Showing papers in "Journal of Composite Materials in 1971"

A General Theory of Strength for Anisotropic Materials

Abstract: An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.

Macroscopic Fracture Mechanics of Advanced Composite Materials

Abstract: The application of classical fracture mechanics to laminated com posites is discussed. A convenient method is presented for predicting the static strength of a flawed specimen. Theoretical predictions are compared with experimental data for specimens containing two types of flaws.

The Influence of Stacking Sequence on Laminate Strength

Abstract: Based upon considerations relating to the nature of the interlaminar 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.

Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic

Abstract: The nonlinear, viscoelastic behavior of a unidirectional, glass fiber-epoxy composite material is characterized by using isothermal, uniaxial creep and recovery tests together with a constitutive equation based on thermodynamic theory. The nonlinear constitutive equation for uniaxial loading is described first, and then fourth-order tensor transformations relating principal linear viscoelastic creep compli ances, uniaxial creep compliance, and fiber angle are summarized. Following a discussion of experimental aspects, creep and recovery data obtained from several different specimens (each having a differ ent fiber orientation relative to the loading axis) are reduced using a graphical shifting procedure and tensor transformations to evaluate all material properties, including the principal creep compliances. As a check on the constitutive theory, the data are shown to be in ternally consistent. Some simplicity in the analytical representation of the data is found; viz. the nonlinear, uniaxial creep compli...

Stress Distribution in Bonded Joints

Abstract: Stress distribution in plates and tubes bonded by stepped joints, assuming generalized plane stress

On the Propagation of Flexural Waves in an Orthotropic Laminated Plate and Its Response to an Impulsive Load

Abstract: The dynamic equations of orthotropic laminated plates are derived from the concepts of Timoshenko's beam theory to include the effects of transverse shear and rotatory inertia. The propagation of flexural waves is discussed. The transient response of a rectangular plate to a normal impact is investigated. We also consider briefly the influence of internal friction related to the damping on the response of the plate.

Approximate Three-Dimensional Solutions for Symmetric Laminates Under Inplane Loading *

Abstract: A three-dimensional equilibrium finite element analysis is used to obtain approximate stress solutions for some finite symmetric laminates under inplane loading. The analysis is based on a comple mentary energy formulation. Obtained stress solutions at the center section of the laminate are compared with solutions for uniform axial strain that are available in the literature. A comparison of the stress distributions obtained at the center and end sections of the laminate shows that a large τyz stress can occur at the end section and a large τxz can occur at the center section. The influence of laminate stacking sequence on the predicted σz is also presented.

Failure Mode and Strength Predictions of Anisotropic Bolt Bearing Specimens

Abstract: A major consideration in the design of a structure made of composite materials is the bolted joint since a bolted joint in a composite material has a significantly lower efficiency than the same joint in metals. Furthermore, the composite joint may fail in unique modes not found in metal joints. This study, in an attempt to further understand the failure characteristics of such bolted joints, investigates the stress concentrations induced in anisotropic plates loaded by means of a single fastener. The development of a prediction capability for both failure mode and ultimate load is the major goal of the early part of this work. Such a capability would allow synthesis rather than analysis to be used in the future design of fastener joints. An implied goal in this study is a relative evaluation of the three proposed anisotropic failure criterion: maximum stress, maximum strain, and distortional energy.

The Laminate Analogy for 2 and 3 Dimensional Composite Materials

Abstract: A previously developed laminate analogy for predicting the elastic stiffness and thermal expansion properties of a randomly oriented short fiber composite is extended to include a large class of fiber reinforced composites possessing very complex geometry. In particular, the stiffness and thermal expansion coefficients of short fiber com posites having biased filaments, misaligned filaments, and variable fiber aspect ratios are determined from a laminate analogy. In addition, the laminate analogy is extended to 2 and 3 dimensional woven fabric composites. Theoretical results for the short fiber com posites show excellent agreement with experimental results, while theoretical results for the woven fabric composites are shown to be qualitatively correct.

