Modulus Of Elasticity In Tension Research Articles

Elasticity characteristics of molybdenum within the temperature range 400–1400 K

We present the results of high-precision investigations of the elasticity characteristics of MChVP commercially pure polycrystalline molybdenum within the temperature range 400–1400 K. The measurements were carried out by using the ultrasonic echo-pulse method. The frequency of the sounding signal was equal to 10 MHz. We establish correlations between the moduli of elasticity in tension and in shear and study the distinctive features of the break in the dependences of the elasticity characteristics of molybdenum near T=900 K. We propose to consider this temperature as one of the physical constants of molybdenum.

Stress/strain behaviour of the equine laminar junction.

The equine laminar junction plays a vital role in transferring the forces of weight-bearing between the epidermal hoof wall and the bone of the third phalanx, but the way in which it performs this function is poorly understood. Using samples from sites varying proximodistally and circumferentially around the hoof, the stress/strain behaviour of this tissue was characterised in three directions: radial tension and proximodistal and mediolateral shear. The influences of toe angle and length were also examined. For all three test directions, the modulus of elasticity increased with increasing strain magnitude. The mean modulus of elasticity in tension was 18.25+/-5.38 MPa (mean +/-1 S.D., N=116; mean strain 0. 25). In proximodistal shear, the mean shear modulus was 5.38+/-1.49 MPa (N=76; mean shear strain 0.48) and in mediolateral shear 2. 57+/-0.91 MPa (N=66; mean shear strain 0.81). In many cases, the individual hoof or horse from which the samples were taken significantly affected the value of the modulus, suggesting that mechanical history may affect the material properties of this tissue. Few biologically significant variations with location, toe length or toe angle were unambiguously demonstrated, suggesting that the material properties of the laminar junction are independent of position, despite apparent regional variations in function, and that foot shape is not a major determinant of material properties.

Effect of pre-cooling and freezing rate on mechanical strength of potato tissues (cv Monalisa) at freezing temperatures

A study was conducted on the effect of different freezing rates (0.5, 1.25 and 2°C/min) and pre-cooling (3°C for 30 min) on the mechanical strength of potato (Solanum tuberosum L.) tissues at temperatures ranging from –3°C to –18°C. The rheological parameters derived from compression, shearing and tension of frozen samples showed that the rheological behaviour of the tissue is directly related to the degree of structural damage. When tissue was frozen at 2°C/min, the rheological parameters declined significantly within the range of –6 to –9°C. Pre-cooling caused a more linear increase in the tissue’s mechanical strength, reducing the number of volumetric changes and the number of dog-bone-shaped specimens with static cracking. In this way it was possible to calculate a temperature coefficient for each rheological parameter giving the degree of loss through freezing. The highest coefficient was for apparent modulus of elasticity in tension (7.87%). For comparative purposes, this study also examined the same rheological parameters obtained between 0 and 40°C. The compression test was the best test for analysis of these effects within the negative range, while the tension test was most sensitive to the effects of temperature in the positive range.

Effects of simulated clinical fabrication heat treatment and artificial weathering on the hardness testing of prosthetics/orthotics polymers

The tensile behavior was compared for five prosthetics/orthotics polymers : Durr-Plex (copolyester), Polypropylene (polypropylene), Subortholen (polyethylene), Surlyn (ionomer), and Uvex (and cellulose acetate butyrate). Tensile properties, yield strength, and modulus of elasticity are related to a number of factors including composition and condition of polymers. The polymers were examined in the as-received and simulated clinical fabrication heat-treated conditions. The simulated clinical fabrication heat-treated specimens were subsequently treated to 2 weeks, 4 weeks, and 8 weeks of artificial weathering conditions, consisting of exposure to cycles of ultraviolet light and heated condensation. Tensile testing was performed on an Instron mechanical testing system, until fracture occurred. The ranges and respective rankings of yield strength and modulus of elasticity in tension were determined. Analysis of Variance (ANOVA) and post hoc Scheffe statistical analyses were performed for different polymers of the same treatment condition, and different treatment conditions of the same polymer. The analysis of variance (ANOVA) showed significant yield strength and modulus differences for the five polymers. The choice of material significantly influences the tensile properties for prosthetics/orthotics polymers. The Uvex polymer had the highest yield strength and elastic modulus, and the Surlyn polymer had the lowest yield strength and elastic modulus. The ranking trend was Uvex > Durr-Plex > polypropylene > Subortholen > Surlyn.

