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Test program to verify theory used in calculating axial thrust uses turbopump instrumented with /a/ proximity transducers for measuring shaft position, /b/ a strain gage thrust bearing carrier to measure axial thrust, and /c/ internal pressure taps to define component pressure gradients used in thrust calculations.
Axial strain can be determined by monitoring the modal pattern variation of an optical fiber. The results of a numerical model developed to calculate the modal pattern variation at the end of a weakly guiding optical fiber under axial strain is presented. Whenever an optical fiber is under stress, the optical path length, the index of refraction, and the propagation constants of each fiber mode change. In consequence, the modal phase term for the fields and the fiber output pattern are also modified. For multimode fibers, very complicated patterns result. The predicted patterns are presented, and an expression for the phase variation with strain is derived.
The results presented here are part of an ongoing research program, to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. A micromechanics approach is employed in this work, in which state variable constitutive equations originally developed for metals have been modified to model the deformation of the polymer matrix, and a strength of materials based micromechanics method is used to predict the effective response of the composite. In the analysis of the inelastic deformation of the polymer matrix, the definitions of the effective stress and effective inelastic strain have been modified in order to account for the effect of hydrostatic stresses, which are significant in polymers. Two representative polymers, a toughened epoxy and a brittle epoxy, are characterized through the use of data from tensile and shear tests across a variety of strain rates. Results computed by using the developed constitutive equations correlate well with data generated via experiments. The procedure used to incorporate the constitutive equations within a micromechanics method is presented, and sample calculations of the deformation response of a composite for various fiber orientations and strain rates are discussed.
Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction proposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite-element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure predicts stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load-cycled problems. Neuber-type corrections were derived and incorporated in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was used on a mechanically load-cycled benchmark notched-plate problem. The predicted material response agrees well with the nonlinear finite-element solutions for the problem. The simplified analysis computer program was 0.3% of the central processor unit time required for a nonlinear finite-element analysis.
Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.
Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.
Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions
A petrofabric study of the Leoville chondrite was performed in order to gain an understanding of its deformation process. Strain values were determined from the chondrules' axial ratios or by the all-object-separation method, and the compaction required to deform Leoville chondrules was calculated from the decrease of radius in the circle-to-ellipse transformation. Structural and strain studies indicate the following order of events experienced by Leoville: (1) formation as an accretionary breccia, (2) compaction and development of foliation, (3) fracturing, possibly due to impact on earth, and (4) terrestrial weathering. Similarities between the axial ratios of chondrules (1.9-2.0) and of the whole meteorite (2.0) indicate either that Leoville deformed homogeneously or that it deformed as a framework of touching chondrules. This amount of strain corresponds to approximately 33 percent uniaxial shortening, assuming constant volume, and is likely to have been caused by compaction due to overburden from progressive accretion on the chondrite body. Diffusional flow is believed to be the mechanism by which olivines in these chondrules deformed.
The definition of effective thicknesses of the ASTM standard 25 percent side-grooved compact specimens to calculate the elastic compliance, elastic SIF, and elastic-plastic J integral is reevaluated. 3D elastic-plastic analyses of polane-strain, smooth, and 25 percent side-grooved compact specimen models are conducted using the ZIP3D code. Calculated compliance, SIFs, and J-integrals are compared with E-813 solutions.
For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.
Two-dimensional finite element analyses of (02/90(8)/02) glass/epoxy and graphite/epoxy composite laminates were performed to investigate some of the characteristics of damage development due to an impact load. A cross section through the thickness of the laminate with fixed ends, and carrying a transverse load in the center, was analyzed. Inclined matrix cracks, such as those produced by a low-velocity impact, were modeled in the 90 deg ply group. The introduction of the matrix cracks caused large interlaminar tensile and shear stresses in the vicinity of both crack tips in the 0/90 and 90/0 interfaces, indicating that matrix cracking may give rise to delamination. The ratio of Mode I to total strain energy release rate, G(I)/G(total), at the beginning of delamination, calculated at the two (top and bottom) matrix crack tips was 60 and 28 percent, respectively, in the glass/epoxy laminate. The corresponding ratio was 97 and 77 percent in the graphite/epoxy laminate. Thus, a significant Mode I component of strain energy release rate may be present at the delamination initiation due to an impact load. The value of strain energy release rate at either crack tip increased due to an increase in the delamination length at the other crack tip and may give rise to an unstable delamination growth under constant load.
