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Natural vibration frequencies of orthotropic and anisotropic simply supported right circular cylinders are predicted using a higher-order transverse-shear deformation theory. A comparison of natural vibration frequencies predicted by first-order transverse-shear deformation theory and the higher-order theory shows that an additional allowance for transverse shear deformation has a negligible effect on the lowest predicted natural vibration frequencies of laminated cylinders but significantly reduces the higher natural vibration frequencies. A parametric study of the effects of ply orientation on the natural vibration frequencies of laminated cylinders indicates that while stacking sequence affects natural vibration frequencies, cylinder geometry is more important in predicting transverse-shear deformation effects. Interaction curves for cylinders subjected to axial compressive loadings and low natural vibration frequencies indicate that transverse shearing effects are less important in predicting low natural vibration frequencies than in predicting axial compressive buckling loads. The effects of anisotropy are more important than the effects of transverse shear deformation for most strongly anisotropic laminated cylinders in predicting natural vibration frequencies. However, transverse-shear deformation effects are important in predicting high natural vibration frequencies of thick-walled laminated cylinders. Neglecting either anisotropic effects or transverse-shear deformation effects leads to non-conservative errors in predicted natural vibration frequencies.
Natural vibration frequencies of orthotropic and anisotropic simply supported right circular cylinders are predicted using a higher-order transverse-shear deformation theory. A comparison of natural vibration frequencies predicted by first-order transverse-shear deformation theory and the higher-order theory shows that an additional allowance for transverse shear deformation has a negligible effect on the lowest predicted natural vibration frequencies of laminated cylinders but significantly reduces the higher natural vibration frequencies. A parametric study of the effects of ply orientation on the natural vibration frequencies of laminated cylinders indicates that while stacking sequence affects natural vibration frequencies, cylinder geometry is more important in predicting transverse-shear deformation effects. Interaction curves for cylinders subjected to axial compressive loadings and low natural vibration frequencies indicate that transverse shearing effects are less important in predicting low natural vibration frequencies than in predicting axial compressive buckling loads. The effects of anisotropy are more important than the effects of transverse shear deformation for most strongly anisotropic laminated cylinders in predicting natural vibration frequencies. However, transverse-shear deformation effects are important in predicting high natural vibration frequencies of thick-walled laminated cylinders. Neglecting either anisotropic effects or transverse-shear deformation effects leads to non-conservative errors in predicted natural vibration frequencies.
The characteristics of thermally induced transverse cracks in T300/5208 graphite-epoxy cross-ply and quasi-isotropic laminates were investigated both experimentally and analytically. The formation of transverse cracks and the subsequent crack spacing present during cool down to -250 F (116K) and thermal cycling between 250 and -250 F (116 and 394K) was investigated. The state of stress in the vicinity of a transverse crack and the influence of transverse cracking on the laminate coefficient of thermal expansion (CTE) was predicted using a generalized plane strain finite element analysis and a modified shear lag analysis. A majority of the cross-ply laminates experienced transverse cracking during the initial cool down to -250 F whereas the quasi-isotropic laminates remained uncracked. The in situ transverse strength of the 90 degree layers was more than 1.9 times greater than the transverse strength of the unidirectional 90 degree material for all laminates investigated.
Propagation of a quasi-neutral plasma beam or cloud across a magnetic field is considered for the case where the transverse dimension of the beam or cloud is sufficiently small compared to ion gyroradii. This situation commonly arises for active experiments in near-earth space. Two mechanisms are presented for transverse deflection of a beam or cloud in the -v0 x B0 direction where v0 is the velocity relative to the ambient medium. In the first, asymmetric escape of ions from an electrically polarized beam or cloud causes transverse deflection by means of a rocket effect. The transverse deflection distance is estimated to be a few times the initial transverse dimension of the beam or cloud. Dissipation occurs within a few times the thermal ion transverse crossing time. In the second mechanism, asymmetric charging results from localized accumulation of incident ions from the ambient medium. This excess positive charge distorts electric equipotentials and drives electron Hall currents that maintain an asymmetric compressed magnetic field region. The asymmetry of the magnetic stress contributes to transverse deflection with the same sign as the rocket effect. The asymmetric magnetic field also focuses incident ions to yield the localized charge accumulation. These ideas are qualitatively consistent with observations of the Active Magnetospheric Particle Tracer Explorers artificial comet releases.
