Effects of Airplane Flexibility on Wing Strains in Rough Air at 5,000 Feet as Determined by Flight Tests of a Large Swept-wing Airplane
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We present a simple picture to calculate the bandgap ($E_g$) of carbon nanotubes (CNT) in the presence of uniform torsional and tensile strain ($\sigma$). We find that under tensile strain, $ absolute value of dE_g/d\sigma$ of zig-zag tubes is approximately equal to $3t_0$, where $t_0$ is the hopping parameter. Further, $ absolute value of dE_g/d\sigma$ decreases as the chirality changes to armchair, where it takes the value zero. The sign of $dE_g/d\sigma$ follows the $(N_x-N_y) *mod 3$(equal to - 1, 0 and +1) rule. In contrast to the above, we show that under torsional strain, $absolute value of dE_g/d\sigma$ of armchair tubes is approximately equal to $3t_0$ and continually decreases as the chirality changes to zig-zag, where is takes a small value. The sign of $dE_g/d\sigma$ again follows the $(N_x-N_y)*mod 3$ rule. Finally, we predict a change in the sign of $dE_g/d\sigma$ as function of strain, corresponding to a change in the value of $q$ that corresponds to the bandgap minimum.
In order to minimize boil off of the liquid oxygen and liquid hydrogen and to prevent the formation of ice on its exterior surface, the Space Shuttle External Tank (ET) is insulated using various low-density, closed-cell polymeric foams. Improved analysis methods for these foam materials are needed to predict the foam structural response and to help identify the foam fracture behavior in order to help minimize foam shedding occurrences. This presentation describes a continuum based approach to modeling the foam thermo-mechanical behavior that accounts for the cellular nature of the material and explicitly addresses the effect of the internal cell gas pressure. A porous media approach is implemented in a finite element frame work to model the mechanical behavior of the closed cell foam. The ABAQUS general purpose finite element program is used to simulate the continuum behavior of the foam. The soil mechanics element is implemented to account for the cell internal pressure and its effect on the stress and strain fields. The pressure variation inside the closed cells is calculated using the ideal gas laws. The soil mechanics element is compatible with an orthotropic materials model to capture the different behavior between the rise and in-plane directions of the foam. The porous media approach is applied to model the foam thermal strain and calculate the foam effective coefficient of thermal expansion. The calculated foam coefficients of thermal expansion were able to simulate the measured thermal strain during heat up from cryogenic temperature to room temperature in vacuum. The porous media approach was applied to an insulated substrate with one inch foam and compared to a simple elastic solution without pore pressure. The porous media approach is also applied to model the foam mechanical behavior during subscale laboratory experiments. In this test, a foam layer sprayed on a metal substrate is subjected to a temperature variation while the metal substrate is stretched to simulate the structural response of the tank during operation. The thermal expansion mismatch between the foam and the metal substrate and the thermal gradient in the foam layer causes high tensile stresses near the metal/foam interface that can lead to delamination.
An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites with a plain weave fiber architecture. In the developed model, the differences in the tension and compression response have also been considered. State variable based viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear stiffness is independent of the stiffness in the normal directions. The developed equations have been implemented into a commercially available transient dynamic finite element code, LS-DYNA, through the use of user defined subroutines (UMATs). The tensile, compressive, and shear deformation of a representative plain weave woven ceramic matrix composite are computed and compared to experimental results. The computed values correlate well to the experimental data, demonstrating the ability of the model to accurately compute the deformation response of woven ceramic matrix composites.
An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites, such as the Reinforced Carbon Carbon (RCC) material used on the leading edges of the Space Shuttle. In the developed model, the differences in the tension and compression deformation behaviors have also been accounted for. State variable viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear response is independent of the stiffness in the normal directions. The developed equations have been implemented into LS-DYNA through the use of user defined subroutines (UMATs). Several sample qualitative calculations have been conducted, which demonstrate the ability of the model to qualitatively capture the features of the deformation response present in woven ceramic matrix composites.
Inclination effect of fatigue cracks on plane strain fracture toughness of 7075-T651 Al alloy, discussing cantilever bending
Temperature effects on electrical resistivity of metallic strain gage materials
This paper describes two new additions to the CompDam fiber kinking model: 1) a failure index for fiber kinking to facilitate interaction between kinking and matrix cracking and 2) a strain-based criterion for fiber rupture to account for fiber breakage before or after fiber kinking. The model formulation is described with the aid of the graphical Considère construction, which is used to determine the conditions for fiber kinking. Verification studies are conducted with single element models to show the behavior of the model in light of the new developments and to evaluate the effect of numerical parameters of the model. The model is used to analyze open hole compression (OHC) specimens with soft, quasi-isotropic, and hard layups. Analysis results are shown for a conventional continuum damage mechanics model using a trilinear constitutive law for fiber damage and for the proposed model to highlight the differences between the two. Comparison with test data highlights the capabilities and remaining gaps in the quantitative prediction of the damage and failure response. While both models can predict many features of the OHC response, accurate prediction of kinking onset in the OHC specimens remains elusive. The results suggest that it is necessary to predict the combined effects of compression and shear loading as well as the structural effects (e.g., ply thickness, strain gradient effect) accurately to match the experimental observations of fiber kinking onset in the three OHC laminates.
