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Buckling of axially compressed circular cylindrical shells with localized or random axisymmetric imperfections, deriving asymptotic approximation formulas for stress calculation
The current work formulated a micromechanical analysis of a cross-ply laminate and calculated the thermal residual stress in a very thick (0/90)(sub 2n) silicon-carbide/titanium laminate. Results were also shown for a unidirectional laminate of the same material. Discrete fiber-matrix models assuming a rectangular array of fibers with a fiber volume fraction of 32.5 percent and a three-dimensional, finite-element analysis were used. Significant differences in the trends and magnitudes for the fiber, matrix, and interface stresses were calculated for unidirectional and (0/90) models. Larger hoop stresses calculated for the (0/90) model indicate that it may be more susceptible to radial cracking when subjected to mechanical loading than the unidirectional model. The axial stresses in the matrix were calculated to be slightly larger for the (0/90) model. The compressive axial stresses in the fiber were significantly larger in the (0/90) model. The presence of the cross-ply in the (0/90) model reduced the constraint on the fiber, producing radial interface stresses that were less compressive, which could lead to earlier failure of the fiber-matrix interface.
The influence of placing interleaves between fiber reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as two dimensional, isotropic, linearly elastic media made of a damaged layer bonded between two half planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface and may extend up to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. The interleaves are modeled as distributed shear and tension springs. Fourier integral transform techniques are used to develop solutions in terms of singular integral equations. An asymptotic analysis of the integral equations based on Muskhelishvili's techniques reveals logarithmically singular axial stresses in the half plane at the crack tips for the broken layer. For the H shaped crack, similar singularities are found to exist in the axial stresses at the interface crack tips in the layer and the half plane. The solution of the equations is found numerically for the stresses and displacements by using the Hadamard's concept of direct differentiation of Cauchy integrals as well as Gaussian integration techniques.
Cure-induced uniform temperature change effects on the stresses, axial expansion, and thermally-induced twist of four specific angle-ply tube designs are discussed with a view to the tubes' use as major space structure components. The stresses and deformations in the tubes are studied as a function of the four designs, the off-axis angle, and the single-material and hybrid reinforcing-material construction used. It is found that tube design has a minor influence on the stresses, axial stiffness, and axial thermal expansion characteristics, which are more directly a function of off-axis angle and material selection; tube design is, however, the primary influence in the definition of thermally-induced twist and torsional stiffness characteristics. None of the designs is free of thermally induced twist.
This paper examines the compressive strength of a fiber reinforced lamina under multi-axial stress states. An equilibrium analysis is carried out in which a kinked band of rotated fibers, described by two angles, is sandwiched between two regions in which the fibers are nominally straight. Proportional multi-axial stress states are examined. The analysis includes the possibility of bifurcation from the current equilibrium state. The compressive strength of the lamina is contingent upon either attaining a load maximum in the equilibrium response or satisfaction of a bifurcation condition, whichever occurs first. The results show that for uniaxial loading a non-zero kink band angle beta produces the minimum limit load. For multi-axial loading, different proportional loading paths show regimes of bifurcation dominated and limit load dominated behavior. The present results are able to capture the beneficial effect of transverse compression in raising the composite compressive strength as observed in experiments.
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Reliable test method based on special strain gauge load transducer for embedment axial stress measurement in electronic modules
NASA's Ares 1 Upper Stage Simulator (USS) is being fabricated from welded A516 steel. In order to insure the structural integrity of these welds it is of interest to calculate the critical initial flaw size (CIFS) to establish rational inspection requirements. The CIFS is in turn dependent on the critical final flaw size (CFS), as well as fatigue flaw growth resulting from transportation, handling and service-induced loading. These calculations were made using linear elastic fracture mechanics (LEFM), which are thought to be conservative because they are based on a lower bound, so called elastic, fracture toughness determined from tests that displayed significant plasticity. Nevertheless, there was still concern that the yield magnitude stresses generated in the flange-to-skin weld by the combination of axial stresses due to axial forces, fit-up stresses, and weld residual stresses, could give rise to significant flaw-tip plasticity, which might render the LEFM results to be non-conservative. The objective of the present study was to employ Elastic Plastic Fracture Mechanics (EPFM) to determine CFS values, and then compare these values to CFS values evaluated using LEFM. CFS values were calculated for twelve cases involving surface and embedded flaws, EPFM analyses with and without plastic shakedown of the stresses, LEFM analyses, and various welding residual stress distributions. For the cases examined, the computed CFS values based on elastic analyses were the smallest in all instances where the failures were predicted to be controlled by the fracture toughness. However, in certain cases, the CFS values predicted by the elastic-plastic analyses were smaller than those predicted by the elastic analyses; in these cases the failure criteria were determined by a breakdown in stress intensity factor validity limits for deep flaws (a greater than 0.90t), rather than by the fracture toughness. Plastic relaxation of stresses accompanying shakedown always increases the calculated CFS values compared to the CFS values determined without shakedown. Thus, it is conservative to ignore shakedown effects.
