Strain Energy Frame Impact Machine (SEFIM)

Strain Energy Frame Impact Machine (SEFIM)

Tuan Kiet Tran , Dong JooKimJournal of Advanced Concrete Technology, volume ( ), pp.10 2012 126-136

Effects of Strain Rate on Tensile Behavior of Reactive Powder ConcreteKazunori Fujikake, Takanori Senga Nobuhito Ueda, , Tomonori OhnoJournal of Advanced Concrete Technology, volume ( ), pp.4 2006 79-84

Behaviour of strain-hardening cement-based composites under high strain ratesViktor Mechtcherine , Fla´vio de Andrade Silva Marko Butler, , Deju Zhu, Barzin Mobasher, Shang-Lin Gao,

Journal of Advanced Concrete Technology, volume ( ), pp.9 2011 51-62

Study on Impact Response of Reactive Powder Concrete Beam and Its Analytical ModelKazunori Fujikake, TakanoriSenga Nobuhito Ueda, , Tomonori OhnoJournal of Advanced Concrete Technology, volume ( ), pp.4 2006 99-108

Edith Mänder

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Journal of Advanced Concrete Technology Vol. 10, 126-136, March 2012 / Copyright © 2012 Japan Concrete Institute 126

Scientific paper

Strain Energy Frame Impact Machine (SEFIM) Tuan Kiet Tran1 and Dong Joo Kim2

Received 24 October 2011, accepted 11 March 2012 doi:10.3151/jact.10.126

Abstract This paper proposes an innovative strain energy frame impact machine (SEFIM) designed to explore direct tensile be-havior of high performance fiber reinforced cementitious composites (HPFRCC) at high strain rates. The proposed sys-tem utilizes an energy frame to store a large amount of elastic strain energy as well as to suddenly generate high rate tensile impact pulse. The prototype of SEFIM demonstrated that the proposed energy frame could store enough elastic strain energy to fail a large-sized tensile specimen at high strain rates in direct tension. The tensile stress versus strain curve of HPFRCC under high rate impact was obtained by using the prototype with the aid of a high speed camera sys-tem and dynamic strain gauges attached on the surfaces of the transmitter bar.

1. Introduction

There is a strong demand to protect the civil and mili-tary infrastructure from catastrophic attacks from ter-rorists as seen in terror attacks across globe in the recent decade. To minimize damage and prevent the collapse of buildings as well as infrastructure from those man-made disasters, it is highly necessary to enhance the resistance of structures at high strain rates such as im-pact and blast loads. High performance fiber reinforced cementitious composite (HPFRCC) is highly expected to be a promising material for the increased resistance of civil and military infrastructure under seismic, impact and blast loads based on the strain hardening behavior and higher energy absorption capacity (Kim et al. 2009). However, it is questioned whether the strain hardening behavior of HPFRCC is valid at high strain rates. Thus, the behavior of HPFRCC at high strain rates should be clearly verified to apply HPFRCC for the safety of in-frastructure under such extreme loads.

Although much research has been performed to in-vestigate the strain rate effects on the behavior of fiber reinforced cementitious composites, to the best knowl-edge of authors, there are only a few references avail-able for the tensile behavior of HPFRCC at higher strain rates, especially using high strength deformed steel fi-bers. Most of them focused on the behavior of engi-neered cement composites (ECC), one type of HPFRCC, using polymeric fibers. Yang and Li (2005) performed uniaxial tensile tests under various strain rates between 10-5 and 10-1 s-1 using a hydraulic testing machine. Douglas and Billington (2005) also examined the strain rate effects on the behavior of ECC for its seismic ap-plications. They reported that the tensile strength of

ECC was noticeably enhanced as the strain rate in-creased until seismic strain rate while the ductility de-creased. Recently, Metchtcherine et al. (2011) reported the tensile behavior of strain hardening cement based composites (SHCC) subjected to low and high strain rates by using a high-rate MTS testing machine. Until the strain rate reached 10-2 s-1 the tensile strength of SHCC was enhanced while the strain capacity was re-duced as the strain rate increased. However, the SHCC produced enhancements in both tensile strength and strain capacity at high strain rates between 10 s-1 and 50 s-1. Maalej et al. (2005) found different rate sensitivity in a hybrid type of ECC blending 1.5 % polyethylene fiber and 0.5 % steel fibers by volume: the tensile strength was clearly enhanced as the strain rate in-creased while the tensile strain capacity in their tests was insensitive to strain rates. The effect of strain rate on the flexural behavior of ultra high performance fiber reinforced concrete (UHPFRC) was also investigated by Bindiganavile et al. (2002) using a drop weight impact testing method and by Parant et al. (2007) using a block-bar device.

