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The fracture process zone in asphalt mixture at low temperature

Xinjun Li a,*, Mihai Marasteanu b

a Turner-Fairbank Highway Research Center, Federal Highway Administration, 6300 Georgetown Pike, McLean, VA 22101, USAb Department of Civil Engineering, 500 Pillsbury Drive S.E., University of Minnesota, Minneapolis, MN 55455, USA

a r t i c l e i n f o

Article history:Received 13 July 2009

Received in revised form 15 February 2010

Accepted 19 February 2010

Available online 24 February 2010

Keywords:

Asphalt mixture

Fracture process zone

Acoustic emission

Micro-crack

Cohesive zone model

a b s t r a c t

The fracture process zone (FPZ) is a key factor to mechanistically characterize materialfracture. This study investigates the FPZ of asphalt mixture at low temperature. The frac-

ture process under a semi-circular bend (SCB) test of seven asphalt mixtures that represent

a combination of different factors was monitored using an acoustic (AE) system with eight

piezoelectric sensors. The size of FPZ was estimated by locating micro-cracks that corre-

spond to 95% AE energy before peak load in the vicinity of the initial crack tip. The exper-

imental data illustrates the significant influence of test temperature on the behavior of the

asphalt mixture. Comparison results showed that the size of the FPZ significantly depends

on air voids and aggregate type, but is less depend on the asphalt content. It was found that

at a very low temperature, different loading rates produced very close FPZ, both for the

width and length. No obvious difference was observed on the width of the FPZ for the three

different initial notch lengths, whereas the length of the FPZ was found significantly

increases with the decrease of the notch length. The size of FPZ was also numerically esti-

mated for one case with the cohesive zone model (CZM) calibrated by experimental data

from the same SCB test. The FPZ size obtained with both methods agrees reasonably witheach other.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

As one of the primary distress modes of asphalt pavements built in the northern climates, low temperature cracking re-

sults in accelerating the deterioration of an asphalt pavement and coincidentally requires maintenance sooner than antici-

pated. Numerous research efforts based on empirical or theoretical methods have been done in the past decades to better

understand the mechanism of this distress and to select materials with improved fracture resistance. By developing exper-

imental protocols or phenomenological models, these research efforts require laboratory tests to determine the material

properties to describe the crack initiation and propagation in an asphalt pavement. The size of the fracture process zone

(FPZ) is a key factor in predicting failure and in selecting the geometry and dimensions of the test specimen. Furthermore,

the process zone size is particularly useful in the numerical simulation of fracture using phenomenological and microme-

chanical models such as the cohesive zone model (CZM) [13]. Therefore, the experimental observation of the process zone

size at a micro level is helpful in calibrating the phenomenological model and improving the accuracy of the simulation.

As a well documented and widely used tool, acoustic emission (AE) methods can be used to characterize the microscopic

fracture processes and therefore to evaluate damage growth in asphalt materials. This method was successfully applied in

understanding the relation between the micro-structural events and the macroscopic performance for the asphalt materials

[412]. In addition, this method was also employed by researchers to study the FPZ during fracture test for various materials.

0013-7944/$ - see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.engfracmech.2010.02.018

* Corresponding author. Tel.: +1 202 493 3089.

E-mail address: [email protected] (X. Li).

Engineering Fracture Mechanics 77 (2010) 11751190

Contents lists available at ScienceDirect

Engineering Fracture Mechanics

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n g f r a c m e c h
http://dx.doi.org/10.1016/j.engfracmech.2010.02.018mailto:[email protected]://www.sciencedirect.com/science/journal/00137944http://www.elsevier.com/locate/engfracmechhttp://www.elsevier.com/locate/engfracmechhttp://www.sciencedirect.com/science/journal/00137944mailto:[email protected]://dx.doi.org/10.1016/j.engfracmech.2010.02.018


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Zietlow and Labuz [13] investigated the intrinsic process zone in rock materials using AE. Specimens from four different rock

types with various grain sizes with a smooth boundary (no notch) were tested in three-point bending. The area that contains

90% of the events that occurred between the beginning of localization (determined to be at 98% load ratio) and snap-back

was considered as the intrinsic process zone. The size of this process zone was found to vary significantly with the grain size

of the material. An approximately linear relation was found between the width of the process zone and the logarithm of the

grain size. Otsuka and Date [14] investigated the behavior of the fracture process zone in concrete materials with various

maximum aggregate size using X-rays and AE techniques. The energy of each individual AE event was calculated and the

area of AE events where more than 95% of the total AE energy occurred before the peak load was referred to the fracture

process zone. Research results showed that, as the loading increases, a zone consisting of numerous micro-cracks accompa-

nied by AE events developed ahead of the notch tip in the specimen. It was also found that the width of the process zone

increased with the increase of the maximum aggregate size, but the length of this zone decreased with the increase of

the maximum aggregate size.

