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At least 127 records · Page 7

Fatigue life prediction in bending from axial fatigue information

Bending fatigue in the low cyclic life range differs from axial fatigue due to the plastic flow which alters the linear stress-strain relation normally used to determine the nominal stresses. An approach is presented to take into account the plastic flow in calculating nominal bending stress (S sub bending) based on true surface stress. These functions are derived in closed form for rectangular and circular cross sections. The nominal bending stress and the axial fatigue stress are plotted as a function of life (N sub S) and these curves are shown for several materials of engineering interest.

Manson, S. S.↗

Buckling of unstiffened and ring stiffened cylindrical shells under axial compression.

Bifurcation stresses and initial postbuckling behavior of both unstiffened and outside ring stiffened circular cylindrical shells under axial compression are analyzed. The shells are assumed to have axisymmetric sinusoidal imperfections with arbitrary wavelengths and amplitudes. It is found that for large imperfection amplitudes and wavelengths both the unstiffened and the stiffened shells have extremely small bifurcation loads. The postbuckling analysis shows that for small imperfection amplitudes the bifurcations from the axisymmetric state are initially unstable and collapse is associated with the bifurcation points. However, for larger values of the imperfection amplitudes the bifurcations are stable. For unstiffened shells the transition from unstable to stable bifurcations can take place at very small values of the load. On the other hand, for stiffened shells it is found that bifurcations at load levels less than about 40% of the classical buckling load have stable initial postbuckling behavior.

Pedersen, P. T.↗

Axial Fatigue Tests at Zero Mean Stress of 24S-T and 75S-T Aluminum-alloy Strips with a Central Circular Hole

Axial fatigue tests at zero mean stress have been made on 0.032- and 0.064-inch 24S-T and 0.032-inch 75S-T sheet-metal specimens 1/4, 1/2, 1, and 2 inches wide without a hole and with central holes giving a range of hole diameter D to specimen width W from 0.01 to 0.95. No systematic difference was noted between the results for the 0.032-inch and the 0.064-inch specimens although the latter seemed the more consistent. In general the fatigue strength based on the minimum section dropped sharply as the ration D/W was increased from zero to about 0.25. The plain specimens showed quite a pronounced decrease in fatigue strength with increasing width. The holed specimens showed only slight and rather inconclusive evidence of this size effect. The fatigue stress-concentration factor was higher for 75S-T than for 24S-T alloy. Evidence was found that a very small hole would not cause any reduction in fatigue strength.

ALUMINUM ALLOYS-STRESSES↗

Critical stress of thin-walled cylinders in axial compression

Empirical design curves are presented for the critical stress of thin-walled cylinders loaded in axial compression. These curves are plotted in terms of nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75. The test data obtained from various sources follow the general trend of the theoretical curve for cylinders with clamped edges, agreeing closely with the theory in the case of short cylinders, but falling considerably below the theoretical results for long cylinders. The discrepancy in the case of long cylinders increases with increasing values of the ratio of radius to wall thickness. Plotting curves for different values of this ratio reduces the scatter in the test data and a certain degree of correlation with theory is achieved. Advantage is taken of this correlation to obtain estimated design curves for cylinders with simply supported edges, for which little experimental information is available. (author)

Batdorf, S B↗

Critical stress of thin-walled cylinders in axial compression

Empirical design curves are presented for the critical stress of thin-wall cylinders loaded in axial compression. These curves are plotted in terms of the nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75.

Batdorf, S B↗

Transfer matrix approach to layered systems with axial symmetry

The stress and displacement distribution in a layered medium is found by means of transfer matrices. The surface loading exhibits axial symmetry, and each layer is of infinite extent in the horizontal direction, of constant depth, and is considered to be linearly elastic, homogeneous, and isotropic. The method developed has the built-in advantage of enforcing interface continuity conditions automatically. Its application to layered composites shows the flexibility with which it predicts the local as well as the global response of the medium.

