Solid Cylindrical Specimens Research Articles

Strain Localization in Solid Cylindrical Clay Specimens Using Digital Image Analysis (DIA) Technique

The strain non-uniformity due to the end restraint for a deforming specimen during triaxial testing of clay specimens was minimized in this study using lubricated end platens. This research presents the evidence of the occurrence of strain localization due to shear banding within the clay specimen by using DIA (Digital Image Analysis) technique. The variation in strain localization patterns of soil specimen is also studied for evaluating the influence of confining stress, loading conditions, stress history, drainage conditions, and soil's microfabric (geometric arrangement of clay platelets) by performing a series of lubricated-end triaxial tests on solid cylindrical specimens of Kaolin clay. This paper presents a comparative study based on the observed orientation of shear band formation, and the intensity of strain localization (by estimating the maximum local strain) within the specimen during its shear deformation process.

Elasticity solution for an axially compressed and encased cylindrical specimen

We present the solution of the linear elasticity equations governing the deformation of an elastic cylinder encased in a tube and subjected to uniform compression on the flat ends. The solutions for the stresses, strains, and displacements in the encased and compressed cylinder are all systematically determined from the basic solution of Lamé's classical elasticity problem of the long tube subjected to internal and external pressures. We first derive the general elastostatic analysis for an encased hollow cylinder, stress-free at the cavity, and later particularize the solution to a solid cylindrical specimen. The effective modulus E eff of the encased sample is found to be a function of the bulk modulus k and Poisson's ratio ν of the material. E eff differs from k except for nearly incompressible materials, where E eff approaches the bulk modulus value. In the incompressible case, we also show how a load applied on the cylinder's flat ends is equivalent to, and can be replaced by, the same load acting on the curved surface. For compressible materials, a more general expression for E eff is found that also accounts for the case deformation. These results explain the deformation of an axially compressed and encased cylindrical specimen tested in compressibility measuring devices such as those described by Matsuoka and Maxwell [Response of linear high polymers to hydrostatic pressure. Journal of Polymer Science 1958; 32:131–59]. The present analysis thus contributes to a better understanding of how this device works and to the interpretation of measurements taken with it.

A laboratory study of normally consolidated kaolin clay

In recent years many researchers have attempted to address the need for a comprehensive understanding of the three-dimensional mechanical behavior of frictional materials. Advances in testing methods have added the capability of studying various aspects of generalized stress–strain behavior in a controlled environment. Strain-controlled true triaxial undrained tests on normally consolidated kaolin clay are performed in this study using a fully automated flexible boundary experimental setup with a real-time feedback control system. The influence of the intermediate principal stress and principal stress rotation on the stress–strain–strength and pore pressure behavior is investigated considering the occurrence of strain localization within the specimen. The strength behavior observed in this study of kaolin clay is used to evaluate existing failure criteria for cohesive soil. Comparative laboratory tests, such as the lubricated end triaxial test on a solid cylindrical kaolin specimen and combined axial–torsional tests on a hollow cylindrical kaolin specimen, were also performed to evaluate the corresponding mechanical behavior in different loading systems. Despite using identical techniques for specimen preparation and a similar consolidation stress state, the soil behavior obtained from the three types of tests showed observable variations, demonstrating the importance of specimen shape and loading–boundary conditions.Key words: normally consolidated clay, stress-strain behavior, pore pressure, anisotropy, testing methods.

Cyclic deformation behavior of an epoxy polymer. Part I: Experimental investigation

AbstractA series of uniaxial cyclic tests were carried out on solid cylindrical specimens of an epoxy resin, Epon 826/Epi‐Cure Curing Agent 9551. The focus of the study was to investigate time‐dependent viscoelastic behavior of this thermosetting polymer material under cyclic loading and to develop a constitutive model with the capabilities to simulate the observed deformation response. The tests include stress‐controlled or strain‐controlled cyclic loading with/without mean stress or mean strain at various amplitudes and loading rates. It was found that the cyclic stress‐strain response of this material is amplitude‐dependent and rate‐dependent, and the response to axial tension is different from that in compression. The stress‐strain loops exhibit more pronounced nonlinearity with high amplitudes or low loading rates. For stress‐controlled cyclic loading with mean stress, ratcheting strain is accumulated, which is of viscoelastic nature, and this is confirmed by its full recovery after load removal. For strain‐controlled cyclic loading with mean strain, the mean stress relaxation occurs, which contributes to the observed longer life in comparison to the stress‐controlled cyclic loading with mean stress. Polym. Eng. Sci. 44:2240–2246, 2004. © 2004 Society of Plastics Engineers.

