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Review of the underlying fundamentals, the performance procedure, and the results of an elastodynamic stress and deformation analysis of hollow balls aimed at providing a clear definition of parametric influences for the development of hollow ball bearing technology. A simplified model is used as a first approximation, and contact stress distributions are obtained with the aid of computer programming and processing.
The concept of surface tension and surface energy of solids was used by Griffith to obtain a criterion for the extension of cracks in brittle materials. Griffith, however, neglected the stresses due to the normal traction at the crack implied by the surface tension. A complete solution to the problem of an elliptic hole in an infinite plate with surface tension loading at the hole is given. Complex potentials are given in closed form in terms of elliptic integrals of the first, second, and third kinds. Stress distributions are studied. For a flat crack, the nature of the singularity at the tip is shown to be radically different from that usually encountered in fracture mechanics. The implications of our analysis for theories of fracture in brittle materials are discussed.
The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution has been evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study has been made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.
Eolian erosion and deposition on earth was studied in order to interpret the eolian land forms of Mars. Emphasis of the wind tunnel studies was on the flow field around models of eolian forms. Areas of the wind tunnel studies include: simulation of the atmospheric boundary layer; velocity profile measurements around different models in the desert boundary layer, and estimating shear stress distributions on the model surfaces; flow visualization techniques; streamline mapping using tuft photographs; and roughness contrasts.
An isotropic sheet stiffened by means of an orthotropic quarter-plate is considered. The quarter-plate is assumed to be perfectly bonded to the metal sheet everywhere except an area of debonding which may develop due to high stress concentrations. The adhesive which has a small constant thickness is treated as a shear spring. The loads are applied at infinity and supposed to be transmitted through the metal plate. Shear stress distribution between the two plates was obtained from the continuity of displacements along an area where they were bonded to each other.
By measuring the change in fracture stress of 203 micrometer diameter fibers of boron on tungsten (B/W) as a function of fiber diameter as reduced by chemical etching, it is shown that the flaws which limit B/W fiber strength are located at the surface and in the tungsten boride core. After etching to a diameter of 188 micrometers m virtually all fiber fractures were caused by core flaws, the average strength being 4.50 GN/sq m. If both the surface and core flaws are removed, the fracture strength, limited by flaws in the boron itself, is approximately 6.89 GN/sq m. This was measured on B/W fibers which were split longitudinally and had their cores removed by chemical etching. The longitudinal residual stress distribution was determined for 102 micrometer diameter B/W and B/C fibers.
By use of the principle of superposition the stiff-flanged shear web is modeled mathematically by an infinite elastic strip with fixed longitudinal edges. The shear-stress intensity factor for a central longitudinal crack is calculated for various values of the ratio of strip width to crack length, h/a, in the range 0.1-10. The interaction of the crack with the boundaries is illustrated by boundary shear-stress distributions for three values of h/a. Some implications of the results for the design of damage-tolerant shear webs are discussed briefly.
A two-dimensional hybrid stress finite element analysis is described which was used to study the local stress field around delamination cracks in composite materials. The analysis employs a crack tip singularity element which is embedded in a matrix interlayer between plies of the laminate. Results are given for a unidirectional graphite/epoxy laminate containing a delamination emanating from a surface crack through the outside ply. The results illustrate several aspects of delamination cracks: (1) the localization of the singular stress domain within the interlayer; (2) the local concentration of stress in the ply adjacent to the crack; (3) the nature of the transverse normal and interlaminar shear stress distributions; and (4) the relative magnitudes of K sub 1 and K sub 2 associated with the delamination. A simple example of the use of the analysis in predicting delamination crack growth is demonstrated for a glass/epoxy laminate. The comparisons with experimental data show good agreement.
A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.