There is, however, no standard test method yet in the investigation of the material behavior at high strain rates, even though John Hopkinson firstly performed the well-known drop-weight tensile test in 1872 (J. Hopkinson 1901). Current high rate test systems can be categorized into four systems according to the way of generating impact pulse: 1) systems based on potential energy (PE), where a large mass swings or falls to strike a specimen at low speed, only generate moderate strain rates between 100 s-1 and 101 s-1 (Bischoff and Perry 1995) because they generally require a significant amount of vertical clearance; 2) systems based on ki-netic energy (KE), where a small mass is propelled at high speed to impact specimen by a gas gun, can gener-ate very high strain rates, e.g. 104 s-1 as reported in Grote et al. (2001); 3) systems that utilized hydraulic machine (HM), a well-designed test machine, generate quite low strain rates, only on the order of 10-1 to 100 s-1;

1Ph.D. candidate, Department of Civil and Environ-mental Engineering, SeJong University, Seoul, Korea. 2Assistant Professor, Department of Civil and Environ-mental Engineering, SeJong University, Seoul, Korea. E-mail: [email protected]

T. K. Tran and D. J. Kim / Journal of Advanced Concrete Technology Vol. 10, 126-136, 2012 127

and, 4) systems based on stress wave propagation (SWP), in which a stress wave is propagated through a long bar to impact upon a specimen, can generate high strain rates in the range 102 to 104 s-1 (Chen and Song 2011).

The Strain Energy Impact Test System (SEITS), which bridges the SWP and KE categories, was recently developed by Kim et al. (2011) as shown in Fig. 1. In SEITS, the internal elastic strain energy accumulated in an energy bar is suddenly released right after the break-ing of coupler to generate a controlled high rate impact pulse as illustrated in Fig. 2. Compared to current im-pact test systems, SEITS is much smaller and more cost effective. SEITS also has the ability to test large-sized specimens which is critical especially for composite materials such as concrete or fiber-reinforced cement composites. And, it can generate a broad range of strain rates by adjusting the amount of strain energy accumu-lated.

It is also very important in studying the behavior of materials at high strain rates that two dynamic effects

including the inertial effect and the pure rate sensitivity of materials should be distinguished. However, both effects can be imposed interdependently and make the problem much more complicated (Wang 2007). Thus, in estimating the pure material response under high strain rates, those two effects should be carefully treated.

In the original SEITS, two tensile specimens are in-stalled vertically as shown in Fig. 1. Thus, the two ef-fects would be more interdependent and severe due to the gravity effect. Moreover, the original SEITS has difficulty installing and performing impact test under a symmetrical load without load eccentricity since the two specimens cannot have an identical material property.

The aim of this research is to develop an innovative test machine that can investigate the direct tensile be-havior of HPFRCC at high strain rates by resolving the aforementioned problems. The first objective is to de-velop a new impact machine that is available for high rate tensile testing of a large-sized HPFRCC specimen with no load eccentricity. And, the second objective is to propose a reliable method of measurement to estimate the pure material response at high strain rates. The first objective is summarized here as reported by Tran and Kim (2011), and the second objective is studied in fur-ther detail in this research.

2. Development of load frame

The HPFRCC specimen should satisfy the size require-ment affected by constituents including fiber and ag-gregate to provide representative response of HPFRCC. However, a large-sized specimen of HPFRCC can in-fluence the measured dynamic material properties par-ticularly in a vertically installed set-up (original SEITS).

These two conflicting requirements impelled the au-thors to develop a horizontal load frame that can convert the compressive stress wave in the energy bar to the tensile stress wave in the specimen without load eccen-tricity and the gravity effect, as illustrated in Fig. 3. The use of a load frame in a horizontal manner brings ad-vantages over the original SEITS: 1) a load frame can produce a high rate tensile stress wave in the specimen without load eccentricity by converting the compressive stress wave in the energy bar; 2) the size of specimen at high strain rates is as same as the specimen investigated in static tests; and, 3) the boundary condition at high strain rates is also as same as in static tests.

In the set-up with the load frame, one end of the specimen is connected to the load frame with a hinged grip system; and, the other end is connected to a fixed support with another hinged grip system as shown in Fig. 3. Both the hinged grip systems and load frame then were placed on a rigid steel plate with rollers to allow free movement. The whole system is then placed on strong floor with a firm anchorage. Once a high rate stress wave is generated in the energy bar at the moment of coupler failure, the high rate stress wave is trans-ferred to the load frame from the energy bar. Then, the

Fig. 1 Prototype of original SEITS (Kim et al. 2011).

