PPT describing Fatigue Behaviour of Concrete

1. Fatigue strength
1

2. Types of fatigue failure in concrete.
• Like metals, concrete specimens too can experience
fatigue failure.
• Fatigue failure occurs at stresses below the strength of the
specimen as obtained in a standard test.
• In the case of concrete, there are two types of fatigue
failure: static fatigue and fatigue due to cyclic loading.
• Static fatigue occurs when a specimen is loaded with a
slowly increasing load i.e. a rate of loading significantly
below that used in standard tests.
• Recall standard tests in concrete usually have a specified
rate of loading (about 2 – 4 minutes to the application of
the total load)
2

3. Why does static fatigue occur?
• Static fatigue can also occur if a load is applied at the
standard rate, but is sustained, i.e. held constant thereafter
at a stress level below the static strength.
• In such situations the specimen may fail prematurely.
• Recall that the strength of concrete is sensitive to the rate of
loading.
• At loading rates higher than in the standard tests, the failure
stress is higher and the strain at failure is smaller. Concrete
appears more brittle at higher loading rates.
• Conversely for loading rates smaller than in the standard
tests, the failure stress is smaller, and the strains at failure
are higher.
• The reason for this is creep. 3

4. Static fatigue: low loading rate
Rapid
3 mins
3days
50 days
Static Fatigue
failure envelope
1.2
1.0
0.8
0.6
0.4
0.2
1.E-3 2.5E-3 3.5E-3 6.5.E-3 ε
term
short
σ
σ
4
(Standard rate)

5. Static fatigue: low loading rate
• Lower loading rates mean that each increment of load ΔP
is held constant and acts over a longer time.
• Since each constant load increment acts longer – more
creep results.
• Lower loading rates therefore trigger more creep strains.
• The creep strains and the resulting micro cracking in the
concrete lowers the strength.
• Static fatigue can lower the strength to about 70 – 80% of
the value as obtained from standard tests.
• However, why does the static fatigue failure envelope
flatten out? The answer is not clear. 5

6. Static fatigue: standard loading rate
• An alternative mechanism for static fatigue involves
situations where the load is applied relatively quickly, (say
at or near the rate of loading in standardized tests) but is
held constant at a value less than the short term strength.
• If the load is held at 70-80% of the short term strength over
a long time, the sustained load will result in sufficient
accumulation of a critical amount of creep (and the
attendant growth of micro cracks) so as to cause failure at
this load itself.
• However for load levels below a threshold value, failure
will not occur – though the concrete will exhibit significant
creep strains. 6

7. Static fatigue: standard loading rate
3 mins
Static Fatigue
failure envelope
1.2
1.0
0.8
0.6
0.4
0.2
2.5E-3 10.E-3 ε
term
short
σ
σ
Strain Limit after 30 years
No fatigue failure due
to static fatigue below
this stress level
7
(But no failure)

8. Cyclic fatigue
• Cyclic fatigue occurs during cyclic loading and is usually
known simply as “fatigue” as distinct from “static fatigue”
• Cyclic loading involves subjecting a specimen to the same
repeated loadings and unloadings sequentially.
• Failure typically occurs after several cycles. The number of
cycles to failure N, depends on the nature of the single
loading cycle. 8

9. Cyclic fatigue
• After a large number of such cycles, the specimen may fail
at stresses smaller than the short term static strength.
• The stress referred to above is usually the maximum or
minimum stress during the cycle.
• However in many materials, if the maximum stress during
a cycle is less than a certain threshold value, fatigue failure
does not occur even after cyclic loading over tens of
millions of cycles.
• The threshold stress below which cyclic loading does not
result in fatigue failure is known as the “endurance limit” of
that material. 9

10. Endurance Limit, S-N curve
10
•Unlike steel, concrete does not have an “endurance limit”.

11. Cyclic loading in concrete
• We consider a concrete specimen subjected to cyclic
loading, with the stress alternating between zero and a
certain fraction (<1.0) of the compressive strength.
• The shape of the loading-unloading stress-strain curve is
found to vary with the number of cycles.
• Initially the loading curve is concave towards the strain
axis.
• Then it straightens and finally becomes concave towards
the stress axis.
• This results in an increase in the elastic strains and a
decreasing value of the secant modulus.
11
σ
t
σc

12. Shape of loading unloading curve
12
•As in case of static fatigue, at failure after many cyclic loading
cycles, the strain at failure is much higher than the failure strain
in short term standardized tests.
400 800 1200 1600 2000
6
-
10
×
ε
Mpa)
(
σ
1 675 341,000 cycles
20

