The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. Plates with one end being up to 3 times narrower than the other end, and the plate being up to 3 time longer than the width of the wide end are considered. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms N_x=P/W(x) and N_y=N_xy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. With nondimensionalization, the analysis is well suited for parametric studies. The analysis uses standard eigenvalue extraction routines and converges using 5 terms in the out-of-plane displacement series. It appears that this analysis captures the buckling response of plates having tapered planform and should be a useful design tool. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5%, in general, and within 15% for the worst cases. In addition to the good agreement between the semi-analytical analysis and the finite element results, the finite element model also suggests that the simplified inplane force resultant distribution assumed in the analysis is valid. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the analytical results regarding the buckling load and the prebuckling plate stiffness. However, the experimental results show that for some cases the analysis underpredicts the number of halfwaves in the buckled mode shape. In the context of the definitions of taper ratio and aspect ratio used in this study, it is concluded that the buckling load always increases as taper ratio increases for a given aspect ratio for plates having simply supported boundary conditions on the parallel ends. There are combinations of plate geometry and ply stacking sequences, however, that reverse this trend for plates having clamped boundary conditions on the parallel ends such that an increase in the taper ratio causes a decrease in the buckling load. The clamped boundary conditions on the parallel ends of the plate are shown to increase the buckling load compared to simply supported boundary conditions. Also, anisotropy (the D₁₆ and D₂₆ terms) is shown to decrease the buckling load and skew the buckled mode shape for both the simply supported and clamped boundary conditions. / Master of Science

The objective of this study was to investigate the bending strength and failure characteristics of AS4/3501-6 and AS4/1806 graphite/epoxy angles sections as a function of processing induced defects and porosity. The angle sections were removed from 30-inch long angles fabricated at Lockheed Georgia Company with two quasi-isotropic stacking sequences, (± 45/90₂/ ∓ 45/0₂), and (± 45/90₂ ∓ 45/0₂)₃. Various degrees of porosity were introduced into the angles using four processing techniques: a standard lay-up, a solvent wipe during lay-up, moisture introduction between plies during lay-up, and a low pressure cure cycle. Two 2.5-inch wide angle sections, each with a 1.5-inch short leg and a 3.0-inch long leg, were bonded together along their long leg to form a T-shaped specimen. Bending of the T-specimen was introduced by pressing up on the underside of the flanges while holding the base of the specimen fixed. The experimental results have shown a significant effect of the processing induced defects on the failure load and bending stiffness for AS4/3501-6 specimens, but not for AS4/1806 specimens. An anisotropic analysis of the angle curved section was performed using Lekhnitskii's stress function approach. Stress and strain fields were studied and two failure criteria (Dual maximum stress and Tsai-Wu) were investigated in order to predict T-specimen failure load and failure mode. Reasonable correlation between prediction and experiments was found for the AS4/3501-6 (± 45/90₂/ ∓ 45/0₂)₃ T-specimens, but both failure criteria were found to be too conservative in predicting failure for the AS4/3501-6 (± 45/O₂/ ∓ 45/90₂)₃, T-specimens. The predicted failure modes were in good agreement with the experimental observations for both Iaminates. / Master of Science

"lnterlayering" - the incorporation of low-modulus film adhesive between the plies of composite Iaminates - has proved to be a successful technique for reducing debilitating out-of-pIane stresses. This work seeks to determine the effect interlayering has on a composite Iaminate's in-plane performance. Two Iaminate systems, an unnotched, 16-ply, quasi-isotropic, AS4/C985 and a centernotched, 32-ply, quasi-isotropic, AS4/C1808, were furnished in an interlayered and baseline (non-interlayered) configuration. The interlayers, 0.0005 in. each in thickness, appeared between each ply in every Iaminate tested. Both configurations of these two material systems were subjected to a regimen of in-plane loading tests. These tests included monotonic tension and compression, fully-reversed (R=-1), tension-compression fatigue cycling, and long-term tensile loading. A new test method, called the Incremental Strain Test (IST), was developed in an attempt to isolate and distinguish the long-term, tensile response of the interlayered and baseline Iaminates. This technique and its utility are described herein. The interlayered Iaminates exhibited superior performance during monotonic and IST loading. Distinctly higher ultimate loads and strains were achieved by the interlayered laminates. The notched fatigue performance of the interlayered Iaminates was sub-standard in comparison to the baseline results at the load level tested. The residual tensile strength of the fatigued interlayered Iaminates fell sharply at an early fraction of the laminates’ total life. The presence of the interlayers did not degrade the laminates’ IST performance. Several non-destructive techniques were used to monitor the damage mechanisms. These results, when combined with the experimental findings, helped explicate the disparity found between the interlayered and baseline Iaminate response. / Master of Science

