Investigating high strain rate effect on FRHSC of Steel and Polyethelene

7/30/2019 Investigating high strain rate effect on FRHSC of Steel and Polyethelene

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Department of Civil and Environmental Engineering

Investigating the high strain rate effect on high strength concrete

reinforced with Steel and Polyethylene fibers

InterimReportVanceKang

U094742A


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Table of Contents

TABLE OF CONTENTS................................................................................................................2

1. INTRODUCTION: ...................................................................................................................3

1.1. OBJECTIVES AND SCOPE........................................................................................................3

1.2. BACKGROUND..........................................................................................................................4

1.2.1. FIBRE REINFORCED CONCRETE (FRC)...........................................................................................4

1.2.2. SPLIT HOPKINSON PRESSURE BAR(SHPB).................................................................................4

2. PRELIMINARY EXPERIMENTAL STUDY....................................................................5

2.1. MIX DESIGN..............................................................................................................................5

2.2. RESULTS....................................................................................................................................6

2.2.1.STATIC TEST RESULTS.........................................................................................................................6

2.2.2 DYNAMIC TEST RESULTS......................................................................................................7

3. COURSE FOR FUTURE:....................................................................................................13

APPENDIX.................... .................. .................. ................. .................. .................. .................. ........14

A1 FIBRE-REINFORCED CONCRETE.........................................................................................14

A2 STEEL AND POLYPROENLENE FIBERS...............................................................................14

A3 ASSUMPTIONS WITH SHPB.................................................................................................16

4. BIBLIOGRAPHY..................................................................................................................23


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1.Introduction:

1.1.Objectives and scope

The objective of this experiment is to investigate the properties of a fibre reinforced

high strength concrete (FRHSC) at varying high strain rates that are between

80-300s-1. The FRHSC is of strength 80-90MPa. The fibres used are a combination of

Steel and Polyethylene of which ratio of its volume to concrete is 0.375% and 0.125%

respectively. A Split Hopkinson Pressure bar (SHPB) is used to deliver the high strain

rate to the material. Failure patterns of the samples as well as the compressive

strength!, critical strain

!and Youngs modulus from SHPB tests will be

investigated and discussed. The later three properties will be used hopefully as a

means to acquire a Dynamic increase factor (DIF) relationship. DIF is a factor used to

express the increase in the physical property of the concrete when subjected to high

strain rate with respect to quasi-static loading.

The SHPB test however has limitations that need to be acknowledged. Firstly, for a

consistent and apt material characterization, it is desired to achieve constant strain rate

and dynamic stress equilibrium within the specimen)(Chen & Song, 2011). These

properties are not easily achieved. Other problems include the fact that the Hopkinson

bar is assumed to be 1-dimensional when in reality is not which results in dispersion.

Experimental errors such as having gaps between the specimen and the SHPB bar that

are hard to eliminate are also causes for concern. As shown briefly, there are


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complexities involved in SHPB test and therefore deduction of results obtained from

experiment has to be analysed with these factors in mind. Therefore in this

dissertation, the different methods proposed by various academicians will be also

explored and reviewed.

1.2. Background

1.2.1. Fibre reinforced concrete (FRC)

More information about the FRC is in the appendix section

1.2.2. Split Hopkinson Pressure Bar (SHPB)

The SHPB set up is as shown. A gas tank on the right fires a projectile 0.5m long that

impacts the input bar producing a strain wave. The strain wave is then measured by

the strain gauges positioned in the middle of the input and output bar that are both 5m

long. The wave initiated at the input bar is called the incident wave !() and the

wave that is transmitted through the specimen and into the output bar is called the

transmitted wave!(). The wave that is reflected at the input bar and specimeninterface is called the reflected wave!(). These 3 time-dependent waves are used tocalculate the strain rate and stress experienced by the specimen.

The 2 approaches used to calculate them using this theory are the 1-wave and 3-wave

equations. They will not be covered in depth in this report but in short 1-wave

equation uses !() and !() to calculate strain rate and stress respectively while the

Figure2SplitHopkinsonPressurebarequipmenttakenfromSHPBusermanual0501


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3-wave equation uses all 3 types of strains to calculate stress and strain

rate! , !() and !().

There are a number of assumptions taken when using the SHPB but due to the

limitation in length of report, it is placed in the appendix section.