Estimating the elastic modulus of concrete made with artificially manufactured lightweight aggregates

Discusses the results of a study of the moduli of elasticity of concretes made with artificially manufactured lightweight aggregates subjected to uniaxial compression and uniaxial tension. Two artificially manufactured lightweight aggregates and one normal weight aggregate (for comparison) were used in the investigation. Concrete mixes designed to have compressive strengths varying from 20 MPa to 60 MPa were used in this study. Presents the results of static and dynamic moduli of elasticity, Poisson′s ratio, ultrasonic pulse velocity, compressive strength and tensile strength tests. Observes that the static modulus of elasticity in tension is nearly equal to the static modulus of elasticity in compression at a stress level of one‐third the ultimate stress. Compressive modulus values are shown to be dependent on the stress level and type of modulus, i.e. either secant or tangent. On the other hand, the tensile modulus is not affected by the stress level. The modulus of elasticity of lightweight aggregate concrete is about 60‐70 per cent of that of normal weight concrete. Compares the test results obtained in this study with research work carried out on other lightweight aggregate concretes by other investigators. Also presents the relationships between static modulus of elasticity, dynamic modulus of elasticity, compressive strength, and Poisson′s ratio, and equations for estimating elastic modulus and Poisson′s ratio.

Measurement of rock elastic moduli in tension and in compression and its practical significance : Stimpson, B; Chen, R Can Geotech JV30, N2, April 1993, P338–347

Measurement of rock elastic moduli in tension and in compression and its practical significance : Stimpson, B; Chen, R Can Geotech JV30, N2, April 1993, P338–347

Measurement of rock elastic moduli in tension and in compression and its practical significance

The moduli of deformation of rock in tension and in compression are generally assumed equal. However, many rocks show different deformation properties when loaded in tension and in compression. This property is usually referred to as bimodularity. In this paper, a new testing technique in which moduli in both tension and compression can be measured on the same specimen in the same compressive loading frame is described. Testing results from halite, potash, granite, and limestone indicate that moduli in compression and in tension are different for at least three of these materials. The new testing technique is validated against the standard uniaxial tension and uniaxial compression tests on potash and halite. Also, results from granite by the new testing technique are comparable with previously published data. The practical significance of rock bimodularity is discussed as well. It is demonstrated that this property significantly influences the deflection and stress distribution in a simple beam problem. Bimodularity also influences the interpretation of indirect rock tension test results and the prediction of roof deflection in underground openings. Ignoring bimodularity overestimates rock tensile strength in most of the indirect rock tension tests and underestimates roof deflection. Key words : rock, elastic modulus, bimodularity, testing technique.

Strength properties of raffia bamboo

The results of tensile and bending tests carried out on specimens of raffia bamboo are presented. Raffia bamboo are natural materials commonly used for the construction of buildings and household furniture in South Eastern Nigeria. The test results show that the material is capable of attaining an ultimate tensile strength of about 150 N/mm 2 and a modulus of elasticity in tension of about 24 kN/mm 2. These strength properties compare favourably with those of most natural timber species and also some oriented polymers used in fibre reinforced concrete.

A new theory for bending of thick sandwich beams

Classical sandwich theory incorporates stretching and bending action in the facings and transverse shear deformation in the core. The theory presented here is intended for sandwich beams with relatively thick facings and moderately stiff cores of either bimodular material (which has different elastic moduli in tension and compression) or ordinary materials. Thus, transverse shear deformation in the facings as well as stretching and bending action in the core are also considered. Both analytical and finite-element results are presented and compared with the existing classical sandwich theory, which is shown to be unconservative in its predictions of both deflections and maximum shear stresses.