Strength and Deformation Properties of Compacted Cement-Mixed Gravel Evaluated by Triaxial Compression Tests

To achieve as possible as a high cost-effective construction of important civil engineering structures, such as bridge abutments, using cement-mixed gravel (CMG) for the backfill, a series of drained triaxial compression (TC) tests were performed on CMG specimens. Two types of well-graded gravels were used. Axial and lateral strains were measured locally on the lateral surface of solid cylindrical specimens. It was found that, for a same cement to gravel ratio by weight, the peak strength qmax tends to become the maximum when compacted at the optimum water content, w opt, for a given compaction energy level. This trend is due largely to the smallest compacted void ratio and partly due to the largest cement content per unit volume associated with the maximum dry density. The other influencing factors include an incidental optimum combination of strength and amount of cement paste that may be attained when compacted at w = wopt· The relationship between the ratio of "qmax at a certain molding water content, w" to "qmax at wopt, qmax.OMC" and the normalized deviation ratio of w from “wopt, | w- wopt | / wopt” is rather unique whether compacted at dry or wet of optimum, for different compaction energies and for the two types of gravel. It is also shown that the initial Young's modulus tends to become the maximum when compacted at wopt while the pre-peak stiffness and post-peak ductility generally increase with an increase in the molding water content. Based on the test results, it is recommended to compact a given type of cement-mixed gravel around at wopt ensuring that the compaction is not made dry of optimum for a given compaction energy.

High Strain-Rate Compressive Characteristics of Carbon/Epoxy Laminated Composites in Through-Thickness Direction

Compressive stress-strain characteristics of carbon/epoxy laminated composites in the through-thickness direction at strain rates of over 1000/s were evaluated using the standard split Hopkinson pressure bar. Three carbon/epoxy laminated composites (i.e., unidirectional, cross-ply and woven) with almost the same thickness were tested at room temperature. Small solid cylindrical specimens were machined such that the direction of the compression loading was perpendicular to the fiber direction of the laminates. The effects of strain rate and reinforcement geometry on the secant modulus at 1% strain, ultimate compressive strength and strain, and total strain energy to failure were examined in detail.

Study on ring compression test using physical modelling and FE simulation

This paper presents a study of the ring compression test using physical modelling experiments and finite element (FE) simulation. Using commercially available modelling clay, material stress–strain relationships were obtained from compression tests of solid cylindrical specimens. A series of ring compression tests were carried out to obtain friction coefficients for a number of lubricants including vaseline, zinc stearate and talcum powder. FE simulations were used to derive the friction calibration curves and to evaluate material deformation, geometric changes and load–displacement results. Friction coefficient values of the tested lubricants are in agreement with the results obtained by other researchers. Further investigation is necessary to determine the effects of material properties, test conditions and use of calibration curves on the ring compression test. It is suggested that the combined use of physical modelling experiment and FE simulation provides a simple and effective means in the study of frictional mechanisms for bulk material deformation.

Measurement of Specific Heat Capacity and Electrical Resistivity of Industrial Alloys Using Pulse Heating Techniques

The determination of the specific heat capacity and electrical resistivity of Inconel 718, Ti-6Al-4V, and CF8M stainless steel, from room temperature to near the melting temperatures of the alloys, is described. The method is based on rapid resistive self-heating of a solid cylindrical specimen by the passage of a short-duration electric current pulse through it while simultaneously measuring the pertinent experimental quantities (i.e., voltage drop, current, and specimen temperature). From room temperature to about 1300 K, the properties are measured using an intermediate-temperature pulse-heating system by supplying a constant current from a programmable power supply and measuring the temperature using a Pt-Pt:13% Rh thermocouple welded to the surface of the specimen. From 1350 K to near the melting temperatures of the alloys, the properties are measured using a millisecond-resolution high-temperature pulse-heating system by supplying the current from a set of batteries controlled by a fast-response switching system and measuring the temperature using a high-speed pyrometer in conjunction with an ellipsometer, which is used to measure the corresponding spectral emissivity. The present study extends the application of these techniques, previously applied only to pure metals, to industrial alloys.

