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A Körmeling STRAIN RATE AND

TEMPERATURE BEHAVIOUR OF

STEEL FIBRE CONCRETE

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STRAIN RATE AND

TEMPERATURE BEHAVIOUR OF

STEEL FIBRE CONCRETE

IN TENSION

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STRAIN RATE AND

TEMPERATURE BEHAVIOUR OF

STEEL FIBRE CONCRETE

IN TENSION

PROEFSCHRIFT ter verkrijging van de graad van

doctor in de technische wetenschappen aan

de Technische Hogeschool Delft,

op gezag van de Rector Magnificus, prof.dr. J.M. Dirken,

in het openbaar te verdedigen ten overstaan van

het College van Dekanen

op dinsdag 3 juni 1986

te 14.00 uur door

HIERONYMUS ANTHONIUS KÖRMEUNG

geboren te Maastricht,

civiel ingenieur

Delft University Press/1986

TR diss

1490

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Dit proefschrift is goedgekeurd door de promotoren

prof.dr.-ing. H.W. Reinhardt

en

prof.dr.ir. Y.M. de Haan

ACKNOWLEDGEMENTS

These investigations were carried out with the backing of the

Netherlands Foundation for the Technical Sciences (STW), future

Technical Science Branch Division of the Netherlands Organisation

for the Advancement of Pure Research (ZWO) Grant No. DOT

00.0056.

The author wishes to thank all the members of the Concrete

Structures Group of the Stevin Laboratory for their collaboration and

encouragement.

The assistance and advice for testing at very low temperatures given

by the Interuniversitair Reactor Instituut (IRI) and the "Low

temperatures" Section of the Physics Department of the Delft

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Contents

CONTENTS

Summary, samenvatting 1 Introduction

2 Load-deformation behaviour in uniaxial tension 2.1 introduction

2.2 influence of the strain rate 2.3 influence of the relative humidity

2.4 influence of multi-axial loading conditions 2.5 influence of temperature

2.6 combined influences

3 Theoretical consideration of strain rate and temperature effects

3 . 1 introduction

3 . 2 deformation k i n e t i c s 3 . 2 . 1 introduction

3.2.2 the deformation kinetics or rate theory equation 3.2.3 rate theory; plastic deformation and fracture

3.2.3.1 linear and non-linear fracture mechanics 3.2.3.2 GF as a material property

3.2.3.3 kinetic energy and fracture toughness 3.2.4 application of the rate theory for solids

3.2.4.1 non-cementitious materials 3.2.4.2 cementitious materials 3.2.5 conclusions 4 Experiments 4.1 introduction 4.2 testing method 4.2.1 hydraulic equipment 4.2.2 the Split Hopkinson bar 4.2.3 low temperature equipment 4.3 scope of the experimental program

4.4 mixture, specimen preparation and handling of the specimens

4.5 results of the tests at 20°C

4.5.1 results of the compressive and tensile splitting tests 4.5.2 results of the uniaxial tensile tests

4.6 results of the tests at 20° and at -170°C

4.6.1 results of the compressive and tensile splitting tests

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Contents

5 Analyses and discussion

5.1 compressive and tensile splitting strength 5.2 uniaxial tensile strength

5.2.1 influence of the strain rate and temperature upon the tensile strength-deformation diagram of concrete

5.2.2 influence of the strain rate and temperature upon the energy absorption of concrete 5.3 the rate theory and concrete

5.3.1 general

5.3.2 behaviour of concrete in region II 5.3.2.1 plain conrete

5.3.2.2 fibre reinforced concrete 5.4 relation to practical engineering 6 Conclusions

Notation References Appendices

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Summary

SUMMARY

Tensile behaviour of concrete is of growing interest to the structural engineer. New developments in design and modern non-linear calculation programs call for information on the tensile behaviour in order to predict deformation and fracture of concrete constructions more accurately. Especially for impact conditions the knowledge of tensile load-deformation behaviour is poor. It is the subject of this investigation to report on the ductility behaviour of plain and steel fibre reinforced concrete under impact tensile loading.

A survey is given of the parameters which are important for the tensile strength such as the influence of strain rate, relative humidity, multi-axial

loading conditions and temperature.

Each parameter exercises its influence upon the shape of the load deformation diagram and thus upon the energy-absorbing capacity of the concrete.

From literature research it has become clear that this field of investigation is very wide, with many unknown aspects. With an eye to the available test techniques, the present state of knowledge and the available theoretical foundation, this investigation was limited to the parameters: deformation rate and temperature. Both these aspects are described with the aid of the theory of deformation kinetics, also known als the rate theory. It is a statistical theory with which the probability of bond failure can be calculated. The attractive forces between gel particles in the cement paste are considered as the bond elements which posess a certain bond energy. This activity occurs at the micro level and is transformed into the macro level by considering the energy absorption at complete failure of the concrete specimens. Limiting conditions for application of the rate theory to the solid material we know as concrete are presented.

For the description of the fracture behaviour of concrete the fictitious crack model of Hillerborg is likely most satisfactorily to model the actual fracture behaviour. In this model the cracks are able to transfer stresses as indicated by the decending branch of the load-deformation diagram.

The influence of the kinetic energy upon the energy absorption or fracture toughness could not be quantified because the actual crack velocity was not

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Summary

known. It was assumed that inertia effects are of minor importance in the observed deformation rate range. The combination of the fictitious crack model and the theory of deformation kinetics results in a sound model in which the energy absorption of concrete can be related to temperature and deformation rate.

An experimental program was initiated to verify whether theory and practise agree. Therefore uniaxial tensile tests at constant deformation rate were performed on dried plain and steel fibre reinforced concrete at two different temperatures, 20°C and -170°C. For the low and intermediate deformation rate tests (4=1.25x10-* to 28 mm/s) hydraulic equipment, and for the high

deformation rate tests (4>103 mm/s) the Split Hopkinson Bar technique was

used. Tensile stress and fracture deformation values are presented. From the load-deformation diagrams obtained the total fracture energy Gp was calculated as the area under the complete curve.

Besides the uniaxial tensile tests, the standard compressive cube strength and tensile splitting strength were determined at both temperatures.

Application of the rate theory to concrete depends on whether in concrete a thermally activated mechanism exists.

For other materials four regions could be distinghuished in the strength-strain rate field comprising two regions with thermally activated actions.

From the experimental results on plain concrete a strain rate and temperature dependence of the total fracture energy GF could be inferred. The rate theory can be applied, although the position of the boundary between thermally and non-thermally activated regions could not be determined accurately. Therefore more experimental results in the intermediate strain rate interval are necessary. However, possible positions are given.

For steel fibre reinforced concrete there is a rate dependence at 20°C but it has disappeared at -170°C. Application of the rate theory appeared not to be possible. Presumably other mechanisms were dominant over a possible thermally activation. Although several possibilities were analysed, no reasonable explanation could be given.

A remarkable fact was the wide scatter in the actual fibre amount within one batch of fibre concrete.

