A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber

Abstract The effect of hydrolytic aging on mechanical responses of Rubber likes materials, in particular, Mullins effect and the permanent set has been modeled. Hydrolytic aging is considered as the result of the competition between two phenomena (1) chain scission and (2) cross-link scission/reformation. Both phenomena were modeled and thus, the strain energy of the polymer matrix is written with respect to three independent mechanisms; i) the shrinking original matrix which has not been attacked by water, ii) conversion of the first network to a new network due to the reduction of the crosslinks, and iii) energy loss from network degradation due to water attacks to ester groups. The model is validated with respect to a set of experimental data. Besides accuracy, the simplicity and few numbers of fitting parameters make the model a good choice for further implementations.

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Pseudo Elastic Analysis of Carbon Reinforced Natural/Styrene-Butadiene Blend Rubber (NSBR) with Ogden Constitutive Model

Materials Science Forum ◽

10.4028/www.scientific.net/msf.928.20 ◽

2018 ◽

Vol 928 ◽

pp. 20-25 ◽

Cited By ~ 1

Author(s):

Li Hong Huang ◽

Xiao Xiang Yang ◽

Jian Hong Gao

Keyword(s):

Constitutive Model ◽

Experimental Results ◽

Mullins Effect ◽

Elastic Analysis ◽

Stress Softening ◽

Styrene Butadiene

In this paper, experimental results that illustrate stress softening in carbon filled natural/styrene-butadiene blend rubber (NSBR) together with Mullins effect are introduced firstly. Then, based on these data, the Ogden constitutive model is derived. The theory of pseudo-elasticity is used in the model. It is found that theory of pseudo-elasticity and Ogden constitutive model is applicable in this composite.

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A constitutive model for stress-strain response and mullins effect in filled elastomers

Journal of Applied Polymer Science ◽

10.1002/app.36596 ◽

2012 ◽

Vol 125 (6) ◽

pp. 4368-4375 ◽

Cited By ~ 10

Author(s):

A. K. Mossi Idrissa ◽

S. Ahzi ◽

S. Patlazhan ◽

Y. Rémond ◽

D. Ruch

Keyword(s):

Constitutive Model ◽

Mullins Effect ◽

Strain Response ◽

Stress Strain ◽

Filled Elastomers

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Stress Softening in Natural Rubber Vulcanizates III. Carbon Black Filled Vulcanizates

Rubber Chemistry and Technology ◽

10.5254/1.3547069 ◽

1966 ◽

Vol 39 (5) ◽

pp. 1544-1552 ◽

Cited By ~ 3

Author(s):

J. A. C. Harwood ◽

A. R. Payne

Keyword(s):

Carbon Black ◽

Amplification Factor ◽

Mullins Effect ◽

Factor X ◽

Stress Strain ◽

Stress Softening ◽

Permanent Set ◽

Different Types ◽

Hydrodynamic Effects ◽

Natural Rubber Vulcanizates

Abstract This paper has confirmed the conclusions of the previous paper that the stress softening (Mullins effect) of a black-loaded vulcanizate is similar in magnitude to the stress softening of a gum rubber if the two vulcanizates are stretched initially to the same stress. The initial stress used in the present work was 180 kg/cm2, which is very near to the breaking stress of these vulcanizates. The similarity of the normalized stress-strain curves for all the vulcanizates, both gum and loaded with 60 phr of different types of black, suggests that the main difference between the stress-strain characteristics of a filled and a pure gum rubber, after the initial stressing cycle, can be accounted for by the strain amplification factor X. The more reinforcing blacks possess the higher X factors, i.e., they stiffen the rubber more than, for example, a fine thermal black. It is concluded that the black is acting mainly in a stiffening capacity due to the hydrodynamic effects of the degenerate carbon black networks. For sulfur crosslinked pure gum vulcanizates, in which the crosslinks are polysulfidic, the stress softening is partly associated with the breakage of polysulfide linkages. These reform in the extended condition and produce a real permanent set, but the major stress softening is attributed to the incomplete recovery of the crosslinked network to its initial random state due to network junctions or similar associations being displaced in a nonaffine way during extension. For example, junctions at the ends of chains which become fully extended at relatively low extensions will be displaced in this way. Thus when the rubber is subsequently strained, the network is already in a preferred disposition.

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Inflation of a Thick-Walled Shell Which Exhibits Stress Softening

Journal of Applied Mechanics ◽

10.1115/1.2789044 ◽

1998 ◽

Vol 65 (1) ◽

pp. 46-50 ◽

Cited By ~ 1

Author(s):

J. B. Haddow ◽

J. L. Wegner

Keyword(s):

Internal Pressure ◽

Strain Softening ◽

Complete Removal ◽

Mullins Effect ◽

Stress Softening ◽

Permanent Set ◽

Virgin State ◽

Rubberlike Material ◽

As Stress

The Mullins effect (Mullins, 1947), also known as stress softening, is exhibited by certain rubberlike materials and refers to changes of the mechanical properties, due to prior deformation. Johnson and Beatty (1995) have investigated the Mullins effect in equibiaxial tension by performing cycles of static inflation and deflation experiments on latex balloons. These experiments show that stress softening results in a decrease in the pressure necessary to inflate a balloon, and in addition, indicate inelastic effects of hysteresis and permanent set. The objective of this paper is to investigate the finite deformation static inflation from the virgin state, followed by quasi-static removal of the internal pressure, of a thick-walled homogeneous spherical shell composed of an incompressible isotropic rubberlike material which exhibits stress softening and permanent set. Since the initial inflation of the shell, due to application of an internal pressure, does not result in a homogeneous deformation, a state of residual stress is present after complete removal of the internal pressure. A procedure is presented for the determination of the response of the shell for the first cycle of inflation and deflation from the virgin state, and the analysis includes strain softening and the inelastic effects of hysteresis and permanent set. It is assumed that, for the initial static inflation of the shell from the virgin state, the internal pressure and stress distribution for a monotonically increasing internal or external radius are the same as for a hyperelastic shell, and also that the magnitude of the permanent set of an element of the material is related monotonically to the deformation at the end of the inflation.

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Pseudo-Elastic Analysis with Permanent Set in Carbon-Filled Rubber

Advances in Polymer Technology ◽

10.1155/2019/2369329 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

LiHong Huang ◽

Xiaoxiang Yang ◽

Jianhong Gao

Keyword(s):

Carbon Black ◽

Constitutive Model ◽

Residual Strain ◽

Volume Fraction ◽

Styrene Butadiene Rubber ◽

Uniaxial Tensile ◽

Butadiene Rubber ◽

Permanent Set ◽

Cyclic Loading And Unloading ◽

Filled Rubber

Via cyclic loading and unloading tests of natural/styrene-butadiene rubber (NSBR) blends at room temperature, the effects of the stretching, rate, temperature, and volume fraction of carbon black in the filled rubber on a permanent set (residual strain) were studied. The results showed that increasing the stretching, rate, and volume fraction of carbon black and reducing the temperature yielded greater residual strain. The uniaxial tensile behaviors of composites with the Mullins effect and residual strain were simulated using the ABAQUS software according to the aforementioned data. An Ogden-type constitutive model was derived, and the theory of pseudo-elasticity proposed by Ogden and Roxburgh was used in the model. It was found that the theory of pseudo-elasticity and the Ogden constitutive model are applicable to this composite, and if combined with plastic deformation, the models are more accurate for calculating the residual strain after unloading.

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