High strain-rate testing: Tension and compression

Details of the split Hopkinson pressure-bar method for obtaining complete stress-strain curves at strain rates on the order of 1000 sec^?1 in either tension or compression are presented. In compression, a gage for measuring radial strain and, therefore, Poisson's ratio is also described. Some typical results are presented for aluminum, and various factors pertaining to the accuracy of the results are discussed.     

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.     

Poisson's ratio determined with strain rosettes

Poisson's ratio appears in general stress-strain equations and is essential to experimental stress analysis. An experimental method using bonded electrical-resistance strain rosettes is described in this paper. The standard use of two strain sensing elements at 90 deg was replaced with “rectangular rosettes” installed back-to-back. The third strain-sensing element was used to calculate the gage alignment error and “true” longitudinal and transver e strains. For 2024-T351 sheet material, an average measured value of 0.312 for Poisson's ratio was obtained.     

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.     

Dynamic behavior of concrete

Concrete and cement-paste specimens, representing a model of the actual structural material and of its adhesive component, respectively, were subjected to static and dynamic tests. Static tests on virgin specimens were carried out in order to evaluate the strength, elasticity and Poisson's ratio of the materials. The dynamic experiments were conducted in order to ascertain the response of the specimens to the propagation of one-dimensional pulses. Transient loading was accomplished by the central longitudinal impact of a 1/2-in.-diam steel sphere on a ballistically suspended 3/4-in.-diam Hopkinson bar of the material at an initial velocity of about 3260 or 1650 ips. The shocked specimens were also subsequently examined to determine whether changes in static material properties had occurred as a result of passage of the waves. Both static and dynamic tests yielded consistent results for a number of specimens cast and cured in identical fashion. Comparison of the properties of the virgin and the shocked specimens indicated little, if any, shock damage. While some minor grain damage was observed in microscopic examination of thin sections taken from some of the shocked specimens, other sections did not indicate any visible cracking of the grains. The wave-propagation process appeared to occur without dispersion and relatively little attenuation, indicating that the material could be represented on a macroscopic scale as an “elastic” substance with a small structural-damping coefficient. The obvious inhomogeneities of the concrete affected the gage response whenever a gage was mounted directly over a piece of aggregate. The dynamic response of the materials has been compared with the response of several types of rocks.     

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.     

A simplified method for eliminating error of transverse sensitivity of strain gage

This paper presents a simplified method for eliminating error of transverse sensitivity of resistance strain gage. It is proved mathematically and mechanically that principal stress and directional angle are true values without any errors if calculated directly from the apparent values of Young's modulus and Poisson's ratio of specimen materials, and from all the apparent-strain readings.     

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON＇S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.     

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.     

Concepts of the photoelastic stress gage

With the photoelastic stress gage birefringence readings are made with light that traverses a path parallel to the surface of the workpiece. Individual stresses are determined in the elastic range of deformation, rather than stress or strain differences. The theory of a circular and linear stress gage is developed, including the influence of Poisson's ratio, and stress gradients. Stresses in the surface of the workpiece are expressed in terms of measured birefringence. Instrumentation is extremely simple. High sensitivity is derived from the relatively long optical-path length through the transducer. Applications should include stress analysis, load analysis and transducer design.     

On the measurement of Poisson's ratio for modeling clay

Resonance testing of Plasticine clay indicates that, for small strains (≤10^?5) in the frequency range 100–3000 Hz, the material can be considered to be a linear viscoelastic solid with parameters which depend on temperature, frequency and prior large-strain history. In order to measure Poisson's ratio, it is necessary to take special precautions to eliminate large straining between small-strain tests of different tensorial character. A simple but effective test configuration for measuring Poisson's ratio is described and test results are displayed.     

Accurate measurement of Poisson's ratio in small samples

A method is described whereby Poisson's ratio was measured in metallic and plastic materials to an accuracy of ±0.003 (3σ limits). A size limitation was imposed in that the test specimens had to be manufactured from a 50.8 mm (2 in.)-diam bar with the maximum stress direction across a diameter.     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.     

