The feasibility study of subscale notched specimens to determine the shear response of composites is presented. The investigation consists of finite element analyses, conventional strain-gaged testing, and photomechanics experiments. Several notch geometries of the subscale specimens are studied, the standard 900 V -notch, U-notch, and circular notch. The investigation is performed on two different material systems, a standard high performance graphite/epoxy (AS4/3501-6) material and an SMC R-28 material reinforced with 28% volume fraction strand glass fiber. The moduli obtained from the subscale specimens are compared with those obtained from the standard specimens. Different degrees of twisting observed in testing the sub scale specimens are discussed. Numerical and experimental results of the SMC R-28 materials are presented. The dependence of the measured shear modulus on the relative orientation of the specimen in the panel is identified. The application of the subscale, circular notched specimens to obtain the shear modulus of the SMC material is discussed. / 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

Molecular order in surfaces is probed for several different repeat unit Spectroscopy (XPS) is chemistries. X-ray Photoelectron used, particularly with angular dependence, to obtain the compositional gradient information from the top 6 run of the surface. It is found that all materials investigated present some kind of preferential and reproducible ordering effect. The ordering ef feet can be present in different forms, such as preferential segregation of a crystalline block to the surface, segregation of a component of different crystalline structure to the surface or orientation of a backbone segment of the polymer towards the surface of the specimen. Polyethylene terephthalate shows an increasing amount of crystalline cyclic oligomer at the surface as the degree of crystallinity of the matrix increases. Block copolyesters unsaturated blocks present containing saturated and the saturated blocks preferentially segregated toward the surface. Crystalline ethylene/chlorotrifluoroethylene alternating copolymer shows the preferential orientation of ethylene groups closer to the surface. The linear polyurethanes studied reveal the surfaces enriched with soft segments, whereas no enrichment was observed for a crosslinked polyurethane. / 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

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 influence of thickness and hole radius on the fracture strengths of Narmco V 5245C-G40-600 graphite/bismaleimide laminates was studied. Tests were run on 8 ply, 40 ply, and 80 ply quasi-isotropic laminates of stacking sequence [0/ ± 45/90]. Both unnotched and notched laminates were tested. Unnotched strength was found to be inversely proportional to thickness. Notched strengths were compared to three different failure models based on the stress distribution around the hole. Damage development around the holes was studied using x-ray radiography. In general, the small holes created more damage than the large holes and the thin laminates were more susceptible to damage than the thick laminates. All notched specimens exhibited matrix cracking in the 90° plies around the hole and vertical splitting in the 0° plies at the edge of the hole. / Master of Science

This investigation concerns the validity and feasibility of using moduli reduction to monitor the effect of fatigue damage in graphite epoxy composites. Five laminate orientations were considered, [O]₄, [90]₄, [±45]_s, [0,90]_s, [0,90,±45]_s, and four inplane-stiffness properties were monitored for each. The stiffness parameters were E_xx, E_yy, G_xy, and v_xy, and were measured using a longitudinal tension test, a rail shear test and a transverse bend test. Nondestructive testing techniques such as C-scan and edge replication were also performed to aid in the observation of damage development. Results describe the response of each laminate orientation in tension-tension fatigue, including a record of changes in the stiffness properties at intervals during fatigue. Longitudinal stiffness (E_xx) and shear stiffness (G_xy) were shown to significantly decrease for the [0,90,±45]_s, laminate following fatigue loading. The inplane stiffness properties for the other four laminates remain essentially unchanged following fatigue loading. Matrix cracking and delamination appears to contribute to the stiffness reductions that occur in the [0,90,±45]_s laminate. / 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

A simple, computationally efficient analysis approach is developed to predict the buckling of geodesically stiffened composite panels under in-plane loads. This procedure accounts for the discrete flexural contribution of each stiffener through the use of Lagrange multipliers in an energy method solution. An analysis is also implemented for the buckling of simply supported anisotropic rhombic plates. Examples are presented to verify results of the stability analyses and to demonstrate their convergence behavior. Analysis routines are coupled with a versatile numerical optimizer to create a package for the design of minimum-mass stiffened panels, subject to constraints on buckling of the panel assembly, local buckling of the stiffeners, and material strength failure. The design code is used to conduct a preliminary design study of structurally efficient stiffened aircraft wing rib panels. Design variables include thickness of the skin laminate, stiffener thickness, and stiffener height. Applied loads are uniaxial compression, pure shear, and combined compression-shear. Two different geodesically stiffened wing nib configurations with increasing numbers of stiffeners are considered. Results are presented in the form of structural efficiency curves and are compared with those for minimum-weight longitudinally stiffened panels and unstiffened flat plates. Trends in design parameters, including skin thickness and stiffener height, stiffener thickness, stiffener aspect ratio, stiffener load fraction, and stiffener mass fraction, are also examined for the geodesic panels under compression and shear. The effects of skin laminate geometry and anisotropy on the local buckling behavior of cross-stiffened geodesic panels are examined using the rhombic plate analysis. / Master of Science

It is important in structural analysis and design, whether deterministic or reliability-based, to know the level of uncertainty for the methods of strength prediction. The uncertainty associated with strength prediction is the result of ambiguity and vagueness in the system. This study addresses the ambiguity component of uncertainty; this includes uncertainty due to randomness in the basic strength parameters (random uncertainty) and systematic errors and scatter in the prediction of strength (modeling uncertainty). The vagueness component is briefly discussed. A methodology for quantifying modeling and random uncertainty is presented for structural failure modes with a well defined limit state. A methodology is also presented for determining the relative importance of the basic strength parameters in terms of their importance to the total random uncertainty. These methodologies are applied to the compressive failure of longitudinally stiffened panels. The strength prediction model used in this analysis was developed in the UK and is widely used in analysis and design. Several experimental sample sets are used in the analysis. Mean values and coefficients of variation are reported for the random and modeling uncertainties. A comparison with results from other studies with several strength prediction algorithms is undertaken for the modeling uncertainty. All of these studies involve longitudinally stiffened panels which fail in axially compressive collapse. Ranges for the mean and coefficient of variation of the modeling uncertainty are presented. / Master of Science