The effects of high pressure on foil strain gages

The purpose of this investigation was to determine whether a linear pressure-strain response was possible for gages subjected to hydrostatic pressures to 140 ksi. This was motivated by the desire to use this information to measure the elastic-plastic behavior of material at the inside surface of thick-walled cylinders subjected to high internal pressure. This paper shows the effects of fluid pressure to 140 ksi on four different types of foil strain gage. Linear pressure-strain curves were obtained for these gages mounted on flat surfaces of tungsten, steel and aluminum specimens. The linear strains of several materials due to pressure are compared with the compressibility constant (1–2ν)/E as calculated from experimentally determined values ofE and ν, whereE is defined as the modulus of elasticity and ν is Poisson's ratio. Experimental results show the percent deviation between the constants to be a function of the material, being greatest for tungsten and least for aluminum. The fact that a linear pressure-strain response was obtained makes it possible to correct the readings for strain gages mounted on flat surfaces of materials subjected to direct hydrostatic pressure. Temperature effects as a function of pressurization rate were investigated. Various gage failures encountered along with photomicrographs showing probable causes are presented.     

Effects of pressure on small foil strain gages

This paper describes the behavior of small foil strain gages under high pressure. Effects of pressure were determined and calibration curves were established in prelininary experiments. The calibrations were then used for correcting measured strains in pressure vessels. Preliminary experiments at room temperature were conducted on small foil strain gages for pressures up to 35,000 psi. The effects of pressure on the gages bonded with a cynoacrylate contact cement, a room-temperature epoxy cement, a high-temperature epoxy cement and a filled epoxy resin were evaluated. Because the contact cement was least affected by pressure and was easiest to apply, it was chosen for use in successive experiments with different gage installations. Calibration curves were determined for strain gages of 0.031-, 0.062- and 0.125-in. gage lengths. The compensating gages were under atmospheric pressure. The calibrations included the pressure effects of gages bonded on both concave and convex surfaces, and the effect of tensile prestrains. Data could be duplicated for successive pressure tests and for several gage installations. The calibration curves proved to be an effective way for obtaining accurate readings from the foil strain gages bonded internally to a pressure vessel.     

Thermal tests of a steam-turbine nozzle-chamber model

This paper describes the measurement of thermal strains and temperatures in a 0.25-scale aluminum-filled epoxy model of a double-flow large-steam-turbine nozzle chamber. A temperature gradient was induced by circulating chilled methyl alcohol through the interior. Strain gages and thermocouples were used to determine surface strains and temperatures at various locations for comparison with a finite-element analysis under development. A uniform cylinder was included on the inlet section of the model for calibration. The maximum measured tensile strain on the interior surface was 0.96 αΔT _n , where ΔT _n was the average temperature difference between the interior surface and the initial temperature. A maximum compressive strain of 0.50 αΔT _n was measured on the outside surface of the nozzle-bowl sidewall.     

New approach to the autofrettage of high-strength cylinders

The usual method of autofrettage (cold working) for gun tubes utilizes hydraulic pressure applied directly to the bore in order to plastically deform the wall of the tube so that favorable residual-stress patterns are produced. The strength of the tube is effectively increased, providing many associated benefits; however, ultra-high hydraulic pressures are required for high-strength steels since plastic-flow pressure is directly proportional to the yield strength of the material. A new method for the autofrettage of high-strength steel cylinders requiring greatly reduced pressures is developed and described herein. An oversize mandrel is forced through the tube to plastically deform the walls. Three methods of forcing the mandrel are investigated. Mechanical-push swaging is used in the autofrettage of short 5-in. long specimens with pull swaging and hydraulic-push swaging being used on specimens 40 in. long. All specimens are made from 4340 steel heat treated to various strengths. Cylinders with wall ratios ranging from 1.5 to 2.8, yield strengths ranging from 90,000 to 180,000 psi, and percent enlargements at the bore ranging from 1.0 to 5.0 are utilized. An engineering analysis is made investigating such factors as percent enlargement and elastic recovery at the bore, the ratio of pressure required for pushing the mandrel to the yield strength of the material, the effects of various lubricants on the frictional forces involved, and the induced three-dimensional stresses in the cylinder walls. Sach's boring-out technique is used to evaluate induced residual-stress patterns. Strains are recorded with electric-resistance strain gages and the associated dynamic and static instrumentation is described. Results are presented in graph form.     

