Stress Softening in Rubber Vulcanizates. Part I. Use of a Strain Amplification Factor to Describe Elastic Behavior of Filler-Reinforced Vulcanized Rubber

1966 ◽  
Vol 39 (4) ◽  
pp. 799-813 ◽  
Author(s):  
L. Mullins ◽  
N. R. Tobin
Keyword(s):  
Volume Concentration ◽  
Spherical Particles ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Factor X ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Stress Strain Relation ◽  
Strain Data ◽  
Volume Swelling

Abstract Measurements of Young's modulus of vulcanized rubbers containing thermal carbon black show the predicted dependence on the volume concentration given by relationships derived for a suspension of spherical particles, for example, that due to Guth, Simha, and Gold which gives E=E0 (1+2.5c+14.1c2). A simple interpretation of the results is that the strain in the rubber is increased by the presence of filler so that the ratio of the average strain to the measured overall strain is given by the factor X=1+2.5c+14.1c2. This factor was used to analyze simple extension stress-strain data obtained at larger extensions. For this purpose the Mooney—Rivlin relation was used to describe the behavior of the rubber phase. Values of C1 independent of the volume concentration and in close accord with measurements of the equilibrium volume swelling of the rubbers were obtained. Values of λ* were also consistent with those of #5#. Analysis of stress—strain data obtained on rubbers containing smaller particle-sized carbon blacks is more complex. For these materials the relation due to Guth, viz., E=E0 (1+2.5c+14.1c2), was chosen. By the choice of suitable values of f, good agreement with the Mooney—Rivlin stress—strain relation was achieved at volume concentrations less than about 0.15.

Theoretical Model for the Elastic Behavior of Filler-Reinforced Vulcanized Rubbers

1957 ◽  
Vol 30 (2) ◽  
pp. 555-571 ◽  
Author(s):  
L. Mullins ◽  
N. R. Tobin
Keyword(s):  
Elastic Properties ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Stress Strain ◽  
Empirical Relationships ◽  
Equilibrium Stress ◽  
Strain Behavior ◽  
Strain Data ◽  
Limited Applicability

Abstract One of the more important advances in rubber science during the past twenty years has been the development of quantitative theories describing the elastic properties of pure-gum vulcanized rubbers. As a result it is now possible to account for their equilibrium stress-strain behavior with considerable success. There is, however, no adequate theory to describe the elastic properties of filler-reinforced rubber vulcanizates and the work described herein is an attempt to provide a basis for such a theory. When a reinforcing filler is added to rubber it produces a large increase in the stiffness of the vulcanizate. This increase is reduced and may be substantially destroyed by deformation. Numerous attempts have been made to describe the increase of stiffness resulting from the introduction of fillers and relationships describing the dependence of the modulus on the concentration and particle shape of the filler have been developed. However, these do not take into account the softening which results from previous deformation and thus have limited applicability. Recently Blanchard and Parkinson have attempted to develop empirical relationships to describe the elastic properties in simple extension of reinforced rubber vulcanizates after they have been previously deformed. They started with the appropriate stress-strain relationships from the classical kinetic theory and introduced two curve-fitting parameters to describe stress-strain data obtained in conventional tensile tests on a Goodbrand machine. In this way they were able to fit the course of the stress-strain data obtained after previous extension at extensions less than those previously applied and to describe the dependence of the parameters on previous deformation. Unfortunately, the significance of the parameters is obscure.

Departures of the Elastic Behavior of Rubbers in Simple Extension from the Kinetic Theory

1955 ◽  
Vol 28 (1) ◽  
pp. 24-35 ◽  
Author(s):  
S. M. Gumbrell ◽  
L. Mullins ◽  
R. S. Rivlin
Keyword(s):  
Kinetic Theory ◽  
Volume Fraction ◽  
Single Parameter ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Strain Behavior

Abstract It is shown that the equilibrium stress-strain behavior of highly swollen rubber vulcanizates in simple extension agrees with the predictions of the kinetic theory. The departures from these predictions which are found in dry or lightly swollen rubbers have been investigated, and it is shown that they can be described in terms of a single parameter C2. The magnitude of this parameter is large in dry rubbers, and decreases to zero at high degrees of swelling ; this decrease occurs linearly with decrease in the volume fraction of rubber. The value of C2 is found to be independent of the nature of the rubber polymer, of the degree of vulcanization, and of the nature of the swelling liquid. The possible significance of this parameter is discussed in light of these observations.