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Samenvatting

Samenvatting

Het gedrag van beton onder trekbelasting heeft steeds meer de 'belangstelling

van de civiel ingenieur. Nieuwe ontwikkelingen in ontwerpen en geavanceerde

niet-lineaire rekenprogramma's vragen om informatie omtrent het trekgedrag om

zo vervormingen en breuk van betonconstructies beter te kunnen voorspellen.

Vooral op het gebied van stootbelasting is de kennis van het

belastings-vervormingsgedrag gering. Het onderwerp van dit onderzoek heeft

betrekking op het taaiheidsgedrag van zowel ongewapend als staalvezel gewapend

beton, onderworpen aan stoottrekbelastingen.

Er wordt een overzicht gegeven van de parameters die van belang zijn voor de

treksterkte, zoals de invloed van belastingsnelheid, relatieve vochtigheid,

meerassige belastingen en temperatuur. Elke parameter oefent afzonderlijk

invloed uit op de vorm van het last-vervormingsdiagram en daarmee op het

energie absorptievermogen van het materiaal beton.

Uit literatuuronderzoek is duidelijk geworden, dat dit onderzoeksgebied zeer

breed i9 met vele onbekende aspecten. Met het oog op de beschikbare

beproevingstechnieken, de huidige kennis en de beschikbare theoretische

ondergrond is dit onderzoek beperkt tot het bestuderen van de invloed van

vervormingssnelheid en temperatuur. Deze beide aspecten kunnen met de theorie

van de vervonningskinetica beschreven worden. Dit is een statische theorie

waarmee de kans op het aangaan of verbreken van bindingen tussen deeltjes

berekend kan worden.

Voor beton worden als deeltjes de geldeeltjes aangenomen.

Dit gebeuren op micro-niveau wordt naar het macro-niveau getransformeerd via de

energie-opname van het volledig bezweken betonnen proefstuk.

Beperkende voorwaarden voor het kunnen toepassen van de vervonningskinetica

theorie op vaste stoffen komen aan de orde.

Om het breukgedrag van beton te kunnen beschrijven, blijkt het fictieve

scheunnodel van Hillerborg goed te voldoen. In dit model worden scheuren in

staat geacht spanningen over te dragen, zoals dat beschreven kan worden met de

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Samenvatting

De invloed van de kinetische energie op de energie-absorptie of acheurtaaiheid kon niet gekwantificeerd worden. Dit komt onder andere door het onbekend zijn van de optredende scheursnelheid. Er is aangenomen dat traagheidseffecten in het beschouwde snelheidsgebied van minder belang zijn.

De combinatie van het fictieve scheurmodel en de vervormingskinetica leidt tot een model, waarmee de energie-opnamecapaciteit van beton gerelateerd kan worden aan de temperatuur en aan de vervormingssnelheid. Een experimenteel onderzoek is gestart om na te gaan of theorie en praktijk overeenkomen. Eenassige trekproeven zijn uitgevoerd zowel op ongewapend als op staalvezel gewapend beton. Als variabelen zijn gekozen een lage, tussenliggende en hoge

vervormingssnelheid (4=1.25xl0~4, 28, 2400 mm/sec) en 2 temperaturen (20°,

-170°C).

Voor de hoge vervormingssnelheidsproeven i s de S p l i t Hopkinson Bar-techniek toegepast, t e r w i j l voor de andere snelheden een hydraulische beproevingsmachine i s gebruikt.

Als resultaat zijn de complete last-verplaatsingsdiagrammen verkregen. Hieruit is de totale breukenergie GF bepaald als oppervlak onder de volledige kromme. Naast de eenassige trekproeven zijn de standaard kubus druksterkte en splijttreksterkte bepaald, zowel bij 20° als bij -170°C.

Het toepassen van de vervonningskinetica-theorie op beton is afhankelijk van het feit of er bij beton van thermische activering gesproken kan worden.

Bij andere materialen kunnen er vier gebieden onderscheiden worden in het sterkte-vervormingsveld, waarvan twee gebieden thermische activering kennen. Voor ongewapend beton gaven de experimenten een vervormingssnelheid en temperatuur afhankelijke totale breukenergie aan. De vervormings-kinetica-theorie kan toegepast worden. Echter door onvoldoende gegevens in het tussenligende vervormingssnelheidsgebied konden de grenzen tussen de eerder genoemde gebieden niet exact vastgesteld worden.

Daarom is volstaan met het geven van een indicatie.

Voor staalvezelbeton is er een vervorminssnelheidsafhankelijk gedrag bij 20°C, maar dit is bij -170°C verdwenen.

Toepassing van de vervonningskinetica-theorie voor vezelbeton bleek niet mogelijk. De oorzaak ligt waarschijnlijk in andere mechanismen die dominant

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Samenvatting

zijn over een eventueel thermisch geactiveerd mechanisme.

Opvallend was dat er binnen de afzonderlijke storten van vezelbeton een grote spreiding gevonden werd in de echt aanwezige vezelpercentages.

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Curriculum vitae

Harry Körmeling

Geboren te Maastricht op 11 april 1949.

In 1976 gehuwd met Tansja Boxelaar, drie kinderen Susanne (1981), Steven (1983) en Jasper (1986). Thans wonende te Hazerswoude.

Diploma HBS-B aan het St.Maartenscollege te Voorburg (1968).

Diploma Civiel Ingenieur aan de Technische Hogeschool Delft (1976), afstudeerrichting Constructieleer/ Materiaalkunde.

Tot 1985 werkzaam als wetenschappelijk medewerker bij de vakgroep Betonconstructies in het Stevin II laboratorium te Delft.

Sinds mei 1985 werkzaam bij BV. Aannemingsbedrijf NBM te Den Haag als researchmedewerker.

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Introduction

1.1

1. INTHODUCTION

Concrete is a very versatile material. Because of its technically and economically favourable properties, it has extensively been used on large scale.

However the unfavourable balance between tensile and compressive strength and the low ductility are reasons for trying to improve the material. Normally the tensile strength of concrete is neglected in structural analysis, but indirectly every member relies on it because tensile strength greatly influences the cracking behaviour, the bond properties of reinforcing steel and the shear behaviour. In engineering practice there is a need to know more about the tensile behaviour of concrete structures subjected to special loading conditions such as, for instance, impact loading. Pile driving, explosions and collisions are present-day examples. More complicated is the question of the

impact resistance of concrete LNG storage containments.

The development of modern non-linear computer programs offer possibilities of introducing tensile strength into the calculations in order to describe structural behaviour more realistically and accurately. With regard to impact behaviour several research programs deal with the improvement of tensile strength alone [39] but very few deal with the improvement of ductility [97,28]. The latter relates to the mutual relation of tensile strength and deformation, enabling the designer to gain a clearer understanding of the material behaviour.