The gross hydrostatic-pressure effect as related to foil and wire strain gages

An analysis of gross pressure effect for strain gages is presented. This is defined as the difference between the predicted hydrostatic strain and the experimental strain. Values of the theoretical strain per unit pressure are based on the Voigt-Reuss-Hill approximation using published values of elastic moduli and compliances. These theoretical values are adjusted by the pressure effect calculated from an equation based on the assumption that the pressure effect is independent of the elastic properties of the substrate. The modified values of theoretical strain per unit pressure are then compared with the experimentally observed values. The differences are small except for the substrate materials of zinc, cadmium and lead. Experimental pressure-strain data are presented for constantan foil gages mounted on tungsten, copper, tin, molybdenum, titanium, cadmium, brass, zinc and lead as well as constantan wire gages mounted on steel, aluminum and magnesium for hydrostatic pressures up to 140 ksi. Data for foil and wire gages mounted with various adhesives are presented and show that the adhesive or backing materials appear to have a relatively minor effect on the over-all gage performance.     

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.     

Response of foil strain gages to hydraulic pressure

A series of tests to determine the effect that hydraulic pressure has on the output of electrical-resistance foil strain gages is described. Tests were conducted on Micro-Measurements gages, type EA-13-125BT-120 for pressures up to 20.7 MPa and frequencies up to 150 Hz, both for purely dilatational strain as well as various combinations of dilatational and distortional strains. The results showed that gage performance due to the combined effects of hydrostatic pressure and distortion of the structure differed from the condition predicted when pressure and distortion were considered separately. Rate of pressurization (and, hence, strain rate) had no measurable effect within practical limits.     

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.     

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.     

Flow of rarefied gas past a “flat” pitot tube

The Monte Carlo method was used to calculate flow past flat Pitot tubes at angle of attack α = 0 for the following flow parameters: Mach number M_∞ = 5, 10, 20, temperature factor t_w = 1, 0.1, and Re₀ ε [0–40]. The calculations were made for two types of molecule: elastic spheres (μ ～ √T) and pseudo-Maxwellian molecules (μ ～ T). It was found that the pressure on the end in the Pitot tube has a strongly nonmonotonic dedependence on Re₀ for t_w = 0.1.     

Simulation of a valveless pump with an elastic tube

A valveless pump consisting of a pumping chamber with an elastic tube was simulated using an immersed boundary (IB) method. The interaction between the motion of the elastic tube and the pumping chamber generated a net flow toward the outlet throughout a full cycle of the pump. The net flow rate of the valveless pump was examined by varying the stretching coefficient (ϕ), bending coefficient (γ), the aspect ratio (l/d) of the elastic tube, and the frequency (f) of the pumping chamber. As the stretching and bending coefficients of the elastic tube increased, the net flow through the valveless pump decreased. Elastic tubes with aspect ratios in the range of 2 ⩽ l/d ⩽ 3 generated a higher flow rate than that generated for tubes with aspect rations of l/d = 1 or 4. As the frequency of the pumping chamber increased, the net flow rate of the pump for l/d = 2 increased. However, the net flow rate for l/d = 3 was nonlinearly related to the pumping frequency due to the complexity of the wave motions. Snapshots of the fluid velocity vectors and the wave motions of the elastic tube were examined over one cycle of the pump to gain a better understanding of the mechanism underlying the valveless pump. The relationship between the average gap in the elastic tube and the average flow rate of the pump was analyzed. A smaller gap in the elastic tube during the expansion mode and a wider gap in the elastic tube during the contraction mode played a dominant role in generating a high average flow rate in the pump, regardless of the stretching coefficient (ϕ), the aspect ratio (l/d) of the elastic tube, or the pumping frequency of the pumping chamber (f).     

