Introduction

Tyres are one of the consumable parts of cars that are very important in terms of safety. Considering the importance of vehicles in today’s society, the importance of tyres becomes even more apparent. Therefore, the role of new technologies in the tyre industry is becoming increasingly important. By producing higher quality tyres and innovating the curing process, higher productivity and profit can be achieved. In the production process, different parts of the tyre are produced and assembled. In the next step, the green tyre is placed in the curing press and the accelerated sulphur curing system is used to create crosslinking and produce the final tyre.

In the curing press step, three main factors determine the quality of the final tyre: the amount of pressure, pressing time and temperature. The pressure effect can be checked for both the amount of pressure and the duration of applied pressure. These factors can affect the structure of the cured rubber. The swelling test was used to study the cured compound structure.

The swelling test and mechanical properties of rubber compounds were studied in some researches [1,2,3,4]. It seems that the effects of pressing time on the structure of tyre tread compound have not still been studied. The effect of pressure level on the vulcanisation step was studied by Wilkinson and Gehman [5]. They vulcanised natural and styrene–butadiene rubbers with common sulphur systems by applying high pressures on the sample (from atmospheric pressure up to 670 MPa). They found that natural rubber (NR) and styrene–butadiene rubber behaved differently. The results showed that the degree of crosslinking in the prepared styrene–butadiene rubbers was higher than the natural rubber.

Earlier studies [6] reported that the effect of pressure on traditional vulcanisation depends on the type of polymer. In the vulcanisation of styrene–butadiene, the modulus of the sample increased as the pressure increased. Also, the modulus of NRs increased slightly as the pressure increased.

In another research, it has been observed that high pressure vulcanised products had lower tensile and hysteresis even when samples with the same crosslink density were compared. This suggests that the crosslinks formed under high pressure have characteristics, which are different from those of traditional vulcanisates [6, 7]. Also, as mentioned, most of the research have considered new rubber compounds. However, an important point to consider is the change in the rubber curing mechanism, without changing the rubber compound used.

The purpose of this study was to investigate the effect of pressing time on the properties of the cured tread compound. Therefore, rubber samples were produced in seven different conditions and then the swelling test was performed to determine the structure of the specimen and the crosslinking. Mechanical tests and optimisation of curing time were also performed. Based on our little knowledge, it seems that the present research is the first study to determine the effects of pressing time on the tyre tread compound.

Materials and methods

Samples preparation

The tread compound, which had been composed in the production line, was randomly taken. Based on ISO 11345, the dispersion grading (DG) was processed by a carbon black dispersion tester. A test sample image was captured and compared to the reference scale digitally, and then, definitive DG value was calculated automatically by the tester. A rating of 10 indicates a state of dispersion resulting in near optimum physical properties while a rating of 1 would indicate structural flaws causing considerably inferior physical properties (1—Worst, 10—Best). For the selected compound, the degree of carbon black dispersion was 9 which indicates the good quality of its mixture. Before the pressing step, the mould was pre-heated. Then, the prepared compounds were pressed for the determined times, which are listed in Table 1. For all samples, the curing process was continued up to 45 min. During the curing process, the pressing temperature was 145 °C and the applied pressure was 110 bar. The samples listed in Table 1 have been chosen according to the used design of experiment.

Table 1 The run number according to different pressing time obtained from design of experiments by Design Expert software
Full size table

Swelling test

The swelling test is a practical and simple test to determine the crosslinking of the matrix. According to ASTM D471-06, this test is conducted for polymer specimens in various solvents such as toluene, benzene, pentane, hexane, heptane, etc., under a temperature of 25, 35, 45 or 55 °C.

In this study, the standard swelling test was carried out in toluene solvent under the temperature of 25, 35, 45 or 55 °C. For this purpose, the cured polymer samples in tensile test mould (having dimensions of 150 by 150 by 2 mm) were cut in the shape of a rectangular (25 by 50 by 2.0 ± 0.1 mm) and their initial weight was recorded. By placing each of the specimens in 50 ml of toluene solvent, they became swelled. Swollen samples were taken out of the solvent at different time intervals. Then, the solvent on the sample wiped up using a tissue. The weighing was performed on an electronic balance with an accuracy of 0.001 g. Samples then quickly transferred to the solvent. According to [8], the error associated with the evaporation of solvents can be neglected because weighing time was accomplished at less than 20 s.