混凝土复合型裂纹扩展的非局部近场动力学建模分析

基于非局部近场动力学理论,构建了修正的能反映混凝土宏观拉压异性和断裂特征的近场动力学本构模型,开发了相应的离散、加载和时间积分算法,实现典型混凝土构件中复合型裂纹扩展过程模拟。在物质点对尺度上定义局部损伤并考虑物质点对的相对转动,通过求解时空微-积分方程实现裂纹的自然萌生与扩展,避免裂尖不连续带来的求解奇异性、网格依赖性和网格重构以及常规近场动力学本构模型的泊松比限制。通过含单边和双边初始裂纹四点剪切混凝土梁裂纹扩展破坏全过程模拟,得到破坏形态、破坏荷载以及完整的荷载-裂纹开口滑移曲线,并与试验和其他数值模拟结果对比,验证了模型的精确性和算法的稳定性。     

Vibration of thick auxetic plates

This short communication investigates the effect of negative Poisson's ratio on the natural frequency of thick plates of arbitrary shape. Using the Mindlin plate theory, it was generally found that as the plate's Poisson's ratio becomes more negative, the Mindlin-to-Kirchhoff natural frequency ratio increases with decreasing rate. Upon comparing (a) the use of the simplified constant shear correction factor and the more accurate variable shear correction factor, (b) with and without rotary inertia, it was found that all the four combinations stated in (a) and (b) do not give appreciable difference when the Poisson's ratio of the plate is positive. However in the case of plates with negative Poisson's ratio, results reveal that when at least one of the simplifying assumptions is used, the Mindlin-to-Kirchhoff natural frequency ratio is overestimated, and that the overestimation further increases when both the simplifying assumptions are used. When benchmarked against Reddy plate theory, the use of variable shear correction factor has almost the same effect as the inclusion of rotary inertia. Hence the use of either variable shear correction factor or rotary inertia is proposed for modeling the vibrational frequencies of conventional and auxetic isotropic plates.     

Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction,elastic Poisson's ratio,Young's modulus and yield strength

In this work the relationship between the structural disorder and the macroscopic mechanical behavior of nanoporous gold under uniaxial compression was investigated, using the finite element method. A recently proposed model based on a microstructure consisting of four-coordinated spherical nodes interconnected by cylindrical struts, whose node positions are randomly displaced from the lattice points of a diamond cubic lattice, was extended. This was done by including the increased density as result of the introduced structural disorder. Scaling equations for the elastic Poisson's ratio, the Young's modulus and the yield strength were determined as functions of the structural disorder and the solid fraction. The extended model was applied to identify the elastic–plastic behavior of the solid phase of nanoporous gold. It was found, that the elastic Poisson's ratio provides a robust basis for the calibration of the structural disorder. Based on this approach, a systematic study of the size effect on the yield strength was performed and the results were compared to experimental data provided in literature. An excellent agreement with recently published results for polymer infiltrated samples of nanoporous gold with varying ligament size was found.     

Principal-stress differences in transverse planes of symmetry

The value of Poisson's ratio for most of the photoelastic materials at critical temperature is very nearly equal to 0.5. This fact can be utilized to determine the values of the displacement function u(r) and the principal-stress differences in the transverse plane of symmetry of an axially symmetric body. This requires a single integrated-retardation pattern. The solutions are applied to the problem of a sphere under diametral compression and the results compared with those obtained from shear-difference method.     

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.     

EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.     

An analytical solution for a linear viscoelastic layer loaded with a cylindrical punch: Evaluation of the rebound indentation test with application for assessing viability of articular cartilage

A general closed-form solution for the so-called rebound indentation test’ is obtained for a cylindrical flat-ended punch indenting a linear viscoelastic layer lying on a rigid substrate. Under the assumption of time-independent Poisson's ratio, we derive closed-form analytical expressions for the contact force (in a displacement controlled regime) and for the indentation displacement (in a load-controlled regime) and we consider in detail the case of standard viscoelastic solid. Our results indicate that the rebound displacement (in other words the indentation displacement in the load-controlled stage) is independent of the relaxed elastic modulus and Poisson's ratio, and also of the layer's thickness. Our analytical solution can be used for layered samples of arbitrary materials exhibiting viscoelastic properties; however, since the rebound indentation test has been recently suggested for assessing the viability of biomedical materials, we have applied our theoretical framework to the identification of materials parameters from experiments on articular cartilage. In this context, we have found a pretty good agreement for the rebound deformation, even until the strain becomes relatively large.