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NASA NTRS1976

The effect of adhesive layer on crack propagation in laminates

The effect of the adhesive layer on crack propagation in composite materials is investigated. The composite medium consists of parallel load carrying laminates and buffer strips arranged periodically and bonded with thin adhesive layers. The strips, assumed to be isotropic and linearly elastic, contain symmetric cracks of arbitrary lengths located normal to the interfaces. Two problems are considered: (1) thin adhesive layers are approximated by uncoupled tension and shear springs distributed along the interfaces of the strips for which only the case of internal cracks can be treated rigorously; (2) broken laminates and the true singular behavior in the presence of the adhesive layer are studied. The adhesive is then treated as an isotropic, linearly elastic continuum. General expressions for field quantities are obtained in terms of infinite Fourier integrals. These expressions give a system of singular integral equations in terms of the crack surface displacement derivatives. By using appropriate quadrature formulas, the integral equations reduce to a system of linear algebraic equations which are solved numerically.

Gecit, M. R.↗

NASA NTRS1976

Flutter and buckling of general laminated plates

An anisotropic buckling and flutter analysis is developed with allowance for both bending-extensional coupling and bending-twisting coupling within the framework of linear small deflection theory for simply supported general laminated plates. The extended Galerkin method is used to obtain approximate solutions to the coupled governing equations. The effects of various anisotropic stiffness parameters on the static and dynamic stability of laminated plates are evaluated, with particular emphasis on assessing the range of applicability of classical orthotropic plate theory. It is shown that bending-extensional coupling and bending-twisting stiffness terms have a destabilizing effect on buckling and flutter, the effect being more pronounced for a small number of layers. For symmetric plates, the number of layers required for orthotropic plate theory to be applicable is generally less for the buckling problem than for flutter. For square plates, aligning the fibers with the direction of airflow over the plate surface results in the highest flutter dynamic pressure.

Sawyer, J. W.↗

NASA NTRS1976

A high order theory for uniform and laminated plates

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.

Lo, K. H.↗

NASA NTRS1976

Progressive failure of notched composite laminates using finite elements

An incremental, nonlinear, finite element program capable of tracing the damage that occurs in a notched laminated composite, before ultimate failure takes place, is described. Computer predictions for the ultimate failure load and failure modes are compared to experimental results for two laminates containing holes and loaded in uniaxial tension. The comparison is quite favorable.

Nuismer, R. J.↗

NASA NTRS1976

Free vibrations of laminated composite elliptic plates

The free vibrations are studied of laminated anisotropic elliptic plates with clamped edges. The analytical formulation is based on a Mindlin-Reissner type plate theory with the effects of transverse shear deformation, rotary inertia, and bending-extensional coupling included. The frequencies and mode shapes are obtained by using the Rayleigh-Ritz technique in conjunction with Hamilton's principle. A computerized symbolic integration approach is used to develop analytic expressions for the stiffness and mass coefficients and is shown to be particularly useful in evaluating the derivatives of the eigenvalues with respect to certain geometric and material parameters. Numerical results are presented for the case of angle-ply composite plates with skew-symmetric lamination.

Andersen, C. M.↗

NASA NTRS1976

Stress concentration factors around a circular hole in laminated composites

Stress concentration factors around a circular hole in a composite laminate are determined. The specific case investigated is a four layer (-45/45/45/-45 degs) graphite epoxy laminate. The factors are determined experimentally by means of electrical resistance strain gages, and analytically by using a hybrid finite element analysis.

Ueng, C. E. S.↗

NASA NTRS1976

Lamination residual stresses in hybrid composites, part 1

An experimental investigation was conducted to study lamination residual stresses for various material and loading parameters. The effects of hybridization on residual stresses and residual properties after thermal cycling under load were determined in angle-ply graphite/Kevlar/epoxy and graphite/S-glass/epoxy laminates. Residual strains in the graphite plies are not appreciably affected by the type and number of hybridizing plies. Computed residual stresses at room temperature in the S-glass plies reach values up to seventy-five percent of the transverse strength of the material. Computed residual stresses in the graphite plies exceed the static strength by approximately ten percent. In the case of Kevlar plies, computed residual stresses far exceed the static strength indicating possible early failure of these plies. Static testing of the hybrids above indicates that failure is governed by the ultimate strain of the graphite plies. In thermally cycled hybrids, in general, residual moduli were somewhat lower and residual strengths were higher than initial values.

Daniel, I. M.↗

NASA NTRS1977

A study of damage zones or characteristic lengths as related to the fracture behavior of graphite/epoxy laminates

Uniaxial tensile tests conducted on a variety of graphite/epoxy laminates, containing narrow rectangular slits, square or circular holes with various aspect ratios are discussed. The techniques used to study stable crack or damage zone growth--namely, birefringence coatings, COD gages, and microscopic observations are discussed. Initial and final fracture modes are discussed as well as the effect of notch size and shape, and laminate type on the fracture process. Characteristic lengths are calculated and compared to each other using the point, average and inherent flaw theories. Fracture toughnesses are calculated by the same theories and compared to a boundary integral equation technique. Finite width K-calibration factors are also discussed.

