RESEARCH PAPER

Nanoindentation approach characterizing strain rate sensitivityof compressive response of asphalt concrete

Daisuke Katsuki • Marte Gutierrez

Received: 1 March 2013 / Accepted: 10 August 2013

� Springer-Verlag (outside the USA) 2013

Abstract This paper presents the results of a study on

the use of nanoindentation test to characterize the strain

rate-dependent compressive response of asphalt concrete.

Nanoindentation is now widely used for characterization

and testing of composite as well as single-phase materi-

als. Using a small piece of sample, nanoindentation tests

can evaluate material behavior and structure in terms of

the elasticity, time-dependent response, yield strength,

damage, crack advance, debonding, and fatigues. In this

study, a mixture of asphalt and calcium carbonate filler

powder filling the intergranular void space of the asphalt

concrete was characterized in terms of strain rate sensi-

tivity at room temperature. The indentation hardness is

observed to continuously decrease during constant

indentation strain rates, but the hardness response clearly

indicates positive strain rate dependency when compared

at the same indentation depths. Following the constant

strain rate tests, indentation creep response of the

asphalt–filler mixture was tested at constant load condi-

tions. The strain rate sensitivity values characterized from

double logarithmic relationships between indentation

hardness and strain rate during constant strain rate and

constant load tests are comparable with that determined

from uniaxial compression test of cylindrical asphalt

concrete samples. The observed indentation size effect on

hardness value was analyzed based on an existing size

effect model. The size effect in the asphalt–filler mixture,

which is stronger than that defined by the model, could

be attributed to a plastically graded surface of asphalt–

filler sample.

Keywords Asphalt concrete � Creep � Hardness �Nanoindentation � Rheology � Strain rate sensitivity �Uniaxial compression

1 Introduction

The most common pavement material consists of coarse

aggregates bonded with asphalt binder or Portland cement.

Asphalt concrete is advantageous in terms of road noise

reduction, flexibility, shorter construction time, and ease of

maintenance. Their rheological properties can be flexibly

modified by adding fillers, fine sands, chemical additives,

and polymers. However, the response of asphalt concrete to

mechanical and thermal conditions manifests themselves in

complicated elasto-viscoplastic ways changing with dam-

age accumulation because of mechanical and chemical

interactions between the constituents (e.g., [41, 42, 50]).

The sensitivities of asphalt concrete need to be evaluated

against prospective chemical, thermal, and mechanical

effects such as climate, rainfall, traffic loads (speed, vol-

ume, and frequency), and aging. Temperature and strain

rate sensitivities are of primary importance for appropriate

constitutive modeling of asphalt concrete.

Prediction of the long-term response of asphalt concrete

is a challenging problem, but is important to minimize life

cycle costs and required maintenance work (e.g., [55]).

Crack advance, fatigue fracturing, and asphalt debonding

strongly shorten the pavement service life. Practical design

approach to hot mix asphalt concrete is expected to

advance from empirical design methods to mechanistic-

D. Katsuki (&) � M. Gutierrez

Civil and Environmental Engineering, Colorado School of

Mines, 1012 14th, Golden, CO 80401, USA

e-mail: dkatsuki@mines.edu

M. Gutierrez

e-mail: mgutierr@mines.edu

123

Acta Geotechnica

DOI 10.1007/s11440-013-0269-9

based ones [17, 34]. Empirical design methods developed

to relate index properties to mechanical responses are

considered to have limited capabilities for the prediction of

long-term conditions. The most advanced design method is

based on full mechanistic approach in which an unified

material model capable of reflecting whole material prop-

erties, for example, plasticity, viscosity, damage evolution,

aging, and healing, is used to predict behavior under var-

ious conditions. The unified model is believed to be real-

ized as a result of continuous improvements in which

existing constitutive models are modified based on micro-

mechanical insights. Micromechanical approach should be

important for the characterization of the effects of struc-

tural degradation on macroscopic response.

The mechanical properties of asphalt concretes have

been extensively studied by means of experimental

approaches. Conventional uniaxial compress/tension and

triaxial compression tests are used to investigate the effects

of loading condition, temperature [23, 42], strain rate [21,

30, 32, 41], damage growth [17, 30, 41, 42, 50], and healing

[33]. In current models, the material parameters are deter-

mined by curve fitting to observed data often without strong

basis for their true relationships with material behavior.

Other more sophisticated models require elaborate test

procedures such as a series of multiaxial loading tests (e.g.,

[41, 42]) to probe individual material parameters. This is

because single macroscopic response of composite material

is usually affected by multiple factors.

In the last two decades, application of nanoindentation

test has been extensively studied for various engineering

materials [12, 38]. Commercially available nanoindenters

are instrumented with precision displacement and force

sensors to perform indentation tests in the nanometer

(10-9 m) scale. Finely shaped indenter tips made of hard

materials, typically diamond, are pushed into the test sur-

face. In addition to single-phase materials, indentation

response of polymeric composite material systems has

been studied (e.g., [5, 22, 31]). Nanoindentation test is a

promising approach to material design. Even a number of

nanoindentation tests require only a small volume of

sample. Thus, sensitivities to several factors can be

investigated by using single piece of sample. For composite

materials, a nanoindenter should be a sensitive probe for

the determination of the mechanical properties of individ-

ual constituents and interfacial properties between con-

stituents. Experimental studies using nanoindentation tests

on microscopic characterization can render useful insights

into micromechanics-based constitutive models.

The principle of indentation test is simple. A typical

relationship between indentation load and tip displacement

into a material surface is illustrated in Fig. 1. Indentation

load, P, usually increases monotonically in a concave up

manner with increasing indentation depth as shown by

curve O–A. Unloading response may be observed as

illustrated by curves A–B. An expression of strain rate in

nanoindentation test _eI can be given by:

_eI ¼1

h

dh

dtð1Þ

where h is indentation depth and t denotes time [35]. Mean

pressure acting on the projected contact area between

specimen and indenter tip, which is referred to as

indentation hardness, is given by:

H ¼ P

Ac

ð2Þ

where P is indentation force and Ac is projected contact

area between specimen and indenter tip. The contact area

of cone indenter tip can be calculated as:

Ac ¼ ph2c tan2 a ð3Þ

where hc is contact depth and a is cone semiangle of the

indenter tip. The contact depth may be estimated by using

the following equation [38, 39]:

hc ¼ h� vP

Sð4Þ

where v is the constant associated with indenter tip

geometry and S is the contact stiffness. Usually, S is

determined as the tangential slope of unloading curve at the

start point of unloading (see Fig. 1). Young’s modulus of

the indented material can be obtained from analysis based

on the contact stiffness [38].

