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NASA NTRS1976

Strain effect on the electronic density of states and dc conductivity of disordered binary alloys

A single-band model calculation is developed for the effect of strain on the temperature variation of the electronic density of states and the electrical onductivity of disordered binary alloys. Experimentally, strain has only a small effect on the temperature variation of the conductivity. Shifts in the Fermi level and distortions of the density of states under different strains are found from the calculations. The small change in the temperature variation of conductivity under strain is a result of competition between these two effects. Methods to extract physical parameters characterizing alloys from measurements of the strain and temperature variation of the resistivity are discussed. Suggestions are also made about materials-selection criteria for strain-gauge applications.

Hwang, H.-C.↗

NASA NTRS1976

Miniature biaxial strain transducer

A reusable miniature strain transducer for use in the measurement of static or quasi-static, high level, biaxial strain on the surface of test specimens or structures was studied. Two cantilever arms, constructed by machining the material to appropriate flexibility, are self-aligning and constitute the transducing elements of the device. Used in conjunction with strain gages, the device enables testing beyond normal gage limits for high strains and number of load cycles. The device does not require conversion computations since the electrical output of the strain gages is directly proportional to the strain measured.

Hoffman, I. S.↗

NASA NTRS1977

Strain gage calibration of a complex wing

Modern complex structural arrangements have complicated the task of measuring flight loads with calibrated strain gages. This paper examines the use of a relatively simple structural model to characterize the load responses of strain gages located on various spars of a delta wing. Strains measured during a laboratory load calibration of a wing structure are compared with calculations obtained from a simplified NASA structural analysis (NASTRAN) model. Calculated and measured influence coefficient plots that show the shear, bending, and torsion characteristics of typical strain-gage bridges are presented. Typical influence coefficient plots are given for several load equations to illustrate the derivation of the equations from the component strain-gage bridges. A relatively simple structural model was found to be effective in predicting the general nature of strain distributions and influence coefficient plots. The analytical processes are shown to be useful in obtaining a good load calibration. The analytical processes cannot, however, be used in lieu of an actual load calibration of an aircraft wing.

Jenkins, J. M.↗

NASA NTRS1979

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Rodal, J. J. A.↗

NASA NTRS1982

Tensile stress-strain behavior of graphite/epoxy laminates

The tensile stress-strain behavior of a variety of graphite/epoxy laminates was examined. Longitudinal and transverse specimens from eleven different layups were monotonically loaded in tension to failure. Ultimate strength, ultimate strain, and strss-strain curves wee obtained from four replicate tests in each case. Polynominal equations were fitted by the method of least squares to the stress-strain data to determine average curves. Values of Young's modulus and Poisson's ratio, derived from polynomial coefficients, were compared with laminate analysis results. While the polynomials appeared to accurately fit the stress-strain data in most cases, the use of polynomial coefficients to calculate elastic moduli appeared to be of questionable value in cases involving sharp changes in the slope of the stress-strain data or extensive scatter.

Garber, D. P.↗

NASA NTRS1983

CLFE2D: A generalized plane strain finite element program laminated composites subject to mechanical and hygrothermal loading

CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.

Buczek, M. B.↗

NASA NTRS1985

Evaluation results of the 700 deg C Chinese strain gauges

Gauges fabricated from specially developed Fe-Cr-Al-V-Ti-Y alloy wire in the Republic of China were evaluated for use in static strain measurement of hot gas turbine engines. Gauge factor variation with temperature, apparent strain, and drift were included. Results of gauge factor versus temperature tests show gauge factor decreasing with increasing temperature. The average slope is -3-1/2 percent/100 K, with an uncertainty band of + or - 8 percent. Values of room temperature gauge factor for the Chinese and Kanthal A-1 gauges averaged 2.73 and 2.12, respectively. The room temperature gauge factor of the Chinese gauges was specified to be 2.62. The apparent strain data for both the Chinese alloy and Kanthal A-1 showed large cycle to cycle nonrepeatability. All apparent strain curves had a similar S-shape, first going negative and then rising to positive value with increasing temperatures. The mean curve for the Chinese gauges between room temperature and 100 K had a total apparent strain of 1500 microstrain. The equivalent value for Kanthal A-1 was about 9000 microstrain. Drift tests at 950 K for 50 hr show an average drift rate of about -9 microstrain/hr. Short-term (1 hr) rates are higher, averaging about -40 microstrain for the first hour. In the temperature range 700 to 870 K, however, short-term drift rates can be as high as 1700 microstrain for the first hour. Therefore, static strain measurements in this temperature range should be avoided.

