Introduction

The world’s natural resources are non-renewable and only available to a limited extent. Nowadays, there is an increase in environmental awareness worldwide. This has consequences on market economies and the related product research and manufacturing1. It is well known that elastomers are of interest in many applications due to their tunable mechanical properties, as well as thermal and chemical stabilities2.

Concerning the increasing interest in applying this material, intensive examinations are necessary. The increasing demand for high performance products with a simultaneous requirement for low price has stimulated the development of numerous efficient techniques. Natural rubber (NR) has been well recognized as one of the most important rubbers, and its properties are usually reinforced by the incorporation of CB to meet engineering demands3. However, the service conditions may bring about aging and degradation as a consequence of time-dependent and temperature-dependent mechanical properties, which can dramatically affect the service lifetime of rubbers. For the long-term properties of rubber-like materials, both the aging and dynamic properties are key factors in engineering applications. It is necessary to determine the thermal aging and mechanical properties of CB filled rubber products as this can help identify what applications the resulting rubbers are suitable for. Hence, reliable characterization techniques for the determination have to be provided. One of many well-established methods that enable accurate quantification of material thermo mechanical properties is dynamic mechanical analysis (DMA)4,5. Although many reports have focused on the aging mechanisms and mechanical performances of aged rubber products6,7,8,9, only a few studies have been provided regarding the thermorheological properties, such as the storage modulus and the loss modulus, which are related to the phase angle (δ) on the basis of stress–strain behavior10,11.

In addition, under cyclic loading, the CB filled rubber exhibits apparent viscoelastic nonlinearity (Payne effect) and hysteresis loss. Payne effect has been ascribed to the mechanisms, such as breakup/reformation of filler network or polymer-filler network, agglomeration/ deagglomeration of filler aggregates, chains desorption from nanoparticles, and disentanglement of adsorbed chains12. Payne effect is very important in the tire industry because dynamic nonlinearity is in the range of strain amplitudes most frequently encountered in reality13. For this reason, many works have been conducted to explain this phenomenon, mainly focusing on the frequency-, prestrain- and temperature-dependence4,12. Currently, an increasing number of researchers are investigating the Payne effect from the aspect of microstructure evolution in a particular experimental situation by using SEM, NMR and AFM14,15,16. Meanwhile, in the process of Payne effect investigation, a series of constitutive models have been proposed to reproduce this kind of mechanical behavior of CB filled rubbers. These models can generally be classified into two groups: filler network structural models and matrix-filler interface bonding and bonding failure models17. Kraus was the first to develop a phenomenological constitutive model to interpret the Payne effect of rubber-like materials, which was based on filler network breakage, by supposing a dynamic equilibrium between the breakage and recovery of weak physical bonds under cyclic loading conditions18,19. Although the Kraus model has been widely used for the effect of thermo-oxidative aging on the Payne effect, there is not much research on this issue. With increasing aging time, a general consensus is that the crosslink density of rubber-like materials changes obviously, which results in a change in mechanical behavior10,20. Li8 demonstrated that the crosslink density of the CB filled rubber vulcanizates aged at 100 and 120 °C, measured by equilibrium swelling method, increases with the increase of aging time. As for the Payne effect, it was reported that both storage and loss moduli increase with increasing aging time21,22, which is mainly due to the increasing crosslink density during the aging process. Besides, it should be noticed that prolonged heating at/over 70 °C is apt to cause post-vulcanization23, which generates more crosslinks23,24. However, it is recognized that there are two competitive mechanisms during aging: chain crosslinking and chain scission25. Hou11 investigated the influence of aging induced network variation on the Payne effect of isoprene rubber vulcanizates, and the results showed that the crosslink density increases first and then decreases with the increase of aging time, and the storage modulus also changes in the same trend, indicating that the crosslinking dominates in the early stage of aging. With proceeding of the aging, polysulfide, disulfide and monosulfide bonds densities change due to breaking and conversion, the bond breaking causes network defects including dangling and free chains, and results in the change of dynamic mechanical properties and hysteresis loss26. It is worth noting that the predominance of the two competitive mechanisms during aging is due to various factors, in particular to the composition of the material25. For example, Wang27 measured the crosslinking density of three kinds of CB filled rubber materials (SIBR-CB, SSBR-CB, and Nd-IR-CB) during the aging process, and the results showed that crosslinking is the dominant reaction in SIBR-CB and SSBR-CB samples, while the Nd-IR-CB sample undergoes scission.