The objective of this research is to investigate the size of the FPZ in asphalt mixtures at low temperatures. Seven asphalt

mixtures combining different factors such as aggregate type, air voids and asphalt content were performed fracture testing at

low temperature with the semi-circular bending (SCB) configuration. The fracture test was also performed using three dif-

ferent loading rates and three different notch lengths to evaluate the influence of the loading rate and notch length. The frac-

ture process of the SCB specimen was monitored using an AE system with eight channels of recording. The approach used by

Otsuka and Date [14] was used in this research to determine the process zone in the fracture test. The effect of various factors

on the FPZ was evaluated by comparing the size of the FPZ. The size of FPZ was also estimated with the CZM calibrated by the

experimental data from SCB and indirect tension test (IDT). The FPZ obtained from the AE method was compared with that

from the CZM method.

2. Laboratory experiment

2.1. Materials and sample preparation

This study was designed to contain a combination of factors expected to have a significant effect on the fracture proper-

ties of asphalt mixtures, and the test matrix is shown in Table 1.

In this study, three asphalt binders with two performance grades (PG) 58-28 and 64-28 were used. PG 58-28 binder was

plain, while PG 64-28 binder was plain or styrene butadiene styrene (SBS) modified. Two different types of aggregate, granite

and limestone, known to have different mechanical and physical properties, were used to prepare the mixtures. The nominal

maximum aggregate size is 12.5 mm. Two levels of air voids, the design value of 4% and 7% representing typical as-con-

structed values, were chosen to study the effect of air voids on fracture properties for further improvement in construction

practice and performance prediction modeling. Two levels of asphalt content, the design value and the design value plus0.5%, were selected to quantify the effect of binder content (and film thickness) on the fracture properties. All mixtures were

gyratory compacted using the Superpave design procedure outlined in SP-2 [15].

Table 1 identifies all seven mixtures. The first part of the identification is the high limit of the binder PG grade, while the

second part represents the modification: P and S are plain and SBS, respectively. The third part is the air voids: 4% and 7%. The

fourth part of the mixture identification is the aggregate type: G and L are granite and limestone, respectively. The fifth part

is present only for the mixtures with the design plus 0.5% asphalt content. For example, 58:P:4:G identifies the mixture pre-

pared with PG 58-28 plain binder, 4% air voids, granite aggregate and optimal design asphalt content.

Two aggregate gradations were prepared based on the aggregate type and are shown in Table 2. These two gradations

were prepared as close as practically possible in an effort to eliminate additional factors that can affect the results. Two de-

sign asphalt contents were used in the mix design: 6.0% for granite mixtures and 6.9% for limestone mixtures and correspond

to an effective binder content of 5.39% and 5.37% for the granite and limestone mixtures, respectively.

For all seven mixtures, cylindrical specimens with 150 mm in diameter and 177 mm in height were compacted using the

Superpave gyratory compactor in the laboratory. The actual air voids for all mixtures are in the range of 1% target air voids.Each of the cylinders was cut symmetrically from the middle of the specimen into two SCB slices with 25 mm each in height.

Table 1

Mixture identification and factor combinations.

Mixture ID Binder and modifier Air voids Asphalt content Aggregate Test temperature, C

4% 7% Design Design+0.5% Granite Limestone

58:P:4:G PG58-28 Plain X X X

58:P:4:G+0.5 X X X

58:P:4:L X X X 6

58:P:4:L+0.5 X X X 18

58:P:7:L X X X

64:P:4:L PG64-28 Plain X X X 30

64:S:4:L PG64-28 SBS X X X

1176 X. Li, M. Marasteanu/ Engineering Fracture Mechanics 77 (2010) 11751190


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The SCB slice cut from cylinders was symmetrically cut into two semi-circular bend samples with an original notch with

15 mm in length and 2 mmin width. In order to investigate the influence of the notch length on the fracture properties, spec-

imens with two additional notch lengths of 5 mm and 30 mm were prepared for mixture 64:S:4:L. IDT specimens with

50 mm thick and 150 mm diameter were cut from the gyratory compacted cylinders for mixture 58:P:4:G+0.5.

The three test temperatures were determined based on the PG low limit of the asphalt binder as follows: temperature

level 1 (TL): 12

below TM; temperature level 2 (TM): binder PG + 10

C; temperature level 3 (TH): 12

above TM. In this study,for the PG -28 the temperatures are as follows: TL =30 C, TM =18 C, TH =6 C.