13. Change in hysteresis with number
of cycles
• The area enclosed between the loading and unloading
curve corresponds to the loss of energy (hysteresis) during
a cycle.
• From the description of the loading unloading curve, it is
clear that hysteresis is large during the initial cycles, then
decreases as the number of cycles increase.
• When fatigue failure is approaching, there is extensive
cracking at the aggregate interfaces.
• At that stage, inelastic strains and hence hysteresis again
increase rapidly.
13

14. Change in hysteresis with stress
amplitude
• Little hysteresis is noticed for loading cycles where the
maximum stress is less than half the compression
strength.
• Significant hysteresis occurs for loading cycles where the
maximum stress approaches the uniaxial compression
strength.
• For such cycles, the slope of the unloading curve reduces
significantly after an initial steep part, and approaches the
strain axis with a relatively gentle slope.
• On reloading the slope is steeper – though less than in the
initial ascending branch.
14

15. Change in extent of hysteresis with
stress amplitude
15
ε
σ
fc

16. Cyclic loading on the softening
branch
• Once the amplitude of the stress cycle reaches the peak
stress, if the specimen is reloaded, the new peak stress is
somewhat smaller than the peak stress of the previous
cycle.
• There is significant softening during each subsequent
cycle: peaks in subsequent cycles are smaller than the
peak stresses during the previous cycles.
• Upon unloading there is a gradual reduction in slope.
• However on reloading there appears to be a stiffness
recovery, although again the slope is smaller than the
previous ascending branch.
16

17. Cyclic loading on the softening
branch
17
ε
σ monotonic
loading
curve

18. Comparison with monotonic loading
• It is found that that in the post peak region, the shape of the
stress-strain curve for the monotonically loaded specimen
closely follows the peaks of the stress-strain curves for the
cyclically loaded specimens.
• Before the widespread availability of loading machines with
feedback control, the post peak portion of the uniaxial
compression curve was sometimes generated through cyclic
loading tests in the post-peak region.
18
Xu et al., Int. Jour. Of
Concrete Structures &
Materials, 12,(68) 2018

19. Two dissipative mechanisms
• Several authors have tried to relate the slope of the
loading and unloading curves under cyclic loading to
energy dissipation during the cyclic loading.
• There appear to be two dissipative processes. The first
process governs energy dissipation during the loading
part of the cycle.
• The damage during loading results in the progressive
reduction of slope of the loading branch of the curves.
• Therefore release of inelastic fracture energy during this
process constitutes the first dissipative mechanism.
• The second process affects energy dissipation during both
loading and unloading parts of each cycle.
19

20. Damping dissipation
• However the effect of the second mechanism, which
provides a damping effect, is most clearly seen during the
unloading part of the cycle.
• Initially during unloading the viscous damping forces are
low. Therefore for a certain strain increment Δε the
change in stress Δσ is relatively high.
• As unloading progresses the magnitude of the viscous
damping forces increase. This slows down the rate at
which stress reduces with strain.
• This results in a gradual reduction of slope of the
unloading curve.
• The recovery of elastic stiffness during the subsequent
reloading, as compared to the stiffness of the unloading
branch, is because of crack closure under compression.
20

21. S-N curves
• For a constant range of alternating stresses, the number of
cycles to fatigue failure increases with reduction in the
maximum stress level in the cycles.
• This is shown by S-N curves where either the maximum
stress, or the ratio of the maximum stress to the short term
static strength (S), is plotted against N (the number of
cycles to failure).
• S-N curves are invaluable design tools.
• Given knowledge of the S-N curve of a material, and
knowledge of the maximum stress level that may occur in
a specimen during a single cycle of design load, it is
therefore possible to predict the fatigue life of the
specimen.
21

22. S-N curves for Concrete
• To define SN curves, it is necessary to perform cyclic tests
for a very large number (more than 1 million) cycles.
• However SN curves for concrete are not very good
indicators of fatigue strength – they have very large
scatter.
• This is partly due to the uncertainty in the short-term
strength of the test specimens, as well as the stochastic
nature of fatigue.
• Thus for concrete specimens the SN curve cannot
accurately determine the number of cycles to failure for a
particular alternating stress.
• They only give an estimate, rather than a prediction, of the
fatigue life of the specimen.
22

23. Range of loading
• The number of cycles to failure also depends on factors
additional to the maximum stress during the cycles.
• It depends on the mean stress, the mode of the maximum
and minimum stress, as well as the range (the range being
the difference between the maximum and minimum stress).
• The mode of the maximum and minimum stress indicates
whether the stress is compressive or tensile, or whether the
loading is uniaxial or flexural.
• Recall that concrete behaviour is highly sensitive to the
mode of loading.
• Expectedly, the fatigue life also shows significant
dependence on the mode of cyclic loading.
23

