DEPARTMENT OF CIVIL ENGINEERING
Report 5-81-3
Experiments on mortar
under single and repeated
uniaxial impact tensile loading
Dipl.-lng. A.J. Zielinski
STEVIN LABORATORY
CONCRETE STRUCTURES
i 1 - 3 ^1
Rapp CTB e t o n
8 1 - 0 1
.>yy'
Delft University of Technology Department of Civil Engineering Report 5-81-3 Research No. 1.2.81.01 February 1981
57Z. s-.^/^z
Technische Hogeschool Eii:li:>::icc::Afdeling: Civiele Techniek Stevinweg 1
postbus 5048 2600 GA Delft
9
cx.l.e.Y i-it)
Experiments on mortar under s i n g l e and repeated uniaxial impact t e n s i l e loading
D i p l . - l n g . A . J . Z i e l i n s k i
Kctpp
Cf
Mailing address: Technische Hogeschool D e l f t Vakgroep Betonconstructies S t e v i n l a b o r a t o r i urn I I Stevinweg 4 2628 CN D e l f t , The Netherlands .^\
n>-. ^ ^
Acknowledgement
The author wish to thank P r o f . D r . - I n g . H.W. Reinhardt and I r . H.A. Kömieling f o r t h e i r c o l l a b o r a t i o n and encouragement. The assistance of G.W. Nagtegaal at experiments is g r e a t f u l l y appreciated. The
draw-ings have been made by Th.A.Steyn and H.F.S. Spiewakowski f o r which the author wish to thank a l s o .
No p a r t of t h i s report may be published without w r i t t e n permission of the author.
3
-CONTENTS page
Notation 5
INTRODUCTION 7
LITERATURE SURVEY 9 .
BASIC CONCEPTS OF FRACTURE MECHANICS 10
TESTING METHOD 13
SCOPE OF THE EXPERIMENTAL PROGRAM 17
MANUFACTURE OF TEST SPECIMENS, TESTING PROCEDURES
AND PROPERTIES OF MORTAR USED 17
SINGLE UNIAXIAL IMPACT TENSILE LOADING TESTS 19
7.1 Results
7.2 Analysis 7.2.1 Behaviour of mortar
7.2.2 Comparison with concrete previously investigated
REPEATED UNIAXIAL IMPACT TENSILE LOADING TESTS 29
8.2 Analysis
8.2.1 Behaviour of mortar
8.2.2 Comparison with concrete previously investigated
page
SUMMARY AND CONCLUSIONS
39
10
REFERENCES
41
APPENDIX I Stress-strain diagrams determined in single
uniaxial impact tensile loading tests
43
APPENDIX II Stress-strain diagrams determined in repeated
Notation
5
-f - tensile strength
f. - uniaxial impact tensile strength
imp "^ ^
f 1 - static tensile splitting strength
f - uniaxial static tensile strength
f' - compressive strength
f* - static compressive strength
E - modulus of elasticity
I - mechanical impedance
o - reflection coefficient
a -
stress rate
a
- static stress rate
a - upper stress limit for repeated loading tests
e - strain
è - strain rate
3 - material and environment parameter
t - time
A, B - regression coefficients
R-^ - coefficient of determination
F - ratio of significance test
SEE - standard error of estimate
P - probability
U - total energy of the system
Un - strain potential energy
U|, - kinetic energy
U^ - surface energy
W - work of applied load
2 c - crack length
Y - surface energy for elastic material (per unit area of crack)
r - surface energy for plastic material (per unit area of crack)
Y_ - dissipative component of surface energy (r = y + Yp,)
7
-Bibliotheek'
afd. Civiele Techniek T H , 1 INTRODUCTION Stevinweg ] - Delft
This investigation is a continuation of the research project "Impact loading" which was carried out under the supervision of CUR-VB (Committee C-35).
The actual reason for the investigation was the need for more experimental data in order to establish the mechanism of concrete fracture under impact tensile loading.
The problem of the behaviour of concrete subjected to impact loading is of considerable importance in engineering practice. In the cases of explo-sions, airplane crashes, ship collisions and pile driving a compressive stress wave can be reflected as a tensile stress wave and can lead to cracking and failure of concrete.
Concrete can be idealized as a system which consists of aggregate particles embedded in cement matrix. It was therefore worth studying the behaviour of mortar (matrix) under uniaxial impact tensile loading and, by means of comparison with the behaviour of concrete, to determine the function of aggregate particles in the fracture process in concrete.
LITERATURE SURVEY
The amount of research on tensile strength of concrete materials,
espe-cially in relation to higher loading rates, is rather limited.
In Fig. 2.1 the results obtained in investigations on concrete performed
in the Stevin Laboratory [ 1, 2 ] at Delft and seven other investigations,
r 4 ] through f 10 ] , have been plotted, with on the horizontal axis the
stress or strain rate (assuming E = constant) and on the vertical axis the
impact to static strength ratio. The increase in tensile strength of
con-crete with increasing stress rate is clearly manifest.
O/Oo
E (1/s)
Fig. 2.1 Survey of results of experiments on tensile strength related
to the loading rate
The recent research of Zech and Wittmann |~ 1 1 ^ showed that bending
strength of mortar increased with increasing loading rate. The highest
rate of loading applied in that investigation was approximately 50 N/mm^ms.
When the loading rate increased by five orders of magnitude, the strength
9
-increased by a factor of 1.5 in the case of high-strength mortar
( f = 55 N/mm^) and by a factor of 1.9 in the case of lower-strength
mortar (f^ = 23 N/mm^).
Mihashi and Izumi |~ 12 ~| > basing themselves on the theoretical stochastic
model of concrete fracture, proposed the following relationship between
strength and stress rate:
1
f = ( f ) ^ ^ (2.1)
0 0
where: f - tensile strength
d - stress rate
3 - material and environment parameter
subscript "o" indicates static test conditions.
In the research program described in detail in f 1 "] , and briefly in
fZ"],
a double logarithmic relationship between strength of concrete and stress
rate was considered in the analysis of the results:
In f = A + B.ln d (2.2)
where A and B are regression coefficients.
The equation (2.2) expresses essentially the same relationship between
tensile strength and stress rate as equation (2.1) and could be easy
applied to statistical analysis of experimental results.
BASIC CONCEPTS OF FRACTURE MECHANICS
^
The behaviour of mortar and concrete subjected to static and impact uni-axial tensile loading will be discussed in further chapters with the aid of fracture mechanics concepts. Therefore the basic ideas of fracture mechanics will here be briefly reviewed; a more comprehensive study on fracture mechanics can be found in |^ 13 ] .
The influence of a crack on the behaviour of an infinite two-dimensional ideal homogeneous, isotopic and brittle material subjected to tension was first analysed by Griffith 1] 14 "| •
He expressed the total energy of the system as follows:
U = (-W + U^) + U3 (3.1)
where: U - total energy of the system W - work of applied load
Up- - strain potential energy U^ - surface energy.
The crack will become unstable and lead to fracture when the decrease in mechanical energy (-W + Up) equals or exceeds the surface energy of the newly formed crack surface.
For a thin plate (plane stress) under constant load the total energy becomes:
U = ZJL^SL + 4 CY (3.2)
where: a - tension normal to the crack plane 2 c - crack length
Y - surface energy (per unit area) E - Young's modulus.