Yeow, Y. T.↗

NASA NTRS1977

Two-dimensional hygrothermal diffusions into a finite width composite laminate

Two dimensional hygroscopic diffusion into composite laminates with free edges was obtained through the use of a second order finite difference scheme. A computer program was developed for the transient nonlinear coupled hygrothermal diffusion into finite width laminates with varying surface conditions along two edges. The formulation permits the diffusion coefficient to be a function of temperature, moisture concentration, and fiber orientation. The moisture distributions thus obtained are necessary for analysis of the moisture induced interlaminar stresses in the vicinity of free edges. It is shown that large diffusion times tend to eliminate the significance of stacking sequence, but gradients within and between layers are significant for all diffusion times.

Farley, G. L.↗

NASA NTRS1977

Theory of ultrasonic diffraction by damage developed in thin laminated composites

The apparent attenuation which would result if certain damage states (transverse cracks and delaminations) are introduced into a graphite/epoxy laminate through which an ultrasonic wave passes is investigated. Experimental data for two different laminates are presented which shows changes in the apparent attenuation of about one db. These changes generally occur at loads which correspond to the range predicted for the formation of the damage. The predicted changes in the attenuation for several simple and common damage states are well within the range of experimental values.

Hayford, D. T.↗

NASA NTRS1977

Static behavior and the effects of thermal cycling in hybrid laminates

Static stiffness, strength and ultimate strain after thermal cycling were investigated for graphite/Kevlar 49/epoxy and graphite/S-glass/epoxy angle-ply laminates. Tensile stress-strain curves to failure and uniaxial tensile properties were determined, and theoretical predictions of modulus, Poisson's ratio and ultimate strain, based on linear lamination theory, constituent ply properties and measured strength, were made. No significant influence on tensile stress properties due to stacking sequence variations was observed. In general, specimens containing two 0-degree Kevlar or S-glass plies were found to behave linearly to failure, while specimens containing 4 0-degree Kevlar or S-glass plies showed some nonlinear behavior.

Liber, T. M.↗

NASA NTRS1977

Use of the short-beam shear test for quality control of graphite-polyimide laminates

The properties of laminated composite materials are strongly affected by many fabrication variables including temperature, time, and molding pressure. It is therefore necessary to have reliable quality control tests to check the properties of manufactured materials. The short-beam shear test is used widely by both manufacturers and researchers as a quality control test in the production of materials and development of new material systems. There are, however, several limitations to the standard test method. This paper presents the results of short-beam shear tests on graphite-polyimide laminates and reports on stiffness-strength relationships and nondestructive evaluation methods which aid in the interpretation of the test data.

Stinchcomb, W. W.↗

NASA NTRS1977

Experimental studies of graphite-epoxy and boron-epoxy angle ply laminates in shear

The nonlinear/inelastic response under inplane shear of a large variety of graphite-epoxy and boron-epoxy angle-ply laminates was tested. Their strength allowables were obtained and the mechanisms which govern their mode of failure were determined. Two types of specimens for the program were chosen, tested, and evaluated: shear panels stabilized by an aluminum honeycomb core and shear tubes. A modified biaxially compression/tension loaded picture frame was designed and utilized in the test program with the shear panels. The results obtained with this test technique categorically prefer the shear panels, rather than the tubes, for adequate and satisfactory experimental definition of the objectives. Test results indicate the existence of a so-called core-effect which ought to be considered when reducing experimental data for weak in shear laminates.

Weller, T.↗

NASA NTRS1977

Composite lamination method

A process was developed for preparing relatively thick composite laminate structure wherein thin layers of prepreg tapes are assembled, these thin layers are cut into strips that are partially cured, and stacked into the desired thickness with uncured prepreg disposed between each layer of strips. The formed laminate is finally cured and thereafter machined to the desired final dimensions.

Dickerson, G. E.↗

NASA NTRS1978

Evaluation and expansion of an analytical model for fatigue of notched composite laminates

The analytical and experimental study performed to expand the existing static and fatigue failure analysis is described. The analytical effort extended the analysis to include interlaminar effects, while the experimental effort developed methods to obtain basic experimental data required as input to the analysis. The static failure analysis for notched laminates was modified to include interlaminar effects near the notch. Three dimensional elastic and two dimensional elasticplastic finite element analysis were performed for some notched laminates.

Ramkumar, R. L.↗

NASA NTRS1978

Titanium/beryllium laminates: Fabrication, mechanical properties, and potential aerospace applications

The investigation indicated that structural laminates can be made which have: a modulus of elasticity comparable to steel, fracture strength of comparable to the yield strength of titanium, density comparable to aluminum, impact resistance comparable to titanium, and little or no notch sensitivity. These laminates can have stiffness and weight advantages over other materials including advanced fiber composites, in some aerospace applications where buckling resistance, vibration frequencies, and weight considerations control the design.

Chamis, C. C.↗

NASA NTRS1977

An experimental investigation on the tensile moduli and strengths of graphite/epoxy laminates

The results of a series of tensile tests on some graphite/epoxy laminates, at rates varying from 0.002 to 2 in./min are examined. The loads were applied at various angles to the fiber directions in each case. The rate-dependent behavior of the stress-strain response is assessed. Evidence is presented to indicate that failure first occurs on inner plies, and that, in some cases, moduli increase with increasing stress (or strain) level. Lamination theory is used to predict the moduli, and comparisons with experiment are given. This theory is also used in conjunction with three failure theories to predict ultimate strengths (with varying degrees of success). Further, two approaches to ply unloading after first-ply failure are used and discussed. One is a standard method found in the literature while the other is a proposed 'strength-of-materials' type of technique which is computationally much simpler.

Yeow, Y. T.↗

NASA NTRS1978

Transverse shear stiffness of laminated anisotropic shells

Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.

Cohen, G. A.↗