Uniaxial Deformation of Rubber Cylinders

1995 ◽  
Vol 68 (5) ◽  
pp. 739-745 ◽  
Author(s):  
P. H. Mott ◽  
C. M. Roland
Keyword(s):  
Strain Curve ◽  
Uniaxial Deformation ◽  
Deflection Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Optical Birefringence ◽  
Parabolic Profile ◽  
Strain Data ◽  
Tension And Compression ◽  
Actual Stress

Abstract Stress, strain and optical birefringence measurements were made on elastomeric cylinders deformed in tension and compression. The birefringence data enables the actual stress to be determined even when the deformation is not homogeneous. In the absence of lubricant, uniaxially loaded rubber cylinders deviate from homogeneous deformation due to bonding of the cylinder ends. The existing analysis to correct the force-deflection curve for the effect of this sticking, strictly valid for infinitesimal strains, is premised on the idea that the deformed cylinder has a parabolic profile. Experimentally, however, it was found that slender rubber cylinders assume a much flatter profile, while maintaining constant volume, when deformed. Nevertheless, the accuracy of the stress-strain curve when the standard correction is applied turns out to be quite good, partially a result of cancellation of two, relatively small, errors. This accuracy was assessed by comparison of force-deflection data from bonded cylinders both to stress-strain data obtained on lubricated cylinders and to the stresses deduced from the measured birefringence.

Inverse Calculation of Uniaxial Stress-Strain Curves From Bending Test Data

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
G. S. Schajer ◽  
Y. An
Keyword(s):  
A Priori ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Inverse Solution ◽  
Surface Strain ◽  
Bending Test ◽  
Stress Strain ◽  
Strain Data ◽  
Tension And Compression ◽  
Priori Information

Uniaxial tension and compression stress-strain curves are simultaneously evaluated from load and surface strain data measured during a bending test. The required calculations for the uniaxial results are expressed as integral equations and solved in that form using inverse methods. This approach is taken to reduce the extreme numerical sensitivity of calculations based on equations expressed in differential form. The inverse solution method presented addresses the numerical sensitivity issue by using Tikhonov regularization. The use of a priori information is explored as a means of further stabilizing the stress-strain curve evaluation. The characteristics of the inverse solution are investigated using experimental data from bending and uniaxial tests.

Experimental Research on Constitute Relation of Concrete under Uniaxial Tension and Compression with Different Strain Rate

2011 ◽  
Vol 250-253 ◽  
pp. 3279-3283 ◽  
Author(s):  
Hai Bin Chen ◽  
You Po Su ◽  
Jun Wei Xing ◽  
Yu Min Zhang
Keyword(s):  
Structural Analysis ◽  
Strain Rate ◽  
Uniaxial Tension ◽  
Theoretical Basis ◽  
Strain Curve ◽  
Strain Ratio ◽  
Test Device ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Tension And Compression

The constitutive relation of concrete under uniaxial tension and compression is an essential theoretical basis for structural analysis of concrete. Because of the lack of sufficient stiffness for ordinary test device, a stable decline branch of stress-strain curve could not be obtained. The condition of realizing the stress-strain complete curve for concrete uniaxial tension and compression is derived. The experiment device for uniaxial tension and compression was designed and fabricated with increasing stiffness method. Experiments were carried out for concrete with grade C30~C60 and strain rate 10-5/s~10-2/s. The equation for stress-strain curve in the rising branch were obtained and so were the complete stress-strain curve of uniaxial tension and compression under different strain ratio, which provide the theoretical basis for concrete structural analysis.

Quantitative Characterization of Cure. I. Relationship between Modulus and Strain of Pure-Gum Natural-Rubber Vulcanizates

1952 ◽  
Vol 25 (3) ◽  
pp. 430-439 ◽  
Author(s):  
R. F. Blackwell
Keyword(s):  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Quantitative Characterization ◽  
Strain Data ◽  
Tentative Explanation ◽  
Natural Rubber Vulcanizates ◽  
The Relationship ◽  
Mooney Equation

Abstract The object of this investigation was to determine whether the relationship between strain (elongation) and modulus is sufficiently close for one to be calculated from the other. Stress-strain data have been recorded for loads of 2–10 kg. per sq. cm. for a series of ACS1 and other pure-gum compounds. It is shown that the strain at a fixed stress (5 kg. per sq. cm.) is uniquely related to the load required to produce an elongation of 100 per cent. A tentative explanation of this observation is given in terms of the Mooney equation for the stress-strain curve. It is shown that the second constant of this equation does not vary greatly from rubber to rubber.

Sensitivity of Stress-Strain Parameters in Leak-Before-Break Evaluations

2007 ◽  
Author(s):  
Nathaniel G. Cofie ◽  
Robert O. McGill ◽  
G. Angah Miessi ◽  
Jim Wu
Keyword(s):  
Fracture Mechanics ◽  
Strain Curve ◽  
Flaw Size ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Approximate Methods ◽  
Critical Flaw ◽  
Leak Before Break ◽  
Actual Stress

