Showing papers in "Journal of Composite Materials in 1974"

Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations

Abstract: Two related criteria based on stress distribution are presented for predicting the uniaxial tensile strength of laminated composites containing through the thickness discontinuities of a general shape. The criteria result in two parameter (unnotched tensile strength and a characteristic dimension) models which are capable of predicting observed discontinuity size effects without resorting to classical concepts of linear elastic fracture mechanics. As a direct consequence of the stress criteria, however, a relationship between Mode I fracture toughness and unnotched laminate tensile strength is determined. Limited comparison of theory to experimental data for circular holes and straight cracks yields good results. The simplicity of the analytical approach coupled with its generality make it of practical value to the designer.

On the Calculation of Interlaminar Normal Stress in Composite Laminate

Abstract: In an effort to improve our understanding of delamination phenomena in composite bodies, an approximate method to define the distribution of the interlaminar normal stress, σ z, along the central plane of a symmetric, finite-width, composite laminate is presented. The approach is based upon a modified version of a recent theory developed by Whitney and Sun and accounts for the influence of the pertinent material and geometric parameters on the shape of the distribution. The accuracy of the approach is demonstrated by comparison with an existing three-dimensional elasticity solution. Finally, an elementary expression for σ z in practical bidirectional laminates is derived.

On the Behavior of Composite Laminates After Initial Failures

Abstract: 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.

Strength Ratios of Composite Materials in Flexure and in Tension

Abstract: Ratios of flexural strengths to tensile strengths for wide varieties of brittle materials have been found to agree very well with Weibull’s statistical strength theory [ 1 4], which has been widely used in the ceramics field [5-14] . Systematic studies to determine if Weibull theory correctly predicts such strength ratios for fibrous-reinforced epoxy composites have not been reported as yet, although much data exist for making such strength comparisons. The purpose of this note is to report data indicating that Weibull theory does correctly predict strength behaviors for certain composite materials and to suggest that other composite systems be tested against this theory. Verification of this result through more detailed studies would be of importance, because less-expensive flexural specimens that are easier to

Thermal Expansions of Heterogeneous Solids Containing Aligned Ellipsoidal Inclusions

Abstract: A theoretical study has been made to predict overall thermal expansion characteristics of a two-phase material consisting of a matrix and aligned ellipsoidal inclusions. The calculation is based on Eshelby's theory on the transformation problem; an approximate method is Introduced to account for the effect of finite concentrations of the inclusions. The following two cases are treated: elastic matrix-elastic inclusions and elastoplastic matrix- elastic inclusions. The results are explicitly obtained when shapes of the inclusions are spherical, disc-shaped, and fiber-shaped. The calculated over all thermal expansion coefficient for the case of elastic matrix-elastic spheres agrees with Kerner's prediction.

On the Effective Moduli of Isotropic Two-Phase Elastic Composites

Abstract: Let us consider a matrix with elastic moduli K1 and G1 (bulk and shear moduli respectively) in which are embedded particles with elastic moduli K2 and G2. The fractional volume of the particles is c2 and the fractional volume of the matrix is cl (Cl + cz 1 ). This two-phase suspension is assumed to be statistically homogeneous and isotropic. The effective bulk and shear moduli are K’~ and G* respectively. -

On the Significance of Effective Modulus Solutions for Fibrous Composites

Abstract: The concept of effective moduli is widely used in the analysis and design of structural fibrous composites. In this approach, composite bodies are treated as laminated systems in which each layer is represented as a homogeneous anisotropic material. This approach, however, breaks down in the presence of non-uniform macroscopic stress fields. In this work, we attempt to examine the physical significance of effective modulus solutions in such cases by comparison with solutions in which the microstructure is recognized. While the meaning of a non-uniform stress field predicted by the effective modulus approach is generally ambiguous, we find, at least in the problems treated here, that the respective stresses averaged over dimensions comparable to fiber spacing agree quite well with corresponding exact averages. An example is presented which demonstrates that the effective modulus stress field cannot predict the correct physical response while the average stresses are at least qualitatively correct. Finally, an elementary approximate theory for the determination of average interlaminar normal stresses in the laminate free-edge problem is developed.