The equilibrium condition dU/dc = 0 implies that the crack will become unstable for stress
11
-If the load is released before spontaneous crack extension occurs, the crack will tend to close up reversibly.
The energies associated with a crack are graphically shown in Fig. 3.1.
crack energy
Fig. 3.1 Energy balance according to Griffith
Griffith's concept was extended by Irwin |~ 15 3 and Orv;an f 16 ^ for non-brittle materials in which plastic zones are formed at the crack tip. The surface energy for such materials r can be expressed as follows:
Y + Y, (3.4)
where y is a term reflecting dissipation of energy in plastic processes. Because of the energy dissipation the stable crack, if unloaded, will not close up reversibly.
When a crack reaches the point of instability or when the loading is applied rapidly, the volume elements next to the crack surface will be accelerated. Therefore for dynamic loading the kinetic energy component U, can be added to the total energy of the system
Under impulsive loading the duration of the stress pulse is very important, since the applied stress must act for some certain minimum time in order to initiate crack growth or to drive a crack to further extension |_ 17 ] .
Glucklich r 18 "1 was the first who pointed out difficulties in direct application of the above-mentioned concepts for analysis of the behaviour of concrete. Cement-based composites are anisotopic, heterogeneous,
multiphase systems with inherent microcracks in the cement matrix phase, interfacial bond microcracks and air voids. Those microcracks are poten-tial sources of crack initiation in fracture process. On the other hand, tougher aggregate particles and air voids may perform a crack arresting action. A few ways in which the growth cracks can be arrested are shown in Fig. 3.2..
Fig. 3.2 Mechanisms of crack arrest
Besides to the direct crack arresting action of aggregate particles (fracturing tougher particles), arrest by blunting as a result of debond-ing of aggregate particles, enterdebond-ing of stress relieved zones between debonded particles, or encountering air voids, can be mentioned. The cracking process is not limited only to the main crack but includes also extensive microcracking in the highly stressed crack tip zones.
Applicability of fracture mechanics to cement-based composites such as cement pastes, mortars and concretes has often been discussed, as in
I" 19, 20, 21 J among others. Some aspects of this problem still require more research work.
13
-TESTING METHOD
The test method applied was actually the same as described in detail in f 1 ~| and is based on the "Split Hopkinson Bar" technique.
The test equipment will be briefly discussed.
It consists of two coaxial elastic bars between which the specimen is sandwiched (Fig. 4.1). incident pulse ''/ / /
T
time \ ^/^. 3-^^X
> V 2 a, = a,= 2 1 ; • [ , . 1 , / A -// V A II . 1 ; I i - l ; I , . I , 2 1 i l i . l >Fig. 4.1 Principle of the Split Hopkinson Bar technique
A stress pulse propagating through the first bar is partly transmitted and partly reflected at the interface between elastic bar and specimen. The ratio between transmission and reflection depends upon the mechanical im-pedance of the materials involved. In the case of an aluminium bar and a concrete specimen, about 80 to 95 percent is transmitted. The transmitted pulse is measured on the second bar and - because of equilibrium - imme-diately gives the force which acted on the specimen.
Fig. 4.2 shows a drawing of the equipment used. The tensile pulse is generated by a drop weight hitting the anvil at the bottom of the lower bar,
Layers of rubber or cardboard between drop weight and anvil cause different contact and lead to different stress rates in the range from 2 to 60 N/mm^ms, By variation of drop height and drop weight, the stress rate can also be varied systematically. The bars must have a certain length in order to provide a uniformly distributed stress pulse; a length if about 20 times the diameter is necessary to keep the specimen and the measuring point force free from unintended reflections. It turned out that at a given wave propagation velocity of about 5000 m/s and a maximum pulse duration of about 2 ms, the bars should be about 5 m long. The diameter of the bars is
11.65m
1 buffer 2 upper bar 3 guide A straingauge 5a upper cooling jacket 5b lower cooling jacket 6 concrete test specimen
a 7 4 x 7 5 m m 7 working platform 8 counterweight 9 lower bar 10 frame 11 drop weight 12 coupling 13 uncoupling K liftingdevice 15 demping material 16 anvil 17 guide tube 18 pneumatic jack 19 frame base /////////y^W//,
15
-determined by the specimen size. A 74 mm bar diameter was chosen in this
investigation. The specimen was glued to the aluminium bars by means of a
filled polyester resin.
For the whole duration of an experiment the strains were measured on the
specimen by contactless LVDTs. The strain of the upper bar was measured by
strain gauges giving the loading force, calculated from a known value of
the modulus of elasticity for aluminium.
Measuring devices are shown in Fig. 4.3 and test record of stress and
strain in Fig. 4.4.
R|
Ti ^ iTr
Q —
^
retardationof the signal
Fig. 4.3 Measuring devices
1 - a m p l i f i e r ; 2-sumator; 3 - t r a n s i e n t recorder; 4-reteradator
In t h i s way the necessary data were a v a i l a b l e to e s t a b l i s h the stress-s t r a i n r e l a t i o n up to f a i l u r e at varioustress-s high ratestress-s of loading.
Fig. 4.4 Record of stress and strain measurements
To facilitate fatigue loading an automatic lifting mechanism was added to
the equipment, which operated with compressed air. It lifted the drop
weight and released it at a preset level.
The frequency of impacts was approximately 16 loading cycles per min. The
maximum upper stress limit was controlled by variation in the drop height
and the application of different layers on the anvil. The disadvantage of
the testing equipment was the fact that a decreasing stress limit influenced
the stress rate.
With decreasing maximum stress the stress rate also decreased and was
between 2 and 6 N/mm^ms.
However, from the single impact loading tests it was known that this
vari-ation is rather small and its effect could be neglected.
tension
G(N/mm^)
compression
17
A typical loading pulse for fatigue tests is shown in Fig. 4.5.
The compression part of the pulse is due to the reflections from the upper
end of the Hopkinson bar. The reflection is greatly attenuated by a shock
damper and the remaining stress is thought to be too low to affect the
tensile strength of the concrete. Therefore this compression part is
neglected in all further considerations,
SCOPE OF THE EXPERIMENTAL PROGRAM
The primary question of this investigation was: how does the loading rate
influence the stress-strain behaviour of mortar subjected to uniaxial tension?
Secondly, what is the effect of uniaxial impact fatigue tensile loading on
the behaviour of mortar?
In order to answer these questions single and repeated uniaxial impact
ten-sile loading tests had to be carried out.
The experiments were performed on mortar (made with 1 mm maximum size of
sand particles, water-cement ratio 0.58 and Portland B cement content
375 kg/m3) at an age of 28 days and amb.ient temperature.
The grading of the sand was as follows:
mm
%
0.5-1
0.25-0.5
0.1-0.25
39.1
27.5
33.3
The quality of the mortar was checked by means of static compressive and
tensile splitting tests.
6 MANUFACTURE OF TEST SPECIMENS, TESTING PROCEDURES AND PROPERTIES OF MORTAR
USED
The details of the mix proportions have already been given in Chapter 5.
The cylindrical specimens of 74 mm diameter and 100 mm length used for
impact tests were drilled from 200 mm cubes.
For static compressive and tensile splitting tests three 150 mm cubes were used.
