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NASA NTRS1993

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

NASA NTRS2018

An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells

The inverse Finite Element Method (iFEM) is a revolutionary methodology for real-time reconstruction of full-field structural displacements and stresses in structures that are instrumented with strain sensors. This inverse problem is commonly referred to as shape and stress sensing, which is well-recognized as an enabling technology for structural health monitoring systems. In this study, an improved iFEM formulation is proposed for shape and stress sensing of laminated composite and sandwich plates and shells. The formulation includes the kinematics of a shear deformation plate theory known as Refined Zigzag Theory (RZT) as its baseline. The present iFEM formulation is based upon the minimization of a weighted-least-squares functional that uses the complete set of section strains of RZT. The improved iFEM methodology is applicable for shape and stress sensing of thin and moderately thick plate and shell structures involving a relatively small number of strain gauges. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. A three-node inverseshell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. For both problems, the experimental strain data are generated numerically by the direct finite element analysis using high-fidelity discretizations. These strains are then regarded as the experimental strains obtained from surface mounted strain gauges or embedded fiber Bragg grating (FBG) sensors. The numerical results demonstrate the superior capability and potential applicability of the i3- RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures.

Kefal, Adnan↗

NASA NTRS2004

Particulate Titanium Matrix Composites Tested--Show Promise for Space Propulsion Applications

Uniformly distributed particle-strengthened titanium matrix composites (TMCs) can be manufactured at lower cost than many types of continuous-fiber composites. The innovative manufacturing technology combines cold and hot isostatic pressing procedures to produce near-final-shape components. Material stiffness is increased up to 26-percent greater than that of components made with conventional titanium materials at no significant increase in the weight. The improved mechanical performance and low-cost manufacturing capability motivated an independent review to assess the improved properties of ceramic titanium carbide (TiC) particulate-reinforced titanium at elevated temperature. Researchers at the NASA Glenn Research Center creatively designed and executed deformation and durability tests to reveal operating regimes where these materials could lower the cost and weight of space propulsion systems. The program compares the elevated-temperature performance of titanium alloy Ti-6Al-4V matrix material to an alloy containing 10 wt% of TiC particles. Initial experiments showed that at these relatively low particle concentrations the material stiffness of the TMC was improved 20 percent over that of the plain Ti-6Al-4V alloy when tested at 427 C. The proportional limit and ultimate strength of the composite in tension are 21- and 14-percent greater than those of the plain alloy. Compression tests showed that the proportional limit is about 30 percent greater for TMC than for the plain alloy. The enhanced deformation resistance of the TMC was also evident in a series of tensile and compressive stress relaxation tests that were made. Specimens were subjected to tensile or compressive strain amplitudes of 0.75 percent for 24 hr followed by a return to zero strain imposed for 24 hr. The stress relaxation data were normalized with respect to the maximum stress for each case and plotted as a function of time in the following graph. Tensile stresses relaxed 19 percent for the TMC and 25 percent for the plain Ti-6Al-4V alloy. Compressive stresses relaxed 25 percent for the TMC and 39 percent for the plain Ti-6Al-4V alloy. The superior deformation resistance of the TMC extends to a creep rate that is 28-percent slower for the TMC when it is loaded to stress levels that are 26-percent higher than for the plain Ti-6Al-4V alloy.

Lerch, Bradley A.↗

NASA NTRS2019

Static Torsion Testing and Modeling of a Variable Thickness Hybrid Composite Bull Gear

Torsional strength of a variable thickness hybrid gear web was measured by performing static testing on the part in a large torsion test frame. The outer rim of the hybrid gear web was fixed to the bottom of the test frame and loading was applied to the web through a shaft. The test setup included the installation of digital image correlation (DIC) systems to obtain deformation and strain measurements from the surfaces of the hybrid gear web and the mechanical test equipment to ensure reliability of the test. The results indicated that the variable thickness hybrid gear web achieved approximately twice the torsional strength compared to that of previous hybrid gear designs. The DIC analysis showed significantly more straining of the loading shaft than the actual test article. Additionally, the results demonstrated the importance and affect that the metallic, lobed interlock features had on the principal strain and out-of-plane displacement fields. The analysis revealed that the fixed outer rim was in fact rotating and a rigid body motion compensation (RBMC) function was computed to determine the actual rotation of the hub and composite web relative to the outer rim. Modeling simulations were performed for the variable thickness hybrid gear web and correlated well with the RBMC rotational deformation seen in the DIC analysis. In addition to benchmarking the load capacity of the hybrid gear web, measuring its strength is useful information to define the parameters needed for dynamic, endurance, and other testing of the part.

