scholarly journals Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

2018 ◽  
Vol 36 (9) ◽  
pp. 1077-1083 ◽  
Author(s):  
Cheng-Sha Wei ◽  
Ai Lu ◽  
Su-Ming Sun ◽  
Xing-Wen Wei ◽  
Xiao-Yu Zho ◽  
...  
Keyword(s):  
Statistical Theory ◽  
Constitutive Model ◽  
Silicone Rubber ◽  
Rubber Elasticity

Modulus of Natural Rubber Crosslinked by Dicumyl Peroxide III. Some Molecular Interpretations, Possible Refinements of Theory, and Conclusions

1977 ◽  
Vol 50 (2) ◽  
pp. 233-252 ◽  
Author(s):  
L. A. Wood
Keyword(s):  
Statistical Theory ◽  
Rubber Elasticity ◽  
Gel Point ◽  
Dicumyl Peroxide ◽  
Stress Strain ◽  
Energy Component ◽  
Mechanical Measurements ◽  
Stress Strain Relation ◽  
The Difference ◽  
Entropy Component

Abstract The qualitative and quantitative agreement of predictions and results demonstrated in the previous sections is a strong confirmation of the essential validity of all the extremely simplified molecular considerations involved, including the general aspects of the statistical theory of rubber elasticity. We know of no previous experimental study extending over as wide ranges of crosslinking and temperature. In fact the crosslinking and temperature have been varied simultaneously on only a few occasions in previous work. An important advantage of the present work over many previous studies is the fact that measurements are made at very small deformations. Thus the results are expressed in terms of the modulus, defined as the limiting value of the ratio of stress to stain at zero deformation. Consequently, the results are independent of the stress-strain relation or equation of state. This means that no consideration needs to be given here, for example to the difference between the stress-strain relation predicted by the statistical theory of rubber elasticity and that given by the Mooney-Rivlin equation or the empirical equation of Martin, Roth, and Stiehler. The present study has shown that the modulus G includes a considerable component arising from internal energy changes as well as that arising from entropy changes. The energy component at room temperature is of the order of half the total when the degree of crosslinking is that normally used with dicumyl peroxide rubbers. It is concluded that the nonzero value of the modulus when extrapolated to zero crosslinking is due to the energy component of the modulus rather than to entanglements. Entanglements acting as pseudo-crosslinks would serve to increase only the entropy component. The gel point, defined as the minimum degree of crosslinking required to form a network, may be located experimentally as the crosslinking at which the slope of the modulus-temperature relation is zero. The value of the modulus G at the gel point is not zero, but is the energy component under this condition; the entropy component of G at the gel point is zero. The amount of dicumyl peroxide required to crosslink rubber to the gel point is the sum of that wasted by reaction with impurities in the rubber and that required to give one crosslink for each rubber molecule. The former quantity was about twice the latter in the work reported here. The entropy component of the modulus as determined from reported values of equilibrium swelling by the Flory-Rehner equation, is found to be significantly larger than that determined from mechanical measurements. However, the quantity computed is smaller than the sum of the entropy and energy components as determined from crosslinking considerations or from mechanical measurements. It increases linearly with crosslinking at a slightly greater rate than the modulus or the entropy component of the modulus. It is concluded that the “front factor” sometimes introduced in statistical theory considerations cannot differ from unity by more than about 7%. The difference is even less than this if allowance is made for entanglements functioning as pseudo-crosslinks.

Solution and Diffusion in Silicone Rubber. I. A Comparison with Natural Rubber

1963 ◽  
Vol 36 (3) ◽  
pp. 642-650 ◽  
Author(s):  
R. M. Barrer ◽  
J. A. Barrie ◽  
N. K. Raman
Keyword(s):  
Statistical Theory ◽  
Natural Rubber ◽  
Silicone Rubber ◽  
Diffusion Coefficients ◽  
Molecular Size ◽  
Low Energy ◽  
Kcal Mole ◽  
Self Diffusion ◽  
Order Of Magnitude ◽  
And Diffusion

Abstract The diffusion and solubility of n- and isobutane and of n- and neopentane has been studied in the range 30° to 70° C, in polydimethylsiloxane rubbers. The solubilities are very similar to those in natural rubbers and show comparable agreement with the statistical theory of polymer penetrant mixtures. Diffusion coefficients are at least an order of magnitude greater in silicone than in natural rubbers. The very low energy of activation, ED, of about 4 kcal/mole is almost invariant among the hydrocarbons studied and is the same as for self-diffusion and viscous flow in this rubber. The low value of ED means that permeabilities of the hydrocarbons increase as the temperature falls. Because diffusion in silicones is less dependent upon molecular size and shape of penetrant than in natural rubber, the silicones are less selective though much more permeable separation barriers.

Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity

1996 ◽  
Vol 69 (5) ◽  
pp. 781-785 ◽  
Author(s):  
Mary C. Boyce
Keyword(s):  
Constitutive Model ◽  
Large Strain ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Rubber Elasticity ◽  
Elastic Materials ◽  
Material Constants ◽  
Salient Features

Abstract The Arruda and Boyce eight-chain network constitutive model for rubber elastic materials is compared to the new Gent constitutive model for rubber elasticity. The salient features of each of the two models are compared. The ability of both models to predict three dimensional large strain deformation is demonstrated showing the near equivalence of these two model constructions as well as their abilities to predict complex three-dimensional deformation with only two material constants.