The mix was compacted for 120 s during casting, and demoulding took place after 2 days, after which the 200 mm cubes were stored under water for 12 days. 14 days after casting, cylinders were drilled and sawed. Then they were kept under water. One day before testing, the cylinders were kept in air at 50% relative humidity in order to satisfy requirements for gluing.
The cylinders were glued between the upper and the lower bar with a filled polyester resin F 88 ^.
For a given loading rate with single uniaxial impact tensile tests or for a given maximum upper stress limit with repeated uniaxial impact tensile tests, the experiments were repeated a few times in order to obtain some idea of the scatter in the results.
The 150 mm cubes used for static tests were kept under water and were tested at an age of 28 days. The applied rate of compressive stressing
4. -4 was 5.10 N/mm^ms, and for splitting it was 10 N/mm^ms.
The results of the static tests are listed in Table 5.1.
Table 6.1 Results of static tests
No.
1
2
3
Comp ressive N/mm^ 28.5 26.9 28.2strength Tensile splitting strength
N/mm2
2.39 2.33 2.08
The mean value of the static compressive strength of mortar was 27.9 N/mm^ with a coefficient of variation of 3.2%.
The mean value of the static tensile splitting strength of this mortar was 2.3 N/mm^ with a coefficient of variation of 7.2%.
The air content of the fresh mortar was 7.5%.
19
-7 SINGLE UNIAXIAL IMPACT TENSILE LOADING TESTS
7.1 Results
15 mortar cylinders were subjected to single uniaxial impact tests per-formed with a stress rate in the range from 6 to 28 N/mm^ms, and the values of the impact tensile strength attained were between 3.1 and 4,6 N/mm^. The results of those tests are listed in Table 7.1, in which values of stress rate (d), corresponding impact tensile strength (f^-^p) and strains at maximum stress level are given,
Table 7,1 Description of single impact loading test results
Nr. of Stress rate d Impact tensile strength f. Strain at a
specimen N/mm^ms N/mm^ %„ 3,12 3.57 3.89 3.10 4.22 3.72 4.26 3.96 3.94 3.46 4.57 4.20 4.54 4.01 3.65 0.20 0.25 0.24 0.22 0.22 0.24 0.21 0.22 0.20 0.21 0.37 0.39 0.37 0.36 .0.30
In most cases, fracture occurred at the central section of the specimen, as can be seen in Fig. 7.1.a. In one case the specimen (Nr. 5) was frac-tured through its full depth into three pieces (see Fig. 7.1.c), and in
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
5.71 10.44 11.32 13.04 13.92 14.31 14.82 15.52 15.75 16.55 20.61 22.75 24.00 24.19 27.73one case the specimen (Nr. 7) was also fractured into three pieces, but not through the full depth (Y shape of fracture can be seen in Fig. 7.1.b)
Fig. 7.1 Three modes of impact tensile fracture of mortar specimen
7.2 Analysis
7.2.1 Behaviour of mortar
The results obtained in impact uniaxial tensile loading tests performed on mortar show a remarkable increase in strength due to a high stress rate
(see Table 7.1). The results of impact tests should actually be compared with the uniaxial tensile strength determined on the same cylindrical specimens in static tests. Because of some technical difficulties during the static uniaxial tensile tests, it was not possible to obtain sufficient data, and therefore the results of splitting tests had to be used as a measure of tensile static strength.
The experimental results of the uniaxial impact tensile tests and static tensile splitting tests were statistically analysed according to equation (2.2).
21
-been determined:
P [Inf = 1.225 + 0.045 In d +2.17^0.105] = 0.95 (7.1)
R2 = 0.81
The results are graphically shown with 95% confidence band in Fig. 7.2. It should be noted that a logarithmic scale has been used on both axes.
f (N/mm2)
G(N/mm^ms)
Fig. 7,2 Influence of high stress rate upon the tensile strength of mortar
The ratio of impact (d = 30 N/mm^ms) to static (d = 10 N/mm^ms) strength computed according to formula (7.1) has a value of 1.76.
That ratio varied between 1.33 and 2.34 for various concrete mixes previ-ously investigated |^ 1 ]] • Since the value of the ratio between static and impact tensile strength of mortar is in the range observed for concrete, the mechanism of static and impact fracture of mortar and concrete sub-jected to tensile loading must be very carefully studied. Particular attention should be paid to crack arresting action of aggregate particles and development of microcracks in the matrix.
In |_ 1 J and |_ 2 J the behaviour of concrete subjected to static and im-pact uniaxial tensile loading was discussed. The explanation for higher impact strength and greater impact strain observed at the moment of frac-ture was suggested.
Under slowly increasing tensile load, the fracture process starts from existing microcracks and macrocracks which have time to chose and develop along the path of least energy requirement, i.e., around aggregate parti-cles and through the weakest zones of the matrix.
Bibliotheek
afd. Civiele Techniek T,H Stevinweg 1 - D s l f t
Due to low overall stress level and relaxation of material the extension of microcracks in other areas of higher strength is rather limited. Under impact tensile loading conditions much energy is introduced into specimens in a short time, and cracks are forced to develop along a shorter path of higher resistance - through stronger matrix zones and some aggre-gate particles. The very rapidly increasing overall tensile stress causes extensive microcracking in other areas, since relaxation cannot occur in the extremely short time of fracture. Also, crack branching can occur due to interactions between the rapidly moving crack front and the aggre-gate particles or other inhomogeneities.
So the two reasons for the higher strength and greater deformation of con-crete under impact tensile loading can be distinguished:
- cracks develop through zones of higher strength;
- extensive microcracking and macrocracking takes place in the whole volume of stressed material.
Mortar used in the research program described in this report can be treated as a rather homogeneous material, in contrast with concrete, which must be considered as a heterogeneous composite of cement matrix and aggregate particles.
The increase in the tensile strength of mortar observed in impact tests can be explained neither by crack arresting action of aggregate particles nor by development of cracks in the stronger zones, since there are no aggre-gate particles and the variation of properties of mortar within the speci-men must be much smaller than in concrete.
The above indicates that the most important reason for higher tensile strength of mortar at higher stress rates must be extensive microcracking and macrocracking.
Mechanisms of static and.impact fracture of mortar subjected to tensile loading are schematically shown in Fig. 7.3.
The existing microcracks grow under rapidly increasing tensile stress; between some of them a process of bridging takes place and continuous fracture planes are formed. In most cases one of such fractured planes is more extended than others and results in the failure of the specimen observed.
23
-The fracture of specimen into three portions confirms the hypothesis that more fractured planes can be developed at the same time under impact ten-sile loading. STATIC IMPACT unloaded existing mircocrocks growing cracks initiation of fracture fracture
Fig. 7.3 Schematic mechanism of mortar fracture under static and impact tensile loading
Unfortunately there was only one satisfactory result of static uniaxial tensile tests on mortar cylinders of 74 mm diameter and 100 mm length. The static stress-strain diagram determined in that test is graphically compared in Fig. 7.4 with impact a-e diagram. The individual stress-strain diagrams are presented in Appendix I. It is to be noted that the impact maximum stresses were 1.9-2.7 times greater than the static ones, and
the corresponding strains were 2-3.9 times greater than in the static case. The much greater deformation of mortar under impact uniaxial tensile load-ing than under static loadload-ing indicates extensive microcrackload-ing in the specimen.