Fracture Toughness and its Relation to Initial Tangent Modulus of Granitic Rock

This paper describes the relationship between fracture toughness and initial tangent modulus, i.e., Young's elastic modulus in tension, of granitic rock. ASTM standard specimens for notched three-point-bend and compact tension tests, which contained various levels of water or were subjected to thermal cycle, were used to correlate fracture toughness to Young's modulus. Furthermore, fracture toughness tests were carried out at high temperature and in pressurized water environment to evaluate the fracture and deformation behaviors under a simulated condition of geothermal reservoir.Based on the linear elastic fracture mechanics, elastic modulus was precisely measured for granitic rock samples by means of a compliance calibration technique prior to fracture toughness tests. Fracture toughness was determined by means of AE technique from an abrupt increasing point of AE activity.The results obtained in this study indicate that a significant increase in fracture toughness (KiAE) appears with increasing elastic modulus (E) and fracture toughness has a simple linear relationship with elastic modulus. Theoretical consideration based on the atomic scale fracture model by Gilman can give an adequate explanation to this relationship between KiAE and E.It is suggested that the effect of water content on the elastic modulus and fracture toughness can be interpreted as the result of internal friction on the micro-crack plane. An optical microscopic study led to a conclusion that the decrease in elastic modulus and fracture toughness with increasing temperatue is due to the increase in thermally-induced micro-crack in the rock sample. The result obtained at high temperature/pressurized water environment may be attributed to highly activated chemical reaction at the crack tip.

Bending of laminated thick beams of bimodular material

The purpose of this analytical investigation is to study the effect of stacking sequence on the static behaviour of thick beams laminated of two different bimodular materials, which have different elastic moduli in tension and compression. Closed-form solutions are presented for two different loading/boundary condition cases, and laminates containing up to six layers are considered.

Transverse Shear Effects in Bimodular Composite Laminates

A closed-form solution for the Timoshenko-type shear correction coefficient (K2) governing the deflection of bimodular composite laminates in cylindrical bending is presented. The bending- stress distribution for a laminate constructed of bimodular materials (which have different elastic moduli in tension and compression) is used in the two-dimensional equilibrium equation to obtain the transverse shear-stress distribution. This shear-stress distribution is used to obtain expressions for the shear correction coefficient (based on equrvalent shear strain energy) and the maximum dimensionless transverse shear stress (τxz) max. Finally, the effects of the elastic-constant ratios on the neutral-surface location and shear correction coefficient for laminates consisting of either unimodular or bimodular materials are studied.

Effect of cold extrusion and heat treatment on the mechanical properties of polypropylene

Polypropylene rods are cold extruded through a die with three nominal area reductions of 18, 40 and 64%. These extrudates are subject to subsequent heat treatments at 100°, 120° and 140 °C for two hours after which this is followed by either air cooling or water quenching. The effect of cold extrusion increases the tensile strength, the elastic moduli in tension and compression as well as the specific impact energy absorption. The 0.2% offset yield strength in tension decreases slightly for the 18 and 40% extrudates but increases above the value of the as-received polymer at 64% cold work. However, cold extrusion decreases the compressive yield strength and the density which is a measure of crystallinity of the cold worked polymer. Cold extrusion followed by heat treatment reduces the elastic moduli but raises the yield strengths of the extrudates. The impact energy absorption shows a sharp increase with annealing temperature and the fracture surfaces display increasing orientation effect with increasing amounts of cold work. Air-cooled and quenched samples do not have any significant differences in these macroscopic mechanical properties. It is apparent that heat treatment increases the density and hence the crystallinity of the cold worked polymer. The improvement is marginally larger for the air-cooled than for the quenched samples. The results of this investigation suggest that it is possible to obtain a combination of mechanical properties of polypropylene by a suitable extrusion-heat treatment process.

Bending of thick beams of bimodulus materials

The literature on bending of beams made of bimodulus materials (which have one value of the elastic modulus in tension and another in compression) is limited. All of the works known to the present investigators are restricted to beams with natural boundary conditions and subjected to specific distributions of normal pressure only. In the present work, the transfer-matrix approach is used to determine the small-deflection static behavior of bimodulus beams, including transverse shear deformation. The neutral surface, i.e. the locus of points having zero axial normal strain, may vary linearly within each element. The effects of axial load and non-natural boundary conditions are considered. As a basis for comparative evaluation, exact closed-form solutions are also presented for special cases in which the neutral-surface location is constant along the beam axis. Results are compared between the two solution methods and are found to give good agreement.