Moreover, the Payne effect reflects a way of hysteresis loss under cyclic loading and the hysteresis loss gradually translates into heat, which can affect the mechanical property on the one hand and can result in thermo-oxidative aging on the other hand. To understand the hysteresis loss mechanism, extensive research has been conducted using experimental investigation or constitutive characterization28,29. However, these works do not pay attention to the influence of thermo-oxidative aging on the hysteresis loss. Therefore, it is necessary to study the effects of thermo-oxidative aging on the Payne effect and hysteresis loss of the CB filled rubber-like materials.

To this end, this paper attempts to study the thermo-oxidative aging-dependence of the Payne effect and hysteresis loss of filled rubber. In the classic theory framework, the Kraus model is employed to model the aging time and temperature dependence of the Payne effect and the comparison is made in detail according to the prediction of hysteresis loss.

Results and discussion

Hysteresis loss

Dynamic mechanical analysis (DMA) is an indispensable and effective tool for determining the viscoelastic properties of polymers and polymer composite materials, such as crosslinking density30, dynamic/complex viscosity and storage/loss compliance31,32.The storage modulus \(E^{\prime}\) or dynamic modulus is typically related to the Young’s modulus and refers to the ability to store energy applied to it for future purposes. The loss modulus \(E^{\prime\prime}\) is often considered as the tendency to dissipate energy33. The loss factor tan δ, as shown in Fig. 1, is defined as the ratio of the loss and storage modulus:

$$\tan \delta = E^{\prime\prime}/E^{\prime}$$
(1)
Fig. 1: Relationship among \(E^{\prime}, E^{\prime\prime}\) and \(\tan \delta\).
figure 1

The loss factor \(\tan \delta\) is defined as the ratio of the loss and storage modulus.

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Generally, the test specimen is loaded with a sinusoidal strain-controlled process, and the strain excitation ε(t) can be expressed in the following form:

$$\varepsilon \left( t \right) = \varepsilon _0 + \Delta \varepsilon \sin \left( {\omega t} \right)$$
(2)

where \(\varepsilon _0\) is the prestrain, \(\Delta \varepsilon\) is the dynamic strain amplitude, and ω is the angular frequency. The corresponding stress response σ(t) of the specimen can be defined as:

$$\sigma \left( t \right) = \sigma _0 + \Delta \sigma \sin \left( {\omega t + \delta } \right)$$
(3)

where \(\sigma _0\) is the static stress, \(\Delta \sigma\) is the stress amplitude, and δ is the phase angle between the applied strain and the resulting stress. The storage modulus \(E^{\prime}\) and the loss modulus \(E^{\prime\prime}\) are determined by standard methods:

$$E^{\prime} = \frac{{\Delta \sigma }}{{\Delta \varepsilon }}\cos \delta$$
(4)
$${\it{{\rm E}^{\prime\prime}}} = \frac{{\Delta \sigma }}{{\Delta \varepsilon }}\sin \delta$$
(5)

By substituting Eqs. (4) and (5) into Eq. (3), the dynamic stress response can also be rewritten as:

$$\sigma \left( t \right) = \sigma _0 \,+\, \Delta \varepsilon \left[ {E^{\prime}\sin \left( {\omega t} \right)\, +\, E^{\prime\prime}\cos \left( {\omega t} \right)} \right]$$
(6)

In addition, in the process of cyclic loading, the strain energy W over one period can be calculated by the following equation:

$$W = {\int}_0^{\frac{{2\pi}}{\omega}} {\sigma {{{\mathrm{d}}}}\varepsilon} = \omega \left( {\Delta \varepsilon} \right)^2{\int}_0^{\frac{{2\pi}}{\omega}} {\left[ {E^{\prime}\sin \left( {\omega t} \right)\cos \left( {\omega t} \right) \,+\, E^{\prime\prime}\cos ^2\left( {\omega t} \right)} \right]} {{{\mathrm{d}}}}t$$
(7)

