Dynamic plastic response of foil gages

Little research has been devoted to the accuracy of the response of resistance strain gages to dynamic plastic strain because of the lack of an easy-to-use comparative strain-measuring technique. The dynamic interferometric strain gage provides a suitable standard of comparison. Foil-gage response is compared directly with interferometric strain-gage response in a longitudinal-impact experiment. The accuracy of the foil gage does not decrease with increasing maximum strain (up to 8 percent). The error in shape of the strain wave does not vary drastically with distance from the point of impact. In contrast to previous work, foil gages are found to be reasonably accurate strain transducers for dynamic plastic strain.     

Dynamic strain measurement with the interferometric strain gage

The interferometric strain gage has a short gage length, high-frequency response and the capability of measuring large plastic strains. Furthermore, the gage is easily ruled directly onto the specimen, and no mechanical or electrical contact needs to be made during the measurement. These features make the interferometric strain gage particularly suitable for dynamic plastic-strain measurement. In this paper, the details of an experimental setup for generating and measuring dynamic plastic strain are given. The photometric techniques of measuring the fringe motion of the interference patterns are describle as well as the data-reduction procedure. A typical result is presented, and the validity of the method is established.     

The diffractographic strain gage

A method for measuring strain using diffraction of light from a single aperture is described, and results of a comparison tensile test with an electrical-resistance strain gage are presented. The “diffractographic strain gage” is shown to have high sensitivity, linearity, accuracy and temperature compensation and the ability to operate in a variety of hostile environments. It is furthermore simple, inexpensive, and the data can be collected by eye without assistance from further instrumentation.     

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.     

Techniques for measuring stress-strain relations at high strain rates

The qualitative dependence of the mechanical behavior of some materials on strain rate is now well known. But the quantitative relation between stress, strain and strain rate has been established for only a few materials and for only a limited range. This relation, the so-called constitutive equation, must be known before plasticity or plastic-wave-propagation theory can be used to predict the stress or strain distribution in parts subjected to impact stresses above the yield strength. In this paper, a brief review of some of the experimental techniques for measuring the stress, strain, strain-rate relationship is given, and some of the difficulties and shortcomings pointed out. Ordinary creep or tensile tests can be used at plastic-strain rates from 10^?8 to about 10^?1/sec. Special quasi-static tests, in which the stress- and strain-measuring devices as well as the specimen geometry and support have been optimized, are capable of giving accurate results to strain rates of about 10²/sec. At higher strain rates, it is shown that wave-propagation effects must be included in the design and analysis of the experiments. Special testing machines for measuring stress, strain and strain-rate relationships in compression, tension and shear at strain rates up to 10⁵/sec are described, and some of the results presented. With this type of testing machine, the analysis of the data requires certain assumptions whose validity depends upon proper design of the equipment. A critical evaluation of the accuracy of these types of tests is presented.     

Errors in high-temperature strain measurements

The results of a technical evaluation of the accuracy of two types of commercially available high-temperature electric-resistance strain gages, and a special high-temperature gage under development at the Liquid Metal Engineering Center (LMEC) are presented. These gages, the BLH type HT 1212-5A, Microdot type SG420, and the LMEC gage, were selected for evaluation because of the need for reliable electric-resistance strain gages for high-temperature stress or strain measurements and process instrumentation in the temperature range of 900 to 1200° F. The BLH gage is rated by the manufacturer as a 1000 to 1200° F gage; the Microdot gage is rated as a 900° F gage. The special LMEC gage was made for use up to 1200° F. Instrumentation of this type is needed to determine or ensure component structural integrity and over-all system reliability of fast breeder reactors.     