Stress diffusion from axially loaded stiffeners into cylindrical elastic shells
Spherical roller bearings have typically been used in applications with speeds limited to about 5000 rpm and loads limited for operation at less than about 0.25 million DN. However, spherical roller bearings are now being designed for high load and high speed applications including aerospace applications. A computer program, SASHBEAN, was developed to provide an analytical tool to design, analyze, and predict the performance of high speed, single row, angular contact (including zero contact angle), spherical roller bearings. The material presented is the mathematical formulation and analytical methods used to develop computer program SASHBEAN. For a given set of operating conditions, the program calculates the bearings ring deflections (axial and radial), roller deflections, contact areas stresses, depth and magnitude of maximum shear stresses, axial thrust, rolling element and cage rotational speeds, lubrication parameters, fatigue lives, and rates of heat generation. Centrifugal forces and gyroscopic moments are fully considered. The program is also capable of performing steady-state and time-transient thermal analyses of the bearing system.
A description is given of a semi-empirical, deterministic analysis for prediction and correlation of fatigue crack growth, residual strength, and fatigue lifetime for fiber composite laminates containing notches (holes). The failure model used for the analysis is based upon composite heterogeneous behavior and experimentally observed failure modes under both static and fatigue loading. The analysis is consistent with the wearout philosophy. Axial cracking and transverse cracking failure modes are treated together in the analysis. Cracking off-axis is handled by making a modification to the axial cracking analysis. The analysis predicts notched laminate failure from unidirectional material fatique properties using constant strain laminate analysis techniques. For multidirectional laminates, it is necessary to know lamina fatique behavior under axial normal stress, transverse normal stress and axial shear stress. Examples of the analysis method are given.
In this study, the fatigue crack growth behavior of fiber bridging matrix cracks in cross-ply SCS-6/Ti-15-3 and SCS-6/Timetal-21S laminates containing center holes was investigated. Experimental observations revealed that matrix cracking was far more extensive and wide spread in the SCS-6/Ti-15-3 laminates compared to that in the SCS-6/Timetal-21S laminates. In addition, the fatigue life of the SCS-6/Ti-15-3 laminates was significantly longer than that of the SCS-6/Timetal-21S laminates. The matrix cracking observed in both material systems was analyzed using a fiber bridging (FB) model which was formulated using the boundary correction factors and weight functions for center hole specimen configurations. A frictional shear stress is assumed in the FB model and was used as a curve fitting parameter to model matrix crack growth data. The higher frictional shear stresses calculated in the SCS-6/Timetal-21S laminates resulted in lower stress intensity factors in the matrix and higher axial stresses in the fibers compared to those in the SCS-6/Ti-15-3 laminates at the same applied stress levels.
The fabrication of metal matrix composites poses unique problems to the materials engineer. The large thermal expansion coefficient (CTE) mismatch between the fiber and matrix leads to high tensile residual stresses at the fiber/matrix (F/M) interface which could lead to premature matrix cracking during cooldown. Fiber coatings could be used to reduce thermal residual stresses. A simple closed form analysis, based on a three phase composite cylinder model, was developed to calculate thermal residual stresses in a fiber/interphase/matrix system. Parametric studies showed that the tensile thermal residual stresses at the F/M interface were very sensitive to the CTE and thickness of the interphase layer. The modulus of the layer had only a moderate effect on tensile residual stresses. For a silicon carbide titanium aluminide composite, the tangential stresses were 20 to 30 pct. larger than the axial stresses, over a wide range of interphase layer properties, indicating a tendency to form radial matrix cracks during cooldown. Guidelines for the selection of appropriate material properties of the fiber coating were also derived in order to minimize thermal residual stresses in the matrix during fabrication.
