An experimental testing and analysis procedure to determine linear viscoelastic properties of asphalt binder microstructural components

Construction and Building Materials 230 (2020) 116999

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An experimental testing and analysis procedure to determine linear viscoelastic properties of asphalt binder microstructural components Thaísa Ferreira Macedo a, Gustavo Adolfo Badilla-Vargas a, Patrícia Hennig Osmari a, Alex Duarte de Oliveira a, Renata Antoun Simão b, Leni Figueiredo Mathias Leite a, Francisco Thiago Sacramento Aragão c,⇑ a b c

Civil Engineering Program, Federal University of Rio de Janeiro/COPPE, Rio de Janeiro, Brazil Metallurgical and Materials Engineering Program, Federal University of Rio de Janeiro/COPPE, Rio de Janeiro, Brazil Department of Civil Engineering, Federal University of Rio de Janeiro/COPPE, Rio de Janeiro, Brazil

h i g h l i g h t s
AFM is a powerful tool to identify microstructural characteristics of binders.
Viscoelastic properties of binder constituents can be determined with AFM.
Binder microstructural properties vary with the material aging condition.
Constituent properties may be used to predict the mechanical behavior of binders.

a r t i c l e

i n f o

Article history: Received 28 April 2019 Received in revised form 6 September 2019 Accepted 15 September 2019

Keywords: Asphalt binder microstructural components Atomic force microscope Linear viscoelastic properties Finite element method Microstructural simulations

a b s t r a c t This study aims to propose a carefully – designed experimental testing and analysis procedure to determine linear viscoelastic properties of asphalt binder constituents in three aging conditions. To this end, three major constituents are identified by topography images and their linear viscoelastic creep compliance functions are determined by nanoindentation tests performed in an Atomic Force Microscope. These material characteristics are used as inputs required by a finite – element – based microstructural model in simulations of a binder mechanical test designed and performed in the laboratory. The strong equivalence between the experimental and the numerical results indicates that the procedure was successfully developed and that the surface analysis performed using AFM data can provide meaningful and realistic insights into the overall binder characteristics and allow the determination of key properties of the material. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Asphalt binder is a versatile material widely used in road construction and has the main function of binding the aggregate particles of asphalt mixtures as well as to facilitate the maintenance of their structural stability. In addition, the inherent viscoelastic behavior of asphalt binders creates a temperature- and a ratedependence in the overall mechanical responses of asphalt mixtures. ⇑ Corresponding author. E-mail addresses: [email protected] (T.F. Macedo), gustavo.badilla@ coc.ufrj.br (G.A. Badilla-Vargas), [email protected] (P.H. Osmari), [email protected] (A.D. de Oliveira), [email protected] (R.A. Simão), [email protected] (L.F.M. Leite), [email protected] (F.T.S. Aragão). https://doi.org/10.1016/j.conbuildmat.2019.116999 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

Such viscoelastic behavior is typically characterized in the laboratory based on rheological properties determined from tests performed in rheometers. However, the deeper understanding on the microscale characteristics of the binder components may provide meaningful and realistic insights into the overall binder characteristics and allow the determination of key properties of the material. This type of sophisticated characterization may also aid and optimize preliminary processes such as the material selection. Several studies have been recently conducted to investigate the complex chemical composition and rheological behavior of asphalt binders. In addition, microstructural analyses using the Atomic Force Microscope (AFM) have also become more frequent in the recent years [1–8]. AFM testing allows the identification of different nanoscale binder constituents, especially catanaphase (often

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named as bee), periphase, and paraphase [9–11]. A fourth phase, the salphase [12,13], has also been observed by some authors. Additional image analysis techniques have also been recently developed to evaluate the material-specific effects of phenomena such as aging on the microstructural characteristics of these constituents and their correlations with the chemical composition and rheological behavior of the binders [1,6,8,9]. In addition to provide microstructural geometric characteristics of the binder constituents, the AFM also allows the determination of mechanical properties with the use of a cantilever and its attached tip that indents the thin asphalt film [2–5,16]. The equipment allows the application of different loads and the acquisition of surface deformation data that may be used to determine stiffness [2], relaxation modulus [5,15], and creep compliance [4,11,14,16]. Although different studies have been recently conducted to evaluate these properties, such efforts are often based on global characterizations of the binders. More recently, some studies have attempted to investigate the linkage between surface and bulk structures [17–19]. Only a few studies characterized the mechanical properties of each individual phase. In addition, these studies typically proposed the use of equations to calculate the material properties indirectly from the AFM testing measurements [5,20,21]. Thus, additional studies that attempt to determine individual binder constituent linear viscoelastic properties directly from AFM testing measurements are required to advance the state-of-the-art knowledge. In this paper, the linear viscoelastic properties of each individual binder microstructural constituent is determined from nanoindentation performed in the AFM. For that, an experimental protocol is carefully developed and adopted. In the procedure, the limits of linearity for each binder constituent are evaluated to allow the further determination of their individual linear viscoelastic creep compliance. Aging – related microstructural changes are also investigated by determining the creep compliance of the individual components at the virgin, RTFOT + PAV – aged, and rejuvenated conditions. To evaluate the validity of the viscoelastic properties determined from the analysis of the AFM testing results and to demonstrate that applicability of the proposed experimental methodology, finite – element based computational microstructural simulations of a laboratory binder test are performed considering the three aging states. In the simulations, the individual creep compliance for the binder constituents are required as key inputs along with their inner geometric microstructural characteristics, previously determined by Osmari et al. [8]. A strong equivalence between the experimental and the numerical results is observed for the three aging conditions evaluated, indicating that the proposed experimental procedure was successfully developed and could in fact provide representative viscoelastic properties of the binder constituents. This equivalence also highlights the ability of the numerical – experimental microstructural modeling approach to predict the overall mechanical behavior of complex and heterogeneous composites such as asphaltic materials from a few geometric and constitutive properties of their constituents. Such approach may be used as an efficient tool to facilitate the optimization of the material selection and composite design activities, reducing the expensive experimental trial and error procedures. In addition, computational microstructural models allow a detailed and comprehensive analysis of the inner microstructural characteristics of the composites, such as the distribution of stresses and strains within their microstructures, which is not possible in purely experimental characterizations.