An analytical study is presented which investigates the cause of the excessive heating in the tile-to-tile gaps of the Shuttle Orbiter Thermal Protection System, as evidenced by the visible discoloration and charring of the filler bar and strain isolation pad used in the attachment of tiles to the aluminum substrate. Techniques are developed to estimate the pressure disturbances due to a stepped tile and to calculate the disturbance-induced mass flow rates in the tile-to-tile gaps, filler bar, strain isolation pad, and the tile itself. A thermal analysis in the tile-to-tile gap is then performed in order to determine the temperature response to the hot gas flow. Calculations are performed at locations on the fuselage and the left wing where damaged filler bars were observed on the first flight of the Shuttle. It is concluded that the steps and gaps must be controlled within tight tolerances during tile installation and the tolerances must be maintained in flight. If the tolerances cannot be maintained, tile-to-tile gap filler may be an alternative.
The edge crack torsion (ECT) test is designed to initiate mode III delamination growth in composite laminates. An ECT specimen is a rectangular laminate, containing an edge delamination at the laminate mid-plane. Torsion load is applied to the specimens, resulting in relative transverse shear sliding of the delaminated faces. The test data reduction schemes are intended to yield initiation values of critical mode III strain energy release rate, G(sub IIIc), that are constant with delamination length. The test has undergone several design changes during its development. The objective of this paper was to determine the suitability of the current ECT test design as a mode III fracture test. To this end, ECT tests were conducted on specimens manufactured from IM7/8552 and specimens made from S2/8552 tape laminates. Several specimens, each with different delamination lengths are tested. Detailed, three-dimensional finite element analyses of the specimens were performed. The analysis results were used to calculate the distribution of mode I, mode II, and mode III strain energy release rate along the delamination front. The results indicated that mode III-dominated delamination growth would be initiated from the specimen center. However, in specimens of both material types, the measured values of G(sub IIIc) exhibited significant dependence on delamination length. Furthermore, there was a large amount of scatter in the data. Load-displacement response of the specimens exhibited significant deviation from linearity before specimen failure. X-radiographs of a sample of specimens revealed that damage was initiated in the specimens prior to failure. Further inspection of the failure surfaces is required to identify the damage and determine that mode III delamination is initiated in the specimens.
A model is described for estimating the impact damage of fiber reinforced composite plates. The displacements and stresses are calculated by a three dimensional transient, finite element method of solution of the governing equations applicable to a linearly elastic body. The region in which damage occurs is estimated using the Tsai-Wu failure criterion. A computer code was developed which can be used to calculate the impact force, displacements and velocities of the plate and the impact body, stresses and strains in the plate, and the damage area. Sample numerical results are presented illustrating the type of information provided by the code. Comparisons between measured and calculated damage areas are also given.
The quadratic isoparametric elements which embody the inverse square root singularity are used for calculating the stress intensity factors at tips of cracks. The strain singularity at a point or an edge is obtained in a simple manner by placing the mid-side nodes at quarter points in the vicinity of the crack tip or an edge. These elements are implemented in NASTRAN as dummy elements. The method eliminates the use of special crack tip elements and in addition, these elements satisfy the constant strain and rigid body modes required for convergence.
The Monte Carlo method was used to investigate thrust imbalance and its first time derivative throughtout the burning time of pairs of solid rocket motors firing in parallel. Results obtained compare favorably with Titan 3 C flight performance data. Statistical correlations of the thrust imbalance at various times with corresponding nominal trace slopes suggest several alternative methods of predicting thrust imbalance. The effect of circular-perforated grain deformation on internal ballistics is discussed, and a modified design analysis computer program which permits such an evaluation is presented. Comparisons with SRM firings indicate that grain deformation may account for a portion of the so-called scale factor on burning rate between large motors and strand burners or small ballistic test motors. Thermoelastic effects on burning rate are also investigated. Burning surface temperature is calculated by coupling the solid phase energy equation containing a strain rate term with a model of gas phase combustion zone using the Zeldovich-Novozhilov technique. Comparisons of solutions with and without the strain rate term indicate a small but possibly significant effect of the thermoelastic coupling.
Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.
The onset and growth of delaminations in unnotched (+ or - 30/+ or - 30/90/90 bar) sub S graphite epoxy laminates is described quantitatively. These laminates, designed to delaminate at the edges under tensile loads, were tested and analyzed. Delamination growth and stiffness loss were monitored nondestructively. Laminate stiffness decreased linearly with delamination size. The strain energy release rate, G, associated with delamination growth, was calculated from two analyses. A critical G for delamination onset was determined, and then was used to predict the onset of delaminations in (+45 sub n/-45 sub n/o sub n/90 sub n) sub s (n=1,2,3) laminates. A delamination resistance curve (R curve) was developed to characterize the observed stable delamination growth under quasi static loading. A power law correlation between G and delamination growth rates in fatigue was established.