Mathematical Simulation of Three-Dimensional Spin Regimes of Gasless Combustion

A three-dimensional mathematical model is constructed for the gasless combustion of a solid circular cylindrical specimen. The steady-stated spin regimes obtained were studied by numerical methods. The structure and mechanism of spin combustion are illustrated and discussed. It is shown how the space–time pattern of spin-wave propagation is complicated as the radius of the cylinder increases. Spin propagation of the front can proceed in a regime in which the structure of the front does not change (for small radii of the sample) or in an unsteady regime, in which the structure of the front undergoes numerous changes over a period. In the second case, a synchronous or alternate “flicker” of the sites is observed on the surface of the cylinder. The nonuniqueness of the combustion regimes is detected. It is shown that the average velocity of propagation of the spin-combustion front is of the order of the velocity of steady front propagation under adiabatic conditions.

Dynamic Heading of Triangular, Hexagonal and Octagonal Shaped Heads at Low Impact Velocities: Some Experiments and an Analysis

The paper presents some typical results of an experimental investigation into the dynamic heading of triangular, hexagonal, and octagonal shaped heads, each at one end of the initially solid cylindrical rod-type specimens made of tellurium lead and commercially pure aluminium which were clamped at the other end in each case. Deformation of the materials into head shapes was conducted under low-velocity dropweight impact situations, and the characteristic die load-time and die movement-time results were observed. The results of die load-die movement curves obtained from these results were compared with those estimated from a modified simple upper bound analysis that takes account of the inertia forces of the undeformed material. Comparison of the dynamic heading results with those observed from similar quasi-static cases suggests that though the dynamic heading loads were, in general, 20-40% higher than the similar quasi-static loads, the estimated dynamic forging loads employing the modified upper bound analysis taking account of the inertia, showed good correlations with the experimental results. These and other results are given and commented upon.

Finite element investigation into the torsion test in the range of large strains and deformations

Torsion tests with thin-walled tubular, solid cylindrical and Lindholm-type tubular specimens were simulated using the finite element code ABAQUS, in the range of large strains and deformations. The results showed that for thin-walled tubular and solid cylindrical specimens the radii of the specimens almost remained straight during torsion; for Lindholm-type tubular specimens the twist angle of the cross-section at the two ends of the gauge section did not stay constant, due to the change of the specimen geometry (i.e. the end effect). A correction which considers the end effect should therefore be introduced when the stress-strain relationship is characterized. Compared with the stress-strain relationship obtained previously from experiment, a distinct difference was noted when conventional formulae were used to convert the torque and twist angle into the shear stress and shear strain. Further, the influence of axial constraint conditions at the two ends of the specimen was examined; the results showed that axial strains and stresses had no significant influence on the definition of the shear stress-shear strain relation, and hence these can be neglected when the stress-strain relationship is characterized.

Evaluation of heat transfer coefficient during heat treatment by inverse analysis

Reliable prediction of the properties of a heat-treated workpiece requires accurate data of the heat transfer coefficient during heat treatment process. In the present investigation, inverse heat transfer formulation using a two-dimensional finite element method was developed as a tool to evaluate heat transfer coefficient during heat treatment. The formulation has a function of providing a time profile of heat transfer coefficient on various surface locations with measured temperature at proper locations within workpiece under heat treatment. By the present formulation, heat transfer coefficients were evaluated for fan and water cooling of heated solid cylindrical carbon steel specimens. Comparison of the obtained heat transfer coefficients against the existing results on heat treatment shows that the obtained values of coefficients have reasonable accuracy, enough to predict the properties of the heat-treated workpiece.

