The Stress-Strain Relationships of Vulcanized India-Rubber. Part I. The Inflection Point

1933 ◽  
Vol 6 (4) ◽  
pp. 486-503 ◽  
Author(s):  
Cecil Wilson Shacklock
Keyword(s):  
Inflection Point ◽  
Applied Load ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Rubber Part ◽  
The Many

Abstract Definition.—The relation between applied load and the resulting extension of vulcanized or unvulcanized rubber may be represented graphically as a curve which is “s” shaped, and there is a point of inflection in the curve. If a load W grams be applied to the rubber, and the resulting length be L, the point of inflection is defined as the point on the curve where the second differential becomes zero and changes sign. More simply, the point of inflection is where the tangent to the curve crosses the curve. It is well known that the point of inflection exists, but there appears to be no reference in the literature to any attempts to determine precisely its position. It is also apparent from the many stress-strain curves of rubber which have been published that the point of inflection varies with both the period of cure and the compounding of the rubber. What follows is an account of some experiments made to investigate the position of the point of inflection in the stress-strain curve of vulcanized rubber.

The Behavior of Raw Rubber When Stretched Isothermally

1938 ◽  
Vol 11 (4) ◽  
pp. 647-652 ◽  
Author(s):  
H. Hintenberger ◽  
W. Neumann
Keyword(s):  
Room Temperature ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Steep Ascent ◽  
Flow Effect ◽  
Vulcanized Rubber ◽  
Flow Phenomena ◽  
Entropy Effect ◽  
The Subject

Abstract The S-shaped form of the stress-strain curve of rubber is today explained in a quite satisfactory way. In the first part of the curve, i. e., the gradual ascent, work must be expended because of the van der Waals forces of attraction of the molecules; in the second part, i. e., the steep ascent, the elasticity is chiefly an entropy effect, which is finally exceeded by crystallization phenomena. The phenomenon of crystallization itself has been the subject of extensive investigations, but in most cases vulcanized rubber has been employed, and because of the various accelerators and fillers which the rubber has contained, the products have been rather ill-defined. It is evident that the phenomena involved in crystallization would be much more clearly defined if the substance under investigation were to be in a higher state of purity. If experiments are carried out with raw rubber, a flow effect is added to the various other phenomena. As a result of this flow effect, Rosbaud and Schmidt, and Hauser and Rosbaud as well, found that the stress-strain curve depends on the rate of elongation at very low extensions, with a greater stiffness at high rates of elongation. As found recently by Kirsch, there is no evidence of any flow phenomena in vulcanized rubber at room temperature. Most investigations have been so carried out that the stress has been measured at a definite elongation. It was therefore of interest to determine the elongation at constant stress, and the changes in this relation with time and with temperature, of various types of raw rubber.

Reinforcement of Butyl with Carbon Black. II. Thermally vs. Chemically Oxidized Blacks

1964 ◽  
Vol 37 (4) ◽  
pp. 1034-1048 ◽  
Author(s):  
A. M. Gessler
Keyword(s):  
Carbon Black ◽  
Chemical Reactivity ◽  
Preceding Paper ◽  
Strain Curve ◽  
Convincing Evidence ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Carbon Particles ◽  
Vulcanized Rubber ◽  
Oxygen Functionality

Abstract The effect of oxidized blacks on the stress-strain properties and bound-rubber content of butyl and SBR was discussed in the preceding paper. Oxidized blacks, when compared with similar untreated blacks, were shown to have a greatly increased reinforcing capacity in butyl. Oxygen functionality on carbon black, it was therefore concluded, is essential in butyl to produce the chemical reactivity which is required between polymer and black if high-order reinforcement is to be obtained. Oxygen functionality on carbon black, it was also demonstrated, is not only not required for enhanced reinforcement in SBR, but it is in fact a deterrent, because it exerts severe restraining effects on the cure of the resulting vulcanizates as well. These interesting results were proposed to provide qualitative but convincing evidence that carbon-polymer bonding, which we believe is requisite to reinforcement, is achieved by different mechanisms in butyl and SBR. In butyl, the unique sensitivity of the stress-strain curve to reinforcing effects was used to speculate on the disposition of carbon blacks in “filled” and reinforced vulcanizates, respectively. With oxidized blacks, reinforcement effects were pictured as stiffening effects which, starting with the gum vulcanizates, caused the stress-strain curve to be shifted without intrinsic changes in its shape. The resulting “reinforced gum,” it was suggested, derived its physical characteristics from the fact that carbon black was included in the vulcanized rubber network. With untreated blacks, in “filled” systems, carbon black was pictured as being enmeshed or entangled in an independently formed vulcanized rubber network. The stiffening effects in this case were attributed to viscous contributions arising from steric restrictions which the occluded carbon particles were thought to impose on both initial movements and the subsequent orientation of network chains when the sample was extended.

