Fatigue and Creep crack growth in Asphalt Materials
Jan Zuidema1, Ad Pronk2 and Fedde Tolman3
Laboratory for Materials Science, Delft University of Technology, R’damseweg 137, 2628 AL, Delft, The Netherlands
2 Ministry of Transport and Public Works / Road and Hydraulic Engineering Division, P.O. Box 5044, 2600 GA Delft, The Netherlands
3 Netherlands Pavement Consultants, P.O. Box 2756, 3500 GT Utrecht, The Netherlands
Traffic loading is one of the main causes of deterioration of asphalt concrete pavements. Asphalt mixtures,
consist of a graded mineral aggregate bound by bitumen and are therefore inhomogeneous visco-elastic
materials, in which defects are always present. When
the stresses are high enough, defects act as crack initiators. Both cyclic loading and constant (non-cyclic)
loading may result in crack initiation and growth. In
this work we compare the crack growth which occurs
in practice due to long-term repetitive traffic loading
(i.e. fatigue) with crack growth due to constant loading (i.e. creep) for two different asphalt materials.
100
K = 0.33 MPam, R = 0.1, f = 10 Hz
a (mm)
80
60
40
20
0
200000 400000 600000 800000
N (cycles)
Figure 1. crack length versus number of cycles
in a constant K test.
We will describe crack growth using the stress intensity factor K, being a geometry independent unifying
parameter. It is assumed that the stress field near the
crack tip may be described by this linear elastic fracture mechanics parameter K, the stress intensity factor, only under certain circumstances of temperature
and frequency. Use of this factor yielded in previous
investigations reasonable results, although it is realized that the material in study is not linear elastic.
In these previous investigations fatigue tests were performed at positive and negative values of the load ratio R (i.e. tensile and compression stresses). The results will be compared with results from constant load
experiments, where the crack growth mechanism is
creep, i.e. slow stable crack growth.
The fatigue tests were also performed at different frequencies. With a simple calculation it is possible to
distinguish for the relative contributions of fatigue
and creep mechanisms on crack growth and for predicting the shift in the fatigue crack growth per cycle,
da/dN, for different frequencies.
It was shown (1,2) that for positive values of the load
ratio R (i.e. only tensile stresses), it was possible to fit
the results for different frequencies into one scatter
band, when the frequency f times the crack growth
rate per cycle, da/dN, was plotted against K. The
crack growth mechanism is creep then, as in this case
the effect of R on the results of the fatigue tests can
be predicted from the results of slow stable crack
growth (creep) under constant loading.
However, for negative R-values (i.e. with also compressive stresses) this was found to be not possible.
Fatigue becomes an important crack growth mechanism in such cases.
In order to investigate the fatigue and creep crack
EXPERIMENTS
Crack growth tests were performed on center-cracked
tensile specimens 390 mm long, 230 mm wide and 30
mm thick (2 mm stone) or 40 mm (8 mm stone) under
fatigue and creep loading conditions.
The first material was sand asphalt with a maximum
aggregate size of 2 mm (Dutch code dab 0/2). The asphalt mix contained 8.5-wt % bitumen 45/60; the
mineral aggregate consisted of 20% Wigro filler, 75%
crushed sand and 5% river sand. The other material
was dense asphalt concrete with a maximum aggregate size of 8 mm (Dutch code dab 0/8). This asphalt
mix contained 7% bitumen 80/100; the mineral aggregate consisted of 31.3% 4/8 stones, 22.4% 2/6
stones, 6.8% V40K filler, 29.6% crushed sand and
9.9% river sand. The test temperature for all tests was
0 ºC.
Fatigue and creep crack growth tests were performed.
Various frequencies and R values were used for the
fatigue crack growth tests. Fatigue tests were performed either with constant load amplitude or with
constant K. In both cases this was achieved by controlling the (sinusoidal) load. The crack length was
found by digital image processing. The procedure is
described in detail by Riemslag (3).
THEORY
The linear elastic K factor for the specimens is:
P
a
K
a sec( )
(1)
t w
w
The accuracy is < 1% for 2a/w  0.8.
In Figure 1 the measured crack length versus the
number of cycles is shown for a constant K test. The
linear result in this figure is the basis for the use of K
as a crack growth controlling parameter, i.e. the crack
growth rate da/dN is independent of the crack length.
