SEARCH · Search NASA

Results for “ELASTIC CONSTANT”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS1991

On the strain energy of laminated composite plates

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Atilgan, Ali R.↗

NASA NTRS1990

High temperature materials characterization

A lab facility for measuring elastic moduli up to 1700 C was constructed and delivered. It was shown that the ultrasonic method can be used to determine elastic constants of materials from room temperature to their melting points. The ease in coupling high frequency acoustic energy is still a difficult task. Even now, new coupling materials and higher power ultrasonic pulsers are being suggested. The surface was only scratched in terms of showing the full capabilities of either technique used, especially since there is such a large learning curve in developing proper methodologies to take measurements into the high temperature region. The laser acoustic system does not seem to have sufficient precision at this time to replace the normal buffer rod methodology.

Workman, Gary L.↗

NASA NTRS1991

Resonant Acoustic Determination of Complex Elastic Moduli

A simple, inexpensive, yet accurate method for measuring the dynamic complex modulus of elasticity is described. Using a 'free-free' bar selectively excited in three independent vibrational modes, the shear modulus is obtained by measuring the frequency of the torsional resonant mode and the Young's modulus is determined from measurement of either the longitudinal or flexural mode. The damping properties are obtained by measuring the quality factor (Q) for each mode. The Q is inversely proportional to the loss tangent. The viscoelastic behavior of the sample can be obtained by tracking a particular resonant mode (and thus a particular modulus) using a phase locked loop (PLL) and by changing the temperature of the sample. The change in the damping properties is obtained by measuring the in-phase amplitude of the PLL which is proportional to the Q of the material. The real and imaginary parts or the complex modulus can be obtained continuously as a function of parameters such as temperature, pressure, or humidity. For homogeneous and isotropic samples only two independent moduli are needed in order to characterize the complete set of elastic constants, thus, values can be obtained for the dynamic Poisson's ratio, bulk modulus, Lame constants, etc.

Brown, David A.↗

NASA NTRS1991

Nonlinear response of resin matrix laminates using endochronic theory

The nonlinear response of laminated, resin matrix fibrous composites is modeled using orthotropic endochronic theory. The theory is formulated in terms of elastic constants and endochronic parameters characterizing the linear and nonlinear response, respectively, of unidirectional composites. All constants and parameters can be determined from normal (tension and/or compression) and shear tests on unidirectional and off-axis specimens. The nonlinear constitutive response relations for the unidirectional lamina are presented and the procedure for determining constants and parameters from test is described. The results are then used to predict the nonlinear response of unidirectional laminae and angle-ply laminates. Comparison between theory and experiment for compression loading of AS4/3502 graphite-epoxy, angle-ply laminates shows excellent correlation.

Mathison, S. R.↗

NASA NTRS1992

Stiffnesses by (TtN) ensemble molecular dynamics

Calculation of elastic constants requires initializing a lattice of atoms, an h matrix defining the computational cell boundaries, and the parameters defining the interatomic potentials, then numerically integrating the equations of motion for the atoms and the computational cell boundaries, calculating strains and stresses at each timestep, and updating at each timestep the average quantities required for calculation of fluctuations. Enforcements of the DYNAMO FORTRAN code included addition of documentation, improved memory management and data flow, and enabling use of several interatomic potentials. Documentation included headers for each subroutine, which document the parameters input to the routine, algorithms employed, and output.

Tibbits, Patrick↗

NASA NTRS1993

Approximating the stress field within the unit cell of a fabric reinforced composite using replacement elements

This report concerns the prediction of the elastic moduli and the internal stresses within the unit cell of a fabric reinforced composite. In the proposed analysis no restrictions or assumptions are necessary concerning yarn or tow cross-sectional shapes or paths through the unit cell but the unit cell itself must be a right hexagonal parallelepiped. All the unit cell dimensions are assumed to be small with respect to the thickness of the composite structure that it models. The finite element analysis of a unit cell is usually complicated by the mesh generation problems and the non-standard, adjacent-cell boundary conditions. This analysis avoids these problems through the use of preprogrammed boundary conditions and replacement materials (or elements). With replacement elements it is not necessary to match all the constitutional material interfaces with finite element boundaries. Simple brick-shaped elements can be used to model the unit cell structure. The analysis predicts the elastic constants and the average stresses within each constituent material of each brick element. The application and results of this analysis are demonstrated through several example problems which include a number of composite microstructures.

