Showing papers in "Experimental Mechanics in 1969"

Stress-strain data obtained at high rates using an expanding ring

Abstract: Dynamic uniaxial tensile stress-strain data are obtained at high strain rates by measuring the kinematics of thin-ring specimens expanding symmetrically by virtue of their own inertia. Impulsively loaded to produce high initial radial velocities, expanding rings are decelerated by the radial component of the hoop stresses. Differential equations of motion are evaluated experimentally to obtain the stress-strain (constitutive) relationships which govern the magnitude of these stresses. Techniques have been developed for producing symmetric radial expansion and measuring resulting displacements precisely as a function of time. Dynamic stress-strain relationships have been obtained for 6061-T6 aluminum, 1020 cold-drawn steel, and 6Al-4V titanium. For each of these materials, displacement-time curves are observed to be parabolic within the resolution of the measurements. Results are presented as true-stress/true-strain relationships.

Determination of mechanical properties of the bones of the skull

Abstract: This paper presents the initial results of a research project concerning the mechanism of head injury. In order to begin to define the mechanism, it is necessary to determine mechanical properties of the various skull bones, organize them into constitutive equations, and develop a structural model of the skull.

Defect microstructure and mechanical properttes in shock-hardened metals - The relationship of defect microstructure and mechanical properties in shock-hardened metals and alloys and the comparison with simply compressed and cold-rolled metals was investigated by transmission electron microscopy

Abstract: This paper is concerned primarily with the direct observation of shock-induced defect microstructures in 70/30 brass, 304 stainless steel and copper; and the attempt to relate the microstructural features observed with experimentally determined mechanical properties. The method of direct observation utilizes both bright- and dark-field transmission electron microscopy. Some attention is also given to the relationship of shock-induced defect structures to those resulting from conventional modes of deformation such as simple compression and cold reduction by rolling. It is shown, through the use of the electron microscope, that structures in stainless steel vary greatly with the mode of deformation. Some consideration is also given to the apparent role of stacking-fault energy in determining residual-shock structures in fcc metals and alloys.

Experimental-theoretical correlations of impulsively loaded clamped circular plates

Abstract: Clamped circular plates are impulsively loaded with sheet explosive, and the resulting large-defection response is monitored using a high-speed streak camera, and dynamic-strain measurements. Dynamic and final-plate deflections as well as strain-time histories of various locations on the plates are compared to deflections and strains obtained with the elastic-plastic structural computer program DEPROSS. It is shown that DEPROSS adequately computes the dynamic response of this highly nonlinear biaxial-stress problem.

Recording dynamic fringe patterns with a Cranz-Schardin camera

Abstract: The requirements of a high-speed recording system in dynamic photoelastic studies are closely met with a Cranz-Schardin camera. This camera, which operates at framing rates between 32,000 and 815,000 frames/sec, is capable of resolving a dynamic fringe pattern with a fringe gradient of 20 fringes/in. traveling with a velocity of 75,000 ips. Design details of the Cranz-Schardin system are given, and typical results obtained are illustrated.

Application of birefringent coatings to glass-fiber-reinforced plastics

Abstract: The application of birefringent coatings to plane-stress problems associated with orthotropic-glassreinforced plastic materials is treated. The improvement in the sensitivity of the birefringent-coating method due to the high strength and low modulus of the glassfiber-reinforced plastic materials is noted. Next, the effect of a mismatch in Poisson's ratio between the specimen material and coating is examined and a correction factor is developed which permits determination of boundary stresses even when the mismatch is large. Finally, the stress-strain relations for an orthotropic material are reviewed and an example of a nonsymmetric stress distribution associated with a symmetric fringe pattern is covered.

Measurement of microscopic plastic-strain distributions in the region of a crack tip

Abstract: Two independent experimental techniques are used to measure the strain distribution within the plastically deformed region around a crack tip. Moire grid interference is used to measure the in-plane strain with the specimen grid engraved directly on the specimen surface. Optical interference is used to measure the through-the-thickness strain over the same engraved area. The testing arrangement allows measurement of at-load strain as well as residual strain. The measured strain distribution is compared with recent work by Swedlow using a finite-element numerical technique and with results of the etch-pit technique used by Hahn and Rosenfield.

