtained. The dispersion and attenuation curves depend on a structure parameter involving the thickness of the layers and can deviate significantly from corresponding results for a continuum “effective-modulus” model. Curves are presented for a specific case with representative material parameters showing the effect of structure and of variations in the parameters of the composite.

In this present work, the effect of stacking sequence on mechanical properties of untreated luffa cylindrica and glass fibre reinforced epoxy hybrid composites has been investigated experimentally. Composite laminates were fabricated by hand lay-up technique. All the composites were made with a total of 4 plies, by varying the number and position of glass layers so as to obtain six different stacking sequences. One group of neat epoxy samples was also fabricated for comparison purpose. Samples were analysed for their mechanical and flexural properties to establish the effect of various stacking sequence. It is found that the optimum properties (tensile and flexural strength) are achieved from hybrid laminate (S5) i.e. by placing two luffa cylindrica fibre mats at the middle when supported by two glass fibre mats on either side.Keywords: Luffa cylindrica-glass hybrid, Tensile strength, Flexural strength, ILSS, SEM

A theory of composite materials is proposed which is based on the continuum theory of mixtures. The constituents of a composite are modeled as superimposed continua which undergo individual deformations. Effects of structure on dynamical processes in composite materials are then simulated by specifying the coupling between the individual constituent motions. A novel feature of this model is the inclusion of diffusion with relative displacement coupling for perfectly bonded composites. A simple one-dimensional form of such a theory is presented, and, when compared with classical solutions for longitudinal wave propagation in laminated materials, predicts some aspects of the dynamical behavior extremely well.

1. Some factors influencing the strength of composite materials were examined. 2. A study was made of the strength properties of graphite-zirconium carbide and graphite-zirconium carbide-zirconium composite materials having varying structures and compositions. It was found that, at 2500‡C, the tensile strength of TsG-25 type composite material is 30% higher than that of dense VPP constructional graphite. 3. It was established that, by varying the degree of impregnation of the zirconium phase with carbon, it is possible substantially to change the physicomechanical properties of the resultant composite material. At 20–2000‡C, the tensile and bend strengths of materials containing residual zirconium are 1.5–3 times those of materials containing the carbide phase alone.

A detailed study of the plasticity and crack-tip blunting effects on toughening materials with rectilinear anisotropy is presented. The most important results are the prediction of the extent of plastic zone and the nature of stress distribution produced by the blunting effect in the tensile mode. The analysis was confirmed experimentally and numerically (finite-element method) on a unidirectional fiber-reinforced composite.

Theoretical and experimental studies were made of the effects of temperature and composition on the thermal expansion of deformed (texturized) Mo-Cu two-phase composite materials, whose component phases differ markedly in their properties. The anisotropy of thermal expansion of such composite materials was investigated, and it was established that their volume expansion shows very little variation with deformation. It is demonstrated that two-phase composite materials can be formulated exhibiting thermal expansion characteristics controlled by their composition and the type and degree of plastic deformation.

Drei Methoden zur Berechnung des mittleren Elastizitatsmoduls vielkristalliner kubischer Metalle werden formuliert als eine Summierung uber die Beitrage der Kristallite zur elastischen Energie. Dadurch kommt man zu einer zwanglosen Erklarung fur die Abweichungen der berechneten Mittelwerte vom beobachteten Modul des Vielkristalls.

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 sand wich plates under cylindrical bending.

An extension of the effective stiffness theory developed for elastic laminates by Sun, Achenbach, and Herrmann [1] is presented in a form suitable for the solution of dynamical processes in composite materials including determination of stresses. A derivation of displacement and stress interface boundary conditions suitable for higher-order theories is presented. The theory is illustrated with dispersion and mode shape results for two examples of steady-state wave propagation.

