Showing papers in "Experimental Mechanics in 1968"

High strain-rate testing: Tension and compression

Abstract: Details of the split Hopkinson pressure-bar method for obtaining complete stress-strain curves at strain rates on the order of 1000 sec−1 in either tension or compression are presented. In compression, a gage for measuring radial strain and, therefore, Poisson's ratio is also described. Some typical results are presented for aluminum, and various factors pertaining to the accuracy of the results are discussed.

Application of holography to photoelasticity: Author reports that the two-beam holographic method may be used to record the birefrignent pattern of a standard two-dimensional photoelastic specimen

Abstract: This paper discusses the exploratory application of holography to photoelasticity. It is shown that the two-beam holographic method may be used to record the birefringent pattern of a standard two-dimensional photoelastic specimen. A special type of polariscope is required. A discussion is presented of the various arrangements required to produce isochromatic, isoclinic, isopachic and combined isopachic and isochromatic fringe patterns. The three-dimensional nature of the holograph is utilized to separate the principal stresses by means of oblique incidence. Both normal- and oblique-incidence fringe patterns are recorded on a single hologram. A brief discussion of the extension to the dynamic case is presented.

Application of holography to photoelasticity.

Abstract: This paper discusses the exploratory application of holography to photoelasticity. It is shown that the two-beam holographic method may be used to record the birefringent pattern of a standard two-dimensional photoelastic specimen. A special type of polariscope is required. A discussion is presented of the various arrangements required to produce isochromatic, isoclinic, isopachic and combined isopachic and isochromatic fringe patterns. The three-dimensional nature of the holograph is utilized to separate the principal stresses by means of oblique incidence. Both normal- and oblique-incidence fringe patterns are recorded on a single hologram. A brief discussion of the extension to the dynamic case is presented.

A new experimental stress-optic method: stress-holo- interferometry

Abstract: This paper describes the application of a new interferometric method by holography to photoelasticity. Interferometric photoelasticity is a well established and elegant method; however, its use is still not commonplace in laboratories engaged in stress-optics. In the past few years, there has been a rapid growth in holographic activities. The stress-optic method described in this paper shows an alternate (holographic) method for determining both isochromatic and isopachic interference families, thus enabling a relatively easy and quick solution to plane-elasticity problems. It is also shown how the two material constants which are required can be determined simultaneously with a single calibration test.

The interferometric strain gage

Abstract: The interferometric strain gage consists of two very shallow grooves ruled on a highly polished surface. The grooves are cut with a diamond and are 4×10−5 in. deep and 5×10−3 in. apart. Coherent, monochromatic light from a He−Ne gas laser incident upon these grooves will produce fringe patterns. A fringe pattern with the fringes parallel to the grooves is formed on each side of the impinging beam. The position of these patterns in space is related to the distance between the two grooves. As this distance changes, the fringes shift. Measurement of these fringe shifts enables one to determine the local strain of the specimen.

New optical methods of moiré fringe multiplication

Abstract: Photographs or other replicas of relatively coarse specimen screens can be analyzed with sensitivities corresponding to screens of many thousands of lines per inch (lpi). Moire fringe multiplication is accomplished by collecting specific groups of diffracted beams emanating from two moire screens in series. Three methods are described and multiplication by factors as high as 30 are demonstrated. Sensitivity and accuracy are increased by the fringe-multiplication factor. Usefulness of full-field mechanical differentiation techniques is extended to cases of correspondingly lower strains. These fringe-multiplication methods apply to both bar-and-space screens and transparent diffraction gratings.

An analysis of metal fatigue based on hysteresis energy

Abstract: Halford's plastic-energy concept for lowcycle fatigue is extended to the medium- and high-cycle ranges. The resulting equations are compared with 74 sets of data in the medium- and high-cycle ranges. The difference in stress between theory and experimental data is less than ±5 percent.

Experimental studies of the postbuckling behavior of complete spherical shells

Abstract: In experiments performed on elastic, complete spherical shells of large radius-to-thickness ratio, pressure and volume-displacement instrumentation and photography were used to study postbuckling behavior. Photographs of a number of the distinct modes observed are presented.

A simple procedure for estimating high-temperature low-cycle fatigue

Abstract: Fatigue life for high temperature reversed strain cycling estimated in first approximation from static tensile and creep rupture properties

Some applications of holographic interferometry

Abstract: Holographic interferometry, a new technique for measuring small displacements, is discussed. Application is made to the measure of surface displacements of strained bodies in two specific examples. The curvature of one face of a statically bent bar was examined in detail and compared with the three-dimensional elastic solution. In the second example, the radial-displacement field was measured in the area of the leading edge of a longitudinal compressional stress wave propagating through a bar.