2. Study objectives and scope The objective of this study is to propose a methodology to determine linear viscoelastic properties of microstructural constituents of a binder in different aging conditions, i.e., virgin, RTFOT + PAV aged, and rejuvenated by means of nanoindentation tests performed in the AFM. The specific objectives of the paper are:
To evaluate the limits of linearity for the viscoelastic mechanical behavior of each microstructural binder constituent;
To determine the linear viscoelastic creep compliance of the binder constituents for the virgin, RTFOT + PAV – aged, and rejuvenated states;
To evaluate the validity of the linear viscoelastic properties determined from the proposed experimental methodology by performing numerical microstructural simulations of a binder testing performed in the laboratory. 3. Materials, laboratory tests, and results A PG 64S-22 binder was selected for the experimental characterizations in this paper. The binder was tested in three conditions: virgin, aged, and rejuvenated. The samples were aged in the laboratory in the RTFO and PAV ovens. Then, the rejuvenation of the RTFOT + PAV-aged binder was promoted by the addition of 12% of a rejuvenator agent classified as AR5 according to ASTM D 4552/10. AR5 is produced in the lubricant plant refining and is composed by aromatic extract. This rejuvenated content was previously determined by Osmari et al. [8], based on the recovery of the material viscosity at a rotational viscometer in three different temperatures (135 °C, 155 °C, and 175 °C). For the nanoindentation tests in the AFM, asphalt binder samples were heated in an oven at 135 °C and then transferred to a spin coater (Fig. 1a), where each sample was submitted to rotation for spraying in the glass plate. After resting for 24 h, the samples were considered ready for testing in the AFM. The AFM tip used for the topographic imaging and for the nanoindentations of the asphaltic binders was a pyramidal – shaped silicon nitride, known in the literature as Berkovich.

3.1. Data acquisition The AFM used in this research was a JPK I, as shown in Fig. 1b. The identification of different phases was done by imaging the samples in the intermittent mode. The tip was then retracted and the oscillation of the cantilever ceased. Specific points (locations) on the surface were chosen and creep tests were performed with forces of 30 nN, 40 nN, 50 nN, 70 nN, and 100 nN. All tests were performed at an environmental temperature of 25 °C, controlled by a hygrothermometer. The procedure proposed by Macedo et al. [22] to determine the creep compliance of each individual binder phase was adopted in this paper and includes the following steps: (1) In the intermittent mode, topography images of the asphalt binder were obtained imaging areas of 10 lm  10 lm (Fig. 2a). It is worth to mention that this frame size is not large enough to be regarded as a representative volume element (RVE). Osmari et al. [8] observed that 40 lm  40 lm is the minimum frame area to be adopted as RVE in studies that attempt to evaluate microstructure geometric characteristics of binder constituents with the AFM. However, the purpose of this first step of the procedure proposed herein was to identify the position of each binder constituent to be further indented for the determination of their creep compliance. Thus, frames smaller than the actual RVE should be preferred to reduce the chance of error related to the positioning of the indenter; (2) The tip was retracted and the AFM set to the contact mode; (3) The specific microstructural phase to be indented (paraphase, periphase, black and white parts of catanaphase) was chosen for the tip indentation. As an example, Fig. 2a shows an indentation in the paraphase; (4) In order to monitor the sample displacements, tip vertical movement into the surface was registered by following the piezoelectric ceramic elongation into the sample when scanning an area of 0.001 lm  0.001 lm. This area is smaller than the tip apex size and thus the tip can be considered to be in a fixed position on the surface (Fig. 2a); (5) Sample displacement was registered, from bottom to top, in an image of 128 pixels  128 pixels, with a line frequency of 10 Hz, therefore scanning a total time of 12.8 s (Fig. 2b); (6) The JPK Instruments software used for obtaining a line profile (Fig. 2c) on the image of 0.001 lm  0.001 lm registered the displacement caused by indentation on the topographic surface.

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Fig. 1. (a) Spin coater; (b) AFM. The equipment stability was checked by repeating the same procedure on silicon surfaces. A deformation smaller than 0.5% was observed, ensuring the validity of the deformation measurements. Repeatability was also checked by performing at least five tests in each region, with each force magnitude. 3.2. Data analysis The deformation data acquired was used to evaluate the linearity of the viscoelastic behavior of the binder constituents by means of the superposition and homogeneity principles. It is well known that viscoelastic materials would be in their linear viscoelastic region when the magnitude of the deformation is sufficiently small or when the deformation rate is sufficiently low relative to the material relaxation time [23]. The superposition principle defines that the deformation response to the combination of two stress inputs, applied at different moments, is equal to the sum of the deformations (outputs) due to the separately acting stresses. On the other hand, the homogeneity principle states that the strain response due to an applied stress should be equal to the multiplication of a scalar by the strain due to that applied stress that was multiplied by that scalar number. This means that if the stress input is multiplied by a constant, the strain output must be multiplied by the same constant. Eqs. (13) and (14) represent the superposition and homogeneity principles, respectively, for materials that are in the linear region:

efr1 þ r2 g ¼ efr1 g þ efr2 g

ð13Þ

efbrg ¼ befrg

ð14Þ

where

where h is the total displacement; hc is the displacement due to the real contact between the asphalt binder and the tip (Fig. 3); he is the elastic displacement;

e ¼ 1  2=p (for a tip considered conic according to solution by Sneddon [26]). Considering Eqs. (15) and (16), hc can be rewritten as:

hc ¼ ð1  eÞh

The contact area between the conical tip and the asphalt binder sample can be calculated as:

Ac ¼

p tan a 2 h cos a c

ð18Þ

where Ac = f(hc) is the contact area tip between the indenter tip and the asphalt binder sample; a is the cone angle of the AFM tip. Finally, after defining the contact area as a function of hc, it is possible to obtain the creep compliance using Eq. (19).

