Scaling laws of Mullins effect in nitrile butadiene rubber nanocomposites

doi:10.1016/j.polymer.2020.122350

Polymer

Volume 193, 10 April 2020, 122350

https://doi.org/10.1016/j.polymer.2020.122350 Get rights and content

Highlights

•
The Mullins effect of rubber nanocomposites involves the microscopic deformation of the matrix.
•
The recovery hysteresis is temperature and velocity dependent.
•
The softening energy loss is accumulative.

Abstract

Rubber nanocomposites experiencing cyclic deformation undoubtedly exhibit Mullins effect whose underlining mechanisms are not yet clear. Herein this effect in nitrile butadiene rubber nanocomposites is systematically investigated for revealing the influences of pre-strain interval, loading and unloading velocities, temperature, filler type and content, as well as crosslinking agent. The results show that the recovery hysteresis energy and accumulative softening energy of the nanocomposites can be superposed onto master curves as a function of microscopic strain of the rubber phase, revealing that both involving the viscoelastic deformation of the rubber phase. Especially the recovery hysteresis highly depending on temperature and loading and unloading velocities is connected to the viscoelasticity of nonideally crosslinked rubber network in the nanocomposites. On the other hand, the accumulative softening energy loss comes from recovery retardation of rubber chains and is somewhat sensitive to the filler, temperature and crosslinking agent. The investigation would be instructive to clarify the physical origin of Mullins effect to produce low dissipation rubber nanocomposites.

Graphical abstract

Introduction

Rubber nanocomposites are widely used in industry [[1], [2], [3], [4], [5]]. They exhibit Mullins effect featured by stress softening and recovery hysteresis during cyclic deformations. Following the pioneering work of Mullins in 1965 [6,7], this effect is extensively investigated whereas its mechanism is far from being clarified [[8], [9], [10], [11], [12], [13], [14]]. Viewpoints of breakup of filler network [[15], [16], [17], [18]] or strain induced crystallization [[19], [20], [21], [22]] are proposed but they are not applicable to the same effect appeared in non-crystalizing gum and low-filling nanocomposites [23,24]. The processes of chain desorption [25,26], slippery [[27], [28], [29]] or bond breakage [30] could possibly explain the hysteresis and stress softening but fails for the viscoelastic recovery of the stretched nanocomposites [14,23,[31], [32], [33]]. The models are hard to reasonably explain this effect over a wide range of conditions [[34], [35], [36], [37], [38]].

In a previous work [23] we divide the energy loss accompanying the Mullins effect into recovery hysteresis and softening energies (E_rh and E_s) and find that E_rh involves in microscopic strain of rubber phase while E_s is associated with both the rubber and filler phases. However, this conclusion is in conflict with that for the nonlinear Payne effect where the decays of both storage and loss moduli beyond the linear viscoelastic region are related to the nonlinear event of the matrix [[39], [40], [41], [42], [43], [44], [45], [46], [47]]. Because the viscoelasticity of the matrix is dependent upon the testing condition, herein influence factors including pre-strains, tensile velocity, temperature, filler type and crosslinking agents on the Mullins effect are systematically investigated. By considering the accumulation characteristic of E_s, we show that the softening also involves in the local deformation of viscoelastic, nonideally crosslinked rubber matrix. The results are illuminating for understanding the Mullins effect based on rubber viscoelasticity.

Section snippets

Materials

Nitrile butadiene rubber (NBR; trademark 4155 acrylonitrile content 41 wt% and density 0.97 g cm⁻³) was obtained from Duokang, China. Carbon black (CB; trademark N330, primary particle size ~30 nm and density 1.86 g cm⁻³) was obtained from Longxin Chem. Stock, China. Hydrophilic and hydrophobic fumed silica products (A200 and R974) were purchased from Evonik Degussa Co., Akron, OH, USA. Antioxidant 6PPD [N-(1,3-dimethylbutyl)-N′-phenyl-p-phenylenediamine], zinc oxide and stearic acid were

Influence of prestrain interval

The Mullins effect is sensitive to prestrain interval (ε_inter) [[49], [50], [51]] for sulfur-vulcanized gum and its CB nanocomposites. This effect was investigated under cyclic deformations at a crosshead velocity 50 mm min⁻¹ with three predetermined prestrain intervals (ε_inter = 0.1, 0.2, and 0.5; see Fig. S1 for σ-ε curves of sulfur-vulcanized gum and its CB nanocomposite with ϕ = 0.24). Following Li et al. [23], the energy losses associated with recovery hysteresis and softening (E_rh and E_s)

Conclusions

By creating master curves of hysteresis energy and accumulated softening energy of the nanocomposites with the reference of the vulcanized NBR gum, it is evidenced that the Mullins effect of the nanocomposites is dominated by the microscopic deformation of the nonideally crosslinked rubber phase. Due to the viscoelastic nature of the rubber phase, the hysteresis energy accompanying the Mullins effect is dependent on velocity of the cyclic deformation of the nanocomposites and the accumulated

CRediT authorship contribution statement

Zhiyun Li: Conceptualization, Methodology, Writing - original draft, Investigation. Fuxiang Wen: Investigation, Resources. Munir Hussain: Investigation, Resources. Yihu Song: Conceptualization, Methodology, Writing - review & editing. Qiang Zheng: Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (U1908221, 51873190, and 51790503).