The use of nanoindentation test to multiscale composite

materials has been recently studied by using shale [3, 40],

Portland cement and concretes [28, 51, 52], and asphalt and

asphalt concretes [26, 27, 45, 49]. Jager et al. [26] and

Stangl et al. [45] examined nanoindentation creep behav-

iors of straight asphalt during constant load-holding period

to determine viscoelastic parameters at temperatures close

to 0 �C. It is demonstrated that the viscoelastic parameter

Fig. 1 A schematic of typical relationship between indentation load

P and displacement h during loading (O–A) and unloading (A–B)

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123

values determined at some indentation load conditions are

comparable to those determined by standard methods.

Tarefder et al. [49] carried out nanoindentation tests by

using spherical and Berkovich pyramidal indenter tips on

different phases of asphalt concretes, i.e., mixture of

asphalt and fine sand smaller than 75 lm, mixture of

asphalt and coarse sand smaller than 4.8 mm, and aggre-

gates. Indentation hardness and Young’s modulus values of

these different phases obtained from nanoindentation

loading and unloading data are reported.

However, current knowledge about nanoindentation

responses of asphalt and asphalt concretes is quite limited.

In one of the previous nanoindentation studies [26], vis-

coelastic parameter values determined at small creep load

condition were found to agree with those determined from

standard test. However, the parameter values determined

by nanoindentation are observed to significantly depend on

the magnitude of holding load during creep. This creep

load dependency was attributed to the asphalt microstruc-

ture but not satisfactorily generalized. In the other previous

study mentioned above [49], the effects of strain rate on

indentation hardness and Young’s modulus values are not

investigated, although these effects are indispensable to

evaluate asphalt concrete.

An interesting and challenging application of indenta-

tion test is prediction of macroscopic properties of mate-

rials. For monolithic materials, the meaning of indentation

hardness has been extensively studied after the pioneering

work [47]. The indentation hardness can be correlated to

uniaxial yield (flow) stress, rY, as:

H ¼ cconrY ð5Þ

where ccon is called constraint factor considered to reflect

the degree of confinement effect provided by test material

surrounding indenter tip. Eq. (5) can be derived from the

Hertz contact model by considering a contact between a

spherical indenter tip and a semi-infinite elastic body.

Assuming the Tresca yield criterion for indented material,

the value of ccon is determined to be 1.1. Considering

another condition at which the vicinity of indented zone

becomes sufficiently plastic, the value is determined to be

2.8 [24]. Tabor proposed ccon = 3 based on careful com-

parison between this equation and his experimental data. In

addition to the material properties, the value of ccon is

considered to be dependent on the ratio of elastic modulus

to yield stress, the friction between the indenter–material

interface, and the indenter tip geometry. For materials with

large values of the elastic modulus/yield stress ratio, e.g.,

metals, a value of ccon & 3 is predicted. For low elastic

modulus/yield stress ratio values, ccon is considered to be

lower and approximately 1.5.

Extracting macroscopic mechanical behaviors of com-

posite materials from their indentation data is a challenging

endeavor. Development of plastic deformation underneath

the indenter tip should be related to a number of micro-

mechanical properties, such as elastic moduli of constitu-

ents, packing density, bonding strength of binder,

resistances of filler grains due to intergranular friction and

rotational resistance, tensile strength, and viscosity of

constituents (e.g., [19]). Thus, the indentation hardness of

composite emerges as a result of combination effect of

these phase properties. The roles of phase properties in the

indentation hardness of composite phase can be formulated

through very complicated homogenization technique [7].

More directly, a numerical method has been developed

aiming at solving inverse problem of indentation into

microstructural model constructed based on a map of phase

properties accessible by using grid nanoindentation [19].

At present, modeling of microstructure of composites

based on indentation test becomes available through these

very sophisticated procedures. For asphalt and asphalt

concretes, there is no study on the relationship between

nanoindentation and uniaxial compression responses.

Higher sensitivities of mechanical responses of asphalt

concretes to temperature and strain rate are interesting and

important features especially in asphalt concrete design.

Experimental data of the strain rate sensitivity of micro-

structure of asphalt composite should be valuable to

develop future applications of indentation test aiming at

direct modeling of composite structure.

This paper is aimed at discussing the applicability of

nanoindentation test to characterize strain rate sensitivity of

asphalt composite subjected to uniaxial compression. For

precise discussion about the relationship between indenta-

tion behavior and uniaxial compression behavior of com-

posite materials, a rigorous analysis of the meaning of

observed indentation behavior is required. However, such

theoretical analysis is not presented in this paper, because it

is out of the scope of this study. Homogenization of

degrading microstructure of composite for calculating the

indentation hardness can be very complicated as seen in the

previous studies (e.g., [7]). On the other hand, the quite

simple form of Eq. (5) proposed for monolithic materials

provides us with a direct insight of potential relationship

between the indentation hardness and uniaxial yield stress.

It should be beneficial for practical engineers and exam-

iners to discuss the observed indentation hardness of

asphalt–filler mixture based on the extremely simple idea

embodied by Eq. (5), although special care is necessary to

avoid unallowable stretch and amplification. In fact, the

relationship between the indentation behavior and uniaxial

response is an interesting topic in research on polymer

composites (e.g., [8]). In homogenization of porous com-

posites such as Portland cement concretes and shales,

porosity plays an important role [19]. The asphalt–filler

mixture is also a multiphase but nonporous material. Thus,

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123

the indentation response of asphalt–filler mixture may be

correlated with the uniaxial compression behavior in a

simpler form compared to the porous composites, because

the effect of porosity is eliminated.