It is well known that in the process of cyclic loading, the energy consists of two parts: the stored energy and dissipated energy. The dissipated energy, named hysteresis loss, can be calculated by the area of the hysteresis loop, which makes the temperature rise of the deformed material. In addition, the dissipated energy is only related to the loss modulus, and it can be expressed in the following form:

$$D = W_{{{{\mathrm{loop}}}}} = \pi \left( {\Delta \varepsilon } \right)^2E^{\prime\prime}$$
(8)

Kraus model

The Payne effect is a representative feature of the behavior of CB filled rubber materials. In other words, with increasing strain amplitude, the storage modulus decreases, and the loss modulus increases at first and then decreases. Kraus was the first to develop a phenomenological constitutive model to interpret the Payne effect of rubber-like materials, which was based on filler network breakage, by supposing a dynamic equilibrium between the breakage and recovery of weak physical bonds under cyclic loading conditions17,18. In the Kraus model, the storage modulus and the loss modulus have the following expressions34:

$$E^{\prime} \left( {\Delta \varepsilon } \right)\, =\,{{E}}_\infty ^{\prime} + \frac{{{E}_0^{\prime} - E_\infty ^{\prime} }}{{1 + \left( {\Delta \varepsilon /\Delta \varepsilon _{{{\mathrm{c}}}}} \right)^{2m}}} = {{E}}_0^{\prime} - \Delta E^{\prime} + \frac{{\Delta {E}^{\prime} }}{{1 + \left( {\Delta \varepsilon /\Delta \varepsilon _{{{\mathrm{c}}}}} \right)^{2m}}}$$
(9)
$$E^{\prime\prime} \left( {\Delta \varepsilon } \right) = E_\infty ^{\prime\prime} + \frac{{2\left( {E_{{{\mathrm{m}}}}^{\prime\prime} - E_\infty ^{\prime\prime} } \right)\left( {\Delta \varepsilon /\Delta \varepsilon _c} \right)^m}}{{1 + \left( {\Delta \varepsilon /\Delta \varepsilon _c} \right)^{2m}}}$$
(10)

where \(\Delta \varepsilon _{{{\mathrm{c}}}}\) is a characteristic value of the strain amplitude at which the loss modulus reaches the maximum value \(E_{{{\mathrm{m}}}}^{\prime\prime}\); \(E^{\prime}_0\) is the storage modulus when the dynamic strain amplitude is <0.01%; \(E^{\prime}_\infty\) and \(E^{\prime\prime}_\infty\) are the asymptotic plateau values of the storage modulus and loss modulus at large strain amplitudes, respectively;\(E^{\prime\prime}_\infty\)usually tends to be 0 for rubber-like materials29; \(\Delta E^{\prime}\left( { \!= \!E^{\prime}_0 - E^{\prime}_\infty } \right)\)is the excess storage modulus; and m is a nonnegative phenomenological exponent, which gives the strain sensitivity of the mechanism of filler-filler contact breakage and defines the shape of the storage modulus and loss modulus curves29,34.

Evaluation of thermo-oxidative aging dependent Payne effect

Figure 2 shows the Payne effect of thermo-oxidative aging samples. In the test dynamic strain range, the storage modulus and loss modulus are shown as a function of the applied dynamic strain amplitude and thermo-oxidative aging time. The storage modulus decreases gradually with increasing strain amplitude and there is a typical loss peek for the loss modulus. It can be seen that in all cases both the storage modulus and loss moduli increase with increasing aging time, which is mainly due to the increase of crosslink density of the material during the aging process22. Besides, it should be noticed that prolonged heating above 70 °C is apt to cause post-vulcanization, which generates more crosslinks23. According to the Kraus model, the material parameters in Eqs. (9) and (10) can be derived by fitting the experimental data. In the process of fitting, it should be noted that the parameter m is a constant value of 0.49. It has been reported that the exponent m is independent of frequency and temperature29, which verifies the accuracy of the fitting results.