A new device for in-situ movement detection and measurement

Abstract: A new device for movement detection in joints is designed using the moire technique. Archimedean spiral grids are used. A space displacement may be evaluated in two planes by vectors of known magnitudes and directions. An extremely simple design is proposed to provide stability for the system being installedin situ over long periods of time.

Three-dimensional photoelastic analysis of a fiber- reinforced composite model

Abstract: A three-dimensional photoelastic analysis using the “stress-freezing” technique was conducted to determine the stress distributions in the matrix of a unidirectionally fiber-reinforced composite model subjected to matrix shrinkage and normal transverse loading. The model, consisting of a square array of polycarbonate rods in an epoxy matrix, simulated a boron-filament-reinforced plastic composite with a fiber-volume fraction of 0.50 at the critical temperature of the matrix epoxy. The effects of matrix shrinkage were separated from those of external loading by analyzing two identical models, one loaded and the other unloaded. The Lame-Maxwell equations of equilibrium were used to separate stresses along axes of symmetry on interior transverse slices. Axial stress components were obtained by subslicing. Results are presented in dimensionless form by dividing the stresses by the average stress through the section. A comparison with theoretical results for a boron-epoxy composite shows excellent agreement, although Poisson's ratio of the model matrix is appreciably different from that of the prototype (0.5 compared to 0.35). One significant result was that the maximum stress occurs in the middle of the matrix section between fibers which is at variance with the theoretical prediction of maximum stress at the interface. Stress-concentration factors vary from 1.80 at the interface to 2.0 at the midpoint of the matrix section between fibers.

High-velocity deformation properties of polyurethane foams

Abstract: This paper presents the results of dynamic uniaxial-stress tests performed on polymer-foam material. A water-blown ester polyurethane foam designated as rigid and a castor-oil-base polyurethane foam designated as semirigid were tested in tension and compression at rates of loading from 10−3 in./in./sec to 103 in./in./sec at room temperature. A gas-operated medium-strain-rate machine was used for rates of loading from 10−3 to about 102 in./in./sec. Tests at higher rates were performed on a split Hopkinson-bar device. Highspeed photographic techniques were used to study dynamic fracture.

Growth of part-through and through-thickness fatigue cracks in sheet glassy plastics

Abstract: Linear-elastic fracture mechanics is used to interpret observations of through-thickness fatigue crack growth in sheet specimens of polymethylmethacrylate, polycarbonate and an unfilled epoxy, and to correlate measurements of the growth of part-through and through-thickness fatigue cracks in sheet polymethylmethacrylate. It is shown that at least one of these materials may be useful for model studies of the growth of part-through thickness fatigue cracks in metallic components.

Applications of holography to fracture mechanics

Abstract: In the development of a theory of fracture mechanics for ductile metals, the role of the zone of constrained plastic deformation which forms in the region of a high stress concentration is of fundamental importance. Consequently, experimental studies of this plastic zone are of considerable interest and have attracted the attention of many investigators using many techniques. The present study represents an effort to extend the interferometric technique through the use of laser holography. In this work, a lens-less picture or hologram of each fracture specimen was exposed while the specimen was under nominal load in the testing frame. After development, the hologram was replaced and illuminated so as to superimpose the reconstructed specimen image on the actual specimen. As a result, subsequent minute deformations of the specimen produced by changes in the applied load result in the formation of readily observable fringe patterns. Theoretically, if sufficient care is taken in positioning the hologram and if the fringe distribution can be measured with sufficient accuracy, a quantitative three-dimensional determination of surface deformations could be made. The photographs taken in this study, while lacking the rigor demanded by the preceding conditions, nevertheless illustrate the nature of this technique and provide a quantitative one-dimensional measure of out-of-plane surface movement.

The grid method

Abstract: Determining strain with grids is one of the oldest and simplest methods of experimental stress analysis. Here, the method is reviewed. Various techniques that have been developed to print, record and analyze grids are discussed, and the types of problems to which the grid method has been applied are presented.