Mechanical Properties of Aluminum-Graphite Composites Prepared by Liquid Phase Hot Pressing:

Abstract: A continuous liquid metal infiltration process has recently been developed for making aluminum-graphite composite wire from commercially available multifiber graphite yarns. Composite specimens have been successfully fabricated by hot pressing the composite wire. The longitudinal properties of both the composite wire and hot pressed specimens approximated rule of mixtures behavior, but the transverse tensile and compressive strengths of the specimens were lower than expected. Examination of the microstructure indicates that better transverse and compressive strengths may be achieved through refinement of the matrix grain size, elimination of continuous networks of intermetallic compounds in the matrix, and homogenization of the matrix alloy constituents.

Investigation of Acoustic Emission During Fatigue Loading of Composite Specimens

Abstract: Strain and load controlled fatigue tests were run on boron-aluminum and boron-epoxy angle-plied specimens. Acoustic emission data was recorded using a gating technique that eliminated most extraneous noise. Various material parameters were monitored during the test. A good corre lation between acoustic emission and damage extent and propagation was obtained. This was evidenced by an apparent first order linear relationship between dynamic compliance and totalized acoustic emission. A basis for an energy based failure model is formulated and discussed.

Stress Intensity Factors for Anisotropic Fracture Test Specimens of Several Geometries

Abstract: Stress intensity factors have been obtained for single-edge-notched, double-edge-notched, and double cantilever beam fracture toughness test specimens using a two-dimensional hybrid stress model fi...

Thickness Expansion Coefficients of Composite Laminates

Abstract: Fahmy and Ragai-Ellozy [1] have recently treated the problem of the thermal expansion coefficient in the thickness direction of a symmetric composite laminate. Unfortunately, however, an error has been made in their analysis. Specifically, Equation (1) of that work should take the form $${a_{3r}} = {a_T} - \frac{1}{{1 - {v_{12}}{v_{21}}}}\left[ {({v_{13}} + {v_{12}}{v_{23}})({a_{1C}} - {a_L}) + ({v_{23}} + {v_{13}}{v_{21}})({a_{2c}} - {a_T})} \right]$$ (1) in the notation of [1]. In particular, v 12 is major Poisson’s ratio.

The Fracture Mechanics of Carbon Fibre Laminates

Abstract: Critical stress intensity factors and fracture surface energies have been measured for a series of 0°/90° carbon fibre reinforced epoxide and carbon fibre reinforced glass composites. The fracture surface energies have been measured by three separate techniques, one of which depends on the applicability of the Griffith-Irwin criterion and the others of which do not. A comparison of these energies and of the dependence of critical stress intensity factors on crack length therefore provides information about the. applicability of linear elastic fracture mechanics to carbon fibre composites.

Ultrasonic Resonance Measurements of Sound Velocity in Thin Composite Laminates

Abstract: 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.

Measurement of the Elastic Moduli of Continuous-Filament and Eutectic Composite Materials

Abstract: Continuous filaments and eutectic composite materials have been treated as homogeneous and orthotropic and transversely isotropic elastic materials, respectively, in stress analysis problems. Based on these assump tions the elastic moduli of boron-epoxy and Al-Al3Ni eutectic composite materials are measured using pulse-echo techniques. The shear wave measurements show that the elastic anisotropy assumed for each material is only an approximation. The measurements are also influenced by defects in the fiber arrangement and, m the eutectic composite, by the presence of a solidification substructure.

Three-Dimensional Mechanical Characterization of Anisotropic Composites

Abstract: The problem of complete characterization of a general linearly elastic, anisotropic material is discussed. An experimental procedure of testing a normally oriented and an obliquely oriented cubical specimen of the material is proposed, from which the 36 constants in the compliance matrix can be determined. A multiaxial test cell for applying homogeneous compressive stresses to the cubical specimen is described and the procedure is applied to Scotchply, a reinforced plastic. The compliance matrix for Scotchply is determined and it is shown to be orthotropic.