2.Preliminary Experimental study

2.1.Mix design

Table 1 Concrete Mix

Mix proportion (kg/m3)

Cement Water C.A. Sand Fiber SP

500 175 900 71729.25

101.21

Table 2 Fiber Properties

% by

VolumeType

Length

(mm)

Diameter

(m)

Aspect ratio

(length/diameter)

Young's

modulus

(GPa)

Tensile

strength

(MPa)0.375 Steel (SF) 13 160 81 200 2500

0.125 Polyethylene (PE) 12 39 308 66 2610

The mix design is as shown in the tables above. The water to cement (w/c) ratio is

0.35 and the fiber content is 0.5% by volume of which 0.375% is SF and 0.125% is

PE. Superplasticizer is added to improve the workability of the mix. The Vebe time is

7 seconds for this mix.

The fibers used are steel and polyethylene both of which are approximately the same

length however the aspect ratio of PE is much higher than that of SF. The tensile

strength of PE is approximately the same as SF but the modulus of SF is almost 4

times as high as that of PE.


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2.2. Results

2.2.1. Static test results

Cylinders of length to diameter ratio of 2 and of diameter 100mm were used to

determine Poisson ratiowhile compressive strengthfyand Youngs modulusE

were determined from the SHPB specimens with length 38mm and diameter 75mm.

Linear variable differential transformer (LVDT) is used to measure bulk deformation,

which is then used to determine the shape of the curve after failure of specimen while

strain gauge used measures value local deformation in the middle of specimen pre-

failure shape of curve andE.

Table 3 Static test results

Ultimate strengthfy (MPa) E(GPa) Poisson ratio

98.8 39.2 0.188

Figure 3 Static Stress vs. Strain curves

0

20

40

60

80

100

120

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Str

ess(MPa)

Strain

LVDT

StrainGauge


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2.2.2.DynamicTestresults

Figure4Incidentstrainpulsegeneratedby0.5mstriker

These3pulseshereshowthedifferenceinmagnitudeofstrainpulseinthe

incidentbardifferentamountofpressureisdelivered.Theperiodofpulsewhich

isdependentuponthestrikerlengthapproximatelythesameasexpectedand

thevelocityoftheprojectileisapproximatelyproportionatethemagnitudeof

stresspulsewhichisgenerated.

Pressure(Bar)Velocityof0.5m

Projectile(ms-1)

(MPa)

14 7.2 851 173

20 10.6 1111 226

26 12.5 1360 276

-1,600

-1,400

-1,200

-1,000

-800

-600

-400

-200

0

200

400

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04

Strain()

Time(s)

14Bar

16Bar14Bar

26Bar

20Bar


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Figure 5 Strain measured with time as measured at the middle of the input and out put bar after impact

This is a time dependent strain gauge response for a specimen subjected to a 31 bars

of pressure, which corresponds to approximately 13.5ms-1 striker speed("NUS RD-

SHPB 0501 user manual," 2006). Only the first 3 waves of are used.

Figure 6 Strain waves after shifting

The strain waves at the specimen bar-interface (which is used to input into the

equations) are assumed to be the same after propagation to the centre of the input and

output bar where the strain gauges are. Therefore the waves are shifted using the

-1,800

-1,300

-800

-300

200

700

1,200

0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 6.00E-03

Strain()

Time(s)

Inputbar

output bar

-2,000

-1,500

-1,000

-500

0

500

1,000

1,500

2,000

1.00E-04 1.50E-04 2.00E-04 2.50E-04 3.00E-04 3.50E-04 4.00E-04 4.50E-04

Strain()

Time(s)

Incident

Reflected

Transmitted


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speed of the wave and the length travelled by the wave to find the strains experienced

by the specimen. Theoretically speaking the period of the incident, reflected and

transmitted wave ought to be the same but it can be hypothesized due to energy loss

in cracking up, wave reverberations in specimen, imperfect contact surface between

the bar and specimen as well as other factors that it has resulted in shorter period in

the transmitted wave.

The stress strain curve has many oscillations instead of a smooth curve due to reason as

discussed earlier. The 3-wave theory shows a more erroneous result as can be seen that

the stress pulse, which is supposed to be compressive, peaks with a tensile stress of

almost 60MPa. This cannot be right, as the strain incident pulse is negative and therefore

cannot possibly generate a tensile pulse. The reason for this is will be elaborated bellow.