It was demonstrated that the equilibrium state was reached at 24 h after the beginning of the test [9]. However, the weighing of the samples was performed every 24 h and continued up to 72 h. At subsequent times, there was almost no change. In the equilibrium state, the weight of the sample is called the equilibrium weight of swelling.

Crosslinking density

According to Flory and Rehner theory [10], the crosslinking density was calculated using Eq. (1):

$$\nu =\rho /2{M}_{c}$$
(1)

where \(\nu\) is the crosslinking density; ρ is the density of polymer samples, and Mc is the average molar mass between crosslinks of the polymer. The Mc is calculated using Eq. (2) [11]:

$${M}_{c}=\left(-{\rho }_{p}.{V}_{s}.{V}_{rf}^{1/3}\right)/\left(\mathrm{ln}\left(-{V}_{rf}\right)+{V}_{rf}+\upchi {V}_{rf}^{2}\right)$$
(2)

where \({\rho }_{p}\), \({V}_{rf}\),\({V}_{s}\) and χ are the density of the polymer, the volume fraction of swollen polymer, the molar volume of the solvent and the interaction parameter, respectively. The interaction parameter χ is calculated using Eq. (3) [11]:

$$\upchi ={\upchi }_{\beta }+({V}_{s}/RT){({\updelta }_{s}-{\updelta }_{p})}^{2}$$
(3)

where \({\delta }_{s}\) and \({\delta }_{p}\) are solubility parameters of solvents and polymer, respectively. Also, \({\upchi }_{\beta }\), R and T are the lattices constant, the gas constant and the absolute temperature, respectively.

The volume fraction of polymer (\({V}_{rf}\)) is calculated using Eq. (4) [12]:

$${V}_{rf}=\left[{m}_{\mathrm{eq}}-F{m}_{\mathrm{in}}/{\rho }_{p}\right]/\left[\left({m}_{eq}-F{m}_{\mathrm{in}}/{\rho }_{p}\right)+\left({A}_{s}/{\rho }_{s}\right)\right]$$
(4)

where meq is the equilibrium weight of the swollen specimens. min is the initial weight of the samples. F is the volume fraction of filler in the polymer. Also, \({\rho }_{s}\) and \({A}_{s}\) are the solvent density and the amount of solvent absorbed by the polymer sample, respectively.

Determination of swelling mechanism

The mechanism of diffusion was investigated using Eq. (5) [13, 14]:

$$\mathrm{log}\,{Q}_{t}/{Q}_{\infty }=\mathrm{log}\,k+n\,\mathrm{log}\,t$$
(5)

where Qt and Q∞ are the mole per cent uptake of solvent at time t and at infinity (equilibrium state), respectively; k is a constant which depends on the structural features of the polymer. The value of n determines the diffusion mechanism. For the Fickian mode, the value of n is 0.5. The Fickian mode occurs when the rate of diffusion of penetrated molecules is much less than the relaxation rate of the polymer chains. For non-Fickian transport, where the n value is 1, the diffusion is rapid in comparison with the simultaneous relaxation process [8, 15, 16].

Diffusion coefficient

The diffusion coefficient can be determined using Eq. (6) [17]:

$${Q}_{t}/{Q}_{\infty }=1-8/{\pi }^{2}\sum_{n=0}^{n= \infty }\frac{1}{({2n+1)}^{2}}\times \mathrm{exp}\left[-D({2n+1)}^{2}{\pi }^{2}t/{h}^{2}\right]$$
(6)

where t is the time and h is the initial thickness of the polymer sheet. For the short time limiting, Eq. (7) can be used [17]:

$$D= \pi ({h\theta /{4Q}_{\infty })}^{2}$$
(7)

where \(\theta\) is the slope of the linear portion of the sorption curve Qt versus t1/2. Since styrene–butadiene rubber swelling is significantly high, correction of diffusion coefficient with the solvent condition is necessary. For this purpose, from the D values, the intrinsic coefficient values D* were calculated using Eq. (8) [18]:

$${D}^{*}=D/{V}_{r}^{7/3}$$
(8)

Permeability coefficient

Permeability coefficient (P) is calculated using an empirical relation (Eq. 9) [8].

$$P={D}^{*} S$$
(9)

where S is the sorption coefficient which defined a ratio of the sorbed solvent mass to the initial polymer weight.