Dðt Þ ¼

r1 = r1(t) and r2 = r2(t) are two different stress histories;

ð17Þ

ðtÞ ðtÞ ¼ Ac r F

ð19Þ

where

b is a constant multiplier.

Indentation tests are generally performed with pyramidal – shaped tips (Fig. 3a) to measure force and depth of penetration, which is key information for the further determination of mechanical properties. However, the pyramidal indenter is generally modeled as a conical indenter [24] (Fig. 3b), axisymmetric with angle a (Fig. 3c) to facilitate calculations based on SIRGHI and ROSSI [25]. With the variation of hc (indentation depth) due to different magnitudes of applied forces (e.g., 30 nN, 40 nN, 50 nN, 70 nN, and 100 nN in this paper), there is an area variation and a consequent change in the calculated stress. Therefore, for the purpose of calculation, the projected area of the circular tip was considered, so that it was possible to calculate a constant stress corresponding to the applied load. From the displacement versus time curves, it was possible to obtain hc using the following Eq. (15):

hc ¼ h  he

ð15Þ

he ¼ eh

ð16Þ

D(t) is the creep compliance; (t) is the output strain evolution function; r is the stress applied, defined by r ¼ AFc ; F is the applied constant force.

3.3. Indentation stress During the indentations, the contact area of the pyramidal tip used to characterize the creep compliance of the binder components continuously increases with the penetration and this results in variations in the calculated stress magnitudes. To overcome this cumbersome experimental challenge, a statistical analysis was conducted to identify a representative constant area that should be adopted to calculate the stress magnitudes and then the creep compliance of each binder constituent during the indentation tests. To this end, different values of hc were defined based on curves of strain versus time, obtained from distinct constant forces applied on the different phases (periphase, paraphase, black and white catanaphase) during the creep compliance tests.

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Paraphase Periphase White bee

Black bee

(b)

(a)

(c) Fig. 2. (a) Identification of the binder microstructural components and of the indentation location represented by a yellow square with area of 0.001 lm2 on the topography image of an asphalt binder sample surface with total area of 10 lm  10 lm and; (b) tip path image on the area to be scanned; and (c) application of a line profile on the 0.001 lm2 image area for the acquisition of strain data by Macedo et al. [22].

The different hc values were evaluated to identify the corresponding projected cross-section area that provided the lowest variability or dispersion in the creep compliance functions calculated using Eq. (19). This evaluation followed the analysis to identify the limits of linearity of the material behavior based on the homogeneity and superposition principles and using the strain histories resulting from the indentations. Thus, the driving concept of this statistical analysis was that the representative projected cross-section area should provide the same creep compliance curves for each constituent regardless of the magnitude of the constant force applied, given that the strain responses to that applied force respected the homogeneity and superposition principles, represented by Eqs. (13) and (14), respectively. The values of hc evaluated were the following: (1) hc : maximum of each test; (2) (3)

part);

to half the area obtained for hc; (5) 10th Percentile hc that represents 10% of all maximal depths obtained in all tests, assuring that at least 90% of the maximum penetration depths included this value; (6) 25th Percentile (1st Quartile) hc that represents 25% of all maximal depths obtained in all tests, assuring that at least 75% of the maximum penetration depths included this value;

(4) Fig. 3. Shape of AFM tips used in indentation experiments: (a) pyramidal tip with triangular projected area; (b) conical tip with circular projected area; (c) schematic representation of a tip indenting a half – space sample with displacement of the tip in the asphalt binder (h), elastic displacement of sample surface at the contact line with the indenter (he), contact depth (hc), contact radius (rc), and cone angle (a) of the indenter (Adapted from SIRGHI and ROSSI, [25]).

hc ; 2 2hc : position of the centroid of the nanoindenter (contact 3 pffiffi hc 2 : position at which the projected area corresponds 2

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This may be due to the size of the black bee and because it is usually comprised between the white bees. In addition, the pyramidal shape of the tip of the AFM may have contributed to this difficulty in obtaining the deformation curves as the edges of the tip may have interacted with the white bees concealing the real value of the creep compliance when higher forces were used. The deformations of the black bee were the lowest for the virgin binder (Fig. 4). Fig. 5 shows the deformation curves of the aged binder for all microstructural phases. Again, the linearity of the paraphrase was observed for a range of loads (30–70 Nn) different than that observed for the other phases (20–50 nN). As for the virgin condition, the determination of the black bee deformation curves was difficult. Finally, Fig. 6 shows the deformation curves for the rejuvenated binder. In that aging condition, the linearity of the mechanical responses of all phases was observed for loads between 30 nN and 100 nN. As for the other aging conditions, it was difficult to obtain the black bee curves. As expected, the aged binder (Fig. 5) presented smaller deformations when compared to the virgin and the rejuvenated materials. The rejuvenated material (Fig. 6) deformed more than the virgin one (Fig. 4). In fact, the deformability of the virgin and rejuvenated materials should be equivalent. This difference is due to strategy adopted by Osmari et al. [8] to define the optimum rejuvenator content that was based on the recovery of the viscosity of the aged binders to the same magnitude of the viscosity of the corresponding virgin binders. The authors mentioned