Embedded strain gages for the measurement of strains in rolling contact

Abstract: The paper describes the use of the embedded-strain-gage technique for the measurement of the strain distribution below a circular surface of contact supporting normal and tangential forces while the bodies in contact are rolling together. A brief description is given of the method used for embedding strain gages at very small depths below the surface of a model sphere of epoxy resin. The rig used for pressing the model against another sphere of the same material, driving one of them and restraining the other, is also described together with the instrumentation. A preliminary series of static tests shows that the measured subsurface strains are in good agreement with Hertz's theory of contact. For tests under rolling conditions, the recorded results of a strain gage under different load levels are easily converted to a common nondimensional scale by photographic enlargement or reduction of the original recorded trace. A special Wheatstone-bridge configuration also permits the direct measurement of orthogonal shear strains by combining the output of the gages of embedded rectangular rosettes. Some typical results are given.

Low-cycle fatigue of 7075-T651 aluminum alloy in biaxial bending

Abstract: The uniaxial and biaxial low-cycle-fatigue life of 7075-T651 aluminum alloy in completely reversed bending is investigated. Uniaxial data is obtained from a cantilever specimen, and round and elliptical simply supported plate specimens are used for nominal strain biaxialities of 1∶1, 1∶075 and 1∶0.50 in the plane of the specimen. Experimental data is correlated on the basis of the total octahedral shearing strain range in which the dependent component strains are calculated using the “effective value” of Poisson's ratio for elastic-plastic loading. Good agreement is obtained oetween the uniaxial and biaxial data when the total octahedral shearing-strain range is plotted against the number of cycles to failure in logarithmic coordinates. Also, it is shown that, in anisotropic materials, the directional uniaxial and biaxial low-cycle properties can be predicted from fatigue properties in any one direction if the anisotropy of fracture ductility is known.

Elastic waves in truncated cones

Abstract: An experimental investigation of elastic waves produced by the axial collision of strikers with truncated 2024 aluminum cones with apex angles of 0.48, 5.38, 20, and 30 deg was performed. Wave propagation was initiated at the small end of all four cones and at the large end of the 0.48-deg and 5.38-deg cones. The striker consisted of a 1/2-in.-diam steel ball or a soft phenol-impregnated fiber cylinder. In most cases, impact was caused by firing the striker from an air gun at approximately 1300 ips; in an additional series of tests, a steel ball was dropped on the cone. The metamorphosis of the pulse at the surface of the target was recorded using both foil and semiconductor resistance strain gages. Data were obtained for periods ranging from 200 to 500 μsec; this permitted the observation of several reflections from the ends of the specimen. In several instances, cylindrical aluminum rods were glued to the cone to form a composite target; this permitted observation of the initial pulse incident on the conical section both from surface strain gage and sandwiched crystal records. Studies were also conduced to ascertain the stress distribution across the base of the 20-deg cone.

Experimental critical loads for perforated square plates: Objective of experimental study is to determine critical loads for simply supported square plates with a circular central hole and to compare these results with those predicted by the ritz energy method

Abstract: Experimentally determined critical loads are presented for simply supported square plates with a circular central hole under the action of uniform edge displacements for hole diameters varying up to seventenths the dimension of the plate. The critical load is defined as the inflection point on the load-deflection curve as measured by a set of dial gages at the edge of the hole. Least-squares-curve fitting techniques are used for reducing all experimental data and the entire set of computations is carried out on the electronic digital computer. Finally, it is shown that the experimental results agree well with the theoretical critical loads as determined by the Ritz energy method.

On the use of the ring test for determining rate sensitive material constants

Abstract: An explosive-ring test is reappraised in light of recently developed material-behavior models and analytical predictive techniques. It is demonstrated in complete detail how this test may be utilized to determine the uniaxial flow laws of rate-sensitive perfectly plastic and strain-hardening materials.

