Stress softening experiments in silica-filled polydimethylsiloxane provide insight into a mechanism for the Mullins effect

Polymer ◽  
2005 ◽  
Vol 46 (24) ◽  
pp. 10989-10995 ◽  
Author(s):  
David E. Hanson ◽  
Marilyn Hawley ◽  
Robert Houlton ◽  
Kiran Chitanvis ◽  
Philip Rae ◽  
...  
Keyword(s):  
Mullins Effect ◽  
Stress Softening ◽  
Insight Into

scholarly journals Stress-Softening in Particle-Filled Polyurethanes under Cyclic Compressive Loading

Polymers ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1588
Author(s):  
Wenshuai Xu ◽  
Mangong Zhang ◽  
Yu Liu ◽  
Hao Zhang ◽  
Meng Chen ◽  
...  
Keyword(s):  
Compressive Loading ◽  
Compressive Load ◽  
Soft Materials ◽  
Constitutive Parameter ◽  
Spherical Indentation ◽  
Mullins Effect ◽  
Stress Softening ◽  
Loading And Unloading ◽  
Load Displacement ◽  
Constitutive Parameters

Elastomer compositions containing various particulate fillers can be formulated according to the specific functions required of them. Stress softening—which is also known as the Mullins effect—occurs during high loading and unloading paths in certain supramolecular elastomer materials. Previous experiments have revealed that the load–displacement response differs according to the filler used, demonstrating an unusual model of correspondence between the constitutive materials. Using a spherical indentation method and numerical simulation, we investigated the Mullins effect on polyurethane (PU) compositions subjected to cyclic uniaxial compressive load. The PU compositions comprised rigid particulate fillers (i.e., nano-silica and carbon black). The neo-Hooke model and the Ogden–Roxburgh Mullins model were used to describe the nonlinear deformation behavior of the soft materials. Based on finite element methods and parameter optimization, the load–displacement curves of various filled PUs were analyzed and fitted, enabling constitutive parameter prediction and inverse modeling. Hence, correspondence relationships between material components and constitutive parameters were established. Such relationships are instructive for the preparation of materials with specific properties. The method described herein is a more quantitative approach to the formulation of elastomer compositions comprising particulate fillers.

Molecular insight into the Mullins effect: irreversible disentanglement of polymer chains revealed by molecular dynamics simulations

2017 ◽  
Vol 19 (29) ◽  
pp. 19468-19477 ◽  
Author(s):  
Chi Ma ◽  
Tuo Ji ◽  
Christopher G. Robertson ◽  
R. Rajeshbabu ◽  
Jiahua Zhu ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Molecular Model ◽  
Polymer Chains ◽  
Mullins Effect ◽  
Key Characteristics ◽  
Dynamics Simulations ◽  
First Time ◽  
Insight Into

For the first time, the key characteristics associated with the Mullins effect are captured by a molecular model.

Stress Softening in Natural Rubber Vulcanizates. IV. Unfilled Vulcanizates

1967 ◽  
Vol 40 (3) ◽  
pp. 840-848 ◽  
Author(s):  
J. A. C. Harwood ◽  
A. R. Payne
Keyword(s):  
Carbon Black ◽  
Natural Rubber ◽  
Molecular Networks ◽  
Mullins Effect ◽  
Total Recovery ◽  
Stress Softening ◽  
Affine Deformation ◽  
Nonaffine Deformation ◽  
Natural Rubber Vulcanizates ◽  
Random State

Abstract Stress softening (Mullins effect) in gum natural rubber vulcanizates is similar in magnitude to that in carbon black filled vulcanizates. The amount of stress softening is slightly greater in vulcanizates cured to produce predominantly polysulfide crosslinks than in those containing monosulfide or carbon to carbon crosslinks. The total recovery of stress softening in the vulcanizates containing monosulfide or carbon to carbon crosslinks suggests that the phenomenon is attributable to a quasiirreversible rearrangement of molecular networks due to localized non-affine deformation resulting from short chains reaching the limit of their extensibility. This nonaffine deformation results in a displacement of the network junctions from their initial random state.

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

2018 ◽  
Vol 928 ◽  
pp. 20-25 ◽  
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.

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

1966 ◽  
Vol 39 (5) ◽  
pp. 1544-1552 ◽  
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.

Inflation of a Thick-Walled Shell Which Exhibits Stress Softening

1998 ◽  
Vol 65 (1) ◽  
pp. 46-50 ◽  
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.

scholarly journals Transversely isotropic cyclic stress-softening model for the Mullins effect

2012 ◽  
Vol 468 (2148) ◽  
pp. 4041-4057 ◽  
Author(s):  
Stephen R. Rickaby ◽  
Nigel H. Scott
Keyword(s):  
Residual Strain ◽  
Transversely Isotropic ◽  
Cyclic Stress ◽  
Elastic Response ◽  
Chain Model ◽  
Mullins Effect ◽  
Softening Function ◽  
Stress Softening ◽  
Cyclic Loading And Unloading ◽  
Isotropic Hyperelastic Material

This paper models stress softening during cyclic loading and unloading of an elastomer. The paper begins by remodelling the primary loading curve to include a softening function and goes on to derive nonlinear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain and creep of residual strain. These ideas are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular, a carbon-filled rubber vulcanizate.

Sign in / Sign up

Export Citation Format

Share Document