-80

-60

-40

-20

0

20

40

60

80

100

120140

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000

Stress(MPa)

Strain()

1 wave

3 wave

Figure7DynamicStressvsStrainwithapplicationof1-Dwaveequations


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The dynamic strength is taken from the peak of the curve.

Figure8Stress/ Strain rate vs Time curves applying 1-wave equation

The strain rate against time experienced by the specimen is shown to be constantly

changing and since there is a need to specify a strain rate for each test, a general guide

is employed by Wang to use the average value of strain rate experienced by the

specimen in the time between the 80% values of the stress of the specimen (as shown

above)(Wang, 2011). This portion of the strain rate curve comes after the highest

peak of strain rate during which the stress has yet to rise and is more consistent. This

high peak is unreliable due to experimental limitations as mentioned before and hence

should not be considered.

Both 1-wave and 3-wave theory shows a delay in rise time of the stress wave as

compared to the strain rate (the 3-wave theory differs only by going negative before

rising). This is due to the delay in transmitted strain !() as observed in the Strain vs.

Time curve as both methods use !() to calculate stress. Therefore the initial portion

of the curve should not be considered for both methods. More experiments have to be

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04 6.E-04 7.E-04

Stress(MPa)/Strainrate(

s-1)

Time(s)

stress

strainrate

80%stressvalue


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conducted to evaluate further the reason for this significant delay but for now it is

hypothesized that it is an experimental error mainly due to the specimen-bar interface.

The data collected for this specimen is summarized below.

Table 4 Dynamic test results

ID Bar Strength( MPa) DIF Strain rate (s-

)

1 wave 3 wave 1 wave 3 wave 1 wave 3 wave

8A-1-1 30.5 125 123 1.27 1.25 264 272

Figure9Typicalfailurepatternforspecimen

Figure9Strainvs.Time(withD30x1mmpulseshaper)aftershifting .


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The pulses observed for a setup using pulse shaper is seen to comparatively much

lesser oscillations (noise) as compared to Figure 6. This is due to absorption of high

frequency components of the wave. The rise up time of the incident pulse is also

delayed which helps the specimen to achieve stress equilibrium before failure as well

as reduce inertia effects(Parry, Walker, & Dixon, 1995).

Figure10StressvsStrain-ratecurveusing1-waveequation

Figure11StressvsStrain-ratecurveusing3-waveequation

Thedatapointsobtainedfromexperimentaltestsasofpresentdoesnot

establishaclearDIFrelationshipbetweenstressandstrain-rate.Thiscouldbe

duetothelackofdatapointsandthepresenceofanomalousdatapoints.

0

20

40

60

80100

120

140

160

180

0 50 100 150 200 250 300

UltStress(MPa)

StrainRate(s-1)

1wave

020

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300

UltStress(MPa)

StrainRate(s-1)

3wave


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Courseforfuture:

2.3.Investigation in the limitation of SHPB

With the limitations of SHPB in mind, more effort will be put into evaluating which

portion of the stress-strain curve is useful, how to evaluate the strain-rate of the

material (which is not universally established) and also if the Youngs Ecan actually

be used from dynamic tests (debatable in literature if it is of any use (Gama,

Lopatnikov, & Gillespie, 2004)).

The transmitted wave as shown is a cause of problem in determining the strain-rate as

well as the stress versus strain curve. As of now, the deviance in results obtained is

predicted to be due to the experimental error but more investigation has to be done in

that respect. If experimental error cannot be eliminated time shifting may not be the

best approach in getting start of pulse and other methods should be employed such as

the high accuracy forward finite-divided difference formula (discussed in the

appendix)

2.4.Investigation of the failure mode of the specimen.

Failure mode of the concrete matrix has not been discussed much in the report but it

can be of useful information. It can tell at high strain rate if the matrix fails due to

fiber pull out or fracture which will better inform the user on the geometrical

properties to consider for future mixes. Therefore surface of the specimen will be

looked at and investigated further


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Appendix

A1 Fibre-reinforced concrete

Concrete is a brittle material with very little ductility and toughness. That is to say

that ordinary concrete cannot take much stress after the maximum is reached. With

fibres in the concrete matrix, the concrete is able to achieve much higher post

cracking ductility and toughness. One must note that the main purpose of fibres is not

to increase ultimate strength of the concrete (which will be more economically done

by adjusting w/c ratio and adding admixtures such as silica fume) (Papworth, 1997).