2 Materials and testing

2.1 Test materials

A hot mix asphalt concrete sample was prepared by using

pavement grade asphalt, calcium carbonate filler, and silica

aggregates. The test surface was polished and finished by

using 0.05-lm alumina suspension to prepare high-quality

test surface. Constant strain rate nanoindentation tests were

carried out on the asphalt–filler mixture samples by using a

Berkovich pyramidal indenter tip at indentation strain rates

ranging from 0.005 to 1.1 s-1 followed by constant load

creep test. In the observed indentation responses of

asphalt–filler mixture, the composite nature of asphalt–fil-

ler mixture should arise, because the main part of inden-

tation depths is greater than a threshold depth defined as

Dchr/10 & 1 lm, where Dchr is the characteristic size of

the largest constituent as proposed in the previous studies

(e.g., [9]). The strain rate sensitivity was characterized at

both conditions of constant strain rates and constant load.

The mechanism of indentation size effect on hardness is

discussed based on an existing size effect model. The

results should be useful for the development of further

applications of the nanoindentation test on the microme-

chanical characterization of asphalt concrete.

The asphalt concrete specimen used for the nanoinden-

tation tests is shaped into disk whose diameter and thick-

ness are 19 and 5 mm, respectively. This specimen is

obtained from the central part of larger disk-shaped asphalt

concrete whose dimensions are 50.8 mm in diameter and

20 mm thick. The asphalt concrete specimen is a com-

pacted mixture of straight asphalt (PG58-28), a filler, and

silica aggregates. The material composition and prepara-

tion procedures are the same with those used in the uniaxial

compression test [30]. The silica aggregate is a coarse-

crushed silica sand whose grain sizes are distributed from

0.2 to 2.8 mm. The filler is a fine calcium carbonate

(whiting) powder whose grain sizes range from several

microns to approximately 30 lm. The mix proportion of

sample in terms of the mass ratio of asphalt–filler–aggre-

gates is 0.115:0.431:1.0.

Brief descriptions of the preparation procedure are as

follows. The straight asphalt and filler mixed at approxi-

mately 160 �C are subsequently added to the silica aggre-

gate preheated up to the same temperature. The hot asphalt

concrete mixture is cast in a preheated cylindrical mold

having 50.8 mm of internal diameter and then compacted

by mechanical tamping in the cylinder by using a hot metal

rod hemispherically ended to remove air bubbles from the

mixture. The mixture is further statically compacted in the

axial direction to a bulk density of 2.35 g/cm3. The axial

compaction stresses do not exceed 5.0 MPa. The sample

temperature is maintained approximately at 160 �C

through the mixing and subsequent static compaction

procedure. After being cooled to the room temperature, the

mixture is extruded out from the mold at axial stress not

greater than 1.0 MPa.

The nanoindentation specimen is obtained from the

above-mentioned asphalt concrete disk as follows. First,

the lateral peripheral part of the asphalt concrete disk is

removed by using a band saw. The central part is shaped

into a rough cylinder whose diameter is several millimeters

larger than the final one to avoid disturbance due to cutting.

The surface layer approximately 5 mm from the surface is

removed. The fresh surface of the specimen is polished by

using wet silicon carbide papers for flatness. This surface,

which is not yet the test surface, is glued to the top end-face

of a sample puck that is aluminum alloy cylinder having a

diameter of 19 mm by using super glue. The lateral face of

the specimen is lapped with wet silicon carbide papers to

reduce the diameter to the sample puck diameter. Subse-

quently, the test surface is polished. At the beginning,

roughly 5-mm-thick material is lapped from the surface.

Then, the surface is progressively lapped using 240, 320,

400, 600, and 1500 grits of wet silicon carbide papers.

Subsequently, the surface is polished by using polishing

pads wetted with 6, 3, and 1 microns of diamond suspen-

sions, respectively. Finally, the surface is finished with 0.3

and 0.05 microns of alumina suspensions on polishing

pads. Residual alumina powders are rinsed out of the test

surface by several repeating cycles of cleaning using

ultrasonic cleaning bath and flushing distilled water.

The locations of indentation test were carefully chosen

to avoid an influence of the presence of silica aggregate on

the indentation response. All indentation points are located

at least 200 lm away from the closest boundary between

silica aggregate and asphalt–filler mixture matrix. In the

previous nanoindentation studies using Portland cement

concrete [9] and shale [16], a 1 lm of diamond paste and a

1 lm of aluminum oxide abrasive disk were used to finish

the test surfaces, respectively. In the latter case, the root-

mean-squared roughness of finished surface was observed

to be ranging from 30 to 150 nm. The asphalt concrete

sample used in this study was prepared by using much finer

50-nm diamond suspension. It may be expected that the

surface roughness is equal to or smaller than that of the

previous study.

Figure 2 shows the nanoindentation specimen prepared.

In Fig. 2a, which shows the polished test surface of spec-

imen, it can be seen that the asphalt–filler mixture phase

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123

can be easily distinguished from the silica aggregate grains

based on the difference in the degree of reflection. The

asphalt–filler mixture is observed to fill the interparticle

void space of the aggregate grains without visible open

pore space.

2.2 Nanoindentation test

Nanoindentation tests were carried out on the polished

surface of asphalt–filler mixture phase by using an instru-

mented MTS XP nanoindenter. Figure 3 is a schematic of

the nanoindenter. Nanoindentation specimen (A) mounted

on sample puck (B) is placed below the indenter tip (C).

The sample puck is fixed to sample tray mounted on x–y

table, although it is not shown in the figure. Indenter col-

umn (D) holding indenter tip is supported with leaf springs

(E). Indentation force is generated by coil/magnet assembly

(G), and indentation displacement is detected with capac-

itance gage (F). The indenter is thermally and acoustically

isolated from the environment by being enclosed in cabi-

net. The ambient temperature of test room is controlled at

23 ± 0.5 �C.

The indentation tests carried out in this study are com-

posed of three test stages. At the start, indentation is carried

out at constant strain rate (CSR). After the indentation

depth reaches a prescribed value, the indentation load is

held constant to test creep response for 120 s of duration.