(7) 50th Percentile (Median) hc that represents 50% of all maximal depths obtained in all tests, assuring that at least 50% of the maximum penetration depths included this value; (8) 75th Percentile (3rd Quartile) hc that represents 75% of all maximal depths obtained in all tests, assuring that at least 25% of the maximum penetration depths included this value. 3.4. Linear viscoelastic behavior To evaluate the linearity of the binder constituent responses, constant forces of 20 nN, 30 nN, 40 nN, 50 nN, 70 nN, and 100 nN were applied during the 12.8 s of the creep tests. The deformation curves obtained are shown in Figs. 4–6 and were used to verify the linearity by means of the superposition and homogeneity principles (Eqs. (13) and (14), respectively). The load magnitudes that guarantee the material linear behavior could be further applied in the nanoindentation tests to determine the linear viscoelastic creep compliance of the binder constituents in the virgin, aged, and rejuvenated conditions. Fig. 4 shows the deformation versus time curves of the binder in the virgin condition for all microstructural phases (periphase, paraphase, white bee, and black bee). To verify the linear behavior of paraphase, periphase, and white bee, a loading range of 30–100 nN was used. For the black bee, however, forces between 20 nN and 70 nN were applied. This last phase was the most difficult to obtain the data.

Superposition (a)

Homogeneity (b) 8.0E-03

Deform. of 30 nN + 70 nN 100 nN 70 nN 30 nN

6.0E-03

Deformation (mm/mm)

Deformation (mm/mm)

Paraphase

8.0E-03

4.0E-03 2.0E-03

0

2

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0

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4.0E-03

14

Deformation (mm/mm)

Deformation (mm/mm)

Periphase

8.0E-03

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6.0E-03

0.0E+00

0.0E+00

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Deform. of 70 x (100/70) 100 nN 70 nN

4.0E-03 2.0E-03

2

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Deform. of 50 x (70/50) 70 nN 50 nN

6.0E-03 4.0E-03 2.0E-03

0.0E+00

0.0E+00 0

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0

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Fig. 4. Deformation evolution functions: (a) superposition and (b) homogeneity to evaluate the linear viscoelastic behavior of the virgin binder constituents.

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Superposition (a)

Homogeneity (b) 8.0E-03

Deform. of 30 nN + 40 nN 70 nN 40 nN 30 nN

6.0E-03

Deformation (mm/mm)

Deformation (mm/mm)

Paraphase

8.0E-03

4.0E-03 2.0E-03

0.0E+00 2

4

6 8 Time (s)

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12

2.0E-03

0 8.0E-03

Deform. of 20 nN + 30 nN 50 nN 30 nN 20 nN

6.0E-03 4.0E-03 2.0E-03 0.0E+00

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Deform. of 30 x (50/30) 50 nN 30 nN

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0 8.0E-03

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6.0E-03

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Deform. of 30 x (50/30) 50 nN 30 nN

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14

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Deformation (mm/mm)

Periphase

8.0E-03

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6.0E-03

0.0E+00 0

Black bee

Deform. of 40 x (70/40) 70 nN 40 nN

6.0E-03 4.0E-03

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Fig. 5. Deformation evolution functions: (a) superposition and (b) homogeneity to evaluate the linear viscoelastic behavior of the aged binder constituents. that a more appropriate strategy would be based on the recovery of other rheological properties such as the dynamic shear modulus. Further studies are required to refine the rejuvenator design procedure adopted to identify the proper amount of rejuvenator to be used in the aged binders. In any case, Osmari et al. [8] observed that the dynamic shear modulus of their rejuvenated binders was smaller than that of the corresponding neat binders. Thus, in this paper, the higher deformability observed for the rejuvenated material was expected.

The dispersion of the creep results for the black bee of the virgin binder was the lowest in relation to the other phases, considering all hc evaluated (Fig. 7), followed by the white bee, the periphase, and the paraphase. It can also be observed that the dispersion varied among the different hc evaluated. For all phases, the largest dispersion was observed for the maximum hc (last column of Fig. 7). The creep compliance of the paraphase of the aged binder (Fig. 8) presented the largest dispersion, with values of up to 2.5  105 for the maximum hc when compared to the other phases (periphase, white bee, and black bee). Among these other

3.5. Creep compliance functions

phases, the lowest creep values were observed for h2c , which also provided the lowest dispersion. The larger creep values with the largest dispersion were observed for the 3rd quartile hc. For all phases of the rejuvenated binder, the largest dispersion on the creep compliance results was observed for the maximum hc (last column of Fig. 9). The lowest dispersions for the periphase, the white bee, and the black bee were

After demonstrating the linearity of the strain responses to different force magnitude ranges, creep compliance functions for each binder constituent were calculated using Eq. (19) for the various projected cross – section areas corresponding to the hc fractions evaluated in the paper. In order to identify the optimum hc and corresponding projected cross – section area to be adopted in Eq. (19), a statistical analysis was performed, as previously described. Figs. 7–9 show the creep compliance evolution for the different binder conditions, i.e., virgin, aged, and rejuvenated, respectively, and phases, i.e., paraphase, periphase, white bee, and black bee, according to the specific hc values evaluated. In the individual graphics, at least two replicates are represented for each applied force, i.e., 20 nN, 30 nN, 40 nN, 50 nN, 70 nN, and 100 nN.

observed for the h2c and the 10th percentile hc. On the other hand, the paraphase showed the lowest creep compliance dispersions for the 10th percentile hc, followed by the 1st quartile hc, the median hc, and the 3rd quartile hc. Considering that the creep compliance is a unit response function to a given Heaviside – type stress input, the creep compliance functions shown in Figs. 7–9 should be identical, regardless of the applied stress, given that the tests were conducted within the limits of linearity. Thus, a statistical procedure was adopted to perform a comparison between the individual and the average creep compliance functions for each graphic. Two statistical parameters were evaluated in the