The main role of the fibres is controlling cracking of concrete matrix allowing the

concrete mass to be able to withstand significant stresses over relatively large strain

capacity in the strain-softening stage (Mindess, 2003). Another important fact to note

is that concrete is a strain-rate dependent material(Soroushian & Obaseki, 1986).

Studies have shown that concrete subjected to higher strain rates tend to have higher

strength and Youngs modulus(Wang, Zhang, & Quek, 2012).

A2 Steel and Polyethylene fibers

There are different kinds of fibres that can be used. The most common of which is

steel fibers (SF) which has been used for many years of which its known advantages

are high modulus of elasticityE, high strengthfy , relatively higher bonding with the

matrix than other fibers resulting in increase in post cracking strength and therefore

toughness to the matrix. All these help to minimise cracking due to changes in

temperature and relative humidity and also increase its resistance against dynamic

loading (A. Benturt & Mindess, 2007). The disadvantage of SF is that they have the

common problem of balling which would reduce the workability of the fresh concrete

and uniformity in distribution of the fiber. This is further aggravated when higher

bond is desired (for smooth steel fiber) and so higher aspect ratio of the fiber is


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employed to increase the surface area in contact. However higher aspect ratio and

higher ratio in volume of fiber promote the occurrence of balling(A. Benturt &

Mindess, 2007).

Polymeric fibres have also become more and more common with different kinds

being designed to serve different purposes. Polyethylene (PE), a polymer fiber is

known to be able to control plastic shrinkage cracking well. Other notable advantages

of it include their alkali resistance and low price(A. Benturt & Mindess, 2007). In

addition, supplementing of PE as proven by Benturt (et. al ?) that while it only had a

small effect on the toughness in static loading, it had a much bigger influence on the

ductility in impact. Also, the addition of these fibers to (A. Benturt, Banthia, &

Mindess, 1986) high strength concrete(HSC) yielded much better results in terms of

toughness during impact testing as compared to normal strength concrete and

therefore would be more efficient when applied to HSC.

Having a hybrid in the mix is also an option. If employed effectively, it aims to utilize

the advantageous properties of both fibers as well as to make the concrete mix more

economical and thereby attaining synergy. Synergy is the term used to describe

fibers that work together in a combination to provide performance exceeding that of

individual fibers(Al Hazmi, Al Hazmi, Shubaili, & Sallam, 2012).

As concluded by Hazmi through testing, high strength concrete with the hybrid of SF

and polypropylene (PP) showed the superior compressive strength, tensile strength

and flexural toughness over SF and PP acting alone. The reason could be that during

hardened stage, SF being stiffer provides first crack strength, while PP having lower E


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provides the improved toughness and strain capacity in the post crack zone(Al Hazmi

et al., 2012).

A3 Assumptions with SHPB

The SHPB is used to deliver high strain rate to specimens in the order of 50s -1 to 104s-

1(Gama et al., 2004). The fundamental assumptions when using 1 dimensional wave

theory to calculate stress and strain of specimen are as follows:

i. Material of bar remains linear elastic when loaded with stress pulsesii. Neutral axis is straight

iii. Axial stress distribution is uniform across the cross sectioniv. System of bars are linear and dispersion freev. Stress equilibrium of specimen assumed and inertia effects ignored

vi.

Bar-specimen interface imperfection ignored

i. Material of bar remains linear elastic

This condition is satisfied as the stress pulse required for the experiment is much less

than the elastic limit of the bar.

ii. Neutral axis is straight

The bars are as straight as it can possibly be made and error with respect to that is

insignificant. However the specimen in contact with the bar may not be perfectly flat

against the bar and is a cause for concern as will be touched on in point 4.

iii. Axial stress distribution is uniform across the cross section

This assumption is important as strain gauges that measure the strains are placed at

the surface of the bars and if the axial stress distribution is not uniform across the


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cross-section then the result obtained is greatly flawed. For strains recorded in the

middle of the bar, this assumption is valid. However this assumption is not so valid at

the bar ends as shown by Wang (2007). The figure shows near the bar end, the stress

in the middle is higher by about 15% than the stress on the surface. This indicates that

the stress experienced by the specimen at the bar end is not completely uniform.