Foye, R. L.↗

NASA NTRS1992

Variable frequency pulsed phase-locked loop method for measuring material nonlinearity

The design of a pressure vessel with an isothermal volume to measure changes in the natural velocities of material continuously over a wide temperature range is reported. Highly sensitive pulsed phase-locked loop technology is used to measure the natural velocity of fatigued aluminum 2024-T4 as a function of pressure at different temperatures. Second derivative variations with respect to pressure and temperature are found to exhibit order-of-magnitude changes at a gauge pressure near 950 kPa at room temperature. This indicates a significant change in certain combinations of second-order and higher-order elastic constants at relatively low pressures. Fractional frequency change as a function of applied pressure for aluminum 2024-T4 with fatigue damage is illustrated.

Yost, William T.↗

NASA NTRS1955

Shearing Effectiveness of Integral Stiffening

Values of coefficients for defining the effectiveness of integral stiffeners in resisting shear deformations of the plate of which they are an integral part are presented for a variety of proportions of rectangular stiffeners with circular fillets. Formulas are given in which these coefficients may be employed to calculate the elastic constants associated with the twisting and shearing of integrally stiffened plates. The size of fillet radius is shown to contribute appreciably to the degree of penetration of the stresses from the skin into the stiffener.

Crawford, Robert F↗

NASA NTRS1994

Thermal expansion and elastic anisotropy in single crystal Al2O3 and SiC reinforcements

In single crystal form, SiC and Al2O3 are attractive reinforcing components for high temperature composites. In this study, the axial coefficients of thermal expansion and single crystal elastic constants of SiC and Al2O3 were used to determine their coefficients of thermal expansion and Young's moduli as a function of crystallographic orientation and temperature. SiC and Al2O3 exhibit a strong variation of Young's modulus with orientation; however, their moduli and anisotropies are weak functions of temperature below 1000 C. The coefficients of thermal expansion exhibit significant temperature dependence, and that of the non-cubic Al2O3 is also a function of crystallographic orientation.

Salem, Jonathan A.↗

NASA NTRS1994

Hydrogen and related materials at high density: Physics, chemistry and planetary implications

Recent studies of low-Z molecular materials including hydrogen to multimegabar pressures (less than 300 GPa) have uncovered a range of phenomena relevant to understanding the nature of the interiors of the outer planets and their satellites. Synchrotron x ray diffraction measurements (to 42 GPa) have been used to determine the crystal structure of the solid (hexagonal-close packed) and equation of state. Sound velocities in fluid and solid hydrogen (to 24 GPa) have been inverted to obtain elastic constants and aggregate bulk and shear moduli. In addition, an improved intermolecular potential has been determined which fits both static and shock-wave data. Use of the new potential for the molecular envelope of Jupiter suggests the need for major revisions of existing Jovian models or a reanalysis of reported free oscillations for the planet. Studies at higher pressures (greater than 100 GPa) reveal a sequence of pressure-induced symmetry-breaking transitions in molecular hydrogen, giving rise to three high-pressure phases (1, 2, and 3). Phase 1 is the rotationally disordered hcp phase which persists from low pressure to well above 100 GPa at high temperature (e.g., 300 K). Phase 2 is a low-temperature, high-pressure phase (transition at 100 GPa and 77 K in H2) with spectral features indicative of partial rotational ordering and crystallographic distortion. The transition to Phase 3 at 150 GPa is accompanied by a weakening of the molecular bond, gradual changes in orientational ordering, strong enhancement of the infrared intramolecular vibrational absorption, and strong intermolecular interactions similar to those of ambient-pressure network solids. Studies of the phase diagram reveal a triple point near 130 K and 160 GPa. Higher pressure measurements of vibrational spectra place a lower bound of approximately 250 GPa on the predicted transition pressure for dissociation of molecular hydrogen to form a monatomic metal.

Hemley, R. J.↗

NASA NTRS1994

Crystalline structure and symmetry dependence of acoustic nonlinearity parameters

A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born-Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face-centered-cubic solids provide a qualitative explanation for the dependence of the acoustic nonlinearity parameters on modal direction.