Mechanical and optical viscoelastic characterization of Hysol 4290: Time and temperature behavior of Hysol 4290 as obtained from creep tests in conjunction with the time-temperature superposition principle

Abstract: Mechanical and optical characterization of Hysol 4290 as a function of time and temperature is presented. The kinetic theory of polymers, the Williams, Landel and Ferry equation and the time-temperature superposition principle, is discussed. Rubber-like elasticity is used as a simple experimental method to ascertain if the time-temperature superposition should be expected to apply. Finally, the glass-transition temperature of Hysol 4290 is established and its importance in correctly assessing experimental data is discussed.

Moiré-fringe interpolation and multiplication by fringe shifting

Abstract: A simple technique of shifting the master grating to increase the sensitivity of moire measurements is proposed. Details of the technique are described and an application of multiplication by three of a 1000-lines/in. grating is given. It is believed that multiplication by five should be obtainable.

Thoughts on the present and future interrelation of theoretical and experimental mechanics

Abstract: During the last five years, the long-overdue improvement in attitude of academic and other research people toward experimental mechanics has begun. This welcome change is attributed, in large measure, to their renewed interest in the behavior of real materials. Many have come to the realization that idealizations which served them so well for past problems are inadequate not only for living systems but for brittle and ductile fracture of metals, for sufficiently detailed prediction of behavior of composite materials, for incisive application of continuum mechanics on the microscale, and for thermodynamics. An attempt is made to bring out general aspects of a few of these problems of current interest and to show how careful experimentation has produced and interacted with new theoretical developments. A distinction is drawn between a true experiment and one which is no more than an analog computation. Illustrations of misleading analogs are given from both fluid and solid mechanics. Except for some remarks on possible difficulties in distinguishing constitutive relations and boundary conditions in living tissues and body fluids, however, thoughts for the future are restricted to the mechanics and the thermodynamics of solids. Emphasis is placed throughout on the fact that a good experiment and a good theory start at very much the same point and have a great deal in common.

Techniques in infrared photoelasticity - Paper discusses the equipment and experimental procedures which have been employed in the extension of photoelastic measurements into the infrared region

Abstract: The extension o photoelastic methods to spectral ranges other than the visible offers several intersting and potentially profitable possibilities These include a clearer understanding of the phenomenon of birefringence and its relationship to material structure and behavior, an increase in the number and types of useful photoelastic materials, and improved measurement of material behavior, including dispersion of birefringence Indeed, confinement to the narrow visible spectrum unduly restricts this powerful experimental tool

The stress concentration in keyways when torque is transmitted through keys: The electroplating method of strain analysis is used to determine the peak stress at the corner of keyway

Abstract: The stress-concentration factor for keyways is obtained by the electroplating method of strain analysis which was recently developed in Japan. The stresses in keyways are examined under most practical conditions. The shaft to be examined is set in a boss and fixed with a key so that the torque is wholly transmitted to the test piece through the key. To obtain the limit value for a shaft twisted only through a key, the fitting is devised so as to minimize the surface friction at the fitted portion. The results are compared to those reported previously by other authors in which local effects of the key are ignored.

Introduction to high-temperature low-cycle fatigue

Abstract: A better understanding of the problem of high-temperature low-cycle fatigue is important in the use of materials at high temperatures. Some of the metallurgical aspects involved in the problem have been emphasized in this paper. There is a need to relate more closely the observed results with our knowledge of metallurgical processes. This can best be done by a closer working relationship between tween the designer, the materials engineer and the metallurgist.

The production of high-density moiré grids

Abstract: The basic principles and methods of the moire method are well known. Here, some of the procedures and equipment developed by the authors for the production and reproduction of high-line-density grids for strain-measurement purposes are described.

Stresses near a Crack in a Rubber Sheet

Abstract: Crack tip stresses in rubber sheet determined by measuring strain field with imprinted grid work

X-ray diffraction study of residual macrostresses in shot-peened and fatiqued 4130 steel

Abstract: A study has been made of the effects of shot peening and fatigue cycling on the residual macrostresses determined by X-ray methods in an austenitized and tempered AISI 4130 steel (150–170 ksi). The results show that the effect of shot peening is to produce a residual compressive macrostress layer 0.014-in. deep. The residual-stress profile (stress vs. depth) exhibits a small negative stress gradient at and near the surface and a large positive stress gradient in the interior. Stress relaxation (due to fatique cycling) which occurred early in the fatigue history of the specimen was found greater at the surface than in the subsurface layers. Stress gradients of the stress profile increased with continued cycling and varied with depth. A correlation appears to exist between stress relaxation and stress gradients at the surface.