References (67)

Y. Song et al.
Concepts and conflicts in nanoparticles reinforcement to polymers beyond hydrodynamics
Prog. Mater. Sci.
(2016)
Y. Song et al.
Linear viscoelasticity of polymer melts filled with nano-sized fillers
Polymer
(2010)
Q. Guo et al.
A thermo-viscoelastic-damage constitutive model for cyclically loaded rubbers. Part II: experimental studies and parameter identification
Int. J. Plast.
(2018)
J. Plagge et al.
A physically based model of stress softening and hysteresis of filled rubber including rate- and temperature dependency
Int. J. Plast.
(2017)
V.N. Khiem et al.
An averaging based tube model for deformation induced anisotropic stress softening of filled elastomers
Int. J. Plast.
(2017)
G. Machado et al.
Theory and identification of a constitutive model of induced anisotropy by the Mullins effect
J. Mech. Phys. Solid.
(2014)
Y.Y. Merckel et al.
Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers
Mech. Mater.
(2013)
Y. Song et al.
Rigid nanoparticles promote the softening of rubber phase in filled vulcanizates
Polymer
(2019)
J. Diani et al.
A review on the Mullins effect
Eur. Polym. J.
(2009)
B. Meissner et al.
A structure-based constitutive equation for filler-reinforced rubber-like networks and for the description of the Mullins effect
Polymer
(2006)

Y. Tomita et al.

Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining

Int. J. Mech. Sci.

(2008)

Cited by (26)