The subject of the research reported in this thesis is the ductility behaviour of plain and steel fibre reinforced concrete under impact tensile loading. The tremendous energy absorbing capacity of such concrete is well known. Cracking of this material is associated with pull-out of the fibres. Due to bond and friction between the fibres and the matrix the absorbed energy is much greater than for plain concrete. This fact is advantageous when large amounts of energy are exerted on the material. An impact load delivers a great deal of energy in a short time. An obvious conclusion is that steel fibre concrete is suitable for absorbing the energy of impact loads. In the present research program,

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1.2

Introduction

impact loads have been "translated" into rates of strain, whereby a link is established with the theory of deformation kinetics. This theory relates deformation processes to energy and temperature. It links the events of the macro and the micro structure, for which purpose in this thesis the macro behaviour is described with fracture mechanics theories. The influence of the temperature is introduced by performing the tests at 20°C and at -170°C. A

wide range of tensile strain rates is used, ranging from G-10'6 to e > 1

(1/s).

Complete stress-deformation diagrams were obtained using a hydraulic equipment for low and intermediate strain rates and the "Split Hopkinson Bar" technique for the high rate loading. Much attention is paid to integrating the test results in a solid material model. In this way the results of the research do not remain in isolation.

This is an essential condition for making the results applicable in actual practice, where information on the general behaviour of the material will be of more real use to the designer than a few specific values. This does, however, entail the further condition that calculations will have to be based on energy considerations.

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Load-deformation 2.1

2. Load-deformation behaviour in uniaxial tension.

2.1 Introduction

Relations between load and deformation give information on the mechanical behaviour of materials. For concretelike materials Fig.2.1 shows the general appearance of such a relation.

u °max GP t

i!

—H\

-f/\\

/ \

E

« ! ^ ^

rA ! ^ —

Fig. 2.1 Tensile stress-deformation curve (deformation controlled).

Characteristic points which can be distinguished are the tangent modulus Eo at the origin, the secant modulus Et at the ultimate stress-strain point, the fracture strain-value €cr at (Tmax, the proportionality limit Fp and the area A under the load-deformation curve, representing the energy absorbed by the specimen.

Ai is the ultimate deformation at the instant when the load is reduced to zero again in the descending branch.

The proportionality limit Fp for plain concrete was determined for unaxial tension by Evans and Marathe [14] as being situated between 68 to 89% of the ultimate stress.

Below this level, load does not create new microcracks. The existing microcracks are mainly due to shrinkage of the cement paste, resulting in bond cracks between aggregate and cement paste. Other causes are, for

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2.2

Load-deformation

plastic shrinkage of fresh concrete, the moisture gradient in the hardened concrete, effects of bleeding and cracks due to changing temperature and humidity may be mentioned.

Above the proportionality limit stable crack growth and creation of new microcracks can be expected until the energy released due to the cracking exceeds the energy demand for crack growth in the specimen. Unstable crack propagation occurs [18]. Popovics [70] explains that, because of diminishing crack arresting action, the failure in tension is caused by a few bridging cracks rather than by numerous cracks.

However, the influence of the cracks upon the behaviour of concrete is a complicated matter for which fracture mechanics tries to find solutions (see also Chapter 3 ) .

Incorporation of steel fibres in concrete has a very pronounced effect on the descending branch of the load-deformation diagram. A determining factor is the critical fibre volume V e n t , which is defined as the volume of fibres which, after matrix cracking, will carry the load which the composite sustained before cracking [26]. This is illustrated in Fig. 2.2.

Fig. 2.2 Influence of critical fibre volume upon the load-deformation diagram.

The fibre volume percentage has only a minor influence upon the maximum load. Improvements of up to 10X as compared with plain concrete are reported [26].

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Load-deformation

2.3

In the next chapters several influences will be discussed which result in a wide variety of load-deformation diagrams. Among those are the influence of the strain rate, the relative humidity, the multiaxial loading conditions and the influence of the temperature.

2.2 Influence of the strain rate

The behaviour of concrete under time-dependent loading is a difficult matter, since different mechanisms govern its strength and deformation behaviour within different strain rate regimes.

Low strain rates up to 10_s 1/s applied to materials result in a type of

behaviour known as creep. At higher rates in the range from 10"4' to 10"*

1/s the behaviour is assumed to be quasi-static. This is actually so when the time of loading is large compared with the wave propagation time through the specimen. Both in creep and in quasi-static tests the inertia forces are small enough to be neglected. Above strain rates of 10+1 1/s , inertia and

wave propagation effects become important. Local and average stress-strain values due to shock waves propagating through the material are to be distinghuished. Between this impact and quasi-static behaviour an

io6 i o 'a 10"8 10"6 Creep Constant load or stress machine Strain vs. time or creep rate recorded Inertia >0? 10» 10"2 IO"2 ; Quasistatic | Hydraulic or • screw machine I I . Constant strain 1 rate test i I forces neglected Isothermal plane stress Increa IO"2 ,0° ; Intermediate ; Strain-rate Pneumatic 1 or I mechanical ■ machines 1 1 Mechanical I resonance in 1 specimen and maching 1 1

ing stress levels .O'4 . o2 ; Bar I Impact i ■ 1 Mechanica i o r I explosive 1 impact 1 1

10" 10 characteristic time (sec 10 10 Strain rate {sec" )

"WZEX

Light-gas gun 1 or 1 explosive driven t ptate impact i 1 1 Elastic- j Shock-wave 1 plastic wave propagation | propagation 1 i i Inertia forces Adiabat important c plane stra n Usual method of loading Dynamic considerations in testing

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2.4

Load-deformation

intermediate material behaviour can be expected for strain rates from 10_ 1

to 10+ 1 1/s. Strain rate effects now become a consideration although the

magnitude of such effects may be quite small or even non-existent. For metals Lindholm [45] reviewed the dynamic aspects of mechanical testing. This is shown in Fig. 2.3. It is a fact that theories about strain rate effects are much more highly developed for metals than for cementitious materials.

Just as with metals, plain concrete shows rate-dependent properties. For creep rate numerous results are available for the tension case. Many of them are summarised by Neville [60]. For the quasi-static range only few results can be found in the literature, while for high strain rates only Birkimer's [3] results can be mentioned. A review of the experimental results in the quasi-static and intermediate strain rate range is given by Körmeling et al [39]. Figs. 2.4 and 2.5, which include the results of their tests, show the rate dependence of stress and fracture strain respectively, while in Fig. 2.6 strain values at maximum loading for different loading rates are presented.

