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In this study, a progressive failure analysis is used to investigate leakage in internally pressurized non-circular composite cylinders. This type of approach accounts for the localized loss of stiffness when material failure occurs at some location in a structure by degrading the local material elastic properties by a certain factor. The manner in which this degradation of material properties takes place depends on the failure modes, which are determined by the application of a failure criterion. The finite-element code STAGS, which has the capability to perform progressive failure analysis using different degradation schemes and failure criteria, is utilized to analyze laboratory scale, graphite-epoxy, elliptical cylinders with quasi-isotropic, circumferentially-stiff, and axially-stiff material orthotropies. The results are divided into two parts. The first part shows that leakage, which is assumed to develop if there is material failure in every layer at some axial and circumferential location within the cylinder, does not occur without failure of fibers. Moreover before fibers begin to fail, only matrix tensile failures, or matrix cracking, takes place, and at least one layer in all three cylinders studied remain uncracked, preventing the formation of a leakage path. That determination is corroborated by the use of different degradation schemes and various failure criteria. Among the degradation schemes investigated are the degradation of different engineering properties, the use of various degradation factors, the recursive or non-recursive degradation of the engineering properties, and the degradation of material properties using different computational approaches. The failure criteria used in the analysis include the noninteractive maximum stress criterion and the interactive Hashin and Tsai-Wu criteria. The second part of the results shows that leakage occurs due to a combination of matrix tensile and compressive, fiber tensile and compressive, and inplane shear failure modes in all three cylinders. Leakage develops after a relatively low amount of fiber damage, at about the same pressure for three material orthotropies, and at approximately the same location.

This papa briefly discusses the influences of through-thickness thermal expansion, a misaligned ply, and a resin-rich slightly thicker ply on the deformations of a curved composite laminate during cool down from tbc cure temperature. Both two-dimensional and three-dimensional level finite-element analyses are used. The deformations are categorized as to radial and tangential deformations and twist, and for each of the three influences, these deformations are quantified. An additional outcome of the study is an indication of the level of analysis needed to study each of these three influences.

This paper discusses the influences of a misaligned layer, a resin-rich slightly thicker layer, and a small thermal gradient on the thermally-induced deformations of large curved composite panels during cooldown from their cure temperature. The deformations represent warpage of the panels due to anomalies that occur during layup, consolidation, and cure. Two-dimensional finite element analyses are used The deformations are categorized as to their impact on circumferential and twist warpage metrics. The results are intended to highlight the sensitivity of manufactured panel shape to the various unwanted effects that can occur during manufacturing.

As a means of improving structural design, the concept of fabricating flat plates containing holes by incorporating curvilinear fiber trajectories to transmit loads around the hole is studied. In the present discussion this concept is viewed from a structural level, where access holes, windows, doors, and other openings are of significant size. This is opposed to holes sized for mechanical fasteners. Instead of cutting the important load-bearing fibers at the hole edge, as a conventional straightline design does, the curvilinear design preserves the load-bearing fibers by orienting them in smooth trajectories around the holes, their loading not ending abruptly at the hole edge. Though the concept of curvilinear fiber trajectories has been studied before, attempts to manufacture and test such plates have been limited. This report describes a cooperative effort between Cincinnati Milacron Inc., NASA Langley Research Center, and Virginia Polytechnic Institute and State University to design, manufacture, and test plates using the curvilinear fiber trajectory concept. The paper discusses details of the plate design, details of the manufacturing, and a summary of results from testing the plates with inplane compressive buckling loads and tensile loads. Comparisons between the curvilinear and conventional straightline fiber designs based on measurements and observation are made. Failure modes, failure loads, strains, deflections, and other key responses are compared.

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. 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 Nx=P/W(x) and Ny=Nxy=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. 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 percent, in general, and within 15 percent for the worst cases. 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 stackling 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.

