Using combined Avrami-Ozawa method to evaluate

Road Materials and Pavement Design

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Using combined Avrami-Ozawa method to evaluate low-temperature reversible aging in asphalt binders Yanjun Qiu, Haibo Ding, Ali Rahman & Enhui Yang To cite this article: Yanjun Qiu, Haibo Ding, Ali Rahman & Enhui Yang (2018): Using combined Avrami-Ozawa method to evaluate low-temperature reversible aging in asphalt binders, Road Materials and Pavement Design, DOI: 10.1080/14680629.2018.1479291 To link to this article: https://doi.org/10.1080/14680629.2018.1479291

Published online: 29 May 2018.

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Road Materials and Pavement Design, 2018 https://doi.org/10.1080/14680629.2018.1479291

Using combined Avrami-Ozawa method to evaluate low-temperature reversible aging in asphalt binders Yanjun Qiua,b , Haibo Dinga,b∗ , Ali Rahman

a,b

a School of Civil Engineering, Southwest Jiaotong b Highway Engineering Key Laboratory of Sichuan

and Enhui Yanga,b

University, Chengdu, People’s Republic of China; Province, Southwest Jiaotong University, Chengdu,

People’s Republic of China (Received 6 February 2018; accepted 3 May 2018 )

This paper aims to reasonably evaluate the reversible aging resistance of asphalt binders and comprehend the effects of low-temperature gradually hardening on fundamental properties of asphalt binders. To do so, extended bending beam rheometer (ExBBR) test with prolonged different conditioning times were performed on different kinds of asphalt binders, and viscoelastic mechanics model (Burgers model) was employed for describing the rheological properties. The combined Avrami-Ozawa equation was applied to characterise the non-isothermal crystallization process of asphalt binders which have a significantly different degree of physical hardening. The results showed that stiffness or m-value obtained from extended BBR test with logarithmic conditioning time has high coefficient of determination. Predicted stiffness and m-value from proposed empirical formula can be used to estimate extended BBR low temperature limiting grade (LTPG) that could be applicable for quality control (QC) purposes in the future. Lastly, the combined Avrami-Ozawa method can be successfully used to describe the non-isothermal crystallization process of asphalt binders used in this study. Keywords: reversible aging; physical hardening; crystallization kinetics; asphalt binder; low temperature

Introduction Low-temperature cracking issues of asphalt pavement or other infrastructures are common problem existed in the north cold region. It is well recognised that a number of factors such as asphalt binder and aggregate properties, mixture design, asphalt layer thickness, layer interfacial bonding conditions and construction management can influence the final asphalt pavement low-temperature cracking resistance performance. Among which, however, asphalt binder quality is the most significant factor that has been observed by most pavement engineers (Hesp, Terlouw, & Vonk, 2000). To boost higher profits, acid or base additives were added into asphalt and asphalt refinery company extracted more light component from crude oil which could be a matter of concern for road agencies about the quality of asphalt binder used in asphalt pavement (Kodrat, Sohn, & Hesp, 2007). What could worsen the problem is that more so-called environmentally friendly additives such as reclaimed asphalt pavement (RAP), waste engine oil and coal liquefaction residue were persuaded to be used in high percentage (Bodley, Andriescu, Hesp, & Tam, 2007; Hesp & Shurvell, 2010; Ji, Zhao, & Xu, 2014). All of these practices aggravated the *Corresponding author. Email: [email protected]