.'imp/'o "I 1 1 O — O Komlos ^ — ^ Heilmann » •« Takeda A A Kvirikadze 0 0 Sneikin Hatano B Sf Birkimer ••x Körmeling 10"b 10"3 10 103 105 107Ó(N/mm2/s 10~s 10"' 10"s 10"J 10"1 101 10J e(1/s)

Fig. 2.4 Stress-rate dependence of concrete in tension [39],

It seems that for higher strain rates an increase in tensile strength as well as in fracture deformation can be expected. The strain increase is a little smaller than the stress increase. From Fig. 2.6 it appears that the fracture strains show a minimum precisely at strain rates which are normal for static

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ie^dsdetQSgation 3 . 5 2.5 Ei m p/ eo [es] i Komlos ^& Heilmann Birkimer Körmeling ^ • o Q ^

«h rtfat» Wt

Mi» l<-tirk

f\i

t e s t i n g . For lower s t r a i n r a t e s t h e fracture.j.ti;aiiL4ncxelaaeö:l.JÉeJt'»»hich the maximum load decreases t o the long-term s t r a i g t h l i m i t . Tjhe contribution of

creep t o the fracture s t r a i n value increases

0 105 103 10' 10' 103 105 107Ó(N/mm2/s

Z£ü iitsiilsv ttiaiia aiienaT 8.S .:sl¥

.1(T.u ,! ,10"' u ,u ,yj ,u 10 10 e l V s ) 10~5 10 -3 10"'

©H . b s c l acesüxB* ;*a YJj-isaa ais/jos-i'i a r k b s i s l u o l j ; - o a l 0 [ £ . E ] i s a i r f i i a , S U £ B V

aiutoBil snoni s l J J i l s *e«(, had a ï s i o r r o o faso-olnia-j a i d i i : teri* b&bslznoo

e £ i « ^ & 5 ^ r a 4 ^ r a £ e s d e g e M ^ q s ^ f a ^ ^ e ^ A tswollot

For s t r a i n r a t e s higher than the s t a t i c s t r a i n rate of 6=1.25*10-6 1/s the f r a c t u r e i s t r a i n increases again. This e f f e c t i s a l s o d i s c u s s e d s i n s i 8 2 1 s

The e f f e c t o f higher s t r a i n s at the very low s t r a i n r a t e s in d i r e c t tension had previously been reported by Rusch and Hiisdojr^od'^dii IOI OSS =£ ■S-ISJK

o.ts-onoD n i s l q -ïo'i 80S =a

Melinger and Birkimer [51] t e s t e d f i b r e reinforced concrete at high s t r a i n SO*esl3B©J1i ioyi^n fitem s^t,#2ê.^is,0n25jmi0ri3ajB& sHÈsi^fibXsmHéi^2M&, 9(6> 43m)9»!SRfiiJ.n.v#&tiga*ejblsT-he> & i i ^ s a * ^ e ^ ! a f # l j*dritfe vofcutte 0<ï*ReénfcagfiSio:of

1*. The svm^m>msen§9fi^foTtei®pf&B!ïG s^njtergfcKtófe Jfe^l^n^tsr.ipfti^tomi. The cylinders were loaded at one end by a longitudinal compressive s t r a i n i n g p u l s e whoqh) t r a v e l l e d down the specimen and r e f l e c t e d a* «G.jtensu0fe = s t r a i n i n g p u l s e at the other end. I f the magnitude of the t e n s i l e s t r a i n produced by the summation o f the i n c i d e n t compressive p u l s e and the r e f l e c t e d t e r i s ü e p u l s e exceeded the c r i t i c a l s t r a i n value, fracture occurred. The r e s u l t s s h o w e d ^ f t j t h e c r i t i c a l fracture stf^«)^s»rI);hS5Ssitrai|a,01-ate00i-ange3 under i n v e s t i g a t i o n varied from three t o s i x times the s t a t i c fracture s t r a i n

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2.6 Load-deformation

Fig. 2.6 Tensile strain values for crmax with increasing strain rate [39].

value. Birkimer [3,4] also calculated the fracture energy at maximum load. He concluded that fibre reinforced concrete had just a little more fracture energy. A relation between fracture strain and strain rate was derived, as follows:

eCr=aê1/3 (2.1)

where tt= 220 for fibre concrete a= 206 for plain concrete

The experimental results are shown in Fig. 2.7. The static value for cCr was

found to be 100 micro strain. When this static value was also included in the formula, empirical relations were calculated for plain concrete as:

£cr= 100 + 109 êl/2 (2.2)

and

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Load-deformation

2.7

For the higher strain rates these formulas show the same results, but for e=1.5 1/s large deviations were observed.

The critical strain energy per unit volume(Uvo 1) is inversely proportional to the rise time (tit) of the strain pulse :

Uvoi=ttl/tR (2.4)

For all the tests Birkimer assumed a linear stress-strain diagram to be valid.

0 = ploin concrete (bottom curvel D = fibrous concrete (top curve)

0 10 20 30 40 i (1 /s )

Fig. 2.7 Fracture strain versus strain rate for plain and fibrous concrete [3].

However, the results only give information up to the peak load. Moreover, for fibre reinforced materials the post-peak range is more important, but no information is given for this. Therefore it is clear that the observed difference between plain and fibre reinforced concrete is small.

Gokoz and Naaman [19] studied the effect of strain rate on the pull-out behaviour of straight fibres embedded in mortar.

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2.8

Load-deforaation

along the boundaries of a solid and a hollow cylinder. The solid part was separated from the hollow part with a deformation velocity ranging from

10-zmm/s to 500 mm/s. The first peak of the load-time diagram, which is

indicative of bond, was sensitive to displacement rate effects above 50 mm/s. F(N)

102 103

v ( mm/s )

Fig. 2.8 Effect of loading velocity on pull-out loads on steel fibres [19].

The second peak and the final load were insensitive to rate effects in the observed area (Fig. 2.8). The values of the second peak as a material characteristic seemed questionable. It was more a characteristic of the test equipment. The post-peak behaviour, which was mainly due to frictional effects, was estimated to be independent of the loading velocity. Also the energy absorbing capability of the steel fibres did not seem to be very sensitive to the loading velocity (Fig. 2.9).

The scatter in energy values obtained is considerable.

Rostasy and Hartwich [74] performed uniaxial tensile tests on steel fibre reinforced and normal concrete. Straight as well as hooked fibres were used in percentages by volume of 0*, 0.75X and 1.5X. The stress rate varied between £= 0.05 and 200 N/mrnZs. Table 2.1 shows their results.

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Load-deformation 2.9

Gf (Nm) 0.15 I 0.10 0D5 UUU10"4 10"3 10"2 10"' 10° 101 102 . 103 v ( mm / s )

Fig. 2.9 Energy absorption capability versus loading velocity for steel fibre concrete [19].

concrete was lower than the strength of the straight fibre concrete. On the other hand, the fracture strain was in general larger for hooked fibre concrete. Assuming better bonding of the hooked fibres, higher values should be expected for the ultimate strength.On examining the stress-deformation curves of the two reference batches, which contained no fibres, it is obvious that the basic quality of the two types of fibre concrete specimens was not the same. The mixes themselves, however, showed no differences in compressive and tensile splitting strength. It seems that some specimens were damaged during handling and/or testing,, which resulted in Young's modulus being too

low. Also, the two hinges in the testing machine allowed instability near the top load.

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2.10 Load-deformation f i b r e volume F= 0.05 F= 200 (Tec (7B pi M B * . n_r " * ■ * ■ •»_r »-r 1. Ft N/mm2 2.85 2.89 4.12 3.36 45.70 52.40 4.55 4 . 6 9 5* tcr %o 0.136 0.189 0.217 0.198 -0. Ft N/mm2 3.48 3.09 4.36 3.88 46.80 48.50 3.45 3.55 75* Ccr %o 0.117 0.157 0.193 0.229 -Ft N/mm2 3.46 2.78 4.34 2.71 43.40 46.70 3.47 3.47 0* tcr

r~

0.130 0.165 0.186 0.194

-Table 2.1 Test results for steel fibre and plain concrete at different stress rates at 220 days age (mean of three tests).