Impacts of deep eutectic solvent on silica/nitrile rubber nanocomposites for high-pressure hydrogen storage applications
2024, Composites Communications
Rubber nanocomposites used for hydrogen (H₂) energy storage demand tailored mechanical and compressed gas permeation properties. Herein, deep eutectic solvent (DES) is used as a promising silica dispersant to mediate the mechanical and gas swelling behavior of nitrile rubber (NBR) nanocomposites. The results reveal that DES improves the mechanical deformational stress and lowers the swelling degree with well-dispersed silica in NBR, allowing the preparation of high-performance nanocomposites with potential applications in preventing H₂ leakage in high-pressure equipment facilities. Under 0.01 and 90 MPa H₂ pressures at 24 °C and 37 °C, the NBR nanocomposites with DES demonstrate lower swellings, and the improved crosslinking density and nanofillers dispersion enhance the mechanical properties while retaining the dissipation of the Mullins effect. This sheds light on the mechanical failure mechanism and the design of tailorable high-pressure rubber sealings.
Inhomogeneities of sulfidic linkages and mullins effect in isoprene rubber vulcanizates vulcanized with sulfur donor agents
2024, Polymer
Gum vulcanizates exhibit the Mullins effect during large-strain cyclic tension. However, the details of the Mullins effect remain unclarified due to the difficulty of analysis of a complicated network structure. The Mullins effect in isoprene rubber (IR) vulcanizates has been systematically investigated to clarify the impacts of network inhomogeneities caused by the distribution of sulfidic linkages. Chemical probe experiments and paraffin swelling have been performed in an attempt to clarify the contribution of the presence of different types of sulfidic linkages. Thermo-oxidative aging at a moderate temperature (353 K) has been used to assess the effect of changes in structural inhomogeneity on the Mullins effect in aged vulcanizates. During cyclic tension deformations, the recovery hysteresis and accumulated softening energy densities normalized by theoretical shear modulus of elastically effective network are influenced by the heterogeneity of network structure only before the onset of crystallization. These findings can be used to inform the design of the network structure and enhance the performance of rubber products.
Influence of polyethylene glycol-based deep eutectic solvent on vulcanization and mechanical properties of natural rubber gum vulcanizates
2024, Polymer
Rubber vulcanization generates volatile organic compounds emissions associated with the intermolecular crosslinking reactions at rather higher temperatures mediated by many kinds of indispensable additive. To achieve the carbon peaking and neutrality targets in China, rubber processing industries call for ecofriendly, green additives to satisfy demands of high-efficiency vulcanization at low temperatures. Herein an oligomer deep eutectic solvent (DES) based on polyethylene glycol is used for the first time for regulating vulcanization kinetics of natural rubber (NR) gums. It is found that DES at 0.2–1.0 phr (parts per hundred parts of rubber) dosages could accelerate the vulcanization at 120–140 °C without marked influences on crosslinking density and storage modulus at vulcanization equilibrium. The vulcanization of DES-containing gums at 120 °C is faster than that of the DES-free one at 140 °C while the DES-containing vulcanizates cured at 120 °C exhibit nonlinear rheological responses being similar to the DES-free one cured at 140 °C. The low-temperature vulcanization in general generates vulcanizates exhibiting higher tensile strength in comparison with those cured at 140 °C. Furthermore, DES could not influence the Mullins effect of the vulcanizates undergoing cyclic tension deformation. The results show that the non-volatile DES could be used to adjust the vulcanization kinetics without impact on the crosslinking density and Mullins effect, paving the way for developing energy-saving green vulcanization technologies.
Effect of deep eutectic solvents on vulcanization and rheological behaviors of rubber vulcanizates
2023, Journal of Cleaner Production
Deep eutectic solvents (DESs) are able to promote vulcanization of rubbers while the mechanisms remain unclear. Herein 4-methyl-5,7-dihydroxycoumarin (DHMC) as hydrogen bond donor (HBD) was used to synthesize DES by reaction with tetrabutylammonium bromide (TBAB) as hydrogen bond acceptor (HBA). The effects of DHMC, TBAB and DES on vulcanization of natural rubber (NR) and isoprene rubber (IR) were studied. It is shown that DES could participate in crosslinking network and adjust crosslinking density (v_c) of the vulcanizates through physical and chemical interactions with NR non-rubber components, zinc oxide (ZnO) activator and N-cyclohexyl-2-benzothiazolesulfenamide (CZ) accelerator. Furthermore, DES influences linear and nonlinear rheological responses and mechanical behaviors of NR vulcanizates. The NR vulcanizates cured at 120 °C with 0.1–0.3 phr (part per hundred parts of rubber) DES exhibit higher tensile strengths and lower v_c in comparison with the control one cured at 140 °C, which is assigned to the more homogenous crosslinking network in the former. This work provides an effective way to modulate the crosslinking network to produce high-strength vulcanizates at lowered vulcanization temperatures and ZnO amount, which is beneficial for the preparation of rubber products with high strengths and low hysteresis energies.
Influence of proteins and phospholipids on strain softening behaviors of natural rubber
2023, Polymer
In natural rubber (NR), the non-rubber components such as protein and phospholipids strongly influence the Payne effect and Mullins effect while the mechanisms are not yet clarified so far. Herein deproteinized NR (DPNR) and transesterified DPNR (TEDPNR) are prepared and rheological behaviors are investigated. It is shown that the non-rubber components greatly retard the terminal flow behavior. In comparison with NR, DPNR and TEDPNR exhibit significant hysteresis and worse recoverability under large amplitude shear. During cyclic tensile deformation, the DPNR vulcanizate behaves similar to the NR one, while the TEDPNR one demonstrates higher deformation energy normalized with theoretical shear modulus and dissipation ratio. It is suggested that both the protein and phospholipids influence the Payne effect of NR gum by forming aggregates and creating intermolecular association. On the other hand, the phospholipids rather than protein strongly influence the Mullins effect by lowering their crosslinking density and associating the rubbery chains. This investigation would be enlightening for understanding the mechanisms of the Payne effect and Mullins effect of the NR materials.
The maximum-strain and strain-interval dependences of microstructural evolution underneath the Mullins effect
2023, Composites Part A: Applied Science and Manufacturing
In situ small-angle neutron scattering (SANS) and constitutive model were combined to investigate silica filled deuterated silicone rubber (SFdSR) under strain rise path at strain rate of 0.001 s⁻¹, with strain intervals from 0.1 to 1. It was found that, (i) The non-linear behaviors are sensitive to strain interval, cycle - number, and maximum strain, etc. (ii) SANS suggests that the cyclic orientation-relaxation of bound rubber can cause accumulative fatigue. (iii) The orientation of bound rubber t_H/t_V − 1 decreases from 9.9 to 3.6 with increasing the strain intervals from 0.1 to 1 for the same macroscopic maximum strain 3.0. Interestingly, the mechanical response softening (E_s) and recovery hysteresis (E_rh), the evolution of bound rubber, and the constitutive analysis consistently suggests a strain threshold of 1.5. Accordingly, the roles of matrix, interface, and filler networks as well as their interactions on the origin of the Mullins effect were discussed.

View all citing articles on Scopus

View full text

Scaling laws of Mullins effect in nitrile butadiene rubber nanocomposites

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Materials

Influence of prestrain interval

Conclusions

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgments

Prog. Mater. Sci.

Polymer

Int. J. Plast.

Int. J. Plast.

Int. J. Plast.

J. Mech. Phys. Solid.

Mech. Mater.

Polymer

Eur. Polym. J.

Polymer

Polymer

Polymer

Polymer

Polymer

Polym. Test.

Int. J. Solid Struct.

J. Mech. Phys. Solid.

Polymer

Int. J. Solid Struct.

Mech. Mater.

Polymer

Polymer

Polymer

Polymer

Polymer

Polymer

Polymer

Polymer

Polymer

Eur. J. Mech. Solid.

J. Non-Newtonian Fluid Mech.

Polym. Test.

Int. J. Mech. Sci.