Fig. 2: Dynamic mechanical modulus vs. strain amplitude.
figure 2

Scatters are the experemental resutls for various aging times and temperatures, and solid lines are the modelling results. a, b The storage modulus and the loss modulus respectively for aging temperature 80 °C, c, d the storage modulus and the loss modulus respectively for aging temperature 100 °C, e, f the storage modulus and the loss modulus respectively for aging temperature 120 °C.

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The Payne effect can be characterized by the difference (\(\Delta E^{\prime} \,=\, E^{\prime}_0 - E^{\prime}_\infty\)) between the maximum value \(E^{\prime}_0\) and minimum value \(E^{\prime}_\infty\) of the storage modulus in the dynamic strain amplitude range, as shown in Fig. 3. It is noted that for all aging temperatures studied, the Payne effect maintains the same trend, which means that the difference between the maximum value and the minimum value at the aging temperatures measured practically increases. Moreover, the Payne effect for aging temperature of 120 °C is more obvious when compared with those for aging temperatures of 80 and 100 °C.

Fig. 3: Changes of Kraus model parameters.
figure 3

a The tendency of the parameter \(E^{\prime}_{0}\) with the aging time for various aging temperatures, b the tendency of the parameter \(E^{\prime}_{\infty}\) with the aging time for various aging temperatures and c the tendency of the parameter \(\Delta E^{\prime}_{0}\) with the aging time for various aging temperatures.

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\(\Delta \varepsilon _{{{\mathrm{c}}}}\) is a characteristic value of the strain amplitude at which the loss modulus reaches its maximum value \(E^{\prime\prime}_m\). Figure 2 shows that \(\Delta \varepsilon _{{{\mathrm{c}}}}\) is a constant value of 0.9%. According to the Kraus model, the material parameter \(E^{\prime\prime}_m\) is shown in Fig. 4. For all aging temperatures, when the aging time reaches 4 days, \(E^{\prime\prime}_m\) increases dramatically. This indicates that an aging time of 4 days can be regarded as the knee point for the studied material, at which the change rate with respect to aging time of the parameters in loss modulus dramatically changes. In addition, it is obvious that there are nearly two linear phases in the tested aging time range for each aging temperature, and the linear fitting results of \(E_m^{\prime\prime}\) are shown in Fig. 4. Therefore, the loss modulus of the tested CB filled rubber can be quantitatively expressed as a function of dynamic strain amplitude and aging time by the following equation:

$$E^{\prime\prime} \left( {\Delta \varepsilon } \right) = \frac{{2E_m^{\prime\prime} \left( {\Delta \varepsilon /0.009} \right)^{0.49}}}{{1 + \left( {\Delta \varepsilon /0.009} \right)^{0.98}}}$$
(11)

where \(E_m^{\prime\prime}\) is a function of aging time, and the expressions of \(E_m^{\prime\prime}\) are shown in Fig. 4. Below, the hysteresis loss on the basis of loss modulus has been discussed by substituting Eq. (11) into Eq. (8).

Fig. 4: Variation of parameter \(E^{\prime\prime}_{{{\mathrm{m}}}}\) with aging time.
figure 4

Scatters are parameter \(E^{\prime\prime}_{{{\mathrm{m}}}}\), and solid lines are linear fit results. a The results for aging temperature 80 ℃, b the results for aging temperature 100 ℃, c the results for aging temperature 120 ℃.

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Prediction of hysteresis loss

Under cycle loading in the process of the dynamic amplitude sweep test, the CB filled natural rubber exhibits hysteresis loss properties because of the out-of-phase stress and strain. The hysteresis loops obtained from the dynamic amplitude sweep test are presented in Fig. 5. Since there are many hysteresis loops and there is no need to show all loops, so the following hysteresis loops are chosen as examples under the conditions of aging times of 2 days and 6 days, aging temperature of 120 °C, and various dynamic strain amplitudes, i.e., 0.5%, 0.7%, 0.9%, 1%, 2%, 3%, 4% and 5%. In addition, the hysteresis losses of other aging and loading conditions are exhibited in Fig. 6. The results show that the slope of the secant to the hysteresis loop decreases gradually with increasing dynamic strain amplitude, which represents the characteristic of the dynamic stiffness of the material. The slope change trend of the hysteresis loop is consistent with the dynamic strain amplitude-dependent storage modulus of Fig. 2, which indicates that the storage modulus decreases with increasing dynamic strain amplitude.