Fatigue in Rubber. Part II

1939 ◽  
Vol 12 (2) ◽  
pp. 332-343 ◽  
Author(s):  
W. J. S. Naunton ◽  
J. R. S. Waring
Keyword(s):  
Carbon Black ◽  
Internal Friction ◽  
High Frequency ◽  
Strain Curve ◽  
Power Input ◽  
Viscous Resistance ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Wide Range ◽  
Rubber Part

Abstract 1. An apparatus is described for measuring the modulus and resilience of rubber over a wide range of frequencies. 2. These measurements can be made at any point in the stress-strain curve of the sample. 3. By increasing the power input, the same apparatus can be used to induce high frequency fatigue in the sample. 4. The earlier work with the torsion head apparatus has been confirmed, namely, that internal friction is greatest near zero strain. 5. High frequency resilience is more independent of degree of vulcanization than tripsometer resilience. 6. Modulus tends to increase with frequency. The effect is least with a rubber gum stock and is greater with compounds containing gas black. 7. Resilience decreases with frequency both in gum and gas black compounds. The decrease is more rapid in the gum compounds. 8. Viscous resistance decreases with frequency and becomes constant at higher frequencies. 9. The modulus of both rubber and Neoprene carbon black compounds decreases with fatigue. 10. The change in modulus with frequency in fatigued stocks is exactly analogous to the change before fatigue in rubber, but there is a slight divergence in the case of Neoprene.

Thermodynamics of Crystallization in High Polymers. VI. Incipient Crystallization in Stretched Vulcanized Rubber

1950 ◽  
Vol 23 (3) ◽  
pp. 576-580 ◽  
Author(s):  
Thomas G. Fox ◽  
Paul J. Flory ◽  
Robert E. Marshall
Keyword(s):  
Theoretical Prediction ◽  
Experimental Determination ◽  
Strain Curve ◽  
Steep Slope ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Hydrostatic Method ◽  
Vulcanized Rubber ◽  
High Polymers

Abstract Experimental determination of the elongation at which crystallization commences in vulcanized rubber has been attempted through measurement of density changes by a hydrostatic method. The critical elongation for incipient crystallization appears to depend on the temperature, in approximate accordance with theoretical prediction. Crystallization sets in at an elongation well below that at which the stress-strain curve assumes a steep slope.

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.

A Contribution to the Characterization of the Plastic-Elastic State

1939 ◽  
Vol 12 (4) ◽  
pp. 799-804 ◽  
Author(s):  
E. Rohde
Keyword(s):  
Characteristic Property ◽  
Strain Curve ◽  
The Other ◽  
Elastic State ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Other Hand ◽  
Puzzling Problem

Abstract The manner in which vulcanized rubber can be deformed and yet return almost completely to its original dimensions after the stress is released is a unique and characteristic property. Technically the problem in testing rubber is to evaluate this property and to define it in terms of the factors which are concerned. To define completely this property of rubber whereby it is susceptible to deformation, it is necessary to know the stress, the elongation, the energy expended, the energy lost, the time and the temperature. The stress, elongation and energy expended are closely related and are characterized by the stress-strain curve, which in turn depends on the time and temperature. In addition, it must be borne in mind that rubber can be deformed either by tension or by pressure, but this will not be discussed further here. On the other hand a rather puzzling problem will be considered, the solution of which brings out the fact that the three variables involved in any deformation, viz.: (1) The time or frequency. (2) The temperature. (3) The interrelated factors: stress, elongation and energy expended, must be varied considerably in order to characterize the phenomena of deformation and that when this is done, unexpected results are obtained.