Enhanced measurement of strain distributions

A theoretical approach is presented that uses multiple strain gages to accurately measure complicated strain distributions. The technique is based on the method of weighted residuals in conjunction with measured strain data and is applicable for arbitrary in-plane strain distributions. Conventional measurements using strain gages are shown to represent a particular case of the approach presented. The experimental characterization of unidimensional strain fields is discussed in detail. Two approaches are presented; these are based on linear and quadratic approximations of the strain field. The strain distribution for two important practical problems is evaluated assuming ideal conditions to assess the performance of the proposed approach. In both cases, the simulated results demonstrate that measurement error resulting from the finite size of a strain gage may be reduced. That is, a larger strain gage may be used for a given maximum admissible error. The method also allows a minimal error of measured nonlinear strains.     

The evaluation of a strain gage having long-time stability characteristics

A standardizing strain gage that meets the requirements for long-time stability of strain measurements is described in this paper. Statistical analyses of the strain calibration results taken over a period of 13 months showed no significant differences between successive calibrations at a 5-percent significance level. From the results of the strain calibrations of 134 gages, the resistance-deformation characteristicdR/dW had a mean of 120.31 ohms/in. with a coefficient of variation of 1.43 percent. Evaluation tests using 6×12 in. concrete cylinders compared the strains measured by the standardizing gage to those measured by the Berry gage. Statistical analyses of these results showed equivalent accuracy of strain measured by the standardizing strain gage at comparable precision.     

Small attachable interferometric strain gages

Laser-based interferometry from two tiny reflective indentations can be used to measure in-plane strain/displacement over a very short gage length (on the order of 100 μm). If the specimen material is not reflective, then some other means of generating the interference patterns must be found. This paper describes two kinds of attachable gages: plated acetate replicas of indentations and reflective foils that are indented after application. In either case, the gage is applied with the techniques used for foil-resistance gages and the gage itself is very small. The manufacturing procedures are described. The results of experiments comparing the strain to that measured with foil-resistance gages are presented. Finally, the small interferometric gage is used to measure strain on one of the metal strips in a foil-resistance gage.     

Measurement of static strain at 2,000° F

This paper describes the work being done at Hughes Aircraft Company using capacitance strain gages to measure static strains at temperatures up to and including 2,000° F. A new configuration of the capacitance gage is described with a gage length of 0.50 in. Methods of attaching the gage have been developed for welding, bonding and flame-spray installations. Instrumentation procedures and methods are defined. Statistical accuracy and test results are discussed on the results obtained from a lot of 60 gages. Results discussed were obtained on Rene 41, titanium and L605 stainless steel. Data analysis on the gage includes gage factor, gage factor vs. temperature, apparent strain, linearity, hysteresis, temperature effects, drift, and zero shift.     

Determination of thermal-expansion characteristics of metals using strain gages

A method has been developed to measure thermal-expansion characteristics of metals using bonded resistance strain gages. The method allows rapid and accurate determination of expansion properties at similar or lower cost (depending on the particular application) than conventional dilatometric techniques. Other advantages include elimination of a need for perfectly flat sample material, elimination of specimen machining, and applicability to structures and components. To utilize this technique, the ‘apparent strain’ of the gage is determined by attaching it to a ‘standard’ material for which the thermal-expansion characteristics are accurately known and subtracting the known thermal response of the material from the total gage output. ‘Apparent strain’ is therefore the temperature-induced output of the gage when bonded to a material having a thermal-expansion coefficient of zero. When the gage is then attached to a test material and cycled through the same temperature range, this ‘apparent strain’ is subtracted from the total gage output to obtain the actual unit-length change of the test material. Using this technique, mean-expansion coefficients of experimental alloys were determined over the temperature range ?320°F (?196°C) to room temperature.     

In situ determination of adhesive shear moduli using strain gages

A new, convenient and cost-effective method of determining in situ adhesive shear moduli using strain gages is proposed and evaluated. Thick-adherend lap shear specimens with stacked gage rosettes at the center of the bond line are loaded in tension for adhesive shear strain measurement. Experimental and numerical results indicate that the test specimen has a nonuniform adhesive shear stress (or strain) distribution in the test section and that this distribution (except at the center point of the bond line) is greatly affected by load eccentricity. In addition to the nonuniformity in the shear stress distribution, the issue of material nonhomogeneity in the gage-covered region affects the strain gage measurement. By taking into account these two issues and assuming linear-elastic behavior, two approaches for converting the gage-measured shear strain into the adhesive shear strain are developed and verified by experiment. It is shown that the strain gage measurement associated with either of two conversion techniques can determine the in situ adhesive shear moduli, which are comparable with moiré experiment and KRG-1 extensometer measurements.     

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.     

Performance of miniature resistance strain gages in low-cycle fatigue

Experimental results describing the behavior of five types of miniature resistance strain gages subjected to cyclic strains of high amplitude are presented. Test procedure and instrumentation are described. Changes in zero drift and changes in gage sensitivity are discussed with respect to various strain gage and test variables. Mechanisms of gage failure, effect of variation of imposed strain and hysteresis in gage response are discussed.     

The application of strip strain gages for measuring residual surface stresses in beryllium

Evaluation and application of tiny, 0.031-in. gage length, constantan foil-strip strain gages for measuring residual surface stresses in beryllium parts are discussed. The strain gages were applied to one side of the beryllium parts at locations known to have high residual surface stresses. Small coupons were machined from the parts and the opposite side of the coupon was chemically milled with a 10 to 20-percent hydrochloric-acid solution. The strain-gage installation was protected with micro-crystalline wax. The etching process required approximately 20 hr at 75°F. Because of their high stability, glass-fiber-reinforced epoxyphenolic strain gages were used rather than the more readily available polyimide-backed strain gages. Details of the strain-gage installation are presented.     

用数理统计方法评定电阻应变计灵敏系数的精度等级

本文采用大子样、小子样抽样理论的数理统计方法,评定电阻应变计灵敏系数的精度等级。     

A shear-compression specimen for large strain testing

A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s⁻¹), up to very high strain rates (2×10⁴s⁻¹ in the present case).     

Biaxial gage factors for piezoresistive strain gages

Theoretical considerations of piezoresistive strain gages show that the change in electrical resistivity depends on the biaxial state of strain at the surface of the specimen to which the gage is bonded. In particular, whenV is the initial voltage across the gage and ( \( \in _{11} , \in _{22} , \in _{12} \) ) is the surface-strain state at the point of attachment, the gage-voltage change ΔV is given by \(\frac{{\Delta V}}{V} = G_{11} \in _{11} + G_{22} \in _{22} + G_{12} \in _{12} \) whereG ₁₁,G ₂₂ andG ₁₂ are the biaxial gage factors. Experiments were conducted on a nominally one-dimensional gage. Kulite type DLP-120-500, bonded to a standard ASTM flat tensile specimen of CR 1018 steel. For this gage, typical values were found to beG ₁₁?26,G ₂₂??1.4 andG ₁₂??1.1. SinceG ₂₂ andG ₁₂ are less than 6 percent ofG ₁₁, it is concluded that contributions from these two factors (called transverse and shear sensitivities) will be significant only when the gage is oriented such that \( \in _{11}<< \left( { \in _{22} , \in _{22} } \right)\) . However, in the interest of completeness and accuracy, all biaxial gage factors should be reported.     

Analysis of elastic waves from two-point strain measurement

Provided that the one-dimensional wave equation applies, strain measurement at two sections of a linearly elastic cylindrical rod makes it possible to determine a number of important quantities at an arbitrary section of the rod; for example, strain, particle velocity and power transmission. The equations needed are derived, and the design of an analogue real-time analyzer is presented. The influence of some principal sources of error is analyzed and it is shown that it should be possible to perform accurate evaluation (errors less than a few percent) during a time interval which is not very long compared to the travelling time for a wave between the two gage positions. Comparisons are made between direct measurement and digital evaluation of strain, and between digital and analogue evaluation of particle velocity and power transmission. The discrepancies are typically less than ten percent during a time interval of 20 travelling times between gages. Although these results do not represent what is achievable, the accuracy is sufficient in several applications and demonstrates the feasibility of the method used.