This stage is referred to as constant load (CL) test. The last

stage is unloading from the constant indentation load. The

indentation strain rate values used for the CSR test are

0.005, 0.02, 0.3, 0.4, 0.7, 1.0, and 1.1 s-1. The indentation

depth values to terminate CSR tests are 8 lm except for

_eI ¼ 0:4 and 1.1 s-1. The termination depth values are 5

and 1 lm at _eI ¼ 0:4 and 1.1 s-1, respectively. The dif-

ferent termination depths of CSR loadings at _eI ¼ 0:4 and

1.1 s-1 were chosen for an attempt to observe the depth

dependency of creep behavior.

A diamond Berkovich indenter, with three-sided pyrami-

dal tip in which the face angle is 65.27�, is used in all the

tests. The effective cone semiangle, a, that is defined as the

cone semiangle of virtual conical tip equivalent to the Ber-

kovich tip in terms of the relationship between tip projected

contact area and depth is 70.3� for the Berkovich tip. Con-

tinuous stiffness measurement (CSM) method [38] is

employed to examine the Young’s modulus. The CSM is a

dynamic measurement method in which small oscillatory

loadings are superimposed at high frequencies on the static

loading. The CSM provides continuous change of Young’s

modulus in depth direction. The frequency and depth of

oscillatory loading used are 45 Hz and 2 nm, respectively.

Applicability of CSM method using small oscillations to theFig. 2 Asphalt concrete sample mounted on aluminum alloy sample

puck prepared for nanoindentation test

Fig. 3 A schematic of instrumented nanoindenter used; A specimen,

B sample puck, C indenter tip, D indenter column, E leaf springs,

F capacitance gauge, and G coil/magnet assembly

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123

asphalt–filler mixture can be considered as follows. Ideally,

the stress–strain relationship of linearly elastic body is

independent of the amount of displacement. In addition, a

contact between the asphalt–filler mixture and indenter tip

seems not as rough as porous composites. The CSM method

has been applied even to porous composites [10]. Figure 4

shows the load–time plots observed during CSR, CL, and

unloading stages at the prescribed conditions.

3 Uniaxial compression response

The uniaxial compression response of the asphalt–filler

mixture observed at constant strain rates [30] is reviewed

here. Figure 5 shows the strain rate sensitivity of uniaxial

stress versus strain curves observed at 22 ± 1 �C. The uni-

axial compression specimens have identical material com-

position with the asphalt–filler mixture phase tested by

nanoindentation. The initial linear stress–strain responses

transition to nonlinear ones at approximately 0.60, 0.63,

0.88, and 1.40 MPa of axial stresses at 4.2 9 10-6,

1.7 9 10-5, 1.7 9 10-4, and 1.7 9 10-3 s-1 of strain rates,

respectively. These axial stresses defining the boundary

between linear and nonlinear responses are considered to be a

yield stress at the respective strain rates. After exceeding

their respective yield points, weak strain-hardening is mobi-

lized. Regardless of strain rate, the asphalt–filler mixture

reaches maximum stress points and subsequently manifests

itself in a strain-softening manner. The values of the maxi-

mum stress and Young’s modulus, given by the tangential

slope of linear portion of stress–strain, increase with

strain rate. In spite of the change in the strain rates of more

than 102 times, the values of axial strain at yield point are

observed in a narrow range from 0.08 to 0.10.

The strain rate dependency of Young’s modulus, E, of

the asphalt–filler mixture can be expressed by the follow-

ing power law function [30]:

E ¼ ES þ EVR _er ð6Þ

where ES is static component of Young’s modulus, EVR is

material constant characterizing strain rate-dependent

component of Young’s modulus, _e is axial strain rate, and r

characterizes strain rate sensitivity. Figure 6 indicates the

strain rate sensitivity of uniaxial yield stress. There exists a

power law relationship similar to Eq. (6) between the yield

stress, rY, and strain rate, _e. Thus, a similar model can be

introduced to describe strain rate dependency of rY as:

rY ¼ rYS þ rYVR _em ð7Þ

where rYS is static component of yield stress, rYVR is

material parameter for strain rate-sensitive yield stress

component, and m is the strain rate sensitivity. Assuming

rYS = 0.06 MPa because of insignificant strain rate

dependency observed when _e� 1:7� 10�5 s-1, the best fit

of Eq. (7), which is shown by using dotted curve, is obtained

by using rYVR ¼ 23:4 MPa•sm and m = 0.53. The value of

strain rate sensitivity m = 0.53 suggests that a response can

be intensified approximately 3, 11, and 38 times higher as

strain rate increased 101, 102, and 103 times, respectively.

4 Nanoindentation test results and discussions

4.1 Microstructure of asphalt–filler mixture

Prior to discussion about nanoindentation results, some

results of the analysis on the microstructure of asphalt–

filler mixture are introduced for the sake of the combined

Fig. 4 Load versus time plots for nanoindentation tests in asphalt–

filler mixture. Creep response of asphalt–filler mixture is tested in

constant load-holding stage after constant strain rate indentation

Fig. 5 Uniaxial compression response of asphalt–filler mixture

specimens at various strain rates and temperature of 22 ± 1 �C [30]

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123

understanding of the relationship between microstructure

and indentation response. Figure 7 shows intact nanoin-

dentation test surfaces of asphalt–filler mixture observed at

different points of the specimen. The white granular objects

are the filler grains that form a densely packed matrix. The

intergranular spaces of filler grains are expected to be filled

and bridged by straight asphalt, although the morphology

of asphalt is not clear in the figures due to the dark color.

Figure 8 compares intact and tested surfaces subjected to

single indentation to indicate a residual impression of

Berkovich indenter tip. The intact surface is shown in

Fig. 8a, and in the center part of Fig. 8b showing the tested

surface, a triangular residual impression of the indenter can

be observed.

Asphalt is composed of asphaltenes and maltenes, and

the latter can be further separated into resin, aromatic, and

saturate fractions. Asphaltene has a higher molecular

weight compared to maltenes and is responsible for the

rheological properties of asphalt. The asphaltene, whose

particle size ranges from 5 to 30 nm, is considered to be

dispersed in a continuous maltenes phase in the form of

micelle with resins [54]. Visual observations on asphalts

carried out by using environmental scanning electron

microscopes (ESEM) [43, 45] suggest that the asphalts

have string-like structures in which strings having diame-

ters ranging approximately from 10 to 15 lm are net-

working. However, different visual observations

employing confocal laser-scanning microscopy (CLSM)

[2] indicate that asphaltene aggregates are 2–7 lm in size

and formed dispersed ‘‘sol’’ structure in the continuous

maltene matrix. This structure hardly changes with aging

due to oxidation.