2.2. Semi-circular bending test

The SCB test setup is shown in Fig. 1. An MTS servo-hydraulic testing system was used to perform the tests. The samples

were symmetrically supported by two fixed rollers and had a span of 120 mm. Teflon tape was used to reduce the friction

from the two rollers. The indirect tension test loading plate was used to load the SCB specimens. The load line displacement

(LLD) was measured using a vertically mounted Epsilon extensometer with 38 mm gauge length and 1 mm range; one end

was mounted on a button that was permanently fixed on a specially made frame, and the other end was attached to a metal

button glued to the sample. Crack mouth opening displacement (CMOD) was recorded by an Epsilon clip gauge with 10 mm

gauges length and a +2.5 and 1 mm range. The clip gauge was attached at the bottom of the specimen. The CMOD signal

was used as the control signal to maintain the test stability in the post-peak region of the test. A constant CMOD rate of

0.0005 mm/s was used and the load and LLD (Pu) were recorded. A maximum contact load of 0.3 kN was applied beforethe actual loading to ensure uniform contact between the loading plate and the specimen. Testing ceased when the load

dropped to 0.5 kN in the post-peak region.

Table 2

Gradations for all mixtures.

Sieve size (mm) Percent passing

Granite Limestone

19 100 100

12.5 95.2 97.2

9.5 83.5 79.1

4.75 65.2 59.6

2.36 47.1 48.6

1.18 33.4 38.6

0.60 23.8 28.8

0.30 12.5 16.9

0.15 7.0 9.2

0.075 5.1 5.4

CMOD

Notch

LLD

Data

Acquisition

AE

SCB

Button

Frame

AE

Acquisition

Fig. 1. Schematic of experimental setup.

X. Li, M. Marasteanu/ Engineering Fracture Mechanics 77 (2010) 11751190 1177


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All tests were performed inside an environmental chamber. Liquid nitrogen tanks were used to obtain the required low

temperature. Prior to testing, the SCB samples were kept in the environmental chamber at the test temperature for 2 h to

avoid any temperature gradient within the sample. The temperature was controlled by MTS temperature controller and ver-

ified using an independent platinum RTD thermometer.

In order to study the influence of loading rate upon the fracture properties, mixture 64:P:4:L was tested using two addi-

tional loading rate (0.00015 mm/s and 0.005 mm/s). In addition to a notch length of 15 mm, mixture 64:S:4:L was tested

with two additional initial notch lengths of 5 mm and 30 mm to investigate the influence of the initial notch length on

the fracture properties. All these tests were performed with the same test procedure as described above.

2.3. Indirect tension (IDT) strength test

The mixture 58:P:4:G+0.5 was also performed the IDT strength test to obtain the parameters for the numerical simula-

tion. In the IDT test, a cylindrical specimen was loaded at TL(30 C) in compression across a diametral plane, similar to the

splitting tension test, also known as the Brazilian test. The strength test determined the tensile strength of a specimen by

loading the specimen at a constant rate of 12.5 mm/min until failure. The specimen dimensions and peak load were then

used to calculate the failure strength.

2.4. AE testing

During the SCB fracture testing, the AE event signals were recorded using four DAQ cards (Model PCI-5112, National

Instruments). Each card had two independent channels which acquired AE signals detected by eight piezoelectric sensors

(Model S9225, Physical Acoustics Corporation). Four sensors were mounted on each side of the specimen using M-Bond

200, a modified alkyl cyanoacrylate. The pre-amplification of the AE signals was provided by eight preamplifiers (Model

1220C, PAC) with a gain set to 40 dB. One of the sensors was used as a trigger, which was often the one closest to the tip

of the initial notch. The trigger level was set at 10 mV in this research. Once the recording was triggered, signals were

band-pass filtered (0.11.2 MHz) and sampled at 20 MHz over 200 ls. Considering the ringing of the resonant sensor, a sleep

time of 9 ms between two consecutive events was prescribed during which the system could not be triggered. The velocity of

propagation of the longitudinal waves was determined by generating an elastic wave by pencil lead (0.5 mm diameter)

breakage on the opposite side of the samples.

The source location of the AE events can be inferred by investigating the differences of the first time of arrival among the

transducers placed at different locations on the specimen. Therefore, it is necessary to determine the arrival time of the elas-

tic waves for each sensor from the recorded AE event. This can be done by measuring the time at which the signal passes a

preset threshold values for each sensor. An algorithm was developed successfully to calculate the AE event source and the

test result from pencil lead breakage indicated an accuracy of 13 mm for travel distances around 100 mm.

