Stress evaluation in low-modulus and viscoelastic materials using phtoelastic glass inclusions

Stressmeters are gages designed to enable stress changes to be determined without the need to know the elasticity moduli of the body being studied. This paper describes a technique by which the magnitude of the greatest principal stress in a biaxial-stress field can be determined from the isochromatic fringe pattern in a hollow-cylindrical-glass stressmeter. The influence of the moduli and Poisson's ratio of the meter and host material on the sensitivity of the meter are discussed in detail. It is shown that, for a wide range of rock and concrete-like materials, a glass stressmeter will enable the stresses to be determined directly from the meter readings. Experiments to investigate the behavior of photoelastic stressmeters in host materials which are creeping under stress are described. Results of tests using frozen sand slabs have shown that under uniaxial stress there is little effect of creep on the meter readings until excessive fracturing occurs. There is also close agreement between the theoretical and experimental values for the meter sensitivity when it is assumed that the Poisson's ratio of the host materials falls to 0.5 during creep. When set in such materials the final sensitivity of the meter is also independent of the modulus of the meter provided that creep is continuous. Experiments are described which show that, in a material which is creeping, the stress can be determined by inserting a stressmeter and measuring the final steady reading.     

The response of strain gages to longitudinally sweeping strain pulses

The current state-of-the-art for estimating the maximum rise time of a strain gage which is subjected to an axially sweeping strain pulse ist _rg≤0.8L/c+0.5μsec wheret _rg is the 10/90 rise time of the strain gage,^* L is the gage length andc is the strain-pulse velocity. This paper shows that the effect of the 0.8L/c term can be significantly reduced by utilizing an analytical compensation technique. In addition, it is shown that the 0.5 μsec additive constant can be reduced to approximately 0.1 μsec by reinterpreting data published by a previous author.     

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.     

Analysis of Slot Orientation in Shear-Compression Specimen (SCS)

This paper presents an analytical treatment as well as experimental measurement of the plastic deformation field in shear-compression specimen (SCS) by using digital image processing (DIC) technique. The results provide a set of useful expressions that relates externally applied displacement and load quantities to the equivalent stress and equivalent plastic strain within the gage section. Based on the analysis, we propose modifying the slot angle of SCS geometry from its original value of 45º to 35.26º in order to enhance the uniformity of stress and strain fields in gage section. It is shown by analysis that this enhancement is essentially because the compatibility and boundary conditions that yield a homogeneous deformation field is naturally satisfied for the particular slot orientation of ???=?35.26°. This conclusion is also supported by experimental evidence that comparatively shows the edge effects for varying slot angles.     

Range-pair-counting fatigue gage

In this paper, the surface roughening phenomenon of an aluminum foil during fatigue process is utilized for monitoring of a variable amplitude stress. It is found that constant mean stress does not affect surface roughness. When the mean stress varies, however, it causes surface roughening. In such a case, the equivalent stress defined by (Σσ _i ^α N _i /ΣN _i )^1/α dominates surface roughness of an aluminum foil, where σ _i andN _i are stress amplitude and the number of cycles counted by the rangepair method, respectively, and α is a gage factor which is peculiar to the foil used. It is concluded that the aluminum foil can be used as the range-pair counting fatigue gage with high accuracy.     

Transient response of bonded strain gages

Transient-response characteristics of bonded strain gages have been studied by measuring the elastic step wave produced in a steel bar. A quenched-steel bar with a circumferential notch is stretched statically along its axis until it fractures at the notch. Thus a new cross section is suddenly created in a bar under static tension. At this moment, a sharp step wave of zero stress is produced from the new section, and it travels in the bar at the velocity of sound. By measuring this step wave with strain gages, it is shown that the rise time of the gage itself is less than 0.5 μs+0.8L/c, whereL is the gage length andc is the velocity of longitudinal elastic wave in the bar.     

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).     

A simple estimate for the effect of cross sensitivity on evaluated strain-gage measurement

The cross-sensitivity factor of a short-wire strain gage can sometimes be estimated by comparison of its gage factor with that of a long gage of similar construction and material. A plot of the error introduced by the usual neglect of cross sensitivity against the known or estimatedtrue ratio of transverse to longitudinal stress or strain yields a quick estimate for any given cross-sensitivity factorn of the gage, any Poisson's ratio ν of the test piece and any stress or strain ratio. It shows whether in any particular test the influence of cross sensitivity warrants further special attention. If the longitudinal strain exceeds the transverse strain, the error is seen to be always less than 1.3n, but if the transverse strain is larger, the error may be so high as to vitiate the result. In computations from rosette measurements, the diagram shows that the larger principal stress can be determined with an error below 1.3n, as can Tresca's and von Mises's criteria of yield, while the error in the smaller principal stress tends to be large for principal strain ratios above +10 or below ?1.5.     

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.     

Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method

A new experimental technique has been developed to investigate the onset of fracture in metals at low and intermediate stress triaxialities. The gage section of a flat specimen has been designed such that cracks are most likely to initiate within the specimen center, remote from the specimen boundaries. Along with the specimen, a biaxial testing device has been built to apply a well-defined displacement field to the specimen shoulders. The stress state within the specimen is adjusted by changing the biaxial loading angle. Using this new experimental technique, the crack initiation in metals can be studied experimentally for stress triaxialities ranging from 0.0 to 0.6. The stress and strain fields within the specimen gage section are determined from finite element analysis. The reliability of the computational model of the test set-up has been verified by comparing the simulation results with laser speckle-interferometric displacement measurements during testing. Sample experiments have been performed on the Al-7Si-Mg gravity die casting alloy. A three-step hybrid experimental–numerical calibration procedure has been proposed and applied to determine a phenomenological crack formation criterion for the Al-7Si-Mg alloy.

Mohr's circle presentation on an oscilloscope

An instrument is described which operates from a single three-element rosette strain gage and displays the diameter of Mohr's circle for stress or strain on an oscilloscope with proper length, position and angle for the determination of principal stress or strain magnitudes and direction. The device combines simplicity of construction and calibration with low cost and versatility of operation. Its useful frequency range is from static to a reasonable fraction of the system carrier frequency. The present design employs a-c gage excitation but the basic concept may be extended to d-c excitation for high-frequency work. Recording of dynamic strains is possible by photography of the oscilloscope trace. Uses have included instruction in elasticity as well as conventional stress analysis.     

Load-Inversion Device for the High Strain Rate Tensile Testing of Sheet Materials with Hopkinson Pressure Bars

A high strain rate tensile testing technique for sheet materials is presented which makes use of a split Hopkinson pressure bar system in conjunction with a load inversion device. With compressive loads applied to its boundaries, the load inversion device introduces tension into a sheet specimen. Two output bars are used to minimize the effect of bending waves on the output force measurement. A Digital Image Correlation (DIC) algorithm is used to determine the strain history in the specimen gage section based on high speed video imaging. Detailed finite element analysis of the experimental set-up is performed to validate the design of the load inversion device. It is shown that under the assumption of perfect alignment and slip-free attachment of the specimen, the measured stress–strain curve is free from spurious oscillations at a strain rate of 1,000 s^?1. Validation experiments are carried out using tensile specimens extracted from 1.4 thick TRIP780 steel sheets. The experimental results for uniaxial tension at strain rates ranging from 200 s^?1 to 1,000 s^?1 confirm the oscillation-free numerical results in an approximate manner. Dynamic tension experiments are also performed on notched specimens to illustrate the validity of the proposed experimental technique for characterizing the effect of strain rate on the onset of ductile fracture in sheet materials.     

The use of a high-modulus-inclusion gage in nonlinear viscoelastic materials

The behavior of an inclusion in a host material subjected to a stress system depends primarily on the ratio of the tangent moduli,E inclusion/E host. An inclusion of suitable material used in the form of a gage will give an identifiable photoelastic-fringe pattern. This pattern is related to the applied biaxial stresses in the diametral plane of the gage, and is independent of the actual modulus and strains in the host material provided that the moduli ratio is more than 300. A program of work has been carried out to verify the use of such an inclusion gage in low-modulus nonlinear viscoelastic materials. The gage geometry used in this work consisted of a hollow cylinder of birefringent material with a ratio of outside diameter to inside diameter of 5 to 1. The host materials were either unfilled or highly filled carboxyl-terminated polybutadiene rubbers. The moduli ratios for both host materials were such that the gages act as rigid inclusions. A theoretical study has also been conducted to find the optimum measuring points within the gage and the fringe patterns created by selected biaxial-stress ratios. The study also showed that the gage sensitivity is virtually independent of Poisson's ratio but depends on the biaxial ratio of the stresses. The values of the sensitivity factor obtained experimentally were close to those derived theoretically. The stressfringe order at the optimum measuring points was obtained by Tardy compensation, and the biaxial-stress ratio determined either from fringe-pattern recognition or by measuring points. Future applications and uses of such a stress-measuring technique will be described.     

Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates

The use of a sliding plate rheometer (SPR) to determine the first normal stress difference of molten polymers and elastomers at high shear rates is demonstrated. The simple shear flow in this instrument is not subject to the flow instabilities that limit the use of rotational rheometers to shear rates often below 1 s⁻¹. However, issues of secondary flow and wall slip must be addressed to obtain reliable data using an SPR. A highly entangled, monodisperse polybutadiene and a commercial polystyrene were the polymers studied. The inclusion of the polystyrene made it possible to compare data with those obtained by Lodge using a stressmeter, which is an instrument based on the measurement of the hole pressure. The data from the two instruments are in good agreement and are also close to the predictions of an empirical equation of Laun based on the storage and loss moduli.     

An analysis tool for piezoelectric gages

The Piezo-electric Gage Analysis System U.S. (pegasus) couples a two-dimensional dynamic structural finite element code to a two-dimensional electrostatics code for analysis of piezoelectric gages. The method has a sound theoretical basis and is built around two powerful finite element anlysis codes. The analysis codes provide the solution of the time dependent stress state in the gage and the solution of the electrostatic equation for each time step. pegasus provides the link between the two codes and the steps required to carry the analysis through to prediction of gage currents. Post-processing of the results allows visual interpretation of the the electric fields within the gage. Here we briefly describe the code and show that it can be a valuable tool for understanding the nature of piezoelectric gages. Received 6 May 1996 / Accepted 31 October 1996     

Monitoring short fatigue cracks with miniature strain gages

An experimental technique to monitor the length and the opening level of a short fatigue crack is presented. It is based on the progressive decrease with crack length of the response of miniature strain gages installed on the surface near the crack plane. A first gage installed close to the crack plane can monitor cracks from 10 μm in depth to half a millimeter where the response saturates. Other gages at larger distances from the crack plane are less sensitive but can monitor longer cracks. The response is measured so that it is independent of strain-gage calibration, Young's modulus and Poisson's ratio. The paper first presents the basic principles and possibilities of the technique as well as a finite-element analysis performed on automatic welded joints with straight-fronted cracks for which the technique has been developed. The results give a correlation between gage response, crack length and gage location and the conditions of replacement of a gage reaching saturation. The practical exploitation of the technique has required further work to derive a continuous calibration of the gage response that includes corrections to account for the gage finite dimensions and the crack-plane inclination. This calibration is shown to give crack lengths that compare well with fractographic marks and typical results that have been obtained on short crack growth at the weld toe are presented. In particular, the resolution of the technique is put into evidence with results on the initial growth of a 0.1 mm nonpropagating crack. The paper finally points out the distinctive features that appear in current works to adapt the technique to the growth of semi-elliptical cracks of low and high aspect ratio.     

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.     

Design considerations and calibration of stress transducers for soil

Strain gage pressure transducers are most frequently used for soil stress state determinations. Their construction, rugged and mechanically resistant, enables them to measure stresses within a wide range (up to 500 kPa) in harsh conditions. Output signals are easily readable and stable. The accuracy of the measurements, however, depends upon proper design and calibration before use in soil. This paper contains information on design considerations and results from calibration tests of transducers of two membrane diameters: 20 and 30 mm. The calibration test stand, as well as calibration procedures, are described in detail. For calibration tests, natural soils were used, as well as steel balls, to simulate the effect of the aggregated structures of arable soils and grain materials. The calibration method considered different soil types as well as soil water content. Soil and its water content were found to have an effect on output scale factor.     

A piezoelectric field-effect strain gage

A new and highly sensitive strain transducer has been developed using a thin-film semiconductor deposited on a polished piezoelectric ceramic substrate. Field-effect coupling has been found to exist between the substrate and film in which the number of mobile carriers in the semiconductor is dependent on the electric-displacement vector of the substrate. Therefore, the conductivity of the semiconducting film can be altered by piezoelectric charge due to a strain applied to the substrate material. An effective gage constant has been calculated in terms of the piezoelectric and elastic constants of the substrate and electronic properties of the film. Experimental devices were constructed by depositingp type tellurium on polished lead-zirconate-titanate ceramic resulting in experimentally observed gage factors as high as 5800 compared to 100–200 for conventional semiconductor gages. The semiconductor film exhibits an electronic instability that limits its use, at present, to transient measurements with frequencies above 1 Hz. Data will also be presented to show that the gage constant is continuously variable between a positive and negative maximum value by altering the magnitude and direction of the substrate-polarization vector. It is believed that these gages will be useful in those cases where extremely small strains (～10^?7) are to be measured or when moderate strains (～10^?4) are to be determined in an electrically noisy background.