Showing papers in "Experimental Mechanics in 1967"

A thin-plate analysis and experimental evaluation of couple-stress effects

Abstract: Couple-stress effects in materials have received much theoretical consideration recently but little or no experimental verification. The first part of this paper deals with a simplified elastic analysis for thin plates with couple stress which should provide a simple experimental approach to the determination of the order of magnitude of these effects. Classical concepts were utilized where applicable and many existing solutions can be modified by the present analysis to include couple stress.

Experimental studies of the buckling of complete spherical shells.

Abstract: Imperfections effect on buckling of complete electroformed spherical shells under uniform external pressure examined in rigid and soft testing systems

Determination of natural frequencies of vibration of a sandwich plate

Abstract: In this paper, an expression is derived for the natural frequencies of vibration of a simply supported sandwich plate. Experimental procedures and results for the subject problem are presented. The experimental data obtained are in good agreement with the theoretical results. A literature survey1, 2 shows that no work has been done on the experimental determination of natural frequencies of vibration of sandwich plates. A general analysis of flexural vibrations of elastic sandwich plates was presented by Yu in Ref. 3. The vibration analysis based upon this theory is, in general, very complicated due to the high order of the equations. It was then simplified4 for low-frequency ranges and for ordinary sandwich plates.

Sharpening and multiplication of moiré fringes: Moiré patterns of modified intensity distribution are analyzed and demonstrated

Abstract: Moire fringe sharpening is produced when the widths of clear and opaque bands in a pair of super-imposed screens are complementary. Fringe multiplication is produced when the frequency of lines in the reference screen exceeds the frequency in the specimen screen by an integral factor. The number of moire fringes then formed corresponds to the greater frequency.

Experimental mechanics at velocity extremes —Very high strain rates

Abstract: The early experimental work of Clark and Wood with regard to von Karman's theory on the effect of material flow and fracture at high strain rates has led to many controversial issues on these effects. Interest has been greatly revived in recent years because of the increased emphasis on such high-velocity forming processes as explosive and capacitor discharge. Considerable new work has been performed by Ling-Temco-Vought, Inc., for the Air Force, the results of which are presented in this paper. Data have been accumulated on tensile and compression specimens, spherical bulging and cylindrical bulging for a wide variety of materials. This high-speed information has been generated with the use of a special projectile impact machine and special presses utilizing various combinations of explosive and capacitor-discharge energy, with strain rates to 101/sec. The effect of velocity on ductility is discussed for total strain distribution, uniform strain, double necking and critical impact velocity. The modes of failure for various part shapes are presented and related to the forming velocity.

Techniques for testing structures permitted to sway.

Abstract: Mechanisms are described that eliminate the restraining effects of the loads and the lateral bracing on test specimens permitted to sway. One mechanism, called the gravity-load simulator, maintains a vertical orientation of load even as a structure sways. The other is a lateral-bracing mechanism which moves freely with a test structure even at large deflections, and it does not require any adjustments during a test. A gravity-load simulator and a lateral-bracing system designed for use in testing full-size building frames on the equipment itself and tests of building frames utilizing the mechanisms show very satisfactory behavior of the gravity-load simulator and the lateral-bracing system. Some actual test setups using the mechanisms are described. Tests on three-story full-size building frames (30-ft high) and a frame-buckling test are included.

New methods in photoelasticity

Abstract: The principle of polarization of scattered light is applied to determine the principal stresses in the interior of a model. On the basis of the theorem which states that “a series of birefringents is equivalent to a unique birefringent, followed by a medium endowed with rotational power,” it can be assumed that, if the characteristics of a series of birefringents are known, it is possible to find the characteristics of an interior section. The measurement of the characteristics of a birefringent (eventually following a medium endowed with rotational power) can be accomplished by means of the new methods, making use of a photomultiplier, a constant-speed rotating analyzer and a servomechanism These new methods of measurement are applicable to two-dimensional photoelasticity.

The mechanical and optical characterization of a solithane 113 composition

Abstract: A complete mechanical and optical characterization is obtained from constant-strain-rate tests for a typical Solithane 113 composition, a urethane-rubber compound having high birefringent sensitivity and excellent optical-transmission properties. Its viscoelastic transition region is found to span about six decades of logarithmic time, somewhat narrower than for other materials of the urethane family.

Detection and study of compressor-blade vibration

Abstract: The many compressor blades in modern axially staged gas turbines are susceptible to vibration. The energy exciting the vibrations comes from many sources which are discussed. The vibratory stresses generated must be experimentally determined. A new device capable of detecting rotor-blade vibration without contact is described.

