The effects of finely dispersed fillers on the fatigue performance ofasphalt binders and asphalt concrete mixes at relatively low tempera-tures are examined. A series of model binder systems containing glassspheres with narrow particle size distributions were used to study theeffect of filler particle size on the fatigue performance of the asphaltmastic. Two mastic systems containing ground limestone fillers, whichpossessed significantly different gradations, also were tested. Fatigueperformance was evaluated by applying a constant torsional strain toeach specimen in a dynamic rheometer at 10�C and 40 Hz. Testing atvarious strain levels allowed the relationship between fatigue life andstrain to be determined for the different systems. The results indicatethat as the particle size of the filler decreases, the fatigue life of theasphalt mastic increases. This observation is a direct result of the modeof fatigue failure in the asphalt mastics and is in agreement with Evans’stheory on crack pinning for failure in filled brittle solids. Constant stressasphalt concrete fatigue tests on both dense- and gap-graded systemsprepared with the two different ground limestone fillers show that theparticle size does not significantly affect the fatigue life of the mixes.These results also confirm that crack pinning is the major mechanismresponsible for improved fatigue performance.

Fatigue cracking can be classified as one of the four main distressesfor pavements in North America (along with rutting, low-temperaturecracking, and moisture damage). Fatigue is the result of a crack ini-tiation process followed by a crack propagation process, which mayeventually cause catastrophic failure throughout the pavement.However, the fatigue process is complex and not completely under-stood. Furthermore, a comprehensive micromechanical model doesnot yet exist to explain the effect of fine particulate fillers in theasphalt binder on fatigue performance.

The work in this paper expands on earlier research dealing withcrack pinning (1). Crack pinning is the term used for the mechanismby which inclusions in a multiphase composite material interactwith, and slow down, the progress of growing cracks. Previous workdealing with crack pinning in asphalt mastics has shown that thismechanism provides a good theoretical basis for explaining thetoughening effect induced by fillers in asphalt binders (1). The goalof this study is to investigate the effect of crack pinning on thefatigue performance of several model asphalt mastic and mix sys-tems containing different-sized fillers. Future research will focus onthe effect that filler particle size has on healing, rutting, and mois-ture damage in asphalt concrete. Ultimately, this knowledge can beused to develop asphalt mixes with superior performance propertiesunder all conditions.

BACKGROUND

Theoretical Treatments of Damage Evolution inMultiphase Materials

As discussed by Park (2), two general approaches are used to studythe behavior of a material with damage: a continuum approach anda micromechanical approach. In the continuum approach, the mate-rial under study is assumed to behave as a homogeneous body. Con-tinuum damage mechanics has been successfully used by Kim andcoworkers in modeling damage accumulation under cyclic loadingwith microdamage healing during rest periods (3). Using the elastic-viscoelastic correspondence principle and the work potential theory,the fatigue lives of several mixtures were predicted with very highaccuracy.

In micromechanical theories, the damage evolution is modeled ona much smaller scale. Evans’s 1972 paper on the crack-pinningmodel (4) is one of the earlier accounts and describes how macro-scopic quantities such as fracture toughness and fracture energydepend on microscopic variables such as interparticle distance, par-ticle size, and microcrack shape, size, and density. Micromechani-cal models are generally more complex than continuum damagetheories, but with this complexity comes a better ability to predictaspects of the failure process previously unknown to the researcher.In 1986, Schapery (5) developed a micromechanical model for pre-dicting effective viscoelastic stress-strain behavior and microcrackgrowth in particle-reinforced rubber. He used a so-called general-ized self-consistent scheme to predict growing microstructural dam-age in the composite. This mathematical model uses a damageparameter to characterize the magnitude of time-dependent micro-cracking within the composite. Since that time, there have beennumerous other publications with varying degrees of complexity.However, there are only a few papers in which micromechanicalmodels for asphalt systems are discussed (1, 6 ).

The 1996 publication by Garcés Rodríguez et al. (1) shows thatEvans’s theory on crack pinning can predict the plane-strain fracturetoughness for asphalt mastics at low temperatures. The goal of thispaper is to further the understanding of this model through fatiguetesting of asphalt mastics and mixes in order to be able to predict theeffect of filler particles on the fracture properties of asphalt mixes.