Cantrell, John H.↗

NASA NTRS1995

Micromechanical models for textile structural composites

The objective is to develop micromechanical models for predicting the stiffness and strength properties of textile composite materials. Two models are presented to predict the homogeneous elastic constants and coefficients of thermal expansion of a textile composite. The first model is based on rigorous finite element analysis of the textile composite unit-cell. Periodic boundary conditions are enforced between opposite faces of the unit-cell to simulate deformations accurately. The second model implements the selective averaging method (SAM), which is based on a judicious combination of stiffness and compliance averaging. For thin textile composites, both models can predict the plate stiffness coefficients and plate thermal coefficients. The finite element procedure is extended to compute the thermal residual microstresses, and to estimate the initial failure envelope for textile composites.

Marrey, Ramesh V.↗

NASA NTRS1995

Modeling the Properties of 3D Woven Composites

An extensive study has been completed of the internal geometry, the mechanisms of failure, and the micromechanics of local failure events in graphite/epoxy composites with three dimensional (3D) woven reinforcement. This work has led to the development of models for predicting elastic constants, strength, notch sensitivity, and fatigue life. A summary is presented here.

Cox, Brian N.↗

NASA NTRS1996

Computational Materials Research

Computational Materials aims to model and predict thermodynamic, mechanical, and transport properties of polymer matrix composites. This workshop, the second coordinated by NASA Langley, reports progress in measurements and modeling at a number of length scales: atomic, molecular, nano, and continuum. Assembled here are presentations on quantum calculations for force field development, molecular mechanics of interfaces, molecular weight effects on mechanical properties, molecular dynamics applied to poling of polymers for electrets, Monte Carlo simulation of aromatic thermoplastics, thermal pressure coefficients of liquids, ultrasonic elastic constants, group additivity predictions, bulk constitutive models, and viscoplasticity characterization.

Hinkley, Jeffrey A.↗

NASA NTRS1997

Trans-Laminar-Reinforced (TLR) Composites

A Trans-Laminar-Reinforced (TLR) composite is defined as composite laminate with up to five percent volume of fibrous reinforcement oriented in a 'trans-laminar' fashion in the through-thickness direction. The TLR can be continuous threads as in 'stitched laminates', or it can be discontinuous rods or pins as in 'Z-Fiber(TM) materials. It has been repeatedly documented in the literature that adding TLR to an otherwise two dimensional laminate results in the following advantages: substantially improved compression-after-impact response; considerably increased fracture toughness in mode 1 (double cantilever beam) and mode 2 (end notch flexure); and severely restricted size and growth of impact damage and edge delamination. TLR has also been used to eliminate catastrophic stiffener disbonding in stiffened structures. TLR directly supports the 'Achilles heel' of laminated composites, that is delamination. As little as one percent volume of TLR significantly alters the mechanical response of laminates. The objective of this work was to characterize the effects of TLR on the in-plane and inter-laminar mechanical response of undamaged composite laminates. Detailed finite element models of 'unit cells', or representative volumes, were used to study the effects of adding TLR on the elastic constants; the in-plane strength; and the initiation of delamination. Parameters investigated included TLR material, TLR volume fraction, TLR diameter, TLR through-thickness angle, ply stacking sequence, and the microstructural features of pure resin regions and curved in-plane fibers. The work was limited to the linear response of undamaged material with at least one ply interface. An inter-laminar dominated problem of practical interest, a flanged skin in bending, was also modeled.