An acoustic emission is generated by the sudden release of energy from localized damage processes. The measurement of

this energy release can thus be related to the fracture resistance of materials. The energy of an electrical signal is propor-

tional to the square of the voltage [16,17] and can be computed using the following equation:

Ei

Ztae

0

V2it dt

where Ei is the AE energy for channel i, Vi the recorded voltage transient for channel i, and tae is the duration of the event for

channel i.

3. Results and discussion

3.1. Mechanical testing results

For the SCB fracture test, the load and the LLD were recorded and the data was used to plot the loaddisplacement curve.

A typical plot of loading versus LLD for three test temperatures is shown in Fig. 2. All seven mixtures investigated exhibited a

similar change in behavior with temperature and loading. At higher low temperature (TH), asphalt mixtures are more duc-

tile and have lower peak loads and larger displacements. At the lowest temperature ( TL), mixtures are brittle and have high

peak loads, and small deformation ability. At the middle low temperature TM, mixtures exhibited an intermediate behavior

between TH and TL.

All mixtures also exhibited a similar trend in the recorded AE events. Limited events were recorded at the higher test tem-

perature and the number of events increased significantly at the lower test temperature. Specifically, a number between 79

and 1008 events were recorded for all seven mixtures tested at 6 C, a number between 1008 and 3025 at 18 C, and

events between 4275 and 6572 were recorded at 30 C. This can be explained by the fact that the asphalt binder displays

viscous and ductile behaviors at higher temperatures and the development of defects is gradual and does not produce emis-

sions that can be detected [4]. A representative plot of AE event with LLD is shown in Fig. 3.



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It can be seen fromthe Fig. 3 that the occurrence of the event before 30% (1 kN) of peak load is negligible and there is very

little change of the AE event accumulation curve. This illustrates that very little or no actual intrinsic damage occurs in this

period. The slope of the event accumulation curve increases until the load approaches the peak load, indicating a faster mi-

cro-crack rate with load increase. The steepest slope in the event accumulation curve occurs between the peak load and

around 50% (1.6 kN) of the peak load in the post-peak region, which indicates that the micro damage occurs very quickly.

When the specimen is in the softening region due to the formation of the critical crack, the event occur rate decreases.

The corresponding source location of the sample shown in Fig. 3 is given in Fig. 4 that plots the location for all recorded

events. For the SCB specimen with initial notch, the crack initiated and propagated from the notch tip along the center line of

the sample. It should be noted that in some specimens the distribution of the events is skewed to one side; this is most likely

due to the non-homogeneity of the test specimens, although substantially more testing is required to validate this statement.

3.2. Fracture process zone (FPZ) size

The approach used by Otsuka and Date [14] was also used in this research to investigate the process zone in the asphalt

mixture specimen. The AE energy for each event was calculated as the integral of the signal amplitude square during the

event duration. Most events had very little energy, which means that these events may contribute very little to the fracture

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Load line displacement (mm)

Load(kN)

TH

= -6 C

TM = -18 C

TL = -30 C

Fig. 2. Typical plot of loading and load line displacement.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.1 0.2 0.3 0.4

Loading Line Displacement (LLD) (mm)

EventCount

0

1000

2000

3000

4000

5000

6000

Load

(kN)

Fig. 3. Typical plot for AE event and load with LLD.



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of the material. To better understand the distribution of the AE energy during the loading process, it is desirable to setup

energy levels and to investigate the distribution of the event number and of the energy sum for these levels. An example

of the distribution of the event number and energy accumulation over the entire loading cycle with four energy levels is gi-ven in Table 3. The four energy levels expressed in relative units are as follows: E1 = 0.05, E2 = 0.60, E3 = 1.5 and E4 = 2.30.

It can be seen that approximately 54% of all events have energy levels less than 0.05 relative units and contribute only

4.6% to the total AE energy, while 3.3% of all events have energy levels above 2.3 relative units and contribute about 40%

of the total energy. From the previous analysis, AE energy release is associated with the initiation and propagation of the

fracture. The distributions of the AE events and AE energy can be used to study the initiation and propagation of the mi-

cro-cracks and the formation of the fracture plane.

The process zone of the material under the testing condition can also be estimated from the distribution of the AE energy

for the AE events occurring before the peak load. Using the same four energy levels used for Table 3, the distribution of the

event count and energy accumulation before peak load is computed and shown in Table 4. The source location of these

events is shown in Figs. 58. Fig. 5 shows the source location for the events with AE energy higher than E4, and Figs. 68

show the source location of events with AE energy higher than E3, E2 and E1, respectively.

