Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates
Abstract
:1. Introduction
2. Experimental Methods
2.1. Sample Preparation
2.2. Measurement Procedure
2.3. Experimental Observations
- There is a reduction in the stress on each successive loading at the same strain amplitude. The reduction is largest between the first and second loading-unloading cycles and becomes less significant in the following cycles (Figure 12). The effects of stress softening are less significant for compounds with lower CB content.
- There are residual strains, known as the permanent set, that increase with the amount of carbon black and that depend on the maximum applied strain.
- The behaviour of rubber is rate dependent, with an enhancement of stress when the deformation rate is increased (Figure 13).
- The material approaches to the virgin loading path whenever the load is increased beyond its previous maximum value (Figure 16).
- The stress–strain path is highly dependent on the loading history (Figure 16). In the following sections, this phenomenon is referred to as the pre-strain effect.
3. Preliminary Remark
3.1. Basics of Continuum Mechanics
3.2. Determination of Model Parameters and Correlation Matrix
4. Nonlinear Viscoelastic Models
4.1. Phenomenological Models
4.1.1. Damage Models
- It has no symmetry during the unloading and reloading phase of each cycle.
- It is not constant after significant peak strain when the material is reloaded to a smaller strain.
- It never returns to the value 1 (there is always a softening when the material is reloaded even at a fixed maximum strain amplitude).
4.1.2. Additive Split of the Stress
4.1.3. Constitutive Laws Based on a Rubber Elasticity Model
5. Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
NR | Natural Rubber |
PHR | Part per Hundred Rubber |
SBR | Styrene-Butadiene Rubber |
NBR | Nitrile Butadiene Rubber |
EPDM | Ethylene Propylene Diene Monomer Rubber |
TARRC | Tun Abdul Razak Research Center |
SMR | Standard Malaysian Rubber |
FEF | Fast Extruding Furnace |
HPPD | Hydroxyphenylpyruvate Dioxygenase |
CBS | N-Cyclohexyl-2-benzothiazole sulfenamide |
DMA | Dynamic Mechanical Analysis |
DFM | Dynamic Flocculation Model |
PRF | Parallel Rheological Framework |
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- | NR2 | NR10 | NR20 | NR30 | NR40 | NR50 | NR60 |
---|---|---|---|---|---|---|---|
Natural Rubber, SMR CV60 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
Carbon Black, FEF N550 | 2 | 10 | 20 | 30 | 40 | 50 | 60 |
Process oil, 410 | - | 1 | 2 | 3 | 4 | 5 | 6 |
Zinc oxide | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
Stearic acid | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
Antioxidant/antiozonant, HPPD | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
Antiozonant wax | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
Sulfur | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |
Accelerator, CBS | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |
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Carleo, F.; Barbieri, E.; Whear, R.; Busfield, J.J.C. Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates. Polymers 2018, 10, 988. https://doi.org/10.3390/polym10090988
Carleo F, Barbieri E, Whear R, Busfield JJC. Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates. Polymers. 2018; 10(9):988. https://doi.org/10.3390/polym10090988
Chicago/Turabian StyleCarleo, Francesca, Ettore Barbieri, Roly Whear, and James J. C. Busfield. 2018. "Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates" Polymers 10, no. 9: 988. https://doi.org/10.3390/polym10090988