The energy absorbed by mortar in impact tests was at least 3,6 times greater than in static tests.
^0(N/mm2) / / / / 9 ,tati<;
-A
impact s 0.1 0.2 0.3 0.^ 0.5 0.5 e(%o)Fig. 7.4 Stress-strain relationships for mortar determined in static and impact uniaxial tensile tests
The extra amount of energy absorbed in impact test was mainly due to the creation of much larger fractured areas and maybe due to dissipation of some strain energy in the form of kinetic energy of rapidly moving elements next to crack surfaces,
7.2.2 Comparison with concrete previously investigated
The direct comparison of results obtained on mortar in this research
program with results previously obtained on concretes with various maximum aggregate size can lead to a better understanding of the function of aggre-gate particles in the tensile fracture process of concrete.
In the research program reported in [ 1 J, 26 different concretes were subjected to uniaxial impact tensile loading. The maximum aggregate size was varied from 8 through 16 to 24 mm, the water-cement ratio was in the
range from 0.40 to 0.50, and the cement content varied between 300 and 375 kg/m^. Other variables were the cement type and quality, and the specimen humidity "dry" or "wet". "Wet" means storage at 100% relative humidity for 28 days, and "dry" means storage at 100% relative humidity for 14 days and then at 50% relative humidity for the next 14 days.
25
-Although there are no properties of concretes previously tested and mortar investigated in this experimental program directly comparable, it seems quite reasonable to use concrete mixes 4, 17 and 25 as a basis for compari-son. Cement content and water-cement ratio were pretty similar in both materials tested. The higher water-cement ratio of mortar (0.58) as com-pared with the water-cement ratios of the above concretes (0.45-0.50) could lead to important differences in the quality of mortars which formed the matrix of the concretes investigated and the quality of the mortar used
in this program.
It was noted [ 2 1 ] that, in general, increasing water-cement ratio resulted in a decrease of fracture toughness of cement-based materials.
The results of static tensile splitting and uniaxial impact tests obtained on the above-mentioned concrete mixes and mortar are graphically compared in Fig. 7.5 to Fig. 7.7.
The corresponding statistical analysis of effects of changes in maximum particle size upon the static and impact tensile strength is summarized in Table 7.2.
Table 7,2 The multiple regression analysis of static and impact tensile tests performed on mortar and concrete
Regression equation: l n f = A + B i . l n d + B2.D
Mix STATIC Number Regression coefficients Coefficient of deter- Standard Nr. IMPACT of test mination R^ due to error of
results A Bj B2 In d In d and X estimate
0.801 - 0.0155 21 0.868 0.174 0.0028 0.50 0.797 - 0.0199 1.091 0.089 0.0150 0.47 0.792 - 0.0248
1.041 0.093 0.0534 0.65
M, 4 M,25 M,17 ST IMP ST IMPST
IMP
6 21 15 416
21
0.85 0.55 0.66 0.58 0.75 0.74 0.088 0.094 0.092 0.094 0.061 0.093f (N/mm2) 10' 10^ Ó(N/mm^ms) f (N/mm2) o o mortar
i
-— 1 'cem. cont. 375 _ w/c 0,58 Omax 1 10" 10' 10TT
t
eem. cont. 375 w/c 050 Dmax. 16 10-' 10' 10^ Ó(N/mm^ms) f (N/mm2) 10' , 10^ Ó(N/mnn'^ms) Fig. 7.5 Fig. 7.6 Fig. 7.7Fig. 7.5 to Fig. 7.7 Differences in static tensile splitting and uniaxial impact tensile strength of mortar and various con-cretes
27
-Mortar and Mix 4 (Fig. 7.5)
There is no great difference between the impact tensile strength of concrete made with maximum aggregate size 24 mm, cement content 375 kg/m3 and water-cement ratio 0.45 and the impact tensile strength of mortar made with 1 mm maximum size of sand particles, the same cement content and water-cement ratio 0.58. The impact strength of concrete seems to be slightly higher than the strength of mortar at the highest loading rates.
This effect is, however, significant only at 90% significance level. The static tensile splitting strength of concrete is evidently
(at 99% significance level) greater than the static strength of mortar.
Mortar and Mix 25 (Fig. 7.6)
It can be seen that the impact tensile strength of concrete made with 16 mm maximum size of aggregate particles, water-cement ratio 0.50 and cement content 375 kg/m^ is higher than the impact strength of mortar. This effect is significant at 99% significance level. The static tensile splitting strength of concrete is also, at 99% significance level, higher than the static strength of mortar.
Mortar and Mix 17 (Fig. 7.7)
The greatest difference in impact tensile strength is observed between concrete made with aggregate particles of maximum size 8 mm, cement content 352 kg/m^ and water-cement ratio 0.48 and the mortar investigated. The impact tensile strength of concrete is, at 99% significance level, significantly higher than the strength of mortar.
The static tensile splitting strength of concrete is higher than the strength of mortar. This effect is significant at 95% signifi-cance level.
In general, the static tensile splitting strength of concrete was higher than that of mortar, and showed a tendency to increase with increasing maximum aggregate size.
This can be explained as follows:
resulted in lower quality of the material as compared with the quality of
the mortar forming the matrix phase of the concretes tested.
Secondly, introduction of large aggregate particles means that the
pre-determined failure plane must comprise more fractured large aggregate
particles or else the failure path will be longer, as the crack has to go
round those particles. In both cases, the result is a greater resistance
to fracture.
It is to be noted that the uniaxial impact tensile strength of concrete
was higher than the strength of mortar. This can be explained by the crack
arresting action of the aggregate particles. The experiments on mortar
showed that extensive microcracking took place under uniaxial impact
ten-sile loading. These microcracks can be stopped by large aggregate particles,
since the fracture through tougher particles requires more energy.
Some of these microcracks could develop around aggregate particles; in
such a case more energy will be absorbed due to extra energy demanded in
order to change the direction of a
very
fast moving crack front.
The difference between uniaxial impact tensile strength of mortar and
con-crete was more pronounced with decreasing maximum size of aggregate
parti-cles used for concrete mixes. Decrease in maximum aggregate size corresponds
to the increase in surface area of the aggregate. The small aggregate
particles are better embedded in cement matrix than large ones and
there-fore they are more efficient in their crack arresting function. Also,
bleeding effects are less.
It should be borne in mind that small aggregate particles embedded in
mortar are not treated as aggregate phase, and aggregate arresting action
is considered to take place mainly due to larger aggregate particles
characteristic of concrete materials.
29
-8 REPEATED UNIAXIAL IMPACT TENSILE LOADING TESTS
8.1 Results
12 results of repeated uniaxial impact tests have been obtained. The upper stress limits varied in those tests between 1.4 times the static tensile splitting strength of mortar and 0.7 times the static strength. Cylinders withstood respectively 2 to 2142 loading cycles. The stress rate varied between 1.9 and 8.3 N/mm^ms.
Table 8.1 Description of repeated impact loading test results
Nr. of Upper stress limit a Stress rate d Number of
'^'^ max specimen N/mm^ N/mm^ms loadings N
1
2
3
4
5
6
7
8
9
10
11
12
3.03 3.21 2.91 2.82 1.95 1.83 1.78 1.77 1.75 1.84 1.87 1.53 5.89 8.29 6.06 7.53 2.97 2.25 • 3.16 3.54 2.49 2.22 3.13 1.922
2
3
5
6
11
12
14
59
73
105
2142The results of repeated impact loading tests are listed in Table 8.1, in which the upper stress limit la , „ ) , the corresponding number of
max
loading cycles that the specimen withstood (N) and the stress rate (d) are given.