All these facts make it difficult to compare the results of hooked and straight fibre concrete in this test program. Omitting the results relating to presumably damaged specimens, a new table can be compiled for straight steel fibre concrete (Table 2.2).

f i b r e volume 1 F= 0.05 F= 200 Ft N/mm2 3.03 4.16 . 5 * Ecr 0.128 0.26 0 Ft N/mm2 3.71 4.77 .75* Ecr

7~

0.126 0.207 Fct N/mm2 3.46 4.53 OX Ccr no 0.130 0.166

Table 2.2 Cleaned test results for straight steel fibre concrete.

From this table it appears that the strength results for 1.5* still deviate for static as well as for impact velocities. The values are too low. For 0.75* fibre reinforcement, the strength is increased by 7* in static loading,

(25)

Load-deforraat ion 2.11

a value which agrees w i t h data reported in the literature. For impact, all the strength results show an increase o f 3 2 * over the static value. T h e fracture strain for plain concrete shows an increase o f 2 8 * . w h i l e t h e fibre concrete values increase b y 6 5 X .

The report shows stress-deformation curves for b o t h types o f fibre concrete up t o 0.8-1.8mm deformation. In t h i s range fibres are not completely pulled out. T h e scatter in t h e descending branches is s o large that n o conclusions are given (Fig. 2.10)

7.5 6.0 4.5 3D 15 0 (N/mm2 A. \ ' " V - u . s —ww. ow - 0.75% - 1 . 5 0 % ■•' OX 0.8 1.2 1.6 2.0 A (mm) 7.5 6.0 4.5 30 15 0

c

.

V

\

(N/mn

\

V X. I2)

-.

t s = fast -■ 0.75% 1.50% 04 0.8 1.2 1.6 20 A (mm)

Fig. 2.10 Stress-deformation curves for steel fibre reinforced concrete at low and high rate loading [74].

More information about the influence of the strain rate upon the behaviour of steel fibre reinforced concrete can be obtained from flexural tests. They are summarized in [40]. Performing the flexural test with the instrumented Charpy pendulum has proved very troublesome to researchers. In several tests on concrete the influences of the test equipment upon the measurements could hardly be separated from the actual material behaviour.

Especially in the post-peak area reflecting stress waves and undesired oscillations are present.

Hibbert concludes that for the peak load and fracture strain both values are increased at impact rates [28]. The fibre pull-out in the post-peak area is

(26)

2.12 Load-deformation

rate independent as far as he could analyse the data.

The results of Suaris and Shah [79] show better agreement with the tests of Rostasy and Hartwich. For higher strain rates more energy is absorbed. Nevertheless they conclude that bond is not significantly influenced by the strain rate. Further research of Naaman and Gopalaratnam shows the increasing influence of fibre volume percentage at higher strain rates upon the modulus of rupture and the absorbed energy, while the aspect ratio has only a minor rate dependence [57]. A new aspect is that now rate sensitivity is also observed in the post peak area. They attribute this effect to the non-aligned fibres in the fracture zone. Finally a higher rate sensitivity was found for weaker matrices, a fact which agrees with the results of Körmeling et al.

[39] for plain concrete.

Conclusions

To obtain a good insight into the behaviour of steel fibre reinforced concrete load-deformation diagrams must be extended to the complete post-peak area. Up to the peak load the fibres cannot do their work, because cracking is still limited. Up to that point the impact behaviour of unreinforced and steel fibre reinforced concrete will not show major differences; peak load and failure strain are both increased for higher strain rates (Birkimer). Tests including post-peak behaviour by Gokos and Naaman show that the first peak load is rate sensitive. They conclude to rate insensitivity for the descending branch, but disturbing effects for test equipment and specimen configurations weaken this conclusion. On analysing the load-deformation curves of Rostasy and Hartwich considerable scatter in the results is observed. This may be caused by previous damage to the specimens. Energy absorption after the peak load is increased for increasing strain rates, while tensile stress and fracture strain both increase with increasing strain rates.

(27)

Load-deformation 2.13

2.3 Influence of the relative humidity.

The moisture content of the cementitious material is a very important parameter [60,90]. To obtain a better understanding of the influence of the relative humidity upon the stress-deformation curve it is necessary to relate this parameter to the internal structure of concrete. The behaviour on the microscopic scale is responsible for macroscopie behaviour. A physical model proposed by Wittmann [90,91], the Munich model, will therefore be discussed.

In 1977 Wittmann published a review of the results of experimental research performed by different researchers in Munich on a fundamental physical-based model for cementitious materials. The starting point was the fact that many characteristic properties of concrete and cement paste seemed to be dependent on the moisture state of the material and its environment. For concrete, a heterogeneous material consisting of cement paste and aggregate, the influences were less strong than for neat cement paste. This indicates that time-dependent behaviour is concentrated in the cement paste. The paste was conceived as a microporous material in which water exists in three different modes:

1. Chemically bound mode, independent of moisture movements.

2. Hydratation mode, which breaks down with decreasing humidity and grows with increasing humidity.

3. Absorbed water, which is in exchange equilibrium with the ambient humidity.

With the aid of thermodynamics the change in surface energy due to absorption of layers with thickness 6 for a given vapour pressure can be expressed as :

Ay = -RT / 6 d(ln p) (2.5) o

where:

(28)

2.14 Load-deformation

R= molecular gas constant T= absolute temperature 6= layer thickness p= vapour pressure

Macroscopic deformation is closely related to the value of the surface energy. Cook and Haque [9] studied the effect of adsorption on the tensile creep and strength reduction of concrete. At a relative humidity of about 0% tensile creep occurred only in consequence of growing microcracks. Rewetting the concrete with water restarted the deformation, while rewetting with macromolecular kerosine had no influence upon the deformation.

Scanning electron microscopic (SEM) observations of the gel structure in a dense paste in equilibrium showed that the hardened cement paste structure consists of nuclei of unhydrated clinker material surrounded by a hydrated gel cover. The inner gel coat was idealised by Grudemo [27] as granular while the outer gel coat was idealised as consisting of columnar particles. An example of the idealied gel structure is shown in Fig. 2.11.

Fig. 2.11 Idealised cement gel structure.

Water is incorporated in the gel coat and is adsorbed around the outer gel coat. Drying may result in shrinkage of the gel coat around the nuclei

(29)

Load-deformation 2.15

restoring the cohesive bonds, so that higher tensile stresses are possible. The contact zone between two adjacent coats of outer gel growing in opposite directions is thought to be the zone of contact with short bonds. Part of the fracture surface seen in scanning electron micrographs must of necessity consist of such broken contact zones.

Other parts of the crack path follow the boundaries of the columnar particles (calcium-silicate hydrate), enter the granular coat and surround the nuclei. It must be emphasised that the inhomogeneous structure also has a crack arresting function (Fig. 2.12). From a mechanical point of view water layers can reduce the internal friction.

