Rheol. Acta 13, 639-643 (1974) I

From the Hungarian Institute for Building Science, Budapest (Hungary)

Failure process of concrete under fatigue loading

By L. Beres

With 5 figures (Received October 27, 1973)

1. Subject of paper The paper deals with the behaviour of concrete under

cyclically repeated central pressure. It presents, on the basis of experimental results, the character of physical changes in the macrostructure of the concrete, due to fatigue loading, as weil as the most important feature of the investigated phenomenon: the mechanism of the concrete fatigue. On the basis of the testing method it discusses also both the changes of strain properties and strength of the concrete, as a function of the number of load cycles.

2. Basic hypothesis and investigation method

It is weil known that concrete (alike other solid materials) deteriorates also under a stress lower than its initial strength, as a result of a eertain number of cyclic loadings. This phenomenon is called concrete fatigue. The basic hypothesis (to be verified later) of the investigation is that:

1. Concrete fatigue is not a sudden qualitative change of the material, but the gradual destruc- tion of the concrete structure. Parallel with this process, as a consequence, both the strain prop- erties and the strength of concrete change.

2. The speed of the fatigue process is deter- mined by the intensity of the repeated loading and the number of load-cycles.

On the basis of theories of failure of brittle materials it can be stated that the starting point, the source of the fatigue failure is always to be attributed to the inhomogeneity, structural defects of the material.

The majority of results obtained so far in con- nection with fatigue phenomena is founded on the testing of metals. So the most acceptable and most complete explanation of fatigue was given so far by the dislocation theory.

Concrete is, however, in view of its structure, much more inhomogeneous than metals. The fundamental reason for this inhomogeneity is the concrete being a conglomerate of materials of different features. The character of the in-

homogeneity and hence also the types of defect sources differ essentially in respect of various (macroscopic, microscopic and submicroscopic) ' depths" of the concrete structure investigations.

The basic hypothesis of our research work is that the fatigue deterioration of concrete is deter- mined fundamentally by macroscopic sources of defects. The connection between coarse ag- gregate and cement mortar, and mainly discon- tinuities of this connection, as weil as in a smaller degree the shrinkage cracks of cement mortar play here an important part. [This assumption is based on our (1, 2) and other authors' exper- mental results (3, 4, 5), related to concrete dete- rioration induced by short-time loading.] Fro'm the above basic hypothesis a testing method can be obviously derived for the indication of the degree of structural deteriorations (damages). The macroscopic deterioration of concrete appears namely in every case as a discontinuity at critical points, or rather as a development of the earlier cracks, i. e. as an increase of the holes found in the structure. The task is to determine the volume of holes in the concrete specimen subjected to fatigue loading. Measur- ing the surface deformations, interrupting from time to time the cyclic loading, and determining from this the volumetric changes, we obtain the quantity sought for: the permanent changes of hole volume.

The other testing method adopted during our research work is based on the assumption of a close correlation between state of internal structure and strength. The main point of this method is to load concrete bodies with a given intensity by various numbers of load cycles: hereupon their strength is determined. These strength values, related to the initial condition (without pre-loading) characterize weil the degree of changes in the concrete structure.

41"

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640 Rheolo9ica Acta, I/ol. 13, No. 3 (1974)

3. Tests based on s t ra in measurements

A series of tests has been carried out to investi- gate older (about 1 year old) specimens of 10 cm x 10 cm x 40 cm size in order to preclude the influence of afterhardening. The concrete has been composed using 372 kg/m 3 Portland- cement and Danubian sand-gravel of max. 20 mm size. The value of the water/cement ratio amounted to 0.50. The short-time strength of the concrete prisms was at the beginning of fatigue testing between 410 and 455 kg/cm 2.

During fatigue testing the minimum concrete stress induced by load cycles was 30 kg/cm 2 for every specimen. The maximum stress varied for the individual specimens between 43 and 93% of the short-time strength. The frequency of the loading apparatus was 500 cycles/min. Specimen deformations have been measured by 6cm long electric strain gauges.