© 2018 Informa UK Limited, trading as Taylor & Francis Group

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concern about the cracking resistance performance of asphalt binder. Therefore, the mechanical behaviour of asphalt binder at low temperature has been gained more attention. In order to rank more precisely the low-temperature performance of asphalt material, different protocols such as 4-mm DSR (Sui, Farrar, Harnsberger, Tuminello, & Turner, 2011), fracture mechanicsbased tests (Bueno, Hugener, & Partl, 2015; Hoare & Hesp, 2000; Niu, Roque, & Lopp, 2014), strain tolerance test (Paliukaite, Verigin, & Hesp, 2015), asphalt binder cracking device (ABCD) test (Kim, Wysong, & Kovach, 2006), Glover-Rowe (G-R) parameter (Mensching, Jacques, & Daniel, 2016), and an alternative BBR testing approach (Falchetto, Moon, Wang, & Riccardi, 2018; Marasteanu & Falchetto, 2018) were proposed as alternative specifications to the conventional strength-based grading test as specified in current AASHTO specification. Recently, observation of premature and excessive cracking test trails or regular contracts of Ontario, Canada has shown that low-temperature performance grade of inferior asphalt tends to lose its grade significantly when the conditioning time prolonged (Hesp et al., 2009; Yee, Aida, Hesp, Marks, & Tam, 2006; Zhao & Hesp, 2006). The phenomenon of mechanical properties of asphalt gradually changing with extending low-temperature conditioning time is called reversible aging which mechanical properties may restore after heating. Most of the currently used characterisation methods of asphalt low-temperature performance only consider the mechanical properties of asphalt after short conditioning time under specific temperature without discussing the detrimental effects of reversible aging on performance ranking. Relative studies have shown that time-temperature superposition may invalid due to the influence of reversible aging when 2 h loading time is replaced by 60s and higher test temperature (Basu, Marasteanu, & Hesp, 2003; Marasteanu, Basu, Hesp, & Voller, 2004). In fact, reversible aging would increase the modulus and decrease the deformation resistance of asphalt material which has significant adverse effects on asphalt pavement. Especially for the northern areas of China or other cold regions, the temperature below 0°C could be continued for several months. As a result, the most crucial matter, currently, is a proper evaluation of the reversible aging resistance of asphalt binder which could play a significant role in relieving cracking and saving the maintenance costs of asphalt pavement. Background Reversible aging in asphalt science The primary purpose of this paper is comparing different theoretical models of reversible aging and thus more reasonably characterise the process of reversible aging. In this respect, a brief review of the existing literature on reversible aging is presented. Note that a systematic review of current practices regarding reversible aging in asphalt science can be found elsewhere (Manolis, Kuckarek, Macinnis, & Brown, 2016). Reversible aging in asphalt science is not a new research topic, though Struik had introduced the reversible aging phenomenon in asphalt binder long before the implementation of SHRP programme (Struik, 1977). However, this topic received little attention due to lack of enough evidence that reversible aging in the binder can convert to the properties of the mixture (Dongre, 2000; Shenoy, 2002). Hesp research group reopened this area of research following the findings on Canadian test roads (Ding, Tetteh, & Hesp, 2017; Evans, Marchildon, & Hesp, 2011; Togunde & Hesp, 2012). Free volume collapse, wax crystallization and asphaltene aggregation were identified as three central mechanisms that lead to reversible aging of asphalt binder (Hesp, Serban, & Shirokoff, 2007). According to the theory of free volume, the volume of polymer consisted of macromolecule that has already occupied the volume and intermolecular gap (Bahia & Velasquez, 2010). Free volume is the necessary space when molecule motions. The higher the temperature is, the greater the free volume will be and help diffusion motion of short chain in polymer segment. At the same time, conformational

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rearrangement will be in progress constantly. In contrast, the free volume will decrease with decreasing temperature. When the free volume reduced below a critical value, the diffusion motion of short chain will be obstructed and stopped. In other words, the molecular will be frozen below that temperature. The terminology of this process is called glass transition, and the corresponding temperature is called glass transition temperature (Tg ). The specific volumetemperature relationship curve presented in Figure 1 can reflect the change of free volume. As can be seen from α1 part, the volume inflation rate of polymer will increase when the temperature is higher than Tg which can be considered as the result of free volume being released. When the tempearture is lower than Tg , thermal expansion of polymer mainly can be contributed to vibrational magnitude and bond lengths changing of the molecules. Theoretical models of reversible aging in asphalt Considering the similarity of mechanical behaviour of creep and reversible aging, Tabatabaee, Velasquez, and Bahia (2012) adjusted a modified creep model to explain the reversible aging behaviour of asphalt binders using the method of analogy. In the proposed reversible aging model, hardening rate, namely relative change in stiffness is proportional to the relative change in volume according to free volume theory. Furthermore, the relative change in volume also can be replaced by relative change in deformation, namely strain. The original Kelvin creep model of asphalt binder low-temperature behaviour can be described using following equation: γ (t) =

τ (1 − e−t(G1 /η1 ) ) G1

(1)

where γ (t) and t are the strain and loading time, respectively; G1 and η1 are the elastic and viscous material constants and τ is the applied stress. The main revised part was replacing applied stress of Kelvin model by the following empirical equation: τT = e(−9(T−Tg ) /(2x) 2

2

)

(2)

In which, T and Tg are condition temperature and glass transition temperature, respectively and 2x is temperature range of glass transition region. As can be seen from the expression, it obeys the Gaussian distribution. However, there is no clear and definite physical meaning of τT . Combining Equations (1) and (2) results in final the

Figure 1.