Thermal deformations and stresses were studied in a silicon-carbide/aluminum filamentary composite at temperatures up to 370 C (700 F). Longitudinal and transverse thermal strains were measured with strain gages and a dilatometer. An elastoplastic micromechanical analysis based on a one-dimensional rule-of-mixtures model and an axisymmetric two-material composite cylinder model was performed. It was established that beyond a critical temperature thermal strains become nonlinear with decreasing longitudinal and increasing transverse thermal-expansion coefficients. This behavior was attributed to the plastic stresses in the aluminum matrix above the critical temperature. An elastoplastic analysis of both micromechanical models was performed to determine the stress distributions and thermal deformation in the fiber and matrix of the composite. While only axial stresses can be determined by the rule-of-mixtures model, the complete triaxial state of stress is established by the composite cylinder model. Theoretical predictions for the two thermal-expansion coefficients were in satisfactory agreement with experimental results.
Starting with the Love equations for bending of extensible shells, "principal stress states" are sought for a thin-walled rod of arbitrary but open cross section. Principal stress states exclude those local states arising from end conditions which damp out with distance from the ends. It is found that for rods of intermediate length, long enough to avoid local bending at a support, and short enough that elementary torsion and bending are not the most significant stress states, four principal states exist. Three of these states are associated with the planar distribution of axial stress and are equivalent to the engineering theory of extension and bending of solid sections. The fourth state resembles that which has been called in the literature "bending stress due to torsional", except that cross sections are permitted to bend and the shear along the center line of the cross section is permitted to differ from zero.
A 3-D finite element model was developed to analyze the fiber-resin behavior near the delamination front in a graphite-epoxy double cantilever beam (DCB) specimen. The specimen interior was analyzed using a typical one-fiber slice, represented by a local 3-D fiber-resin model. The resin stresses were computed for the resin-rich layer at the ply interface as well as for the regions between the fibers close to the delamination front. However, the computed strain energy release rate G sub I along the delamination front varied by less than two percent, and was within about four percent of the plane-strain value. The von Mises yield criterion was used to estimate the extent of yielding near the delamination front. The yielding extended ahead of the delamination and also developed between the fibers. Although the fibers had only a negligible effect on G sub I, they caused yielding within the ply and therefore could influence delamination fracture toughness. The normal and shear stresses at the fiber-resin interface were computed near the delamination front. These results suggest that multi-axial stress criteria may be required to analyze fiber-resin interfaces.
The focus of this study is on the suitability in the application of classical laminate theory analysis tools for filament wound pressure vessels with adhesive laminated joints in particular: pressure vessel wall performance, joint stiffness and failure prediction. Two 18-inch diameter 12-ply filament wound pressure vessels were fabricated. One vessel was fabricated with a 24-ply pyramid laminated adhesive double strap butt joint. The second vessel was fabricated with the same number of plies in an inverted pyramid joint. Results from hydrostatic tests are presented. Experimental results were used as input to the computer programs GENLAM and Laminate, and the output compared to test. By using the axial stress resultant, the classical laminate theory results show a correlation within 1% to the experimental results in predicting the pressure vessel wall pressure performance. The prediction of joint stiffness for the two adhesive joints in the axial direction is within 1% of the experimental results. The calculated hoop direction joint stress resultant is 25% less than the measured resultant for both joint configurations. A correction factor is derived and used in the joint analysis. The correction factor is derived from the hoop stress resultant from the tank wall performance investigation. The vessel with the pyramid joint is determined to have failed in the joint area at a hydrostatic pressure 33% value below predicted failure. The vessel with the inverted pyramid joint failed in the wall acreage at a hydrostatic pressure within 10% of the actual failure pressure.