Hobart, H. F.↗

NASA NTRS1985

Residual thermal and moisture influences on the strain energy release rate analysis of edge delamination

A laminated plate theory analysis is developed to calculate the strain energy release rate associated with edge delamination growth in a composite laminate. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. The strain energy release rate, G, increased when residual thermal effects were combined with applied mechanical strains, but then decreased when increasing moisture content was included. A quasi-three-dimensional finite element analysis indicated identical trends and demonstrated these same trends for the individual strain energy release rate components, G sub I and G sub II, associated with interlaminar tension and shear. An experimental study indicated that for T300/5208 graphite-epoxy composites, the inclusion of residual thermal and moisture stresses did not significantly alter the calculation of interlaminar fracture toughness from strain energy release rate analysis of edge delamination data taken at room temperature, ambient conditions.

Obrien, T. K.↗

NASA NTRS1983

Closed-loop strain controlled testing at elevated temperatures with a non-contacting gage

Normal strains were measured over a 100 micron gage length at a distance of 50 microns from the edge of a notch using a non-contacting, laser-based interferometric technique. Tests were performed at 600 C under direct strain control from this interferometric 'micro-gage'. A minicomputer system, that produced a voltage analog of strain as a final output, controlled the strain measuring apparatus. This analog output was used directly as the feedback signal to a closed-loop, electrohydraulic mechanical test system. This allowed both strain rate and strain amplitude to be controlled at the notch root of the specimen.

Martin, J. F.↗

NASA NTRS1986

Residual thermal and moisture influences on the strain energy release rate analysis of edge delamination

Obrien, T. K.↗

NASA NTRS1989

Procedures for characterizing an alloy and predicting cyclic life with the total strain version of Strainrange Partitioning

Procedures are presented for characterizing an alloy and predicting cyclic life for isothermal and thermomechanical fatigue conditions by using the total strain version of strainrange partitioning (TS-SRP). Numerical examples are given. Two independent alloy characteristics are deemed important: failure behavior, as reflected by the inelastic strainrange versus cyclic life relations; and flow behavior, as indicated by the cyclic stress-strain-time response (i.e., the constitutive behavior). Failure behavior is characterized by conducting creep-fatigue tests in the strain regime, wherein the testing times are reasonably short and the inelastic strains are large enough to be determined accurately. At large strainranges, stress-hold, strain-limited tests are preferred because a high rate of creep damage per cycle is inherent in this type of test. At small strainranges, strain-hold cycles are more appropriate. Flow behavior is characterized by conducting tests wherein the specimen is usually cycled far short of failure and the wave shape is appropriate for the duty cycle of interest. In characterizing an alloy pure fatigue, or PP, failure tests are conducted first. Then depending on the needs of the analyst a series of creep-fatigue tests are conducted. As many of the three generic SRP cycles are featured as are required to characterize the influence of creep on fatigue life (i.e., CP, PC, and CC cycles, respectively, for tensile creep only, compressive creep only, and both tensile and compressive creep). Any mean stress effects on life also must be determined and accounted for when determining the SRP inelastic strainrange versus life relations for cycles featuring creep. This is particularly true for small strainranges. The life relations thus are established for a theoretical zero mean stress condition.

Saltsman, James F.↗

NASA NTRS1989

Development and characterization of PdCr temperature-compensated wire resistance strain gage

A temperature-compensated resistance static strain gage with potential to be used to 600 C was recently developed. Gages were fabricated from specially developed palladium-13 w/o chromium (Pd-13Cr) wire and platinum (Pt) compensator. When bonded to high temperature Hastelloy X, the apparent strain from room temperature to 600 C was within 400 microstrain for gages with no preheat treatment and within 3500 microstrain for gages with 16 hours prestabilization at 640 C. The apparent strain versus temperature relationship of stabilized PdCr gages were repeatable with the reproducibility within 100 microstrain during three thermal cycles to 600 C and an 11 hours soak at 600 C. The gage fabrication, construction and installation is described. Also, the coating system used for this compensated resistance strain gage is explained. The electrical properties of the strain sensing element and main characteristics of the compensated gage including apparent strain, drift and reproducibility are discussed.

Lei, Jih-Fen↗

NASA NTRS1991

Measurements of fuselage skin strains and displacements near a longitudinal lap joint in a pressurized aircraft

Strains and displacements in a small area near a longitudinal lap joint in the fuselage skin of a B737 aircraft were measured during a pressurization cycle to a differential pressure of 6.2 psi while the aircraft was on the ground. It was found that hoop strains were higher than longitudinal strains at each location; membrane strains in the unreinforced skin were higher than in the joint; membrane strains in the hoop direction, as well as radial displacements, tended to be highest at the mid-bay location between skin reinforcements; significant bending in the hoop direction occurred in the joint and in the skin near the joint, and the bending was unsymmetrically distributed about the stringer at the middle of the joint; and radial displacements were unsymmetrically distributed across the lap joint. The interpretation of the strain gage data for locations on the bonded and riveted lap joint assumed that the joint did not contain disbonded areas.