The Effect of Solvents on the Stress-Strain Curve of Vulcanized Rubber

1930 ◽  
Vol 3 (1) ◽  
pp. 19-21 ◽  
Author(s):  
H. A. Tiltman ◽  
B. D. Porritt
Keyword(s):  
Tensile Strength ◽  
Marked Effect ◽  
Strain Curve ◽  
Theoretical Interest ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Cohesive Forces ◽  
Effect Of Solvents ◽  
Vulcanized Rubber ◽  
Permanent Effect

Abstract (1) The results indicate that the rigidity of a piece of vulcanized rubber is considerably reduced by the absorption of small amounts of a solvent; thus, at a strain of 6 ( = 600 per cent elongation) the absorption of 5 per cent by weight ( = 8 per cent by volume) of benzene lowers the rigidity by 21 per cent. (2) The greatest effect is produced by the first 20 or 30 per cent (by weight) of absorbed benzene, further absorption having a less marked effect on the stress-strain curve. (3) The absorption of solvent seems to have very little effect on the breaking elongation, although the tensile strength is considerably lowered. This conclusion, however, is probably no longer true in the case of rubber swollen by immersion in liquid, where the absorption is very much greater than in the present tests. (4) Absorption of solvent followed by complete drying appears to produce a slight, but technically negligible, permanent effect on the stress-strain curve. It is evident from these results that when it is necessary to use solvents, either in the process of manufacture or the after-treatment of rubber products, these should be selected as free as possible from high-boiling constituents liable to be permanently retained by the rubber with consequent detriment to its strength. A conclusion of some theoretical interest is that since all the stresses in the present investigation were calculated on the dimensions of the original dry rubber, the low rigidity of swollen rubber cannot be ascribed simply to the “dilution” of the rubber by the absorbed liquid, but must be due to a loosening of the cohesive forces between the ultimate particles of the material.

Thermodynamics of Stressed Vulcanized Rubber

1930 ◽  
Vol 3 (2) ◽  
pp. 304-314 ◽  
Author(s):  
Roscoe H. Gerke
Keyword(s):  
Modulus Of Elasticity ◽  
Strain Curve ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Permanent Set ◽  
Vulcanized Rubber ◽  
Laws Of Thermodynamics

Abstract The first and second laws of thermodynamics are applied to the stretching of vulcanized gum rubber stocks. Equilibrium stress-strain curves without appreciable hysteresis are described. The modulus of elasticity of vulcanized rubber for higher elongations obtained from the equilibrium stress-strain curve is capable of giving agreement with predictions of the second law of thermodynamics and the Joule heat effect. The modulus of elasticity from the equilibrium stress-strain curve is practically independent of the time of cure for a range of cures for elongations less than 600 per cent. The customary stress-strain curves show the rubber to be stiffer with increased cure. These facts are additional evidence that the important effect caused by vulcanization is a greater resistance to plastic flow or permanent set.

A modified version of MATLAB application window for predicting the weld bead profile and stress–strain plot of AA5052 CMT weldment using ER4043

SIMULATION ◽  
2021 ◽  
pp. 003754972110315
Author(s):  
B Girinath ◽  
N Siva Shanmugam
Keyword(s):  
Strain Curve ◽  
Weld Bead ◽  
Welding Parameters ◽  
Bead Geometry ◽  
Hybrid Technique ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Weld Bead Geometry ◽  
Inference System ◽  
Engineering Stress

The present study deals with the extended version of our previous research work. In this article, for predicting the entire weld bead geometry and engineering stress–strain curve of the cold metal transfer (CMT) weldment, a MATLAB based application window (second version) is developed with certain modifications. In the first version, for predicting the entire weld bead geometry, apart from weld bead characteristics, x and y coordinates (24 from each) of the extracted points are considered. Finally, in the first version, 53 output values (five for weld bead characteristics and 48 for x and y coordinates) are predicted using both multiple regression analysis (MRA) and adaptive neuro fuzzy inference system (ANFIS) technique to get an idea related to the complete weld bead geometry without performing the actual welding process. The obtained weld bead shapes using both the techniques are compared with the experimentally obtained bead shapes. Based on the results obtained from the first version and the knowledge acquired from literature, the complete shape of weld bead obtained using ANFIS is in good agreement with the experimentally obtained weld bead shape. This motivated us to adopt a hybrid technique known as ANFIS (combined artificial neural network and fuzzy features) alone in this paper for predicting the weld bead shape and engineering stress–strain curve of the welded joint. In the present study, an attempt is made to evaluate the accuracy of the prediction when the number of trials is reduced to half and increasing the number of data points from the macrograph to twice. Complete weld bead geometry and the engineering stress–strain curves were predicted against the input welding parameters (welding current and welding speed), fed by the user in the MATLAB application window. Finally, the entire weld bead geometries were predicted by both the first and the second version are compared and validated with the experimentally obtained weld bead shapes. The similar procedure was followed for predicting the engineering stress–strain curve to compare with experimental outcomes.

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