Pyridinium High Polymers—A New Class of Oil-Resistant Synthetic Rubbers

1957 ◽  
Vol 30 (1) ◽  
pp. 338-351
Author(s):  
W. B. Reynolds ◽  
J. E. Pritchard ◽  
M. H. Opheim ◽  
G. Kraus
Keyword(s):  
Zinc Oxide ◽  
Statistical Theory ◽  
Ternary System ◽  
Rubber Elasticity ◽  
New Class ◽  
Organic Halides ◽  
Low Levels ◽  
High Polymers

Abstract Copolymers of butadiene and 2-methyl-5-vinylpyridine are readily vulcanized by heating in the presence of organic halides. The number of effective crosslinks can be readily calculated from moduli of swollen stocks using the statistical theory of rubber elasticity. Crosslinking depends upon the amount and activity of the quaternizing agent. However, even at low levels of halide concentration, it appears that several quaternary groupings are necessary for each effective crosslink. Zinc oxide greatly increases the moduli of the swollen copolymer-halide systems. However, sulfur and accelerator alone have little effect on the same system and these agents do not further increase the moduli of the swollen ternary system, copoylmer-halide-zinc oxide.

Ozone Attack on Rubber Vulcanizates

1959 ◽  
Vol 32 (1) ◽  
pp. 257-268 ◽  
Author(s):  
D. J. Buckley ◽  
S. B. Robison
Keyword(s):  
Statistical Theory ◽  
Stress Relaxation ◽  
Crack Growth ◽  
Quantitative Study ◽  
Specific Problem ◽  
The State ◽  
Rubber Elasticity ◽  
General Knowledge ◽  
Initial Work ◽  
Work Done

Abstract The effect of the attack of ozone on rubber vulcanizates is well known in a qualitative way. Only recently have efforts been made to study this problem quantitatively. Because of this the state of knowledge on this subject is not so satisfactory as that obtained for ordinary oxidation. A quantitative study of the rate and extent of the reaction of ozone with rubber vulcanizates and the cracking under strain is discussed herein. The general knowledge on this subject tells us that ozone attack results in the cracking of the surface of vulcanizates. Cracking occurs only when the specimen is under some strain during exposure to ozone. The broad quantitative problem then becomes one of defining the factors controlling the reaction while the specific problem relating to cracking becomes one of measuring such crack generation and crack growth in vulcanizates under strain. The method used in this work may be described as follows. A sample is stretched and allowed to relax until most of the pertinent stress relaxation has taken place. Ozone is then admitted to the stretched and relaxed sample. As cracking occurs the stress in the sample decreases and the length increases. The effect of the ozone produced cracks may be considered as related to change in form of work. The initial work done on the sample by stretching is derived from an equation expressing the network-statistical theory of rubber elasticity. The cracking is considered as a transformation of work to form new surface.

scholarly journals A Comparison of the Hart-Smith Model with Arruda-Boyce and Gent Formulations for Rubber Elasticity

2004 ◽  
Vol 77 (4) ◽  
pp. 724-735 ◽  
Author(s):  
G. Chagnon ◽  
G. Marckmann ◽  
E. Verron
Keyword(s):  
Constitutive Model ◽  
Large Strain ◽  
Constitutive Models ◽  
Rubber Elasticity ◽  
Material Parameters ◽  
Strain Responses ◽  
Smith Model

Abstract The present paper demonstrates that the Hart-Smith constitutive model and the more recent Arruda and Boyce eight chains and Gent constitutive models are closely related. The ability of these three models to predict both small and large strain responses of rubbers is highlighted and equations that relate their material parameters are established.

Classical Theories of Rubber Elasticity

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Experimental Data ◽  
Free Energy ◽  
Statistical Theory ◽  
Network Model ◽  
Network Theory ◽  
Elementary Theory ◽  
Reference Points ◽  
Rubber Elasticity ◽  
Historical Aspects ◽  
Basic Reference

This chapter describes three molecular theories of rubber elasticity. Section 2.1 outlines the elementary theory of Kuhn and Treloar, which is of particular importance since it presents the basic elements of rubberlike elasticity in a very transparent way. Section 2.2 presents the phantom network model developed by James and Guth, and section 2.3 presents the affine network model developed by Wall and Flory. Historical aspects of the theories have been given in an article by Guth and Mark, and in a book prepared as a memorial to Guth. Finally, the major features of both theories are briefly summarized in a review. Separately, the James-Guth theory has been reviewed by Guth and by Flory, and the phantom network model of section 2.2 is based on the Flory treatment. The affine network model has been described in detail in Flory’s 1953 book. This model is described in section 2.3 by generalizing the phantom network model (as was done in one of Flory’s subsequent studies). The simple, elementary statistical theory described in section 2.1 paved the way to the current understanding of rubber elasticity. Further progress in the understanding of rubberlike systems was possible, however, only as a result of the two more precise and accurate theories: the phantom network and the affine network theories. Despite their differences, these two theories and the corresponding molecular models have served as basic reference points in this area for more than four decades. They still serve this purpose for the interpretation and explanation of experimental data. The differences between the assumptions and the predictions of the two models have led to serious disagreements during their development, as may be seen from the original papers cited earlier. The main point of disagreement was the magnitude of the front factor that appeared in the expression for the elastic free energy and the stress. For tetrafunctional networks, the James-Guth phantom network theory predicts one-half the value of the front factor obtained by the Wall-Flory affine network theory.

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