A numerical and experimental investigation of the bending behavior of six eight-ply graphite-epoxy circular cylinders is presented. Bending is induced by applying a known end-rotation to each end of the cylinders, analogous to a beam in bending. The cylinders have a nominal radius of 6 inches, a length-to-radius ratio of 2 and 5, and a radius-to-thickness ratio of approximately 160. A (+/- 45/0/90)S quasi-isotropic layup and two orthotropic layups, (+/- 45/0 sub 2)S and (+/- 45/90 sub 2)S, are studied. A geometrically nonlinear special-purpose analysis, based on Donnell's nonlinear shell equations, is developed to study the prebuckling responses and gain insight into the effects of non-ideal boundary conditions and initial geometric imperfections. A geometrically nonlinear finite element analysis is utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the buckling and post buckling responses of both geometrically perfect and imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. Extensive experimental data are obtained from quasi-static tests of the cylinders using a test fixture specifically designed for the present investigation. A description of the test fixture is included. The experimental data are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles. Buckling end-rotations, moments, and strains are reported, and predicted mode shapes are presented. Observed and predicted moment vs. end-rotation relations, deflection patterns, and strain profiles are illustrated for the post buckling responses. It is found that a geometrically nonlinear boundary layer behavior characterizes the prebuckling responses. The boundary layer behavior is sensitive to laminate orthotropy, cylinder geometry, initial geometric imperfections, applied end-rotation, and non-ideal boundary conditions. Buckling end-rotations, strains, and moments are influenced by laminate orthotropy and initial geometric imperfections. Measured buckling results correlate well with predictions for the geometrically imperfect specimens. The postbuckling analyses predict equilibrium paths with a number of scallop-shaped branches that correspond to unique deflection patterns. The observed postbuckling deflection patterns and measured strain profiles show striking similarities to the predictions in some cases. Ultimate failure of the cylinders is attributed to an interlaminar shear failure mode along the nodal lines of the postbuckling deflection patterns.

The influence of crenulated noncircular fibers on the micromechanical stress states due to a transverse strain and to a temperature change in carbon/carbon composites is examined using the finite element method. Stresses at the interface of both fully bonded and fully disbonded fibers having two crenulation amplitudes and with two fiber volume fractions are presented. In each case, these interface stresses are compared to stresses at the interface of circular fibers which have the same degree of disbond and fiber volume fraction and are under the same loading conditions. For the disbonded cases, deformed meshes showing locations of fiber/matrix contact are also included. In addition to the interface stress states, selected composite properties are also computed and compared in each case examined. Interest in studying noncircular fibers stems from a desire to increase the transverse properties of carbon/carbon by introducing a mechanical interlocking between the fiber and the matrix. Results presented here indicate that this interlocking does in fact occur. Evidence from the interface stress data suggests, however, that any possible advantage of this interlocking may be outweighed by the disadvantage of stress concentrations which arise at the interface due to the crenulated geometry of the fibers.

Test results from the compression loading of (+ or - Theta/ - or + Theta)(sub 6s) angle-ply IM7-8551-7a specimens, 0 less than or = Theta less than or = 90 degs, are presented. The observed failure strengths and modes are discussed, and typical stress-strain relations shown. Using classical lamination theory and the maximum stress criterion, an attempt is made to predict failure stress as a function of Theta. This attempt results in poor correlation with test results and thus a more advanced model is used. The model, which is based on a geometrically nonlinear theory, and which was taken from previous work, includes the influence of observed layer waviness. The waviness is described by the wave length and the wave amplitude. The theory is briefly described and results from the theory are correlated with test results. It is shown that by using levels of waviness observed in the specimens, the correlation between predictions and observations is good.

To study the influence on overall deformations of the time-dependent constitutive properties of fiber-reinforced polymeric matrix composite materials being considered for use in orbiting precision segmented reflectors, simple sandwich beam models are developed. The beam models include layers representing the face sheets, the core, and the adhesive bonding of the face sheets to the core. A three-layer model lumps the adhesive layers with the face sheets or core, while a five-layer model considers the adhesive layers explicitly. The deformation response of the three-layer and five-layer sandwich beam models to a midspan point load is studied. This elementary loading leads to a simple analysis, and it is easy to create this loading in the laboratory. Using the correspondence principle of viscoelasticity, the models representing the elastic behavior of the two beams are transformed into time-dependent models. Representative cases of time-dependent material behavior for the facesheet material, the core material, and the adhesive are used to evaluate the influence of these constituents being time-dependent on the deformations of the beam. As an example of the results presented, if it assumed that, as a worst case, the polymer-dominated shear properties of the core behave as a Maxwell fluid such that under constant shear stress the shear strain increases by a factor of 10 in 20 years, then it is shown that the beam deflection increases by a factor of 1.4 during that time. In addition to quantitative conclusions, several assumptions are discussed which simplify the analyses for use with more complicated material models. Finally, it is shown that the simpler three-layer model suffices in many situations.