The definition of glass transition temperature (Tg ) using free volume theory.

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equation of hardening rate that can be rewritten as follows: V S e(−9(T−Tg ) /(2x) ) ≈ = (1 − e−tc (G/η) ) V0 S0 G 2

γ ≈

2

(3)

where G and η are fitting parameters of the proposed model and tc is conditioning time. In this model, reversible aging is driven by the excess internal energy due to the deviation of asphalt from thermodynamic equilibrium within the glass transition region. Figure 2 shows the hardening rate as a function of conditioning time using the analogous creep model. As can be inferred from the figure and equation, the most severe situation of reversible aging will occur under the glass transition temperature. Bahia and Anderson (1993) proposed using shift factor as the parameter to evaluate the severity of reversible aging. In this method, time-temperature equivalence principle of viscoelastic material was applied and the stiffness master curve of asphalt binder after prolonged conditioning time was horizontally shifted to the reference condition. Shift factor was calculated using macro programme solver in Excel spreadsheet. The higher degree of shifting indicates the more severity of reversible aging in asphalt. The main advantage of this method is that it does not need to consider the variation of stiffness with loading time. More recently, Freeston, Gillespie, Hesp, Paliukaite, and Taylor (2015) have tried using Avrami isothermal crystallization kinetics to analyze the reversible aging process of asphalt binder when conditioning time being extended at constant cold temperature. Original Avrami equation can be expressed by: log (−ln[1 − X (t)]) = log Z + n log t

(4)

where X (t) as a function of time is the degree of crystallization; t is the conditioning time; Z is the initial crystallization rate constant; and n is the Avrami exponent which depends on the crystal dimension and time dependence of nucleation. For detail explanation of the Avrami exponent interested readers may refer to elsewhere (Avrami, 1941). Nucleation is assumed to be site-saturated, where crystals are formed before the crystallization process begins, or continuous, where the number of nuclei increases linearly with time (Freeston et al., 2015). The Avrami exponent can measure how quickly the phase change reaches equilibrium. Moreover, the higher Avrami exponent becomes, the faster the system reaches equilibrium. It has found that using substituted Avarami equation can reasonably fit both creep stiffness, S(60s), and m-value obtained from bending beam rheometer (BBR) test. The

Figure 2.

Creep analogous model of reversible aging.

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improved Avarami equation can be rewritten as follows: 1 − X (t) =

S(60s)t − S(60s)∞ n = e−Zt S(60s)0 − S(60s)∞

(5)

1 − X (t) =

m(60s)t − m(60s)∞ n = e−Zt m(60s)0 − m(60s)∞

(6)

Furthermore, Rigg et al. (2017) made efforts to model the non-isothermal hardening processes caused by reversible aging within the Ozawa theoretical framework. Non-isothermal phase transformation kinetics were applied to analyze the results obtained from differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) of three-point bending tests. The Ozawa exponent m which depends on the dimensions of the crystal growth can be calculated using the following equation: log(− ln [1 − C(T)]) = log K(T) − m log()

(7)

where C(T) is relative crystallized fraction at a given temperature; K(T) is temperature dependence mechanical parameters (G* or δ) obtained from DMA; and  is cooling rate which can be calculated by plotting K(T) versus temperature. Earlier research has shown that K(T) versus log of cooling rate had higher linear correlation (Ozawa, 1971). Therefore, the value of K(T) at four or three selected cooling rates can be extrapolated to relative higher and lower cooling rates to be used as the initial K0 and infinite K∞ values, respectively. By using the following equation, one may calculate 1 − C(T): Kt − K∞ (8) 1 − C(T) = K0 − K∞ By combining Equation (7) with Equation (8), and plotting the log(−ln[1 − C(T)]) versus log of cooling rate one could determine the Ozawa exponent.