Evaluation of high-elongation foil strain gages for measuring cyclic plastic strains

The behavior of a certain type of high-elongation foil strain gages (l/32-in. gage length) was checked against the indications of a clip-on extensometer under conditions of cyclic plastic strain (strain range 0.5 percent to 2.8 percent). The gages exhibited limited capability of measuring cyclic plastic strains. Transverse and axial strain measurements by means of the gages enabled determination of Poisson's ratio for elastic and plastic conditions. Results are tabulated and discussed.     

On the measurement of strain in the hostile environment of high-pressure water (80 MPa)

The measurement of strain on a structural member in the presence of high-pressure water environment requires waterproofing of the gages as well as understanding of the pressure effect on the foil gages. Two new waterproofing methods are developed to protect the gage under these extremely high pressures. This study has resulted in a new compensating method which eliminates the effects of temperature and pressure simultaneously. The waterproofing materials studied during this investigation are superior to other earlier techniques reported in literature since they provide protection up to 11,500 psi (80 MPa) while previously existing techniques failed before this pressure. Also, these studies on the pressure effect deal with the realistic situation of coated strain gages in a water environment, as compared to previous studies which dealt with uncoated strain gages in an oil environment.     

Measuring small internal pressures along a tube during steady flow

A tube that can accurately measure small strains and pressure profiles during flow of non-Newtonian paste explosives has been designed and strain gaged. Equiangular rosette strain gages were installed along the length of a 6-mm-diam, 0.46-m-long thin-walled aluminum tube. The rosettes were oriented in the classical stress-gage configuration to measure circumferential stress and, hence, internal pressure independent of other stresses. The tube was static calibrated on a floating-piston pressure calibrator. Steady flow calibration was accomplished by extruding a viscous Newtonian silicone oil. Inlet pressure ranged from 0.52 to 2.1 MPa (75 to 300 psi). For the low-pressure 0.52-MPa silicone-oil extrusion, the full-scale strain levels varied from 6 to 53 μm/m. For all eight strain-gage stations, the maximum deviation from a linear pressure profile was equivalent to 0.5 μm/m. A pulsed-current-excitation signal-conditioning and digital data-acquisition system provided the necessary stability and precision to measure these unusually low-strain levels accurately.     

Measurement of Residual Elastic Strains in a Titanium Alloy Using High Energy Synchrotron X-Ray Diffraction

Residual elastic strains in a bent bar of titanium alloy Ti-6Al-4V were measured using high energy diffraction on station 16.3 at SRS Daresbury. Using a single bounce Laue crystal monochromator, diffraction peaks were collected for reflections (00.2), (10.1), (10.2) and (11.0) from the hcp alpha phase of the titanium alloy. Reference values of the lattice spacing for each of the reflections were found from the diffraction pattern collected from a stress-free sampling volume. The residual elastic strain values calculated on the basis of each reflection were then computed and plotted as a function of position across the bent bar. The average macroscopic residual elastic strain was computed using an averaging procedure taking into account the multiplicity of each reflection. Energy dispersive white beam diffraction from the same bent bar was used to collect diffraction patterns over the range of lattice spacings between 0.8 and 2.2 Å. Detector calibration was carried out using the procedure described in Liu et al. (2005) and detailed interpretation of the energy dispersive profiles was carried out allowing the identification of average residual elastic strains in the two principal phases present in the titanium alloy considered, the α-Ti hcp and the β-Ti bcc phases. Peak-specific residual strain profiles computed on the basis of monochromatic measurements show significant differences reflecting the variation in the elastic and plastic properties with grain orientation, i.e., crystal anisotropy. Using the contrast between the elastic and plastic properties of different directions within the α-Ti hcp lattice, the difference between residual elastic strains measured for (00.2) and (11.0) reflections was plotted, as well as the ‘difference strain’ between (00.2) and (10.1) reflections. These profiles show a good qualitative correlation with the plastic strain profile introduced by inelastic bending that was computed from the analysis of Pawley refinement of the energy-dispersive diffraction measurements.     