Figure 13 Axial stress distribution over the cross section 0.5D frombar end (Reproduced from Wang (2007))

iv. System of bars are linear and dispersion freeWhen the striker hits the input bar, stress pulses of varying frequencies are generated

due to the two dimensional nature of wave propagation; contrary to the assumption of

1D wave propagation (waves travel at a constant speed c = E/. Pulses of higher

frequencies travel slower than those of lower frequencies that results in the

undesirable phenomena known as wave dispersion. Wave dispersion is reflected in

the noise (oscillation of the wave) observed in the data.


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Figure 14 Wave dispersion (reference?)

This graph shows the incident and reflected pulse after the pulse wave generated by

the striker propagates from the strain gauge to the free end of the incident bar and

back. Since the same strain gauge is used to measure the pulses, any difference in

shape of pulse is not caused by the fault of the recording system. From the

comparison of both pulses it is can be concluded that due to the difference in speed of

waves, the reflected wave gets more distorted with distance travelled and hence the

difference in shape from the incident pulse.

This can be corrected using Fourier Transform(Follansbee & Frantz, 1983) or by

using a softer object placed between the input bar and the striker which acts as a pulse

shaper. The pulse shaper helps to absorb high frequency components of the wave

resulting in a pulse with lesser noise (can be seen in the Results section where a

smoother curve is obtained).

v. Stress equilibrium of specimen assumed and inertia effect ignoredStress equilibrium is achieved not instantaneously but after a certain number of

reverberations within the specimen. It is proposed by Davies that the number is


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-times(Gama et al., 2004). It is important that the specimen be able to reach stress

uniformity before failure in order to obtain useful data.

Inertia effect gets more pronounced when the specimen size gets longer in length in

the axial direction. A thinner specimen will also allow for a shorter time for specimen

to reach equilibrium (due to the shorter distance travelled by wave). It is

recommended by Davies and Hunter that the optimum Length/ Diameter ratio is

approximately 0.43 and since specimen used in this experiment has a ratio of 0.5,

inertia effect can be an issue. The specimen length cannot be reduced too much due to

requirements by the code to meet the minimum dimensions that is affected by the

maximum aggregate size. Reducing the specimen length too much will result in

failure to record the bulk property of the concrete matrix.

vi. Bar-specimen interface imperfection ignoredThere is an uncertainty as the stress wave propagates from the incident bar to the

specimen and then towards the transmission bar. The impedanceIin 1-D stress wave

theory is defined as the ratio of the force applied to the point mass to the velocity of

the point mass and theoretically it is purely influenced by density , areaA and wave

velocity c.

=cA

1-D theory goes on to show that when there is an impedance mismatch, part of the

stress wave will not be transmitted but be reflected. M. A. Kaiser proposed a

coefficient to represent this ratio introducing as the transmission coefficient,

=!

!


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Based on energy conservation, wave that is not transmitted is reflected at any given

boundary. Based on the specimen and bar properties our transmission coefficient is

as such (subscripts 12 and 23 represent incident bar-specimen interface and specimen-

output bar interface):

This show that only 20% of the incident wave that reaches the specimen would be

transmitted and 75% of that transmitted wave will be transmitted to the output bar.

This means that the remaining 25% of the wave within the specimen is reflected back

into the specimen. Part of this portion of the wave is trapped within the specimen

and will eventually die off after a period known as the stress bleed-off period. The

phenomenon of bleed-off contributes to the noise of the strain recorded.

In determining the start of the dynamic stress-strain curve, the start of the pulse

should be identified properly. Currently the method employed is time-based meaning

the start of the strain pulse is based on the shifting of the reflected and the transmitted

pulse using the velocity of the wave though the bar and then through the specimen.

There are 2 problems with this approach. Firstly the velocity of the wave through

specimen is very rough estimate due to its high anisotropic nature and secondly there

is a high degree of uncertainty of the time for wave propagation at the specimen-bar

interface known as the transit time (which is completely ignored in our 1-D wave

theory). This uncertainty is due to the gap between specimen and the bar due to the

finishing of the specimen not being completely smooth and also the concrete

specimen having small holes that if not filled with grease is filled with air. Both air

12 0.20

23 0.75


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and grease introduces uncertainties to the experiment and negatively affect the strain

pulse recorded when using time to determine the start of pulse.