Thermodynamic analysis

The thermodynamic approach is of great importance for understanding the rubber–filler interaction in the nanocomposite. It is well known that a crosslinked elastomer cannot be dissolved but can be swelled in several solvents. This swelling depends on the elastomer crosslinking density and solvent used; a highly crosslinked material will show a limited swelling. Nevertheless, if the material presents a low crosslinking density, a higher swelling degree will be expected. This expansion of the rubber in the presence of a solvent will significantly modify the conformational entropy and the elastic Gibbs free energy (G). The major hypothesis of Flory and Rehner is that the free energy change of swelling an elastomer consists of two contributions, which they assumed to be separable and additive. These are the free energy of mixing, \(\Delta {\mathrm{G}}_{\mathrm{mix}}\), and the free energy of elastic deformation, \(\Delta {G}_{\mathrm{elas}}\). Thus, the free energy change accompanying the absorption of a diluent was assumed to be given by Eq. (10) [19]:

$$\Delta {G}_{\mathrm{tot}}= \Delta {G}_{\mathrm{mix}}+ \Delta {G}_{\mathrm{elas}}$$
(10)

Also the elastic Gibbs free energy can be determined from the Flory–Huggins Eq. (11) [20]:

$$\Delta G=RT[\mathrm{ln}\left(1-{V}_{rf}\right)+{V}_{rf}+\upchi {{V}_{rf}}^{2}]$$
(11)

The \(\Delta G\) defined in Eq. (11) can be related to the thermodynamic sorption constant, which can be calculated from Eq. (12).

$$K_{S} = { }\frac{{{\text{ Solvent}}\,{\text{ mass }}\,{\text{absorbed}}\,{\text{ by }}\,{\text{the}}\,{\text{ sample}}}}{{{\text{Solvent}}\,{\text{ molar }}\,mass\,{ } \times \,{\text{Polymer}}\,{\text{mass}}}}$$
(12)

The enthalpy of sorption \({\Delta H}_{S}^{0}\) can be computed using Van’t Hoff relation [13]

$$\frac{{d\log K_{S} }}{{d{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 T}}\right.\kern-0pt} \!\lower0.7ex\hbox{$T$}}}} = \frac{{\Delta H_{S}^{0} }}{{2.303{ }R}}$$
(13)

The enthalpy of the sorption can be obtained by plotting the \(\mathrm{log}{K}_{S}\) versus \(\frac{1}{T}\).

George et al. observed that the equilibrium sorption and diffusion of styrene–butadiene rubber increase with increase in temperature. It is due to the increase in void regardless of the nature of the crosslinks [13].

The variation of diffusivity and permeability coefficient with temperature is described by the following Arrhenius relationship:

$$D = D_{0} \left( {e^{{ - \frac{{E_{D} }}{RT}}} } \right) ,\log D = \log D_{0} - \frac{{E_{D} }}{2.303\, RT}$$
(14)
$$P = P_{0} \left( {e^{{ - \frac{{E_{P} }}{RT}}} } \right) ,\log P = \log P_{0} - \frac{{E_{P} }}{2.303\, RT}$$
(15)

where \({E}_{D}\) and \({E}_{P}\) are the activation energies of diffusion and permeation, respectively, and \({D}_{0}\) and \({P}_{0}\) are the pre-exponential factors [13]. From the activation energy of a diffusion in a given system, information of the network (in which the diffusion takes place) can be obtained [16]. The sign of the enthalpy change (positive or negative) is a measure of the absorption mechanism that can be Henry or Langmuir type, respectively [21].

Tensile test

The tensile test was performed according to ASTM-D 412 standards. This test is the most common type of tests performed on rubber parts. This test was performed by a dynamometer (Hounsfield-H10ks-England). Tensile strength, ultimate elongation and 300% modulus (stress at 300% of initial length) are the results of this test.