Materials and methods Materials The asphalt binders used in this study included various sources and modification technologies that commonly used in the west part of Sichuan province, China. The sample codes and Superpave regular limiting grade temperatures are shown in Table 1. Styrene–butadiene rubber (SBR) and styrene–butadiene-styrene (SBS) polymer modified asphalts are finished products which specific amounts of polymer were added to base asphalt in asphalt refinery. Three unmodified asphalts are provided by pavement regulatory agency for quality assurance (QA). Specifically, Sample A, Sample C and Sample E are three unmodified asphalt binders from Karamay crude oil source, Kunlun crude oil source and Korean SK crude oil source, respectively. Sample B and Sample D are commercial modified asphalt binders and the base asphalt binders are from Qinhuangdao and Korean shuanglong crude oil sources, respectively. Test methods Extended bending beam rheometer (ExBBR) test Considering the embrittlement of asphalt sample when being conditioned for a long time, the applied force changed from 980 mN as specified in AASHTO specification to 370 mN. Three duplicate specimens were manufactured and tested for each sample. For viscoelastic materials,

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Table 1. Superpave regular limiting grade temperatures. Sample code

Modification type

A B C D E

Unmodified SBR polymer Unmodified SBS polymer Unmodified

High grade (°C)

Intermediate grade (°C)

Low grade (°C)

64.1 67.1 83.3 79.7 69.9

19.1 15.3 18.2 16.1 21.5

− 27.4 − 26.7 − 28.4 − 28.9 − 27.6

the strain varies with time under constant stress. Figure 3 shows the strain response under constant stress when running the BBR test. The viscoelastic behaviour of asphalt can be described by some mechanical models composed of mechanical elements. The Burgers model which consisting of two spring elements and two dashpots in series connection can be used to describe the mechanical behaviour of asphalt, as is shown in Figure 4. The creep compliance of this model is determined based on the following equation: J (t) =

t 1 1 + + (1 − e−(E1 t/λ1 ) ) E0 λ0 E1

(9)

In which, E0 and λ0 are instantaneous elastic modulus and viscosity coefficient which represent instantaneous deformation recovery and permanent deformation capability, respectively. E1 is also called delayed elastic modulus. E1 and λ1 can be used to characterise viscoelastic properties

Figure 3.

The strain response under constant stress when running the BBR test.

Figure 4.

The burgers model.

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which are related to deformations developed gradually under loading and will not completely recover after removing the load immediately. Four viscoelastic parameters of Burgers model can be obtained by nonlinear least-squares data fitting of force-deformation curve acquired from BBR test. The relaxation time (τ0 = λ0 /E0 ) and the delay time (τ1 = λ1 /E1 ) are also two important derived parameters from Burgers model (Wang, Dang, You, Hao, & Huang, 2012). The longer the relaxation time becomes, the shorter the speed for stress relaxation turns, and it is worse for stress dissipation. The shorter the delay time becomes, the closer the characteristic of material to elastic deformation becomes. Dynamic mechanical analysis (DMA) The third generation of discovery hybrid stress-controlled rheometer (DHR-3) equipped with an environmental chamber and air chiller system was used in this study. The cooling accessory was also chosen for drying the air gas and preventing air moisture from freezing in the chiller, otherwise the cooling gas outlet may be obstructed. In addition, rheometer is usually used to evaluate the performance of asphalt binder at high or medium temperatures owing to the limit of instrument compliance. In other words, high torques generated in testing asphalt binder using parallel plate geometries at low temperature may lead to severe compliance errors in measured data. Using smaller 4-mm diameter parallel plate or torsional rectangular bar instead of regular parallel plate geometry are effective ways to use rheometer for characterising the low-temperature of asphalt binder (Soleimani, Walsh, & Hesp, 2009; Sui et al., 2011). Although 4-mm parallel plate geometry consumes less amount of material than a torsional rectangular bar, it was found that it could provide unreliable results due to the relatively low gap. However, precise control of thermal contraction of the geometry during the test is unavoidable which was challenging to maintain in this condition. Therefore, self-made stainless steel moulds (Figure 5) for the torsion bar test were used to prepare the samples. The dimension sizes were determined according to Iliuta (2006). Dynamic mechanical analysis and cooling system used in this study are shown in Figure 6. Temperature sweep started from 0°C to − 18°C at 6°C intervals were performed using four different cooling rates, namely 30°C/h, 15°C/h, 6°C/h and 3°C/h. The frequency used in this study was 0.1 rad/s according to trial tests to better differentiate the properties. Phase angle was chosen as performance parameter since it is more important for the characterisation of asphalt binder low-temperature behaviour (Soleimani et al., 2009). The constant strain of 0.02% was used to keep it within the linear viscoelastic (LVE) region. The test specimens were trimmed and transferred into ethanol thermostatic bath at 10°C for about 5 min. Then, the sample was demolded and inserted into the rheometer. Careful consideration should be given to avoid excessive deformation. The rheometer gap was automatically adjusted to allow the

Figure 5.