Phillips, Edward P.↗

NASA NTRS1990

A semi-micromechanic interlaminar strain analysis on curved-beam specimens

Experimental analyses were performed for determination of interlaminar strains in circumferentially unidirectional curved beam specimens. Semi-circular and semi-elliptic carbon-epoxy specimens were subjected to opening mode tensile loadings. Whole field measurements were recorded at load levels from about 5 to more than 90 pct of failure loads. Contour maps of displacement fields were obtained by using moire interferometry, using reference gratings of 2400 lines/mm or 60,690 lines/in. Whole field contour maps of circumferential and interlaminar strains were obtained by using moire interferometry in a semi-micromechanic scale. Various anomalous effects were observed in the displacement fields. The zig-zag fringe patterns indicated that the fiber orientation in each layer was not truly circumferential. This deviation from the unidirectionality caused free-edge effects, such as interlaminar shear strains even at the axis of symmetry and the altered normal strains in the thickness direction. In the resin rich zones between layers, the tensile interlaminar strain was excessively large due to the large compliance. As the result of the combined effect of these anomalous behaviors, the values of the interlaminar tensile strains were larger than those predicted analytically. The modulus E sub 3 was actually smaller than the assumed value E sub 2 by 20 pct.

Joh, Duksung↗

NASA NTRS1991

High strain rate properties of off-axis composite laminates, part 2

Unidirectional off-axis graphite/epoxy and graphite/S-glass/epoxy laminates were characterized in uniaxial tension at strain rates ranging from quasi-static to over 500 s(sup -1). Laminate ring specimens were loaded by internal pressure with the tensile stress at 22.5, 30, and 45 degrees relative to the fiber direction. Results were presented in the form of stress-strain curves to failure. Properties determined included moduli, Poisson's ratios, strength, and ultimate strain. In all three laminates of both materials the modulus and strength increase sharply with strain rate, reaching values roughly 100, 150, and 200 percent higher than corresponding static values for the 22.5(sub 8), 30(sub 8), and 45(sub 8) degree laminates, respectively. In the case of ultimate strain no definite trends could be established, but the maximum deviation from the average of any value for any strain rate was less than 18 percent.

Daniel, I. M.↗

NASA NTRS1992

On testing models for the pressure-strain correlation of turbulence using direct simulations

Direct simulations of homogeneous turbulence have, in recent years, come into widespread use for the evaluation of models for the pressure-strain correlation of turbulence. While work in this area has been beneficial, the increasingly common practice of testing the slow and rapid parts of these models separately in uniformly strained turbulent flows is shown in this paper to be unsound. For such flows, the decomposition of models for the total pressure-strain correlation into slow and rapid parts is ambiguous. Consequently, when tested in this manner, misleading conclusions can be drawn about the performance of pressure-strain models. This point is amplified by illustrative calculations of homogeneous shear flow where other pitfalls in the evaluation of models are also uncovered. More meaningful measures for testing the performance of pressure-strain models in uniformly strained turbulent flows are proposed and the implications for turbulence modeling are discussed.

Speziale, Charles G.↗

NASA NTRS1951

Analysis of plane-plastic stress problems with axial symmetry in strain-hardening range

A simple method is developed for solving plane-plastic-stress problems with axial symmetry in the strain-hardening range which is based on the deformation theory of plasticity employing the finite-strain concept. The equations defining the problems are first reduced to two simultaneous nonlinear differential equations involving two dependent variables: (a) the octahedral shear strain, and (b) a parameter indicating the ratio of principal stresses. By multiplying the load and dividing the radius by an arbitrary constant, it is possible to solve these problems without iteration for any value of the modified load. The constant is determined by the boundary condition. This method is applied to a circular membrane under pressure, a rotating disk without and with a central hole, and an infinite plate with a circular hole. Two materials, inconel x and 16-25-6, the octahedral shear stress-strain relations of which do not follow the power law, are used. Distributions of octahedral shear strain, as well as of principal stresses and strains, are obtained. These results are compared with the results of the same problems in the elastic range.

Wu, M H Lee↗

NASA NTRS1994

High temperature strain gage technology for gas turbine engines

This report summarizes the results of a six month study that addressed specific issues to transfer the Pd-13Cr static strain sensor to a gas turbine engine environment. The application issues that were addressed include: (1) evaluation of a miniature, variable potentiometer for use as the ballast resistor, in conjunction with a conventional strain gage signal conditioning unit; (2) evaluation of a metal sheathed, platinum conductor leadwire assembly for use with the three-wire sensor; and (3) subjecting the sensor to dynamic strain cyclic testing to determine fatigue characteristics. Results indicate a useful static strain gage system at all temperature levels up to 1350 F. The fatigue characteristics also appear to be very promising, indicating a potential use in dynamic strain measurement applications. The procedure, set-up, and data for all tests are presented in this report. This report also discusses the specific strain gage installation technique for the Pd-13Cr gage because of its potential impact on the quality of the output data.

Fichtel, Edward J.↗