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This work discusses the deformations of various unsymmetric composite panels due to thermal and mechanical loads. Chapter 2 focuses on the warpage of large unsymmetric curved composite panels due manufacturing anomalies. These panels are subjected to a temperature change of -280°F to simulate the cooling from the autoclave cure temperature. Sixteen layer quasi-isotropic, axial-stiff, and circumferentially-stiff laminates are considered. These panels are intended to be symmetric laminates, but are slightly unsymmetric due to the manufacturing anomalies. Rayleigh-Ritz and finite-element models are developed to predict the deformations. Initially, to serve as a basis for comparison, warpage effects due to orthotropic thermal expansion properties in perfect panels are investigated and are found to produce deformations not captured in two-dimensional theories. This is followed by the investigation of the effects of ply misalignments. Ply misalignments of 5° are incorporated into the laminate, one layer at a time, to produce unsymmetric laminates. It is found that ply misalignments produce warpages much larger than those induced by orthotropic thermal expansion properties. Next, unsymmetric laminates resulting from ply thickness variations are investigated. Layers 10% thicker than nominal are incorporated into the laminate, one layer at a time, while the remaining layers are of uniform thickness. Due to the change in fiber volume fraction of the thicker layers, corresponding material properties are modified to reflect this change. The results show that ply thickness variations cause warpages of about 25-50% of those induced by ply misalignments. Finally, warpage of panels due to nonuniform cooling due to inplane thermal gradients during cure is investigated. A thermal gradient of 0.1°F/in. is used to construct six inplane distributions. It is found that the warpages induced by thermal gradients are very small. The warpages are negligible with respect to those induced by ply thickness variations or ply misalignments. Deformations induced by thermal gradients depend primarily on the magnitude of the thermal gradient, but not on the pattern of distribution. Overall, ply misalignments cause the most warpage, followed by ply thickness variations. Important variables for these imperfections are, the through-thickness location of the imperfections, the orientation of the layer containing the imperfections, and the lamination sequence. All cases show that geometric nonlinearities are important to accurately predict the deformations induced by these imperfections. Chapter 3 discusses the deformations of composite plates that are intentionally fabricated to be unsymmetric. Such plates, if flat, might be considered in applications where bending-stretching coupling effects can be used to advantage. It is assumed the laminates are cured at an elevated temperature and then cooled 280°F. Significant deformations result because of the high level of asymmetry in the laminate construction. Accordingly, geometric nonlinearities are included in the models. Four cross-ply laminates and three angle-ply laminates are considered. Four-term and 14-term Rayleigh-Ritz models are developed, together with finite-element models to model the deformations. Actual specimens were constructed and the deformations measured to compare with predictions. The results show that agreement between predictions and the experimental results are good. The 14-term Rayleigh-Ritz model is found to be the most useful due to its ability to find multiple solutions, its physical basis, and computational efficiency. Chapter 4 discusses the deformations of initially flat aluminum, symmetric, and unsymmetric composite plates due to axial endshortening under various boundary conditions, the aluminum and symmetric plates serving as a baseline. Seven plates are considered, each with three boundary condition combinations, namely, clamped ends and sides (CL-CL), clamped ends with simply-supported sides (CL-SS), and simply-supported ends and sides (SS-SS). Generally, the boundary conditions play a key role in the deformation characteristics of the plates. The aluminum and symmetric cross-ply plates have no out-of-plane deformations until classic buckling, or primary instability, then each exhibits two stable solutions. Each also exhibits secondary instability that results in two stable solutions. The symmetric laminates show less of a dependence on the boundary conditions compared to the unsymmetric laminates. Unsymmetric laminates show a mixture of characteristics. Some cases exhibit primary instability, other cases do not. Some cases exhibit secondary instability, while some case do not. The unsymmetric cross-ply laminates have only one stable solution after secondary buckling, while most other laminates and boundary condition combinations have two stable solutions. It is interesting to note that for the unbalanced unsymmetric [302/90/0]2T laminate, the boundary conditions controlled the sign of the out-of-plane deflection from the onset of axial endshortening. Generally speaking, the CL-CL cases carry the most load, followed by the CL-SS, and then the SS-SS cases. Like all the problems discussed in Chapter 2 and 3, geometric nonlinearities are found to be important for this case as well. / Ph. D.