Bahar, L. Y.↗

Approximations for column effect in airplane wing spars

The significance attaching to "column effect" in airplane wing spars has been increasingly realized with the passage of time, but exact computations of the corrections to bending moment curves resulting from the existence of end loads are frequently omitted because of the additional labor involved in an analysis by rigorously correct methods. The present report represents an attempt to provide for approximate column effect corrections that can be graphically or otherwise expressed so as to be applied with a minimum of labor. Curves are plotted giving approximate values of the correction factors for single and two bay trusses of varying proportions and with various relationships between axial and lateral loads. It is further shown from an analysis of those curves that rough but useful approximations can be obtained from Perry's formula for corrected bending moment, with the assumed distance between points of inflection arbitrarily modified in accordance with rules given in the report. The discussion of general rules of variation of bending stress with axial load is accompanied by a study of the best distribution of the points of support along a spar for various conditions of loading.

Warner, Edward P↗

Axial Fatigue Tests at Zero Mean Stress of 24S-T Aluminum-alloy Sheet with and Without a Circular Hole

Axial fatigue tests were made on 189 coupon specimens of 0.032-inch 24S-T aluminum-alloy sheet and a few supplementary specimens of 0.004-inch sheet. The mean load was zero. The specimens were restrained against lateral buckling by lubricated solid guides described in a previous report on this project. About two-thirds of the 0.032-inch specimens were plain coupons nominally free from stress raisers. The remainder contained a 0.1285-inch drilled hole at the center where the reduced section was 0.5 inch wide. S-N diagrams were obtained for cycles to failure between about 1000 and 10 to the 7th power cycles for the plain specimens and 17 and 10 to the 7th power cycles for the drilled specimens. The fatigue stress concentration factor increased from about 1.08 for a stress amplitude causing failure at 0.25 cycles (static) to a maximum of 1.83 at 15,000 cycles and then decreased gradually. The graph for the drilled specimens showed less scatter than that for the plain specimens.

TESTING MACHINES, FATIGUE↗

Experimental Techniques Verified for Determining Yield and Flow Surfaces

Structural components in aircraft engines are subjected to multiaxial loads when in service. For such components, life prediction methodologies are dependent on the accuracy of the constitutive models that determine the elastic and inelastic portions of a loading cycle. A threshold surface (such as a yield surface) is customarily used to differentiate between reversible and irreversible flow. For elastoplastic materials, a yield surface can be used to delimit the elastic region in a given stress space. The concept of a yield surface is central to the mathematical formulation of a classical plasticity theory, but at elevated temperatures, material response can be highly time dependent. Thus, viscoplastic theories have been developed to account for this time dependency. Since the key to many of these theories is experimental validation, the objective of this work (refs. 1 and 2) at the NASA Lewis Research Center was to verify that current laboratory techniques and equipment are sufficient to determine flow surfaces at elevated temperatures. By probing many times in the axial-torsional stress space, we could define the yield and flow surfaces. A small offset definition of yield (10 me) was used to delineate the boundary between reversible and irreversible behavior so that the material state remained essentially unchanged and multiple probes could be done on the same specimen. The strain was measured with an off-the-shelf multiaxial extensometer that could measure the axial and torsional strains over a wide range of temperatures. The accuracy and resolution of this extensometer was verified by comparing its data with strain gauge data at room temperature. The extensometer was found to have sufficient resolution for these experiments. In addition, the amount of crosstalk (i.e., the accumulation of apparent strain in one direction when strain in the other direction is applied) was found to be negligible. Tubular specimens were induction heated to determine the flow surfaces at elevated temperatures. The heating system induced a large amount of noise in the data. By reducing thermal fluctuations and using appropriate data averaging schemes, we could render the noise inconsequential. Thus, accurate and reproducible flow surfaces (see the figure) could be obtained.