The visual observation results obtained by employing

ESEM and CLSM differ significantly. The latter visual

observation result using CLSM [2] is considered to be true.

This is because the asphalt sample used in the latter

observation must have fewer artifacts caused by sample

preparation. In the observations using ESEM [43, 45], the

maltene phases were removed from the surfaces of asphalt

samples by using beam vaporization technique to observe

asphaltene structure, whereas the CLSM asphalt samples

require no sample preparation. Asphalt microstructures are

sensitive to chemical and temperature conditions.

A scale comparison between typical indentation sizes

and the microstructure of tested asphalt–filler mixture is

shown in Fig. 9. The Berkovich tip is represented as a

conical tip having 70.38 of the cone semiangle. The

microstructure of asphalt–filler mixture is represented

schematically as a composite system in which asphalt is

bridging the filler grains. The filler grains ranging from a

few microns to 30 lm are arranged to have intergranular

spaces for 2–7-lm-sized asphaltene aggregates [2].

Assuming applicability of the expanding cavity model [29]

for the indentations on the asphalt–filler mixture,

Fig. 6 Strain rate sensitivity of unconfined compression yield stress

of asphalt–filler mixture

Fig. 7 Intact test surfaces of asphalt–filler mixture prepared for

nanoindentation. White granular objects are filler grains of calcium

carbonate

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123

development of hydrostatic hemispherical core can be

expected underneath the contact area. Application of the

cavity expansion model for the asphalt–filler mixture sub-

jected to indentation can be justified as follows. The cavity

expansion model has been used to solve problems in which

rigid cones and flat piles penetrate in granular matrix (e.g.,

[14]). In addition, a DEM simulation demonstrated validity

of the cavity expansion model for granular material (e.g.,

[53]). In the asphalt–filler mixture, a hydrostatic pressure

core underneath the indenter tip can be generated more

easily compared to clean granular materials. This is

because the asphalt filling the pore space between the filler

grains can behave as though in a manner of viscous fluids.

As seen in Fig. 9, some medium–large-sized filler grains

ranging from 10 to 30 lm can be involved in the hydro-

static core corresponding to 4- and 8-lm-deep indentations.

Such filler grains are likely to enlarge the size of the

hydrostatic core, or if they are not, the presence of bigger

grains should at least not decrease the size. This is because

the stiff filler grains involved in hydrostatic core can dis-

turb structure located outside of the core by being rotated

and displaced. The CaCO3 filler grains, which are expected

to have the Young’s modulus of roughly 80 GPa (e.g.,

[25]), should be stiffer than asphaltene aggregates. The

expanding cavity model assumes hemispherical plastic

zone developed outside of the hydrostatic core. The rela-

tive plastic zone radius defined as the ratio of plastic zone

radius to hydrostatic zone radius is observed to range from

2 to 8 for typical engineering materials [13]. In such plastic

zone, a number of filler grains can be involved.

Sink-in and pileup of specimen surface adjacent to the

contact area can be major sources of error in analysis of

nanoindentation test results. A finite-element analysis [4]

indicates that pileup is most significant in materials that do

not work harden. On the other hand, pronounced sink-in is

observed in non-work-hardening materials having low E/

rY value or strain-hardening materials. The effect of

Poisson’s ratio on surface profile seems negligible [4]. The

asphalt–filler mixture tested is weak strain-hardening

material as observed in Fig. 5. The values of E/rY calcu-

lated based on the uniaxial compression test results are

12.5, 11.5, 11.4, and 8.93 at strain rates of 4.2 9 10-6,

1.7 9 10-5, 1.7 9 10-4, and 1.7 9 10-3 s-1, respec-

tively. These values are distributed close to the lower limit

of E/rY values investigated in [4]. Thus, the tested asphalt–

filler mixture seems to be categorized in weak strain-

hardening material with low E/rY value. Surface profiles

of materials in this category are unlikely to have significant

sink-in and pileup. In this study, the pileup and sink-in

effects are assumed to be negligible in the contact area

calculation, although direct measurement or visual obser-

vation of surface profile is required to confirm the appro-

priateness of this assumption. Comparing pileup and sink-

in, pileup is more expected because the mixture should be

incompressible. Therefore, there may exist a possibility

that the contact area is underestimated.

Fig. 8 Change of test surface due to nanoindentation: a initial surface

and (b) indented surface on which an impression is observed inside

dotted triangle. Sink-in and pileup are not obvious in the surrounding

part of indented surface

Fig. 9 A schematic scale comparison of microstructure of asphalt–

filler mixture used and 4- and 8-lm-deep indentations. The cone angle

of indicated indenter tip is 70.3�, which is the effective cone angle of

Berkovich tip

Acta Geotechnica

123

Correction of contact depth based on Eq. (4) using

contact stiffness obtained from unloading curve may not be

suitable for viscous materials. For highly viscous materials,

unloading curves could not provide correct contact stiff-

ness due to creep deformation generated even during

unloading. It is assumed in this study that the contact depth

is identical to the indentation depth. In fact, the depth

recovery during unloading is observed to be quite small.

The ratio of the final depth after unloading to the maximum

indentation depth is approximately 0.95. This assumption

potentially overestimates the contact area. This overesti-

mation of contact area and the underestimation due to the

possible surface pileup may offset each other.

4.2 Indentation responses in constant strain rate (CSR)

and constant load (CL) tests

The indentation response of the asphalt–filler mixture

during CSR, CL, and unloading stages is shown in Fig. 10.

Figure 10b shows the same curves in smaller scales to

compare the CSR indentation response. The indentation

load monotonically increases with indentation displace-

ment at any strain rates. There is a general tendency that

the indentation response becomes stiffer as the strain rate

increases. The indentation load values compared at 3.0 lm

of indentation depth are 0.42, 0.69, 2.3, 3.8, 4.5, and 5.8

mN for _eI = 0.005, 0.02, 0.3, 0.4, 0.7, and 1 s-1, respec-

tively. As discussed later, a skin effect of asphalt is con-

sidered to become absent at h = 3.0 lm. Thus, the

comparison of indentation curves at this depth is appro-

priate to eliminate the skin effect from the indentation

resistance.

