Compression Stress Strain of Rubber

1933 ◽  
Vol 6 (1) ◽  
pp. 126-150 ◽  
Author(s):  
J. R. Sheppard ◽  
W. J. Clapson
Keyword(s):  
Hollow Sphere ◽  
Compressive Force ◽  
Strain Curve ◽  
The Other ◽  
One Dimension ◽  
Compression Stress ◽  
Stress Strain ◽  
Strain Data ◽  
Tensile Forces ◽  
Strain Axis

Abstract 1. A relation of simple form between compressive force and equivalent two-way tensile forces is developed. 2. Based on this relation, a new method for determining the compression stress strain of rubber is outlined, which avoids difficulties and errors inherent in direct compression. It consists in applying tensile forces simultaneously in two directions, and, from these and the strained dimensions, in computing the compressive force that would have produced the same deformation. 3. The mode of applying the two-way tensiles is to inflate a hollow sphere of rubber; the experimental data required to determine the compression stress strain are pressure of gas in, and dimensions of, the inflating hollow sphere. 4. The method has been applied to cold-cured pure-gum rubber in the form of toy balloons which, in its ordinary elongation stress strain, shows a breaking elongation of about 650 to 700 per cent and a tensile of 30 to 40 kg. per square centimeter. While the numerical values obtained on this stock have no special significance, as they will vary from stock to stock, the following are examples: breaking compression, about 97.3 per cent; breaking compressive force, 6000 to 9000 kg. per square centimeter (on original cross section); hysteresis, 29 to 35 per cent of work of compression to near rupture. 5. As a common measuring stick by which to gage degree of strain in deformations of different types—e. g., increasing one dimension (and diminishing the other two) as against diminishing one dimension (and increasing the other two)—energy seems the best. Energy at break for ordinary elongation stress strain was 50 to 70 kg. cm. per cubic centimeter, and for compression stress strain was 89 to 103 kg. cm. per cubic centimeter. 6. The compression stress-strain data may, if desired, be expressed in terms of two-way tensiles vs. two-way elongations. Energy of compression may be computed either as twice the area subtended between such a curve and the strain axis, or as the area between the compression stress strain and the strain axis. 7. It is strongly indicated that the compression stress strain of rubber is continuous with the ordinary elongation stress strain when both are plotted in the same units, and that the complete stress strain should accordingly be considered as a single continuous curve having an elongation branch and a compression branch with the origin as dividing point. 8. The analytic features of the complete stress strain are described. 9. Granting the observed concavity of the upper part of the elongation stress strain, and the thesis of continuity between elongation and compression, a point of inflection is bound to exist theoretically. 10. Implications of the thesis of continuity are: (1) An equation for the stress-strain curve must fit the complete curve; it is not sufficient that it fit the elongation branch only. (2) It is impossible to compute the compression stress strain from the ordinary (one-way) elongation stress-strain data. The two sets of data are related empirically. 11. When compressive force and equivalent two-way tensiles are based on actual cross sections, stress conditions at a point are expressed and we have the simple rule: Pressure at a point is numerically equal to the transverse tensions which, substituted therefor, will maintain the same strain.

scholarly journals Dynamic Characteristics of Sandstone under Coupled Static-Dynamic Loads after Freeze-Thaw Cycles

2020 ◽  
Vol 10 (10) ◽  
pp. 3351
Author(s):  
Bo Ke ◽  
Jian Zhang ◽  
Hongwei Deng ◽  
Xiangru Yang
Keyword(s):  
Energy Absorption ◽  
Dynamic Characteristics ◽  
Shear Failure ◽  
Strain Curve ◽  
Peak Stress ◽  
Peak Strain ◽  
Compression Stress ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Freeze Thaw

The effect of temperature fluctuation on rocks needs to be considered in many civil engineering applications. Up to date the dynamic characteristics of rock under freeze-thaw cycles are still not quite clearly understood. In this study, the dynamic mechanical properties of sandstone under pre-compression stress and freeze-thaw cycles were investigated. At the same number of freeze-thaw cycles, with increasing axial pre-compression stress, the dynamic Young’s modulus and peak stress first increase and then decrease, whereas the dynamic peak strain first decreases and then increases. At the same pre-compression stress, with increasing number of freeze-thaw cycles, the peak stress decreases while the peak strain increases, and the peak strain and peak stress show an inverse correlation before or after the pre-compression stress reaches the densification load of the static stress–strain curve. The peak stress and strain both increase under the static load near the yielding stage threshold of the static stress–strain curve. The failure mode is mainly shear failure, and with increasing axial pre-compression stress, the degree of shear failure increases, the energy absorption rate of the specimen increases first and then decreases. With increasing number of freeze-thaw cycles, the number of fragments increases and the size diminishes, and the energy absorption rates of the sandstone increase.