The extension of linear elastic fracture mechanics (LEFM) from metallic alloys to advanced fiber composite laminates is considered. LEFM is shown to be applicable to both isotropic and anisotropic homogeneous continua; the applicability of LEFM to advanced fiber composites is thus dependent on the validity of a homogeneous continuum model for such materials. An experimental program to determine the validity of such a model for graphite/epoxy laminates is reviewed. Such laminates are found to have an apparent fracture toughness, from which it is inferred that a homogeneous material model is appropriate for the particular specimen geometry and composite laminates considered. Strain energy release rates are calculated from the experimentally determined fracture toughnesses of the test laminates. These strain energy release rates fall into two distinct groups, corresponding to fracture across fibers and fracture between fibers. The latter case is further investigated. It is concluded that matrix fracture is governed by the tensile stress normal to the crack path.

The mechanical behaviour of composite materials is examined. As far as is possible, the subject is discussed in terms of general principles, and the aim throughout has been to relate the behaviour of the composite to the geometrical arrangement and the properties of the component phases. Since the greatest advances have been made in the understanding of unidirectional fibrous composites these are given prominence, but where possible the discussion is made to include laminates and other structures. The review is divided into six sections: introduction, elastic-plastic properties, fracture, cracks and notches, creep and fatigue

Strength of anisotropic composite materials subjected to any state of combined stress, predicted from basic strength characteristics of unidirectional layer

Strength of structural composites of orthotropic materials with arbitrary thickness and orientation including lamination and anisotropy effects

An attempt has been made to calculate the isotropic third-order elastic constants of a polycrystalline solid in terms of the single-crystal constants using the methods employed by Voigt and Reuss in the second-order case. The application of these calculations to a variety of different materials shows that the discrepancy between the two methods is much greater than in the case of second-order constants.

Certain aspects of the handle of fabric laminates are related to properties of the component fabrics. Particular attention is paid to a theoretical prediction of the bending stiffness of a laminate from the bending and tensile properties of its components. This theoretical stiffness is a minimum value; if, in practice, the observed stiffness is much greater than this, it may generally be assumed that excess of adhesive or of melted foam is the cause. The paper also reports work on other features of the bending behaviour, such as the degree of recovery from bending, and on the shearing behaviour. The work is concluded by a brief study of some faulty laminates.

Methods of analysis of the elastic stiffness properties of fibre composite materials are reviewed. The use of these properties in the analysis of structural composites is outlined. Typical results are presented for composite material properties, for laminate properties and for plate problems in which material stiffness is a significant design criterion. The influence of material design upon structural design is illustrated.

Hooke's law, which is the foundation of the mathematical theory of elasticity, is unfit to describe satisfactorily the phenomena in elastic bodies even if we limit the scope of our research to ideal elastic deformations. We call a deformation ideally elastic, if the deformations disappear completely and if the energy stored up in the body is given back without loss, when the load is removed.

Recently we have seen many experimental data published on the static properties of the glass fabric reinforced plastics (F. R. P.), but there have been few reports so far which have treated the influence of environmental temperature and the glass content of the specimen.It is intended in this paper to describe (the influence) of the glass content and the environmental temperature on the static behaviour of F. R. P. in which satin woven, plane woven and roving woven fablics are used for reinforcement. On the other hand we made analysis to predict the elastic moduli in flexure of composite laminates and determined their flexure strength by the use of these calculated moduli with the assumption that the F. R. P. materials will keep their elastic properties till the moment of fracture.

This paper and a subsequent one will present the results of an investiga tion which analytically relates the fiber/matrix nonlinearities to the post- yielding behavior of symmetric laminates made from unidirectional plies. This first paper is primarily concerned with the behavior of the single ply and the means for anticipating its response within a laminate. Boron and carbon/epoxies are considered along with a metal matrix composite. The qualitative features of the response of these unidirectional materials to normal, shear, and combined loads are discussed. The analysis (based on triangular finite element idealizations of regularly-spaced inclusion arrays) anticipates the level of nonlinearity that has been observed in composite shear and transverse tensile tests. Also, it reveals a nonlinear coupling that may exist between the combined shear and normal stress response.