An automated process for three-dimensional photoelastic analysis: A fully automated process for obtaining and processing data from slices of a stress-frozen three-dimensional photoelastic model is described

Abstract: The use of two monochromatic light sources to obtain two isochromatic patterns permits a fully automated shear-difference analysis of the stress distribution in a three-dimensional photoelastic model. A development is given of the logic necessary to process the data taken from an automated polariscope as well as the design details of the polariscope.

Crack-opening displacements and normal strains in centrally notched plates

Abstract: Experimentally determined crack-opening displacements of stationary and running cracks and of inclined stationary cracks in centrally notched plates are reported in this paper The moire-fringe technique was used for the determination of displacement fields in test specimens of magnesium, 7075-T6 and 7178-T6 aluminum alloys Experimentally determined crack-opening displacements were compared with corresponding re ults based on theoretical models of Westergaard, Dugdale, Craggs and Craggs-Dugdale In addition, normal-strain fields derived from the moire-fringe data were compared with static or dynamic strain fields of these theoretical models The results of this investigation indicate that while the Dugdale crack is a fair model of a stationary crack in ductile materials, the Craggs crack appears to be a better representation of a running crack in the ductile materials investigated

Moiré-fringe multiplication by means of filtering and a wave-front reconstruction process

Abstract: Two principal problems associated with the practical application of moire fringes are to obtain sufficient sensitivity for measuring small strains and to develop a simple and inexpensive technique for engraving lines on the surface of a model. This paper deals with simple solutions to both problems. It is shown that the maximum number of fringes that can be observed for a given model is independent of the gratings utilized and depend only on the geometry of the employed optical system. Examples of moire patterns corresponding to the equivalent of 6000 lines per inch and patterns of the derivatives of the displacements corresponding to the same number of lines illustrate the paper.

Thermally generated stress waves in a dispersive elastic rod

Abstract: The propagation of thermally generated stress waves in a dispersive elastic rod was investigated both experimentally and analytically.

Mechanical-optical properties of polycarbonate resin and some relations with material structure - Polycarbonate is an excellent model material, but heat treatment is required. Dependence of birefringence on time and wavelength is described by normalized creep and normalized retardation parameters. Dispersion of birefringence is related to the spectral transmittance

Abstract: Polycarbonate resin possesses optical and mechanical properties which make it particularly suitable for certain experimental investigations, including two-and three-dimensional photoelastic analysis. The ductility and transparency of this material might be usefully employed in photomechanical investigations of plastic and viscoelastic response. The similarity of the stress-strain law of polycarbonate to that of mild steel could simplify the similitude problem. In addition, its spectral transmittance in visible and infrared makes polycarbonate useful for studies of material properties and structure. The optical creep of polycarbonate is respresented by a normalized creep coefficient. The relationship of this factor to the theory of viscoelasticity is discussed, and the conditions for a valid calibration of birefringent materials are reviewed. The wavelength dependence of relative retardation is represented by the normalized retardation, from which the dispersion of birefringence can be deduced. The stress-birefringence-time-wavelength characteristics of two brands of polycarbonate resin were determined. Because of residual birefringence, it was necessary to heat treat the resin at about 146°C, and properties of both annealed and unannealed resins are presented. Retardation was measured over the visible and near-infrared portions of the electromagnetic spectrum (407 nm to 1900 nm). There exists a definite relationship between dispersion of birefringence, which amounts to 14 percent in visible, and the infrared spectral transmittance, which is indicative of material structure.

Thermal-stress concentration caused by structural discontinuities

Abstract: The transient thermal-stress concentrations produced by cracks, sharp and round notches, and fillets, in plates were measured photoelastically and compared to values computed numerically by finite element and finite-difference techniques. The stresses near the tips of the cracks and the notches were singular and observed to agree with isothermal linear elastic fracture mechanics. Stresses near the root of the fillets were always less than the theoretical maximum, αE(T−T initial ), but often greater than the maximum stresses measured in a straight-edged plate subjected to similar thermal conditions.