Crack Pinning

Asphalt binders behave as brittle thermoplastic materials when sub-jected to low temperatures and high rates of loading (1). Thisbehavior can cause the material to fracture relatively easily under

Crack Pinning in Asphalt Mastic and ConcreteRegular Fatigue Studies

Benjamin J. Smith and Simon A. M. Hesp

Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6,Canada.

Transportation Research Record 1728 ■ 75Paper No. 00-1233

applied mechanical or thermal stresses because the energy-absorbingprocesses only operate in a highly localized region around the cracktip (7, pp. 434–452). The addition of a second particulate phase tothe brittle matrix causes the energy-absorbing mechanisms to oper-ate within a much greater volume of material rather than simplywithin the immediate vicinity of the crack tip (7, pp. 434–452).Thus, the amount of energy required for fracture to occur increases.

Crack pinning is the main mechanism by which filler particlesincrease the toughness of brittle matrices. Lange (8) first proposedthe crack-pinning theory in 1970 after reporting that the fractureenergy of an epoxy could be dramatically increased by the inclusionof rigid particulate filler. In 1972, Evans (4) expanded on Lange’swork and carried out a detailed investigation focusing on many dif-ferent aspects of the crack-pinning mechanism. According to thetheory, interactions between the moving crack front and the second-phase dispersion cause the fracture energy of the brittle matrix toincrease. As the crack front propagates through the multiphasematerial, the inclusions impede, or pin, the crack front, causing it tobow out between the obstacles (forming secondary semi-ellipticalflaws) until it breaks away from the pinning positions [see Figure 1(9, p. 45)]. In the initial stages of crack propagation, a new fracturesurface is formed and the length of the crack front is increasedbecause of the change of the crack shape induced when the front ispinned between obstacles. Energy is required to create the new frac-ture surface and, by analogy with the theory of dislocations, mustalso be supplied to the newly formed length of the crack front. Thefront is assumed to possess a so-called line energy (7, pp. 434–452).Evans developed an expression for the overall fracture energy, ΓIc,of the composite, which includes both energy terms as well as a termthat accounts for additional energy-absorbing mechanisms aroundthe particles in the brittle matrix (4):

where

γ0 = fracture energy of the unmodified matrix (J/m2),TL = so-called line tension of crack (N), andγa = term to account for energy-absorbing plastic deformations

around the particles (J/m2).

ΓIc = + +γ γ02

1T

CL

a ( )

76 Paper No. 00-1233 Transportation Research Record 1728

Evans’s theory also predicts that this increase in fracture energydepends on the volume fraction of filler and is independent of parti-cle size (4; 7, pp. 434–452). Several researchers have given directevidence of this mechanism in various composites by studying thefracture surface of the material using scanning electron micrographyand other topographic techniques (7, pp. 434–452; 8; 10; 11).Images of fracture surfaces clearly show the “tails” or “steps”behind filler particles caused by the interaction of the crack frontwith the second-phase dispersion.

Recently, Garcés Rodríguez et al. (1) demonstrated that the rela-tive in-creases in fracture toughness and energy that were observedfor particulate-filled asphalt binders can be predicted by Evans’stheory of crack pinning. Furthermore, the increases were found tobe dependent only on the volume fraction of the filler since theparticle size had no effect over a range as wide as 4 to 114 µm (seeFigure 2). This finding provided indirect evidence that the modelaccurately describes crack growth in filled asphalt systems. Theseresults were obtained with fracture tests on notched mastic sam-ples and therefore pertain to specimens in which unstable crackgrowth preceded brittle failure. This paper presents results thatfocus on the effect of filler particle size on performance in thestable crack growth regime.

Fatigue Failure

Fatigue has been defined as “the phenomenon of fracture underrepeated or fluctuating stress, having a maximum value less than thetensile strength of the material” (12). In general, fatigue in asphaltmixes is a three-stage process consisting of (a) crack initiation, thedevelopment of microcracks; (b) crack propagation, the develop-ment of macrocracks out of microcracks resulting in stable crackgrowth; and (c) disintegration, the collapse and final failure of thematerial because of unstable crack growth (13).

Most quantitative models based on fracture mechanics deal withthe second phase of the fatigue process since it is assumed that thisstage takes up most of the fatigue life (14, p. 61). The crack propa-gation phase can be described by Paris’s law, which relates the rateof crack growth to fundamental properties of the material andexperimental conditions (15):

APPROACH PINNING BOWING BREAKAWAY

CRACK FRONTPROPAGATION

FIGURE 1 Schematic drawing of crack-pinning mechanism [after Phillips and Harris(9, p. 45)].

where

c = crack length (m),N = number of load repetitions,

∆K = difference between maximum and minimum stress intensityfactor K in dynamic loading (N/m3/2), and

A, n = Paris law fracture parameters for asphalt concrete.