Characteristic types of diagrams, indicating the relations between volumetric changes belong- ing to minimum stress and the number of load cycles are shown in fig. 1. Here the curves 1 - 4 correspond to the parameter of a 1 > a 2 > aa > a4 stress maxima.

By means of the investigation of individual curves we also obtained an answer regarding character and reasons of changes, induced by fatigue loading.

~2 min

83 min

volume chenge

0 = at "2trons

)me 6~. t | . i . . . . . . . . . . . . . . . . . . . .

ig number of cycles

Fig. 1 vide text

The specimen, subjected to maximum stress, shows from the first load cycles on an intensive volume increase (structural loosening), and so the deterioration results very quickly, after some (or several hundred) cycles of load.

In the initial phase Of the loading pr0cess, at lower stress maxima a volume decrease (structural compaction) can always be observed. With the reduction of stress level, however, the ratio of the compaction period to the entire useful life time gradually increases. For curve 3, however, although the loosening process has begun, there is no possibility at all for full deterioration, in consequence of the technical upper limit of the highest number of cycles (1-2 millions), i.e. the stopping of the investiga- tion.

Independently of this, curves 2 and 3 show processes of identical character, developing, however, during different periods of time (num- bers of load cycles).

For curve 4 of volumetric change, resulting under minimum stress, only the phase of volume reduction (compaction) can be indicated. It is presumable that in the case of certain not too low stress level maxima intensive loosening begins with the increase of the number of load- cycles, followed by real deterioration. In this case it becomes obvious that the character of the curve is identical with curves 2 and 3. On the basis of test data obtained till now, however, it is not possible to state whether a real stress level actually exists, at which structural deterioration, inducing rupture of the concrete specimen do not come into being, not even in the case of a theoretically infinite large number of load cycles.

So the individual curves fundamentally differ from one another regarding the place of their minima. This point can be called the beginning of the intensive structural decomposition. The beginning of the intensive structural loosening and the state of full deterioration of the specimen - on the basis of above explanation - can be given as the function of stress maximum of fatigue load and the number of load cycles.

Fig. 2 shows the approximative presentation of this relationship. Assuming a linear relation between the maximum stress level, pertaining to the beginning of loosening, resp. to that of dete- rioration, and the logarithm of the number of load cycles, the straight lines have been deter- mined on the basis of the minimum mean- square error from our test data.

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Bres, Failure process of concrete under fatigue loadin 9 641

maximum stress-level

Ro ,o,~ i [] / /

0.7 : i / I " : maximum com I

O.,o., ~~,~~ 1~~~~ ,~ o.~ ~, .....

l fatigue l imit

oT --[ . . . . . F - q -~ 7 -~- ~= I I0 tO 2 I0 ~ I0 ~ I s I0 n

number of cyc les

Potsson's ratio v="

i

0 t 0 I0 10 2 10 ~

Fig. 3 vide text

~ _ ~ maximum B stress-level

5:0.7~ ~ i

I - 4 ]s o.63

,i . . . . . . . . : !I + ~ ! = ~ i

tO' I0 ~ I0 6 I0 ~ number of cycles

Fig. 2 vide text

We may obtain very useful information also through the investigation of the quotient of transversal and longitudinal strains, i.e. of Poisson's ratio of cyclic load (v), resulting from repeated loading (see fig. 3). By the initial value of about 0.35 v it has been proved that strains due to fatigue load effects are mainly of viscous character. The corresponding 0.5 value decreases in consequence of delayed elastic strains and initial structure compaction to the measured value. The increase of Poisson's ratio

beyond a certain number of cycles, depending on the load intensity, refers to structure loosening. It can be attributed to this that prior to the rupture much greater values of the Poisson's ratio than 0.5 can also be found.