The gross hydrostatic-pressure effect as related to foil and wire strain gages

Abstract: An analysis of gross pressure effect for strain gages is presented. This is defined as the difference between the predicted hydrostatic strain and the experimental strain. Values of the theoretical strain per unit pressure are based on the Voigt-Reuss-Hill approximation using published values of elastic moduli and compliances. These theoretical values are adjusted by the pressure effect calculated from an equation based on the assumption that the pressure effect is independent of the elastic properties of the substrate. The modified values of theoretical strain per unit pressure are then compared with the experimentally observed values. The differences are small except for the substrate materials of zinc, cadmium and lead. Experimental pressure-strain data are presented for constantan foil gages mounted on tungsten, copper, tin, molybdenum, titanium, cadmium, brass, zinc and lead as well as constantan wire gages mounted on steel, aluminum and magnesium for hydrostatic pressures up to 140 ksi. Data for foil and wire gages mounted with various adhesives are presented and show that the adhesive or backing materials appear to have a relatively minor effect on the over-all gage performance.

Moiré topography of curved surfaces

Abstract: A physical surface presents a macroscopic curvature and a microscopic curvature, associated with roughness, which is superimposed on the former. Moire techniques developed in this paper deal with the measurement of partial slopes and macroscopic curvatures of cylindrical and conical shells due to loading. Two distinct techniques are presented, capable of measuring both the undeformed shape of the shell, as well as small departures from the initial shape due to loading. The first one yields the deflection-contour pattern of the loaded shell by bringing into interference the lines of a reference grating, placed close to the matt surface of the shell, and their shadows cast on this surface. The second one provides patterns of partial-slope contours by bringing into interference the reflected lines of a reference grating, placed at a distance apart from the specularly reflecting surface of the shell, and a second grating named the specimen grating. For the complete definition of the surface, an orthogonal set of partial-slope contour or curvature patterns is needed. Either method is sufficient for the evaluation of the moment and strain distribution of the loaded shell, with the second method being more sensitive and accurate. Illustrative examples are given for both methods.

Buckling of unstiffened conical shells under combined loading

Abstract: An experimental program was conducted in order to determine the family of interaction curves for the buckling of unstiffened conical shells under combined axial compression, torsion, and external or internal pressure. Careful experimental technique permitted many repeated buckling tests on the same aluminumalloy shell without noticeable damage and yielded reliable interaction curves. Results of combined-loading tests are presented and compared with linear theory. Test results show that the interaction curve for compression-torsion-pressure loading is defined by superposition of compression-pressure, torsion-pressure and compression-torsion behavior.

The generic nature of the absolute-retardation method of photoelasticity

Abstract: The method of absolute-retardation measurements does not depend upon the use of any specific interferometer. Any one of the many extended field interferometers can be employed, including the Series, Michelson, Mach-Zehnder and Fizeau types. Where adequate monochromatic purity of light source is available, reflections from the two surfaces of the model can form the interferogram, thus dispensing with the necessity of any separate optical interferometer.

Experimental and theoretical determination of frequencies of elastic toroids: Paper describes an experimental investigation conducted to determine the accuracy and the convergence of the method of internal constraints in the case of toroid

Abstract: Experiments are described which determine natural frequencies of five toroidal models whose major diameters are of 10 in. and whose minor diameters vary from 0.25 to 2 in. The experimentally determined frequencies are compared with the theoretical frequencies derived using the elementary theories for the in-plane and out-of-plane vibrations of circular rings of R. Hoppe and J. H. Michell, as well as the method of internal constraints. The comparative results for the frequencies are presented in tabular form.

On the definitions of strain and their use in large-strain analysis

Abstract: It is pointed out that when strains are computed from a displacement field, the engineering definition of strain(l f −l i )/l i has advantages in respect to other definitions used in finite-strain theory Tensorial transformations can still be used easily by means of Mohr's circle Illustrations for the case of Eulerian and Lagrangian strains are shown The comments may be of particular interest to experimental analysts

Transient analysis in a fracturing magnesium plate

Abstract: Transient displacement and strain distributions in the vicinity of running-crack tips were determined experimentally in centrally notched magnesium plates. The moire-fringe technique was used together with a Q-spoiled laser which was the light source for single-flash photography. The specimen was designed such that net-section yield occurred prior to fracture and, thus, the crack propagated through the yielded region. Displacement distributions in the vicinity of such running-crack tips were found to vary as $$\sqrt r $$ for radial distances as close asr=0.08 in. Transient moire-fringe patterns were then differentiated graphically to obtain longitudinal strain distributions in the vicinities of running-crack tips. These transient-displacement and transient-strain distributions were compared with equivalent static results. For this ductile material, both the transient and static results showed qualitative agreement with the displacement and strain distributions in an infinitely elastic plate in the region ahead of the crack tip. For the region above the crack tip, the transient and static results differed appreciably.