Bearing capacity of the water as occurs in compression will be of minor importance in tension. So the influence of water can be expected to be concentrated upon reduction of surface energy.

t t t

Fig. 2.12 Crack growth mechanisms [23].

Over the whole scale of relative humidities different mechanisms are distinguished. For low values of RH water will first be adsorbed in monomolecular layers around the dry gel particles.

Experiments showed that for a low relative humidity of 1% the cement paste

consisted of a colloidal structure of hydration products which, according to the principle of least energy, had high surface or boundary energy. This energy had primary bonds of 300-800 kJ/Mol and weak Van der Waals bonds of

(30)

2.16 Load-deformation

8-20 kJ/Mol. For highly porous materials with a very large internal surface the weak Van der Waals bond energy for the total surface of the pores was much larger than the primary bond energy existing near the few contact areas. The Van der Waals bond energy seemed to be in good agreement with the surface energy.

Higher moisture content resulted in multimolecular layers, while excess water was stored in pores and cavities. The adsorbed water layers decreased the surface energy so that the material was allowed to expand. This process was continued for higher RH values, weakening the Van der Waals bonds more and more. When the adsorbed water layer thickness exceeded the particle distance,

a water pressure was developed acting in opposition to the surface energy. The primary bonds were kept intact. Separation of the gel particles occurred when the water pressure was larger than the Van der Waals bond. This phenomenon could be observed at 40-60* RH. The water layer pressure had an extra reducing effect upon the energy state, resulting in a more defonnable material. Experiments by Klug [35], who measured the deformation as a function of the relative humidity, showed that above 42% RH, there occurred extra deformation which was due to the combined action of weakening of the surface energy and raising of the spelling water pressure at high RH. Fig.. 2.13 shows this effect, where the relative deformation (Jl/1) is plotted versus the relative humidity. The shaded area reflects the influence of the spelling water pressure.

For fixed age and careful curing, the chemically bound mode and the hydratation mode can be expected to be constant for specimens of the same batch. All attention can be paid to the role of adsorbed water and the

influence of relative humidity upon strength and deformation.

It is assumed for the present that the temperature is constant. Temperature changes have a distinct influence.

(31)

Load—deformation 2.17

.Ai/idcr

3

)

0 20 40 60 80 100

P/P

0

(%)

Fig. 2.13 Relative deformation of mortar caused by changing relative humidity [90].

According to Griffith's fracture theory for brittle materials, a relation between the relative tensile stress and the relative surface energy can be derived.

MTo; Yo Yo (2.6)

where Co is the stress for surface energy Yo > obtained for dry gel particles.

Experiments by Pihlajavaara [67] on 40mmx40mmx160mm mortar prisms were in agreement with this formula. The results are represented in Fig. 2.14. Above 55% RH a faster decrease of strength is measured than could be expected from decreasing surface energy alone. The spelling pressure of the water is considered to be responsible for. the rapid decrease.

(32)

2.18 Load-deformation 1.00 0.75 0.50 0.25 0 / 0 D>5 O

I

RH = 5 5 % O A: C: W = 3 :1:0.5 D A: C: W = 5 : 1 : 0.75

^

n

Ï

V

02 0U 0JB' 03 10 AY(cal/g)

Fig. 2.14 Bending strength of mortar in relation to the surface energy change (67].

Rusch and Hilsdorf showed in [76] that the surface energy decreased for higher relative humidities. This is illustrated in Fig. 2.15.

Q75 100 j„-Aj (cal/g)

Fig. 2.15 Surface energy related to the relative humidity.

A similar relation as shown in Fig. 2.14 is given for compressive tests on mortar cylinders.Only the results show a minimum value at a RH of 55X with an

increasing stress ratio for higher relative humidities. Pihlajavaara [67] attributes this fact to capillairy forces. It does not exist in bending tests.

(33)

Load-deformation 2.19

Young's modulus was obtained from small cylinders of hardened cement paste (d,1=10,600mm) in compression. As appears from Fig. 2.16, up to 40* RH the modulus shows a marked decrease, which is attributed to the . decrease in

surface energy.

The influence of this mechanism extended to higher relative humidities results in the dotted lines in Fig. 2.16. In reality an increase in Young's modulus was observed for compression tests above 40% RH.

If it is assumed that this increase in stiffness is also due to capiHairy forces, Young's modulus for tensile tests can be expected to follow the dotted line.

E t k N / m m

2

)

100 RH(%)

Fig. 2.16 Change of Young's modulus with changes of relative humidity for mortar [91].

Conclusions:

For the stress-deformat ion curves it. can be concluded that in tension the maximum stress and the stiffness decrease with increasing relative humidity. For the stress a marked decrease occurs above 55* RH while for Young's

(34)

2.20 Load-deformation

modulus the decrease is small above 4 0 * RH.

It is difficult to make a prediction concerning the descending branch.

The influence of the moisture content upon the bond behaviour of steel fibres in concrete will not be dealt with. It would be outside the scope of this research program. Aspects which should be studied then are the influence of the moisture content upon adhesion and friction.

2.4 Influence of multi-axial loading conditions.

The uniaxial stress-deformation behaviour describes in fact a very particular situation. Boundary conditions are chosen in such a way that lateral external stresses will not occur. In a structural element multiaxial loading conditions will most probably exist. Their interaction will result in an increase or a decrease in bearing capacity, depending on their direction of action.

Experiments showed that uniaxial compressive loads generate tensile stresses in a lateral direction.

Failure of the material occurs when these tensile stresses reach a critical value. Obviously, the tensile stresses can be reduced by a lateral compressive load and can be increased by a lateral tensile load, influencing in this way the bearing capacity in the principal direction.

150

V^H/pjL

-Q25 0 025 0.50 075 100 1.25 °2/o(-1/0) Fig. 2.17 Biaxial strength of concrete.

(35)

Load-defonnat ion 2.21

Experimental data of multiaxial loading in which one or more axes are tensile loads are difficult to find. Not least because of the experimental difficulties in performing such a test, Nelissen [59] obtained considerable scatter in his biaxial loading experiments. However, for tension-compression tests he showed that the ultimate tensile strength and strain both decreased with increasing compressive load in the second direction. Fig. 2.17 shows the ultimate strength of biaxially loaded concrete as presented by Van Mier [52]. More results from the literature were reviewed by Eibl et al. [11].

The behaviour of concrete in triaxial states of stress and strain exhibits highly complex aspects. Most experimental results concern triaxial compression. Cedolin et al [7] extended the behaviour in compression to the tensile stress state as shown in Fig. 2.18, which represents the failure surface for tensile states of stress. The intersection of this surface with the coordinate planes represents the biaxial behaviour according to Fig. 2.17. Experimental data relating to triaxial tension are not available, but Cedolin et al. proposed, as a hypotheses, a tension cut-off criterion for 0"3= Q2- Ft ( <Tt=uniaxial tensile strength).