The strain rate sensitivity of nanoindentation response

can be more clearly observed in a relationship between the

indentation hardness and displacement shown in Fig. 11. It

is observed that the hardness values decrease with

increasing tip displacement. The decreasing rates of hard-

ness are significant especially when h \ 4 lm. The sig-

nificantly higher values of hardness at the shallow depths

may be attributed to skin effect. Oxide films covering the

specimen surface and work hardening during polishing of

test surface can provide higher resistance compared to the

deeper zone. The skin effect seems to become insignificant

when approximately h [ 0.5 lm, because the depth

dependencies of hardness at lower strain rates _eI of 0.005

and 0.02 s-1 become significantly weak at this depth range.

There exists a strong trend in which the hardness becomes

higher with indentation strain rate. For instance, the hard-

ness values at h = 3.0 lm are observed to be 1.90, 3.07,

10.3, 17.1, 20.1, and 25.8 MPa for _eI = 0.005, 0.02, 0.3,

0.4, 0.7, and 1 s-1, respectively. It can be seen in the tested

depth ranges that the hardness values continuously

decrease as the indentation tip penetrates deeper. A

dimensional analysis [11] suggests that the indentation

hardness at constant indentation strain rate reaches a con-

stant value, because the indentation force is proportional to

the square of indentation depth:

P ¼ CPh2 ð8Þ

where CP is material constant. The continuous decrease in

hardness implies that size effect of indentation [37] is not

negligible. The hardness increases with decreasing inden-

tation size [18].

Figure 12 shows the depth profile of Young’s modulus

measured by means of the CSM method. The depth

dependency of Young’s modulus seems to be analogous to

that of H–h relationship indicated in Fig. 11 when

h \ 2 lm. The strain rate dependency of Young’s modulus

becomes less clear as the indentation depth increases. The

highest and lowest values of Young’s modulus at

h = 3.0 lm are 0.72 and 1.2 GPa observed at _eI = 0.005

and 0.4 s-1, respectively. The higher hardness induced by

Fig. 10 Strain rate sensitivity of nanoindentation response of

asphalt–filler mixture: relationship between indentation load and

depth at whole scale (a) and at lower scale (b)

Acta Geotechnica

123

higher strain rate is likely to result in the higher modulus.

Therefore, it may be reasonable to consider that the

dynamic Young’s modulus depends on the strain rate,

although this dependency is not strong. The dynamic

modulus may be more sensitive to the frequency of oscil-

latory loading specified to be 45 Hz in this study. At the

small depths approximately \0.5 lm, the sharp decline of

dynamic modulus is observed regardless of strain rate. This

would ensure that the skin effect is limited within this

range of depth.

Figure 13 shows the indentation creep behavior

observed at CL test stage following the CSR tests carried

out at different strain rates. It can be generally observed

that the creep displacement becomes higher as the inden-

tation force increases.

4.3 Strain rate sensitivity characterization using

hardness–strain rate relationship

The strain rate sensitivity of the nanoindentation test results

can be characterized by using [36]:

m ¼ d log Hð Þd log _eIð Þ : ð9Þ

Figure 14 shows the relationships between hardness and

indentation strain rate observed in both CSR and CL tests.

While the load is held constant during CL test, the hardness

as well as the indentation strain rate continuously decreases

with time. The indenter tip is continuously pushed into the

material to keep the load constant as a material indented

relaxes. As a result, the hardness in CL test decreases

because of the continuous increase in contact area. The

hardness values plotted as the CSR test results are obtained

at h = 5.0 lm. At h = 5.0 lm, the most reliable value of

strain rate sensitivity can be determined. This is because

the h = 5.0 lm is the deepest depth at which six CSR

indentation hardness data are available (the CSR loading at

0.4 s-1 was terminated at h = 5.0 lm). Using the larger

depth value for analyzing CSR data aims at reducing the

effect of length scale on indentation hardness when they

are compared with the indentation hardness values

observed during CL test carried out at further depths. The

strain rate sensitivity value determined from the CSR

results is 0.50. This m value is comparable to the value

determined for the uniaxial yield stress. Note that the

hardness values need to be compared at the same inden-

tation depth in this method. It is confirmed that the values

of sensitivity, m, determined by using the CSR test results

are hardly dependent on the indentation depth. The values

are almost constant in a narrow range from 0.49 to 0.51

even when the m value is determined at h = 1.0, 2.0, 3.0,

Fig. 11 Depth profile of indentation hardness observed during

constant strain rate tests

Fig. 12 Depth profile of elastic modulus of asphalt–filler mixture

obtained by using continuous stiffness measurement method at 45 Hz

Fig. 13 Indentation creep response of asphalt–filler mixture under

constant load conditions

Acta Geotechnica

123

4.0, 6.0, 7.0, and 8.0 lm. Also in the CL test results, the

log H versus log _eI data emerge as linear relationships. The

m value varies from 0.15 to 0.45, and this variation in

m value seems to be attributed to the indentation size

effect.

Extraction of the strain rate sensitivity by using the

limited number of indentation data may not be reliable. The

most critical factor causing the error in strain rate sensi-

tivity should be a variation in local microstructure of

asphalt–filler mixture. A large deviation of local packing

density of filler grains may result in inconsistent strain rate

dependency of indentation behavior. Repeatability of

microscopic indentation can be confirmed by comparing

two indentation curves observed at very close indentation

rates of _eI ¼ 1 and 1.1 s-1. The difference in indentation

load between these data is 0.16 mN at 1.27 lm of depth.