Leak-before-break (LBB) evaluations involve the use of deterministic fracture mechanics to establish the margin between critical and leakage flaw sizes in order to assure that leaks can be detected by the plant leak detection system before a through-wall flaw reaches critical flaw size. When the material is semi-ductile, the fracture mechanics evaluations involve the use of elastic-plastic fracture mechanics (EPFM) consisting of the J-integral and tearing modulus (J/T) analyses. An important input into the J/T analyses is the Ramberg-Osgood (R-O) material stress strain parameters which describe the stress-strain curve of the material of interest. These are also key inputs in the determination of leakage associated with through-wall flaws. If the stress-strain curve of the material of interest is available, the R-O parameters can be determined from power law curve fit. However, in most cases, archival material of existing plant piping is not readily available to determine the actual stress-strain curve. In the absence of the actual stress-strain curve, several approximate methods for determining the R-O parameters from basic mechanical properties have been proposed in the literature. These approximate methods however produce different sets of R-O parameters. In this paper, the effect of using different sets of R-O parameters from three R-O formulations on LBB analyses results is investigated. EPFM analyses are performed to determine the critical through-wall flaw lengths with the various sets of the R-O parameters for various materials and various pipe sizes. The same sets of parameters are then used to determine the leakage associated with through-wall flaws. The results of the evaluation indicate that different sets of R-O parameters can yield different critical flaw sizes as well as leakage flaw sizes, thus resulting in different margins in LBB evaluations. Considering the margins involved in LBB evaluations (factor of two on critical flaw size and factor of 10 on leakage), it is believed that these differences are small enough that any of the three correlations presented in this paper for determination of the R-O parameters can be adequately used in LBB evaluations employing EPFM analyses.

Deformation Behavior of a Magnesium Alloy Sheet with Random Crystallographic Orientations

2014 ◽  
Vol 611-612 ◽  
pp. 27-32 ◽  
Author(s):  
Takayuki Hama ◽  
Tsuyoshi Mayama ◽  
Hirohiko Takuda
Keyword(s):  
Deformation Behavior ◽  
Strain Path ◽  
Strain Curve ◽  
Path Dependency ◽  
Alloy Sheet ◽  
Mg Alloy ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Tension And Compression ◽  
Crystallographic Orientations

In the present study, the deformation behavior of a cast Mg alloy sheet that had random crystallographic orientations was studied both experimentally and numerically. Although the crystallographic orientations were random, the stress-strain curve was asymmetric between tension and compression: the flow stress under tension was higher than that of compression. Moreover, the stress-strain curve exhibited a strain path dependency: a slightly sigmoidal curve occurred under tension following compression, while it did not occur under compression following tension. Clearly, such tendencies were similar to those observed in rolled Mg alloy sheets although the tendencies were less pronounced in the cast Mg alloy sheet. A crystal plasticity finite-element method was used to understand the mechanism of these results. Simulation results showed that the asymmetry and the strain path dependency in the stress-strain curves occurred in the cast Mg alloy sheet because of the asymmetry in the activity of twinning between tension and compression as in the case of rolled Mg alloy sheets.

Plastic Flexure of Mild Steel Beams of Rectangular Cross-section

1952 ◽  
Vol 166 (1) ◽  
pp. 112-122 ◽  
Author(s):  
K. K. Shackell ◽  
J. H. Welsh
Keyword(s):  
Yield Stress ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Strain Curve ◽  
Bending Moment ◽  
Steel Beams ◽  
Stress Tests ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Tension And Compression

The paper describes tests on a 0–28 per cent carbon steel in tension and compression, and in flexure of beams of rectangular cross-section, to a maximum strain about three times that at the initial yield. The object of these tests-was to investigate the shape of the stress-strain curve immediately after the initial yielding, and to determine whether in a case such as flexure the upper yield stress could be relied upon as a criterion of design. The results from this material indicate that the stress-strain curve falls rapidly but not immediately from the upper to the lower yield value, and that a beam is capable of withstanding a slightly greater bending moment than would be predicted by calculations based on the direct stress tests including the upper yield stress.

scholarly journals Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

2016 ◽  
Vol 46 (1) ◽  
pp. 53-64
Author(s):  
V. Rizov
Keyword(s):  
Strain Curve ◽  
Beam Theory ◽  
Integral Approach ◽  
J Integral ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Non Linear ◽  
Tension And Compression ◽  
Parametric Analyses ◽  
Strain Equation

Abstract Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.

Generalised Stress-Strain Data for Aluminium Alloys and certain other Materials

1955 ◽  
Vol 59 (530) ◽  
pp. 152-158
Author(s):  
Anthony J. Barrett ◽  
Maureen E. Michael
Keyword(s):  
Strain Curve ◽  
Tangent Modulus ◽  
Mathematical Form ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Wide Range ◽  
Analytical Work ◽  
Engineering Problems ◽  
Strain Data ◽  
Characteristic Values

In many engineering problems it is necessary, from time to time, to deduce from only a few characteristic values data which would ideally be obtained from a complete stress-strain curve. For instance many handbooks, used in design offices and published by materials manufacturers and others, contain values of Young's modulus and minimum guaranteed, or typical, values of various proof stresses for materials. From these, estimates of strain, tangent modulus or ratio of stress to tangent modulus appropriate to known stress values may be required, or various processes involving integration of the stress-strain curve may have to be carried out. Even when a complete stress-strain curve is available from a special test, the differentiation and integration of it, which may have to be repeated several times, are timeconsuming processes. Also, in analytical work involving the use of materials beyond the limit of proportionality, it is desirable to have available a generalised mathematical form of the stress-strain curve in order that the results obtained may be applied to a wide range of actual materials simply by the substitution of appropriate coefficients. These and many other applications will be familiar to the reader.

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