Elastoplastic Crack Propagation in a Transversely Loaded Unidirectional Composite

Abstract: A finite element numerical analysis is developed to model crack initiation and subsequent propagation in a unidirectionally reinforced composite incorporating a matrix material exhibiting elastoplastic stress-strain response. A monotonic but otherwise arbitrary stress-strain curve is admissible, along with elastic unloading-reloading behavior. A simple crack representation model is utilized in place of a classical fracture mechanics approach, with octahedral shear stress-octahedral plastic shear strain being the governing criterion for both yielding and failure. Numerical results, which model a specific set of actual experimental data for a 40 volume percent boron/aluminum composite, are presented and discussed.

The Effect of Crack Length and Bond Strength on the Delamination Process in Borsic-Al Composites

Abstract: The effect of crack length and fiber-matrix bond strength on the delamination process in unidirectional Borsic-Al composites has been examined using Single-Edge-Notch specimens. The transverse tensile strength, σT, was used as an indirect measure of the fiber-matrix bond strength, which was altered through variations in hot pressing during composite fabrication. In composites with weak fiber-matrix bonds (σT = 3.2 ksi), the net-section stress at delamination, σ D, was observed to decrease with increasing crack length. Variations in crack length did not significantly alter the basic fracture mechanism in which the delamination process led to notch insensitivity. Increases in the fiber-matrix bond strength (σT increased from 3.2 ksi to 13.2 ksi) caused a marked increase in σD but did not change the general delamination process. Through the use of cross-plied composites, the transverse strength was raised to 16.6 ksi and delamination was suppressed. This led to notch-sensitive fracture behavior and a substan...

Thermal Expansion of Laminated Fiber Composites in the Thickness Direction

Abstract: The thermal expansion coefficients of a laminated fiber composite of balanced construction along any two orthogonal axes in the plane of the laminate have been calculated by Halpin and Pagano [ 1 ] . These coefficients are given in terms of the laminate construction, and the following properties of the ply: longitudinal and transverse Young’s moduli EL and ET, the major Poisson’s ratio vLT, the in-plane shear modulus GLT, and the longitudinal and transverse coefficients of thermal expansion aL and aT. The validity of their analysis has been confirmed experimentally [ 1, 2] . . The present work, however, is concerned with the thermal expansion of such laminates along the thickness direction. Here, one must take into account the Poissons’ effects of the in-plane strains in the plies. The &dquo;free&dquo; thermal expansion coefficient of all plies along the thickness direction is obviously identical to aT. The &dquo;restrained&dquo; or actual coefficient a3r of any ply is given by: .

Interfacial Slip Around Rigid Fiber Inclusions

Abstract: Interface slip in a composite material is modeled by considering a finite length, rigid line inclusion (fiber) embedded in a two-dimensional elastic matrix with sliding fiber-matrix interface cracks extending from the fiber tips. The crack faces are assumed to remain in contact; the resulting fric tion forces between the crack faces are taken to be constant. A closed form solution for this problem is presented which is used to study the stable size of interface cracks based on the concept of a critical stress intensity factor. The relaxation of axial fiber force as a result of constant load debonding is examined. In addition, the change in fiber force due to stable unbonding under monotonic increasing loads is considered. Finally, the loading conditions leading to closed sliding cracks are identified.

Attenuation and Dispersion Characteristics of Various Plastics in the Frequency Range 1-10 MHz

Abstract: It is observed experimentally that PMMA, phenolic and various polyester resins exhibit little dispersion but significant frequency-dependent attenuation for dilatational waves in the frequency range 1-10 MHz. It is also shown that the shape of a low amplitude stress pulse propagating through a material with the above characteristics becomes significantly altered after propagating only a few cm. Thus the stress pulse distortion observed in plastic matrix-type composite materials may not be attributed to geometrical dispersion and attenuation alone; material attenuation in the matrix must be considered. The representation of these plastics by a standard linear viscoelastic solid is shown to provide an adequate model of the experimental data for the stated frequency range.