Most specimens fractured at the centre section, and the fractured plane closely resembled that in the single impact loading tests. In one case the specimen (Nr. 3) was fractured throughout its full depth into three portions.
8.2 Analysis
8.2.1 Behaviour of mortar
The impact fatigue tensile tests performed on concrete showed that repeated
loading led to a substantial decrease in the impact tensile strength of
concrete and that concrete fatigue failure in tension was of a progressive
nature [ 1, 3 ] .
It had been shown that the relationship between the maximum applied stress
during fatigue testing or relative maximum applied stress, i.e., maximum
stress expressed by means of static tensile splitting strength and the
logarithm of the number of impacts reflected rather good fatigue behaviour
of concrete.
Results shown in Table 8.1 indicate that the number of impacts that the
mortar specimen could withstand decreased with increasing upper stress
limit. Those results are graphically presented in Fig. 8.1 and Fig. 8.2
with absolute or relative value of maximum applied stress on the vertical
axis against the number of impacts on a logarithmic scale. It should be
noted that three results of single uniaxial impact loading tests obtained
at the lowest impact rates of stressing are also shown in those figures.
Those 15 results have been statistically analysed according to the formulas
(8,1)_ and (8.2)
a
= A, + Bn.ln N (8.1)
max 1 ^
^ '
aJ^
= A2 + B2.1n N (8.2)
•splwhere: a - upper stress limit
f 1 - static tensile splitting strength
:| N - number of impact loadings
Ai, A2, Bi, B2 - coefficients.
The regression coefficients A^, A2, Bj, B2, and coefficients of determina
-tion have been computed and 95% confidence bands determined.
P = fa = 2.82-0.268 In N + 2.17 . 0.428] = 0.95 (8.3)
'- max - -'
^ '
31
-P [ "lÊÜ = 1.24-0.118 In N +2.17 . 0.189] = 0.95
~ spl
R2= 0.66
(8.4)
Fig. 8.1 and Fig. 8.2 show a very rapid decrease in the impact tensile
strength of mortar due to repeated loading.
.Omox ( N / m m 2 )
Fig. 8.1 Relationship between the uniaxial impact fatigue tensile strength of mortar and the number of loading cycles
2.0 1.5 1.0 0.5 0 ^max /fspl
L^JT-- • 1 "~~ •"-- ^ ^ ^ - - ^ 0^ 1 o • —-y 1
o , ^ ^ ^ - - ^ 0^ 10N
Fig. 8.2 Relationship between the relative impact fatigue tensile strength of mortar and the number of loading cycles
After a small number of loading cycles (ca. 10 cycles) the impact tensile strength of mortar was reduced from the value of about 1.5 times the static tensile splitting strength to ca. 0.8 times the static strength.
The impact fatigue tensile strength oscillated about the level of 0.80-0.65 times the static tensile splitting strength for greater number of impact loadings (up to approx. 2000 loading cycles).
The behaviour of mortar subjected to repeated uniaxial tensile loading will be discussed with the aid of fracture mechanics concepts.
The energy introduced in a loading pulse causes extension of cracks accom-panied by transformation of strain energy into surface energy of newly formed cracks.
Mortar can be treated as a brittle, rather homogeneous (compared with con-crete) material with inherent microcracks and air voids which cause stress concentration zones where the crack initiation process takes place during early loading cycles. After crack initiation, stable crack growth occurs, which is the longest phase in the fatigue life of the material. During stable crack growth, the released strain energy is entirely absorbed by surface energy increase and other energy dissipating mechanisms (for example inelastic strains). If the external load is removed, a crack will tend to close up.
The subsequent impact loading pulses will again cause the elastic defor-mation of material and stress concentrations. This can lead either to further extension of already developed groups of cracks or initiation of macrocracks from other existing microcracks. Since the energy requirement for crack growth increases with increasing length of crack (due to possible arresting action of air voids and other potential arresters), it is possible that some cracks will not grow further when a certain length is reached and other smaller cracks will develop. Here a pulse character of the impact loading is very important, because for crack extension a certain stress level must not only be attained, but must also be sustained for some time necessary to compel a crack to extend.
The location of inherent microcracks in mortar is randomly distributed, and therefore the process of bridging of cracks will not necessarily take place at the same time for different specimens, i.e., during impact fatigue loading with the same stress pulses the continuous fracture of specimens may not occur after exactly the same number of loading cycles.
Since mortar is a rather homogeneous material, the cracks will not be stopped very often by obstacles. Under fatigue loading performed with a high level of stress pulses the extension of cracks must be very rapid, for much energy is introduced with each loading pulse. With impact fatigue loading with lower stress limits, however, a continuous fracture will not be formed so quickly. A larger number of shorter cracks will be formed instead, which, through heterogeneous bridging, will cause failure of the specimen.
33
-The development of cracks in the course of impact fatigue tensile loading is confirmed by the large specimen deformations observed. The stress-strain relationships at different stages of fatigue loading are shown in Appendix II.
It is to be noted that mortar behaved quite elastically through the greater part of its fatigue life. Only in the last phase of fatigue loading, for a few loading cycles before failure occurred, the cracks that had developed now linked up with one another and the deformations were much more pro-nounced,
At comparable stress level the fatigue fracture strains were larger than the strains observed in the single impact tensile tests.
For lower values of the upper stress limits the strains at the moment of fatigue fracture decreased, but were still greater than the static strain, and their values were in the range of single impact loading strains.
2.2 Comparison with concrete previously investigated,
It is worth studying how the presence of aggregate particles in concrete influences behaviour under impact fatigue loading.
Results obtained on mortar in this research program can be compared with results of impact fatigue loading on concrete reported in [ l , 3 ] . Four concrete mixes were subjected to impact fatigue tensile loading. All of them were made with 16 mm maximum aggregate size, Portland B cement content either 325 or 375 kg/m^, water-cement ratio of 0.40 or 0.50, and kept in "dry" or "wet" conditions.
In Fig. 8.3 to Fig. 8.10 results of uniaxial impact fatigue loading on mortar and various concretes are graphically compared.
The corresponding statistical analysis is summarized in Table 8.2,
The maximum aggregate size was chosen as the most important single variable reflecting the difference between mortar and concretes.