From comparisons of high speed data with low speed closure procedures using variable mean density, there does not appear to be any appreciable influence of compressibility upon turbulent shear stress modeling in compressible turbulent boundary layers, even for extreme cases such as Mach 14 to 20 with a change in density across the layer of up to a factor of 100. Other evidence of apparent lack of compressibility caused new physics which may alter the shear stress for the compressible boundary layer cases including: (1) fluctuation Mach number was generally less than 1; (2) the shear stress distribution through the boundary layer was not a function of Mach number for zero pressure gradient flows; (3) the Morkovin hypothesis was valid up to Mach 5 (based on fluctuation data); (4) profile N power was not a function of Mach number, at least up to Mach 10; and (5) the nondimensional burst period was approximately the same as that for low speed.
The performance of the NASTRAN level 16.0, twenty node, isoparametric bricks (CIHEX2) at thermal loading was studied. A free ceramic plate was modelled using twenty node bricks of varying thicknesses. The thermal loading for this problem was uniform over the surface with an extremely large gradient through the thickness. No mechanical loading was considered. Temperature-dependent mechanical properties were considered in this analysis. The NASTRAN results were compared to one dimensional stress distributions calculated by direct numerical integration.
The paper considers a thin elastic bidirectional symmetric composite laminate subjected to a uniform axial strain. All interlaminar stresses are determined by a zeroth-order perturbation analysis of the governing equations. The method of solution considers the laminate to be composed of an interior region (removed from the free edge) and a boundary layer region. The interior region is analyzed by dropping terms related to powers of the thickness-to-width ratio in the dimensionless elasticity equations. The boundary layer region is studied by introducing a stretching transformation to the governing equations. A uniform solution is then formed by satisfying Prandtl's matching principle of perturbation theory. Results for a four-layer bidirectional graphite-epoxy laminate are compared with existing finite-difference results. It is shown that the perturbation analysis provides more insight into the stress distribution near the free edge.
A finite-element approach has been developed for computing nonlinear flutter characteristics of rectangular isotropic panels with stream-alined side edges, based on aerodynamic forces from supersonic two-dimensional quasi-steady aerodynamic theory. Stress distributions and panel oscillation frequencies were determined from the analysis. The finite-element formulation, solution procedure, and convergence characteristics are presented. Comparisons are made with linear flutter and large-amplitude vibration results and demonstrate that good accuracy is obtained. Non-linear flutter results are presented for effects of aerodynamic damping, length-width ratio, initial in-plane forces and boundary-support conditions. Comparisons with experimental results are also presented.
A new calculation of the effects of thermal stresses during growth on silicon ribbon quality is reported. Thermal stress distributions are computed for ribbon growth under a variety of temperature profiles. A growth rate of 55 cu cm/min with a single ribbon was achieved. The growth of RTR ribbon with a fairly uniform parallel dendritic structure was demonstrated. Results with two approaches were obtained for reducing the Mo impurity level in polycrystalline feedstock. Coating the Mo substrate with Si3N4 does not effect thermal shear separation of the polyribbon; this process shows promise of improving cell efficiency and also increasing the useful life of the molybdenum substrate. A number of solar cells were fabricated on RTR silicon grown from CVD feedstock.
A two-dimensional, linear-elastic, finite element analysis of selected graphite/polyimide rail shear test specimens was made to determine the mechanical loading and the effect of heating the specimen to a uniform temperature. The presence of specimen free edges and their influence on the accuracy of the rail shear test is discussed. Parameters include the length-to-width ratio of the specimen and the ply layup for symmetric, balanced laminates. Results presented include shear and normal stress distributions and the deflection behavior of various specimens caused by the mechanical loading and elevated temperature.
Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.
Structures prepared from materials with different thermal and mechanical properties by means of fiber-strengthened binders can fail in a number of ways. The present lecture is focused on failures through debonding at the metal or at the fiber-reinforced plastic. A method for calculating the stress distribution in adhesive layers as a function of the load is outlined, and its usefulness in providing insight into the behavior of bonds in hybrid structures is noted. Means of eliminating the unfavorable effects of temperature, humidity, creep and relaxation on the bonds in the manufacture of hybrid structures are examined, along with test methods developed for such structures.
Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results of this study are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.