Discussed are the results of several approaches recently considered for improving the interfacial adhesion of LaRC-TPI/graphite composites. Two approaches were investigated, namely altering the matrix and altering the fiber. As a result, three types of LaRC-TPI laminates were produced: amorphous/AS-4, amorphous/XAS, and semicrystalline/AS-4. The laminates were characterized using the transverse tensile test, scanning electron microscopy, optical microscopy, and thermal analysis.

The postbuckling failure of square composite plates with central holes is analyzed numerically and experimentally. The particular plates studies have stacking sequences of: (+ and - 45/0/90)(sub 2S); (+ and - 45/0(sub 2))(sub 2S); (+ and - 45/0(sub 6))(sub S); and (+ and - 45)(sub 4S). A simple plate geometry, one with a hole diameter to plate width ratio of 0.3 is compared. Failure load, failure mode, and failure location are predicted numerically by using the finite element method. Predictions are compared with experimental results. In numerical failure analysis the interlaminar shear stresses, as well as the inplane stresses are taken into account. An issue addressed in this study is the possible mode shape change of the plate during loading. It is predicted that the first three laminates fail due to excessive stresses in the fiber direction, and more importantly, that the load level is independent of whether the laminate is deformed in a one-half or two-half wave configuration. It is predicted that the fourth laminate fails due to excessive inplane shear stress. Interlaminar shear failure is not predicted for any laminates. For the first two laminates the experimental observations correlated well with the predictions. Experimentally, the third laminate failed along the side support due to interlaminar shear strength S(sub 23). The fourth experimental laminate failed due to inplane shear in the location predicted, however material softening resulted in a different failure load from predictions.

This paper summarizes a study focused on understanding the failure mechanisms present in a plate with a centrally located circular hole loaded inplane into the postbuckling range of deflections. The study was numerical and experimental in nature and had as a goal the a priori prediction of failure using existing failure data from several sources, together with a stress analysis. The maximum stress failure criterion was used to predict failure and both intra- and interlaminar stresses were considered. Four laminates were considered. The phenomenon of modal interaction, or the jumping from one deformed configuration to another, is discussed. With this jumping, the plate configuration may change from one half-wave in the loading direction to two half-waves in the loading direction. The study concludes that the failure in (+/-45/0/90)2s and (+/-45/2(2))2s laminates is due to fiber compression failure and is predictable. The failure load is, for the most part, independent of response configuration. The (+/-45/0/(6))s laminate fails due to interlaminar shear along the simple support, while the response and failure of the (+/-45)4s laminate is governed to a large degree by material nonlinearities and progressive failure.

An alternative powder prepregging technique is discussed that is based on the deposition of powder onto carbon fibers that have been moistened using an ultrasonic humidifier. The dry fiber tow is initially spread to allow a greater amount of the fiber surface to be exposed to the powder, thus ensuring a significant amount of intimate contact between the fiber and the matrix. Moisture in the form of ultrafine water droplets is then deposited onto the spread fiber tow. The moisture promotes adhesion to the fiber until the powder can be tacked to the fibers by melting. Powdered resin is then sieved onto the fibers and then tacked onto the fibers by quick heating in a convective oven. This study focuses on the production of prepregs and laminates made with LaRC-TPI (thermoplastic polyimide) using this process. Although the process appears to be successful, early evaluation was hampered by poor interfacial adhesion. The adhesion problem, however, seems to be the result of a material system incompatibility, rather than being influenced by the process.