Table 8.2 The multiple regression analysis of impact fatigue tensile tests performed on mortar and concrete
Regression equations: 1) a = A + B^.ln N + ^2.0
a
2) -J^^ = A + Bi.ln N + B2.D ' f „-, '• ^ max
spl
Mix Number Equa- Regression coefficients Coefficient of deter- Standard Nr. of test tion mination R^ due to error of
results A Bi Bo In N In N and X estimate
M,21 28 M,22 29 M,23 50 M.25 35 1 2 1 2 1 2 1 2 2.887 1.240 2.944 1.256 2.713 1.158 2.650 1.151 -0.327 -0.120 -0.357 -0.129 -0.249 -0.085 -0.246 -0.091 0.071 0.0099 0.085 0.014 0.057 0.0007 0.1147 0.0210 0.48 0.56 0,45 0.58 0.35 0.63 0.60 0.45 0.72 0.70 0.76 0.75 0.71 0.63 0.90 0.76 0.580 0.211 0.545 0.194 0.403 0.148 0.350 0.147
Fig. 8.3 to Fig. 8.10 Comparison of fatigue behaviour of mortar and con-crete subjected to repeated uniaxial impact tensile loading
- 35 Omax ( N / m m 2 )
5Ur
4 3 21 0- -o mortar \ ^ n o ^ " " " ^ .^ o u o 1 cem. cont. w/c Dmax hum. 3 75 0,58 1 wet — • • 3oO • - « ^ ^ • o ^ o ' ^ « - - ^ 1 10' cem. cont. w/c Dmax. hum. 325 0,50 16 dry - ^ 0 ^ 10^ lO^ •C"^
10 F i g . 8.3,Omax/fspl
F i g . 8.4 ,Omax ( N / m m 2 ) 6 ( - o - - o m o r t a r J cem. cont. 375 w/c 0,58-Dmax. 1 hum. wet concrete cem. cont. 325 w / c 0,50 Dmax 16 hum. wet2 Of^nisi/iiEi
F i g . 8.5 F i g . 8.6.Omax ( N / m m 2 ) o - - o mortar cem. cont. 375 w/c 0,58 Omax. 1 hum. w e t concrete cem.cont. 375 w/c O.AO Dmax. 16 hum. dry 2.0, 1.5 1.0 0.5 Omox/^spl 3 3
L ° ^
o
" " " " " ^ o V
• o -o mortar ••__*• * • • 0' 1( • D2 • • concrete o """^ ~~.. 10-^ 10 N F i g . 8.7 F i g . 8.8 Omax ( N / m m 2 ) o - - o - m o r t a r cem. cont. 375 „ w/c 0,58 Dmax. 1 hum, wet concrete f • F b ^ -Ö5IT 10' 10^ cem. cont. 375 w/c 050 D m a x 16 hum. dry 10^ 10^ N F i g . 8.9 Omax/f spl F i g . 8.1037
-Mortar and Mix 21 (Fig. 8.3 and Fig. 8.4)
It is to be noted that concrete made with 325 kg/m^ Portland B cement content, water-cement ratio of 0.50, maximum particle size 16 mm kept in "dry" conditions behaved essentially in the same way under impact fatigue loading as mortar made with 375 kg/m^ Portland B cement content, water-cement ratio of 0.58, maximum sand particle size 1 mm and kept in "wet" conditions. The only difference can be seen for values of impact strength under single loading.
Mortar and Mix 22 (Fig. 8.5 and Fig. 8.6) i.
Actually the same as above can be concluded about the differences in behaviour of the concrete made with the same mix proportions as Mix 21, but kept in "wet" conditions, and the behaviour of the mortar investigated.
Mortar and Mix 23 (Fig. 8.7 and Fig. 8.8)
The absolute values of the impact fatigue tensile strength of con-crete made with 375 kg/m^ Portland B cement content, water-cement ratio 0.40, maximum particle size 15 mm and kept in "dry" conditions were somewhat higher than the strength of the mortar tested.
The decrease in strength of concrete had also a more continuous character, i.e., with increasing number of impact loading cycles the strength decreased progressively. For mortar a rapid decrease in strength was observed mainly for a small number of loading
cycles with relatively high maximum stress limit. For larger number of loading cycles the variation in strength was smaller.
In terms of relative impact fatigue strength it can be seen that concrete and mortar behaved in the same manner through the greater part of the fatigue life.
Mortar and Mix 25 (Fig. 8.9 and Fig. 8.10)
The greatest difference in fatigue behaviour is seen to exist
between mortar and concrete made with 375 kg/m^ Portland B cement
content, water-cement ratio 0.50, maximum aggregate size 16 mm,
kept in "dry" conditions. The fatigue strength of concrete was
higher than that of mortar. It can be noted that the fatigue
frac-ture process of concrete had a less rapid character.
In general, it can be concluded that the direct crack arresting action of
aggregate particles was not very strongly manifest in the fatigue fracture
of concrete. Broken aggregate particles were seldom observed in fatigue
fractured planes, which seems to confirm that the direct arresting action
of tougher particles was not of great importance.
It is very likely that the tensile fatigue fracture of concrete is mostly
determined by progressive crack growth in the mortar matrix whose fracture
toughness depends on the mix proportions and especially the water-cement
ratio.
Concretes made with higher cement content and water-cement ratio can be
described as a more heterogeneous material with many air voids and
inter-facial microcracks performing crack arresting action. Therefore such
con-cretes were less sensitive to impact fatigue loading and showed higher
fatigue tensile strength than relatively homogeneous mortar.
Concretes with low cement content and low water-cement ratio can be treated
as more brittle and homogeneous materials (fewer voids and interfacial
cracks) and are therefore sensitive to repeated loading which compels
cracks to extend rapidly.
39
-SUMMARY AND CONCLUSIONS
The behaviour of mortar subjected to single and repeated uniaxial impact tensile loading was investigated by means of the Split Hopkinson Bar technique.
The mortar tested was made with 1 mm maximum size of sand particles, water-cement ratio 0.58, 375 kg/m^ Portland B water-cement content. At an age of 28 days it exhibited a static compressive strength of 27.9 N/mm^, and a static tensile splitting strength of 2.3 N/mm^.
15 single impact tensile loading tests were performed with stress rates ranging from 6 to 28 N/mm^ms. The corresponding impact tensile strength varied between 3.1 and 4.6 N/mm^.
-4 The ratio between impact (at d = 30 N/mm^ms) and static (at d = 10 N/mm^ms) tensile strength computed according to the double logarithmic
relationship between strength (f) and stress rate (d)
In f = A + B.ln d
had a value of 1.76.
This remarkable increase in tensile strength of mortar due to high stress rates was discussed and explained with the aid of fracture mechanics concepts.
It was suggested that the higher impact tensile strength of mortar observed was caused by simultaneous extensive microcracking in the whole volume of the specimen stressed. This hypothesis was confirmed by 2-3.9 times greater impact strains than static strains measured and by cases of fracture in which specimens had fractured into three pieces.
Much more energy was absorbed in the impact tensile fracture process than in the static.
12 results were obtained in repeated uniaxial impact tensile loading tests performed with stress rates ranging from 1.9 to 8.3 N/mm^ms. Fatigue tests showed a very rapid decrease in impact tensile strength with increasing number of loading cycles.
The impact tensile strength decreased from about 1.5 times static tensile splitting strength (f -j) to about 0.8 f -, for 10 loading cycles, and further oscillated at the level (0.8-0.65).f -, for larger numbers of
impacts up to approx. 2000 loading cycles.
Large fatigue strains observed and fracture of mortar specimens into three
pieces indicated extensive microcracking.
The fatigue impact tensile fracture of mortar seemed to be controlled by
progressive microcracking of the material and a heterogeneous crack-bridging
process leading to failure observed.
Comparison of results of this research program with results obtained on
various concretes previously investigated showed that the direct crack
arresting action of tough aggregate particles was of great importance
for the mechanism of concrete fracture under single impact tensile loading.