The above figures indicate that the higher energy events tend to localize near the neutral line within the specimen where

the ultimate fracture area is formed. As a result, it was considered that these events are related directly to the fracture of theasphalt mixture and this area, in which approximately 95% of the total AE energy sum before peak load is released, can be

assumed as a fracture process zone. A rectangle, as contains 90% of these events, was drawn to represent the fracture process

zone determined by this method. For the asphalt mixture from 58:P:4:G+0.5 tested at 30 C and shown above, the fracture

process zone is about 58 mm in width and 3035 mm in length.

0

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Notch

Fig. 4. Typical location plot for all events.

Table 3

Event number and energy distribution with energy levels for the entire loading process.

Event count % of total event count Energy sum, relative unit % of total energy sum

>E4 187 3.3 662.4 39.7

>E3 320 5.6 912.6 54.8

>E2 667 11.7 1248 74.9

>E1 2595 45.6 1609.2 96.5

E4 17 2.1 64.5 33.7

>E3 31 4.0 90.9 47.5

>E2 78 10.0 135.1 70.6

>E1 336 43.0 183.3 95.8


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It is noted that the process zone reported in this research is relatively large compared to the ligament in the SCB speci-

men. More research is therefore needed to further validate the findings of this study by testing specimens with much larger

fracture ligaments.

3.3. Effect of factors on process zone size

It is generally agreed that as a material parameter, the size of fracture process zone may be dictated by many factors such

as the inhomogeneities due to the grain size and preexisting cracks or voids in the material. Therefore, the identification and

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Notch

Fig. 5. Location of events with AE energy levels >E4 that represents 34% of the energy sum before peak load.

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Notch


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evaluation of the factors significantly affecting the characteristics of this localized zone are of importance in predicting fail-

ure and in selecting the geometry and dimensions of the standard test specimen.

Under the method discussed above, the fracture process zone is assumed to be the zone located by the AE events corre-

sponding to 95% AE energy before peak load. With this approach, the process zone size is obtained for mixtures with differentfactors such as aggregate type, asphalt content, air voids and different loading conditions and initial notch length to inves-

tigate their effects on the size of this zone.

3.3.1. Effect of temperature on FPZ size

It is well recognized that asphalt mixtures are very temperature dependent materials. Temperature plays a significant

role with respect to the behavior of the asphalt materials. Therefore, it is of interest to investigate the effect of temperature

on the fracture process zone size.

Two typical plots that represent the FPZ at two different temperatures, the TM and TL, are shown in Figs. 9 and 10 for mix-

ture 58:P:4:G+0.5. At the highest temperature (TH) very limited events were recorded and the FPZ could not be determined.

The comparison of the FPZ for the two temperature levels shows that there is no obvious difference with the width but

the process zone is about 8 mm shorter at the temperature level TM than at the temperature level TL. This is unexpected con-

sidering the development of FPZ is an energy dissipation zone and it is responsible for an increase in toughness at a lower

temperature when the material is more brittle. One possible explanation for this unexpected behavior can be the fact thatthe asphalt material is more viscous and ductile at higher temperatures and the development of defects is gradual and does

not produce emissions that can be detected. This also explains the fact that substantially more AE events were recorded at TLthat at TM, as is shown in previous section.

Due to the unexpected results for different temperatures, the comparison and discussion in the following sections are un-

der the same and lowest temperature TL(30 C), at which the asphalt materials are considered to be very brittle.

3.3.2. Effect of aggregate on FPZ size

Two aggregates were evaluated in this research: granite and limestone. The plots shown as Figs. 10 and 11 represent the

FPZ for two mixtures prepared with granite and limestone, respectively. Fig. 10 represents mixture 58:P:4:G+0.5, while

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Process Zone

Notch


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30

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55

6065

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch

Fig. 9. Process zone for 58:P:4:G+0.5 at TM.



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Fig. 11 represents mixture 58:P:4:L+0.5. The comparison of the FPZ size shows that the lengths of the FPZ from these two

mixtures are very close. However, the FPZ of the mixture prepared with limestone is approximately 5 mm wider than that

of the mixture with granite. The narrower FPZ from the mixture with granite aggregate means that the micro-cracking oc-curred in a smaller area ahead the preexisting crack tip before the crack began to propagate.

Differences between the two aggregate types are also found from both tests by visual inspection of the fracture surface

after testing, as shown in Fig. 12. No obvious difference was observed between the fracture surfaces at the high temperature.

However, at the two lower temperatures, visual observations indicate that a significant portion of the fracture passes

through the aggregate particles in the limestone mixture while the crack passes through the interface between the mastic

and the aggregate in the granite mixture. This indicates that the granite aggregate has a greater crack resistance at lower

temperatures than does the limestone aggregate.