A Theory of Machining of Fiber-Reinforced Materials

Abstract: A theory of the machining of fiber-reinforced materials is pre sented. The analysis is restricted to plane deformations of incom pressible composites reinforced by strong parallel fibers. Complete deformation and stress fields, as well as estimates of the forces re quired to maintain continuous machining, are derived. The results apply to both elastic and plastic stress responses.

Analysis of the Rail Shear Test-Applications and Limitations

Abstract: A detailed theoretical and experimental analysis of the rail shear test is presented. A Fourier series solution is obtained for the stresses in an idealized rail shear specimen. The theoretical results are quali tatively verified on fiber reinforced rubber composites. Rail shear data on the modulus and strength of current high-modulus rein forced composites is compared to predicted values obtained from lamination theory. Results show that, despite definite limitations, the rail shear test can be useful in the determination of the in-plane shear properties of a laminated composite.

A Model for Stress Wave Propagation in Composite Materials

Abstract: A theoretical model is developed to describe stress wave propaga tion in plate laminate composites. The dispersive effects in the com posite are accounted for by direct analogy with a viscosity effect in the model. The model gives excellent predictions of steady and tran sient wave shapes and velocities, and of the attenuation of short stress pulses. It averages out only the fine structure which results from in dividual reverberations between the plates of the composite. The success of the theoretical model for plate laminate composites should provide a basis for good semi-empirical modeling of the stress wave propagation characteristics of a wide variety of composite materials.

Dynamic Compressive Strength and Failure of Steel Reinforced Epoxy Composites

Abstract: Results of an experimental program systematically evaluating the deformation and fracture of steel wire reinforced epoxy composite systems are presented. The program involved mechanical testing in the strain rate range 10-5 to 103/sec and impact testing of composite specimens using massive elastic targets at strain rates approximately 104/sec. Specific results presented include static and dynamic prop erties, strain rate sensitivity, information on the nature and character of dynamic fracture, influence of specimen geometry and reinforce ment spacing, and high speed photographs of dynamic failure modes. Further, a simplified energy criterion is proposed for predicting failure modes and critical velocities.

Analysis of Composite Failure Mechanisms Using Acoustic Emissions

Abstract: Acoustic emission monitoring has been used to record the sounds which emanate from such diverse processes as deformation of structures [1], geologic movements [2] and crack propagation in metals [3]. In most cases the approach is to simply record the acoustic response and then attempt to establish some correlation between the number of acoustic events and the load applied. Very little has been done to correlate observed emissions with a well defined sound source resulting from a specific deformation mechanism. As an outgrowth of our continuing efforts to analyze failure mechanisms in composites we have been able to isolate three basic failure mechanisms by optical means. These mechanisms, which were caused by tensile load of epoxy specimens containing only a few fibers, are [4]: 1) Fiber Fracture 2) Matrix Cracking 3) Interfacial Debonding. It is interesting to note that the local heterogeneity of advanced composites where very strong and stiff fibers are incorporated in a relatively weak and low modulus matrix may be an advantage in acoustic emission analysis. Fiber fractures are clearly audible and have been observed in tests of boron-epoxy composites without the aid of acoustic monitoring equipment. In more homogeneous materials the ability to discriminate between specific events in the failure process is a good deal

Finite-Element Analysis of Interlaminar Shear in Fibrous Composites

Abstract: A capability of determining the effects of shear deformation in the interlaminar regions of laminated fibrous composites is highly desirable, since these effects can be important with respect to strength and other properties of the composite. The particular problem of interlaminar shear stresses in an edge region has been treated analytically for the simple case of an infinite strip loaded along its length so that stress is independent of the longitudinal coordinate [1, 2]. The present work is intended to provide a practical capability for a more general treatment, and involves the application of a finite-element method of analysis. It is limited here to cases of generalized plane stress, in the sense that bending and warping of the laminate are not considered, and only elastic deformation is treated.

Further study of composite laminates under cylindrical bending.

Abstract: 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.