Tear strength test

The tear strength was performed according to ASTM-D 624 standards. In this test, the strength of a rubber specimen against rupture progression is measured. Like the tensile test, this test was performed by a dynamometer. Also, in this test, the tear strength (in Newtons per millimetre) is the result of calculating the division of the tear force by the thickness of the sample that has been used.

Hardness test

On the other hand, the hardness test was determined according to ASTM-D 2240 standards. In this test, a penetrating object with a specific geometric shape was pushed into a rubber sample under a certain condition. In other words, the amount of load required to press a needle-shaped needle into a rubber specimen determines the hardness of the rubber. This test was performed on Shore A criterion and by the hardness tester of (ZWICK-3100-Germany).

Resilience test

ASTM-D 1054 standard was used to determine the resilience of samples. When measuring the resilience, the rate of return of energy is actually measured during a short hit deformation. In this test, a pendulum-shaped hammer was dropped from a certain height on the sample, and the height that this hammer rises after hitting the sample was measured. This test was performed by the WALLACE-Dunlop Tripsometer R2-England. The hammer was first set at a 45-degree angle, and after hitting the specimen, the angle at which the hammer went up there was recorded, and resilience percentage calculated by Eq. (16).

$$\mathrm{resilience\, percentage} =\frac{1-\mathrm{cos}(\theta )}{1-\mathrm{cos}(45)}\times 100$$
(16)

Abrasion test

Abrasion test was performed by the abrasion metre of (ZWICK-6102H04-Germany) and according to ASTM-D5963 standards. For each sample, the initial mass and the final mass were measured and the lost volume was calculated according to Eq. (17). The density of the desired compound was also measured by a densitometer (Brabender-843606001-Germany). When measuring the lost volume, the smaller number indicates a greater abrasion resistance.

$${\text{Abrasion}} = \frac{{{\text{ Initial }}\,{\text{mass}}\, - { }\,{\text{Final}}\,{\text{ mass}}}}{{{\text{Density}}}}$$
(17)

Design of experiment and statistical evaluation

The design of experiments was performed using the response surface method (RSM) and the obtained results were analysed using Design Expert® (version 7.0.0, Stat-Ease, Inc, USA). Pressing time was the only variable in one-factor design.

In one-factor RSM design, owing to a lack of fit and pure error determination for a cubic model, seven levels of a single factor (0, 7.5, 15, 22.5, 30, 37.5, 45 in this this study) plus replicates at first, last and centre point are needed.

Results and discussion

Swelling and its mechanism

Figure 1 shows the mole per cent uptake of solvent versus time for different samples. The trend of all curves is similar to each other, and the rate of swelling is high in the initial stages. Initially, Qt rapidly increases as time increases. After a while, the intensity of absorption decreases and eventually swelling stops. In other words, the rate of absorption and desorption become the same. For free pressure samples, the absorption rate of the solvent is initially lower but eventually, more solvent is absorbed and the equilibrium state is established after more time passes.

Fig. 1
figure 1

The sorption curves showing the mole per cent toluene uptake of different samples at 25 °C

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According to Eq. (3), the changes in the time trend in the initial part are expected to be linear. This fact for free pressure cured sample is shown in Fig. 2. As stated before, the diffusion coefficient can be obtained by using the slope of the linear part of sorption curve. In addition, Fig. 2 shows that the deviation of obtained results from the straight line is negligible, so the diffusion coefficient is well calculated. Using this method, the diffusion coefficients for all samples are calculated and is shown in Fig. 3.

Fig. 2
figure 2

A linear part of sorption curve for free pressure cured sample at 25 °C

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Fig. 3
figure 3

The intrinsic diffusion coefficient (measured by swelling test) as a function of pressing time at different temperatures

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According to Eq. (5), by plotting \(\mathrm{log}\frac{{Q}_{t}}{{Q}_{\infty }}\) versus \(\mathrm{log}t\) (as shown in Fig. 4 for free pressure cured sample), the values of n and k were obtained which has been shown in Table 2. According to the obtained values of n which tended to 0.6, there is not a major deviation from the Fick’s law. Therefore, this proves that the diffusion mechanism of toluene is Fickian, and the assumption of Fick’s law for all calculations can be correct.