This difference of load is equal to 8.0 % of the average of

two load values. This insensitivity of indentation behavior

to a variation in local microstructure may be related to the

softness of asphalt–filler mixture. Generally, more brittle

materials tend to have higher variability in strength (e.g.,

[48]). Compared to Portland cement concretes that are

typical brittle material, the asphalt–filler mixture is much

more ductile as seen in Fig. 5. In addition, the indentation

load–depth curves seen in Fig. 10 are generally consistent

regarding the rate effect. The higher the indention strain

rate is, the higher the contact stiffness is. Such consistency

in indentation response should not emerge, if the effect of

local microstructural variation is significant. Another

potential mechanism is that the asphalt–filler mixture is not

porous. In homogenization of porous composites such as

Portland cement concretes and shales, pore space plays an

important role [19]. Furthermore, the effects of a variation

in local microstructure and indentation scale on the m value

determination can be less significant by increasing the

length scale of indentation. As the indentation depth

increases, the number of constituent elements of tested

sample involved in the deformed zone should increase. As

a result, the effect of variation in local microstructure

should be less pronounced and more homogenized. The

insensitivity of m value to CSR indentation depth may

confirm that after several microns of indentation, the effect

of indentation length scale on m value (not on indentation

hardness) decreases a negligible level. In microscopic

indentation responses of nonporous composites, the influ-

ence of local porosity variation is eliminated. These points

can guarantee a minimal reliability of the dataset obtained.

In the CSR test, characterization of the strain rate sen-

sitivity based on Eq. (9) seems to be straightforward.

However, using the CSR indentation data to extract the

strain rate sensitivity as a compatible value with that of

sample subjected to uniaxial compression needs to be jus-

tified. Precise definition of the meaning of observed

indentation hardness is not presented, because it is out of

the scope of this manuscript. However, the strain rate

sensitivity determined from the CSR indentation hardness

may be acceptable as a material property of the asphalt–

filler mixture, if the microstructural change experienced

during indentation is independent of indentation strain rate.

The morphology of uniaxially compressed cylindrical

samples of asphalt–filler mixture is observed to be insen-

sitive to the strain rate. Even the asphalt concrete samples

that have more complicated microscopic structure due

to the presence of silica grains indicate a negligible effect

of strain rate on their morphology. These observations

confirm that strain rate can have a negligible effect on

morphology of the asphalt–filler composite phase subjected

to indentation.

On the other hand, the validity of CL creep test for strain

rate sensitivity characterization is sometimes questionable.

It is considered that the plastic zone created underneath the

hydrostatic core is continuously expanded during a CL test

(e.g., [44]). As assumed in some phenomenological vis-

coelastic models such as Burgers model, general creep

behavior can be separated into transient and stationary

components modeled using the parallel unit of spring-

dashpot and the single dashpot, respectively. In the primary

creep stage, the transient component is predominant. In a

material subjected to CL test, the most outside region of

plastic zone should be always at the primary stage in which

the transient component is predominant, whereas the

internal region of plastic zone should be at the secondary

stage in which the stationary creep is predominant. This

means that the strain rate may not be uniform in the plastic

zone.

Fig. 14 Strain rate sensitivity of indentation hardness of asphalt–

filler mixture observed in constant load creep test. CSR reg. and UC

denote regression line for CSR indentation data points and uniaxial

compression test data, respectively

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123

In Fig. 14, the uniaxial compression yield stress data of

asphalt–filler mixture are also indicated for comparison. It

is seen that the CL test data obtained at 4.7, 7.1, and 12 mN

coincide with the uniaxial yield stress at 1.7 9 10-3 s-1 of

strain rate. The data plots obtained from CSR test at

h = 5.0 lm and CL tests at 0.92 and 14 mN are located

lower than those of uniaxial yield stress. Some previous

studies show that the constraint factor in Eq. (5) for com-

posites can increase from 3 with the friction angle [12, 20].

The comparable or lower values of indentation hardness

compared to uniaxial yield stress may suggest that the

indentation hardness at a length scale of microns is not

affected by intergranular friction of filler grains.

Although the determined values of m are not consistent,

the linearity of log H versus log _eI relationships in the CL

tests is satisfactory. In addition, the m values from CL tests

except for that observed at P = 1.8 mN (cross-plots) are

comparable and in a narrow range from 0.37 to 0.45.

Moreover, this m value range is not largely different from

the m values determined from the CSR uniaxial compres-

sion and indentation tests. From these points, it is believed

that CL indentation test would still be valid in the strain

rate sensitivity characterization. More consistent m value

may be obtained by correcting the observed m values based

on knowledge about the continuous growth of nonuniform

plastic zone.

The exceptional CL test data at P = 1.8 mN is consid-

ered to be strongly affected by the indentation size effect.

This is because the indentation depth range in which this

result is obtained is obviously smaller than those of other

tests as shown in Fig. 13. The indentation depth range at

P = 1.8 mN is from 1.2 to 2.7 lm, whereas those of the

others are more than 5 lm. The considerably higher

hardness values during the CL test at P = 1.8 mN ranging

from 10 to 22 MPa are also likely to be an evidence of the

indentation size effect.

4.4 Indentation size effect in hard filler-containing soft

composite material system

Nix and Gao [37] developed a model of indentation size

effect based on the studies of [15] and [46]. The indenta-

tion size effect on hardness is given by:

H

H0

¼ffiffiffiffiffiffiffiffiffiffiffiffiffi

1þ h�

h

r

ð10Þ

where H0 is the hardness that would arise from the

statistically stored dislocations [1] alone, in the absence of

any geometrically necessary dislocations, and h* is a length

characterizing the depth dependency of the hardness. The

model describes the effect of geometrically necessary

dislocations advancing in indented material on observed

hardness. The size effect becomes more significant as the

indentation size decreases. Figure 15 indicates the depth

dependency hardness in the CSR indentation test in the

relationship of [H/H0]2 with h-1. The determination of the

H0 values is discussed below. From the CSR indentation

test results (Fig. 14), the strain rate dependency of hardness

is given by:

H ¼ CH hð Þ _em ð11Þ

where CH(h) is a function of indentation depth because the

hardness decreases as the indentation depth increases. The

value of m was observed to be constant at approximately

0.50 regardless of depth. The depth dependency of

hardness may be given by:

CH hð Þ ¼ Chhn ð12Þ

where Ch and n are material constants. These values are

determined to be 54.7 MPa/lmn and -0.742 from the CSR

indentation data, respectively. It is assumed that the H0

values at respective strain rates are observed at h = 30 lm.

This is based on an idea that indentation up to a depth

comparable to the largest constituent size in material seems

sufficient to reach a state in which statistically stored dis-

locations are predominant. If the data plots are observed to

be linear relationships, the model could be applicable.