Effective Electrical, Thermal and Magnetic Properties of Fiber Reinforced Materials:

Abstract: We present here bounds for the effective conductivity (permittivity, permeability) of a fiber reinforced material in terms of volume fractions and a geometric factor. The results are simple algebraic expressions. Two parameters, G1 and G2 are needed to describe the fiber and matrix geometries, respectively. Both parameters lie between 1 and 1; 1 represents a circle and 1 a parallel lamella. We show 4 2 4 2

Stiffness and Strength of Two Glass-Fiber Reinforced Cement Laminates:

Abstract: A general description is given of the load-deformation charac teristics in tension, compression and bending of two types of thin cement laminate reinforced with short random glass fibers. Cyclic loading in tension is used to demonstrate that stiffness decreases and residual strain increases as cracking damage accumulates. The dam age depends on the greatest strain previously reached. There is no evidence that the presence of fibers delays the onset of cracking. Bending strains can be predicted by assuming linear strain distribu tions. Bending stress distribution is markedly non-linear. The bending test is an insensitive indicator of the onset of cracking.

On the Use of Shell Theory for Determining Stresses in Composite Cylinders

Abstract: Applying Vlasov-Ambartsumyan shell theory to anisotropic and laminated cylinders, equations are developed for calculating the stresses in a composite tube under combined axial load, torsion, and internal pressure. Comparison to results obtained from exact elasticity theory shows that the shell equations are capable of predicting, with a reasonable degree of accuracy, the large stress gradients found in highly anisotropic tubes. Thus the shell theory provides the experimentalist with a set of closed form expressions for readily defining the proper specimen dimensions for precise characterization of unidirectional and laminated composite tubes. A modification to the shell theory, in which the effects of transverse normal strain are included is also discussed. Numerical results show that such a modification is necessary for determining stresses induced by free thermal expansion. It is also shown that certain classical thin shell kinematic relations are incapable of predicting stresses in composite tubes.

Frequency as a Parameter in Delamination Problems--A Preliminary Investigation

Abstract: rational methods of analysis and design, but also for a tool to detect imperfections and failures and measures to rectify them. In a laminate, there is every possibility that the bond may weaken and propagate, eventually leading to a catastrophic failure. Such an unbonding may go undetected during testing on an assembly line. One method of locating flaws is ultrasonic testing which may give only qualitative results. However, a more quantitative approach is desired. It is proposed that the natural frequency may be a parameter to reflect the unbonding or weakening of the composite. The principal aim is to construct a model which nearly corresponds to the actual behavior. To this effect, the dynamic properties of a delaminated shell

Concise Property Transformation Relations for an Anisotropic Lamina

Abstract: Composite materials analysis frequently requires the transformation of quantities of analysis (stress, strain, etc.) and material properties from one coordinate system to another. Methods and expressions for obtaining these transformations are found in many works (Ref.’s 1, 2 for example); however, the general expressions for property transformations appear in lengthy notation. A new matrix is introduced below which, when used in their derivation, allows the general property transformation relations to be written in concise, matrix notation. A positive rotational transformation is illustrated in Figure 1 for an anisotropic lamina with principal axes (1, 2) and reference axes (x, y). Stress vectors and modified strain vectors (where shear strain is premultiplied by 1/2 ) transform according to

Vibration response - A non-destructive test for fatigue crack damage in filament-reinforced composites

Abstract: Vibration response NDT for fatigue crack damage in laminated filament-reinforced epoxy composites

Plastic behavior of some composite materials

Abstract: Based on the simplest deformation theory of plasticity, an attempt is made to predict the overall plastic behavior of two-phase reinforced composites under polyaxial stresses. An ideal composite is...