Elastic-plastic Poisson's ratio of borsic--aluminum

Abstract: Poisson's ratio as a function of tensile strain has been examined for four volume fractions of unidirectional Borsic-reinforced aluminum composites. Linear relationships were found between Poisson's ratio and filament volume fraction during Stage I (elastic filaments-elastic matrix) and Stage II (elastic filaments-plastic matrix) deformation which could be correlated to filament and matrix values of Poisson's ratio. These results confirm that a simple rule-of-mixtures relationship may be used to predict composite Poisson's ratios as a function of filament volume fraction. The marked increase in the Poisson's ratio of the matrix upon yielding causes an abrupt rise in the slope of the composite Poisson's ratio versus longitudinal strain curve. This sudden increase may be used as an accurate method of determining matrix yield in filament-reinforced, metal-matrix composites.

A Derivation of Invariants of Fourth Rank Tensors

Abstract: Invariants associated with rotation about a particular axis are derived for fourth rank tensors as they are used in two-dimensional and three-dimensional elasticity. The method is based on the obse...

The Use of Artificial Viscosity to Compute One-Dimensional Wave Propagation in Composite Materials:

Abstract: A new and simple numerical method is presented for computing large amplitude, one-dimensional wave propagation in composite materials. The method deals with values of stress, particle velocity, and displacement that are averaged over several unit cells of the composite. The principal advantage of the method over previous macroscopic approaches is that it uses the numerical oscillations and the artificial viscosity already present in one-dimensional hydrocodes to model the geometric and dissipative dispersions of the composite material. The hydrocodes (such as PUFF or WONDY) may be used in their present form without additional dispersion relations. The method is shown to correspond to a definite physical constitutive material model. Comparisons of computational results with this method are made with those from previous models and with experimental measurements.

Macroscopic Fracture Mechanics of Glass Reinforced Polyester Resin Laminates

Abstract: Failure stresses for (a) plate specimens of glass chopped strand mat (CSM) and plain weave fabric-reinforced polyester resin laminates containing holes of various sizes, and (b) box-section beams of CSNI/polyester resin laminate containing a notch or hole in the tension flange were determined. Experimental values were compared with predicted values calcu-Iated from separately determined critical stress intensity factor, Kc, values. The Kc values were corrected using Irwin's crack tip zone correction factor together with an equivalent yield stress. For both types of specimen measured and predicted failure stresses were in reasonably good agreement.

Compressive Strength of Unidirectional Fibrous Composites

Abstract: Among many papers concerning the compressive strength of unidirectional fibrous composites, the analysis by Rosen [ 1I is well known, although it does not always agree with the experimental results. Several workers [2-~j tried to explain this difference, but achieved only limited success. Lager and June [5] measured the compressive strength of boron-epoxy composite materials and the result agreed with Rosen’s analysis if a modified elastic modulus was employed. However, the theoretical basis of this modification is not explained. If the fibers in a composite materials are not straight due to initial curvature the compressive strength will be lowered. First, it is assumed that this initial curvature is parallel to each other as shown in Figure 1 (a). The analysis can be carried out under the following assumptions: (i) The deformation is two dimensional; (ii) The influence of normal strain of matrix parallel to the fiber axis and that of Poisson’s ratio can be neglected; (iii) there is neither deflection nor moment at both ends of a certain length of fibers. Let x-axis be taken in direction of compressive load P..Tle initial curvature of fiber is represented by f(x), and the position of the deformed fiber is represented by y. The compressive load causes increased fiber curvature and induces shearing strain in the matrix as follows:

Longitudinal Tensile Behavior of Unidirectional Carbon-Carbon Composites

Abstract: The increasing interest in utilizing carbonaceous-fiber-reinforced carbon matrix materials in high temperature structural applications has resulted in the generation of an increasing amount of experimental data, primarily for unidirectionally reinforced systems. While the longitudinal tensile strength and stiffness properties presently being achieved are attractive relative to those of unreinforced carbonaceous materials such as bulk graphite, they remain well below their apparent potential. Utilizing micromechanical analyses and taking into consideration the highly anistropic crystallo graphic structure of graphite, possible explanations for the observed properties degradation have been formulated. Suggestions for modifying the fabrication and thermal processing as a means of improving axial properties, and tensile strength in particular, are presented.

Internal Damping in a Fiber-Reinforced Composite Material

Abstract: In a previous investigation 1 I of stress waves in fiber-reinforced composite materials, a vibration resonance method was used for finding the elastic moduli and damping coefficients of various materials in the frequency range 0-10,000 Hz. The resulting data were used to compute velocities and attenuations of stress pulses in thin composite rods. Such computations require a knowledge of the internal damping over a wide (theoretically infinite) frequency domain. Based upon a Fourier type of analysis, it was found that the range of frequency covered by the vibration data accounted for approximately 50% of the total response; on the other hand the frequency range 0-2.0 hiHz contributed over 99.5% of the response. In the computations it was therefore necessary to extrapolate the measured data over the range 10,000 Hz to 2.0 MHz. This extrapolation naturally introduced considerable uncertainty into the analysis. The purpose of this note is to demonstrate that ultrasonic, attenuation measurements may be combined with low frequency vibration data in order to characterize the internal damping over a wide frequency range. Solutions to stress-wave problems of the type considered previously can then be based upon interpolated data rather than less reliable extrapolated information. A simple technique for measuring damping in the ultrasonic frequency range is described, and experimental results are presented for a glass-epoxy composite material.

Damping Characteristics of Composite and Porous Materials

Abstract: It has been shown by the authors that the damping capacity of structural members can be increased considerably, either by proper introduction of stress concentration [ I ], or with the help of inserts of special high-damping alloys [ 2 ] . In the present work, the effect, of high-damping particulate inclusions, on the over-all damping capacity of a composite material has been investigated theoretically. It is observed that most of the high-damping alloys have poor rigidity and rigid materials possess low damping capacity. To date, most of the composite materials have been developed to improve the mechanical properties such as stiffness, tough-

Transformations for Elliptical Holes Applied to Finite Element Analysis

Abstract: *This work was conducted in part under USAF Contract F33b15-71-C1239. The stress behavior around holes in composite materials is of interest for the design of cut-outs and attachments. In addition, basic studies directed at understanding the behavior of composites are done on specimens with circular or elliptical holes. Representing the geometry of an elliptical hole can require more effort than constructing a representation for a circular hole. This is particularly true when many different sizes and orientations of an ellipse are to be modeled. This note presents a method for transforming the problem of a single elliptical hole in an anisotropic material to a problem of a circular hole in a different anisotropic material. Several examples are presented. The numerical analysis used here is based

Anelastic creep of boron fibers

Abstract: High performance fibers of boron, silicon carbide, and alumina form the basis for the recent advances made in metal matrix composites. In matrices such as aluminum, titanium, and nickel-base alloys, these fibers provide materials of both high specific strength and modulus over a wide range of temperatures [ 1, 2, 3, 4]. The boron fiber has, in the past, received the greatest emphasis among these fibers because of its ability to maintam high levels of specific strength over a wide temperature range despite its being abraded and handled during composite fabrication. In contrast, both SiC and A1203 are extremely surface flaw sensitive. This article points up another major difference between boron and the other high performance fibers; boron exhibits anelastic creep. The phenomenon to be described can be readily demonstrated by a simple experiment. A boron fiber, held by hand in a loop, is heated with a match. Upon release of the fiber, it is observed that it has taken a curved form. Now, by reheating the unconstrained fiber loop, once again with a match, the fiber can be returned