Fig. 5: Steady-state hysteresis loops.
figure 5

The hysteresis loops of the material aged at 120 ℃ for different periods of time: a 2 days and b 6 days. The curves are obtained under various dynamic strain amplitudes, i.e. 0.5%, 0.7%, 0.9%, 1%, 2%, 3%, 4% and 5%.

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Fig. 6: Hysteresis loss as a function of aging time.
figure 6

The symbols represent the hysteresis loss under various dynamic strain amplitudes, i.e. 0.5%, 0.7%, 0.9%, 1%, 2%, 3%, 4% and 5%. The hysteresis loss increases with the aging time and dynamic strain amplitude for various aging temperatures: a 80 ℃，b 100 ℃ and c 120 ℃.

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The hysteresis loss plays an important role in the tearing energy and fatigue crack growth rate of the rubber-like materials35. To quantify the energy dissipation, the integrated area of the hysteresis loop was calculated, as shown in Fig. 6. The results depict that the hysteresis loss increases with the aging time and dynamic strain amplitude for each aging temperature. Generally, the hysteresis is caused by friction between the rubber matrix and filler particles36. In addition, with increasing of aging time, more ruptured chains and low-molecular-weight products are generated37, which results in obvious hysteresis responses. It can be seen that the hysteresis loss of the specimen aged at 120 °C is more remarkable, which may be related to stronger internal friction and impact between CB fillers and the molecular chains.

It is apparent that the hysteresis loss curves at various dynamic strain amplitudes are parallel to each other. It is well known that the experimental curves of rubber-like materials can usually be shifted horizontally or vertically to accelerate the prediction of the mechanical properties. On the basis of this method, a master curve at a reference dynamic strain amplitude of 1% has been constructed by vertically shifting the curves at other strain amplitudes, and the results are shown in Fig. 7. The corresponding vertical shift factors of the hysteresis loss are shown in Fig. 8, and the results reflect that the vertical shift factors are proportional to the dynamic strain amplitudes. More interestingly, for the same strain amplitude, the vertical shift factors at the different aging temperatures are identical, which indicates that the vertical shift factors are irrelevant to the aging temperature. Thus, if the vertical shift factors can be determined, the hysteresis loss versus aging time of the material at arbitrary dynamic strain amplitude can be obtained as the following equation:

$$D\left( {t,\Delta \varepsilon } \right) = \phi D\left( {t,\Delta \varepsilon _0} \right)$$
(12)

where D is the hysteresis loss, t is the aging time, \(\Delta \varepsilon\) is the dynamic strain amplitude, \(\Delta \varepsilon _0\) is the reference dynamic strain amplitude, and \(\phi\) is the shift factor.

Fig. 7: Master curve of hysteresis loss.
figure 7

The master curve at a reference dynamic strain amplitude of 1% has been constructed by vertically shifting the curves at other strain amplitudes for various aging temperatures: a 80 ℃, b 100 ℃ and c 120 ℃.

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Fig. 8: Vertical shift factors versus dynamic strain amplitude.
figure 8

The vertical shift factors are proportional to the dynamic strain amplitudes, and for the same strain amplitude, the vertical shift factors for different aging temperatures are identical.

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As mentioned above, the hysteresis loss for all cases indicated in Fig. 6 can be predicted by taking Eq. (11) into Eq. (8), which shows that the hysteresis loss can be constructed as a function of aging time and dynamic strain amplitude. It should be noted that \(E_m^{\prime\prime}\) is a function of aging time, and the corresponding expressions of different aging temperatures are shown in Fig. 4. The theoretical prediction results are shown in Fig. 9 along with the test results. It is obvious that the model prediction results are in good agreement with the experiments. It means that, once the Payne effect is known, the hysteresis loss for a given applied strain amplitude at arbitrary aging conditions can be predicted.

