Effect of the temperature and strain rate on the tension response of uncured rubber: Experiments and modeling
Introduction
The uncured rubber material presented during the production process of rubber products usually undergoes a series of processes, such as mastication, calendering/extrusion, building and final vulcanization processes, which involve not only the obvious rate response but also intense temperature variation. For instance, the temperature during calendering/extrusion exceeds 100 °C, and it is higher during the vulcanization process. Hence, if the mechanical properties of uncured rubber depend on the strain rate and temperature, the whole production of rubber products is actually a complicated thermomechanical coupling process. In recent years, as a result of the improvement of finite element simulation technology, the realization of the simulation of this process is becoming possible. To accomplish this, research on the properties of uncured rubber, including the rate dependence and temperature effect, is becoming important and necessary.
The mechanical properties of uncured rubber have received much attention, and the tensile deformation behaviors under different loading scenarios have been reported by several investigators in recent years (1, Dal et al., 2018; Feng et al., 2016; Zopf et al., 2015; Zopf and Kaliske, 2017). The experimental data indicates that the stress response of uncured rubber exhibits rate-dependent and nonlinear elastic-inelastic behaviors involving strong hysteresis and shape recovery under cyclic loading conditions (Kaliske et al., 2010). Furthermore, several constitutive models, including the molecular network model (Li et al., 2019) and phenomenological models (Feng et al., 2016; Kaliske et al., 2010; Zopf and Kaliske, 2017), have been proposed to characterize the distinct deformation behaviors of uncured rubber. Among all these studies, the strain rate effect, which is easier to control, has been thoroughly researched and is discussed in detail in our recent contribution (Li et al., 2019). However, the temperature effect, despite its great influence on the mechanical properties of uncured rubber, has almost not been investigated due to the difficulty in the control of the experimental conditions and the complication of the constitutive relationship. In view of the high-temperature environment during calendaring, the extrusion processes or vulcanization processes, the development of understanding and creating a model capable of explicitly describing the temperature dependence, in parallel with the strong rate dependence of this composite under a large deformation, is an important issue to address.
Currently, few models exist that attempt to predict the time and temperature dependence of elastomers for general strain histories. Classical hyperelastic models or the micromechanism-inspired models developed for crosslinked rubber do not apply to uncured rubber due to the lack of crosslinks, which provide the material with elasticity. Therefore, it is of theoretical as well as practical interest to explore the underlying physical mechanisms of uncured rubber to develop a rate-temperature dependent constitutive model. For general carbon black filled rubber, the material is usually considered to be composed of a hard and a soft phase, that is, carbon black fillers and the molecular chain matrix (Mullins and Tobin, 1957). Furthermore, it can be supposed that the molecular chain matrix is a combination of two types of network arrangements: cross-linked chain network and free chain networks (Guo et al., 2018). For uncured rubber, a similar assumption could also be made that two types of network rearrangements are considered: carbon black filled chain network and free chain networks, which are composed of entangled and nonentangled free chain networks, as shown in Fig. 1. Without a crosslinked network, the adhesion between rubber molecular chains and carbon black particles, together with the entanglement between the free chains, are supposed to provide the elasticity of the uncured rubber. The entangled and nonentangled free chains are responsible for the strong hysteresis and shape recovery behaviors during deformation. Based on this interpretation, the mechanical properties of uncured rubber may be newly understood and described. Moreover, it provides a good framework for the establishment of the constitutive relationship.
Moreover, it should be noted that for filled or unfilled elastomers, stress softening occurs in the first cycles of loading, referred to as the Mullins effect (Mullins, 1948), which becomes unnoticeable in subsequent cycles. Numerous works have been devoted to the characterization of the Mullins effect based on the continuum mechanics approach (Simo, 1987), microstructural changes (Hanson et al., 2005), or macromolecular models (Diani et al., 2006). Among these, network alteration theories are a category of macromolecular models that have been developed to date (Bueche, 1960; Chagnon et al., 2006; Harwood et al., 1965). Recently, Khajehsaeid (2016) developed a physically motivated network alteration theory based on the morphology of filler-chain interactions. This developed theory was suggested to estimate the network evolution during deformation well and provided a useful tool for modeling the effect of Mullins-softening.
This study aims to investigate the influences of the temperature and strain rate on the mechanical behaviors of uncured carbon black filled rubber. The paper is planned as follows: Section 2 presents the testing system and the material formulation. To measure large strain data of the uncured rubber with high precision, a noncontact optical method is employed during the tests. Section 3 discusses the uniaxial tensile experimental investigation, which involves different temperatures and strain rates. The influences of both characteristics on the tensile mechanical properties are systematically discussed and the test results are microscopically explained. Based on this information, Section 4 proposes a rate-temperature dependent constitutive model to capture the combined features of the stress–strain data and further presents the model calibration and validation based on the present experiments. Finally, in Section 5, the paper ends with some concluding remarks.
Section snippets
Testing system and materials
This experimental setup is made of a tensile testing machine, a high-temperature environmental chamber and a data-image synchronous acquisition device, as demonstrated in Fig. 2. The automated grid method (AGM) (Sirkis and Lim, 1991), a kind of noncontact optical technique, was employed to accurately measure the whole strain field of the sample (Li et al., 2016). This method can adequately eliminate the end effect for soft materials. The data-image acquisition device consists of a CCD video
Experimental result and discussion
The monotonic tensile and cyclic loading tests were conducted under different loading scenarios to evaluate the tensile mechanical response of the uncured rubber and the effects of the temperature and strain rate upon it. To assess the repeatability of the experimental data, each test is carried out on three different specimens.
Basic equations
The deformation gradient F can be decomposed into a product of distortional and dilatational parts (Lee, 1969):where the distortional and dilatational parts are given by (Bergström, 2015):
Hence, the left Cauchy–Green tensor can be written as: in which the distortional part of the left Cauchy–Green tensor can be additively decomposed as: where devB* is the
Conclusion
In the present study, the tensile mechanical properties of uncured rubber were investigated at different temperatures and strain rates. Experimental investigations show that both the temperature and strain rate have strong influences on the tensile mechanical responses of uncured rubber. As the temperature increases, the elasticity of uncured rubber dramatically decreases, while the viscoplasticity is greatly enhanced. The magnitude of the experimental stress at a certain stretch approximately
Declaration of Competing Interest
The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
Acknowledgment
This work was funded by the National Natural Science Foundation of China (Nos. 11902229 and 11502181) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB22040502 XDC06030200). The support of the long-term technological cooperation project between Giti Tire Company and USTC is gratefully acknowledged.
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