If the crack growth under constant amplitude fatigue
loading conditions is due to a pure creep mechanism,
then the crack growth rate da/dt = f da/dN is not fre-
quency-dependent. If we compare two situations with
different fatigue loading frequencies f1 and f2 we obtain in a pure creep case
f1·(da/dN)f1= f2·(da/dN)f2
(2)
where (da/dN)f is the increase in crack length per cycle for frequency f.
However, if we have a pure fatigue crack growth
mechanism, there is no frequency dependence of
da/dN. In this case:
(da/dN)f = (da/dN)f
(3)
1
2
Thus when we perform tests at different frequencies,
we will obtain overlapping results in the case of a
pure creep crack growth mechanism when we plot
f da/dN versus K. This was found in (1) for fine
sand asphalt for all positive R values, but not for negative R - values. It was concluded that for positive Rvalues the growth mechanism is pure creep and for
negative R-values it is a mix of fatigue and creep
mechanisms. We now assume that a simple superposition of both
1000
100
da/dt ( m/sec)
growth rate behavior in asphalt mixes further, a new
series of experiments was conducted on centercracked tensile specimens.
10
P = 5 kN (dab 0/8)
1
P = 5 kN (dab 0/8)
da/dt = 878 K^3.65 dab 0/8
P = 4 kN
P = 4.8 kN
0.1
da/dt = 330 K ^4
0.1
1
K (MPam)
Figure 2. Creep crack growth tests of both
materials.
fatigue and creep parts is permitted.
The pure fatigue part of da/dN can be found by meas-
uring the real da/dN and calculating da/dN for pure
creep, using a creep crack growth relation. Subtraction then delivers the pure fatigue part.
spread the trendlines for 1 Hz and 10 Hz are separated
by a factor of about 10. The result at 29.3 Hz does not
fit so well compared with the other two.
RESULTS
In figure 2 creep crack growth results are shown. The
crack growth rate da/dt is plotted against K.
Tests were performed under constant load conditions.
Very much spread in results is found for the coarse
dab 0/8. A possible cause may be the material inhomogeneity. Trend lines are plotted trough the results.
Type of “Paris relations” can be found for the da/dt
versus K, see figure 2.
da/dN (m/cycle)
100
10
1
1 Hz
10 Hz
29.3 Hz
fit for 1 Hz
fit for 10 Hz
fit for 29.3 Hz
0.1
100
crack length (mm)
90
0.01
80
0.1
1
K (MPam)
70
60
50
Figure 4. crack growth rate versus K for
three frequencies for dab 0/8.
40
30
20
f=29.3 Hz, R=0.18, DeltaP=7.9 kN
10
f=10 Hz, R=0.1, DeltaP=7 kN
f=1 Hz, R=0.1, DeltaP=7 kN
0
0
100000
200000
N (cycles)
300000
Figure 3. crack length versus number of cycles
for three frequencies for dab 0/8.
In Figure 3 results are shown of crack length versus
number of cycles for dab 0/8. The crack growth started at about 24 mm for the three tests. The mechanical
parameters are almost identical except for the frequency. It can be seen that about 10 times more cycles are needed for crack growth until 50 mm for the
test at 10 Hz compared with the test at 1 Hz. This
points to a creep mechanism of crack growth. This
fact is also visible in Figure 4 where the crack growth
rate da/dN is plotted against K. Despite the large
In Figure 5 the effect of R is shown for da/dN versus
K plots for material dab 0/8. The trendlines and the
corresponding formulae are also shown. The fat lines
through the data points are predictions based on a calculation of da/dN – K using the creep data of Figure
2. These creep equations form the basis for the prediction of da/dN (or f da/dN) versus K, when a pure
creep crack growth mechanism is present.
For calculation of the creep part of da/dN the sinusoidally varying K fatigue loading signal is divided into
100 steps per cycle. For each step the crack growth
increase is calculated using the creep equations. The
result of the calculation matches the measurements
quite reasonable for these R-values of 0.5 and 0.1. In
Figure 6 a plot is shown for dab 0/2. Besides R=0.5,
also a negative R=-1 is used for these results. The
same calculation of da/dN is also performed here.