The direct crack arresting action of aggregate particles was less strongly
pronounced in the fatigue fracture process in concrete. However, other
mechanisms of crack arrest, associated with the presence of the aggregate
phase in the matrix, seemed to be quite essential to the fatigue behaviour
of concrete.
41
-10 REFERENCES
1. Körmeling, H.A., Zielinski, A.J., Reinhardt, H.W., "Experiments on concrete under single and repeated uniaxial impact tensile loading", Stevin Report 5-80-3, Delft 1980.
2. Zielinski, A.J., Reinhardt, H.W., Körmeling, H.A., "Experiments on concrete under uniaxial impact tensile loading", Rilem Matériaux et Constructions, No.80, 1981.
3. Zielinski, A.J., Reinhardt, H.W., Körmeling, H.A,, "Experiments on concrete under repeated uniaxial impact tensile loading", Rilem Matériaux et Constructions, No.81, 1981.
4. Komlos, K., "Investigation of rheological properties of concrete in uniaxial tension", Materialprüfung 12 (1970) No. 9, pp. 300-304.
5. Heilmann, H.G., Hilsdorf, H., Finsterwalder, K., "Festigkeit und Ver-formung von Beton unter Zugspannungen", Deutscher Ausschuss für Stahl-beton. Heft 203, Berlin, 1977.
5. Takeda, J., Tachikawa, H., "Deformation and fracture of concrete subjected to dynamic load", Proc. of the International Conference on the "Mechanical behaviour of materials", Kyoto, 1971, Vol. IV.
7. Kvirikadze, O.P., "Determination of the ultimate strength and modulus of deformation of concrete at different rates of loading". Int. Symp. 'testing in situ of concrete structures" Budapest, 1977, pp. 109-117.
8. Birkimer, D.L., Lindemann, R., "Dynamic tensile strength of concrete materials". Journal ACI, January 1971, Title No. 68-8, pp. 47-49.
9. Sneikin, A.E., Nikolaeb, V.L., "On elastic properties of concrete at tension". Magazine "Beton i jelezobeton", No. 9, Moscow 1959.
10. Hatano, T., "Theory of failure of concrete and similar brittle solid on the basis o f strains", Tokyo, Nov. 1967.
Bibliotheek
afd. Civiele Techniek T.H» Stevinweg 1 - Delft
Zech, B., Wittmann, F.H., "Variability and mean value of strength of concrete as function of load". Journal ACI, Sept.-Oct. 1980.
Mihashi, H., Izumi, M., "A stochastic theory for concrete fracture", Cement and Concrete Research, Vol. 7, 1977, pp. 411-422.
Lawn, B.R., Wilshaw, T.R,, "Fracture of brittle solids", Cambridge University Press, 1977,
Griffith, A,A,, "The phenomena of rupture and flow in solids", Philosophical Transactions, Royal Society of London, Series A, Vol, 221, 1921.
Irwin, G.R., "Fracture Dynamics", Fracturing of Metals, American Society of Metals, Cleveland, Ohio, 1948.
Orwan, E., "Fundamentals of brittle behaviour in metals", Symposium on Fatigue and Fracture of Metals, John Wiley & Sons, New York, 1950.
Kalthoff, J.F., Shockey, D.A., "Instability of cracks under impulse loading". Journal of Applied Phisics, Vol. 48, No. 3, 1977,
Glucklich, J., "Fracture of plain concrete". Journal of the Engineering Mechanics Division, December 1963.
Radjy, F., Hansen, T.C., "Fracture of hardened cement paste and con-crete", Cement and Concrete Research, Vol. 3, 1973.
Swamy, R.N., "Fracture mechanics applied to concrete". Development in concrete technology - I, Applied Science Publishers Ltd., London, 1979.
Ziegeldorf, S.,"Fracture mechanics parameters of hardened cement paste, aggregates and interfaces", Institut für Baustofftechnologie, Univer-sitat Karlsruhe, 1980
-
43-APPENDIX I Stress-strain diagrams determined in single uniaxial impact tensile loading tests
.o(N/mm2) .o( N / m m 2
A
/ / / \ Nr : 1 0.1 0.2 0.3 0.^ 05 05 £ ( % o ) / / / / ^ \ ... >^ \ , N j Nr\i
. 2 \ 0.1 0.2 0.3 O.C 05 05 £ (7oo ) .0( N/mm2) .0(N/mm2) / / / / /f\.
\V
V Nr : 3 0.1 0.2 0.3 0.4 05 06 £ ( 7oo ) / / / / \N
\ Nr : L 0.1 0.2 03 0.4 05 06 £ ( % o ) .0(N/mm2) / / / / / \ ^ \ \ Nr 1 : 5 .0(N/mm2) / / / / - ^ \ Nr \ . ; 6 0.1 . 0.2 0.3 0.^ 05 06 0.1 0.2 0.3 0.4 05 06.G(N/nnm2)
A
/A
/ / \S
\ Nr ; 7 .0( N/mm2) 0.1 0.2 0.3 0.4 05 05 £ ( % o ) / / / /A
\ \ , Nr •* : 8 0.1 0.2 0.3 0.4 05 06 .0( N/mm21 .0(N/mm21A
/ ' ^ \ \ Nr :9 0.1 0.2 0.3 0.4 05 06 £ ( % o ) / / / / , ^ / ^ ^*v Nr :10V
0.1 0.2 0.3 04 05 05 . 0 ( N / m m 2 ) . 0 ( N / m m 2A
A
/ / f Z' / — , Nr \ \ \ : 11 \ , \ 0.1 0.2 0.3 0^ 0.5 0.6 £(7ool y / /v
/ / (/""^^ Nr : 12 \ \ 0.1 0.2 0.3 0.^ 0.5 0.6 £(7oo)45 .0( N/mm2) / / / / / f Nr \
N
: 13 \ \ 0.1 0.2 0.3 04 05 06 £ ( %o 1 0(N/mm2)A
/ / /X
/ Nr \k
> 0.1 0.2 0.3 04 05 06 £ ( %o ) , 0 ( N / m m 2 )A
/ / • VN
NrN,
N :15 \ 0.1 0.2 0,3 04 05 06 £ ( 7oo )APPENDIX I I S t r e s s - s t r a i n diagrams determined in repeated u n i a x i a l impact t e n s i l e loading tests .0(N/mm2: .0(N/mm2
y
0/
1 0
1X
2 0. Mr : I F ( ) : number o l o a d i n g X rX-'
3 0 aciure 4 0. f cycles 5 0. 6 / //A
V
(2)y.