Near-net shape forging of a crown gear: some experimental results and an analysis

This paper presents a few salient results of an experimental investigation made into the quasi-static progressive incremental closed-die forging of crown gear forms starting initially from both solid and hollow circular cylindrical specimens made of tellurium lead as the model material. The detailed observations made on the die loads and the deformation modes, etc. at various incremental stages are given and these are compared with those based on an upper bound simulation of forging of the crown gear with rectangular and trapezoidal shaped teeth. The tooth profile patterns are also compared with the resultant CAD outputs based on the upper bound analysis. Reasonably good correlations between the experimental observations of die loads and tooth profile patterns with those estimated from theoretical simulations were obtained and these and other results given are commented upon.

Application of Laser Polarimetry to the Measurement of Specific Heat Capacity and Enthalpy of the Alloy 53Nb–47Ti (mass%) in the Temperature Range 1600 to 2000 K by a Millisecond-Resolution Pulse Heating Technique

The determination of the specific heat capacity, enthalpy, and electrical resistivity of the alloy 53Nb–47Ti (mass%) in the temperature range 1600 to 2000 K is described. The method is based on rapid resistive self-heating of a solid cylindrical specimen from room temperature to the maximum temperature of interest by the passage of a subsecond-duration electric current pulse through the specimen and on simultaneously measuring the pertinent experimental quantities. The experimental quantities measured are the current through the specimen, voltage drop across the effective specimen, specimen radiance temperature at two wavelengths, and normal spectral emissivity of the specimen. The present study extends this technique, previously applied to pure metals, to the determination of specific heat capacity and enthalpy of the alloy, 53Nb–47Ti. The measured properties were compared to those calculated from a thermodynamic description of the Nb–Ti system.

Multiaxial Experiments and Constitutive Modeling of Superplasticity

In the first part of the paper, multiaxial experiments of 5083Al alloy are carried out at 833K at constant strain-rates to elucidate the characteristic features of superplastic deformation under general forming conditions. Monotonic tension, compression and torsion tests were performed by using solid circular cylindrical specimens together with thin-walled tubular specimens. The values of the equivalent strain-rate of von Mises type are specified as 2 × 10 -3 , 1 × 10 -3 , 5 × 10 -4 and 2 × 10 -4 s -1 . The significant strain-rate dependence of flow stress and the material softening due to cavity growth are observed under the tension tests. The results of the tension and compression tests show that the material hardens under tension while it softens under compression. The comparison between tension and torsion tests shows that the equivalent flow stress of von Mises type under torsion is much smaller than that of the tension at the same equivalent strain-rate of von Mises type. Based on these observations, a constitutive model of superplasticity is then formulated based on the finite deformation theory. The rate of deformation tensor is divided into the sum of the elastic and inelastic parts, and the former part is represented by the isotropic linear elastic law. The inelastic part is modeled based on the invariant theory by employing the steady-state creep law of hyperbolic sine type and by taking account of the effects of yielding, grain and cavity growth. The rate of drag stress is assumed to be the sum of the terms due to the grain and cavity growth. The evolution equation of the grain growth is formulated by taking account of static growth and strain-induced growth. The evolution equation of the cavity volume fraction is represented by the sum of the two terms due to cavity diffusion and viscoplastic deformation. Comparison of the results of the proposed model with those of the experiments shows that the proposed model gives satisfactory predictions.

Hemispherical total emissivity of niobium, molybdenum, and tungsten at high temperatures using a combined transient and brief steady-state technique

The hemispherical total emissivity of three refractory metals, niobium, molybdenum, and tungsten, was measured with a new method using a combined transient and brief steady-state technique. The technique is based on rapid resistive self-heating of a solid cylindrical specimen in vacuum up to a preset high temperature in a short time (about 200 ms) and then keeping the specimen at that temperature under steady-state conditions for a brief period (about 500ms) before switching off the current through the specimen. Hemispherical total emissivity is determined at the temperature plateau from the data on current through the specimen, the voltage drop across the middle portion of the specimen, and the specimen temperature using the steady-state heat balance equation based on the Stefan–Boltzmann law. Temperature of the specimen is determined from the measured surface radiance temperature and the normal spectral emissivity; the latter is obtained from laser polarimetric measurements. Experimental results on the hemispherical total emissivity of niobium (2000 to 2600 K), molybdenum (2000 to 2700 K), and tungsten (2000 to 3400 K) are reported.