A generalized method for photoelastic studies of transient thermal stresses

Abstract: This paper describes the apparatus and experimental method which was developed for generalized studies of transient thermal stresses in photoelastic models of many different shapes under a variety of steady-state or transient temperature conditions. It explains how the desired temperature gradients are established in the models and how rapidly changing temperature and stress profiles are monitored during a test.

The strain-rate effect and the incremental plastic wave in copper

Abstract: An experimental investigation was conducted to determine the degree of sensitivity of commerically pure copper to strain rate and to note the effect of this sensitivity on the velocity of propagation of shearing strain in copper. Thin-walled cylindrical specimens of copper were loaded in torsion to eliminate the effects of radial inertia. All specimens were annealed and then cold worked in torsion to obtain necessary specimen uniformity. Quasi-static tests were performed on short-length specimens to determine the shearing stress-strain curve of copper at a very low strain rate. The strain-rate sensitivity of copper at low strain rates, from 3×10−4/sec to 5/sec, was tested by loading short specimens at a very slow continuous rate and then suddenly increasing the strain rate. A quasi-static test was also performed to determine the effect of creep on prestressed copper. Dynamic tests involving strain rates up to 500/sec were performed on long specimens with a torsional impact machine. Specimens were tested under stress-free and prestressed initial conditions. The prestressed specimen was loaded at a slow, continuous rate before impact to avoid the undesirable effects of creep which would have occurred with a static preload. Results from the quasi-static tests showed that copper is noticeably sensitive to strain rate in the low strain-rate regions, but that the sensitivity becomes almost constant as the strain rate is increased. Results from the dynamic tests showed that large strains propagated at speeds which agreed well with speeds predicted by the strain-rate-independent theory of plastic-wave propagation. The lower-level strains in the prestressed specimen, however, propagated at much higher speeds than are predicted by the strain-rate independent. Because radial-inertia effects were not present, this discrepancy in measured and predicted speeds for low-level strains must be due to the strain-rate sensitivity of copper.

A multiple-pulse ruby-laser system for dynamic photomechanics: Applications to transmitted- and scattered-light photoelasticity - Paper describes a new ultrahigh-speed multiple-frame recording system in which a ruby laser is sequentially modulated and the light pulses are synchronized with the camera and event

Abstract: An ultrahigh-speed multiple-frame recording system for two- and three-dimensional dynamic photomechanics has been developed and is described here. The output from a ruby laser is modulated with a Pockels cell to produce a train of short, intense, monochromatic and polarized light pulses. Pulse widths of 50 nsec and repetition rates of up to 170,000 pulses/sec are obtained. These light pulses are synchronized with a “smear camera” and the event to produce a multiple-frame record of the phenomenon. The simplified camera requirements necessary for this purpose are indicated. The system is demonstrated by recording two-dimensional dynamic and scattered-light isochromatic fringe patterns. The capability of multiple recording of scattered-light fringe patterns, achieved here for the first time, has a tremendous potential for three-dimensional dynamic stress analysis. The developed system is also well suited for dynamic moire, interferometry and holography.

Study of residual stresses in linearly varying biaxial-stress fields

Abstract: A theory has been developed for the calculation of relaxation strains effected by drilling a hole in a plate with a linearly varying stress field. With this theory, a technique was developed for the measurement of residual stress at the toe of tee-fillet welds. The above technique was employed for the measurement of residual stresses at the toe of tee-fillet welds in 11/2-in. HY-80 steel with the fillet in the as-welded, ground, shot peened, ground and shot peened, and mechanically peened condition. It was found that experimental data conform to the assumed theory, and that residual stresses in aswelded tee-fillet welds in both the transverse and longitudinal directions approach the yield strength of the steel. It was also found that residual stresses are reduced approximately 25 percent by grinding, 50 percent by shot peening and 50 percent by grinding and shot peening. Mechanical peening drastically affected residual stresses by converting high tension at the toe of the fillet weld to high compression of approximately the same magnitude.