Three-Point Bending at Large Deflections of Beams with Different Moduli of Elasticity in Tension and Compression

Abstract An analytical investigation of three-point bending at large deflections was carried out with materials exhibiting different moduli of elasticity in tension and in compression. It was found that the solutions developed by the authors elsewhere for equal moduli materials were still valid, provided that load and beam depths were replaced by equivalent values derived by multiplying the actual values by factors that were functions of the moduli ratio only. The moduli ratio, even for small deviations from unity, was found to influence the behavior of the system considerably. Interaction with friction at the supports could render experimental results unreliable, and hence complete knowledge of the reaction forces during the bending test, both by magnitude and direction, appears to be necessary. Experimental evidence appears to support the present theoretical predictions.

Uniaxial Tension Tests on Cement-Stabilized Granular Materials

Abstract This paper presents details of tests to evaluate the suitability of a double scissor friction grip system, initially developed for conventional concrete, for determining uniaxial tensile strength of cement-stabilized granular materials suitable for use in roadbase construction. The system is examined in terms of the variability of the results, the significance of fracture location, and the distribution of strain, and is judged to show promise. Test results on a cement-stabilized gravel, typical of roadbase materials used in the United Kingdom, are given, including the stress-strain characteristics in tension, the moduli of elasticity in tension and compression, and the strengths in tension, compression, and flexure.

Investigation of the stability of the physicomechanical properties of carbon fibers 1. Dependence of Young's modulus on the cross-sectional area of the fiber

The modulus of elasticity in tension and the density of various carbon fibers (re-inforcement for high-modulus carbon-reinforced plastics) have been studied. There is an experimentally confirmed dependence of the modulus of elasticity on the orientation and density of the monofilament which explains the variation of this characteristic in a fiber bundle. It is shown that the principal factor determining the modulus of elasticity and its stability in a bundle of carbon fibers is the orientation and its variation for the individual fibers.

A Circular Cylindrical Shell with Different Elastic Moduli in Tension and Compression

Little attention has been paid to materials with different deformation responses to simple tension and compression, except to certain types, such as concrete. Yet, recently developed new materials, certain composites or high-polymers are said to exhibit more or less the avobe described behaviors. In this paper, as an example of analysis of plate or shell made of such materials, a circular cylindrical shell subjected to a uniform internal pressure is investigated. Since the elastic constants of these materials in a deformed body which depend on the sign of stress are unknown in advance, numerical analysis is performed by a successive approximation method, starting from an appropriately assumed stress state close to the desired solution. Results show that distributions of membrane force and bending moments in the circular cylindrical shell vary considerably with difference between tensile and compressive moduli of elasticity. Since precise experimental data on these materials are however still lacking, publication of such data is eagerly being waited for.

Elastic characteristics of graphitoplastics and impregnated graphites

The effect of aging on the moduli of elasticity of graphitoplastics and resin-impregnated graphites has been directly investigated. The dependence of the modulus of elasticity in tension and compression on the normal stress in the specimen cross section has been studied for the same materials.

Buckling of circular cylindrical shells with different moduli in tension and compression

An exact solution is derived for buckling of circular cylindrical shells with different elastic moduli in tension and compression under arbitrary combinations of axial and lateral pressure. The combinations include those in which one component of pressure causes tension. Classical buckling theory, by which is implied a membrane prebuckled shape, is used for simply supported edge boundary conditions. General results in a form analogous to Batdorf's classical k-Z form are presented for several ratios of tensile to compressive elastic moduli. Differences in tensile and compressive moduli are observed to cause significant differences in the buckling loads. This situation is particularly acute when only a small tensile loading component exists in conjunction with an apparently dominant compressive loading component. For example, if a small axial tensile loading is present in a principally external pressure loading environment, a reduction of 17% in the external pressure buckling load from the zero axial load case can occur for a tensile modulus that is half the compressive modulus. The present results are important because current composite materials often have significantly different elastic moduli in tension and compression.