24. Dependence on mean stress
• Mean stress and alternating stress
interact to determine the fatigue life.
• The combined influence of both on fatigue life is captured
by an empirical equation proposed by Goodman:
• For a specified number of cycles, say ‘N’ to fatigue failure,
this relation predicts that the peak value of the alternating
stress occurs when the mean stress of each cycle is zero.
• The magnitude of the alternating stress, for fatigue failure
in N cycles, reduces linearly with increase in mean stress.
)
( min
max 

 

alt
)
(
2
1
min
max 

 

mean
)
1
(
static
mean
fat
alt



 


24

25. Goodman Diagram
25
alt

mean

static

fat

FATIGUE
FAILURE
SAFE
Example of
Goodman diagram

26. Mode of loading
• Under uniaxial tensile loading cycles, when both the
maximum and minimum stresses are tensile, the rate of
decline in strength with number of cycles is smallest.
• On the other hand, experiments with alternating tension –
compression stresses show S-N curves with a distinctly
steeper slope than purely tensile cyclic loading.
• Similarly, uniaxial compressive loading cycles, when both
maximum and minimum stress are compressive, show a
faster accumulation of fatigue damage than purely tensile
loading cycles.
26

27. Mode of loading
1
.8
.6
.4
.2
0
102
104
106
108
cycles (log scale)
S
compression
tension
27

28. Effect of aging on fatigue strength
• Concrete strength increases with age. Thus the fatigue
strength also increases with age.
• This can be accounted for if the strength of concrete under
monotonic loading at the appropriate age is used as the
basis to compute fatigue life.
• Thus the effect of aging would be automatically
incorporated in the SN curve.
• However the effect of aging is relatively small for most
concretes and should not cause a major difference, if
neglected.
28

29. Time between loading and
unloading
• The time between loading and unloading, i.e. the
frequency of the loading and unloading cycles also has a
small influence on fatigue strength.
• This influence is noticeable particularly at low frequencies
e.g. frequencies of less than 1 Hz.
• A reduction in the frequency of loading i.e. an increase in
time between loading and unloading cycles lowers the
fatigue strength.
• This is due to the increase in creep strains because of the
larger time gap between loading and unloading cycles.
29

30. Non-constant stress range
• During realistic cyclic loadings, it is quite possible that the
range of stress will not remain constant throughout the
loading cycles.
• A particular value of maximum stress and a certain stress
range may be applied for say N1 cycles, following which
the maximum stress and the stress range may change and
remain constant for a further N2 cycles and so on.
• As an example one might consider wave loading on
offshore or coastal structures.
• During a storm of short duration, such a structure is
subjected to cyclic loads with large maximum stresses. But
once the storm subsides, the stresses are smaller.
30

31. Wave loading on coastal structures
31
A storm surge

32. Miner’s rule
• The individual contribution of one particular loading to
fatigue damage is assumed equal to the ratio of the
number of cycles ni at a given stress amplitude i to the
number of cycles of failure, Ni at that stress amplitude.
• Miner’s rule assumes that failure will occur when the total
damage contribution M, accumulated from a history of
such loadings is equal to unity.
• For a particular loading i, Ni is obtained from the S-N curve
of the material for that mode of loading.
1
=
∑
=
+
+
=
1
=
2
2
1
1
K
i i
i
k
k
N
n
N
n
N
n
N
n
M 
32
…

33. Alternative definition of fatigue
• However because of the large scatter associated with SN
curves, Miner’s rule for concrete is not very accurate.
• The inaccuracy in the SN curves for concrete has led to a
search for alternative ways of quantifying fatigue damage
in concrete structures.
• Recall that long term damage in concrete structures occurs
mostly due to creep.
• Hence it has been suggested that fatigue damage be
calculated based on the rate of creep.
33

34. Secondary creep rate
34

35. Alternative definition of fatigue in
concrete
• Instead of relating the number of cycles to failure to the
maximum stress over the cycles, this approach aims to
relate the number of cycles to failure to the secondary
creep rate.
• The secondary creep rate is the “stable” creep rate: it is
the rate at which creep strains continue increasing over the
long term – after transient effects have died down.
• High values of secondary creep rate are likely to result in
faster accumulation of a critical magnitude of creep strains
(and attendant damage) required to induce failure.
35

36. Alternative definition of fatigue
36