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Superposition (a) 8.0E-03

Deformation (mm/mm)

Deformation (mm/mm)

Deform. of 30 nN + 70 nN 100 nN 70 nN 30 nN

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6 8 Time (s)

Fig. 6. Deformation evolution functions: (a) superposition and (b) homogeneity to evaluate the linear viscoelastic behavior of the rejuvenated binder constituents.

analysis: the standard deviation and the normalized root square error. Figs. 10–12 show the results for this analysis considering measurements obtained at 12.8 s. It is noteworthy that the paraphase results were plotted in separated graphics because of the distinct deformation magnitudes experienced by this binder component in comparison to the other phases. As shown in Figs. 10 and 11 for virgin and aged binders, respectively, the smallest standard deviations were observed for the 10th Percentile hc and h2c cases for the periphase, black bee, and white bee. On the other hand, for the paraphase, the 10th Percentile hc case resulted in the clear lowest dispersion. In the case of the rejuvenated binder (Fig. 12), the smallest standard deviations were observed for the h2c cases for the white and black bees. However, for the paraphase and the periphase, the 10th Percentile hc case showed lowest dispersion. The root square error was determined with respect to the average creep function for each case and further normalized by the root square error value of the 10th Percentile hc. Figs. 10–12 show that the lowest normalized error corresponded to the 10th Percentile hc and to h2c for all binder conditions. Therefore, considering both the standard deviation and the root square error analyses, the 10th Percentile hc was selected and used to calculate the projected cross-section area of indentation and the creep compliance function (Eq. (19)) for each binder microstructural phase and aging condition.

Fig. 13a, b, d show the average creep compliance functions determined using the 10th Percentile hc for each binder constituent of the virgin, aged, and rejuvenated binders, respectively. To allow a more detailed analysis of the data plotted in Fig. 13b for the creep compliance of the aged binder, this figure is plotted in a different scale in Fig. 13c. As shown in Fig. 13a, for the virgin binder, the paraphase appeared to be the most deformable binder constituent (largest creep compliance), followed by the black bee, the white bee, and finally by the periphase, which was the stiffest phase. For the rejuvenated binder (Fig. 13d), the paraphase also presented the largest creep compliance, followed by the black bee and by the periphase, which presented similar creep compliance functions, and finally by the white bee, which presented the stiffest behavior. Unlike the virgin binder, the periphase was the stiffest phase of the rejuvenated binder, which indicates that the different binder constituents may present varying susceptibility to aging. As expected, the aged binder (Fig. 13b) presented the lowest creep compliance, indicating that this was the stiffest material. In addition, Fig. 13c clearly shows that the paraphase was the constituent most susceptible to aging. In the virgin and rejuvenated conditions, the creep compliance of the paraphase was larger than those of the other phases, whereas for the aged material, the paraphase presented the lowest creep compliance.

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Fig. 7. Creep compliance functions considering various hc fractions for the different constituents of the virgin binder.

Fig. 8. Creep compliance functions considering various hc fractions for the different constituents of the aged binder.

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Fig. 9. Creep compliance functions considering various hc fractions for the different constituents of the rejuvenated binder.

Fig. 10. (a) and (b) standard deviation for the hc calculation in the periphase, white bee, black bee, and paraphase considering different hc fractions; (c) and (d) normalized root squared error for hc as measured in the different phases for the virgin binder.

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Fig. 11. (a) and (b) standard deviation for the hc calculation in the periphase, white bee, black bee, and paraphase considering different hc fractions; (c) and (d) normalized root squared error for hc as measured in the different phases for the aged binder.

These different mechanical characteristics are most likely related to the different chemical composition of each microstructural component. Further studies are required to correlate the creep compliance characteristics of the binder components to their chemical compounds.

4. Numerical – experimental microstructural modeling 4.1. Experimental testing protocol To evaluate the validity and demonstrate the applicability of the individual creep compliance functions shown in Fig. 13, a laboratory test was developed and simulated using the integrated numerical – experimental microstructure modeling approach. This experiment consists of applying load in a constant rate over the whole surface of the sample without allowing any lateral displacement. Fig. 14 shows the experimental testing configuration, including the load application device. It also shows the dimensions of the metallic mold used to accommodate the sample during testing. Before testing, the binder and the mold were heated for 15 min at 135 °C in an oven. Then, 5 g of the heated binder were poured into the mold and placed over a scale. The sample – mold set was allowed to cool down to the ambient temperature and then placed into an environmental chamber to keep the testing temperature at 25 °C. Axial compressive loads were applied to the binder specimens by the actuator of a universal MTS testing machine using a plunger that fitted exactly into the mold. A contact load of 50 N was initially applied and further increased to 200 N at a rate of 10 N/s. The binder was tested in the three aging conditions evaluated in this paper, i.e., virgin, RTFOT + PAV – aged, and rejuvenated.

4.2. Numerical simulations The individual creep compliance functions shown in Fig. 13 were used to determine the linear viscoelastic properties of the binder constituents required as inputs by the computational microstructure model. For this, the collocation method was adopted to identify the Prony series coefficients of each creep compliance function. Following the procedure of interconversion between linear viscoelastic material functions proposed by Park and Schapery [27], the corresponding relaxation modulus Prony series coefficients could be calculated to be used as inputs in the virtual testing designed and analyzed with the finite – element – based commercial software ABAQUS. Along with the individual component linear viscoelastic properties, the inner geometric characteristics of such constituents are required as inputs by the computational model. For that, the procedure proposed by Osmari et al. [8] was adopted in this paper. According to Osmari et al. [8], square – shaped microstructures measuring 40 lm  40 lm can be regarded as RVEs. Thus, for the virtual testing simulations performed to characterize the overall creep compliance of the binders based on the individual creep compliances of their components, these sample dimensions were adopted. The geometric characteristics of the binder components within frames measuring 40 lm  40 lm were obtained from AFM topography images and are presented in Table 1. A digital image analysis was performed using AUTOCAD to properly define the boundaries of each component in the images. Then, the treated RVE images were saved in the ‘‘dxf” AUTOCAD file format and further used to fabricate the virtual samples for the finite element simulations in ABAQUS. Fig. 15 shows the microstructures for the three aging conditions evaluated.

