The grid-shift technique for moiré analysis of strain in solid propellants

Moiré principles and procedures were surveyed with a view toward adaptation to measurement of complex strain distribution in solid propellants. Compliant coating and photosensitive materials were selected for grid reproduction. The most flexible of the several possible procedures for recording moiré data was found to be grid photography. A novel “grid-shift” technique employing coarse grids was developed for point-by-point determination of surface displacement derivatives, and the grid-shift relations for large strain and large rotation were derived. The technique is extremely versatile, permitting the analysis of strain of dynamically deformed specimens in nonambient environmental conditions of temperature, pressure or atmosphere. The utility of the technique was demonstrated by application to static and dynamic problems.     

Performance of metal-foil strain gages during large cyclic strains

Constantan-alloy gages with polyimide backing were bonded to axial-fatigue specimens which were tested under cyclic loading. Constant-strain ranges between 0.0075 and 0.04 were applied to each specimen by means of a clip on extensometer, and the strain-gage signals were monitored for gage accuracy and life. Gage life varied upwards from about four cycles at the highest strains investigated. Although significant zero shift occurred, strain ranges were generally measured within five percent over most of the life of the gage. The gage-performance information obtained will aid in later study of local strain and low-cycle fatigue in notched members.     

Precision strain standard by moiré interferometry for strain-gage calibration

Moiré interferometry is proposed as an alternative to extensometers to define the strain field used for calibration of electric strain gages. Measurements were conducted with a real reference grating of 1200 lines/mm (30,480 ?/in.), a gage length of 41.67 mm (1.640 in.), and a strain excursion of 2000 μm/m. Results showed a standard deviation of 1.1 μm/m at each load level and probable error within 2 μm/m for the 2000 μm/m excursion. Critical factors for accuracy are change of gap between specimen and reference gratings that might occur during loading, and the quality of collimation of incident light. A hollow uniaxially loaded test specimen interrogated by moiré interferometry is recommended for a strain standard of 99.9-percent accuracy.     

Application of faraday's effect in static and dynamic holographic photoelasticity

The basic principle of applying Faraday's effect to achieve the separation of fringes in static and dynamic holographic photoelasticity, and a study and application of Faraday's light rotator are described in this paper. It is proposed that Faraday's light rotator be used for automating photoelastic instrumentation for measuring isoclinics and the decimal orders of isochromatic fringes.     

Strain gages in cryogenic environment

The increasing use of cryogenics in all fields of endeavor necessitates the use of strain gages for stress analysis of structures under extreme temperatures. This has been a continuing program at the McDonnell Douglas Astronautics Co.'s Strain Gage Engineering Laboratory (Huntington Beach facility). Many characteristics of strain gages were investigated, and a majority of the commercial strain gage types were evaluated. Tests results are presented, as well as composite curves, showing the comparison between various types of strain gages.     

Measurement of surface strain rates in glaciers using embedded wire strain gages

Natural scientists and engineers are continuing to seek an understanding of the mechanism of flow and deformation of glaciers. A necessary component of this exploration is the accurate determination of strain rates in glacier ice. The purpose of this investigation was to develop a strain-measuring method which is dependable and precise under difficult field conditions. The measuring technique which was developed uses unbonded electrical-resistance strain gages which consist of single strands of 5-mil Constantan wire 10-ft long. Six gages are embedded in the glacier-ice surface in the form of two delta rosettes in order to obtain strain at a point with some redundancy of data in this two-dimensional problem. The rigid-body rotation of the gage anchor posts was measured by sensitive inclinometers in order to assess the effect of pressure melting on the strain data. The data are interpreted using cross-correlation and best-fit programs to yield maximum shear-strain rate and average normal-strain rate. Strain readings were conducted over a period of eight days on the Ptarmigan Glacier near Juneau, Alaska. The maximum shear-strain rate at the surface ranged from 0.25 to 1.2×10^?6/hr., which agrees with estimates derived from known flow rates. The wire gages were found to adhere to the ice well enough to make the gage anchor posts unnecessary—pressure melting is therefore insignificant. A tolerance of ±6.0 microstrain was determined for the strain gages.     

The interferometric strain gage

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. In this paper, the theory of the measurement is developed first. The strain, ∈, is given by ∈=ΔFλ/d _o sin α _o where ΔF is the average fringe shift of the two patterns, λ is the wavelength of light,d _o is the initial distance between grooves, and α _o is the angle between the incident light beam and the fringe patterns. A procedure for making static measurements with the interferometric strain gage is presented. The sensitivity for these measurements is 0.5 percent strain per fringe shift, and the maximum strain is 4 percent. The method is evaluated by comparing its results with other accepted means of measuring large plastic strain. These other techniques are: post-yield foil gages, a 2-in. clip gage, and an Instron testing machine. The average percent difference among these techniques is less than 0.4 percent based on a full-scale measurement of 4-percent strain. The interferometric strain gage has the following features: a gage integral with the specimen surface, a very short gage length, relatively easy application, and the ability to measure large strains.     

Low-cycle fatigue in welds

Hour-glass-shaped specimens were made from ASTM A-516, grade 55, steel plates which had been welded together. The specimens were manufactured so that the weld material was at the minimum section. The specimens were strain cycled about zero mean strain and the results were compared with tests conducted on specimens taken from the parent material. When the total strain range vs. cycles to failure was plotted on log-log coordinates, the curves for both the welded and parent-material specimens had nearly the same slope; however, the curve for the welded specimens was displaced downward from that of the parent material. Thus, for a given strain range, the parentmaterial specimens had lives approximately six times greater than the welded specimens. Two-level cumulative-damage tests on the welded specimens indicate that using Σn/N=1.0 is reasonably accurate.     