The optical-rotation effect in photoelastic shell analysis

Abstract: A difficulty commonly encountered in the three-dimensional photoelastic analysis of thin-shell structures1–9 is the so-called optical rotation effect4,8–10 which, in spite of some noteworthy efforts, has not yet been fully elucidated. The objective of this paper is to show how modern descriptions of polarized light can be advantageously used to predict the influence of the rotation effect on optical observations. Use will be made of the Poincare sphere representation of polarized light and of the associated Mueller calculus. Because these subjects may be unfamiliar, the fundamental concepts involved are briefly discussed in each case and readily available supplementary references are given.

Analysis of scattered-light methods in photoelasticity

Abstract: The use of scattered light for nondestructive analysis of general photoelastic models is becoming quite common and, during the last few years, several methods have appeared in the literature to determine the directions of the secondary principal stresses and their differences at any general point. Among the methods suggested, some are mentioned as “exact” and some “approximate”. Even the exact methods have limitations in their applicability for a generally stressed model. The present discussion attempts to bring out the inaccuracies involved in the various exact methods. Also, a few modifications to improve the accuracy and a new method called the Mini-max method are proposed.

Electromagnetic velocity-transducer studies of plastic waves in aluminum bars

Abstract: In this investigation, annealed aluminum rods were subjected to dynamic compressive impact loading of duration of the order of 560 μsec to study the propagation of longitudinal plastic waves, using an electromagnetic transducer to record particle velocities at four stations approximately three inches apart. Test results indicate that any given level of particle velocity propagates along the bar with a constant speed, not affected by the strain rate, within the range of strain rates encountered. Good agreement was found between the propagation speeds observed for different levels of velocity (averaged over all tests) and predictions of the von Karman rate-independent plastic-wave-propagation theory based on a single dynamic stress-strain curve almost coinciding with the static curve.

Thermally induced natural-frequency variations in a thin disk

Abstract: A number of studies has shown that natural frequencies and, accordingly, the minimum critical speed for the formation of a standing wave in thin, rotating, circular disks can be beneficially altered by purposely induced initial membrane stresses. The possibility of controlling natural frequencies by induced thermal membrane stresses, rather than initial stresses, has received some previous theoretical attention and is experimentally examined here for a stationary, constant-thickness, centrally clamped, circular disk. The primary advantages of thermal membrane stresses are manifested in the inherent flexibility in adjustment of the thermal as opposed to the initial stresses. Increases in the minimum critical speed, which is proportional here to the zero nodal circle—two nodal-diameter natural frequency, of 20 percent were determined with moderate heating. This can be considered a relatively small critical-speed increase when compared with variations expected in many common rotating disk environments. A thermal model, which utilizes as input the peripheral disk heat flux and the controlled disk temperature at some known radius, is shown to predict the temperature distribution and natural frequencies with reasonable accuracy. The applicability of this model enhances the potential practicality of the induced thermal-membrane-stress method of natural frequency and/or critical speed control.

Internal-strain measurements of longitudinal pulses in conical bars

Abstract: Longitudinal stress waves in a truncated 20-deg solid cone were investigated using embedded semiconductor strain gages. The cone, composed of an aluminum-filled epoxy, was struck normally at its small end with a 1/2-in.-diam steel ball traveling at a velocity of 170 jps. The results show the magnitude of the resulting stress wave to be nonuniform over a plane cross section perpendicular to the cone axis, the strain being greater at the center of the cone than near the surface, and the nonuniformity to increase with distance of travel from the impact end. The surface-strain measurements were compared with the one-dimensional theory of longitudinal waves in cones developed by Landon and Quinney as solved by Kenner and Goldsmith for a onehalf cycle sine-squared input pulse, and found to be in qualitative agreement with this theory, but to vary significantly in strain magnitude due to the strain nonuniformity over plane cross sections. The nonuniformity was compared with the Pochhammer-Chree theory for stress waves in cylindrical bars when that theory was evaluated for a cross section equivalent to the cone cross section. The trends of the deviations were similar, but the variations measured in the cone were consistently greater than that predicted by the theory.