Moulds used for torsion bar test.

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Figure 6.

Dynamic mechanical analysis and cooling system used in this study.

sample to be free of movement in the axial direction and therefore no axial constraint stress developed. Combined Avrami equation and Ozawa equation Liu and coworkers (S. Liu, Yu, Cui, Zhang, & Mo, 2015) proposed a new equation by combining Ozawa equation and Avrami equation, which could be successfully used to analyze the nonisothermal crystallization of several polymers. Hence, this method was also employed in this study to investigate the non-isothermal crystallization of asphalt binders. Avrami equation can link relative degree of crystallization (X (t)) and conditioning time (t). Ozawa equation can link C(T) and cooling rate (). In fact, for any system, crystallization process is bound up with conditioning time and temperature. Under non-isothermal conditions, for the same system, and when the cooling rate is , conditioning time and temperature have following relationship: t=

|T − T0 | 

(10)

where T0 is the temperature when t = 0. Based on Equation (10), and by combining Equations (4) and (7), for any system, at the conditioning time of t, there must exist the corresponding degree of relative crystallinity at the temperature T. In other words, when the degree of relative crystallinity C(T) is kept to a constant value, one can find corresponding X (t) at the temperature T and cooling rate of . So, following equation can be written: log(−ln[1 − X (t)]) = log(−ln[1 − C(T)])

(11)

log Z + n log t = log K(T) − m log()

(12)

By reorganising the Equation (12), the following formula can be obtained:   n K(T) 1/m − · log t log  = log Z m

(13)

If F = (K(T)/Z)1/m and = (n/m), then Equation (13) can be expressed as: log  = log F(T) − a · log t

(14)

According to Equation (14), when the degree of relative crystallinity is kept to a constant value, by plotting log  versus logt, a can be calculated as the negative value (slope)

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and F(T) as the antilog of the intercept. The physical meaning of F(T) is the value of cooling rate, which should be chosen at unit crystallization time when the measured system amounts to a certain degree of crystallinity. F(T) can be used to characterise the speed of crystallization.

Results and discussion Bending beam rheometer test results Grade loss of different asphalt binders with extending conditioning time was shown in Figure 7. It can be seen that sample A has the slowest hardening trend among the tested samples and sample E has the most severe hardening trend. Grade loss of sample A was 3.4°C when the conditioning time extended to 120 h. However, the grade loss of sample E can even reach 8°C after conditioning in the bath for 120 h, in other words, using sample E in PG-28 zone may dramatically result in losing the confidence that in a given year no damage due to cold temperatures occurs. Overall, all the samples tested in this study experienced gradually hardening with grade loss at extended conditioning time; more importantly, the degree of hardening depends on crude oil source. The linkage between conditioning time and BBR parameters are shown in Figure 8. It is evident that stiffness or m-value obtained from extended BBR test with logarithmic conditioning time has a high value of the coefficient of determination. This observation has practical value as the predicted m-value and stiffness can be used to estimate extended BBR low temperature limiting grade (LTPG) that could be beneficial for quality control (QC) purposes in the future. The empirical formulas used to predict stiffness or m-value of 120 h conditioning time are shown in formulas (15) and (16), respectively. To further validate the reliability of presented empirical formula, stiffness or m-value at two different test temperatures and 120 h conditioning time versus predicted values using proposed formulas is shown in Figure 9. It is evident that all the measured data were located around the contour line and empirical formulas have a high accuracy of prediction.

Figure 7.

Sth = S1h + ln t × (S24h − S1h )/(ln 24 − ln 1)

(15)

mth = m1h + ln t × (m24h − m1h )/(ln 24 − ln 1)

(16)

Grade loss of different asphalt binder with extending condition time.

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Figure 8.