Johnston, Joel P.↗

NASA NTRS1965

Ground testing at MSFC

The large-scale field collection of acoustic data and their analysis are described in this review. The entire sound-field program has the purpose of solving complex problems of excessive noise propagation associated with the static test firing of large space-booster powerplants. The site of data collection has been Mississippi Test Facility (MTF), where far-field sound-propagation and correlated meteorological measurements were initiated in 1962. The statistical evaluation of sound-measurement data shows that the polar distribution of sound in the springtime (at MTF) is determined mainly by the temperature field of the atmosphere. Greater deformation of sound-intensity polar distribution occurs in the autumn as a result of the influence of the wind field. The data on sound attenuation as a function of distance from its source revealed attenuation in excess of the expected magnitude. The excess was mainly between 1 and 10 kilometers from the source, with maximum attenuation (17 to 18 decibels) near 6 kilometers. Excess sound attenuation was compared with calculated sound dispersion. For all sound frequencies in all seasons the deviation between reference and empirical attenuation values formed a bell-shaped distribution on a semilogarithmic plot. The physical causes for the sound- attenuation behavior are considered to be atmospheric diffraction and scattering effects. Statistical analysis of sod-intensity extremes indicated amplification of the sound signals by focusing which could be expected along selected azimuths. Empirical amplification values showed the maximum occurring in winter (50 decibels at 22 kilometers). For the analysis of correlation between empirical sound data and local atmospheric sound- propagation conditions, #e concept of analytical classification of sound-velocity profiles has been developed. Examination of over a quarter-million individual sound-velocity profiles indicates that 33 profile types for heights up to 3 kilometers constitute the empirical possibilities of sound-propagation conditions in southeastern United States. Since the focusing qualities of each sound- velocity profile can be determined as a class characteristic, the overall probabilities of focusing occurrence can he obtained. The severity of focusing, as based upon lateral spread of focusing areas, has been determined. The data for MTF indicate focusing is most severe in winter, with the direction toward east being most affected. Sound propagation is a fluctuating phenomenon because atmospheric conditions vary continuously. A measuring system for analyzing the nonstationary sound-propagation phenomena has been established. The analysis of the acoustic fluctuation data is sup- posed to provide "dynamic” perturbation functions of sound, which are to be superimposed on the related characteristic sound-velocity-profile type. The ultimate result of the program will be the establishment of reliable contingency tables showing the relationship between atmospheric parameters and far-field sound intensities. These data will be the basis for more accurate sound-propagation forecasting for static firing tests.

STATIC TESTING↗

NASA NTRS1972

Computer program: Jet 3 to calculate the large elastic plastic dynamically induced deformations of free and restrained, partial and/or complete structural rings

A user-oriented FORTRAN 4 computer program, called JET 3, is presented. The JET 3 program, which employs the spatial finite-element and timewise finite-difference method, can be used to predict the large two-dimensional elastic-plastic transient Kirchhoff-type deformations of a complete or partial structural ring, with various support conditions and restraints, subjected to a variety of initial velocity distributions and externally-applied transient forcing functions. The geometric shapes of the structural ring can be circular or arbitrarily curved and with variable thickness. Strain-hardening and strain-rate effects of the material are taken into account.

Wu, R. W.↗

NASA NTRS1981

Simplified solution for stresses and deformations

A shortcut is presented to the classical Hertzian solution for local stress and deformation of two elastic bodies in contact, which employs simplified forms for the ellipticity and for the complete elliptic integrals of the first and second kinds as a function of the geometry. Unlike previously proposed simplified formulas whose range of applicability was limited to ellipticities equal to, or greater than one, the present method extends the range of validity to include ellipticities less than one; in which the semimajor axis in the elliptical contact lies in a direction parallel to the rolling, rather than being perpendicular, as in previous studies. An auxiliary shear stress parameter is also expressed in simplified form as a function of the geometry, permitting a shortcut calculation to be made for the location and magnitude of the maximum subsurface shear stress.

Hamrock, B. J.↗

NASA NTRS1990

Convection-driven tectonics on Venus

An analysis is presented of convective stress coupling to an elastic lithosphere as applied to Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity, and a Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. An elastic-plastic analysis is carried out for the deformation of a model Venus lithosphere. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere.

Phillips, Roger J.↗

NASA NTRS1991

Analysis of laminated composite shells under internal pressure

A closed form solution is presented that predicts the response of filament wound composite shells subjected to internal pressure. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity coupled differential equations are developed using Lekhnitskii's stress function approach. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Detailed stress distributions of (45) off-axis unidirectional and (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio and stacking sequence.