4. Tests based on the investigation of strength changes

Specimens and testing conditions corre- sponded to those described above. Only the quality of the concrete was different from the lormer one. (Cement content 200 kg/m3; water/ cement ratio: 0.73.)

relofive strength

R ~ r=~o

1.1

1.0

0.9

0.8

0.7

O.6

O.5

0.,~

r i I I Q~O , I

9

oo:, ooo r~:'~ '~Y'"i' l ' '' ' ' - '~ '~

~:::" 1/"7~i'"~' / q= I+ 0.~35~o-0.900~2 +0"082~ ~ ?= S~,r 2 _

/ ,=Ar',g ~- ] Fig. 4 vide text

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642 Rheologica Acta, Vol. 13, No. 3 (1974)

In the course of the investigation about 100 specimens have been subjected to cyclic fatigue loads of various intensities. Each group of spec- imens has been loated up to a number of cycles of 15000, 100000, and 700000 and then static short-time strength of the specimens has been determined.

The quotient of the strength of specimens (specific change of strength: r=R/Ro), pre- loaded to various cycle numbers (R) and that of specimens without pre-loading (Ro) has been plotted in fig. 4, as a function of stress level I-i. e. the quotient s = O'max/Ro) of the stress maximum of cyclic load and the strength of specimens without pre-loading]. The diagram also shows the curves of approximate polynomes describ- ing the strength changes of the specimens pre- loaded to the same number of cycles.

According to these curves the cyclic load results in an increase of strength in the lower stress ranges and mainly at low cycle numbers. This can be explained by the initial compaction of the concrete structure. With the increase of the number of load cycles, however, the stress range inducing strength increase will be gradually reduced.

In higher stress ranges, however, a reduction of strength can be observed after relatively few load cycles already, indicating a very early beginning of deterioration of the concrete structure.

Fig. 5 shows the effective strength change of concrete due to cyclic load, with contour lines, on the basis ofour tests, as function o~he logarithm

moximurn stress-leve[ ~mox S=-~-

1.0 r

05

relative strength

l r=& Ro

L r=0.6 ,/~/ r = O. 7

r=0.8 r=O.9

~x r=0.95 r=1.0 r=1.01

- = r~a~

r= 1.01

106 n number of cycles 7)(10"

_r=l.05 "

fotigue limit # - -

I0 ~ I IO s 1.5xlO'

Fig. 5 vide text

of the cycle number of preloading (lgn), as well as of the stress level (max/R0).

Summary

The investigations proved that fatigue deterioration of compressed concrete is caused by the gradual destruc- tion and loosening of the concrete structure.

It has been proved that changes induced by cyclic load- ing in the concrete structure can be well described quali- tatively by means of the strains, resp. the volumetric changes of specimens, as well as by means of its change of strength.

In consequence of the fatigue load the concrete volume initially decreases (structure compression), and then it increases (structure loosening); the rupture occurs at a volume greater than in unloaded condition (thus in considerably loosened condition). The limit of the compac- tion and the loosened state may be given by the cycle num- ber referring to the maximum of volumetric change. This cycle number can be regarded asthe characteristic value of the fatigue process.

The ratio of the duration of the compaction and the loosening state within the entire useful life time varies depending on the stress level. In extreme cases, hence at lower stress (at least to the investigated cycle number) only a compaction state, but at a stress level near to the shorttime strength only a loosening state can be observed.

The value of Poisson's ratio, computed from trans- versal and longitudinal strains, induced by repeated loading of concrete, is initiallyobetween 0.3-0.4. This value indicates a viscous and slightly delayed elastic character of the strain. This value may be reduced by the initial compaction of the structure, but it is vigorously increased by the loosening prior to failure.

The tests proved also that the strength for a given cycle number of a concrete subjected to repeated loading is in close correlation with the structural state at a given point of time. The structural compaction, regarding its tendency, is connected with the increase of strength; its loosening, however, is connected with the decrease of strength.

As a result of structural deterioration induced by cyclic loading the actual fatigue (failure) limit is preceded by a considerable range of reduced strength.

Zusammenfassun9 Die Untersuchungen zeigen, da der Ermdungs-

bruch des unter Druck stehenden Betons durch die fortschreitende Zerstrung des Betongefges hervor- gerufen wird.