Kaiser proposes a mathematical solution as an alternative to the identification of the

start of the pulse, which is not dependent on time. For a perfect strain history, the

strain rate leading up to the pulse edge should be zero. Since the measured strain,

though close to zero is never zero due to noise, this algorithm searches for a number

of consecutive derivatives of the same sign and there is not change then the start of

the pulse is determined. This numerical derivative algorithm is as follows

! ! = !!! + 4 !!! 3 !

2

Where i is the index referring to the data point and h is the sample rate of the signal.

This method though currently not employed here can be considered to deal with

uncertainty for the initial portion of the strains recorded in this experiment(Kaiser,

Wilson, Wicks, & Swantek, 2000) .


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# 20#

Wave$equations:$#

#

1-wave equation:! ! =

!

!!

!!! !

! ! =

2!!

!!

!!

!

! ! = ! !

!

!

!"

2-wave equation:

! ! =

!! !!

!!

=

!!

!!

[!! ! !! ! !! !

! ! = ! !

!

!

!"

! ! =

!!

2!![!! ! + !! ! + !! ! ]

! ! : Time-dependent stress

! ! : Time-dependent strain rate

! ! :!Time-dependent strain!! ! :!Time-dependent incident strain!!

! :!Time-dependent reflected strain!!(!): Time-dependent transmitted strain

!!: Wave speed in bar (!! =E/= 5090ms-1)

!!: Length of specimen

!!: Area of specimen

!: Area of bar

E: Youngs modulus of bar


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3.Bibliography

Al Hazmi, H. S. J., Al Hazmi, W. H., Shubaili, M. A., & Sallam, H. E. M. (2012).

Fracture energy of hybrid polypropylene-steel fiber high strength concrete.Paper presented at the 6th International Conference on High Performance

Structures and Materials, HPSM 2012, June 19, 2012 - June 21, 2012, New

Forest, United kingdom.Benturt, A., Banthia, N., & Mindess, S. (1986). The response of reinforced concrete

beams with a fibre concrete matrix to impact loading. The International

Journal of Cement Composites and Lightweight Concrete, 8(3), 6.

Benturt, A., & Mindess, S. (2007).Fibre Reinforced Cementitious Composites (2nd

ed.). USA & Canada: Taylor & Francis.

Chen, W. W., & Song, B. (2011). Testing Conditions in Kolsky Bar Experiments. 37-

75. doi: 10.1007/978-1-4419-7982-7_2Follansbee, P. S., & Frantz, C. (1983). Wave propagation in the split Hopkinson

pressure bar. Transactions of the ASME. Journal of Engineering Materials

and Technology, 105(1), 61-66.Gama, B. A., Lopatnikov, S. L., & Gillespie, J. W. (2004). Hopkinson bar

experimental technique: A critical review.Applied Mechanics Reviews, 57(4),

223. doi: 10.1115/1.1704626

Kaiser, M. A., Wilson, L. T., Wicks, A. L., & Swantek, S. D. (2000). Experimental

techniques for the Hopkinson bar.AIP Conference Proceedings, 505(1), 1103-

1108.

Mindess, S. (2003). Concrete (2nd ed.).

. NUS RD-SHPB 0501 user manual. (2006) (pp. 38): Robust Dynamics Pte Ltd.Papworth, F. (1997). Use of steel fibres in concrete. (Presented at The Concrete

Institute of Australia, NSW Branch, 1997).Parry, D. J., Walker, A. G., & Dixon, P. R. (1995). Hopkinson bar pulse smoothing.

Measurement Science & Technology, 6(5), 443-446. doi: 10.1088/0957-

0233/6/5/001

Soroushian, P., & Obaseki, K. (1986). STRAIN RATE-DEPENDENT

INTERACTION DIAGRAMS FOR REINFORCED CONCRETE

SECTIONS.Journal of the American Concrete Institute, 83(1), 108-116.

Wang, S. (2011) BEHAVIOR OF PLAIN AND FIBER-REINFORCED HIGH-

STRENGTH CONCRETE SUBJECTED TO HIGH STRAIN RATE

LOADINGS. (pp. 150). Singapore.Wang, S., Zhang, M.-H., & Quek, S. T. (2012). Mechanical behavior of fiber-

reinforced high-strength concrete subjected to high strain-rate compressive

loading. Construction and Building Materials, 31, 1-11. doi:

10.1016/j.conbuildmat.2011.12.083

Documents

Investigating high strain rate effect on FRHSC of Steel and Polyethelene