Fig. 9: Hysteresis loss prediction results vs. experiments.
figure 9

Scatters are the experimental results, and solid lines are the model prediction results. a, b The results for aging temperature 80 ℃, c, d the results for aging temperature 100 ℃, e, f the results for aging temperature 120 ℃.

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To summarize, the effects of thermo-oxidative aging on the Payne effect and hysteresis loss of CB filled natural rubber vulcanizates were investigated. In the dynamic strain amplitude sweep tests, it can be observed that both the storage modulus and the loss modulus increase with increasing aging time and aging temperature. The Payne effect becomes increasingly obvious with increasing aging time for higher aging temperatures. The hysteresis loss increases with the aging time and dynamic strain amplitude for the aging temperatures. It is apparent that the hysteresis loss curves at various dynamic strain amplitudes are parallel to each other, and a master curve can be constructed at a reference dynamic strain amplitude by vertically shifting curves for other strain amplitudes. The corresponding vertical shift factors of the hysteresis loss are proportional to the dynamic strain amplitudes. Based on this relationship, an accelerated method to predict the hysteresis loss versus aging time of the material at arbitrary dynamic strain amplitude has been proposed. The Kraus model is used to describe the Payne effect and a viscoelastic model consisting of dynamic strain amplitude and loss modulus is used to calculate the energy dissipation. The model predictions are in good agreement with the experimental results.

Methods

Materials

The material used for mechanical testing in this work is CB filled natural rubber vulcanizate with a Shore-A hardness of 69, which is provided by Zhuzhou Times New Material Technology Co., Ltd. China. The main formulation is as follows: 100 phr natural rubber (Thailand RRS3), 56 phr carbon black (N330), 2.2 phr sulfur, 2 phr antioxidant, 5 phr zinc oxide, 0.8 phr vulcanization accelerator, and 2 phr stearic acid.

Thermal-oxidative aging

In the scope of this research work, thermo-oxidative aged vulcanizates were subjected to dynamic mechanical excitations. Thermo-oxidative aging of vulcanizate strips was carried out in a temperature-controlled air-aging oven. To keep the specimen’s surface temperature isothermal, the specimens were hung in the aging oven, as shown in Fig. 10. The previous work by Li8 demonstrated that the change of mechanical properties, such as elastic modulus, tensile strength, tear strength, etc., of the aged CB filled natural rubber vulcanizates depend on the aging temperature, and the higher the aging temperature, the more pronounced change in mechanical properties. To investigate the influences of aging temperature and aging time on the Payne effect and the hysteresis loss of the CB filled rubber vulcanizates, the selected aging temperatures for the specimens in this work were 80, 100 and 120 °C, and the aging time ranged from 1 day to 6 days.

Fig. 10: The specimens in the aging oven.
figure 10

Vulcanizate strips are hung dispersedly in the temperature-controlled air-aging oven to ensure uniformly aging.

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Dynamic mechanical analysis (DMA)

In this paper, the specimens with dimensions of 25 × 5 × 2 mm3 for DMA tests were cut from the thermo-oxidative aged vulcanizate strips, and all tests were carried out with a Gabo Eplexor 500 N test machine working in the tensile mode. First, the specimens were preconditioned with a cyclic strain-controlled process to exclude the Mullins effect. The Mullins effect corresponds to a softening phenomenon during the first few cycles. The first 6 cycles were chosen to exclude the Mullins effect, and the dynamic strain amplitude was 15% during these cycles, which was not less than the maximum dynamic strain amplitude in the subsequent Payne effect investigation. Afterward, the specimens were sinusoidally stretched at a constant temperature of 23 °C and a fixed frequency of 10 Hz. The prestrain was 10%, and the dynamic strain amplitudes ranged from 0.1% to 5% in steps of 0.1%. The storage modulus, loss modulus and hysteresis loop versus dynamic strain amplitude under various thermo-oxidative aging times were recorded.