3.3.3. Effect of air voids on FPZ size

It is believed, but not well-documented, that the air voids in the asphalt mixtures is one of a major factors that affect the

size of the FPZ. Figs. 13 and 14 plot the FPZ for the 4% air voids and 7% air voids, respectively. The comparison result shows

that the mixture with 7% air voids has a much bigger FPZ than the mixture with 4% air voids. This illustrates that the micro-cracking occurred in a much bigger area ahead the crack tip in the mixture with more air voids before the peak load. In other

words, the material with higher air voids was more damaged at the micro scale level due to higher air voids.

3.3.4. Effects of asphalt content on FPZ size

The comparison of the FPZ for the mixtures with two different asphalt contents was also performed in this research.

Fig. 15 plots the FPZ for mixture prepared with the optimum asphalt content, while Fig. 10 is the plot for mixture with

the optimum asphalt content plus 0.5%. It can be seen that there is no obvious difference in the FPZ size between the two

asphalt contents.

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch

Fig. 10. Process zone for 58:P:4:G+0.5 at TL.

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Process Zone

Notch

Fig. 11. Process zone for 58:P:4:L+0.5 at TL.



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3.3.5. Effect of loading rate on FPZ size

In order to investigate the influence of the loading rate on the FPZ size, the figures that plot the FPZ for the three loading

rates studied in this research are shown in Figs. 1618. These three figures show the result for three CMOD rates,

0.00015 mm/s, 0.0005 mm/s and 0.005 mm/s, respectively. The data in these figures is from mixture 64:P:4:L and at the tem-

perature level TL.

Fig. 12. Typical fracture surfaces for mixtures with different aggregate.

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Process Zone

Notch

Fig. 13. Process zone for 58:P:4:L at TL.

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Process Zone

Notch

Fig. 14. Process zone for 58:P:7:L at TL.



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The recorded event number is significantly different for different loading rate at the lowest temperature level. Slower

loading rate resulted in longer testing time and more AE events were collected. However, no obvious difference with the

FPZ size can be observed from the testing data. The limited data obtained in this study appears to confirm the conclusion

that the fracture process zone is a property of the material. However, substantially more testing is required to validate this

statement.

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Process Zone

Notch

Fig. 15. Process zone for 58:P:4:G at TL.

0

5

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15

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25

30

35

40

45

50

55

6065

70

75

-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch

Fig. 16. Process zone for 64:P:4:L at TL and loading rate of 0.00015 mm/s.

0

5

10

15

2025

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch




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3.3.6. Effect of notch length on the FPZ size

The fracture process zone for the samples with different initial notch lengths was also investigated. Figs. 1921 represent

the FPZ at the temperature level TL

for notch length of 5 mm, 15 mm and 30 mm, respectively.

The results show that there is no obvious difference in the width of the FPZ for all three different notch lengths. However,

the length of the FPZ significantly changes with the notch length. The general trend is the shorter notch length, the longer

FPZ. Specifically, the length of the FPZ for the sample with 5 mm notch length is around 47 mm, 40 mm for the sample with

0

5

10

15

20

2530

35

40

45

50

55

60

65

70

75

-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch

Fig. 19. Process zone for 64:S:4:L at TL and 5 mm notch length.

0

5

10

15

20

25

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40

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6065

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-75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75

Process Zone

Notch




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15 mm notch length, and 25 mm for the sample with 30 mm notch length. It should be noted that the length of the FPZ is

large compared to the specimen ligament, especially for the geometry with 30 mm long notch, and therefore testing on spec-

imens with much larger ligaments is necessary for further study.

4. Numerical simulation of FPZ

4.1. Cohesive zone model

Cohesive zone model (CZM) has been constructed based on the LeonovPanasyuk [18]Dugdale model [19] and are suc-

cessfully applied to simulating the fracture behavior of various engineering materials. Just as in the LeonovPanasyukDug-

dale model, so in the cohesive zone model, only an additional parameter characterizing the length of the plasticity zone or

that of the cohesive zone, was introduced. Using information of fractal fracture in the cohesive zone model [20] does not

affect the fact of the matter because only the cohesive zone length increases and no other parameter is introduced. The Leo-

novPanasyukDugdale model, as well as the cohesive zone model use Khristianovichs hypothesis [21], as is concerned with

the absence of singularity at the crack tip. The classical fracture mechanics can not handle infinitely large magnitudes. When

this hypothesis is used, all solutions comprising singularity are excluded from consideration. However, if one uses the Neu-

berNovozhilov approach [22,23], then the class of solutions for solid with a structure can be extended if the integrable sin-

gularity is present. Following the NeuberNovozhilov approach, Kornev [24,25] proposed some new model which extended

the class of solutions and used both the length and width for description of the process zone.