Yuan, F. G.↗

NASA NTRS1993

Modeling the densification of metal matrix composite monotape

We present a first model that enables prediction of the density (and its time evolution) of a monotape lay-up subjected to a hot isostatic or vacuum hot pressing consolidation cycle. Our approach is to break down the complicated (and probabilistic) consolidation problem into simple, analyzable parts and to combine them in a way that correctly represents the statistical aspects of the problem, the change in the problem's interior geometry, and the evolving contributions of the different deformation mechanisms. The model gives two types of output. One is in the form of maps showing the relative density dependence upon pressure, temperature, and time for step function temperature and pressure cycles. They are useful for quickly determining the best place to begin developing an optimized process. The second gives the evolution of density over time for any (arbitrary) applied temperature and pressure cycle. This has promise for refining process cycles and possibly for process control. Examples of the models application are given for Ti3Al + Nb, gamma TiAl, Ti6Al4V, and pure aluminum.

Elzey, D. M.↗

NASA NTRS1998

Buckling Analysis of Anisotropic Curved Panels and Shells with Variable Curvature

A buckling formulation for anisotropic curved panels with variable curvature is presented in this paper. The variable curvature panel is assumed to consists of two or more panels of constant but different curvatures. Bezier functions are used as Ritz functions Displacement (C(sup 0)), and slope (C(sup 1)) continuities between segments are imposed by manipulation of the Bezier control points. A first-order shear-deformation theory is used in the buckling formulation. Results obtained from the present formulation are compared with those from finite element simulations and are found to be in good agreement.

Jaunky, Navin↗

NASA NTRS1998

Constitutive Theory Developed for Monolithic Ceramic Materials

With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.

Janosik, Lesley A.↗

NASA NTRS2018

Real Time Detection of Damage During Quasi-Static Loading of a Single Stringer Panel Using Passive Thermography

Real time nondestructive evaluation is required for composites load testing. The early detection and measurement of damage progression is important to understand failure modes. A single stringer panel was subjected to quasi-static loading to induce deformation which can result in the formation of delamination damage between the stiffener flange and skin. Passive thermography was used to detect damage in real time as a function of the applied load. The loading was stopped when damage growth was detected. Of particular interest was the early detection of damage formation which can be challenging, as compared to cyclic fatigue loading. Passive thermography data were acquired and processed in real time and revealed damaged areas due to heating from fiber breakage and delamination formation. The processed thermal imagery was also compared to acoustic emission and ultrasound data.

Zalameda, Joseph N.↗

NASA NTRS1978

Monitoring regional crustal deformation with horizontal geodetic data

The National Ocean Survey is developing an automated system to derive parameters of horizontal crustal motion from existing geodetic data by the process of least squares estimation. The estimated parameter will describe crustal motion as a function of geographic position. The system will first be tested in the Imperial Valley region of southern California, using data from 8 individual field projects spanning four decades of time.

Snay, R. A.↗

NASA NTRS1974

Thermal regime and temperature stresses in bodies during thermoradiational heating

An approach is developed to the application of the perturbation method for the solution of problems with essential external nonlinearities, based on identification in the boundary condition of a small nonlinear complex which is considered a perturbing function. The solutions obtained in the first approximation with error of 1 to 2% in calculating the unsteady temperature fields are then used to determine the temperature stresses and deformations in solid bodies of classical form.

Chistopyanova, N. V.↗

NASA NTRS1992

Ablative subduction - A two-sided alternative to the conventional subduction model

The plausibility of a two-sided fluid-based model of lithospheric subduction that is based upon current views of lithospheric structure is examined. In this model the viscous lower lithosphere flows downward, and the brittle upper lithosphere deforms in passive response. This process is potentially double-sided, since it is found that even a buoyant plate can be dragged downward by a dense descending neighbor. Thus an apparent overriding plate may be worn away by a process of viscous ablation, with the rate of ablation a function of plate buoyancy. This process, called 'ablative subduction,' makes it possible to simply interpret observations concerning slab profiles, interplate seismicity, back arc tectonics, and complex processes such as double subduction and subduction polarity reversal. When experiments modeling the evolution of simple fluid 'slabs' are performed, slab profile is found to be strongly influenced by ablation in the overriding plate. When ablation is weak, as when a buoyant continent borders the trench, deformable slabs adopt shallow Andean-style profiles.

Tao, Winston C.↗

NASA NTRS1987

Thermoplasticity of coupled bodies in the case of stress-dependent heat transfer

The problem of the thermal stresses in coupled deformable bodies is formulated for the case where the heat-transfer coefficient at the common boundary depends on the stress-strain state of the bodies (e.g., is a function of the normal pressure at the common boundary). Several one-dimensional problems are solved in this formulation. Among these problems is the determination of the thermal stresses in an n-layer plate and in a two-layer cylinder.

Kilikovskaya, O. A.↗

NASA NTRS1986

A mechanism for tectonic deformation on Venus

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface-density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the Venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.

Phillips, Roger J.↗