Aging of Stretched Rubber

1928 ◽  
Vol 1 (1) ◽  
pp. 106-112
Author(s):  
Arthur Kelly ◽  
Bert S. Taylor ◽  
Webster N. Jones
Keyword(s):  
Direct Relationship ◽  
Strain Curve ◽  
Ultra Violet ◽  
The Other ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Test Strips ◽  
Ultra Violet Light ◽  
Violet Light ◽  
Early Stages

Abstract Sunlight aging under tension of many compounds including the following has been investigated: tire tread shoe upper, tube stocks, golf ball thread, jar rubber, solid tire, bathing cap stock, channel rubber. With some of these stocks the sunlight aging as been compared with unstretched samples by Geer oven, Bierer bomb, and ultra-violet light methods. The stretching of the test strips accelerates deterioration in sunlight, ultra-violet light, and Geer oven. Stretched samples have not yet been tested in the Bierer bomb. The rate of deterioration was not proportional to the degree of stretch in any of the stocks in the early stages of exposure. In sunlight there is a critical elongation for each stock at which the deterioration progresses more rapidly than at any other in the early stages of aging. No direct relationship was found between the results of sunlight aging and the other methods employed. Stretched strips aged in ultra-violet light were found to give softer stress-strain curves than the unaged samples, whereas sunlight aging under the same conditions stiffens the stress-strain curve.

Preparation and Use of Cyclized Rubber as a Stiffening Resin in Rubber

1956 ◽  
Vol 29 (3) ◽  
pp. 1034-1042
Author(s):  
H. J. J. Janssen
Keyword(s):  
Stress Gradient ◽  
Strain Curve ◽  
Inert Atmosphere ◽  
Homogeneous State ◽  
Cohesion Energy ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Order Of Magnitude ◽  
Strain Axis ◽  
Aliphatic And Aromatic Hydrocarbons

Abstract The condition for miscibility of low-molecular liquids is that the cohesion-energy densities should be of the same order of magnitude. The permissible difference decreases sharply as the molecular weight is increased, and a solution of equal amounts of rubber and polystyrene separates into two layers at room temperature when the concentration rises above 2 per cent, whereas low-molecular aliphatic and aromatic hydrocarbons are completely miscible. The undiluted polymers can, however, be mixed to an apparently homogeneous state on the mill if the correct mixing temperature is chosen. Presumably the extreme length of the polymer molecules allows them to be caught and dispersed separately in the stress gradient between the rolls. That the mixture is not stable and tends to separate into the components on extension, even after vulcanization of the rubber, can be deduced from the bending of the stress-strain curve towards the strain axis—generally an indication of irreversible changes in structure for many materials. This tendency to irreversible separation, which is a disadvantage for any application, can be suppressed by the formation of primary bonds between the two polymers. There are at present three methods to produce such bonds : (1) covulcanization (if the added polymer is unsaturated); (2) mastication in an inert atmosphere; (3) graft polymerization. If a sufficient number of such bonds has been formed, the added polymer can no longer be extracted from the vulcanized compound by solvents, and the bend in the stress-strain curve has disappeared.

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.

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.

Accurate Evaluation Method for the Hydraulic Bulge Test

2013 ◽  
Vol 554-557 ◽  
pp. 33-40 ◽  
Author(s):  
J. Mulder ◽  
Henk Vegter ◽  
Holger Aretz ◽  
A.H. van den Boogaard
Keyword(s):  
Evaluation Method ◽  
Spherical Surface ◽  
Strain Curve ◽  
Local Strain ◽  
Bulge Test ◽  
Stress Strain ◽  
Measuring Systems ◽  
Optical Measuring ◽  
Strain Data ◽  
Work Hardening Coefficient

Optical measuring systems provide much more detail on the deformation of the blank in the bulge test than conventional contact height measuring systems. A significant increase in accuracy of the stress-strain curve can be achieved by fitting the surface to more complicated equations than the traditional spherical surface and by considering the local strain data to approximate the curvature for the midplane. In particular an ellipsoid shape is shown to be very accurate in describing the surface of the blank. Contact height measuring systems provide insufficient data to fit a surface to an ellipsoid shape and to establish local strain data. Pragmatic equations are proposed using the work hardening coefficient from the tensile test to approximate the same accuracy in stress-strain curves as obtained by optical measuring systems using the before mentioned evaluation method.