Hinders, Mark↗

NASA NTRS1997

Determination of Residual Stress in Composite Materials Using Ultrasonic Waves

The performance of high temperature composites can be significantly affected by the presence of residual stresses. These stresses arise during cooling processes from fabrication to room temperature due to mismatch of thermal expansion coefficients between matrix and fiber materials. This effect is especially pronounced in metal matrix and intermetallic composites. It can lead to plastic deformations, matrix cracking and fiber/matrix interface debonding. In this work the feasibility of ultrasonic techniques for residual stress assessment in composites is addressed. A novel technique for absolute stress determination in orthotropic materials from angular dependencies of ultrasonic velocities is described. The technique is applicable for determination of both applied and residual stresses and does not require calibration measurements on a reference sample. The important advantage of this method is that stress is determined simultaneously with stress-dependent elastic constants and is thus decoupled from the material texture. It is demonstrated that when the principal plane stress directions coincide with acoustical axes, the angular velocity data in the plane perpendicular to the stress plane may be used to determine both stress components. When the stress is off the acoustical axes, the shear and the difference of the normal stress components may be determined from the angular dependence of group velocities in the plane of stresses. Synthetic sets of experimental data corresponding to materials with different anisotropy and stress levels are used to check the applicability of the technique. The method is also verified experimentally. A high precision ultrasonic wave transmission technique is developed to measure angular dependence of ultrasonic velocities. Examples of stress determination from experimental velocity data are given. A method is presented for determination of velocities of ultrasonic waves propagating through the composite material with residual stresses. It is based on the generalized self-consistent multiple scattering model. Calculation results for longitudinal and shear ultrasonic wave velocities propagating perpendicular to the fibers direction in SCS-6/Ti composite with and without residual stresses are presented. They show that velocity changes due to presence of stresses are of order 1%.

Rokhlin, S. I.↗

NASA NTRS1999

Ultrasonic Nondestructive Characterization of Adhesive Bonds

Adhesives and adhesive joints are widely used in various industrial applications to reduce weight and costs, and to increase reliability. For example, advances in aerospace technology have been made possible, in part, through the use of lightweight materials and weight-saving structural designs. Joints, in particular, have been and continue to be areas in which weight can be trimmed from an airframe through the use of novel attachment techniques. In order to save weight over traditional riveted designs, to avoid the introduction of stress concentrations associated with rivet holes, and to take full advantage of advanced composite materials, engineers and designers have been specifying an ever-increasing number of adhesively bonded joints for use on airframes. Nondestructive characterization for quality control and remaining life prediction has been a key enabling technology for the effective use of adhesive joints. Conventional linear ultrasonic techniques generally can only detect flaws (delamination, cracks, voids, etc) in the joint assembly. However, more important to structural reliability is the bond strength. Although strength, in principle, cannot be measured nondestructively, a slight change in material nonlinearity may indicate the onset of failure. Furthermore, microstructural variations due to aging or under-curing may also cause changes in the third order elastic constants, which are related to the ultrasonic nonlinear parameter of the polymer adhesive. It is therefore reasonable to anticipate a correlation between changes in the ultrasonic nonlinear acoustic parameter and the remaining bond strength. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasonic wave passes through a nonlinear material. It seems that such nonlinearity can be effectively used to characterize bond strength. Several theories have been developed to model this nonlinear effect. Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented. Recently, a comparison between the experimental and simulated results based on a similar theoretical model was presented. A through-transmission setup for water immersion mode-converted shear waves was used to analyze the ultrasonic nonlinear parameter of an adhesive bond. In addition, ultrasonic guided waves have been used to analyze adhesive or diffusion bonded joints. In this paper, the ultrasonic nonlinear parameter is used to characterize the curing state of a polymer/aluminum adhesive joint. Ultrasonic through-transmission tests were conducted on samples cured under various conditions. The magnitude of the second order harmonic was measured and the corresponding ultrasonic nonlinear parameter was evaluated. A fairly good correlation between the curing condition and the nonlinear parameter is observed. The results show that the nonlinear parameter might be used as a good indicator of the cure state for adhesive joints.

Qu, Jianmin↗

NASA NTRS2001

Fracture Behavior of a Stitched Warp-Knit Carbon Fabric Composite

Tests were conducted on several types of fracture specimens made from a carbon/epoxy composite. The composite material was stitched prior to introducing epoxy resin. Boeing, used this material to develop a composite wing box for a transport aircraft in the NASA Advanced Composites Transport Program. The specimens included compact, extended compact, and center notched tension specimens. The specimens were cut from panels with three orientations in order to explore the effects of anisotropy. The panels were made with various thicknesses to represent a wing, skin from tip to root. All fractures were not self-similar depending on specimen type and orientation. Unnotched tension specimens were also tested to measure elastic constants and strengths. The normal and shear strains were calculated on fracture planes using a series representation of strain fields for plane anisotropic crack problems. The fracture parameters were determined using a finite element method. Characteristic distances for critical tension and shear strains were calculated for each specimen and a failure criterion based on the interaction of tension and shear strains was proposed.

Poe, Clarence C., Jr.↗