Schapery (16–19) was the first to demonstrate that there is a rela-tionship between A and n and the fracture energy and other funda-mental materials properties of the material. This relationship showsthat A is strongly dependent on the inverse of the fracture energy ofthe material (20):

where Γ is the fracture energy of the material in joules per squaremeter and m is the slope of the graph of log compliance versus logtime [for the other variables and a further explanation of this equation,the reader is referred to the report by Lytton et al. (20)].

Since the fracture energy of the material is influenced signifi-cantly by crack pinning, it follows that the rate of crack growth dur-ing the crack propagation phase of fatigue will also be affected bythis mechanism. Ultimately, the fatigue performance of the asphaltmix will improve because of the addition of a second particulatephase to the asphalt binder. However, there are no reports in the lit-erature on how this improved fatigue performance depends upon theparticle size of the filler. This paper focuses on that issue in order tofurther the understanding of the crack-pinning mechanism in asphaltmastics and mixtures.

AD m w t

Idt

m m n

mt

t

=( )

( )+

∫11 2

1

12 20

43

λ π

σΓ

∆

( )

dc

dNA K n= ( )∆ ( )2

Smith and Hesp Paper No. 00-1233 77

EXPERIMENTAL

Materials

Asphalt Binder

The only binder used in this project was a paving-grade bitumenfrom a Venezuelan crude source (B85). It had a penetration value of85, a penetration index of −0.8, an asphaltene content of 11.9 per-cent by weight, and a ring-and-ball softening point of 47°C. Afterrotating thin-film oven aging, the penetration decreased to 54 andthe ring-and-ball softening point increased to 52°C.

Particulate Fillers

The glass spheres used as model fillers were solid A-type (soda-limeglass) spheres produced under the trade name Spheriglass by Pot-ters Industries of Cleveland, Ohio, and were the same as those usedin the earlier work by Garcés Rodríguez et al. (1). The average par-ticle radii for the glass spheres used in the modified asphalt binderswere 2.0, 5.5, 17.5, and 57.0 µm. The size distribution data for theseglass spheres are given in Figure 3, which shows that the spheresizes were all narrowly distributed and hence useful for model stud-ies on the effect of particle size.

In addition, two ground limestone fillers (Limestones A and B),produced under the Wigro trade name by Anker-Poort of Winter-swijk, the Netherlands, were used for both mastic and mix studies.The size distributions for these fillers are also given in Figure 3.

Asphalt Concrete

The aggregate used for the asphalt concrete was a standard mix of crushed gravel (three fractions), natural sand (two fractions),

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6

Volume Fraction, υo

(a)

(b)

FIGURE 2 Fracture energy increase for glass-filledasphalt binders compared with theoretical predictions for(a) noninteracting semi-elliptical secondary cracks and (b) interacting secondary cracks (particle radii: solidcircle, 2 µm; solid triangle, 5.5 µm; solid square, 24.5 µm; and open circle, 57 µm) [after Garcés Rodríguez et al. (1)].

0

25

50

75

100

0 15

Sieve Size, micrometer

0

25

50

75

100

0 15

Particle Diameter, micrometer (0.45-power scale)

Particle Diameter, micrometer (0.45-power scale)

A

B

0 10 32 63 125 250 1000

A B C D

(a)

(b)

0 10 32 63 125 250 1000

FIGURE 3 Size distributions for (a) model fillersA–D and (b) limestone fillers A and B.

manufactured sand (one fraction), and the limestone-based fillers.This aggregate had an optimum binder content of 6.2 percent byweight of the dense-graded aggregate and 7.0 percent by weightfor the stone mastic asphalt mix. A total of six asphalt concreteslabs were made with different gradations, filler type (regular andcoarse), and binder content. The compositions for all six slabs aregiven in Table 1, and their gradations are given in Figure 4.

