The strength of notched and impact damaged laminates was studied. The solution for a plate containing an elliptic opening and inclusion was used as given by Lekhnitskii. The solution for the infinite plate, combined with laminate analysis to determine the ply stresses, and the average stress criterion proposed by Whitney and Nuismer were used to predict the notched strength. However, unlike Whitney and Nuismer, the average stress criterion was used at the ply level. The strength of off-axis unidirectional laminates was predicted by using a matrix oriented failure criterion applied at a critical point on the boundary of the hole. A good agreement between the experimental and predicted data was obtained. On the other hand, an attempt made to predict the notched strength of angle-ply laminates was not as successful. This is believed to be due to the different failure modes existing among different [± 𝛉]_s laminates. The controversy on whether the characteristic dimension is a material or geometric property, together with the belief that the physics of fracture of composites is better represented at the ply level, have motivated the author to seek an invariant equation which describes the dependence of the characteristic dimension, D₀. A quantitative approach to determine the characteristic dimension in the average stress criterion was proposed. A good agreement between experimental and predicted data was found. It was also found that contrary to prior claims, the value of D₀ does not depend on the diameter of the hole, when used at the ply level. Moreover, the strength of quasi-isotropic laminates loaded at an angle ϕ with respect to the material x-axis was also studied. Again, excellent agreement between experiment and predictions was shown. The tensile strength after impact (TSAI) was investigated. An approach based on modeling the delaminated area as an elliptic inclusion was used. The difference between the compliances of the plate and the inclusion was assumed to be proportional to the ratio of the delaminated areas. At low impact energy, a reference area was used. The results obtained using this approach gave good agreement with the experimental data. / Ph. D.

The relationships between fatigue damage, stress redistribution, and residual stiffness and strength were investigated for notched graphite epoxy laminates during fulIy-reversed cyclic loads. Two material systems, AS4/3501-6 and AS4/1808, two lamination arrangements, (0,45,90,-45)_s₄ and (0,45,0,-45)_s₄, and two notch configurations, central hole and opposing semi-circular edge notches, were used to obtain a fundamental understanding of the fatigue effect in specimens under low and high cycle lifetimes. Damage was evaluated with penetrant-enhanced X-ray radiography and Iaminate deply. Tensile and compressive residual strengths were measured at three stages of damage development. A recently developed nondestructive testing technique, Stress Pattern Analysis by Thermal Emission, was implemented to obtain full-field measurements of surface stresses during damage initiation and growth. A new micromechanical theory of the adiabatic thermoelastic effect in Iaminated fiber composites was conceived to assist the interpretation of SPATE measurements. / Ph. D.

The present work discusses a new moderate rotation theory for anisotropic shells, proposed by Schmidt and Reddy. All aspects of the derivations are explicitly covered and a finite element formulation of the theory is developed for the solution of test cases. Specific forms of the equations for rectangular plates, cylindrical and spherical shells are derived and the respective finite elements are implemented in a computer code. In order to compare the results, two other theories are implemented: a refined von Karman type shell theory and a shell theory proposed by Librescu. A finite element computer code based on a degenerate 2-D shell theory is also used. A set of cases involving anisotropic shells in bending, buckling and postbuckling permit an evaluation of all these models and form a basis for future developments. / Ph. D.

The results of a numerical study of interlaminar stresses within unsymmetrically laminated plates is presented. The focus of the study is upon the linear thermoelastic response of thin square laminated composite plates subjected to extensional, compressive, or thermal loading. Symmetric and unsymmetric 0/90, +45/-45, and 0/+45 laminate stacking sequences are examined to determine the effects of mismatch between adjacent layers in Poisson’s ratio, coefficient of mutual influence, and coefficients of thermal expansion. Since the out-of-plane (transverse) deflections of unsymmetric laminates are typically large, a geometrically nonlinear kinematic description is used to account for the large displacements and rotations. The geometrically nonlinear three-dimensional boundary value problems are formulated from nonlinear elasticity theory and approximate solutions are determined using the finite element method. A total Lagrangian, displacement-based, incremental finite element formulation is implemented using Newton’s method. Geometrically nonlinear global/local finite element analysis is used to obtain improved free edge stress predictions. For laminates subjected to external loading, the mismatch in material properties between adjacent layers causes interlaminar stresses to arise near the free edges. For unsymmetric laminates under external loading, the mismatch in material properties about the geometric midplane causes out-of-plane deflections. For the laminates and loading conditions considered, the results of this study show that the out-of- plane deflections of unsymmetric laminates reduce interlaminar shear stresses. In addition, the out-of-plane deflections reduce interlaminar normal stresses for some laminates and increase these stresses for others. For the two-layer unsymmetric laminates considered, the effect of out-of-plane deflections upon interlaminar normal stress was shown to be dependent upon the type of in-plane strain mismatch (i.e., normal and/or shear) caused by the dissimilar material properties. The results also show that as the out-of-plane deflections become large, the effects of geometric nonlinearity upon this stress-deformational response become important. These conclusions apply to extensional, compressive (prior to a change in mode shape), and thermal loading. The numerical results include interlaminar stresses for laminated plates which have buckled as a wide column under compressive loading. / Ph. D.