The Evaluation of Carbon Blacks

1929 ◽  
Vol 2 (2) ◽  
pp. 237-242
Author(s):  
D. F. Cranor ◽  
H. A. Braendle
Keyword(s):  
Optimum Concentration ◽  
The Other ◽  
General Category ◽  
Performance Tests ◽  
Stress Strain ◽  
Laboratory Performance ◽  
Carbon Blacks ◽  
Other Hand ◽  
Strain Data

Abstract In conclusion, it is shown that the “Delta A function” provides an instrument for the classification of carbon blacks as regards their usefulness to the rubber compounder. It is an index of widely inclusive character and not only indicates performance at optimum concentration, but also the range of effectiveness. The writers have undertaken exposition of the special applications of this to the classification of carbon pigments, pointing out the precautions necessary for its accurate use. We believe it important to supplement the “Delta A function” with other stress-strain data, also with laboratory performance tests, and finally with service records, when it is necessary to differentiate between carbons of the same general category. On the other hand, we believe no study of carbons or other pigments is complete unless “Delta A” values are included. Acknowledgment is gratefully made for the valuable suggestions of W. B. Wiegand and also the cooperation of Binney & Smith Co., who supplied all of the carbon blacks investigated and gave permission to publish the data covered by this paper.

A Mathematical Treatment of a Theory of Rubber Structure

1935 ◽  
Vol 8 (1) ◽  
pp. 23-38
Author(s):  
T. R. Griffith
Keyword(s):  
Elastic Modulus ◽  
Plastic Flow ◽  
Strain Curve ◽  
The Other ◽  
Stress Axis ◽  
Mathematical Treatment ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Joule Effect ◽  
Vulcanized Rubber

Abstract A brief consideration of the work that has been done on the structure of rubber convinces, one that the elasticity is wholly or at least mainly explained by a consideration of the kinetics involved. The fact that when a strip of stretched rubber, one end of which is free, contracts when it is warmed, contrary to the behavior of most bodies, and that it becomes warmed on stretching, commonly known as the Gough-Joule effect, pp. 453–461, would lead one to suspect .that there is a connection between the kinetic energy of the rubber molecule and its elasticity. Lundal, Bouasse, Hyde, Somerville and Cope, Partenheimer and Whitby and Katz have reported observations, principally stress-strain curves, which show that vulcanized rubber has a lower modulus of elasticity at higher temperatures, i. e., it becomes easier to stretch as the temperature is raised. On the other hand, Schmulewitsch, Stevens, and Williams found that the elastic modulus increases with the temperature. Williams shows that the softening of vulcanized rubber with rise of temperature is due to an increase of plasticity. In order to get rid of plastic flow, he first stretches the specimen several times to within about 50 per cent of its breaking elongation, and then obtains an autographic stress-strain curve of the rubber stretched very quickly. He finds that in this case the rubber actually becomes stiffer with rise of temperature, increasing temperatures causing the stress-strain curves to lean progressively more and more toward the stress axis. He concludes that rise of temperature has two effects, one a softening due to increase of plasticity, rendering plastic flow more easy, the other an actual stiffening of the rubber due to rise of temperature. It is not easy to explain the latter effect on any theory which does not take kinetics into account.

scholarly journals The mechanism of plastic deformation of crystals. Part II.—Comparison with observations

1934 ◽  
Vol 145 (855) ◽  
pp. 388-404 ◽  
Keyword(s):  
Elastic Limit ◽  
Large Range ◽  
Strain Curve ◽  
Pure Metal ◽  
The Other ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Essential Characteristic ◽  
Small Strains ◽  
Plastic Stress

According to the theory give in Part I the strain-hardening or plastic stress strain curve for a pure metal should be parabola. In figs. 1, 2, and 3, Part I, Parabolas are drawn, the parameters being chosen so that they lie as close as possible to the points which represent actual observations. It will be seen that for aluminium and gold the agreement is good. For a single crystal of copper the agreement is not good, but, on the other hand, the plastic stress-strain curve for polycrystalline specimens of copper which is shown in fig. 1 is very nearly parabolic over a large range. The observations for iron seem to show that there is a small finite elastic limit, i. e. , S T may be finite. Parabolas corresponding with the existence of a small elastic limit and with no elastic limit have been drawn. It seems that the observed points lie rather closer to the former curve. In any case, the observed curves have the essential characteristic of the theoretical ones that they are very steep at small strains, but get less and less steep as the strain increases.

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