Preparation Methods

Asphalt Mastics

Rigden originally proposed the concept of free binder volume inwhich the binder in a mastic is assumed to be either free or bound(21). His concept assumes that a fraction of the bitumen can beregarded as fixed in the space between the filler particles at theirmaximum dry packing configuration, whereas the remaining bitu-

78 Paper No. 00-1233 Transportation Research Record 1728

men volume is free. As a result, the functional volume percentageof the “solid” phase is larger than the actual compositional volumepercentage, whereas the functional volume percentage of the “liq-uid” phase is smaller (22). Heukelom found that the stiffness offiller-bitumen mixtures depends primarily on the apparent or bulkvolume percentage of filler (22).

In this study, it was deemed important that the stiffnesses of thedifferent mastics be equal in order to compare their performanceunder constant strain fatigue testing. In order to achieve this equalstiffness, the mastics were prepared so that they contained the samebulk volume percentage of filler. The samples modified with glassfiller were prepared so that the bulk volume percentage of filler was50 percent (i.e., 50 percent free asphalt cement), and the sampleswith the ground limestone filler were prepared using a bulk volumepercentage of 65 percent (i.e., 35 percent free asphalt cement).

Mastics were prepared by slowly adding known amounts of thefiller to the required amount of asphalt (in order to obtain the desiredbulk volume percentage of filler) at approximately 140°C. Sampleswere stirred for a minimum of 30 min or until the additive was welldispersed in the asphalt binder. Dispersion was verified by observ-ing small samples under an optical microscope. After homogeniza-tion, samples were cast into a mold and placed in a freezer atapproximately −10°C. The specimens were dumbbell-shaped andpossessed the following dimensions: 14.0 mm long, 2.5 mm thick, 4.0 mm wide in the middle, and 8.0 mm wide at the ends. Each sam-ple was molded so that both ends adhered to small plastic spacersthat fit into the test fixture, allowing for easy mounting in therheometer. After 30 min, the samples were demolded and placed ina refrigerator at 0°C for 15 min, at which point they were mountedin the rheometer (torsional fatigue tester). Six different binders weretested in this study: four modified with glass filler and two modifiedwith ground limestone filler.

Asphalt Concrete

Asphalt concrete slabs were compacted with a laboratory slabcompactor (Type 2849, Matériels des Laboratoires des Ponts etChaussées of Angers, France) to a thickness of 8 cm at a temperature

FIGURE 4 Sieve analysis of recovered aggregate from asphaltconcrete slabs.

TABLE 1 Asphalt Concrete Recipes

Mixture

Aggregate (wt %) 1 2 3 4 5 b 6 b

Coarse 8-11 mm 20.4 20.4 20.4 20.3 50.8 50.8

Coarse 4-8 mm 20.4 20.4 20.4 20.3 13.1 13.1

Coarse 2-6 mm 15.3 15.3 15.3 15.6 13 13

Manufactured Sand 27.6 27.6 27.6 27.5 6.4 6.4

Natural Sand A 3.1 3.1 3.1 2 3.2 3.2

Natural Sand B 6.1 6.1 6.1 3.8 3.2 3.2

Limestone Filler A (regular) 7.1 - 7.1 - 10.3 -

Limestone Filler B (coarse) - 7.1 - 10.5 - 10.3

Binder (B85) a 5.8 6.2 6.2 6.2 7.0 7.0

Average Air Voids Content, vol % 4.0 4.1 3.4 3.7 3.6 4.0a Parts of binder per hundred parts of aggregate.b Stone mastic asphalt recipes.

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80

Sieve Size, micrometer and mm (0.45-power scale)

Mix 1

Mix 2

Mix 3

Mix 4

Dense Graded Control Points

Mix 5

Mix 6

0 63 500 2 4 8 11.2

at which the binder viscosity equaled 280 centistokes. After cooling,trapezoidal test specimens 160 mm high, 30 mm thick, 20 mm wideat the top, and 55 mm wide at the bottom (with an accuracy of ±0.1 mm) were cut from within the inside of the slab. Air voids foreach specimen were determined before testing by weighing eachspecimen above and under water. Only samples with air voids withinthe average ±0.5 percent range were tested. Until testing, all sampleswere stored at 10°C.

Testing Methods

Torsional Fatigue Tests on Asphalt Mastics

Fatigue testing of the asphalt mastics was performed in a dynamicrheometer (Rheometrics RDA II) using a rectangular torsion testfixture. This method of testing is common in fatigue work and con-sists of applying torsional oscillations under constant strain ampli-tude to the specimen. In these constant strain tests, the initiationand propagation of cracks causes the stiffness of the specimen todecrease, resulting in a reduction in stress as the test proceeds (13).The fatigue life is defined as the number of load repetitions atwhich the stiffness of the specimen, G*, is reduced to 50 percentof its initial value. The loading arrangement results in the applica-tion of a sinusoidally varying shear strain of constant amplitude tothe specimen.