Several damage modes, including fiber breakage, delamination, and transverse cracking, have been observed to contribute to the mechanical degradation of fiber-reinforced composite laminates. In this investigation, the effect of transverse cracking on laminate stiffness was studied. Four. glass-epoxy laminates ([0,90₃]_s, [90₃,0]_s, [0,90]_s, and [0,±45]_s) were evaluated. Two experimental test sequences were performed. In the first test sequence, longitudinal stiffness was measured at various stages of damage development. Damage development was monitored via edge replication. In the second test sequence, four laminate stiffnesses (E_xx, v_xy, G_xy, and D_yy) were measured in the undamaged and near-saturation damage states. Two analytical models were evaluated. A one dimensional shear lag model was used to predict longitudinal stiffness as a function of crack density for the [0,90₃]_s and 90₃,0]_s laminates. Correlation between theory and experiment was good. A modified laminate analysis was used to predict four laminate stiffnesses (E_xx, v_xy, G_xy, and D_yy). Except for the [0,±45]_s case, a laminate in which significant amounts of damage - s other than transverse cracking were observed, agreement between pre- · dieted and observed stiffness changes was good. / Master of Science

The objective of this study was to investigate the out-of-plane tensile strength of graphite/epoxy laminates as a function of porosity. An experimental test program was designed to apply tension to the faces of circular graphite/epoxy specimens in a direction perpendicular to the laminate mid-plane. The specimens were removed from the webs of angle sections fabricated by Lockheed Georgia Company using (AS4/1806 and AS4/3501-6 graphite/epoxy material systems with a stacking sequence of (±45/90₂/ ±45/0₂)_S or (±45/0₂/ +̅ 45/90₂)_S. The specimen porosities were the result of four distinct processing methods: a baseline hand lay-up, low pressure cure-cycle, a solvent wipe of pre-preg to remove resin, and the addition of water between pre-pregs. The experimental results have shown a significant reduction in the out-of-plane tensile strength as a function of increasing void content. The volume fraction of pores, pore geometry, size, and orientation were determined for a representative number of specimens by metallography and optical analysis methods. This data was combined with the out-of-plane tensile data and used in the theoretical model, prepared by Brown et al, to predict the out-of-plane strength as a function of porosity. The predicted strength values compared very well with the experimental data when the pores were found to be uniformly distributed throughout the laminate. / Master of Science

Dynamic instability in a laminated composite plate is studied using the finite element technique. The governing equations are derived based on the first order shear deformation theory with a linear strain-displacement relationship. The regions of instability for the resulting set of coupled Mathieu equations are obtained using a method of simultaneous diagonalization. Boundary frequencies generated using a first subdeterminant approximation to the infinite determinant are compared with those obtained by using the more accurate second subdeterminant as well as with frequencies from an analytical solution. These values are verified by checking the nature of responses near the boundaries between stability and instability. Results are presented for plates with different laminations, boundary conditions, thicknesses, number of layers, etc. Some unstable regions for a damped plate are also shown. Results from the first order plate theory are compared with those from a higher order shear deformation theory. / Master of Science