An experimental study of the effects of prestrain on the propagation of small disturbances in neoprene filaments

A small disturbance was caused to propagate along a long, slender, prestrained Neoprene filament. The particle velocity of the pulse was measured at two stations along the length of the filament by means of electromagnetic transducers which operate on the Faraday principle. Particle velocity vs. time data were obtained from oscilloscope photographs of the transducer outputs for each level of prestrain from 0 percent up to 400 percent engineering strain. The two particle-velocity records for each level of prestrain were subjected to linear viscoelastic analysis which employed the use of numerical Fourier transforms of the particle-velocity records. Computer programs were written which allowed computation of the numerical transforms and from them the computation of the phase velocity and attenuation coefficients of the material over the narrow frequency bandwidth of the Fourier spectra of the particlevelocity pulses. Data analysis revealed that, at a given frequency, the phase velocity increases significantly and that the attenuation coefficient decreases significantly with an increase in prestrain level over the range of prestrains of the tests. These material properties, that of a decreasing attenuation and an increasing phase velocity with increasing prestrain, are suggestive of the open possibility of the ability of the material to develop and support a shock wave for a large-amplitude disturbance.     

Test for sheet-metal formability with coupon and circular specimens

Formability in sheet metal is defined as the locus of the limiting strain. The initiation of localized thinning, which manifests itself as a groove, is taken as the criterion of failure. The deformation of circular and coupon specimens is discussed with particular reference to the effect of the process parameters on the strain ratios at the critical section. Curves are presented for the formability of aluminum sheets with failure in both the direction of rolling and that perpendicular to it.     

Strain behavior of pressurized cracked thick-walled cylinders

External circumferential strains were measured on large thick-wall pressure vessels containing internal fatigue cracks, using bonded strain gages. When strains measured over the cracks become compressive they predict impending failure. Normalization by the Lamé strain relates them to the fraction of fatigue life consumed and provides estimates of longevity.     

Strain-ratio measurements by an interferometric device

An interferometric experimental device capable of measuring lateral strains with a sensitivity of 5×10^?6 is described. The results of lateral and axial strain measurements during creep and isochronous tests on polymethyl-methycrylate (PMMA) are presented, and values for strain ratio (the ratio of lateral to axial strains) are calculated. The values display excellent repeatibility and are within the range of values recently published in the literature.     

A summation strain-gage alternative to oblique incidence in photoelastic coatings

A special strain gage (PhotoStress^® Separator Gage, Measurements Group, Inc., Raleigh, NC) designed to measure the sum (? ₁ +? ₂) of the principal strains, is used in conjunction with photoelastic-coating measurements (? ₁ -? ₂) to establish the value of each principal strain (? ₁ and? ₂). The summation strain signal is effectively independent of angular orientation (measurement direction), and by design, the gage negates soldering risks, self-heating, and localized-reinforcement considerations normally associated with strain-gage measurements on plastic parts.     

The moiré method for measuring large-plane nonhomogeneous deformations

Moiré-fringe equations have been developed for directly determining the components of Green's and Cauchy's deformation tensors from measurements of fringe pitch and angle. The equations, which were previously verified for large-plane homogeneous deformations, are used to determine the deformation-tensor components for nonhomogeneous strain fields. The results are compared to theoretical values. Specifically, the deformations investigated are pure bending of a rectangular block, and extension of a tapered plane specimen.     

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

Two independent experimental techniques are used to measure the strain distribution within the plastically deformed region around a crack tip. Moiré 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.     

Multi-scale Measurement of (Amorphous) Polymer Deformation: Simultaneous X-ray Scattering,Digital Image Correlation and In-situ Loading

This paper presents a method to investigate the behaviour of polymers on different scales during deformation using simultaneously collected synchrotron X-ray scattering, digital image correlation (DIC) and tensile loading. The method is demonstrated through experiments made on specimens of amorphous polycarbonate. Deformation is measured in-situ, simultaneously across different scales from the macroscopic deformation, measured using sensors on the tensile machine, to the full-field mesoscopic deformation, measured using DIC, down to the deformation of the nano-scale structure, studied using small and wide angle X-ray scattering (SAXS/WAXS). The DIC reveals highly inhomogeneous deformations that render conventional techniques for measuring deformation, such as extensiometers, virtually useless. The X-ray scattering is measured in several spatial points during continuous loading giving the evolution of the microstructure with respect to both spatial location and load level. The spatial mapping of the scattering reveals characters that would not be observed when only measuring at the centre point or measuring on a large area of the specimen, e.g. wide beam SAXS/WAXS or small angle neutron scattering (SANS). With these data, the macroscopic and the mesoscopic deformation can be correlated to the behaviour of the microstructure providing relevant information when developing micro-mechanical based constitutive models. The experimental results shown here indicate a direct correlation between the major principal strain direction and the maximum anisotropy direction of the SAXS patterns. The current approach can be extended to any kind of polymeric materials or polymer-based nano-composites.     

Experimental Technique to Characterize the Plastic Behaviour of Metallic Materials in a Wide Range of Temperatures and Strain Rates: Application to a High-Carbon Steel

This paper presents high temperature quasi-static and dynamic tensile testing. Samples are heated by an induction system controlled with a pyrometer. A high-speed camera (500 fps) is used to determine displacement fields with a digital image correlation software. For such tests a specific marking procedure of the sample is applied. This method is used to characterize the mechanical behaviour of a C68 high-carbon steel at temperatures up to 720 °C. Stress-strain curves are given from room temperature up to 720 °C at strain rates ranging from 400 /s to 4 × 10² /s.