Fig. 4
figure 4

The plot of \(\log \left( {\frac{{Q_{t} }}{{Q_{\infty } }}} \right)\) versus log t for free pressure cured sample at 25 °C

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Table 2 The calculated values of n, k and R2 at 25 °C for different samples
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In all graphs, the values of R2 were very close to 1, which indicates the validity of the proposed equation. Although the pressing time had not any effect on diffusion type, the values of n and k related to free pressure samples are less than other samples.

Crosslinking density

The swelling test was repeated three times for each cured sample and the crosslinking density was calculated. The mean results were used as the final result for each sample. Figure 5 shows the diagram of the crosslinking density versus the pressing time. The samples which were made in the zero-pressure condition have the lowest amounts of crosslinking density. A low-dense crosslinking structure in a polymeric network prepares enough space for more diffusion. In addition, an increase in crosslinking, which is observed in other samples causes a decrease in their diffusion property. It also can be found in Fig. 5 that the crosslinking increases significantly as the pressing time value increases up to 22.5 min. After that, up to 45 min, it is observed that crosslinking density is almost constant and has slight variation.

Fig. 5
figure 5

The crosslinking density (measured by swelling test) as a function of pressing time

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Statistical analysis for crosslinking density was done using Design Expert software and the software suggested a second-order model (P value < 0.05). Equation (18) is the proposed model which can be used to obtain the crosslinking density of similar samples for each value of pressing time at 25 °C.

$${\text{ Crosslinking}}\, {\text{density}} \,=\, 3.38119 \times 10^{ - 4} + 7.07646 \times 10^{ - 7} \left( {{\text{time}}} \right)^{1} - 1.04821 \times 10^{ - 8} \left( {{\text{time}}} \right)^{2}$$
(18)

Intrinsic diffusion coefficient

The diffusion coefficient was calculated using the first section of the curves and replicated three times for each cured sample. The average data were used as the final result for each sample. Figure 3 shows the diagram of the intrinsic diffusion coefficient versus the pressing time. As seen, the increase in temperature increased the slope of the initial part of the sorption curve, and then, the rubber diffusion rate increased. Also, the vulcanised samples in the free pressure condition have the highest D*. It seems this result was obtained because the elastic property of the chains creates empty spaces between the chains, which lead to a low-dense crosslinking network. However, by pressing the samples during the curing period, the density of crosslinking increased. The density and stability in the structure of the three-dimensional rubber network increase as the density of crosslinking increases. Moreover, in a polymeric dense structure, the internal elastic stresses will not allow to create spaces for solvent penetration. With the increase in the pressing time up to 20 min, the D* decreased. As can be seen, the minimum D* was obtained at 20 min. After that, up to 45 min, there was no main change in this value. Due to this fact, after about 20 min, the curing process can continue in atmospheric pressure. The effect of pressing time on the filler at the curing stage can also be noted. In the samples with less pressing time, the carbon black aggregates did not break down, and the diffusivity increased due to the voids. On the other hand, the accumulation of carbon black in the rubber substrate reduces the effective contact surface area of ​​the polymer chain. Therefore, the number of effective particles that can prevent the penetration of molecules is reduced and this increases the diffusion coefficient, especially at high temperatures.

According to Design Expert software, a third-order model was suggested to fit the obtained results (P value < 0.0001). Equation (19) presents the mentioned model, which can be used to obtain the intrinsic diffusion coefficient of similar samples for each value of pressing time at 25 °C.

$$D^{*} \,= \,1.24237 \times 10^{ - 4} - 5.19829 \times 10^{ - 6} \left( {{\text{time}}} \right)^{1} + 2.13505 \times 10^{ - 7} \left( {{\text{time}}} \right)^{2} - 2.59015 \times 10^{ - 9} \left( {{\text{time}}} \right)^{3}$$
(19)

Permeability coefficient

Figure 6 presents the dependence of permeability on the intrinsic diffusion coefficient. It can be observed from Fig. 6 that the relationship between P and D* is linear. It found out that S is the same for all samples and independent of pressing time. The statistical analysis for the permeability coefficient showed that the results were similar to the intrinsic diffusion coefficient, which proved S is constant.