Nr : 2F 1 ( ) : number of l o a d i n g cycles » : iracfureVr
£ ( % o ) 0.1 ' 0.2 0.3 04 0.5 0.6 £ ( 7 o o ) . G ( N / m m 2 . 0 ( N / m m 2 //
/ // ^
Nr : 3 F ( ) : number o l o a d i n g X [X'
aciure • f cycles 0.1 0.2 0.3 0.4 0.5 0.5 £ (7oo )y
•^y
7 ^ Nr . i F 1 ) ; number o loading X : r ^ ( 3 , •acture f cycles ">v^r 01 0.2 0.3 04 0.5 0.5 £ (7oo) . 0 ( N / m m 2 ) / / / ' " Nr : 5 F ( 1 : number of l o a d i n g cycles 0.1 0.2 0.3 0.^ 0.5 0.6 £ ( % o ) . G ( N / m m 2 ) Nr : 6 F 1 '. number of loading cycles f fracture 0.1 0.2 0.3 0./. 0.5 0.6 £ ( % o )47 -. 0 ( N / m m 2 ) . 0 ( N / m m 2 ) / ^ ( 1 1 ) ^ f s Nr : 7F 1 ) : number o l o a d i n g X r aciure . ^ 1 ' f cycles 0.1 0.2 0.3 0^ 0.5 0.5 £(7oo)
7
^X
^ ^ mr Nr : 8 F 1 ) : number o loading X : fracture f cycles 0.1 0.2 03 04 0.5 0.5 £ ( 7 o o ) . 0 ( N / m n n 2 . 0 ( N / m m 2 ) 0.1 0.2 0.3 0^ 0.5 0.5 £ ( 7 o o ) ( 1 0 1 / / (50) Nr : lOF ( 1 : number of loading cycles 0.1 0.2 0.3 04 0.5 0.6 £ ( % o ) . G ( N / m m 2 : . 0 ( N / m m 2 ) 150)W/f
// ft l ' >^ 100) ^ - ^ ^ Nr : 11F ( 1 ; number of l o a d i n g cycles \ ( 1 0 5 ) 0.1 0.2 0.3 04 0.5 0.6 E ( 7 O O )' i y /
i/
JOOO) Nr ; 12F ( ) : number of loading cycles 0.1 0.2 0.3 04 0.5 0.5 £ ( 7oo )Stevin-reports published by the division of concrete structures:
SR - 1 Leeuwis, M, "Kruip en krimponderzoek op ongewapend beton, Collectaneum onderzoeken 1958-1970". (2 delen), out of print.
SR - 2 Froon, M. "Hoogwaardig beton" (1972).
SR - 3 Walraven, J.C. "De meewerkende breedte van voorgespannen T-balken" (1973). out of print.
SR - 4 Nelissen, L.J.M. "Het gedrag van ongewapende en gewapende betonblokken onder geconcentreerde belasting" (1973).
SR - 5 Nelissen, L.J.M. "Stress-strain relationship of light weight concrete and some practical consequences" (1973).
SR - 5 Bruggeling, A.S.G. "De constructieve beïnvloeding van de tijdsafhankelijke doorbuiging van betonbalken" (1974).
SR - 7 Stroband, J., Tack, P.J. "Kolomvoetverbinding met geïn-jecteerde stekeinden" (1974).
SR - 8 Christiaanse, A.R., van de Vrande, L.W.J.W., van Rooden, R.J.W.M. "Het gedrag van stalen voetplaatverbindingen (2 delen) (1974).
SR - 9 Uijl, J.A. den, Bednar,J. "Onderzoek naar het verankerings-gedrag van gebundelde staven" (1974).
SR -10 Nelissen, L.J.M. "Twee-assig onderzoek van grindbeton" (1970).
SR -11 Meuzelaar, L.C., Smit, D.R., Brakel, J,, Zwart, J,J. "Ponts a haubans en béton précontraint" (1974).
SR -12 Bruggeling, A.S.G., den Boer, L.J. "Eigenschaften von stahlfaserbewehrtem Kiesbeton" (1974).
SR -13 Boer, L.J. den. "Fibre reinforced concrete" (1973). Conference on properties and applications of fibre rein-forced concrete and other reinrein-forced building materials.
SR -14 Uijl, J.A. den. "Met bamboe gewapend beton onder herhaalde belasting" (1975). out of print.
SR -15 Dijk, H.A. van, L.J.M. Nelissen, van Stekelenburg, P.J.
"Het gedrag van kolom-balkverbindingen in gewapend beton" (1975).
SR -16 Brunekreef, S.H. "Gedeeltelijk voorgespannen beton; Op buiging belast" (1977).
SR -17 Betononderzoek 1971-1975 (met samenvatting in het Engels (1976).
SR -18 Bruggeling, A.S.G. "Time-dependent deflection of partially prestressed concrete beams" (1977).
SR -20 Corrosie van wapening in beton; de kwestie "Monoliet"-(1977).
SR -21 Corrosie van wapening in beton; Proefresultaten (1977). SR -22 Bednar, J., Reinhardt, H.W. "Onderzoek naar de krimp
en kruip van lichtbeton" (1977).
SR -23 Uijl, J.A. den. "Krachtsoverdracht tussen beton en voor-spanstrengen" (1978).
SR -24 Reinhardt, H.W. "Contribution of the fibres to the load bearing capacity of a bar and fibre reinforced concrete beams" (1978).
SR -25 Stekelenburg, P.J. van. Walraven, J . C , Mathews, M.S. "Development of a semicylindrical shaped roof in ferro-cement" (1978).
SR -25 Walraven, J.C. "Mechanisms of shear transfer in cracks in concrete. A survey of literature" (1978).
SR -27 Reinhardt, H.W. "On the heat of hydration of cement" (1979).
SR -28 Pat, M.G.M., Fontijn, H., Reinhardt, H.W., Stroeven, P. "Erosie van beton" (1979).
SR -29 Walraven, J . C , Vos, E., Reinhardt, H.W. "Experiments
on shear transfer in cracks in concrete. Part 1: Description of results" (1979).
SR -30 Walraven, J.C. "Experiments on shear transfer in cracks in concrete. Part 2: Analysis of results" (1979).
SR -31 Gremmen, C. "Beton met grof grind als toeslagmateriaal".
SR -32 Körmeling, H.A., Reinhardt, H.W., Shah, S.P. "Static and dynamic testing of concrete beams reinforced with fibres and continuous bars" (1979).
SR -33 Huyghe, G.F., Walraven, J . C , Stroband, J. "Onderzoek naar voorgespannen kanaal platen" (1980).
SR -34 Körmeling, H.A., Zielinski, A.J., Reinhardt, H.W. "Experiments on concrete under single and repeated uniaxial impact tensile loading" (1980).
SR -35 Vos, E., Reinhardt, H.W. "Bond resistance of deformed bars, plain bars and strands under impact loading" (1980).
SR -36 Betononderzoek 1976-1980 (1980).
SR -37 Reinhardt, H.W. "Schaalwetten b i j proeven met beton-c o n s t r u beton-c t i e s " (1980).
SR -38 Walraven, J.C. "Aggregate i n t e r l o c k : a t h e o r e t i c a l and experimental a n a l y s i s " ( d i s s e r t a t i e ) (1980). SR -39 Walraven, J.C. "The influence o f depth on the shear
strength of l i g h t w e i g h t s t r u c t u r a l members without shear reinforcement" (1980).
SR -40 Bruggeling, A.S.G., Oostlander, L . J . "Concentrated load on a t h i c k - w a l l e d c y l i n d e r " (1980).
SR -41 Pat, M.G.M. " K r u i p s p r e i d i n g . Deel 1 : P r o e f r e s u l t a t e n " (1980) SR -42 Pat, M.G.M.,Reinhardt, H.H. " V a r i a b i l i t y of creep of
li'i c o n c r e t e - a n a l y s i s o f t h e r e s u l t s " ( 1 9 8 0 )
SR -43 Z i e l i n s k i , A . J . "Experiments on m o r t a r under s i n g l e and r e p e a t e d u n i a x i a l impact t e n s i l e l o a d i n g " (1981)