Predicting buckling loads from vibration data: The experimental fundamental frequency is utilized in predicting upper and lower bounds for column-buckling loads when edge partial fixity can be represented by torsional springs. Elastic buckling is assumed

Abstract: There are analytical methods for predicting the buckling loads of columns with the boundaries ideally fixed, i.e., simply supported or built-in, or partially fixed. Vibration-test results may furnish a practical method of measuring the fixity. In this investigation a beam, that may or may not be loaded as a column, is assumed to have a torsional spring at each end such that a zero torsional stiffness corresponds to a simply supported end and an infinite torsional stiffness corresponds to a built-in end. From a Rayleigh-Ritz analysis, the buckling load and the fundamental frequency of the beam are each computed as a function of the torsional stiffness. This procedure leads to a one-to-one nondimensional relationship between the buckling load and the natural frequency. From these calculations, it is seen that regardless of the degree of clamping of one end relative to the other end, all that is needed to predict the buckling load within a 15-percent range is a knowledge of the theoretical buckling load of the simply supported column; the theoretical fundamental frequency of the simply supported beam; and the experimental fundamental frequency. Experimental results are presented to support the theory.

A dynamic photoelastic investigation of stress-wave propagation in cones

Abstract: The embedded-polariscope method was employed to isolate the central plane in cylindrical and conical models subjected to axial loads. Light-field isochromatic-fringe patterns associated with each of the five models studied were recorded by using a multiple-gap camera. Results obtained indicate that the maximum stress decays with distance propagated approximately as indicated by the elementary one-dimensional wave theory.

Gap effect in moiré fringes observed with coherent monochromatic collimated light

Abstract: The phenomenon of the repetitive patterns observed beyond the plane of grating, when using monochromatic collimated light, is discussed. A more complete derivation and discussion of the equation giving the distance from the grating, where the reproduction of the grating will be located, than those introduced previously in the literature is given. The derived equations and the presented discussion are important in the process of moire-pattern observation and in the process of copying masters. Experimental data concerning the location of the gratings and tolerances of this location for a given value of the contrast in the formation of moire patterns, or in copying gratings, are given.

Stress waves in pyramids by photoelasticity

Abstract: The propagation of stress waves in pyramids was studied photoelastically with the application of a laser-photomultiplier tube system and an internal polariscope for recording moving fringes. Dispersion and attenuation of stress waves were considered in a straight bar, a 5-deg pyramid, and a 20-deg pyramid made of Hysol 4290 epoxy plastic. In the straight bar and 5-deg pyramid, longitudinal waves propagate without any dispersion even though the waves attenuate as they progress down the models; in the 20-deg pyramid, however, the dispersion of the stress waves is quite significant. The distributions of the axial and radial stresses and the photoelastic fringe patterns obtained on the 20-deg pyramid show that the stress wave front is spherical with the maximum stress along the central axis of the pyramid. A one-dimensional theory of wave propagation without correction factors in a small-angle infinite cone compares well with the experimental results.

Stress concentrations in bolt-thread roots

Abstract: The apparent geometric origin of fatigue fractures in oversize shank bolts is considered in this report. Bolt-nut interaction between the bolt and both a standard nut and a special nut are investigated. The “frozen stress” method of three-dimensional stress analysis was used to determine the magnitudes and locations of points of stress concentration in plastic models of both the oversize shank bolt and a standard bolt in combinations with standard and special nuts. The results indicate that, for installations in which the special nut is used, bolt geometry may be the controlling factor in determining the fatigue life of the boltnut combination, because the stress-concentration factors due to the nut loading are of the same order of magnitude as the stress-concentration factors due solely to bolt geometry. On the other hand, for installations in which standard nuts are used, the nut-induced stress-concentration factors are much larger than those due to bolt geometry; so, bolt geometry will have less effect on the fatigue performance of the combination. If the nut is threaded onto the bolt so far that the first loaded thread of the nut is in the thread-runout area of the bolt, fatigue performance of the installation will be greatly reduced due to the combination of stress-concentration factors from thread loading and section change and, again, bolt geometry may be a prominent causative factor.

Rapid interpretation of moiré photographs

Abstract: The paper describes the possibilities of rapidly and conveniently obtaining results by means of the reflection moire method. The moire photographs are produced with the aid of a screen provided with a finely ruled grid. The contrast of the photographs is increased by optical means. By displacement of two equal moire photographs, moire fringes of second order for the curvature or the twist are obtained. It is shown how charts can be produced which indicate: