Dynamic response of strain gages up to 300 kHz

Dynamic response of foil strain gages is investigated in the ranges of up to approximately 300 kHz in frequency, 2000 in strain and 750 s^–1 in strain rate. Impulsive input is applied to the gages using elastic wave pulses in a circular bar. The input is determined by measuring the velocity of the bar end with a laser interferometer. It was confirmed that deviations from the static gage factors do not exceed–5 percent within the frequency range up to 45 kHz, 110 kHz and more than 290 kHz for 20-mm, 10-mm and 3-mm gages, respectively, and that the gage length is the dominant factor in the gages' frequency characteristics. This paper also mentions self-generated voltages.     

Development of temperature-compensated resistance strain gages for use to 800°C

This paper describes the development and evaluation of temperature-compensated resistance strain gages for use to 800°C. These gages included single-element gages and double-element half-bridge gages. The filament of single-element gages was fabricated from specially developed Fe–Cr–Al–V–Ti–Y alloy wire. When bonded to high-temperature Ni-based alloy GH39 after stabilization at 800°C for one hour, the apparent strain from room temperature to 800°C was less than 2000 m/m. Double-element gages were fabricated from Pt–W–Re–Ni–Cr–Y alloy wire (active grid) and Pt–Ir alloy wire (compensating grid). When bonded to different high-temperature alloy specimens and stabilized, and when ballast resistance in series with the compensating grid adjusted suitably, the gages' apparent strains from room temperature to 800°C were less than 2400 m/m.Effects of preoxidization of Fe–Cr–Al wire on the characteristics of the single-element gages are described.     

Effect of pressure on electrical resistance strain gages

The pressure effect is defined as the indicated strain response minus the expected response of a strain gage under hydrostatic pressure. The problem is that the expected strain response only considers the strains at the test surface and neglects the grid compression perpendicular to this surface. In this paper, this effect will be included in the analysis, and a simple equation is derived relating the pressure effect to the grid compressibility. The relation is tested by comparing predictions with literature data. It turns out that for most constantan gages the pressure effect is about 0.55/MPa and is independent of the grid design. Furthermore, it is shown that the alternative way of calculating the pressure effect from gage factor and transverse sensitivity (using Bridgman factors) does not compare well with measurements.This research was undertaken while the author was at the University of Salerno, Italy.     

Strain gage evaluation with four-point bending at moderate temperatures

This paper describes the application of the traditional four-point bending technique to conduct strain gage performance tests at moderate temperatures. The tests measure the apparent strain, linearity, drift, creep and hysteresis behavior to ascertain the reliability of strain gages to be used in the testing of experimental cylindrical vessels subjected to thermal loading. The four-point bending rig was designed to take advantage of the advances in personal computer datalogging and graphical processing software. The test rig is designed to provide a thermal barrier to minimize the heat losses and thermal isolation of the test beam while maintaining structural continuity. A low wattage and lightweight electric foil heater incorporating a precise temperature controller minimizes weight and enhances temperature stability. Gage performance data on five candidate strain gages at temperatures ranging from ambient to 215°C (419°F) are presented, and the evaluation procedure is outlined. The strain gage with the most acceptable performance was identified within the validity limits from ambient to a temperature of 215°C and from zero to a maximum strain of 1000 .     

Sensitivity of the shear gage to normal strains

This paper documents an experimental study that was conducted to demonstrate the sensitivity of the shear gage to the presence of normal strains. The shear gage is a specially designed strain gage rosette that measures the average shear strain in the test section of notched specimens such as the losipescu, Arcan and compact shear specimens. These specimens can have complicated stress states with high shear and normal strain gradients. To evaluate the sensitivity of the shear gage to normal strains, shear gages were tested on an Arcan specimen. The Arcan specimen is a notched specimen that can be loaded in pure shear (90 deg), pure tension (0 deg) and at intermediate 15- deg increments. The shear modulus for an aluminum specimen was determined at each of these loading angles. It was found that the gages display nearly zero sensitivity to normal strains ( _x, _y). Moiré interferometry was used to document the shear and normal strain distributions in the test section and to provide an independent method for determining the average shear strain. These results reinforce the robust nature of testing with the shear gage.     

Present state of experimental stress analysis by strain gages in Japan

This paper describes the present state of strain gages, measuring devices and stress-cycle counters in Japan. Details are given to the following items: (1) electric-resistance-wire strain gages, (2) vibrating-string gages, (3) magnetostriction gages, and (4) stress-cycle counters. Items (1) and (2) manufactured in Japan are comparable to those manufactured in other advanced countries. Item (3) was specially developed in Japan. Research on item (4) is now in progress.This Field Report is based on a paper presented, by title only, at the 1960 SESA Spring Meeting held in Indianapolis, Ind., on May 18–20.     

Axial damping in metal-matrix composites. II: A theoretical model and its experimental verification

In the companion paper we describe a new experimental technique for resolving the phase difference between two electrical sinusoidal signals to an accuracy of 2/2¹⁶ or 9.587×10^–7 radians. In this paper we demonstrate the use of that technique in measuring the intrinsic material damping of metal-matrix composites in axial tension using strain gages. In particular, the influence of ply, angle, , on the axial damping of a Pitch 55 graphite/6061 aluminum [±]_s laminate is studied at a fixed frequency, a fixed strain level, and at room temperature. Recently, Ni and Adams proposed a model for predicting theflexural damping of a liminate from the flexural damping properties of a lamina. A close agreement between the model and the experiment was observed. As far as we know these are the first measurements of intrinsic material damping of metal-matrix composites.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Airfoil design with external flow suction

A method is proposed for the numerical-analytic design of a high-lift airfoil with slit air suction from the external flow within the framework of ideal fluid theory. The suction slit is represented by a channel with constant wall velocity. Examples of the design of wing profiles with non-detached flows having lift coefficientsC _y =2.68 and 4 and maximum relative velocities over the profile [_max|/=2 and 2.2 are given. A scheme for an aircraft of the flying wing type with internally located engines and pay load is briefly discussed.Kazan', Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 23–28, November–December, 1996.     

Evolution of Vortex Structures on the Leeward Side of a Delta Wing

Results of an experimental study of a supersonic flow around the leeward side of a delta wing are presented. The experiments are performed on three delta wings with leading–edge sweep angles = 68°, 73°, and 78° for Mach numbers M =2—4 and angles of attack = 0—22°. Data on the structure and position of internal shock waves are obtained; the size and location of primary and secondary vortices are found. New regimes of the flow around a delta wing are identified. The chart of flow regimes around delta wings is refined and extended.     

Non-persistence of Homoclinic Connections for Perturbed Integrable Reversible Systems

The dynamics of an analytic reversible vector field (X,) is studied in with one real parameter close to 0; X=0 is a fixed point. The differential D_x (0,0) generates an oscillatory dynamics with a frequency of order 1—due to two simple, opposite eigenvalues lying on the imaginary axis—and it also generates a slow dynamics which changes from a hyperbolic type—eigenvalues are —to an elliptic type—eigenvalues are —as passes trough 0. The existence of reversible homoclinic connections to periodic orbits is known for such vector fields. In this paper we study a particular subclass of such vector fields, obtained by small reversible perturbations of the normal form. We give an explicit condition on the perturbation, generically satisfied, which prevents the existence of a homoclinic connections to 0 for the perturbed system. The normal form system of any order admits a reversible homoclinic connection to 0, which then does not survive under perturbation of higher order. It will be seen that normal form essentially decouples the hyperbolic and elliptic part of the linearization to any chosen algebraic order. However, this decoupling does not persist arbitrary reversible perturbation, which finally causes the appearance of small amplitude oscillations.     

Displacement type unified equation for bending, buckling and vibration of conical shells and its applications

By using Donnell's simplication and starting from the displacement type equations of conical shells, and introducing a displacement functionU(s,,) (In the limit case, it will be reduced to cylindrical shell displacement function introduced by V. S. Vlasov) and a generalized loadq,(s,,),the equations of conical shells are changed into an eighth—order solvable partial differential equation about the displacement functionU(s,,). As a special case, the general bending problem of conical shells on Winkler foundation has been studied. Detailed numerical results and boundary coefficients for edge unit loads are obtained.The project supported by the National Natural Science Foundation of China.     

Factors influencing non-circular ring vortex motion

Non-circular ring vortices are innately unstable, giving rise to a range of new phenomena. Here we report on our and Heertsch's [1] experiments in which vortices were generated at rectangular holes and nozzles with aspect ratios 2<<20. Different piston histories were also used. For forestrokes alone we were able to confirm the typical non-splitting motion of the primary vortex. On introducing a backstroke following the forestroke even for values of as low as 2 — values which should not give rise to splitting vortices — vortices could be made to split into 2, 3 or 4 secondary vortices. For cases where they rejoined the process was significantly different to that predicted by theory [2]. For 3 for a nozzle geometry the splitting angle is extremely sensitive to the stroke (length) so long as splitting takes place, whereas for 9>>5 the splitting angle tends to become independent of the stroke. This sensitivity on the stroke is reduced for vortices generated at a hole geometry. For all cases investigated here the splitting angle seems to be relatively insensitive to the Reynolds number. Vortices generated at hole geometries also tend to be less stable than those generated at tube geometries. Finally, the dependence of the splitting angle on the stroke length only scales with the nozzle breadth for 7>>5.

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Sommario Vortici ad anello non circolari sono intrinsecamente instabili e danno luogo ad una gamma di nuovi fenomeni. In questo articolo vengono riportati gli esperimenti degli Autori e di Heertsch in cui sono generati vortici in ugelli e fori rettangolari con rapporti geometrici =2÷20. Sono state anche usate differenti storie del moto del pistone. Nel caso in cui si usi solo la corsa in avanti si è stati capaci di confermare il moto tipico del vortice primario senza divisione del vortice stesso. Introducendo una corsa inversa, subito dopo la corsa in avanti, persino per pari circa a 2 — valore in cui il vortice non si dovrebbe dividere — i vortici si potevano dividere in due, tre o quattro vortici secondari. Nei casi in cui si verificava la riconnessione, l'evoluzione del processo era molto differente rispetto alla teoria. Per <3, per una data geometria dell'ugello, l'angolo di separazione è estremamente sensibile alla lunghezza della corsa, mentre per =5÷9 l'angolo di separazione tende a diventare indipendente dalla corsa. Questa sensibilità è ridotta per vortici generati in fori. In tutti i casi l'angolo di separazione sembra abbastanza indipendente dal numero di Reynolds. Vortici generati in corrispondenza di fori tendono ad essere meno stabili di quelli generati in ugelli. Infine, la dipendenza dall'angolo di separazione sulla lunghezza della corsa scala con l'ampiezza dell'ugello solamente per =5÷7.

     

On the vanishing of the additive measures of strain and rotation for finite deformations

Explicit formulae for the finite strain and rotation measures are given, in the cases when either one of the infinitesimal tensors of strain and rotation vanishes. Conversely, when the finite strain or rotation measure vanishes, explicit formulae for the infinitesimal tensors of strain and rotation are also obtained.     

Analytical evaluation of stress-strain test data

An analytical model for deducing the actual stress-strain properties from laboratory test results is discussed. As an illustration, an elastic bilinear material is used for unconfined cylindrical compression test conditions, as simulated with a finite element analysis. The results obtained are applicable for assisting in evaluating measured strength and stiffness properties of some clay soils, concrete test cylinders, concrete cores, and rock cores.The quantitative results of this study can be used for interpreting measured stress-strain data for unconfined compression test conditions. The error in measured results is shown to be influenced by Poisson's ratio, length-to-diameter ratio of the specimen, end condition, and ratio of inelastic modulus to initial elastic modulus. Curves for adjusting the measured results to the theoretical results are presented.Nomenclature D specimen diameter - E _i initial elastic stiffness modulus - E _y elastic stiffness modulus beyond the yield stress, plastic or inelastic modulus - L specimen length - axial strain - _av average strain - _g gage length strain - _y yield strain - Poisson's ratio - compressive stress - _av average stress - _t theoretical compressive stress - _y yield stress - _ym measured stress at the yield strain     

An improved method for the measurement of strong flow birefringence

An improved procedure is proposed to solve the problem of measuring strong birefringence on flowing samples which have a retardation larger than /2 The procedure can be applied to devices which are based on the modulation of the polarization vector with a high-speed rotating half-wave plate. It uses two optical configurations which have different responses to the retardation. By combining the information obtained from the two configurations, one can easily and accurately determine the actual retardation of the sample, irrespective of the quadrant in which the measured retardation is located, provided the sample is isotropic. This technique can also overcome the problem of large errors occurring in the vicinity of = (2m+1)/2 due to the limited sensitivity around these values of . The use of the technique is illustrated with measurements on an isotropic solution of poly(benzyl glutamate) in m-cresol, which is strongly birefringent during shear flow.     

Light-induced kinetic effects in a single-component gas with a small change in molecular cross section due to excitation

Linearized transport equations for describing the light-induced effects in a single-component gas are proposed. The equations were obtained by expanding the initial transport equations in the small parameter/ — the relative change in molecular cross section on excitation. The linear equations are solved numerically by the moment method.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 149–154, May–June, 1992.The author wishes to thank M. N. Kogan and N. K. Makashev for their interest in his work and for discussing the results.     

Solidification behavior of the theta system 2-propanol/poly(n-butyl methacrylate)

Thermoreversible gelation of the system 2-propanol/poly (n-butyl methacrylate) — as detected by D'SC or dielectric experiments — does not manifest itself in a straightforward manner in the dynamic-mechanical properties. Its occurrence can, however, be seen in many ways: i) For constant composition of the system and a reference temperature lower than T _gel, the storage modulus G is larger than the loss modulus G in the glass transition zone of the master curve and both vary in an almost parallel manner with the angular frequency over almost two decades (whereas this feature is normally found for other gelling systems within the rubber plateau or the flow region). ii) The entanglement molecular weight obtained from G_max is markedly less max than the entanglement molecular weight in the melt divided by ₂, the volume fraction of the polymer. iii) The temperature influences change from WLF like to Arrhenius-like behavior as T is lowered in the case of highly concentrated polymer solutions; analogous considerations hold true as ₂ is increased at constant T. iv) For sufficiently low temperatures, the activation energy of flow exhibits a maximum in the concentration range where the gelation is — according to DSC experiments — most pronounced. Like with ordinary non-gelling systems it is possible to construct master curves. On the basis of Graessley's theory identical dependencies are obtained for the variation of the entanglement parts of the stationary viscosity with shear rate and for the dependence of the entanglement part of the complex viscosity on the frequency of oscillation. Zero shear viscosity and limiting value of the complex viscosity for vanishing as a function of ₂ match smoothly and exhibit two points of inflection.     

Modelling Shock/Boundary-Layer Interaction with Nonlinear Eddy-Viscosity Closures

An investigation is reported of several nonlinear eddy-viscosity models, both from a fundamental point of view and as a basis for resolving turbulence transport in transonic flows, with particular emphasis placed on shock-induced separation. The models are first analyzed by reference to a homogeneous shear flow and a plane channel flow, after which they are applied to two transonic flows with strong shock-wave/boundary-layer interaction including separation. The computational results demonstrate that nonlinear models with coefficients appropriately sensitized to strain and vorticity invariants, yield results which are superior to a standard linear low-Re k– model often claimed to give the best predictive performance among low-Re k– models which do not contain ad-hoc corrections. While this superior performance is partly associated with the functional dependence of the linear coefficient on strain and vorticity, this cannot be separated from the role of at least some nonlinear terms which interact with that coefficient, especially in complex strain fields featuring large streamline curvature and irrotational straining.     

Structural transitions in wormlike micelles

We investigate the effect of excess salt and simple shear on the dynamics and structure of semi-dilute aqueous solutions of cetyltrimethylammonium bromide and sodium salicylate. Small-amplitude oscillatory rheological measurements suggest a structural evolution from an entangled to a multi-connected network as the salt concentration is increased. Steady-shear measurements, however, show a significant departure from the Cox-Merz rule. At low salt concentrations, this departure occurs at high shear rates with ^{* –0.92±0.08} and ^{–0.51±0.06} and is attributed to the formation of large shear-induced structures. The critical shear rate _c at which the Cox-Merz rule fails approximates the inverse of the terminal relaxation time, . At high salt concentrations, however, the departure occurs at both low and high shear rates and is attributed to the formation of a multi-connected network. Small-angle light scattering (SALS) under shear was used to probe the mesoscopic structure and revealed novel scattering patterns exhibiting two-fold symmetry at low salt concentration and four-fold symmetry at high salt concentration. The SALS patterns were in qualitative agreement with the formation of large scale anisotropic structures at high shear rates and a multi-connected network at high salt concentrations.     

Shear softening and thixotropic properties of wheat flour doughs in dynamic testing at high shear strain

Shear softening and thixotropic properties of wheat flour doughs are demonstrated in dynamic testing with a constant stress rheometer. This behaviour appears beyond the strictly linear domain (strain amplitude ₀ 0.2%),G,G and |^*| decreasing with ₀, the strain response to a sine stress wave yet retaining a sinusoidal shape. It is also shown thatG recovers progressively in function of rest time. In this domain, as well as in the strictly linear domain, the Cox-Merz rule did not apply but() and | ^*())| may be superimposed by using a shift factor, its value decreasing in the former domain when ₀ increases. Beyond a strain amplitude of about 10–20%, the strain response is progressively distorted and the shear softening effects become irreversible following rest.