However, such trends cannot be seen clearly in the figure,

although data plots at _eI = 0.3 s-1 are in a good agreement

with Eq. (10).

To discuss the inapplicability of the size effect model to

the tested asphalt–filler mixture, the nanoindentation model

originally proposed for crystalline materials is reviewed.

The indentation size effect on hardness is obvious, but it is

not describable by using the original size effect model.

Figure 16 illustrates the assumed material deformations

affected by geometrically necessary dislocations for the

derivation of original model [37]. The indented material is

assumed to accommodate the indenter tip by forming rings

of geometrically necessary dislocations in a concentric

fashion. The spacing of individual geometrically necessary

dislocations is denoted by s. The parameter H0 is the

asymptotic value of hardness that should be observed at

infinite indentation depth and defined as:

H0 ¼ cconsS ð13Þ

where sS is shear flow stress required to cause statistically

stored dislocations only and is likely to be a function of

the density of statistically required dislocations. The

parameter ccon is the constraint factor. The characteristic

indentation depth h* originally defined for crystalline

materials is:

h� ¼ 81

2bkc tan2 b

lH0

� �2

ð14Þ

Acta Geotechnica

123

where b is the Burgers vector characterizing the magnitude

of dislocation in a crystal lattice, kc is a constant depending

on the crystalline lattice system, and l is the shear

modulus.

For the asphalt–filler mixture, the characteristic material

length may be given in the following form:

h� ¼ h� b; l; H0; dð Þ ð15Þ

where d is characteristic length scale for microscopic dis-

locations. In granular composite materials, the character-

istic length scale may be the grain size of the hardest

constituent in composite system. In the asphalt–filler

mixture, the filler grains are possibly the unit of charac-

teristic length scale. This is because the hard grains of filler

can survive and remain in intact shape during indentation.

Therefore, the geometrically necessary dislocations should

preferentially occur at interfaces between asphalt and filler

grains that are more susceptible to damage.

It can be seen from Fig. 15 that the tangential slope of

[H/H0]2 versus h-1 becomes lower as the indentation depth

increases (i.e., h-1 decreases). There are indications that

the [H/H0]2 versus h-1 curves seem to follow Eq. (10)

when h-1 \ 0.2 lm-1 (i.e., h [ 5 lm). The curves

decrease in the tangential slope as the value of h-1

decreases and seem to move into a different phase at that

depth range. Assuming applicability of Eq. (10) at

h [ 5 lm, a potential mechanism of the deviation of the

observed size effect from Eq. (10) at the shallower depth

can be thought of as the effect of plastically graded surface

[6]. The surface of asphalts is susceptible to oxidation and

can be stiffer. Also, the microstructure of asphalt binder

can be another factor of forming the graded surface. The

previous indentation study exploring the microstructure of

asphalt binders [26] showed that the creep compliance of

asphalt binders significantly depends on the indentation

force and increases with load due to a string-like structure

of asphalt. The higher load caused the deeper indentation.

Thus, this observation indicates that the deeper zone of

asphalt binder can be lower in the indentation hardness.

These two potential mechanisms can result in the plasti-

cally graded surface of asphalt–filler mixture in which the

indentation hardness becomes lower with increasing depth.

The intensive size effect of asphalt–filler mixture seen in

Fig. 15 can be attributed to the effect of plastically graded

surface in addition to the size effect expressed by Eq. (10).

It is demonstrated that the strain rate sensitivity of

asphalt–filler mixture can be characterized by means of the

relationship between indentation hardness and indentation

strain rate observed at various constant strain rates. The

constant load indentation creep test is possibly available for

the rate sensitivity characterization, but caution is required

for indentation size effect on the sensitivity value. Even in

CSR test, the hardness is indentation size dependent. The

analysis on the indentation size effect of hardness suggests

that the asphalt–filler mixture has a plastically graded

surface causing the stronger size effect.

5 Conclusion

The asphalt–filler mixture bridging coarse aggregates in

asphalt concrete was characterized in terms of strain rate

sensitivity by means of nanoindentation test. The asphalt

concrete specimen was carefully prepared by being polished

with diamond suspension and subsequently finished with

0.05 lm of alumina suspension. Initially, the indentation

loading was carried out at constant indentation strain rates

Fig. 15 Depth dependence of indentation hardness during CSR test

Fig. 16 A schematic illustrating indentation size effect after [37].

Characteristic strength is assumed to be dependent on filler grain size

Acta Geotechnica

123

ranging from 0.005 to 1.1 s-1 (CSR test). After the inden-

tation depth reaches the specified values, the indentation

load was held constant to test creep behavior (CL test).

The strain rate dependency of the asphalt–filler mixture

subjected to uniaxial compression test was reviewed. The

strain rate sensitivity value was determined to be 0.53 in

terms of uniaxial yield stress. During CSR tests, the

indentation hardness, H, continuously decreased as the

indentation depth increases. It was demonstrated that the

strain rate sensitivity can be characterized by comparing the

CSR indentation hardness values at the same indentation

depths. The determined sensitivity value was approximately

0.50, and this value was not depth dependent. The strain rate

sensitivity values were determined to be in a range from

0.37 to 0.45 when the hardness versus strain rate data during

CL creep tests were used. These values were smaller than

those of the uniaxial compression and CSR indentation test

values. The satisfactory linearity of H versus _eI relations

during CL tests and the sensitivity value range close to those

of the other tests supported the potential capability of CL

creep test for characterizing the strain rate sensitivity of

asphalt–filler mixture.

The indentation size effect on the hardness observed in

the asphalt–filler mixture was discussed based on the

analysis using the size-dependent hardness model in which

geometrically necessary dislocations were assumed as the

mechanism of size effect [37]. The observed size effect

was more significant than that of the model predicted. The

stronger size effect was attributed to the indentation depth

dependency of the plastically graded surface of asphalt-

binder mixture caused by a surface oxidation and string-

like structure of asphalt binder.

Acknowledgments Financial support provided by the National

Science Foundation under grant no. CMS-0625927 is gratefully

acknowledged. The author appreciates Masood Hashemi and Todd

Mellema providing us technical support for nanoindentation testing

and asphalt bitumen, respectively.

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