Simple sandwich beam models have been developed to study the effect of the time-dependent constitutive properties of fiber-reinforced polymer matrix composites, considered for use in orbiting precision segmented reflectors, on the overall deformations. The 3- and 5-layer beam models include layers representing the face sheets, the core, and the adhesive. The static elastic deformation response of the sandwich beam models to a midspan point load is studied using the principle of stationary potential energy. In addition to quantitative conclusions, several assumptions are discussed which simplify the analysis for the case of more complicated material models. It is shown that the simple three-layer model is sufficient in many situations.

Closed-form linear response solutions are presented for the bending response of thin-walled laminated composite cylinders. Displacements and intralaminar stresses are computed using the Donnell theory, and interlaminar stresses are computed using 3D equilibrium equations of elasticity. Laminates with stacking sequencies and an aluminum cylinder are used to illustrate the displacement response, intralaminar, and interlaminar stresses for two length-to-radius ratios of 1 and 5. Data obtained indicate that if only fiber breakage causes ultimate failure, material failure will occur on the compression side of the cylinders, at the ends, due to fiber compression. The interlaminar normal stress is an order of magnitude smaller than the interlaminar shear stresses and it is not likely to initiate failure.

This paper discusses the thermally-induced geometrically nonlinear response of symmetrically laminated composite plates. The plate response is due to a temperature increase that is uniform in the plane of the plate but has a slight gradient through the thickness. The case of a completely uniform temperature increase but with an initial out-of-plane imperfection in the plate is also considered. Because they are closely allied problems, thermal buckling and postbuckling are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, these responses are investigated for two laminates, a (+/- 45/0/90)s and a (+/- 45/02)s, under two different simple support conditions.

A new numerical procedure for determining load proportioning in multiple-hole mechanical joints in composite plates is presented. The joints are loaded in double lap fashion in tension with pins through the holes. The commercial finite-element program ABAQUS is used to predict the load proportioning among holes using two independent plane stress finite-element models, one representing the composite inner lap and one representing the two steel outer laps, interacting through rigid circular surfaces. The circular surfaces effectively represent rigid pins. Load proportioning is predicted for a number of geometries. Excellent correlation with experimental data is obtained. Experimental and computed surface strains are also found to compare well. The assumption of a radial cosine distribution of contact stress between pin and hole is shown to be substantially in error for some holes.

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a (+/- 45/0/90) and a (+/- 45/02), under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axis not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports deflect more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

This paper discusses an investigation into the thermal 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 temperature change varying linearly along the length of the plate. The effects of the principal material axes not being aligned with the edges of the plate are also investigated. The buckling response is studied using variational methods, specifically the Trefftz criterion. A Rayleigh-Ritz formulation is used to obtain numerical results from the formulations for the prebuckling response and the buckling response.

The gains in buckling performance are explored that can be achieved by deviating from the conventional straightline fiber format and considering the situation whereby the fiber orientation in a layer, or a group of layers, can vary from point to point. The particular situation studied is a simply supported square plate with a centrally located hole loaded in compression. By using both a sensitivity analysis and a gradient-search technique, fiber orientation in a number of regions of the plate are selected so as to increase the buckling load relative to baseline straightline designs. The sensitivity analysis is used to determine which regions of the plate have the most influence on buckling load, and the gradient search is used to find the design that is believed to represent the absolute maximum buckling load for the conditions prescribed. Convergence studies and sensitivity of the final design are discussed. By examining the stress resultant contours, it is shown how the curvilinear fibers move the load away from the unsupported hole region of the plate to the supported edges, thus increasing the buckling capacity. The tensile capacity of the improved buckling design is investigated, and it is shown that both tensile capacity and buckling capacity can be improved with the curvilinear fiber concept.

The potential gain in buckling resistance is explored by using the curvilinear format with a plate containing a centrally located circular hole and subjected to a uniaxial compressive load. The buckling loads for a uniform stress loading and simple support boundary conditions were examined. The method of analysis is outlined for the buckling improvement study. Several designs that represent an improvement over a baseline quasi-isotropic design (a design that is quite good for buckling resistance) are discussed. The tensile load of these designs is examined. A recommended design is presented that not only shows an improved buckling capacity, but also shows improved tensile performance. Follow-on activities are also discussed.