Brittle behavior of large mild steel elements, glass plasticity, and fatigue specimen size sensitivity are manifestations of strain-energy size effect. Specimens physical size effect on material cracking initiation occurs according to flaw distribution statistics. Fracture size effect depends on stability or instability of crack propagation.
An experimental study was conducted to determine the effects of ply thickness in composite laminates on thermally induced cracking and changes in the coefficient of thermal expansion, CTE. A graphite-epoxy composite material, P75/ERL 1962, in thin (1 mil) and thick (5 mils) prepregs was used to make cross-ply laminates, ((0/90)(sub n))s, with equal total thickness (n=2, n=10) and cross-ply laminates with the same total number of plies (n=2). Specimens of each laminate configuration were cycled up to 1500 times between -250 and 250 F. Thermally induced microdamage was assessed as a function of the number of cycles as was the change in CTE. The results showed that laminates fabricated with thin-plies microcracked at significantly different rates and reached significantly different equilibrium crack densities than the laminate fabricated with thick-ply and n=2. The CTE of thin-ply laminates was less affected by thermal cycling and damage than the CTE of thick-ply laminates. These differences are attributed primarily to differences in interply constraints. Observed effects of ply thickness on crack density was qualitatively predicted by a combined shear-lag stress/energy method.
Experimental results are reported for torsional fatigue specimens of high-strength steel 4370 and tensile bars of mild steel A-106 which present evidence of a hydrogen-induced strain-aided hardening effect. These results are consistent with the postulate that hydrogen suppresses ductile processes required for crack initiation at large plastic strains.
Specimen design effects on Al and Ti alloy plane strain fracture toughness at room and cryogenic temperatures, discussing crack propagation and rolling directions orientations
A semianalytical method was developed for determining elastoplastic cyclic stresses and strains at notch roots in metallurgically bonded metal laminates. The method is based on the Neuber equation, which was used with an effective stress-strain curve for the laminate. It was applied to laminates containing a circular hole which were subjected to one cycle of reversed loading. The laminates consisted of two elasto-perfectly-plastic materials with different yield strengths and with either equal or different Young's moduli. A laminate of high-strength titanium alloy with alternate layers of commercially pure titanium was also analyzed. The accuracy of the method was evaluated by comparing the stresses and strains with those calculated from a finite-element analysis. The results estimated by the simple method based on the Neuber equation agreed closely with the results computed from the more elaborate finite-element analysis.
A series of experiments were performed to study the effect of creep strain and temperature on the fatigue life of the graphite epoxy laminate composite. It was concluded that sustained periods of static loading have significant retardation effects on the fatigue life of the laminated composite and that a cyclic loading with a higher frequency preceeding the one with a lower frequency also prolongs the fatigue life. A creep crack model was proposed which can provide interpretations for the experimental results.
Short time creep and creep recovery were investigated by means of the endochronic theory of viscoplasticity. It is shown that the constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation can all ber derived from the general constitutive equation by imposing appropriate constraints. In this unified approach, the effect of strain-hardening is naturally accounted for when describing creep and creep recovery. The theory predicts with reasonable accuracy the creep and creep recovery behaviors for Aluminum 1100-0 at 150 C. It was found that the strain-rate history at prestraining stage affects the subsequent creep. A critical stress was also established for creep recovery. The theory predicts a forward creep for creep recovery stress greater than the critical stress. For creep recovery stress less than the critical stress, the theory then predicts a normal strain recovery.
Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra L = (β g 0 L 3 ∆T)/(𝑎v)) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.
An experimental investigation of the compression behavior of laminated specimens made from graphite-epoxy tape, graphite-thermoplastic tape and graphite-thermoplastic fabric was conducted. Specimens with five different stacking sequences were loaded to failure in uniaxial compression. Some of the specimens had central circular holes with diameters up to 65 percent of the specimen width. Other specimens were subjected to low speed impact with impact energies up to 35 J prior to compressive loading. This investigation indicates that graphite-thermoplastic specimens with holes have up to 15 percent lower failure stresses and strains than graphite-epoxy specimens with the same stacking sequence and hole size. However, graphite-thermoplastic specimens subjected to low speed impact have up to 15 percent higher failure stresses and strains than graphite-epoxy specimens with the same stacking sequence and impact energy. Compression tests of graphite-thermoplastic specimens constructed of unidirectional tape and fabric indicate that the material form has little effect on failure strains in specimens with holes or low speed impact damage.