In this study, an analytical procedure to predict the strength and failure of laminated composite structures under monotonically increasing static loads is presented. A degenerated 3-D shell finite element that includes linear elastic and plastic material behavior with full geometric nonlinearity is used to determine stresses at selected points (Gauss quadrature points in each element) of the structure. Material stiffness (constitutive) matrices are evaluated at each Gauss point, in each lamina and in each element, and when the computed stress state violates a user selected failure criterion, the material stiffness matrix at the failed Gauss point is reduced. The reduction procedure involves setting the material stiffnesses to unity. Examples of isotropic, orthotropic, anisotropic and composite laminates are presented to illustrate the validity of the procedure developed and to evaluate various failure theories. Maximum stress, modified Hills (Mathers), Tsai-Wu (F₁₂ = 0), and Hashin's failure criteria are included. The results indicate that for large length-to-thickness ratios, the geometric nonlinear effect should be incorporated for both isotropic and anisotropic structures. The nonlinear material model influences the behavior of isotropic structures with small length-to-thickness ratios, while having nearly no effect at all on laminated anisotropic structures. Of the four failure theories compared, each predicts failure at nearly the same load levels and locations. Hashin's criterion is particularly noteworthy in that the mode is also predicted. / Ph. D.

Composite laminates are prone to delamination at free edges, straight edges or at holes, due to the mismatch at interfaces where two adjacent plies have different fiber orientations and/or different material properties. The linear analysis of the mismatch at the edge results in a mathematical singularity. That phenomenon occurs in a boundary layer and has to be treated mathematically and physically as such. In the literature it is called the "Boundary Layer Effect" or simply the "Edge Effect". It is of great importance to recognize and be able to predict delamination locations at edges prone to such events. The goal of this research was to create a model capable of providing such a prediction. In an effort to generalize the model, the more complicated case of a free edge at holes in the composite laminate was chosen rather than the case of a straight free edge. A sequel of three major efforts was completed: 1) Development of the analysis of the free-edge effect at a hole in a composite laminate, 2) Performance of an extensive experimental program to provide data for the creation of the prediction model, and 3) On the basis of the analysis, establishment of the model, and comparison with the experimental results. The prediction model consists of two major products of the analysis, the order of the singularity and the strain energy release rate. Both are useful in locating the interface most prone to delaminate and the point along the hole circumference where it initiates. Two material systems (AS4/3501-6 and AS4/1808) and two stacking sequences [(0/45/0/-45)_s)₄] and [ (0/45/90/-45)_s)₄]s , quasi-orthotropic and quasi-isotropic respectively, were quasi-statically tested under tension and compression. The specimens were X-rayed after each loading stage in order to locate the initiation of delaminations. The fact that both materials consisted of the same type of fibers, was an excellent opportunity to examine the performance of the matrix and its influence on the process of delamination. Matrix dependent behavior was successfully examined and studied through the experiments and the prediction model. Results showed good correlation and high sensitivity to the type of matrix material involved. / Ph. D.

Compressive loads can cause local buckling in composite laminates that have a near-surface delamination. This buckling causes load redistribution and secondary loads, which in turn cause interlaminer stresses and delamination growth. The goal of this research effort was to enhance the understanding of this instability-related delamination growth in laminates containing either an embedded or an edge delamination. There were three primary tasks: 1) development of a geometrically nonlinear finite element analysis named NONLIN3D; 2) performance of a parametric analytical study to determine the effects of strain, delamination shape, and delamination size on the distribution of the strain energy release rate components along the delamination front; and 3) performance of a combined experimental and analytical study of instability-related delamination growth (IRDG). Two material systems (AS4/PEEK and IM7/8551-7) and two stacking sequences (0/90/90/0)₆ and (90/0/0/90)₆ were examined. The laminates were fabricated with Kapton inserts between the fourth and fifth plies from the top surface to give an initial delamination. The analysis predicted a large variation of G_I and G_II along the delamination front. The G_III component was always small. The location of maximum G_I and G_II depended on the delamination shape and applied strain. In general, the strain-energy release rates were small except in a small region. Hence, delamination growth was expected to occur over only a small portion of the delamination front. Experiments corroborated this prediction. The laminate stacking sequence had a large effect on the shape of the deformed region, the direction of delamination growth, and the strain at which delamination growth occurred. These effects were predicted by the analysis. The G_I component appeared to govern initial delamination growth in the IM7/8551-7 laminates. Matrix ply cracking generally accompanied delamination growth. In some cases fiber micro-buckling also occurred shortly after delamination growth occurred. / Ph. D.