10/0/-0.1) -0.1/-0.1/-0.1)

<v°2 T7

V°2

>0

3 'L

Fig. 2.18 Failure surface for tensile stress states.

A combination of biaxial compressive loading and unaxial tensile loading for concrete was described in [5]. It showed that very small tensile stresses of 2% of the compressive load had no influence upon the failure load. When this tensile stress was increased to 10* of the compressive load a reduction of nearly 50% in the failure load was observed.

(36)

2.22 Load-deformation

Biaxial tension-compression experiments by Zielinski [98] showed that the

tensile stress-strain curve was not affected by lateral compressive loads

below 1/3 f'cyi for concrete with (fjyi=55 N / m m2) . For low quality

concrete (f'Cyl =14N/mm2) this limit is much lower. In the discussion in

Chapter 2.6 more information is given about this research program.

Experiments on strain softening of concrete under triaxial loading conditions

have recently been published [52]. Most of the results relate to compression

tests, but a very few relate to compression-tension-compression loading. Fig.

2.19 shows this results.

f t (N/mm2) 0, n (o/1/o)

h

f I-1/0.2/-0.1 / ' ^ . ^ v ^ ^=r— 0.5 1.0 1.5 2.0

e(%)

Fig. 2.19 Strain-softening at triaxial loading.

Although it relates to only two separate results, which makes a general

conclusion difficult, it suggests a decrease in the maximum stress when a

lateral compressive loading is applied.In this diagram, the descending branch

seems to be rather unaffected by the compressive loading.

Conclusion

Load-deformation curves are influenced by the multiaxial loading conditions.

Below a certain level of the lateral compressive load the tensile stress

strain diagram is not affected by this load. This level seems to be dependent

(37)

Load-deformation 2.23

strength is observed. As for the magnitude of the strain the behaviour is not quite clear.No information was found with regard to the behaviour of fibre reinforced concrete in controlled multiaxial loading conditions.

2.5 Influence of temperature

The influence of the temperature upon the load-deformation behaviour of concrete under tensile loading will next be reviewed. Many materials show a temperature dependent behaviour. Temperature influences can therefore also be expected for concrete under tensile loading. At high temperatures lower strength values are observed, while an increase in strength is expected at lower temperatures.

This is illustrated in Fig. 2.20 in which the relative compressive strength is plotted versus the strain. The decrease in maximum strength and the increase in fracture strain for higher temperatures is manifest.

u

U 8

12

E(%)

Fig. 2.20 Stress-strain relationship for dense concrete at various temperatures [50].

There is a marked difference in the low temperature range between air-dry specimens, oven-dried specimens and specimens which are completely saturated

(38)

2.24 Load-deformation

[55,20]. This is clearly shown in Fig. 2.21, in which the effect of the moisture content and temperature upon the increase of the compressive strength is represented. The moisture content w is expressed as a percentage of dry weight (105<>C).

Saturated concrete with a water/cement ratio of 0.70 has twice the compressive strength of concrete with a water/cement ratio of 0.50 [20,93]. Literature research shows that there are no data available on the pure tensile stress-deformation behaviour of concrete at very low temperatures. The only information on tensile strength relates to the tensile splitting strength or to the flexural strength. Several authors have tried to correlate these strengths with the compressive strength at low temperatures [20,62]. Experiments for compressive and tensile splitting strength at very low temperatures are fairly easy to perform. Empirical equations have been derived, of which those of Goto and Miura include temperature T as well as moisture content w.

In the temperature range up to 120°C the equation is:

fc(T)= fc(T„) + [12 - ^ - J j g J P ^ Jw (2.7)

while below -120°C

fc(T)= fc(TR) + 10.7w (2.8)

TR is defined as the room temperature.

The tensile splitting strength can be approximated by:

fBPiit.(T)= 0.214fc(T)3"» (2.9)

for temperatures between +20°C and -160°C.

Fig. 2.21 shows the graphical representation of the compressive strength increase as given by the last term of equations (2.7) and (2.8).

Okada and Iguro neglected the influence of the moisture content and derived the following equations:

(39)

Load-deformat ion 2.25

fc(T)= fc(Tn) + 5 . 3 - 0.84T - 0.0027T2 (2.10)

and

faput. (T)= 2.4 + 0.06 fc(T) (2.11)

for a temperature range of -10°C to -200°C.

One of the lines in Fig. 2.21 represents the Okada equation for the compressive strength difference. Their formula fits well for moisture contents between air-dry and saturated concrete.

Goto and Muira paid attention to the fact that the tensile and the compressive strength tend to decrease more slowly with temperature below -100°C so that the relation between splitting tensile strength and compressive strength needed an adjustment.

Aft(N/mm

2

)

-40 0

T(°C)

Fig.. 2.21 Increase in compressive strength for moist,air-dried and oven-dried concrete related to the temperature.

(40)

2.26 Load-deformation

In a reviewing publication Reinhardt [72] assumed the ratio between compressive strength at room and at other temperatures to be the same for the tensile strength over the whole temperature range so that :

M

T

1__ =

MT)

ft (20°) fc(20°) (2.12)

The compressive strength ratio can be taken from Fig. 2.22.

fclT)/(

c

l20°)

1,1 >^**" ***"**—

I

wet dry 1 1 20

^--200 -100 0 100 200 300 400 T(8C)

Fig. 2.22 Temperature dependence of the compressive strength of concrete [72].

The changes in behaviour around -100° C can be explained by the fact that below this temperature all the water in the pores is frozen [75]. The freezing point of the water in the pores is dependent on the pore size diameter; the smaller the size, the lower the freezing point. At -100°C it is assumed that all the water is frozen. Rostasy's compressive strength curve shows a jump at that particular point (see Fig. 2.21). This jump was also found by Yamane [93] and Tognon [84] but has disappeared in the formulas derived.

(41)

Load-deformation 2.27

The results of the equations for tensile splitting strength of Goto et al, Okada et al and Reinhardt are shown in Fig. 2.23 assuming a compressive strength of 45 N/ma* at +20° C.

Klices and PIanas [12] performed tensile splitting tests to check the formulas of Goto/Miura and Okada/Iguro. For dried concrete the Goto/Miura solution gives an underestimation of 16* while the Okada/Iguro equation gives an overestimation of 12*. For wet concrete the Goto/Miuara equations predict values 25% too high.

fSpl (N/mm2)

Fig. 2.23 Temperature dependence of the tensile splitting strength of concrete with different moisture contents.

Data on the bending strength of concrete were given by Tognon [84], Yamane [93] and Okada [62]. Okada's curves resembled the compressive behaviour at low temperatures while Tognon's data showed a distinct decrease in flexural strength from -50°C to -100°C followed again by an increase. Yamane'a results indicated an increase up to -50°C followed by a decrease after which the test was stopped.

No data were available concerning the deformation behaviour of concrete in uniaxial tension at low temperatures.