Since the cohesive crack concept was proposed, large amount of literatures on the application of CZM have been accumu-

lated. Needleman [26] developed an interface element to implement the cohesive zone into finite element computation

frame. In asphalt area, Souza et al. [27] applied the cohesive zone model to predicting the damage evolution in an indirect

tension test (IDT) specimen of viscoelastic asphalt mixture, and Paulino et al. [2] modeled the fracture behavior of a simply

supported beam. Li and Marasteanu [3] have applied the cohesive zone model to a semi-circular bend (SCB) specimen and

extensively investigated the low temperature cracking of asphalt mixtures. An algorithm has been developed to calibrate the

CZM specifically for the tested asphalt mixture and the numerical simulation has shown good agreements with experimental

data.

In the concept of a cohesive crack, the physical fracture is ideally localized into a small zone defined by two imaginary

surfaces and the bulk material outside this zone is still undamaged. The traction can be transferred across these two surfaces.

Once the traction at certain location (point A) along the cohesive crack exceeds the prescribed threshold, these two surfaces

start to open and crack initiates at point A numerically. The damage is considered to start accumulating at point A. However,

point A does not correspond to the physical crack tip, where no or negligible traction could be transferred across the crack.

Therefore, point A should only be related to the nucleation of micro-crack and the softening of material. As load increases,

the separation increases and the traction decreases and finally vanish at point A. This time point A can indeed be deemed as

the physical crack tip at which no traction should be transferred. At the same time, there is a point B along the cohesive crack

and some distance away from point A has just reached the prescribed threshold and start softening due to micro-cracking.

The range between points A and B along the cohesive crack corresponds to a zone full of micro-cracks but not complete sep-

aration, which meets the definition of FPZ of a crack.

Three material parameters, cohesive energy potential (U), traction (T) or cohesive strength (r) and separation (D) of the

two virtual surfaces or separation displacement (d) are needed for the CZM. The traction, as acting on the crack surfaces,

changes non-linearly with the change of the separation of the two virtual surfaces and the three parameters are related

in the form

0

5

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Process Zone

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T@U

@D

It should be noted that only two of the three parameters are independent. The traction and separation of the crack are

difficult parameters to measure and are therefore usually obtained from mathematical formulations. The TD curves were

described by various functions including exponential, polynomial and bilinear forms. In this research, an exponential form of

the cohesive energy potential is used to describe the non-linear behavior of the asphalt material in the form

T exp1T0D

Dcexp

D

Dc

where T0 and Dc are the peak traction of the material and the critical normal separation when the normal traction is

equal to T0, respectively. The implementation of an exponential CZM is shown in Fig. 22. It should be noted that the trac-

tion and separation are normalized by T0 and Dc, respectively. The cohesive crack is implemented into finite element

analysis through a zero-thickness interface element. A 2-D four-node interface element was formulated. The model using

this interface element was tested by the analytical solutions on an elastic double cantilever beam. The details are referred

to Li and Marasteanu [3].

4.2. Simulation results

In the cohesive zone model, three materials parameters were used: the fracture energy, the peak traction and the critical

separation corresponding to the peak traction. Given any two of them, the third parameter can be derived. The fracture en-

ergy was calculated from the SCB test using the RILEM (Runion Internationale des Laboratoires et Experts des Matriaux)

Technical Committee TC 50-FMC method [28]. The peak traction is related to material tensile strength, while the critical sep-

aration could not be measured. To better present the fracture behavior in asphalt materials, the CZM parameters were cal-

ibrated with respect to the experimental data. Since the peak traction is related to material strength, which can be estimated

from the IDT, it is more convenient to calibrate the peak traction than the characteristic separation.

In this study, only one mixture, 58:P:4:G+0.5, was simulated at the lowest temperature of 30 C. Tensile strength and

modulus was calculated from the IDT strength test as 20 GPa and 4.99 MPa, respectively. The fracture energy was calculated

from the SCB test as 555 J/m2. The peak traction was varied with the fixed fracture energy from experiments and the sim-

ulated loaddisplacement curve was compared to the experimental one. The closest comparison resulted in the best calibra-

tion of the CZM. As shown in Fig. 23, the simulated and experimental determined loaddisplacement curves agree very well.

As the result, the calibrated traction was 60% of the tensile strength measured with IDT test.

The tractions along the whole cohesive crack were monitored during the entire fracture process. When the traction at the

initial crack tip increased to the peak traction and then decreased to 10% of this value, the distance between the initial crack

tip and the point at which the traction equals to the peak traction was measured and considered as the length of FPZ. The

data showed the simulated FPZ was 34.8 mm long, while the experimental determined FPZ was 33 mm long based on AE

energy method.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6 7 8 9

Normalized Separation

NormalizedTra

ctionCohesive Zone

Crack Tip

0

Traction

(a) (b)

Fig. 22. (a) Concept of cohesive fracture at a crack tip and (b) exponential traction-separation relationship for cohesive crack.