Buckling loads of thick-walled orthotropic and anisotropic simply supported circular cylinders are predicted using a higher-order transverse-shear deformation theory. A comparison of buckling loads predicted by the conventional first-order transverse-shear deformation theory and the higher-order theory show that the additional allowance for transverse shear deformation has a negligible effect on the predicted buckling loads of medium-thick metallic isotropic cylinders. However, the higher-order theory predicts buckling loads which are significantly lower than those predicted by the first-order transverse-shear deformation theory for certain short, thick-walled cylinders which have low through-the-thickness shear moduli. A parametric study of the effects of ply orientation on the buckling load of axially compressed cylinders indicates that laminates containing 45 degree plies are most sensitive to transverse-shear deformation effects. Interaction curves for buckling loads of cylinders subjected to axial compressive and external pressure loadings indicate that buckling loads due to external pressure loadings are as sensitive to transverse-shear deformation effects as buckling loads due to axial compressive loadings. The effects of anisotropy are important over a much wider range of cylinder geometries than the effects of transverse shear deformation.
Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.
A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.
The transverse and longitudinal tensile properties of the oxide dispersion strengthened nickel base alloys MA-793, MA-754, MA-755E, and MA-6000E were determined at 760 C. Transverse tensile strengths were comparable to longitudinal strengths. Transverse ductility levels generally were less than two percent elongation. Both tensile and yield strengths increased with increasing strain rate over the range 0.001 to 0.05 per second. Ductility was not strain rate sensitive, but related to grain size and grain aspect ratio. The fracture mode of most alloys changed from transgranular for longitudinally oriented specimens to intergranular for transverse specimens. Transverse properties of DM MAR M-200 + Hf were also determined for comparison.
Thermally induced transverse cracking in T300/5208 graphite-epoxy cross-ply laminates was investigated experimentally and theoretically. The six laminate configurations studied were: 0/90(3)s, 0(2)/90(2)s, 0(3)/90s, 90/0(3)s, 90(2)/0(2)s, and 90(3)/0s. The thermal load required to initiate transverse cracking was determined experimentally and compared to a theoretical prediction. Experimental results for the accumulation of transverse cracks under cyclic thermal loading between - 250 and 250 F for up to 500 thermal cycles are presented. The calculated in situ transverse-lamina strength was determined to be at least 1.9 times the unidirectional-lamina transverse tensile strength. All laminate configurations exhibited an increase in crack density with increasing thermal cycles.
Buckling loads of thick-walled, orthotropic, simply-supported right circular cylinders are predicted using a new higher-order transverse shear deformation theory. The higher-order theory shows that, by more accurately accounting for transverse shear deformation effects, the predicted buckling load may be reduced by as much as 80 percent compared to predictions based on conventional transverse shear deformation theory. A parametric study of the effect of ply orientation on the buckling load of axially compressed cylinders indicates that laminates containing 0 deg plies are the most sensitive to transverse shear deformation effects. Interaction curves for buckling of cylinders with axial compressive and external pressure loadings indicate that buckling loads due to external pressure loadings are much less sensitive to transverse shear deformation effects than those due to axial compressive loadings.
The natural vibration frequencies of orthotropic and anisotropic, simply supported right circular cylinders are predicted using a theory which takes into account higher-order transverse shear deformation effects. A comparison between results based on first-order transverse shear deformation theory and the higher-order theory indicates that an additional allowance for transverse shear deformation has a negligible effect on the predicted natural vibration frequencies associated with long wavelengths, but significantly reduces the natural vibration frequencies associated with short wavelengths. Results of a parametric study of ply orientation for two classes of laminates indicates that while stacking sequence affects natural vibration frequencies, cylinder geometry and mode shape are more important in accurately predicting transverse shear deformation effects. Transverse shearing effects are less important in predicting natural vibration frequencies associated with long wavelength than in predicting axial compressive buckling loads.
Experimental studies conducted at NASA Lewis on SiC reaction-bonded Si3N4 composite system showed that transverse stiffness and strength were much lower than those predicted from existing analytical models based on good interfacial bonding. It was believed that weakened interfaces were responsible for the decrease in tranverse properties. To support this claim, a two-dimensional FEM analysis was performed for a transverse representative volume element. Specifically, the effect of fiber/matrix displacement compatibility at the interface was studied under both tensile and compressive transverse loadings. Interface debonding was represented using active gap elements connecting the fiber and matrix. The analyses show that the transverse tensile strength and stiffness are best predicted when a debonded interface is assumed for the composite. In fact, the measured properties can be predicted by simply replacing the fibers by voids. Thus, it is found that little or no interfacial bonding exists in the composite, and that an elastic analysis can predict the transverse stiffness and strength.
A study is made of the effect of mesh distortion on the accuracy of transverse shear stresses and their first-order and second-order sensitivity coefficients in multilayered composite panels subjected to mechanical and thermal loads. The panels are discretized by using a two-field degenerate solid element, with the fundamental unknowns consisting of both displacement and strain components, and the displacement components having a linear variation throughout the thickness of the laminate. A two-step computational procedure is used for evaluating the transverse shear stresses. In the first step, the in-plane stresses in the different layers are calculated at the numerical quadrature points for each element. In the second step, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of transverse shear stresses. Numerical results are presented showing no noticeable degradation in the accuracy of the in-plane stresses and their sensitivity coefficients with mesh distortion. However, such degradation is observed for the transverse shear stresses and their sensitivity coefficients. The standard of comparison is taken to be the exact solution of the three-dimensional thermoelasticity equations of the panel.
