The effects of layer waviness on the compression response of T3001P1700 carbon/polysulfone composite laminates were investigated both experimentally and analytically. A three-step procedure was used to fabricate isolated layer waves into the central 0° layer of [90₂,/0₂/90₂/0₂/90₂/0_2w]_S laminates. The influence of various layer wave geometries on the static compression strength and compression fatigue life were determined experimentally. Moire interferometry was used to investigate the disturbance in the displacement fields and the modes of deformation associated with layer waviness under compression loading. The state of stress in the vicinity of the layer waves and the influence of the layer waves on static compression strength were predicted using a planestrain finite element analysis which included material nonlinearity. / Ph. D.

The free vibration and nonlinear transient analysis of imperfect laminated structures with emphasis on computational methods for accurate and efficient analysis are studied. The evaluation of interlaminar stresses is also studied by approximating global displacements of laminated plates. Free vibration response of imperfect laminated structures is studied in the presence of geometric and stress imperfections. The stress imperfections are the initial stresses as caused by preloads. Using a 48 degrees of freedom thin shell element, the effect of complex, arbitrary in-plane and out-of-plane loads on the transverse vibrations of thin arbitrarily laminated plates, cylindrical panels, and hyperbolic shells without and with geometric imperfections is analyzed. The, effects of geometric parameters (aspect ratio and panel curvature) and material properties (varying the number of layers but keeping the same laminate thickness) of imperfect plates are examined. The nonlinear transient response of imperfect structures is next obtained using the direct time integration schemes as applied to the full set of equations and also using reduction methods. Two time integration schemes, the Newmark method and the Wilson () method, are first tested on a series of linear and nonlinear examples without and with geometric imperfections. Reduction methods using the normal modes and Ritz vectors as the base vectors are employed to reduce the size of the nonlinear problem and thus save computational resources. The resulting reduced (but still coupled) set of equations is integrated in a step-by-step fashion using the aforementioned time integration schemes along with an iterative scheme for dynamic equilibrium. Also, the nonlinear dynamic response of imperfect plates subjected to impact loads is studied. The evaluation of the loads (due to a projectile) depends on a contact law which relates contact forces with indentation. The well-known Hertzian law and its previously proposed modification are incorporated. The transient response of an example problem is obtained using both full and reduced equations of motion. Finally, for accurate determination of interlaminar shear and normal stresses of laminated structures, a postprocessor for displacement-based finite element solutions of laminated plates under transverse loads is developed. The postprocessor can be used for the finite element solutions that have been obtained using either the classical laminated plate theory or the first order shear deformation theory. The equilibrium equations of elasticity are integrated directly. These equations include the influence of the products of in-plane stresses for geometrically nonlinear problems. To obtain accurately the derivatives of in-plane stresses the finite element nodal displacement data is first interpolated using polynomials with global support (Le., the interpolating polynomials are defined over the whole domain). Two types of polynomials, Chebyshev and a class of orthogonal polynomials that can be generated for a given location of known data points are used. / Ph. D.

The effect of specimen size on the uniaxial tensile stress/strain response of sublaminatelevel scaled composite specimens, and the four point flexure load/deflection response of ply- and sublaminate-level scaled composite specimens was investigated. Three laminates were studied in the tensile program, namely [+30/-30/90₂]_ns, [+45/-45/0/90}_ns and [90/0/90/0|_ns, where n = 1, 2, 3, 4. Two material systems were used, namely AS4/3502 graphite/epoxy and APC-2 graphite/PEEK, to investigate the relative effect of resin toughness. Three laminates were also studied in the flexure program, The baseline lay-ups were (±45/0/90}_2ns, [0/90/0/90J_2ns and [±45/±45J_2ns, where n = 1, 2, 4. Ply- and sublaminate-level scaling were used to increase specimen thickness. All flexure specimens were of AS4/3502 graphite/epoxy. Enhanced X-ray radiography and edge photomicroscopy were used to examine damage development in specimens loaded to various fractions of their ultimate stress. This nondestructive examination was coupled with observations of critical events in the stress/strain response to try to correlate scaling effects with the damage development in the specimens. Analytical and numerical methods were employed in order to understand the stresses driving certain damage modes observed. 2-D and 3-D finite element models were used to find delamination stresses in an undamaged laminate, and an approximate clasticity approach was used to find stresses duc to cracks in the 90° plies. It was found that the tensile strength of the [+30/-30/90₂]_ns and [+45/-45/0/90}_ns laminates gencrally increased as n increased. This effect was more pronounced for the matrixdominated [+30/-30/90₂]_ns. Both the [+30/-30/90₂]_ns and the quasi-isotropic [+45/-45/0/90}_ns laminates seemed to be approaching a maximum strength, beyond which the strength scaling either stops, or is reversed. As # increased from 1 to 4, these two laminates exhibited a delay in the onset of certain damage mechanisms, such as delamination and transverse matrix cracking. The [90/0/90/0|_ns laminates showed no tensile strcss/strain response scaling effects, although the stress at which first ply failure occurred was found to increase as 7 increased. (±45/0/90}_2ns and [±45/±45J_2ns flexure specimens showed no strength scaling cffects when sublaminate-level scaling was uscd, but significant decreases in s{rength were found when specimen size was increased using ply-level scaling. [0/90/0/90J_2ns specimens showed no global load/deflection scaling effects. / Ph. D.