Fig. 6
figure 6

The dependence of P on D* for tread compound

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Results of thermodynamic analysis

By using Eqs. 14 and 15, the activation energy of the diffusion and permeability process was determined, and from the slope of \(\mathrm{log}D\) and \(\mathrm{log}P\) vs. 1/T, the values of \({E}_{D}\) and \({E}_{P}\) were calculated, respectively. Figures 7 and 8 show the plot of \(\mathrm{log}D\) and \(\mathrm{log}P\) versus 1/T for seven samples at different temperatures, respectively. As shown, the graphs are linear and follow the Arrhenius relation. Also, the negative slope of these graphs indicates positive activation energy for the process, which is an expected fact. A similar graph of the permeability coefficient also shows a similar trend to the diffusion coefficient, and again, it is observed that as the temperature increases, the diffusion coefficient increases.

Fig. 7
figure 7

Plots of \(\mathrm{log}D\) versus \(\frac{1}{ T}\) by using Arrhenius relation at 7 different pressing times

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Fig. 8
figure 8

Plots of \(\mathrm{log}p\) versus \(\frac{1}{ T}\) at 7 different pressing times

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To further investigation of the temperature effect on the mechanism of rubber diffusion, the enthalpy changes of the specimens were evaluated using the Van't Hoff relation. The adsorption constant, which is a thermodynamic quantity, was calculated, and then \({\Delta H}_{s}^{0}\) was calculated from the slope of line \(\mathrm{log}{K}_{S}\) versus 1/T. As shown in Fig. 9, the \(\mathrm{log}{K}_{S}\) with 1/T was increased for all samples. In other words, as the temperature of the swelling test increases, the adsorption constant decreases. Then, the mobility of the polymer chain increases, and thus, the desorption process becomes dominant. The slope of the lines is positive. Therefore, according to the Langmuir mechanism, the polymer contains sites where the solvent molecules fill them with heat release and changes of enthalpy are negative.

Fig. 9
figure 9

The plots of \(\mathrm{log}{K}_{S}\) versus \(\frac{1}{ T}\) by using Van’t Hoff relation at 7 different pressing times

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The thermodynamic effects of the elastomer chains swelling were also investigated. The change in Gibbs free energy was calculated from the Flory–Huggins relation. The free energy of mixing is negative because the solvent entropy increases. However, as portions of crosslinks are stretched and elongated during elastic deformation, the probability of random arrangement of the unit decreases. As a result, the entropy of the polymer segment decreases, and the expression \(\Delta {G}_{\mathrm{elas}}\) is positive. Since ΔG is related to elastic behaviour, it increases as the elasticity increases. Also, a rise in the total volume of voids increases the amount of swelling. It causes less Gibbs free energy. Small voids can act as easily permeable parts of the polymer network, thereby increasing sample swelling [13].

As can be seen in Fig. 10, the trend of obtained ΔG is similar to diffusion and permeability, and its positivity indicates a small swelling equilibrium constant. Swelling decreases with increase in pressing time, and as a result, the amount of ΔG increases. It is stemmed from the smaller voids and less permeability.

Fig. 10
figure 10

Changes of Gibbs free energy as a function of pressing time at 25 °C

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Tensile test results

As shown in Fig. 11, the cured sample without pressure has the lowest tensile strength and with increase in the duration of pressure up to 22.5 min, the tensile strength increases. Then, up to the point of 45 min, a decrease was experienced, but the changes were minor, and the tensile strength was almost constant. Figure 12 shows that the sample without pressure has the minor elongation. This value increases with increase in the duration of pressure up to 22.5 min. After that, it is almost constant up to 45 min. As can be seen in Fig. 13, this trend is also experienced for the 300% modulus and with increase in the duration of pressure from 0 to 15 min, the modulus increases. After that, it can be said that the changes are almost insignificant and the trend of modulus changes has been constant.