The result of the calculation matches very good for
R=0.5, but not for R=-1. In the latter case a calculation based only on creep equations is obviously not
allowed when also compression stresses are involved.
10
da/dN (m/cycle)
predictions
ing the da/dN at a different frequency. We have found
that f da/dN (and da/dN ) at K = 0.7 MPam is 1/3
due to creep and 2/3 due to fatigue (for R = -1 and
f = 29.3 Hz).
100.0
1
R = 0.1
y = 478.12x4.0731
0.1
R = 0.5
0.01
0.01
y = 27.372x4.6731
R2 = 0.7734
0.1
1
fda/dN (µm/sec)
R2 = 0.8367
10.0
R = 0.5
R = -1
1.0
R = 0.5
R = -1
K (MPam)
Figure 5. R-effects and predictions for
dab 0/8.
Note that in Figure 6 f da/dN is plotted versus K in
stead of da/dN as in Figure 5.
A very good result is obtained for a positive R = 0.5
value with only tensile stresses
For the negative R = -1 value the prediction does not
fit the actual results.It is assumed that a fatigue contribution to da/dN is present in this situation
We can use the measurement results to find the pure
fatigue contribution. The real f da/dN at K = 0.7
MPam and R = -1 is assumed to consist of a superposition of pure creep and pure fatigue parts. The real
f da/dN value = 3 m/s. The creep part = 1 m/s, as
calculated. This leads to a pure fatigue f da/dN of 2
m/s.
PREDICTION OF da/dN AT A DIFFERENT
FREQUENCY
The foregoing result offers the possibility of predict-
pure creep
prediction
Power (R = 1)
0.1
0.1
1.0
K (MPam)
10.0
Figure 6. R-effects and predictions for dab
0/2.
We can now predict da/dN at f = 2.93 Hz . When the
frequency is lowered by a factor of 10, from 29.3 to
2.93 Hz, only the pure creep part of the real da/dN
( 1/3 of the total value) will be affected.
This part will increase by a factor of 10, see equation
2. The fatigue part will be unaffected by a frequency
change. This leads to:
(da/dN) 2.93 = 10 1/3 (da/dN) 29.3 + 2/3
(da/dN) 29.3 = 4 (da/dN) 29.3
(4)
A change in frequency by a factor of 10 will thus lead
to a change in crack growth rate by a factor 4 for
R=-1, see Figure 7.
CONCLUSIONS
The asphalt material dab 0/8 shows a much larger
crack growth rate than the material dab 0/2. Predictions of da/dN, based on creep crack growth data,
seems justified for positive values of R, thus for tensile stresses. For negative R-values the prediction
doesn’t work so well. It is assumed that fatigue plays
a role under these circumstances. We conclude that it
seems justified to divide the crack growth rate at negative R-values into pure fatigue and creep parts. The
total crack growth rate da/dN can be found by simple
addition of the pure fatigue and creep crack growth
rate parts.
da/dN (m/cycle)
10
1
2.93 Hz
0.1
29.3 Hz
R = -1 and P = 10 kN
0.01
0.1
1
K (MPam)
Figure 7. results of identical tests (except
for the frequency) for dab 0/2
SYMBOLS USED
a
f
K
N
P
deltaP
R
t
w
= length of a single crack (in mm)
= frequency
= stress intensity factor (MPam)
= number of cycles
= load (in kN)
= Pmax - Pmin
= load ratio = Pmin/Pmax = Kmin/Kmax
= specimen thickness
= specimen width
REFERENCES
10
1) Kleemans, C.P., Zuidema, J., Krans, R.L., Molenaar, J.M.M. and Tolman, F., Fatigue and
Creep Crack Growth in Fine Sand Asphalt Materials, Journal of Testing and Evaluation, Vol. 25,
No. 4, July 1997, pp. 424-428.
2) Jan Zuidema, Johan Schulte, Rutger L. Krans and
Fedde Tolman, Creep-Fatigue Interactions during
Crack Growth in a Fine-Sand Asphalt Concrete
Mixture, ECF12 Fracture From Defects, pp 15331538, Vol III, september 1998, Sheffield
3) Riemslag A.C., Crack growth in polyethylene,
Delft University Press, ISBN 90-407-1453-3,
Delft, 1997.