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Fig. 12. (a) and (b) standard deviation for the hc calculation in the periphase, white bee, black bee, and paraphase considering different hc fractions; (c) and (d) normalized root squared error for hc as measured in the different phases for the rejuvenated binder.

Fig. 13. Creep compliance functions of the binder microstructural components for the different aging conditions considering the 10th Percentile hc: (a) virgin, (b) and (c) aged (plotted in different scales), and (d) rejuvenated.

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Plunger + mold

(a)

(b)

Fig. 14. Testing configuration: (a) mold dimensions, and (b) COPPE/UFRJ MTS servo – hydraulic press during test.

Table 1 Area fractions for the binder constituents evaluated in this study [8]. Material

Paraphase

Periphase

White bee

Black bee

Virgin Aged AR5 rejuvenated

0.250 0.210 0.240

0.700 0.730 0.700

0.025 0.030 0.030

0.025 0.030 0.030

Fig. 15. Microstructures for the different binder aging conditions: (a) virgin, (b) aged, and (c) rejuvenated.

In ABAQUS, the images were discretized for the generation of finite element meshes. The size of the meshes was defined based on a convergence study, performed individually for each of the three analyzed structures (one for each aging condition). In the convergence study, three-node linear plane stress triangular elements (CPS3 in ABAQUS) measuring 0.1 lm, 0.3 lm, and 0.5 lm were evaluated. The vertical displacement on the top edge and the total energy in each virtual sample were monitored. As shown in Table 2, the use of elements smaller than 0.5 lm resulted in very small differences in the monitored variables which do not justify the expensive computational cost of the simulations performed with the elements measuring 0.1 lm and 0.3 lm. As also indicated in the table, a significant increase on the number of finite elements was observed when these two finer meshes were used. For instance, for the virgin binder, the number of elements required by the 0.5 lm mesh (27,383) corresponded to 54% and

7% of the number of elements required by the 0.3 lm (51,115) and the 0.1 lm (368,785) meshes, respectively. Thus, the 0.5 lm element was adopted for the simulations. After the mesh definition, two distinct simulations were conducted with the virtual samples, as illustrated in Fig. 16. First, the overall creep compliance of the binders was determined based on simulations of RVEs of the binder microstructures. In these simulations, the binder constituents were modeled as linear viscoelastic materials. For that, the coefficients of the individual relaxation modulus Prony series functions converted from the AFM creep compliance functions were used as model inputs. A discontinuous Heaviside step function was applied as input force to the top edge of the heterogeneous virtual RVE samples, while the rotation and the vertical and horizontal displacements at the bottom edge were constrained. The stress input function was calculated by dividing the applied force by the width of the

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T.F. Macedo et al. / Construction and Building Materials 230 (2020) 116999 Table 2 Mesh convergence study. Aging condition

Element size (lm)

# of elements

Vertical displacement (lm)

Total energy (J)

Virgin

0.1 0.3 0.5

368,785 51,115 27,383

16.73 16.73 16.72

6.5E07 6.4E07 6.4E07

Aged

0.1 0.3 0.5

389,184 55,570 32,027

18.31 18.30 18.30

7.9E07 7.8E07 7.8E07

Rejuvenated

0.1 0.3 0.5

383,392 56,962 33,416

16.55 16.55 16.55

6.1E07 6.1E07 6.1E07

Fig. 16. Schematic representation of the two sets of simulations performed in this paper.

top edge, i.e., 40 lm, given that a unit thickness was assigned to the two-dimensional virtual samples. It is noteworthy that the magnitude of the input function is irrelevant, given that no damage was modeled in the simulations of this paper. The strain evolution function was determined by dividing the displacements of the top edge by the height of the virtual RVE samples, i.e., 40 lm.

The overall creep compliance was then calculated by dividing the resulting strain function by the applied stress. Fig. 17 shows the distributions of the stress tensor component normal to the sample horizontal edges (r22 ) within the virtual heterogeneous RVE samples after the first set of simulations. The figure illustrates one of the most attractive features of the microstructural modeling approach, which is the possibility to analyze the localized stress magnitudes within the complex microstructures of particulate composites such as asphaltic materials. Fig. 17a shows the stress distribution r22 within the virtual RVE sample of the virgin binder. A significant heterogeneity on the microstructural stress levels can be observed. The lowest stress levels indicated by the dark red colors typically occurred in the paraphase, which was expected because this phase presented the largest creep compliance (lowest stiffness) in Fig. 13a. On the other hand, Fig. 13a indicated that the periphase exhibited the lowest creep compliance (largest stiffness). This justifies the larger stress magnitudes (green colors) experienced by the periphase in Fig. 17a. Fig. 17b shows that the aged binder presented a pretty uniform stress distribution within most of the virtual RVE sample. This results from the similar creep compliance functions obtained in the AFM for the different microstructural phases of the aged binder, as shown in Fig. 13b. Thus, given that the phases presented similar deformability characteristics, they should also experience similar levels of stresses during the tests. The stress distribution of the rejuvenated material (Fig. 17c) showed an intermediate behavior between the virgin and the aged binders. Although the creep compliance curves for the virgin and rejuvenated binders were similar, the spatial distribution of the phases and their geometry may have influenced the stress distribution within the rejuvenated sample. Further studies are required to confirm this hypothesis.