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4.3. Discussion

The numerically determined FPZ reasonably agreed with the experimental determined FPZ. This indicated that the cali-

brated CZM can predict not only the loaddisplacement curve, but also the size of FPZ. The consistency of CZM in estimating

two aspects of fracture behavior approves the effectiveness of CZM in describing the essence of fracture phenomenon and

validates the calibration procedure of CZM parameters.

However, the discrepancy exists between the simulation and experiment. This can be partly explained from two aspects.

First, the numerical simulation can only provide the results at the end of each step. The simulated length of FPZ is then af-

fected by the step length and the size of the mesh. Smaller step and finer mesh are expected to lead to more accurate sim-

ulated length. Second, given the concept of CZM, there is no thickness of a cohesive zone and thus all physical fracture should

be concentrated only along the crack. Obviously, this is not completely true. From the location of micro-cracks located by AE

technique, the physical fracture was distributed within a band around of the macro-crack instead of a non-thickness line.

Consequently, the FPZ should have certain width as shown in the experimental data. However, this feature cannot be effec-

tively described by the CZM.

Finally, the size of FPZ was around 30 mm from both experiment and numerical computation. Compared with the dimen-

sions of most geometries employed in fracture tests in asphalt materials, e.g. the single edge notched beam, the compact

tension disc, and the IDT specimen, this FPZ is large enough to invalidate the direct application of linear elastic fracture

mechanics (LEFM). It should be cautious to explain LEFM results and it is necessary to employ non-linear fracture mechanics

and investigate the size effect on the determination of fracture resistance of asphalt mixtures in laboratory, as shown by

Wagoner and Buttlar [29].

5. Summary and conclusions

The fracture process zone, a key factor in predicting failure and in selecting the geometry and dimensions of the test spec-

imen, was investigated in asphalt mixtures at low temperature. Seven asphalt mixtures combining different factors such as

aggregate type, asphalt content and air voids were performed fracture testing at three low temperatures using the SCB geom-

etry. The effects of the initial notch length and the loading rate on the fracture properties were also investigated. An acoustic

emission system with eight channels of recording was used to monitor the failure process during the fracture testing.

The experimental data shows that test temperature strongly affects the behavior of the asphalt mixture. The amount of

recorded AE event significantly increases when the temperature decreases. The AE occurrence rate was also found to vary

with the loading during test procedure, in which the period between the peak load and around 50% of the peak load in

the post-peak region has the fastest micro-cracking occurrence rate.

The analysis on the AE event energy distribution shows that most events contribute negligibly to the total energy while a

small number of events make significant contribution. The fracture process zone was obtained using the event locations that

corresponds to 95% of total AE energy before peak. The experimental data obtained in this study illustrates that the fracture

process zone at a lower temperature is longer than that at a higher temperature, while there is no significant difference in the

width. This is unexpected and is possibly due to the viscous nature of asphalt material at higher temperature. Asphalt mix-

ture with limestone was found to have an obviously wider FPZ than that from mixture with granite. The mixture with 7% air

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5

Displacement (mm)

Load(N

/mm)

Experiment

Simulation

Fig. 23. Experimental and simulated loaddisplacement curve from a SCB test.



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voids was found to have substantially bigger FPZ than the mixture with 4% air voids. No obvious difference was found for the

mixtures with the two asphalt contents investigated in this research. The three loading rates employed in this study were

found to produce very close FPZ, both for the width and length. No obvious difference was observed on the width of the

FPZ for the three different initial notch lengths. However, it was found that the length of the FPZ significantly increases with

the decrease of the notch length.

The cohesive zone model was applied to simulating the fracture behavior and estimating the size of FPZ for one case. It

was found that the numerically determined FPZ shows reasonable agreement with experimentally determined FPZ. The cal-

ibrated CZM cannot only predict the loaddisplacement curve, but also estimate the size of FPZ. This consistent effectiveness

in describing two different aspects of fracture behavior validates the calibration procedure for CZM parameters. The limita-

tion of CZM and the numerical simulation determines the discrepancy between the numerically and experimentally deter-

mined FPZ.

It also should be noted that the process zone reported in this research is relatively large compared to the ligament in the

SCB specimen. More research is therefore needed to further validate the findings of this study by testing specimens with

much larger fracture ligaments.

Acknowledgements

This research was conducted at the University of Minnesota and was sponsored by Federal Highway Administration Na-

tional Pooled Fund Study 776. This support is gratefully acknowledged. The authors are also grateful with Dr. Xue Lis help in

the numerical simulation.

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