The thermo-mechanical response of unidirectional P100 graphite fiber/6061 aluminum matrix composites (v_f = 0.47) was investigated at four temperatures: -150°F, +75°F, +250°F and +500°F, using test methods developed at Virginia Tech. Two types of tests, off-axis tension and Iosipescu shear, were used to obtain the desired properties. Good experimental-theoretical correlation was obtained for E_xx, v_xy and G₁₂. It is shown that E₁₁ is temperature independent, but E₂₂, v₁₂ and G₁₂ generally decrease with increasing temperature. Compared with rather high longitudinal strength, very low transverse strength was obtained for the graphite/aluminum. The poor transverse strength is believed to be due to the low interfacial bond strength in this material. The strength decreases significantly with increasing temperature. The tensile response at various temperatures is greatly affected by the residual stresses caused by the mismatch in the coefficients of thermal expansion of fibers and matrix. The degradation of the aluminum matrix properties at higher temperatures has a deleterious effect on composite properties. The composite has a very low coefficient of thermal expansion in the fiber direction. / M.S.

The normal stress ratio theory for crack extension in anisotropic materials is studied analytically and experimentally in order to evaluate its validity. The theory is applied within a macroscopic-level analysis of a single center notch of arbitrary orientation in a unidirectional composite material. The bulk of the analytical work of this study applies an elasticity solution for an infinite plate with a center line crack to obtain critical stress and crack growth direction predictions. An elasticity solution for an infinite plate with a center elliptical flaw is also used to obtain qualitative predictions of the location of crack initiation around the border of an actual rounded notch tip. The analytical portion of the study includes the formulation of a new crack growth theory that includes local shear stress. Predictions of the normal stress ratio theory are obtained for the problems of a unidirectional tensile coupon with a horizontal center notch and a unidirectional losipescu shear specimen with a vertical center notch, each with an arbitrary fiber orientation. These predictions are subsequently compared to experimental results. It is shown that the normal stress ratio theory exhibits a strong ability to correctly predict crack extension direction. Predicted critical stresses correlated well with experimental stresses at crack initiation. Use of the elliptical flaw analysis resulted in significant agreement with observed locations of crack extension, while still providing correct crack extension direction predictions. It is suggested that future analytical studies include application of the normal stress ratio theory as a predictor of critical stresses and its application within a rounded notch tip analysis. Also, future experimental efforts should include performing the critical shear tests identified in this study which could not be performed using the Iosipescu specimen. / M.S.

An exact solution is presented for the large deformation response of a simply supported orthotropic cylindrical panel subjected to a uniform line load along a cylinder generator. The cross section of the cylinder is circular and deformations up to the fully snapped through position are investigated. The orthotropic axes are parallel to the generator and circumferential directions. The governing equations are ·derived using laminated plate theory, nonlinear strain-displacement relations, and applying variational principles. The response is investigated for the case of a panel loaded exactly at midspan and for a panel with the load offset from midspan. The mathematical formulation is one-dimensional in the circumferential coordinate. Solutions are obtained in closed-form. An experimental apparatus was designed to load the panels. Experimental results of displacement controlled tests performed on graphite-epoxy curved panels are compared with analytic predictions. This study demonstrates that panel shallowness, material orthotropy, and stacking sequence can influence the nonlinear static response. Initial geometric imperfections, observed during testing, were found to influence the response of the panels. However, the overall correlation of analytic and experimental results were good. / M.S.

The strength reduction of a graphite-epoxy laminate due to dropping plies is investigated experimentally and analytically. Laminates were tested under uniaxial tension and compression. All the laminates were flat on one side with the plies dropped from the middle of a [( ± 45/0/90)_s (N_d) ( ± 45/0/90)_s]_T laminate, where N_d denotes the number of dropped-plies and their orientations. A total of 54 specimens were tested consisting of eight dropped-ply configurations, or values of N_d. This geometry creates an eccentric load path which causes local bending moments in the region of the ply drop-off. The strength of a laminate with dropped-plies is less than the strength of its thin section, and the compression specimens exhibited a lower strength than a tension specimen of the same configuration and width. For the laminates in this study, the reduction in strength is directly related to the axial stiffness change between the thick and thin sections of the laminate. The three-dimensional state of stress in the laminate was evaluated by the finite element method. The magnitude of the interlaminar stresses at the ply drop-off for N_d = [0₄]_T are greater than for N_d = [90₄]_T . The initial failure event for N_d = [0₄]_T was a delamination between the dropped plies and upper sublaminate at the drop-off. The tensile interlaminar failure criterion predicts this as the critical location in the finite element model as well. However, the tensile interlaminar criterion underestimates the failure initiation load. The cause for this may be due to the inaccuracies in the modeling of the ply drop-off geometry in the finite element analysis. The magnitude of the stresses at the ply drop-off are sensitive to changes in the finite element mesh geometry. The N_d = [90₄]_T laminates were stronger than the N_d = [0₄]_T laminates and the N_d = [90₄]_T laminates failed in the thin section away from the drop-off. / M.S.