Fig. 17. Distribution of r22 within the virtual samples of the asphalt binder for the aging conditions: (a) virgin, (b) aged, and (c) rejuvenated.

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A second model was designed to reproduce the testing configuration shown in Fig. 15 and previously described in the paper. Virtual simulations of the compressive axial tests performed in the laboratory were conducted. In this second set of simulations, the virtual samples were modeled as homogeneous materials with linear viscoelastic behavior described by the overall creep compliance functions of the virtual RVE samples obtained from the first set of simulations. These Prony series coefficients of the homogenized creep compliance functions were used to determine the Prony series coefficients of the corresponding relaxation moduli, which were used as model inputs in the second set of simulations. A ramp stress was applied as input load to the top edge of the homogeneous RVE samples. The input stress function was calculated to reproduce the loading configuration of the experimental tests. In the laboratory, a ramp force varying from 50 N to 200 N in a rate of 10 N/s was applied by the actuator of the testing equipment to the top surface of the binder samples. The equivalent applied stress function was calculated from the division of the applied force by the cross-section area of the samples, i.e., 1.98  108 m2, and applied to the top edge of the virtual samples in the simulations. It is noteworthy that the top edge width was 19.8 mm, which corresponded to the diameter of the experimental testing samples. In the two-dimensional simulations, the thickness of the virtual samples was considered as unitary. The rotation and vertical displacements at the bottom edge were constrained, while only the displacements of the nodes at the lateral edges were constrained, and those were allowed to rotate. The vertical displacement at the top edge of the virtual samples was monitored and divided by the height of the virtual sample (24.3 mm) to calculate the corresponding strain history. Fig. 18 shows the displacements that the binder experienced for each aging condition after 15 s of simulation. As expected, the aged binder presented the lowest final displacement (Fig. 18b), given that it was the stiffest material. On the other hand, the microstructures of the virgin and of the rejuvenated binders (Fig. 18a and c, respectively) presented similar deformability, which was significantly higher than that of the aged binder. The difference between the deformability of the virgin and of rejuvenated binders has been already justified by the rejuvenator dosage strategy adopted by Osmari et al. [8]. Figs. 19 and 20 show comparisons between the results obtained in the laboratory and in the corresponding simulations for the different binder aging conditions. Fig. 20 shows the strain evolution with the testing time, while Fig. 20 shows the stress-strain relationship. The strong correlation between the numerical and the experimental results shown in Figs. 19 and 20 highlights two main facts:

1.6E-02

Deformation (mm/mm)

14

Numerical - virgin binder Experimental - virgin binder Numerical - aged binder

1.2E-02

Experimental - aged binder Numerical - rejuvenated binder

8.0E-03

Experimental - rejuvenated binder

4.0E-03

0.0E+00 0

5

10

15

Time (s) Fig. 19. Strain evolution curves resulting from the experimental tests and the corresponding simulations for the different binder aging conditions evaluated.

Fig. 20. Stress-strain curves resulting from the experimental tests and the corresponding simulations for the different binder aging conditions evaluated.

1. The objective of this research, which was the development of an experimental procedure for the determination of viscoelastic properties of microstructural components of asphalt binders was achieved with high degree of success; 2. The numericalexperimental microstructural modeling approach is an efficient tool and can be used to predict the mechanical behavior of complex and heterogeneous particulate composites, such as asphaltic materials. The in-depth understanding of the individual behavior of composite constituents made possible by the microstructural

Fig. 18. Vertical displacement after 15 s of simulation of the tests performed in the laboratory for different binder aging conditions: (a) virgin, (b) aged, and (c) rejuvenated.

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modeling may result in the optimization of the constituent selection and composite design activities and in the consequent fabrication of composites that are more resistant to loads actions and environmental agents.

that strong correlation also highlights the efficiency of the numerical-experimental microstructural modeling approach as an efficient tool that can be used to predict the mechanical behavior of complex and heterogeneous particulate composites, such as asphaltic materials.

5. Summary and conclusions

Declaration of Competing Interest

This research proposed the careful development of an experimental testing and analysis procedure for the determination of linear viscoelastic properties of asphaltic binder constituents from tests performed in the atomic force microscope (AFM). Using the heat cast method, samples of a PG 64-22 S binder in the virgin, aged, and rejuvenated conditions were fabricated and tested in the AFM in topographic scans to identify the geometric characteristics of the microstructural constituents of the binder. In this work, the microstructural constituents were referred to as phases and corresponded to white bee, black bee, periphase, and paraphase. Tests were also performed in the AFM for the determination of individual linear viscoelastic properties of each microstructural constituent. For that, a study was initially carried out to identify the load levels that ensured the linearity of the mechanical responses of the constituents. Next, nanoindentations at specific positions were performed. An additional statistical procedure was required to overcome challenges related to the calculation of creep compliance functions based on a constant representative area. From the results obtained, it can be concluded that:
AFM is a powerful testing tool for the identification of detailed microstructural characteristics of asphalt binder constituents;
Using a carefully-developed experimental procedure, such as the one proposed in this research, mechanical properties of binder microstructural constituents can be determined;
The microstructural binder constituents behave as viscoelastic materials, since their mechanical responses are functions of the loading time;
The microstructural constituents of the binders have individual viscoelastic properties, which vary with the aging condition;
The mechanical properties of the microstructural components of the binders are probably related to the chemical characteristics of these components. An additional study was carried out to demonstrate the validity of the creep compliance functions determined for each binder microstructural constituents at different aging conditions and to illustrate the applicability of the experimental procedure adopted in this research. For this, two sets of numerical simulations were conducted. First, the overall creep compliance of the binders was determined from simulations of their representative volume elements. In those simulations, the complex inner microstructural geometric characteristics of the binder components and their individual creep compliance functions (both determined from the AFM testing results) were used as model inputs. The overall creep compliance functions were then used as model inputs in the second set of simulations. For those, the binders were considered as homogeneous and linear viscoelastic materials. Boundary conditions were employed to simulate axial compressive tests performed in the laboratory using a servohydraulic MTS universal testing machine. The strong correlation between the numerical and experimental results indicates that the main objective of this work, i.e., the development of an experimental procedure for the determination of linear viscoelastic properties of asphalt binder microstructural components, was achieved with high degree of success. In addition,