After fabrication, the specimens were mounted in the rheometeraccording to the mounting procedures found in the instrument man-ual (23). Next, the oven was closed so that the specimen temperaturecould equilibrate to the desired testing temperature. Cooling to theoven was provided by liquid nitrogen. After 15 min of equilibration,the fatigue test was started. All specimens were tested at 10°C and40 Hz with applied strains set between 0.15 and 0.6 percent.

Two-Point Bending Fatigue Tests on Asphalt Concrete

The trapezoidal asphalt concrete samples were glued onto metalsupport shoes that were securely attached to the two-point bendingfatigue test frame. All mixture fatigue tests were also conducted at10°C and 40 Hz but were instead performed in a constant stressmode in order to keep the total testing time manageable. The testswere stopped when the deflection reached a 100 percent increaseover the initial value (i.e., when a 50 percent decrease in stiffnesswas reached). The data acquisition was performed using LabViewsoftware (version 4.1, National Instruments of Austin, Texas).

RESULTS AND DISCUSSION OF RESULTS

Mastic Fatigue Results

The mastic fatigue results are given in Figure 5. The data show thatparticle size has a small effect on the fatigue life for the model glasssphere systems tested at a bulk filler volume percentage of 50 per-cent. The limestone systems tested at a bulk filler volume percent-age of 65 percent showed a larger dependence on particle size withregard to the fatigue life of the asphalt mastic. These observationsare not surprising since the fatigue crack growth process is moreinsidious than the unstable crack growth process that occurs in the

Smith and Hesp Paper No. 00-1233 79

fracture energy test used by Garcés Rodríguez et al. (1) (Figure 2).Fatigue cracks can slowly wind their way through a mastic and findless hindrance from the secondary obstacle phase as compared withmacroscopic cracks, which are forced to propagate within a veryshort period of time.

Pell (24) found that two different types of fracture occur at lowand high temperatures in asphalt mastics under constant torsionalstrain fatigue testing. The failure at low temperatures originates ata single nucleus and propagates very quickly, resulting in a failuresurface inclined to the axis of the specimen at an approximate angleof 45 degrees. At temperatures above 0°C, because of the extremelylow rate of crack propagation, failure originates at a large numberof nuclei, and the microcracks eventually link up to form whatappears to be an orthogonal fracture. All the mastic specimenstested in this study exhibited this type of orthogonal fracture sur-face. As Pell pointed out in his 1962 paper, the occurrence of thedifferent types of failure depends not only on the temperature orstrain value (24) but also on the magnitude of the resulting stressat the tip of the crack. Before multiple microcracks have time toform and propagate, a single nucleus can progress to catastrophicfailure provided the stress concentrations at the crack tip are highenough (24).

The results show that smaller obstacles are more effective at pin-ning cracks in the situation where a large number of microcracks ini-tiate and then slowly propagate and coalesce to form the fracturesurface. Because of the slow propagation of the microcracks, it ispossible for some of these growing cracks to advance around thelarger filler particles rather than becoming pinned between obstacles.As the size of the particles decreases, the interparticle distance alsodecreases (at a constant volume fraction of filler), making it more dif-ficult for the progressing cracks to get around the inclusions. As a result, more cracks become pinned and subsequently bow outbetween the filler particles. In essence, as the size of the second-phasedispersion decreases, a larger number of growing microcracks becomepinned by obstacles and the fatigue life of the material increases

FIGURE 5 Results from constant strain torsional fatiguetests on asphalt mastics.

1

10

100

1000

0.1 0.8

4 micron

11 micron

35 micron

114 micron

1

10

100

1000

0.1 0.8

Torsional Strain, %

Limestone A

Limestone B

because of the crack-pinning mechanism. This effect of the particlesize is only evident because of the nature of fatigue failure in theseconstant strain experiments (very slow propagation of a large num-ber of microcracks). These observations provide indirect evidencethat the crack-pinning mechanism improves the fatigue life of theasphalt mastic specimens under these experimental conditions.

