Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates

Abstract

Modelling the viscoelastic behavior of rubber for use in component design remains a challenge. Most of the literature does not consider the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). Previous studies have either focused on the behaviour at small strains and small strain rates or in fast loading conditions that result in low cycle fatigue or tearing phenomena. There is a lack of understanding of the dynamic response of natural rubber suspension components when used in real vehicle applications. This paper presents a review of popular viscoelastic nonlinear constitutive models and their ability to model the mechanical behaviour of typical elastomer materials such as Natural Rubber (NR) incorporating different PHR (Parts per Hundred Rubber, XX) of carbon black. The range of strain and strain rate are typical for the materials used in rubber suspensions when operating in severe service operating conditions, such as over rough terrain or over pot-holes. The cyclic strain is applied at different amplitudes and different strain rates in this medium strain range. Despite the availability of many models in the literature, our study reports that none of the existing models can fit the data satisfactorily over a wide range of conditions.

Modeling the Full Time-Dependent Phenomenology of Filled Rubber for Use in Anti-Vibration Design

“…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 Characterisation of all this materials under cyclic tensile tests is available in [14] and it is briefly recalled in this section for the sake of completeness. Uniaxial tension tests were conducted using an Electropulse Instron Test Machine.…”

“…The results display strong nonlinearity, large hysteresis, complex Mullins behaviour (Figures 2 and 3b), cyclic stress relaxation ( Figure 3a) and permanent set. Full detail of all the experimental results can be found in [14].…”

“…Comparison of the new model with experimental data loaded with cyclic uniaxial test with uniform maximum strain amplitude [14]. Subfigures (a-c) show respectively the behaviour for NR2, NR40 and NR60.…”

“…The multiscale nature of polymers is reflected by different computational methods for specific length and time scales: quantum (∼10 −10 m, ∼10 −12 s), atomistic (∼10 −9 m, ∼10 −9 -10 −6 s), mesoscopic (∼ 10 −6 m, ∼10 −6 -10 −3 s) or macroscopic scale (∼10 −3 m, ∼1 s) [11][12][13]. At the top level, phenomenological macroscopic models can roughly be classified into three categories [14] damage models, rheological models with serial and parallel combination of elastic and viscous elements and the constitutive equations based on a rubber elasticity model. Damage models [15][16][17] are unable to differentiate between an unloading and a subsequent reloading with one consequence being that they cannot predict the cyclic stress softening phenomenon.…”

“…More specifically, stress decreases logarithmically [25][26][27]. In a recent review article [14] it was found that no predictive model was able to fully reproduce cyclic stress softening to a satisfying quality. In the next sections a new approach based on a recently proposed model [28] is presented.…”