Fig. 11
figure 11

Tensile strength changes according to the pressing time

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Fig. 12
figure 12

The graph of ultimate elongation (%) based on the pressing time

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Fig. 13
figure 13

The changes of 300% modulus according to the pressing time

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Last section (crosslinking density) also showed that increasing the duration of pressure increases the crosslinking density and decreases intrinsic diffusion coefficient. This means that the tensile strength, elongation and modulus increase with decrease in porosity in the specimens, and the crosslinking density increases. For example, the non-pressurised cured sample with the largest cavities had lower tensile strength.

Statistical analysis was performed in Design Expert software. The proposed software model for tensile strength, which is a third-order model (P value < 0.0001) exists in Eq. 20:

$$\sigma = \left( {14.944} \right) + \left( {0.399} \right)t - \left( {0.016} \right)t^{2} + \left( {1.899 \times 10^{ - 4} } \right)t^{3}$$
(20)

Here, the σ is the tensile strength (MPa) and the t is the time (min). The software also proposed Eq. (21) for ultimate elongation (%), which is a linear model in terms of time (P value < 0.05).

$$\delta =\left(413.317\right)+(0.425)t$$
(21)

Here, the \(\delta\) is the percentage of elongation and the t is the time (min). For the 300% modulus, Eq. (22) is proposed as a third-order model (P value < 0.05),

$$\mathrm{Modulus}\,=\,\left(10.437\right)+\left(0.249\right)t-\left(1.003\times {10}^{-2}\right){t}^{2}+\left(1.118\times {10}^{-4}\right){t}^{3}$$
(22)

in which the modulus is 300% in megapascals and t is the time in min, and with the help of Eq. (22), the modulus of 300% can be obtained for similar samples for any value of pressing time.

Tear strength test result

As can be seen in Fig. 14, when the duration of pressure application is zero, the lowest tear strength is observed and the tear resistance increases with increase in the amount of pressing time to about 15 min. From 15 to 45 min, the changes in tear strength are almost negligible and can be said to have been proven. The results of the tear test are in good agreement with the proposed trend for the crosslinking density. Since there are no initial grooves on the specimen in tensile strength test, the pores in the specimen can be start point of rupture, and consequently, the specimen with more pores has less resistance to yield. However, in the case of tear test, due to the existence of the initial groove, the effect of the specimen strength on the tear test result is greater than the pores. Therefore, the harder specimen is more resistant to tear.

Fig. 14
figure 14

The graph of changes in tear strength based on the pressing time

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Statistical analysis was performed by placing average of the results in Design Expert software. The proposed software model (Eq. 23) was a quadratic function of time (P value < 0.0001),

$$\mathrm{Tear}=\left(21.17\right)+\left(0.496\right)t-\left(8.683\times {10}^{-3}\right){t}^{2}$$
(23)

in which the tear strength is in Newtons per millimetre and t is the time (min).

Hardness test result

According to Fig. 15, it can be seen that the free pressure samples have the lowest hardness, and the hardness increases with increase in pressing time up to 15 min. But, when the duration of pressure is between 15 and 45 min, the hardness is constant and does not change much. As shown, the crosslinking density increased with increase in pressure duration. This trend was observed for hardness, which indicates that as the crosslinking density increases, the hardness also increases.

Fig. 15
figure 15

The graph of measured hardness changes based on the pressing time

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According to the statistical analysis, the software proposed Eq. (24), a second-order model (P value = 0.0005), where the hardness in the Shore A and t is time in minutes.

$$\mathrm{Hardness}=\left(57.244\right)+\left(0.464\right)t-\left(6.449\times {10}^{-3}\right){t}^{2}$$
(24)

Resilience test result

Figure 16 shows that in the pressure-free curing mode, the sample has the highest percentage of resilience and this amount has decreased with increase in the duration of pressing time to 22.5 min. After that, by increasing the duration of pressure time, the resilience is slightly increased compared to the minimum value. But in general, the changes are insignificant and remain constant until the duration of 45 min pressure. According to the results obtained for the intrinsic diffusion, it seems that the percentage of resilience is directly related to the intrinsic diffusion. With increase in pressing time, the intrinsic diffusion decreases due to the reduction of pores, which is also significant for the percentage of resilience. It means that resilience and intrinsic diffusion are directly related and with decrease in the intrinsic diffusion, resilience also decreases slowly.

