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

Huang, Lihong; Yang, Xiaoxiang; Gao, Jianhong

doi:10.1155/2019/2369329

Cited by 11 publications

(10 citation statements)

References 21 publications

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“…The sample did not fully return to its original state when unloaded to a zero stress. The residual strain (permanent set) was produced and determined as the difference between the strain of the last unloading curve and the first (virgin) loading curve [33]. The results for SBR vulcanizates are presented in Table 5.…”

Section: Resultsmentioning

confidence: 99%

Organic Zinc Salts as Pro-Ecological Activators for Sulfur Vulcanization of Styrene–Butadiene Rubber

2019

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Organic zinc salts and complexes were applied as activators for sulfur vulcanization of styrene–butadiene elastomer (SBR) in order to reduce the content of zinc ions in rubber compounds as compared with conventionally used zinc oxide. In this article, the effects of different organic zinc activators on the curing characteristics, crosslink densities, and mechanical properties of SBR as well as the aging resistance and thermal behavior of vulcanizates are discussed. Organic zinc salts seem to be good substitutes for zinc oxide as activators for sulfur vulcanization of SBR rubber, without detrimental effects to the vulcanization time and temperature. Moreover, vulcanizates containing organic zinc salts exhibit higher tensile strength and better damping properties than vulcanizate crosslinked with zinc oxide. The application of organic zinc activators allows the amount of zinc ions in SBR compounds to be reduced by 70–90 wt % compared to vulcanizate with zinc oxide. This is very important for ecological reasons, since zinc oxide is classified as being toxic to aquatic species.

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Section: Resultsmentioning

confidence: 99%

Organic Zinc Salts as Pro-Ecological Activators for Sulfur Vulcanization of Styrene–Butadiene Rubber

2019

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“…where W0 (λ, λÀ1/2) indicate the strain energy in the stretching pathway and W (λ, λ À1/2 , η) for releasing path, and Φ (η) indicate the damage function of the material during the stretch and releasing states. 43 This function determines the energy dissipated during one cyclic loading and it is controlled by variable η which is given by equation ( 7)…”

Section: Ogden Pseudo-elasticity Modelmentioning

confidence: 99%

“…where W m is the maximum value of W; r, β and m are Mulling effect parameters; and erf(x) is the Gaussian error function obtained as following 43 erf ðxÞ ¼ In the loading process, η is equal 1, and in the unloading process, η was declined in a range of 0 < η ≤ 1. Finally, with the above introduction, the stresses are given by…”

Section: Ogden Pseudo-elasticity Modelmentioning

confidence: 99%

“…The analytical expression of the strain energy for hyperplastic materials od Ogden 39,42 (1972, 1982) method is given as followsThe uniaxial stretch is given as followsFor uniaxial tensile stress, the Ogden ( N = 3) strain energy is given at the following equation 43 The stress tensor for anisotropic material is obtained as followsThe Mullins effect is estimated by applying a strain energy term and a damage function as defined by equation (6)where W0 (λ, λ−1/2) indicate the strain energy in the stretching pathway and W (λ, λ −1/2 , η) for releasing path, and Φ (η) indicate the damage function of the material during the stretch and releasing states. 43 This function determines the energy dissipated during one cyclic loading and it is controlled by variable η which is given by equation (7)where W m is the maximum value of W; r, β and m are Mulling effect parameters; and erf(x) is the Gaussian error function obtained as following 43 In the loading process, η is equal 1, and in the unloading process, η was declined in a range of 0 < η ≤ 1. Finally, with the above introduction, the stresses are given byThe MATLAB package was applied to fit the Ogden constitutive parameters through the Levenberg–Marquardt nonlinear least-squares technique.…”

Section: Ogden Pseudo-elasticity Modelmentioning

confidence: 99%

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Study Mullins effect of polyurethane reinforcement with halloysite nanotube by molecular dynamics simulation

Pebdani

2022

Journal of Elastomers & Plastics

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Molecular dynamics simulation was applied to study the irreversible strain through loading and unloading cyclic tests of polyurethane (PU) reinforced with halloysite nanotube (HNT). The influences of the stretching cycle rate, different temperatures, the volume of halloysite nanotube and the density rate of the hard and soft domain of PU were studied on the permanent set. The results illustrate that the residual strain was increasing when the stretching loading is increasing, for example, with increasing strain load to 250% the residual strain increased to 55%. In contrast, the increasing volume fraction of HNT and hard part content of PU lead to lower residual strain. The recovery of the permanent set is achievable by increasing temperature from 1 K to 200 K residual strain is decreased to 52%. An Ogden constitutive and the theory of pseudo-elasticity were adopted to simulate this composite in the ABAQUS software. This model has proposed a reasonable prediction of plastic deformation.

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“…Thus the size of the fracture free cavity stretch range, λ a ∈ [1 λ c ), reduces at higher expansion rates. (b) Representative Mullins effect observed in cyclic uniaxial testing of natural/styrene-butadiene (NSBR) rubber (Huang et al, 2019). The different colours correspond to different loading cycles.…”

Section: Mullins Effectmentioning

confidence: 99%

Probing local nonlinear viscoelastic properties in soft materials

Chockalingam,

Roth,

Henzel

et al. 2020

Preprint

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Minimally invasive experimental methods that can measure local rate dependent mechanical properties are essential in understanding the behaviour of soft and biological materials in a wide range of applications. Needle based measurement techniques such as Cavitation Rheology (Zimberlin et al., 2007) and Volume Controlled Cavity Expansion (VCCE, Raayai-Ardakani et al. (2019a)), allow for minimally invasive local mechanical testing, but have been limited to measuring the elastic material properties. Here, we propose several enhancements to the VCCE technique to adapt it for characterization of viscoelastic response at low to medium stretch rates (10 −2 -1 s −1 ). Through a carefully designed loading protocol, the proposed technique performs several cycles of expansion-relaxation at controlled stretch rates in a cavity expansion setting and then employs a large deformation viscoelastic model to capture the measured material response. Application of the technique to soft PDMS rubber reveals significant rate dependent material response with high precision and repeatability, while isolating equilibrated states that are used to directly infer the quasistatic elastic modulus. The technique is further established by demonstrating its ability to capture changes in the rate dependent material response of a tuneable PDMS system. The measured viscoelastic properties of soft PDMS samples are used to explain earlier reports of rate insensitive material response by needle based methods: it is demonstrated that the conventional use of constant volumetric rate cavity expansion can induce high stretch rates that lead to viscoelastic stiffening and an illusion of rate insensitive material response. We thus conclude with a cautionary note on possible overestimation of the quasistatic elastic modulus in previous studies and suggest that the stretch rate controlled expansion protocol, proposed in this work, is essential for accurate estimation of both quasistatic and dynamic material parameters.

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

Cited by 11 publications

References 21 publications

Organic Zinc Salts as Pro-Ecological Activators for Sulfur Vulcanization of Styrene–Butadiene Rubber

Organic Zinc Salts as Pro-Ecological Activators for Sulfur Vulcanization of Styrene–Butadiene Rubber

Study Mullins effect of polyurethane reinforcement with halloysite nanotube by molecular dynamics simulation

Probing local nonlinear viscoelastic properties in soft materials

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