Experimental and theoretical studies of explosive-induced large dynamic and permanent deformations of simple structures

Abstract: Explosive-loading and structural-response measurement techniques are described for obtaining definitive large dynamic and permanent-deformation data on simple structures which undergo (a) two-dimensional deformations, or (b) general three-dimensional deformations. In the former category, explosively loaded structures discussed include freely suspended single-layer circular rings, freely suspended unbonded concentric rings, and flat circular plates with clamped edges. Representing category (b) is an explosively loaded cylindrical panel with clamped edges. To define the impulse which was imparted explosively to these structures, appropriate impulse-calibration tests were performed on high-explosive-loaded single-layer and unbonded double-layer specimens; these testing techniques and the results obtained are discussed.

Similarity in Thermoelasticity

Abstract: A set of similarity relationships is developed and discussed for use in the study of transient and steadystate thermal displacements, strain and stresses between model and prototype. The similarity relationships are shown to be dependent upon the existing state of stress in the thermally loaded member. Their utilization in the design or analysis of data for such experimental techniques as photoelasticity and the moire method is cited.

A dual-observation method for determining photoelastic parameters in scattered light

Abstract: A dual-observation method is developed for determining photoelastic parameters in scattered light. Using this method, the intensities of scattered light along two directions of observation, making an angle of 45 deg in a plane normal to the beam, are recorded simultaneously without rotation of either the beam or the model. Photoelastic parameters are evaluated from these records. The theory of the method, the apparatus and techniques, as well as an illustrative experiment, are reported.

Propagation of a stress pulse in a viscoelastic rod

Abstract: Experimental work is reported on the propagation of a stress pulse in a viscoelastic waveguide. The data obtained are compared with results of analysis using one-dimensional wave-propagation theory.

Effect of photographic-film nonlinearities on the processing of moiré-fringe data

Abstract: It is shown that the effect of the nonlinear characteristic curve of a film on a narrow-band moire signal is to generate, for each narrow-band component of the moire signal, an infinite number of narrow-band, high-order harmonics of the fundamental argument. According to this result, the elimination of the film nonlinearity can be achieved by means of band-pass filters. Two examples are given to show that the elimination predicted theoretically can be achieved in practice.

On the direct measurement of very large strain at high strain rates

Abstract: When dynamic plastic strain exceeds 4-percent deformation in completely annealed polycrystalline aluminum, difficulties in the optical measurment of strain occur because of changes in the diffuse-ambient-background light arising from the growth of a mottled surface, or “organe peel.”

Stress concentrations due to sharp notches

Abstract: A photoelastic technique has been developed to determine accurately the fringe order of a sharp notch, i.e., as small as 0.0019 in. in radius, to within ±0.0004 in. of the boundary. The stress is frozen into the specimen, enabling careful study of the specimen. Experimental results are discussed and compared to values obtained from some existing theoretical solutions.

A comparison of stress-concentration factors in hyperbolic and U-shaped grooves

Abstract: A two-dimensional photoelastic study was made of a statically loaded tension bar with symmetrical hyperbolic grooves in series with a section containing U-shaped grooves. The influence of the depth of the grooves was examined, and stress-concentration factors were determined using the self-calibrating source of stress-concentration method.

Moiré fringes as parametric curves

Abstract: Advantage is taken in this paper of the parametric properties of families of curves to express in a simple manner several fundamental properties of moire fringes. Attention is called, in particular, to the necessary limitations on the angle of rotation of two gratings, and on the magnitude of their difference in pitch, to obtain an easily interpretable moire-fringe pattern.

Two types of high-temperature weldable strain gages: Ni−Cr half-bridge filaments and Pt−W half-bridge filaments

Abstract: The historical development of the single active and “true” (zero gage factor) dummy weldable strain gage is reviewed. The combination of these devices into a half-bridge gage results in transducers capable of static-strain measurements at temperatures of 650 and 950° F for Ni−Cr alloy elements and Pt−W alloy elements, respectively. General application notes concerning these instruments are also included.