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined in detail for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. Hole diameters of one, three, and six inches in plates 18 inches long, 12 inches wide, and 0.1 inches thick were considered. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. It was found that the global/local interface should not be placed inside or through any region where the stress field exhibits three-dimensional effects. Interlaminar stress results obtained from the global/local analyses compared well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. The Testbed, which is under continuing development by the Computational Structural Mechanics Group, now the Computational Mechanics Branch, was used throughout this investigation. Specific processors used during the analyses are described in general terms herein. The application of this global/local technique is not limited to this software system, and was developed and described in as general a manner as possible. The methodology developed is thus applicable to other large-scale structural analysis systems. / Master of Science

The present work presents the results of an investigation of properties of polyphenylene sulfide (PPS) reinforced with random, continuous glass fibers, approximately 30% by weight. The investigation included both characterization of the mechanical properties and nondestructive inspection of the material. The objectives of the nondestructive inspection program were twofold: i) to determine nondestructive testing techniques were most responsive to developing damage and ii) to identify the damage modes using the nondestructive testing methods. The mechanical testing program involved the study of three types of specimens: straight sided tensile coupon, dogbone, and streamline. The streamline specimen typically fails in the narrow region and therefore appears to be relatively unaffected by stress concentrations induced by the specimen geometry. Results are given for all three specimen types and comparisons made for the measured mechanical properties. Several nondestructive testing methods, including C-scan, ultrasonic attenuation, acoustic emission, X-ray radiography, and edge replication, were applied to study the damage developed under quasi-static tension loading of this material. The C-scan, edge replication, and X-ray radiography tests were performed both initially and after intermediate stages of loading. These three tests appear to be unresponsive to the developing damage. That is, these techniques were unable to detect any distinctive patterns around the regions of final failure. The most responsive NDT techniques are ultrasonic attenuation and acoustic emission. Both of these methods yield quite distinct changes with increasing load. The acoustic emission tests, for example, show an extremely rapid rise in count rate at loads of about two-thirds of ultimate. The ultrasonic attenuation measurements display maxima and minima when taken in real-time as the specimen is loaded. In an effort to determine the damage mechanisms in the material and to understand the results of the NDE tests, virgin and damaged specimens were destructively examined with the aid of a scanning electron microscope (SEM). The SEM appears to show that the acoustic emission production is corning from cracking of the transverse glass fibers. The results of all tests to date are presented together with recommendations and conclusions for the application of nondestructive test methods to PPS. / Master of Science

The behavior of ARALL (ARamid ALuminum Laminates) subjected to tension-tension cyclic loading was experimentally investigated as a first step towards the understanding of the fatigue damage mechanisms in Arall laminates, and the relationships between damage and stiffness change, remaining strength and life. / Master of Science

Optimization methods are used to find areas of maximum disagreement between the failure criteria of Tsai and Hart-Smith. The Tsai criterion is quadratic in the stresses and employs a selective and progressive ply-by-ply degradation scheme to predict ultimate load. Hart-Smith’s criterion is based on a fiber shear failure of the fibers and also predicts ultimate load. Both compression-compression and tension-shear combinations are identified as areas of large difference in predicted failure loads. Graphite-epoxy specimens are designed to maximize the difference in the failure loads computed from the two criteria under uniaxial tension. Both on-axis and ten-degree off-axis specimens are designed and tested. The laminates that maximize the difference in these criteria exploit the manner in which they treat the effect of in-plane shear on the failure prediction. Test results indicate little difference in the failure prediction for the on-axis test. However, the off-axis tests show that the Tsai criterion predicts failure much closer to the test results. / Master of Science

An analytical/experimental investigation was performed to study the effect of material nonlinearities on the response of composite tubes subjected to combined axial and torsional loading. An elasticity based analytical model was developed to predict stresses and deformations in composite tubes subjected to combined thermomechanical loading. Material nonlinearities were modeled using the Endochronic Theory. The effect of residual stresses on subsequent mechanical response was included in the investigation. Subsequently, experiments were performed on P75/934 graphite/epoxy tubes with a stacking sequence of [15/1/ ± 10/0/-15], using pure torsion and combined axial/torsional loading. The in-plane material properties needed for incorporation into the analytical model were determined using tests on flat coupons made from P75/934. In the presence of residual stresses. the analytical model predicted a reduction in the Initial shear modulus of a tube subjected to torsional loading. Experimentally. a difference in the nonlinearity of the stress-strain response was found between pure torsion loading and combined proportional loading. This difference is due to coupling between axial loading and shear strain. These phenomena were predicted by the nonlinear analytical model where a linear model did not. The experimentally observed linear limit of the global shear response was found to correspond to the analytically predicted first ply failure. The observed nonlinear response thus appears to be due to a combination of material response at the ply level and gradual damage accumulation. Further, based on cyclic torsion tests, the failure of the tubes was found to be path dependent above a certain critical load level. / Master of Science

Analysis of the effects of matrix cracking on composite laminates is a well-known problem which has attracted considerable attention for the past decade. An approximate analytical solution is introduced in this thesis to study this type of problem. The subjects of primary concern are the degradation of effective laminate properties, such as axial stiffness, Poisson's ratio, shear modulus, and coefficient of thermal expansion, as a function of crack density and the axial stress redistribution due to the existence of matrix cracks. Both transverse cracks (2-D problem) and cross (transverse and longitudinal) cracks (3-D problem) are studied. Results for graphite/epoxy cross-ply laminates are presented and compared to those of other approaches. Some other materials, for instance, glass/epoxy, are also studied. The results and comparisons will appear where appropriate. In general, the agreement between the results of the present analysis and those of other approaches, in particular, the finite element method, is good for the lower crack density. The present study shows that Poisson's ratio may be a good indicator of the degree of damage for a cracked laminate. / Master of Science

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