The authors declared that there is no conflict of interest Acknowledgements This study was financed in part by the Brazilian Coordination for the Improvement of Higher Education Personnel (CAPES) Finance Code 001. The authors are grateful for the scholarships and the financial support received from the Brazilian National Council of Technological and Scientific Development (CNPq), from the Carlos Chagas Filho Foundation for Research Support in Rio de Janeiro (FAPERJ), from CENPES/PETROBRAS, and from the National Laboratory of Materials and Structural Models of the University of Costa Rica (LanammeUCR). References [1] L. Loeber, G. Muller, J. Morel, O. Sutton, Bitumen in colloid science: a chemical, structural and rheological approach, Fuel 77 (1998) 1443–1450, https://doi. org/10.1016/S0016-2361(98)00054-4. [2] A. Jäger, R. Lackner, C. Eisenmenger-Sittner, R. Blab, Identification of four material phases in bitumen by atomic force microscopy, Road Mater. Pavement Des. 5 (2004) 9–24, https://doi.org/10.1080/ 14680629.2004.9689985. [3] E.R. Dourado, R.A. Simão, L.F.M. Leite, Mechanical properties of asphalt binders evaluated by atomic force microscopy, J. Microsc. 245 (2012) 119–128, https:// doi.org/10.1111/j.1365-2818.2011.03552.x. [4] R.G. Allen, D.N. Little, A. Bhasin, Structural characterization of micromechanical properties in asphalt using atomic force microscopy, J. Mater. Civ. Eng. 24 (2012) 1317–1327, https://doi.org/10.1061/(ASCE) MT.1943-5533.0000510. [5] R.G. Allen, D.N. Little, A. Bhasin, R.L. Lytton, Identification of the composite relaxation modulus of asphalt binder using AFM nanoindentation, J. Mater. Civ. Eng. 25 (2013) 530–539, https://doi.org/10.1061/(ASCE)MT.19435533.0000615. [6] R.G. Allen, D.N. Little, A. Bhasin, C.J. Glover, The effects of chemical composition on asphalt microstructure and their association to pavement performance, Int. J. Pavement Eng. 15 (2014) 1–14, https://doi.org/10.1080/ 10298436.2013.836192. [7] P.K. Das, H. Baaj, S. Tighe, N. Kringos, Atomic force microscopy to investigate asphalt binders: a state-of-the-art review, Road Mater. Pavement Des. (2015) 1–26, https://doi.org/10.1080/14680629.2015.1114012. [8] P.H. Osmari, F.T.S. Aragão, L.F.M. Leite, R.A. Simão, L.M.G. Motta, Y.R. Kim, Chemical, microstructural, and rheological characterizations of binders to evaluate aging and rejuvenation, Transp. Res. Rec. 2632 (2017) 14–24, https:// doi.org/10.3141/2632-02. [9] C. Davis, C. Castorena, Implications of physico-chemical interactions in asphalt mastics on asphalt microstructure, Constr. Build. Mater. 94 (2015) 83–89, https://doi.org/10.1016/j.conbuildmat.2015.06.026. [10] I. Menapace, E. Masad, A. Bhasin, D. Little, Microstructural properties of warm mix asphalt before and after laboratory simulated long-term ageing, Road Mater. Pavement Des. 16 (2015) 2–20, https://doi.org/10.1080/ 14680629.2015.1029692. [11] Y. Veytskin, C. Bobko, C. Castorena, Nanoindentation and atomic force microscopy investigations of asphalt binder and mastic, J. Mater. Civ. Eng. 28 (2015) 1–16, https://doi.org/10.1080/10298436.2014.993393. [12] J.-F. Masson, V. Leblond, J. Margeson, Bitumen morphologies by phasedetection atomic force microscopy, J. Microsc. 221 (2006) 17–29, https://doi. org/10.1111/j.1365-2818.2006.01540.x. [13] J.P. Aguiar-Moya, J. Salazar-Delgado, V. Bonilla-Mora, E. Rodríguez-Castro, F. Leiva-Villacorta, L. Loría-Salazar, Morphological analysis of bitumen phases using atomic force microscopy, Road Mater. Pavement Des. 16 (2015) 138– 152, https://doi.org/10.1080/14680629.2015.1029672. [14] R.A. Tarefder, A.M. Zaman, W. Uddin, Determining hardness and elastic modulus of asphalt nanoindentation, Int. J. Geomech. 10 (2010) 106–116, https://doi.org/10.1061/(ASCE)GM.1943-5622.0000048. [15] D. Jelagin, P.L. Larson, Measurement of the viscoelastic properties of bitumen using instrumentes spherical indentation, Exp. Mech. 53 (2013) 1233–1244, https://doi.org/10.1007/s11340-013-9725-6. [16] Y. Veytskin, C. Bobko, C. Castorena, Nanoindentation investigation of asphalt binder and mastic viscoelasticity, Int. J. Pavement Eng. 17 (2016) 363–376, https://doi.org/10.1080/10298436.2014.993393.

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