BBR parameters changing with conditioning time (a: Stiffness; b: m-value).

where t is conditioning time; Sth is the stiffness at the conditioning time of t (h); and mth is the m-value at the conditioning time of t (h). Determination of burgers model parameters Four Burgers parameters and derived parameters (relaxation time and delay time) of asphalt binders in all measured conditioning times and types of asphalt binders are presented in Table 2. Among which, the relaxation time is of paramount importance for the characterisation of asphalt binder at low temperature. The physical meaning of relaxation time is the characteristic time for a system to reach an equilibrium condition after a disturbance. The longer relaxation time of asphalt binder at low-temperature means longer time is required for an asphalt system to dissipate accumulated stress. Figure 10 shows the relaxation time of different asphalt binders with extended conditioning time. As expected, relaxation time extended with extended conditioning time. It should be noted that longer relaxation time which is undesirable according to the current specification because of lower m-values, resulted in the slower development of thermal stresses, which is a desirable property (Marasteanu & Basu, 2004). Consequently, the longer relaxation time is not necessarily detrimental to the low-temperature performance. For instance, for climates characterised by extremely cold temperatures, it is not apparent that shorter relaxation time leads to better performance since thermal stresses may develop faster and can result in cracking occurrence before relaxation can occur. However, for climates in which the temperature stays at reasonable low values for prolonged periods time, the binders with shorter relaxation time hold better performance since they can dissipate stress promptly (Marasteanu, 2004).

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Figure 9. Stiffness or m-value at two different test temperatures and 120 h conditioning time versus predicted values (a: Stiffness; b: m-value).

Table 2. Results of four burgers parameters, relaxation time and delay time. Sample code A

B

C

D E

Condition time (h)

E0 (MPa)

E1 (MPa)

1 24 120 1 24 120 1 24 120 1 24 120 1 24 120

418 489 521 357 338 432 322 370 413 323 371 425 389 422 433

249 337 396 229 248 324 204 283 348 194 271 345 285 369 433

λ0 (MPa)

λ1 (MPa)

33,136 54,569 67,632 34,840 40,765 56,112 29,448 44,180 66,271 27,875 39,766 57,078 46,495 65,610 83,976

8899 11,569 12,724 8093 7997 9969 7043 9297 11,219 6896 8452 10,034 9364 11,700 12,796

τ0 (s)

τ1 (s)

79 111 129 97 120 130 91 119 160 86 107 134 119 155 193

35 34 32 35 32 30 34 32 32 35 31 29 32 31 29

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Figure 10.

Relaxation time of different asphalt binders with extending condition time.

Figure 11.

Phase angle versus logarithmic cooling rate. (a) Sample A; (b) Sample E.

Non-isothermal crystallization kinetic analysis In order to compare the differences in low-temperature reversible aging behaviour of asphalt binders, only sample A and sample E were chosen in this part as these two asphalt samples have an obvious different degree of physical hardening. Phase angle versus the corresponding cooling rate of these two samples at the fixed temperature of − 18°C is shown in Figure 11. As can be

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Figure 12.

13

Test of the Ozawa equation with non-isothermal crystallization. (a) Sample A; (b) Sample E.

seen, the relationship of phase angle versus logarithmic cooling rate presents straight line for two samples. The value of phase angle (δ) was extrapolated to a cooling rate of 40°C/h and 0.01°C/h to be used as the initial δ(0) and infinite δ(∞) values. Ozawa non-isothermal crystallization kinetic analysis were performed and the degree of relative crystallinity C(T) were calculated according to the method suggested by Rigg et al. (2017). By using Equation (7), plots of ln [−ln(1 − C(T))] versus logarithmic cooling rate are shown in Figure 12. It can be seen that zigzag broken lines were obtained for two asphalt binders using Ozawa equation. The changing slope shows that Ozawa exponent (m) during primary crystallization process is not a constant. As a result, reliable kinetic parameter cannot be obtained from Ozawa method. This can be attributed to the secondary crystallization (T. Liu, Mo, Wang, & Zhang, 1997). At each degree of crystallinity, there is corresponding conditioning time (t) according to BBR isothermal Avrami analysis (Freeston et al., 2015). According to Equation (14), plots of log  as a function of log t are presented for asphalt binders at three degrees of crystallinity in Figure 13. It is evident that there is a good linearity (coefficient of determination ranged from 0.95 to 0.96 for sample A and from 0.94 to 0.99 for sample E, respectively) between two parameters and a series of parallel lines corresponding to three degrees of crystallinity were acquired. Nonisothermal crystallization kinetics parameters of asphalt binders at different relative degrees of crystallinities by the new equation are shown in Table 3. It can be inferred that sample E has higher F(T) than sample A. In other words, sample E has higher crystallization rate than sample A.

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Figure 13.

Plot of log  versus log t during non-isothermal crystallization. (a) Sample A; (b) Sample E.