As composites are introduced into more complex structures with out-of-plane loadings, a better understanding is needed of the out-of-plane, matrix-dominated failure mechanisms. This work investigates the transverse tension fatigue characteristics of IM6/3501 composite materials. To test the 90 degree laminae, a three-point bend test was chosen, potentially minimizing handling and gripping issues associated with tension tests. A finite element analysis was performed of a particular specimen configuration to investigate the influence of specimen size on the stress distribution for a three-point bend test. Static testing of 50 specimens of 9 different sized configurations produced a mean transverse tensile strength of 61.3 Mpa (8.0 ksi). The smallest configuration (10.2 mm wide, Span-to-thickness ratio of 3) consistently exhibited transverse tensile failures. A volume scale effect was difficult to discern due to the large scatter of the data. Static testing of 10 different specimens taken from a second panel produced a mean transverse tensile strength of 82.7 Mpa (12.0 ksi). Weibull parameterization of the data was possible, but due to variability in raw material and/or manufacturing, more replicates are needed for greater confidence. Three-point flex fatigue testing of the smallest configuration was performed on 59 specimens at various levels of the mean static transverse tensile strength using an R ratio of 0.1 and a frequency of 20 Hz. A great deal of scatter was seen in the data. The majority of specimens failed near the center loading roller. To determine whether the scatter in the fatigue data is due to variability in raw material and/or the manufacturing process, additional testing should be performed on panels manufactured from different sources.
The influence of specimen polishing, configuration, and size on the transverse tension strength of two glass-epoxy materials, and one carbon-epoxy material, loaded in three and four point bending was evaluated. Polishing machined edges, arid/or tension side failure surfaces, was detrimental to specimen strength characterization instead of yielding a higher, more accurate, strength as a result of removing inherent manufacture and handling flaws. Transverse tension strength was typically lower for longer span lengths due to the classical weakest link effect. However, strength was less sensitive to volume changes achieved by increasing specimen width. The Weibull scaling law typically over-predicted changes in transverse tension strengths in three point bend tests and under-predicted changes in transverse tension strengths in four point bend tests. Furthermore, the Weibull slope varied with specimen configuration, volume, and sample size. Hence, this scaling law was not adequate for predicting transverse tension strength of heterogeneous, fiber-reinforced, polymer matrix composites.
Multiscale transverse structures in the magnetic-field-aligned flows have been frequently observed in the auroral region by FAST and Freja satellites. A number of multiscale processes, such as broadband low-frequency oscillations and various cross-field transport effects are well correlated with these structures. To study these effects, we have used our three-dimensional multifluid model with multiscale transverse inhomogeneities in the initial velocity profile. Self-consistent-frequency mode driven by local transverse gradients in the generation of the low field-aligned ion flow and associated transport processes were simulated. Effects of particle interaction with the self-consistent time-dependent three-dimensional wave potential have been modeled using a distribution of test particles. For typical polar wind conditions it has been found that even large-scale (approximately 50 - 100 km) transverse inhomogeneities in the flow can generate low-frequency oscillations that lead to significant flow modifications, cross-field particle diffusion, and other transport effects. It has also been shown that even small-amplitude (approximately 10 - 20%) short-scale (approximately 10 km) modulations of the original large-scale flow profile significantly increases low-frequency mode generation and associated cross-field transport, not only at the local spatial scales imposed by the modulations but also on global scales. Note that this wave-induced cross-field transport is not included in any of the global numerical models of the ionosphere, ionosphere-thermosphere, or ionosphere-polar wind. The simulation results indicate that the wave-induced cross-field transport not only affects the ion outflow rates but also leads to a significant broadening of particle phase-space distribution and transverse particle diffusion.
The influence of specimen polishing, specimen configuration, and specimen size on the transverse tension strength of two glass epoxy materials loaded in three and four point bending was evaluated. Polishing machined edges, and/or tension side failure surfaces, was detrimental to specimen strength characterization instead of yielding a higher, more accurate, strength as a result of removing inherent manufacture and handling flaws. Transverse tension strength was sensitive to span length due to the classical weakest link effect. However, strength was less sensitive to volume changes achieved by increasing specimen width. The Weibull scaling law over-predicted changes in transverse tension strengths in three point bend tests and under-predicted changes in transverse tension strengths in four point bend tests. Furthermore, the Weibull slope varied with specimen configuration, volume, and sample size. Hence, the utility of this scaling law for predicting transverse tension strength is unclear.