Anisotropy in Elastic Deformation of Granular Materials

Inherent and stress state-induced anisotropy in the elastic deformation properties of granular materials were investigated experimentally. Both axial and lateral principal strains of large square-prismatic and small solid cylindrical specimens were measured locally. Very small strain-amplitude cyclic normal stresses were applied in the vertical and horizontal directions at various isotropic and anisotropic stress states. Elastic deformation properties are inherently anisotropic with the Young's modulus being larger in the vertical direction than in the horizontal direction at isotropic stress states. The Young's modulus is stress state-dependent, becoming more anisotropic as the stress state becomes more anisotropic. The elasticity is of hypo-elastic type. Deformations do not become totally elastic even after the application of a large number of stress cycles of relatively large amplitude along a fixed stress path.

A combined transient and brief steady-state technique for measuring hemispherical total emissivity of electrical conductors at high temperatures: Application to tantalum

A new method for measuring hemispherical total emissivity of electrically conducting materials at high temperatures (above 1500 K) using a feedback-controlled pulse-heating technique has been developed. The technique is based on rapid resistive self-heating of a solid cylindrical specimen in vacuum up to a preset high temperature in a short time (about 200 ms) and then keeping the specimen at that temperature under steady-state conditions for a brief period (about 500 ms) before switching off the current through the specimen. The specimen is maintained at constant temperature with a feedback control system which controls the current through the specimen. The computer-controlled feedback system operates a solid-state switch (composed of field-effect transistors). The sensing signal for the feedback is provided by a high-speed optical pyrometer. Hemispherical total emissivity is determined at the temperature plateau from the data on current through the specimen, the voltage drop across the middle portion of the specimen, and the specimen temperature using the steady-state heat balance equation based on the Stefan-Boltzmann law. The true temperature of the specimen is determined from the measured radiance temperature and the normal spectral emissivity: the latter is obtained from laser polarimetric measurements. The experimental quantities are measured and recorded every 0.2 ms with a 12-bit digital oscilloscope. To demonstrate the feasibility of the technique, experiments were conducted on a tantalum specimen in the temperature range 2000 to 2800 K. The results on hemispherical total emissivity are presented and are compared with the data given in the literature.

The Influence of Boundaries on the Volumetric Behavior of Solid and Hollow Cylindrical Specimens of Glass Beads

Laboratory shear tests were conducted on moderately dense assemblies of large and small glass beads in both solid and hollow cylindrical triaxial devices using either stress-controlled or strain-controlled lateral boundaries. The specimens were sheared in triaxial compression and extension, maintaining the mean stress constant, and volume strains were monitored. The results indicated that the mold used in preparing the specimen created a strong but localized ordering of particles at the boundary and that this type of initial fabric had an important effect on the volumetric behavior of the hollow cylinder specimens. There were also indications that the strain-controlled and the stress-controlled boundaries produced significantly different volume strains at the initial stage of shearing and that increasing the degree of strain-control decreased the amount of initial contraction. In order to compliment these observations, additional triaxial compression and extension tests were carried out with a series of solid cylindrical specimens of different diameters using the small glass bead assembly. The mean stress was again fixed and care was taken to eliminate friction at the top and bottom boundaries. In triaxial extension, the smaller diameter specimens exhibited densification greater than that of the larger diameter specimens. In triaxial compression, the volume change was approximately the same for all diameter specimens. These results support the presence of an initial local anisotropy associated with the mold and indicate that specimens should be at least 150 particle diameters in thickness in order that this anisotropy be negligible.

Biaxial fatigue crack initiation life prediction of solid cylindrical specimens with transverse circular holes

Multiaxial fatigue crack initiation lives of solid cylindrical specimens with transverse circular holes were investigated. Neuber's rule and the finite element approach were both used to obtain the local stresses and strains of the hole. Neuber's rule applied for the hole in this study failed to estimate the local stress state under combined push-pull and torsional fatigue loading. Several prediction models for multiaxial fatigue lives were used to examine the expirimental results with the assistance of the local strain approach through the finite element analysis in this study. It was found that the maximum stress on the hole edge was uniaxial, and all models gave good predicted results by using only push-pull fatigue data of smooth specimens.