(42)

2.28 IiOad-deformat ion

For compression, stress-strain curves were obtained for water-saturated plain and fibre reinforced concrete [75]. The curve for air-dried concrete has also been added. The saturated concrete behaves in a more and more linearly elastic manner as the temperature is lower. This effect is much smaller for air-dry concrete (Fig. 2.22). The fracture strain, however, is in both cases larger for low temperatures than for higher temperatures. From Fig. 2.24 it also appears that Young's modulus increased for air-dry concrete by a factor of 1.45 and for water-saturated concrete by a factor of 2.25. The addition of 1.5% by vol. of hooked steel fibres showed an increase of both maximum load and fracture strain, as was also seen at room temperature.

fc(N/mm2) 160.

£(%o)

Fig. 2.24 Stress-strain curves for concrete in compression at +20°C and -170°C [75].

(43)

Load-deformation 2.29

The stress-strain curves are not complete, but have been plotted only up to the maximum load. Therefore energy considerations can be given only for the first part of the streos-strain curve.

The increase in both strength and failure strain indicates that the energy absorption capacity of concrete increases when the temperature becomes lower. The contribution of the elastic energy to the total energy is relatively greater as the temperature is lower.

The literature gives very little information on the behaviour of steel fibre reinforced concrete at very low temperatures. In analogy with the bond behaviour of round and deformed bars the energy absorption of steel fibre conrete can be expected to increase with decreasing temperature. Yamane et al

[93] found that the bond strength of round steel bars (d=19mm) increased at -196°C by 480* for wet concrete and by 40* for air-dried concrete. The deformed bars (d=16mm) only showed an increase of 100* at -70°C for wet concrete.

A few load-slip relations can be found in [66] and are shown in Fig. 2.25.

Vfc20

'0.00 0D5 Q10 0.15 0.20 025 0.30 A ( m m )

Fig. 2.25 Load-slip relations for pull-out tests of reinforcement bars out of wet, air-dried and oven-dried concrete [66].

(44)

2.30 Load-deformation

The pull-out tests at -160°C ended in premature failure of the specimens. Nevertheless the results indicate a large increase in stiffness for wet stored specimens at -160°C. Stiffness of dried concrete is only 30* that of wet concrete.

CONCLUSIONS

No direct information on the behaviour of steel fibre reinforced concrete under uniaxial tensile loading at very low temperatures is available.

For the tensile (splitting) strength formulas are proposed which start with the compressive strength at a particular temperature. Experimental results show that for dried concrete these formulas can be used, but that for wet concrete too large deviations will occur.

For flexural strength a limited number of test results is available.

Stress-strain curves for concrete at very low temperatures are obtained only in compression. Maximum stress and fracture strain both increase with decreasing temperature.

Pull-out tests on round bars at -160°C resulted in premature failure of the concrete.

Nevertheless an increase in stiffness is observed which can also be expected for fibre reinforced concrete.

(45)

Load-def onnat ion 2.31

2.6 Combined influences

From what precedes it will be clear that a load-deformation curve of concrete has less meaning when the boundary conditions are not known. The influences were treated separately in the previous chapters. In reality a mixture of influences will occur. The combinations are schematicly shown in Table 2.3 in which the numbers of the chapters of the particular aspects are given.

è RH 2-3 D Temp.

Table 2.3 Scheme of chapters in which typical parameters are discussed

Results of low strain rate loading and different relative humidity are difficult to analyse, because the contribution of creep deformation can hardly be distinguished from that of real fracture deformation. Of the total deformation it is known that higher moisture content causes higher deformation values. Creep experiments are normally performed at constant loading, while the experiments as given in Table 2.3 need constant strain rate experiments.

In [81J the effect of the moisture content of the specimen upon the impact tensile strength was studied. For three mixes with different cement content and water-cement ratios no significant difference in strength was found for wet or dry concrete.

Results of experiments under multiaxial impact loading with tension in one or more directions are even more scarce than such experiments under static loading. However, two experimental programs have been found, one performed by

(46)

2.32 Load-deformation O^N/mm2 *0. 8 9 10 10%. 9^ ^ s ^^J ^ w S t a t i c / o - ( N / n m « f ^ Impact ' S S 8 . 1 I 1 I 1 I t 0.0 5.0 8.5 1.0 9.9 9.7 4 _ . * ^ 3 _ ^ ^ V ^ 2 2 s 1 /l 7/x 0

W~

ar

-9 ,o,

1*

ez ~o 2

7

^ 7

1 200 150 Z,{Vrmlm)

100

50

-50

-100 EjllO^m/m) No. - 1 2 3 4 5 Static/ Impact .jlN/ran-) S O.U S 7.5 I 0.0 I 6.9 3 o ^ J ' V i — 1

^ \

0,(N/mm2) 13 1 j i 1/5 r2 o. E2 '0, _ 1 _ ~ B2

200

150

e^lO^m/m)

100

50

-50 -100 E2(10"6m/m)

Fig. 2.26 Stress-strain curves for two types of concrete in biaxial tensile-compressive loading [98].

Takeda et al.[80] and a recent one by Zielinski [98]. The tests of Takeda et al concerned a biaxial compressive loading combined with a uniaxial tensile

loading. The influence of the confining pressure upon the tensile stress was not the same for static and for impact loading. Zielinski's results for biaxial compression-tension loading are represented in Fig. 2.26 for two concrete qualities. The diagrams show the tensile stress-tensile strain values for static (S) and impact (I) loading for various lateral compressive stresses.

(47)

Load-deformation 2.33

Conclusions from these diagrams are that for compressive stresses smaller than 0.33f'cyi the stress-strain curves were little affected both in static as in impact loading. For higher compressive loading the diagrams were more curved, while the tensile stress decreased. For high-strength concrete the fracture strain increased while for low strength concrete the fracture strain decreased.

Results of multiaxial experiments with the moisture content or the temperature as a parameter are not known. The influence of the relative humidity and the temperature upon the compressive strength of concrete is already shown in Fig. 2.21 and 2.24 of Chapter 2.5 for low as well as for high temperatures. Polivka et al . [68] performed compressive tests on cylinders with a moisture content of 5.4-5.9%. The test temperature was 20°C and 150°C.

At high temperature, the strength and fracture deformation were considerably reduced, as is apparent from Table 2.4.

Results of tensile experiments with moisture content and temperature as parameters are not known.

T fc £c K

20° C ï ï Ï

150°C 0.34 0.53 0.75

Table 2.4 Influence of high temperatures upon strength, strain and stiffness of concrete [68].

Finally, the combination of strain rate and temperature remains. For uniaxial tensile tests no data are available in this case either. Splitting tensile tests at higher strain rates were performed by Scheuermann et al [77]. Splitting tensile tests at 20°C and -165°C were performed at strain rates of 6*10"s and 0.4 1/s by Scheuermann. The results presented in Fig 2.27 showed a remarkable difference in behaviour between low temperature impact and room temperature impact. The increase in strength at high strain rates cannot be detected at low temperatures. No explanation for this behaviour is given.

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Warto było jednak na początku prac zaznaczyć, że oczekiwania badaczy mogą być inne, a powtarzanie się tematów nie jest wadą badań, ale ciekawą wskazówką analityczną, przy