Low frequency Lamb waves in composite laminates were investigated theoretically and experimentally. To have a general solution for Lamb wave propagation in multilayered composite laminates is not practical due to a large number of boundary conditions needed to be satisfied at the interlaminar interfaces. Various approximate theories have been proposed to model low frequency Lamb wave propagation in composite laminates. In the present study, an approximate solution was derived from an elementary shear deformation plate theory and was shown to work well in the low frequency, long wavelength region. A simple method, similar in configuration to the acousto-ultrasonic technique, was used to measure Lamb wave phase velocities. Low frequency Lamb waves, usually in the range of 10 kHz to 1 MHz, were generated. Dispersion curves of the lowest symmetric Lamb mode and the lowest antisymmetric Lamb mode were obtained. The experimental data were compared with the results obtained from the approximate solution for the lowest Lamb modes in the low frequency, long wavelength region for a unidirectional laminate, a symmetric cross-ply laminate, a symmetric quasi-isotropic laminate and an aluminum plate. There is good correlation between the data and the results obtained from the approximate solution, which suggests that the lowest Lamb modes are modeled adequately by the present theory in these cases. This experimental procedure of measuring phase velocities can be used to characterize laminated composite plates with and without damage since each material and stacking sequence gives distinct lowest symmetric and antisymmetric curves. Stiffness reduction of composite laminates caused by damage can be related to the change in Lamb wave propagation speed. Damage in the form of transverse cracks in the 90° plies of a [90/90/90/0], graphite/epoxy laminate reduced the phase velocities of the Lamb modes. The lowest antisymmetric mode is sensitive to stiffness reduction in composite plates. Consequently, axial stiffness reduction in [0/45/0/45/0/45], and [0]₁₂ woven graphite/polyimide composite laminates was monitored by the lowest antisymmetric Lamb mode. / Ph. D.

In this work, a finite element formulation and associated computer program is developed for the transient large deformation analysis of laminated composite plate/shell structures. In order to satisfy the plate/shell surface traction boundary conditions and to have accurate stress description while maintaining the low cost of the analysis, a newly assumed displacement field theory is formulated by adding higher-order terms to the transverse displacement component of the first-order shear deformation theory. The laminated shell theory is formulated using the Updated Lagrangian description of a general continuum-based theory with assumptions on thickness deformation. The transverse deflection is approximated through the thickness by a quartic polynomial of the thickness coordinate. As a result both the plate/shell surface tractions (including nonzero tangential tractions and nonzero normal pressure) and the interlaminar shear stress continuity conditions at interfaces are satisfied simultaneously. Furthermore, the rotational degree of freedoms become layer dependent quantities and the laminate possesses a transverse deformation capability (i.e. the normal strain is no longer zero). Analytical integration through the thickness direction is performed for both the linear analysis and the nonlinear analysis. Resultants of the stress integrations are expressed in terms of the laminate stacking sequence. Consequently, the laminate characteristics in the normal direction can be evaluated precisely and the cost of the overall analysis is reduced. The standard Newmark method and the modified Newton Raphson method are used for the solution of the nonlinear dynamic equilibrium equations. Finally, a variety of numerical examples are presented to demonstrate the validity and efficiency of the finite element program developed herein. / Ph. D.

This paper discusses an investigation into thermal buckling and post-buckling of symmetrically laminated composite plates. In this study, thermal buckling is investigated for laminates under two different simple support conditions, fixed and sliding. These laminates are subjected to the conditions of a uniform temperature change and a linearly varying temperature change along the length of the plate. Postbuckling in the presence of a uniform temperature change and nonlinear response to imperfections in the form of a thermal gradient through the thickness of the plate and a lack of initial flatness are also studied. The buckling response is studied using variational methods, specifically the Trefftz criterion. Postbuckling and responses to imperfections are studied using nonlinear equilibrium conditions. A Rayleigh-Ritz formulation is used to obtain numerical results from the formulations for the prebuckling response, the buckling response, and the post-buckling and imperfection responses. The analyses are applied to graphite-reinforced materials with (± 45/0₂)_s and (± 45/0/90)_s lamination sequences. Numerical results are obtained for these laminates and also for the case of these laminates being rotated 30° inplane. For the first laminate, for example, such a rotation results in a (+75/ — 15/30₂)_s. stacking sequence. Such skewing of the principal material directions may be encountered when using fiber-reinforced materials in a structurally tailored design. In addition, the influence on thermal buckling of a lack of ideal boundary conditions in the form of boundary compliance and thermal expansion, which would occur in any real set-up, are investigated. / Master of Science