Lerch, Brad A.↗

Thrust measurement in a 2-D scramjet nozzle

The two-dimensional thrust nozzle presents a challenging problem. The loading is not axisymmetric as in the case of a cone and the internal flow presents some design difficulties. A two-sting system has been chosen to accomodate the internal flow and achieve some symmetry. The situation is complicated by the fact that with the small ramp angle and the internal pressure on the nozzle walls, loading is predominantly transverse. Yet it is the axial thrust which is to be measured (i.e., the tensile waves propagating in the stings). Although bending stress waves travel at most at only 60% of the speed of the axial stress waves, the system needs to be stiffened against bending. The second sting was originally only used to preserve symmetry. However, the pressures on each thrust surface may be quite different at some conditions, so at this stage the signals from both stings are being averaged as a first order approximation of the net thrust. The expected axial thrust from this nozzle is not large so thin stings are required. In addition, the contact area between nozzle and sting needs to be maximized. The result was that it was decided to twist the stings through 90 deg, without distorting their cross-sectional shape, just aft of the nozzle. Finite element analysis showed that this would not significantly alter the propagation of the axial stress wave in the sting, while the rigidity of the system is greatly increased. A Mach 4 contoured nozzle is used in the experiments. The thrust calculated by integrating the static pressure measurements on the thrust surfaces is compared with the deconvolved strain measurement of the net thrust for the cases of air only and hydrogen fuel injected into air at approximately 9 MJ/kg nozzle supply enthalpy. The gain in thrust due to combustion is visible in this result.

Tuttle, Sean↗

Stability optimization of laminated composite plates

The optimum design of plates with orthotropic layers under axial compression and shear is discussed. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of + alpha sub i and - alpha sub i with respect to the plate axis. The fiber directions which give the highest axial buckling stress and the highest shear buckling stress are found by utilizing a mathematical optimization technique for various aspect ratios of the plates. Inhomogeneity in the direction of the plate thickness (stacking sequence) is taken into account in this analysis.

Hirano, Y.↗

Design, Fabrication and Test of Composite Curved Frames for Helicopter Fuselage Structure

Aspects of curved beam effects and their importance in designing composite frame structures are discussed. The curved beam effect induces radial flange loadings which in turn causes flange curling. This curling increases the axial flange stresses and induces transverse bending. These effects are more important in composite structures due to their general inability to redistribute stresses by general yielding, such as in metal structures. A detailed finite element analysis was conducted and used in the design of composite curved frame specimens. Five specimens were statically tested and compared with predicted and test strains. The curved frame effects must be accurately accounted for to avoid premature fracture; finite element methods can accurately predict most of the stresses and no elastic relief from curved beam effects occurred in the composite frames tested. Finite element studies are presented for comparative curved beam effects on composite and metal frames.

Lowry, D. W.↗

Mean-flow measurements in a supersonic three-dimensional turbulent boundary layer

Measurements are presented of the mean flow in a supersonic turbulent boundary layer subjected to a constant weak transverse pressure gradient. The temperature and longitudinal velocity and the axial shear stress were only slightly affected by the three-dimensionality but a clearly defined crossflow component appeared, in the manner suggested by theory and confirmed in earlier experiments. The flow deflection angle and transverse-velocity component achieved a self-preserving form so long as the transverse-pressure gradient remained constant, and both achieved a maximum at the sublayer edge; the deflection angle seemed to decrease again between the latter and the surface. An empirical relation was found between the pressure-gradient strength and the maximum in the crossflow, and the dependence of the latter on distance from the surface was used to test analytical crossflow predictions. The data are in general agreement with Van Den Berg's law of the wall. The data also support the so-called parabolic law following a relaxation distance, especially if inviscid gradients are accounted for, and if the normal coordinate is contracted by the compressibility transformation.

Demetriades, A.↗

Instability of capillary jets with thermocapillarity

Long axisymmetric liquid zones are subject to axial temperature gradients which induce steady viscous flows driven by thermocapillarity. The approximately parallel flow in a cylindrical zone is examined for linearized instabilities. Capillary, surface-wave and thermal modes are found. Capillary breakup can be retarded or even suppressed for small Prandtl number and large Biot number B, which measures heat transfer from the liquid to the surrounding atmosphere. In the limiting case B approaches infinity the zone becomes an isothermal jet subject to axial 'wind stress' on its interface. It is then possible to suppress capillary breakup entirely so that one can maintain long coherent jets.

Xu, J.-J.↗