Fig. 16
figure 16

The changes in the resilience (%) based on the pressing time

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The model proposed by the software is Eq. 25, a third-order model (P value = 0.0006) in which the resilience and t (time) are in percentage and minutes, respectively.

$$\mathrm{Resilience} \%=\left(34.919\right)-\left(1.011\right)t+\left(0.038\right){t}^{2}-\left(4.347\times {10}^{-4}\right){t}^{3}$$
(25)

Abrasion test result

Figure 17 shows that the abrasion resistance of different samples does not change with the pressure time. Statistical analysis of the results of abrasion showed that the proposed software model is a linear model (P value = 0.0107) and is like Eq. (26):

$$\mathrm{Abrasion}=\left(0.097\right)+\left(0.894\times {10}^{-4}\right)t$$
(26)

in which the abrasion (missing volume) is in cubic centimetres and t is the time in minutes. Equation (26) confirms that the duration of pressure application has a negligible effect on abrasion resistance. This finding contradicts the observed changes in crosslink density among different samples. The discrepancy could be attributed to the type of crosslinking and the intrinsic differences between abrasion resistance and other mechanical properties. It is important to consider that abrasion resistance is influenced by the material's ability to withstand and dissipate frictional forces, whereas other mechanical properties are crucial for withstanding mechanical stress. Network crosslinking and interpenetrating polymer networks are known to distribute and dissipate frictional forces more effectively. Conversely, if the crosslinking primarily leads to a linear structure, it may not efficiently distribute and dissipate frictional forces, resulting in a lack of improvement in abrasion resistance. Further investigation and optimisation of the crosslinking process, along with consideration of other relevant factors, may be necessary to achieve the desired improvement in abrasion resistance.

Fig. 17
figure 17

The graph of changes in the amount of abrasion based on the pressing time

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Optimisation

According to the performed analyses, the optimal time of applying pressure has been obtained using Design Expert software. The software determined the optimal point according to the optimal targeting for different variables and results. The determination of the optimal point was based on the calculating the desirability function. Objectives and upper and lower optimisation limits for different variables and characteristics were considered according to Table 3. The selection of goals and intervals for this optimisation was fully customised and aligned with the internal standards of the tyre factory’s quality control department, in which permissible ranges are defined for certain parameters such as hardness and resilience, while other parameters such as tensile strength and abrasion are considered as maximum and minimum values, respectively. It should be noted that in this research, the goal was to find the shortest pressing time, so it has been applied in the software accordingly.

Table 3 The constraints applied to determine the optimal point
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The software determined the optimal point as described in Table 4. The optimal conditions for simultaneous optimisation of all characteristics (desirability) are equal to 71.1 per cent. As a result, according to the optimisation, the time of 13 min and 42 s is the most suitable for applying pressure, and after that, the process of curing the tyre tread compound can go up to 45 min without applying pressure. It is worth noting that this optimisation can be tailored to different goals, resulting in different optimal points.

Table 4 The optimal point determined by the software
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Conclusion

As mentioned, most research has looked at new rubber compounds. However, the point that is less mentioned here is the change in the rubber curing mechanism to improve the properties and reduce the curing time without changing the compound used. In this study, the effect of pressing time on the sulphur curing process of tread compound was investigated in different time periods. The results showed that in comparison with other samples, the vulcanised samples in free pressure condition had the lowest amounts of crosslinking density, tensile strength, 300% modulus, tear strength and hardness.

One of the most important results of this study was to show the dependence of the swelling and mechanical properties of the tyre tread compound on the pressing time. Therefore, it is not necessary to complete the curing step in the mould but according to the optimisation, about 14 min out of 45 min of curing time should be done in the mould and after that, it is possible to complete the curing process outside the mould. This will reduce the cost and energy consumption. Further studies are still required to understand the optimised time of pressing other tyre compounds and finally, according to this research, with more studies and experiments on green tyre curing, reducing the stopping time of tyres in the tyre curing press can be sought.