The effects of time and stress level were investigated in cross-ply laminates to gain more understanding on the damage events in composites. Analytical predictions of the effect of stress level were performed for the case of linear elastic materials. The predictions were based on energy methods and linear elastic fracture mechanics. Damage was simulated with a Monte Carlo numerical scheme. The predicted results corresponded well with experimental data in the literature. Experimental testing was performed on cross-ply laminates to gain a better understanding of the effect of time and rate on matrix cracking. The tests were performed on Kevlar/epoxy and graphite/epoxy [0/90₃]₈ laminates. The results indicate that the stress levels required for matrix cracking are a function of how fast the specimens were loaded. Also, significant time dependent damage was observed in cross-ply laminates which were subjected to sustained loads. / Master of Science

A higher-order shear deformation theory is used to analyze laminated anisotropic composite plates for deflections, stresses, natural frequencies, and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, satisfies the stress-free boundary conditions on the top and bottom planes of the plate, and, as a result, no shear correction coefficients are required. Even though the displacements vary cubically through the thickness, the theory has the same number of dependent unknowns as that of the first-order shear deformation theory of Whitney and Pagano. Exact solutions for cross-ply and anti-symmetric angle-ply laminated plates with all edges simply-supported are presented. A finite element model is also developed to solve the partial differential equations of the theory. The finite element model is validated by comparing the finite element results with the exact solutions. When compared to the classical plate theory and the first-order shear deformation theory, the present theory, in general, predicts deflections, stresses, natural frequencies, and buckling loads closer to those predicted by the three dimensional elasticity theory. / Master of Science

This study consisted of two main parts, the thermoviscoelastic characterization of Kevlar 49/Fiberite 7714A epoxy composite lamina and the development of a numerical procedure to predict the viscoelastic response of any general laminate constructed from the same material. The four orthotropic material properties, S₁₁, S₁₂, S₂₂, and S₆₆, were characterized by 20 minute static creep tests on unidirectional ([0]₈, [10]₈, and [90]₁₆) lamina specimens. The Time-Temperature-Superposition-Principle (TTSP) was used successfully to accelerate the characterization process. A nonlinear constitutive model was developed to describe the stress dependent viscoelastic response for each of the material properties. A new numerical procedure to predict long term laminate properties from lamina properties (obtained experimentally) was developed. Numerical instabilities and time constraints associated with viscoelastic numerical techniques were discussed and solved. The numerical procedure was incorporated into a user friendly microcomputer program called Viscoelastic Composite Analysis Program (VCAP), which is available for IBM ‘PC’ type computers. The program was designed for ease of use and includes graphics, menus, help messages, etc. The final phase of the study involved testing actual laminates constructed from the characterized material, Kevlar/epoxy, at various temperature and load levels for 4 to 5 weeks. These results were then compared with the VCAP program predictions to verify the testing procedure (i.e., the applicability of TTSP in characterizing composite materials) and to check the numerical procedure used in the program. The actual tests and predictions agreed, within experimental error and scatter, for all test cases which included 1, 2, 3, and 4 fiber direction laminates. The end result of the study was the development and validation of a user friendly microcomputer program that can be used by design engineers in industry to predict thermoviscoelastic properties of orthotropic composite materials. / Ph. D.

In this study, a computational model for accurate analysis of composite laminates and laminates with including delaminated interfaces is developed. An accurate prediction of stress distributions, including interlaminar stresses, is obtained by using the Generalized Laminate Plate Theory of Reddy in which layer-wise linear approximation of the displacements through the thickness is used. Analytical, as well as finite-element solutions of the theory, are developed for bending and vibrations of laminated composite plates for the linear theory. Geometrical nonlinearity, including buckling and post-buckling are included and used to perform stress analysis of laminated plates. A general two-dimensional theory of laminated cylindrical shells is also developed in this study. Geometrical nonlinearity and transverse compressibility are included. Delaminations between layers of composite plates are modeled by jump discontinuity conditions at the interfaces. The theory includes multiple delaminations through the thickness. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational models presented herein are accurate for global behavior and particularly appropriate for the study of local effects. / Ph. D.