Asphalt Mix Fatigue Results

The asphalt mix results are given in Figure 6. The data show thatthere is little or no effect of particle size on the fatigue performanceof the different mixes. The differences between Mixes 1 and 2 can beexplained through the higher binder content in Mix 2 since lowerstiffness in a constant stress test results in larger strains and thusreduced fatigue life. The binder content was increased in order to pro-duce two mixes of the same voids content. The differences betweenMixes 5 and 6 can also be explained through a higher binder content(Mix 6 was inadvertently prepared with 7.2 percent by weight ofbinder instead of the 7 percent called for in the recipe). However, thefatigue performance for these two mixes is very similar, which oncemore indirectly supports the proposed crack-pinning mechanism.Mixes 3 and 4 show identical fatigue results even though they wereprepared with two very different fillers (7.1 percent limestone A ver-sus 10.5 percent limestone B). The gradation for these two mixesabove 63 µm looks the same even though they were made with ratherdifferent amounts of natural sand and limestone filler.

These results are in agreement with Evans’s theory of crack pin-ning and previous fracture studies performed on asphalt mastics(1), which show the increase in fracture energy of the composite tobe independent of particle size. The asphalt mix fatigue studieswere performed under constant stress. In this mode of testing, a

80 Paper No. 00-1233 Transportation Research Record 1728

crack will initiate and subsequently propagate explosively, result-ing in a completely fractured specimen (13). Therefore, fractureresults from the propagation of a single macrocrack rather than thecoalescence of numerous microcracks. In this type of fatigue frac-ture, the particle size does not significantly affect the fatigue life ofthe specimen since the moving crack front interacts with the obsta-cles in the manner described by the crack-pinning mechanismregardless of the dispersion size.

CONCLUSIONS

Given the results that were obtained in this study, the followingconclusions can be drawn:

1. The crack-pinning mechanism does appear to operate inasphalt mastics undergoing damage from fatigue loading cycles.

2. The size of the second-phase dispersion affects the fatigue lifeof the material when failure occurs through the slow propagationand coalescence of numerous microcracks (i.e., in a constant strainmode of fatigue failure). In this situation, the fatigue life of theasphalt mastics increases with decreasing particle size.

3. In the case where a single crack causes failure of the specimen,particle size does not significantly influence the fatigue life.

ACKNOWLEDGMENTS

Simon Hesp thanks Johan Plantinga, Dirk Jongeneel, and Frans vanSchoot of the Shell Research and Technology Centre in Amsterdam,the Netherlands, for assistance during the mixture fatigue work. Theauthors are grateful to Gerard ten Dolle of the WinterswijkscheSteen- en Kalkgroeve of Winterswijk, the Netherlands, for supply-ing and analyzing the ground limestone filler samples. Queen’s Uni-versity and Shell International Chemicals are acknowledged for thesupport that made Hesp’s sabbatical year in Amsterdam possibleand successful. Shell International Oil Products is thanked for mak-ing the mixture fatigue facilities available to Hesp. Todd Hoare isthanked for proofreading of the manuscript.

REFERENCES

1. Garcés Rodríguez, M., G. R. Morrison, J. R. vanLoon, and S. A. M.Hesp. Low Temperature Failure in Particulate-Filled Asphalt Bindersand Asphalt Concrete Mixes. Journal of the Association of AsphaltPaving Technologists, Vol. 65, 1996, pp. 159–192.

2. Park, S. Development of a Nonlinear Thermo-Viscoelastic ConstitutiveEquation for Particulate Composites with Growing Damage. Ph.D. dis-sertation. University of Texas at Austin, 1994.

3. Kim, R. Y., H. Lee, and D. Little. Fatigue Characterization of AsphaltConcrete Using Viscoelasticity and Continuum Damage Theory. Jour-nal of the Association of Asphalt Paving Technologists, Vol. 66, 1997,pp. 520–569.

4. Evans, A. G. The Strength of Brittle Materials with a Second-Phase Dis-persion. Philosophical Magazine, Vol. 26, 1972, pp. 1327–1344.

5. Schapery, R. A. A Micromechanical Model for Non-Linear Viscoelas-tic Behavior of Particle-Reinforced Rubber with Distributed Damage.Engineering Fracture Mechanics, Vol. 25, Nos. 5/6, 1986, pp. 845–867.