The effects of high pressure on foil strain gages on convex and concave surfaces

The present investigation was undertaken to determine whether a linear pressure-strain response could be obtained for gages mounted on convex and concave specimens subjected to hydrostatic pressures to 140 ksi. This is an extension of a previously reported work where flat surfaces only were considered. Linear pressure-strain curves were obtained for five different types of foil strain gage having gage lengths varying from 1/16 to 1/4 in. These were mounted on steel, aluminum and magnesium specimens having diameters ranging from 1/4 in. convex to 3/8 in. concave. The inverse slope of the pressure-strain curves was compared with the compressibility constant 1–2v)/E to determine a percent deviation. In this constant,v andE are Poisson's ratio and the modulus of elasticity respectively. Experimental results show the percent deviation to be a function of the compressibility constant of the material and the radius of curvature and that these two parameters are inter-related. The percent deviation was found to be essentially independent of gage length for the range of specimen configurations investigated except where the radius of curvature of the specimen induces problems in mounting the gages. Since a linear pressure-strain response was obtained, it is possible to correct the strain readings for gages mounted on specimens of varied hydrostatic compressibility and geometrical configuration.     

Projectile acceleration in a single-stage gun at breech pressures below 50 MPa

Experimental studies were carried out to investigate projectile acceleration in a single-stage gun at breech pressures below 50 MPa. The gun was driven by firing either liquid or solid propellant. In-bore projectile velocity was continuously recorded using the well-known, precise VISAR interferometer technique so that accurate projectile acceleration data could be deduced. Both the attained projectile acceleration and muzzle exit velocity depend upon the charge-to-mass ratio and the pressure at which the blow-out disk ruptures. The results obtained from these experiments render information on the interplay between propellant combustion and projectile acceleration for low in-bore pressure regimes, and they provide the input data required for adequate numerical simulation.     

超高速撞击实验的三级压缩气炮技术

介绍了弹速8km/s、氮气驱动三级压缩气炮技术的研究背景。论述了以三级压缩替代二级压缩 在提高氮气驱动多级气炮上限弹速方面的意义。讨论了弹径10mm 的57-37-10三级气炮的驱动气压、泵管 初充气压与发射弹速及高压气室荷载之间的关系。简述了57-37-10三级压缩气炮主要部件的工程设计,通 过实验数据和实物照片表述了57-37-10三级压缩气炮研究工作的进展情况。     

An equiangular rosette-type extensometer

For complete determination of the state of stress at a surface point of an elastic body, it is in general necessary to measure the strain in three directions. This is usually made by means of strain rosettes of the bonded resistance-wire type. In this paper, a new type of extensometer is described which is capable of measuring the strains in three directions simultaneously.The extensometer consists of three parallel and equidistant legs which are flexibly connected to a central part and supplied with sharp indentors. The change in distances between equivalent points of these legs is proportional to the surface strains. Unbonded resistance wires or reluctance gages have been used for converting the displacements into electrical signals. Attachment is achieved by means of permament magnets or rubber cups.Restoring forces from flexible connections and strained wires are analyzed in detail. For an extensometer with 12 mm gage length and supplied with strained wires, these forces were found to be 21 g for a principal strain sum of 0.001 and 19 g for a principal strain difference of 0.001. When using reluctance gages, these figures are reduced to 5.8 and 12 g, respectively.Paper was presented by title at 1958 SESA Spring Meeting held in Cleveland, Ohio, on May 14–16.