An investigation of shear response for various composite material systems is presented. The uniformity of the strain fields is studied experimentally and numerically for different specimen configurations. Conventional strain gage measurements and the moiré interferometry technique are employed to obtain information of actual deformation of the specimen. Based on the contour maps of displacement obtained from moiré tests, the localized hybrid method is used to quantify the magnitude and scale of the nonuniform deformation in the real strain fields. The finite element analysis is also performed for predicting the global nonuniformity of the strain fields. It is shown that the significant nonuniformity in shear deformation observed in experimental results can not be predicted by the existing analytical and numerical models. It is considered that the nonuniformity is primarily at a local level, which is associated with the material inhomogeneity. The implication of the local non-uniform deformation fields on the material property evaluation and failure prediction are discussed. The nonlinearity of shear response is investigated experimentally by performing strain gage and moiré tests. Curve fitting techniques proved to be a convenient and effective tool for characterizing the nonlinear shear response of composites. It is suggested that not only the initial shear modulus but also other coefficients of the fitting function be used for the evaluation of nonlinear shear behavior of a composite. The experimental results show that the nonlinearity has no significant effect on the shear strain distribution, verifying the validity of correction factors in the nonlinear range. Shear stress at a selected shear strain level is suggested as an engineering definition for shear strength of composites. The shear response of some novel composites is also investigated, the test results of which are presented. / Ph. D.

Free-edge effects in composite laminates were studied experimentally. Strains were determined and compared on a ply-by-ply basis for the curved edges of a hole in thick composite panels and along the straight free-edge of the panels. The experimental technique of moire interferometry was extended to take measurements of in-plane deformations on singly-curved surfaces. A replication scheme was developed to produce high-frequency diffraction gratings on singly-curved surfaces. Two different techniques were developed to interrogate specimen gratings on 25.4 mm (1 in.) diameter holes. Eight thick composite laminates from three material systems were tested in uniaxial compression on a screw-driven testing machine. Interlaminar deformations were measured at the straight free-edge on four of the specimens. Strain distributions on the straight free-edge were compared with FEM results for two specimens. Good agreement was obtained for one specimen while poor agreement was obtained for the other. / Ph. D.

A new method of stress analysis which combines an experimental technique — moire interferometry, and a numerical method — finite element analysis, is presented. In this localized hybrid method, the displacement fields which the moire experiments provide in some local regions of interest are used as input data for finite element stress analyses. Two important and controversial problems in the mechanics of composites are investigated using the localized hybrid method. One is a thermally loaded bimetal plate, and the other involves the Iosipescu shear specimen popularly used to determine the shear modulus and strength of a fiber reinforced composite. Before applying the localized hybrid analysis, the mechanics of the problems are discussed individually, through a numerical study and strength of materials analysis. Based on these fundamental studies, the localized hybrid method is applied to stress or strain analyses of moire experimental results, and special techniques of this method are developed to handle these data. For the thermally loaded plate, several finite element models, simulating 2-D and 3-D mechanics, are used to assess the stress state at the interface near the free surface, and identify a boundary layer. It is shown that high gradients and stress turnaround are documented in stress component normal to the interface, along the surface line crossing the interface, and a boundary layer is identified in the small region near the interface around the free surfaces. These observations are also confirmed by the hybrid analysis of moire experimental results. However, additional variations of the localized hybrid method were needed to capture the three-dimensional nature of the problem. A comparison of numerical results with experimental data resolved an apparent anomaly between experiments and mechanics principles. For the Iosipescu shear specimen, the 3-D mechanics associated with twisting is proposed for accounting for the inconsistent and variable results in the literatures. The results form the localized hybrid analysis indicate that uniformity and purity of shear stress state in the test section cannot be accomplished for each fiber orientation specimens; the 0° specimens suffer from a load proximity effect, the 90° specimens are affected by apparent in- and out-plane bending, and the 0°/90° specimens are midway between those. Several variations of the localized hybrid method of stress analysis have been presented for three-dimensional problems in the mechanics of solids. It is showed that the approach developed not only provides a powerful and efficient technique for the reduction of experimental data, but also gives a good insight into the mechanics of the experimental observations. / Ph. D.