Es wird bewiesen, da die im Betongerge unter dem Einflu zyklischer Belastungen sich vollziehenden Ver- nderungen mit Hilfe der Deformationen bzw. der Volumennderungen des Probekrpers sowie durch seine Festigkeitsnderung qualitativ gut beschreibbar sind.

Unter wiederholter Belastung nimmt das Beton- volumen zuerst ab (Gefgeverdichtung), anschlieend aber wieder zu (Gefgeauflockerung), und der Bruch erfolgt erst beim Erreichen eines Betonvolumens, welches grer ist als im unbelasteten Zustand, d.h. im Zustand einer starken Auflockerung. Der Grenz- zustand zwischen Verdichtung und Auflockerung lt

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Bres, Failure process of concrete under fati9ue loadin9 643

sich mit der zur maximalen Volumennderung ge- hrenden Zyklenzahl bestimmen. Diese kann als Kennzahl fr den Ermdungsvorgang betrachtet wer- den.

Das Verhltnis der Zeitdauern von Verdichtungs- und Aufloekerungsvorgang ist von der Intensitt der Beanspruchung abhngig. In den Extremfllen, also bei niedriger Belastung ist (wenigstens bis zur unter- suchten Zyklenzahl) nur der Verdichtungsvorgang, dagegen im Falle einer Beanspruchungsintensitt in der Nhe der kurzfristigen Belastbarkeit nur der Auf- lockerungsvorgang beobachtbar.

Die Poisson-Zahl des Betons - berechnet aus den durch die zyklischen Belastungen verursachten Quer- und Lngsdeformationen - liegt zu Anfang zwischen 0,3 und 0,4. Ein solcher Wert deutet darauf, da eine viskose und nur wenig elastisch verzgerte Form- nderung vorhanden ist. Dieser Wert kann durch die erst erfolgende Verdichtung des Gefges vermindert, durch die anschlieende Auflockerung des Gefges vor dem Bruch dagegen wesentlich erhht werden.

Die Untersuchungen beweisen auch, da die Festig- keit des periodisch belasteten Betons bei einer bestimm- ten Zyklenzahl eng mit dem Gefgezustand zu dem betreffenden Zeitpunkt korreliert ist. Als Tendenz ist erkennbar, da die Verdichtung des Gefges mit einer Festigkeitszunahme und seine Auflockerung mit einer Festigkeitsabnahme verbunden ist.

Als Folge der Gefgezerstrung durch die zyklische Belastung gibt es schon vor der effektiven Ermdungs-

grenze (Bruchgrenze) ein Bereich mit wesentlich ver- ringerter Festigkeit.

References 1) Bres, L., RILEM Bulletin, New Series, No. 36,

pp. 185-190 (1967). 2) Bres, L., Relationship ofDeformational Processes

and Structure Changes in Concrete. Structure, Solid Mechanics and Engineering Design. The Proceedings of the Southampton 1969 Civil Engineering Materials Con- ference, pp. 6434551.

3) Bennet, E. W. and N. K. Raju, Cumulative Fatigue Damage of Plain Concrete in Compression. Structure, Solid Mechanics and Engineering Design. The Proceed- ings of the Southampton 1969 Civil Engineering Materials Conference. pp. 1089-1102.

4) Shah, S. P. and S. Chandra, ACI Journal, Pro- ceedings 67, No. 4, p. 816 (1970).

5) Antrim, J. D., The Mechanism of Fatigue in Cement Paste and Plain Concrete. Highway Research Record, No. 210, pp. 95-107 (1967).

Author's address: Dr. L. Bres Hungarian Institute for Building Science David F. u. 6 Budapest XI (Hungary)

Fr die Schriftleitung verantwortlich: Dr. W. Meskat, 5090 Leverkusen, Mhlenweg 90 a Anzeigenverwaltung und Verlag: Dr. Dietrich SteinkopffVerlag, 6100 Darmstadt, Saalbaustrae 12, Postfach 1008

Gesamtherstellung: Druckerei Dr. A. Krebs, Hemsbach/Bergstr. und Bad Homburg v. d. H.

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