Stress-Strain Data for Vulcanized Rubber under Various Types of Deformation

1944 ◽  
Vol 17 (4) ◽  
pp. 813-825 ◽  
Author(s):  
L. R. G. Treloar
Keyword(s):  
Mechanical Properties ◽  
Network Model ◽  
Large Deformations ◽  
Pure Shear ◽  
Molecular Network ◽  
Satisfactory Explanation ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Strain Data ◽  
Good For

Abstract Stress-strain data are given for two types of vulcanized rubber: (1) an 8% S rubber, and (2) a latex rubber. The types of deformation studied were simple elongation, 2-dimensional extension (or compression), pure shear, and combined elongation and shear. Comparison with the theoretical relations based on the molecular-network model shows the agreement to be good for the 2-dimensional extension, but less good for simple elongation and shear. The effect of combined elongation and shear is satisfactorily accounted for. It is concluded that the theory provides a satisfactory explanation of rubberlike elasticity, and forms a useful basis for the description of the mechanical properties of rubber subjected to large deformations of any type.

The Stress-Strain Relation of Natural and Synthetic Rubbers

1944 ◽  
Vol 17 (4) ◽  
pp. 826-836
Author(s):  
A. J. Wildschut
Keyword(s):  
Carbon Black ◽  
General Formula ◽  
Stress Axis ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Axes Of Symmetry ◽  
Natural And Synthetic

Abstract It is shown that Hatschek's formula for the stress-elongation curve of rubber—better known as Ariano's formula—does not hold for normally vulcanized rubber. The observation has been made that the stress-elongation curves of natural and synthetic rubbers follow nonrectangular hyperbolae closely and practically up to the point of rupture. The axes of symmetry of these hyperbolae make angles of about 40° with the stress-axis in the case of pure-gum mixtures and about 30° for carbon black mixtures. A general formula has been derived which holds for all the rubbers investigated.

A method of calculation for thermoforming plastics sheets

1970 ◽  
Vol 5 (1) ◽  
pp. 49-57 ◽  
Author(s):  
J G Williams
Keyword(s):  
Large Strain ◽  
Rubber Elasticity ◽  
Thickness Variation ◽  
Stress Strain ◽  
Simple Method ◽  
Method Of Calculation ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Approximate Form ◽  
Strain Data

Stress-strain data for polymethylmethacrylate at the moulding temperature of 160°C are analysed by a rubber elasticity representation. It is shown that large strain solutions may be obtained for simple geometries with an approximate form of stress-strain relation and examples are given of predictions of profile and thickness variation for blown domes and other axisymmetrical shapes. Forming pressures and loads are predicted by an iteration extension of the simple method together with examples of predictions for shapes formed with conical dies. The comparison of experimental and theoretical values is generally good.

Finite Deformation and Nonlinear Elastic Behavior of Flexible Composites

1988 ◽  
Vol 55 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Shen-Yi Luo ◽  
Tsu-Wei Chou
Keyword(s):  
Present Theory ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Flexible Composites ◽  
Elastomeric Matrix ◽  
Eulerian Description ◽  
Stress Strain Relation ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

The flexible composites discussed in this paper are composed of continuous fibers in an elastomeric matrix. The usable range of deformation of these composites is much larger than that of conventional rigid composites. Due to the material as well as geometric factors, the stress-strain relations for these composites are generally nonlinear under finite deformations. A constitutive model has been developed based upon the Eulerian description. The material nonlinear stress-strain relation is derived by using the stress energy density referring to the deformed volume. The stretching-shear coupling and the effects of the in-plane reorientation of fibers are also considered in the theoretical analysis. Comparisons are made between predictions of the present theory and experimental data for tirecord/rubber and Kevlar/silicone-elastomer flexible composite laminae; very good correlations have been found.

The Elastic Behavior of Vulcanized Rubber

1933 ◽  
Vol 1 (2) ◽  
pp. 45-48
Author(s):  
H. Hencky
Keyword(s):  
Simple Function ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Tension And Compression ◽  
Elastic Coefficients

Abstract Up to extensions of about 270 per cent the elastic behavior of vulcanized rubber can be represented analytically by a very simple function. The stress-strain diagrams for tension and compression are quite different; nevertheless this asymmetrical behavior is satisfactorily taken care of by employing only two elastic coefficients.

Relation between Stress Strain Behavior and Equilibrium Volume Swelling for Peroxide Vulcanizates of Natural Rubber and cis-1,4-Polyisoprene

1967 ◽  
Vol 40 (2) ◽  
pp. 673-678 ◽  
Author(s):  
G. M. Bristow
Keyword(s):  
Natural Rubber ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Strain Behavior ◽  
Equilibrium Volume ◽  
Equilibrium Swelling ◽  
Tentative Evidence ◽  
Volume Swelling ◽  
Natural Rubber Vulcanizates

Abstract Data are reported for the elastic behavior, as described by the parameters C1 and C2, and the equilibrium swelling in n-decane, νr, for cumyl peroxide vulcanizates of natural rubber and cis-1, 4-polyisoprene. For natural rubber vulcanizates the correlation between C1 and νr can be described in terms of the original Flory Rehner equation with χ= 0.41. Tentative evidence is presented which favors this equation rather than the later modified form in which the term in νr1/3 is replaced by one in (νr1/3− νr/2).

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

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