Steady Wave Analysis of Wave Propagation in Laminates and Mechanical Mixtures

Abstract: A mechanical theory is developed for the propagation of steady waves in laminated media. This analysis treats wave propagation parallel and perpendicular to the laminate plates. It predicts the response of the composite from a knowledge of the component vol ume fractions and mechanical equation of states. Under the restric tion of fluid or hydrodynamic materials, the results yield a hydro dynamic prediction which is independent of composite geometry. Consequently, the analysis is equally applicable to mechanical mix tures. Theoretical calculations are compared to experimental Hu goniot results for a cloth laminate quartz phenolic, a plate laminate and three mechanical mixtures of Al2O3 in epoxy. Excellent agree ment is obtained at low stresses, if the expected deviations caused by material strength are recognized. Thermodynamic effects caused by deviations of the loading path from that of a single shock become more predominant as the stress increases. Models describing both the strength and thermodynamic ...

Shock Parameters in a Two Component Mixture

Abstract: A thermodynamically consistent procedure, based on the Gibbs free energy, is described for computing the thermodynamic properties of a mixture in equilibrium at constant pressure and temperature. This is used to compute temperatures, pressures, Gruneisen parameters and sound velocities on the Hugoniot for mixtures of polyethylene and quartz. The results show that a simple mass-weighted average for the Gruneisen parameter is inaccurate and that the mixture of two mate rials for which Γ/V = constant does not itself have a constant value of r/V. Some comments are made on problems of equilibrium of stress and temperature in composite materials.

Stress Gradients in Laminated Composite Cylinders

Abstract: In a recent paper [1], (see also [2]) it was shown that extremely severe stress gradients can exist in the wall of a unidirectional, helical-wound cylinder under the common loadings applied in the laboratory, i.e., axial loading, internal pressurization, and torsion. In that study it was found that the stress gradients were drastically reduced in an orthotropic, symmetric laminated cylinder, such as an angle-ply. In fact, for the case of torsion, the shear stress distribution almost coincides with that which occurs in an isotropic cylinder. While an analogous smoothing of the stress field occurs under other loadings, the axial normal stress under axial loading and the hoop stress under internal pressure are somewhat different from the respective isotropic results. For example, refer to Figure 12 in [1]. In order to complete the treatment of the geometric design of tubular characterization specimens, the remaining stress components, e.g., the hoop and shear stresses induced in the axial loading experiment, should be considered. It is therefore the purpose of this note to present some results in this regard for laminated cylinders.

Stress Concentrations Near a Discontinuity in Fibrous Composites

Abstract: Stress concentration factors are defined for the fiber and matrix in an axially loaded unidirectional composite which has a discontinuous fiber Effects of variations in fiber volume fraction, end-gap size, and modulus ratio are studied by using a linearly elastic finite-element analysis Results show that the fiber stress concentration factors reach a maximum value of 1.5 and then remain relatively unchanged The matrix stress concentration factors, however, are shown to increase rapidly with decreasing end-gap size and increasing modulus ratio.

Diagonal Tension Behavior of Boron-Epoxy Shear Panels

Abstract: In previous articles [1, 2, 3, 4, 5, 6], analysis procedures and experimental results have been presented for the buckling, vibration, and bending behavior of thin laminated composite plates. All of these papers have dealt with linear, small deflection behavior. The post-buckling, large-deflection behavior of laminated plates has not been considered, and in fact, such behavior has been virtually ignored since the low interlaminar strengths of these plates was thought to preclude appreciable post buckling strength. The present paper presents an experimental study of the post shear buckling, diagonal tension behavior of rectangular laminated boron-epoxy plates clamped on each edge. The linear theory buckling load is also compared to the experimental results.

Fracture Toughness Measurements in Unidirectional Glass-Reinforced-Plastics

Abstract: no general theory exists for the analysis of the crack-propagation behavior of filament-wound composite materials with an arbitrary winding angle; however, the failure of unidirectional composites can be analyzed with the existing theory of fracture mechanics, since crack extension is achieved by the formation of plane surfaces and can be completely described by the single parameter, crack length. In addition, the unidirectional composite is probably a more sensitive indicator of the influence of changes in materials variables than any other layup angle, since the reinforcing effect of the fibers is minimized. The studies summarized here were undertaken to develop suitable techniques for the application of fracture mechanics concepts to unidirectional GRP composites and to apply these techniques in determining the effects of material variables. To