Table 3. Non-isothermal crystallization kinetics parameters of asphalt binders at different relative degrees of crystallinities by the new equation. Sample code A E

C(T) (%)

F(T)

α

20 50 80 20 50 80

1.7025 1.8694 2.0514 1.9374 2.1883 2.4652

1.7067 1.6996 1.7397 1.8379 1.8146 1.8315

Conclusions This study mainly evaluated the reversible aging properties of different kinds of asphalt binders used in Sichuan province, China. The findings allow the following conclusions to be drawn: (1) All the samples tested in this study experienced gradually hardening at extended conditioning time, and the degree of hardening depends on crude oil sources. (2) Predicted stiffness and m-value obtained from constructed empirical formula can be used to estimate extended BBR low temperature limiting grade (LTPG) that could be useful for QC purposes in the future.

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(3) The combined Avrami-Ozawa method can be successfully used to describe the nonisothermal crystallization process of asphalt binders used in this study. Acknowledgements Haibo Ding thanks the China Scholarship Council for the financial support that was provided to study at Queen’s University and Prof. Simon Hesp for his continuous encouragement.

Funding This study was supported by the National Natural Science Foundation of China under [grant number 51778541].

ORCID Ali Rahman

http://orcid.org/0000-0003-3076-7942

References Avrami, M. (1941). Granulation, phase change, and microstructure kinetics of phase change. III. The Journal of Chemical Physics, 9(2), 177–184. Bahia, H., & Anderson, D. A. (1993). Glass transition behavior and physical hardening of asphalt binders. Journal of the Association of Asphalt Paving Technologists, 62, 93–129. Bahia, H., & Velasquez, R. (2010). Understanding the mechanism of low temperature physical hardening of asphalt binders. Paper presented at the 55th Annual Meeting of the Canadian Technical Asphalt Association, Edmonton, Canada. Basu, A., Marasteanu, M., & Hesp, S. (2003). Time-temperature superposition and physical hardening effects in low-temperature asphalt binder grading. Journal of the Transportation Research Board, 1829, 1–7. Bodley, T., Andriescu, A., Hesp, S., & Tam, K. (2007). Comparison between binder and hot mix asphalt properties and early top-down wheel path cracking in a northern Ontario pavement trial. Journal of Association of Asphalt Paving Technologists, 76, 345–389. Bueno, M., Hugener, M., & Partl, M. (2015). Fracture toughness evaluation of bituminous binders at low temperatures. Materials & Structures, 48(9), 3049–3058. Ding, H., Tetteh, N., & Hesp, S. (2017). Preliminary experience with improved asphalt cement specifications in the city of Kingston, Ontario, Canada. Construction and Building Materials, 157, 467–475. Dongre, R. (2000). Effect of physical hardening on stress relaxation behavior of asphalt binders. Paper presented at the Eurasphalt and Eurobitume Congress, Barcelona, Spain. Evans, M., Marchildon, R., & Hesp, S. (2011). Effects of physical hardening on stress relaxation in asphalt cements. Journal of the Transportation Research Board, 2207, 34–42. Falchetto, A. C., Moon, K. H., Wang, D., & Riccardi, C. (2018). Investigation on the cooling medium effect in the characterization of asphalt binder with the bending beam rheometer (BBR). Canadian Journal of Civil Engineering. doi:10.1139/cjce-2017-0586 Freeston, J. L., Gillespie, G., Hesp, S., Paliukaite, M., & Taylor, R. (2015). Physical hardening in asphalt. Ottawa: Canadian Technical Asphalt Association. Hesp, S., Serban, I., & Shirokoff, J. (2007). Reversible aging in asphalt binders. Energy & Fuels, 21(2), 1112–1121. Hesp, S., & Shurvell, H. (2010). X-ray fluorescence detection of waste engine oil residue in asphalt and its effect on cracking in service. International Journal of Pavement Engineering, 11(6), 541–553. Hesp, S., Soleimani, A., Subramani, S., Phillips, T., Smith, D., Marks, P., & Tam, K. (2009). Asphalt pavement cracking: Analysis of extraordinary life cycle variability in eastern and northeastern ontario. International Journal of Pavement Engineering, 10(3), 209–227. Hesp, S., Terlouw, T., & Vonk, W. (2000). Low temperature performance of SBS-modified asphalt mixes. St Paul, MN: Association of Asphalt Paving Technologists. Hoare, T., & Hesp, S. (2000). Low-temperature fracture testing of asphalt binders: Regular and modified systems. Journal of the Transportation Research Board, 1728, 36–42.

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