6. Little, D. N., R. L. Lytton, D. Williams, and Y. R. Kim. An Analysis ofthe Mechanism of Microdamage Healing Based on the Application ofMicromechanics First Principles of Fracture and Healing. Journal of theAssociation of Asphalt Paving Technologists, Vol. 68, 1999, pp. 501–542.

7. Kinloch, A. J., and R. J. Young. Fracture Behavior of Polymers. Else-vier Applied Science Publishers Ltd., London, England, 1985.

8. Lange, F. F. The Interaction of a Crack Front with a Second-Phase Dis-persion. Philosophical Magazine, Vol. 22, 1970, pp. 983–992.

0.01

0.1

1

10

70 100 200

0.01

0.1

1

10

70 100 200

Force, N

Mix 1

Mix 2

Mix 5

Mix 6

0.01

0.1

1

10

70 100 200

Mix 3

Mix 4

FIGURE 6 Results from constant stress two-pointbending fatigue tests on asphalt mixtures.

9. Phillips, D. C., and B. Harris. In Polymer Engineering Composites(M. O. W. Richardson, ed.), Applied Science Publishers, London, 1977,p. 45.

10. Lange, F. F. Fracture Energy and Strength Behavior of a SodiumBorosilicate Glass-Al2O3 Composite System. Journal of the AmericanCeramic Society, Vol. 54, 1971, pp. 614–620.

11. Lange, F. F., and K. C. Radford. Fracture Energy of an Epoxy CompositeSystem. Journal of Materials Science, Vol. 6, 1971, pp. 1197–1203.

12. Cooper, K. E., and P. S. Pell. The Effect of Mix Variables on the FatigueStrength of Bituminous Materials. Report LR633. United KingdomTransport and Road Research Laboratory, Crowthorne, Berkshire,England, 1974.

13. Jacobs, M. M. J. Crack Growth in Asphaltic Mixes. Ph.D. thesis. DelftUniversity of Technology, Delft, The Netherlands, 1995.

14. Monismith, C. L., J. A. Deacon, J. Craus, and S. C. S. R. Tangella. Sum-mary Report on Fatigue Response of Asphalt Mixtures. Report SHRP-A-32. Strategic Highway Research Program, National ResearchCouncil, Washington, D.C., Feb. 1990.

15. Paris, P. C., and F. Erdogan. A Critical Analysis of Crack PropagationLaws. Journal of Basic Engineering, Series D, Vol. 85, No. 3, 1963,pp. 528–534.

16. Schapery, R. A. A Theory of Crack Initiation and Growth in Visco-ElasticMedia; I: Theoretical Development. International Journal of Fracture,Vol. 11, No. 1, 1975, pp. 141–159.

Smith and Hesp Paper No. 00-1233 81

17. Schapery, R. A. A Theory of Crack Initiation and Growth in Visco-Elastic Media; II: Approximate Methods of Analysis. InternationalJournal of Fracture, Vol. 11, No. 3, 1975, pp. 369–388.

18. Schapery, R. A. A Theory of Crack Initiation and Growth in Visco-ElasticMedia; III: Analysis of Continuous Growth. International Journal ofFracture, Vol. 11, No. 4, 1975, pp. 549–562.

19. Schapery, R. A. A Method for Predicting Crack Growth in Non-Homogeneous Visco-Elastic Media. International Journal of Fracture.Vol. 14, No. 3, 1978, pp. 293–309.

20. Lytton, R. L., J. Uzan, E. G. Fernando, R. Roque, D. Hiltunen, and S. M. Stoffels. Development and Validation of Performance PredictionModels and Specifications for Asphalt Binders and Paving Mixes.Report SHRP-A-357. Strategic Highway Research Program, NationalResearch Council, Washington, D.C., Oct. 1993.

21. Rigden, P. J. The Use of Fillers in Bituminous Road Surfacings: AStudy of Filler-Binder Systems in Relation to Filler Characteristics.Journal of the Society of the Chemical Industry, Vol. 66, 1947, p. 290.

22. Heukelom, W. The Role of Filler in Bituminous Mixes. Journal of theAssociation of Asphalt Paving Technologists, Vol. 34, 1965, pp. 1–36.

23. Rheometrics Asphalt Analyzer Owner’s Manual. Rheometrics, Inc.,Piscataway, N.J., 1992.

24. Pell, P. S. Fatigue Characteristics of Bitumen and Bituminous Mixes.In Proc., International Conference on Structural Design of AsphaltPavements, Ann Arbor, Mich., Aug. 1962.