The study focuses on the axisymmetric deformation response of unsymmetrically laminate cylinders loaded in axial compression by known loads. A geometrically nonlinear analysis is used. Though buckling is not studied, the deformations can be considered to be the prebuckling response. Attention is directed at three 16 layer laminates: a (90 sub 8/0 sub 8) sub T; a (0 sub 8/90 sub 8) sub T and a (0/90) sub 4s. The symmetric laminate is used as a basis for comparison, while the two unsymmetric laminates were chosen because they have equal but opposite bending-stretching effects. Particular attention is given to the influence of the thermally-induced preloading deformations that accompany the cool-down of any unsymmetric laminate from the consolidation temperature. Simple support and clamped boundary conditions are considered. It is concluded that: (1) The radial deformations of an unsymmetric laminate are significantly larger than the radial deformations of a symmetric laminate, although for both symmetric and unsymmetric laminates the large deformations are confined to a boundary layer near the ends of the cylinder; (2) For this nonlinear problem the length of the boundary layer is a function of the applied load; (3) The sign of the radial deformations near the supported end of the cylinder depends strongly on the sense (sign) of the laminate asymmetry; (4) For unsymmetric laminates, ignoring the thermally-induced preloading deformations that accompany cool-down results in load-induced deformations that are under predicted; and (5) The support conditions strongly influence the response but the influence of the sense of asymmetry and the influence of the thermally-induced preloading deformations are independent of the support conditions.

The gains in structural efficiency are investigated that can be achieved by aligning the fibers in some or all of the layers in a laminate with the principal stress directions in those layers. The name curvilinear fiber format is given to this idea. The problem studied is a plate with a central circular hole subjected to a uniaxial tensile load. An iteration scheme is used to find the fiber directions at each point in the laminate. Two failure criteria are used to evaluate the tensile load capacity of the plates with a curvilinear format, and for comparison, counterpart plates with a conventional straightline fiber format. The curvilinear designs for improved tensile capacity are then checked for buckling resistance. It is concluded that gains in efficiency can be realized with the curvilinear format.

The gains in buckling performance are explored that can be achieved by deviating from the conventional straightline fiber format and considering the situation whereby the fiber orientation in a layer, or a group of layers, can vary from point to point. The particular situation studied is a simply supported square plate with a centrally located hole loaded in compression. By using both a sensitivity analysis and a gradient-search technique, fiber orientation in a number of regions of the plate are selected so as to increase the buckling load relative to baseline straightline designs. The sensitivity analysis is used to determine which regions of the plate have the most influence on buckling load, and the gradient search is used to find the design that is believed to represent the absolute maximum buckling load for the conditions prescribed. Convergence studies and sensitivity of the final design are discussed. By examining the stress resultant contours, it is shown how the curvilinear fibers move the load away from the unsupported hole region of the plate to the supported edges, thus increasing the buckling capacity. The tensile capacity of the improved buckling design is investigated, and it is shown that both tensile capacity and buckling capacity can be improved with the curvilinear fiber concept.

The influence is investigated of a curvilinear fiber format on load carrying capacity of a layered fiber reinforced plate with a centrally located hole. A curvilinear fiber format is descriptive of layers in a laminate having fibers which are aligned with the principal stress directions in those layers. Laminates of five curvilinear fiber format designs and four straightline fiber format designs are considered. A quasi-isotropic laminate having a straightline fiber format is used to define a baseline design for comparison with the other laminate designs. Four different plate geometries are considered and differentiated by two values of hole diameter/plate width equal to 1/6 and 1/3, and two values of plate length/plate width equal to 2 and 1. With the plates under uniaxial tensile loading on two opposing edges, alignment of fibers in the curvilinear layers with the principal stress directions is determined analytically by an iteration procedure. In-plane tensile load capacity is computed for all of the laminate designs using a finite element analysis method. A maximum strain failure criterion and the Tsai-Wu failure criterion are applied to determine failure loads and failure modes. Resistance to buckling of the laminate designs to uniaxial compressive loading is analyzed using the commercial code Engineering Analysis Language. Results indicate that the curvilinear fiber format laminates have higher in-plane tensile load capacity and comparable buckling resistance relative to the straightline fiber format laminates.