At start

Apply force to stretch system and store elastic strain energy

Specially designed coupler suddenly fractures or releases

Pulse travels towards specimen and crushes it

(a)

(b)

(c)

(d)

Pull bar Energy barCoupler

Specimen

Fig. 2 Schematic showing operation of original SEITS (Kim et al. 2011).


load frame converts the compressive stress wave in the energy bar to the tensile stress wave in the specimen.

2.1 Modeling The validity of the proposed system was examined us-ing a numerical tool prior to building a prototype. Nu-merical simulations have been carried out using a com-mercial code LS-DYNA (Hallquist 2009). The numeri-cal analysis has been performed for the two following reasons: 1) to examine whether the load frame is able to deliver a high rate tensile stress wave to the specimen, and 2) to investigate the way of measuring the pure ma-terial response. Eight node solid elements are used in modeling the whole system and specimen, and interpen-etration between parts in the system is prevented by using the contact features in LS-DYNA. Stretching the system is simulated by applying displacement control at the end of the pull bar. A friction coefficient μ = 0.5 is assigned between the specimen and the pins as well as between the pins and grips for keeping both ends of specimen during test.

ASTM A29 Grade C1045 steel is used for an energy bar, a coupler, load cells, grips and load frame. The properties of materials employed in the simulation are provided in Table 1. The time step in the simulation is automatically determined in the commercial code LS-DYNA to ensure stability of the dynamic simulations and is less than 0.0001 second. Figure 3 shows the de-tailed model used in the numerical analysis.

In the simulation, the material properties of the HPFRCC specimen are referenced from Kim et al. (2011). The tensile stress – strain curve is provided in Fig. 4. In the material model used for the specimen in the simulation, the strain rate sensitivity was not con-

sidered in order to explore how to obtain pure material behavior at high strain rates.

2.2 Discussion of simulation results When the coupler fractures, the elastic strain energy stored in the energy bar is suddenly released at the end of the energy bar. A high rate stress wave is created and propagated to the opposite end of the energy bar as shown in Fig. 5a. Then, the stress wave is transferred to the load frame as shown in Fig. 5b. The stress wave then transfers from load frame to the specimen and makes the tensile specimen fail as illustrated in Fig. 5c. This result proves that the proposed load frame is able to convert the compressive stress wave to a tensile stress wave at high strain rates.

Figure 6 shows the equivalent stress history of the specimen measured from load cells A and B denoted in Fig. 3. There is no compressive stress wave prior to the tensile stress wave in the histories of stresses measured load cells. Thus, the tensile specimen fails only under the pure tensile stress wave. However, the stress histories from load cells A and B are quite different. The differ-ence comes from the following reasons: 1) the stress has been attenuated as it transferred between two load cells; 2) the dissimilar wave impedance between steel, for load cells and grips, and concrete specimen made the wave profile changing; and, 3) the sudden change in the ge-ometry of transmitting medium (grip system) produced a distortion of wave profile.

It is also noticeable that the stress history measured from load cell A consists of high frequency components

Fig. 3 Finite element modeling of proposed version of SEITS using load frame.

Table 1 Properties of materials employed in simulations.

Energy Bar Test set-up and frame Coupler

Steel Steel Steel

E (MPa) 200100 200100 200100

ν 0.28 0.28 0.28 σu

(MPa) 828 828 552 (or 621)

ρ (t/m3) 8.027 8.027 8.027

εu - - 0.08

Fig. 4 Tensile stress-strain response of HPFRCC used in simulation (Kim et al. 2011).


in comparison with that from load cell B. This dispersion phenomenon originates from the transversal inertial effect and it can be explained by the Rayleigh approxi-mate solution of wave propagation in a solid cylindrical bar with radius a (Wang, 2007):

22 21

o

C avC

πλ

⎛ ⎞≈ − ⎜ ⎟⎝ ⎠

(1)

where C is wave velociy, Co is constant wave velocity, v is particle velocity, λ is the wave length.

From above equation, it can be seen that high fre-quency waves (λ are small or short waves) propagate slower, and low frequency waves (long waves) propagate faster. This is the main reason the signal at load cell B appeared the low frequency component for some first wave fronts, since low frequency waves came first.

The first wave fronts of stress histories from load cells A and B in Fig. 7 are similar to the incident and transferred stress histories in Split Hopkinson Pressure

Bar system if the load cells A and B are considered as incident and transmitter bar, respectively. Thus, the wave front in load cell A represented an applied load and the wave front in load cell B represented the resis-tance of specimen. The peak stress from load cell A is 38 MPa, which is bigger than assigned maximum tensile strength (14 MPa) of the specimen in the simulation, so it provides enough force to fail the specimen. However, the peak stress of load cell B is 22 MPa which is not matched with the assigned maximum tensile strength although it should be matched since it represented the resistance of specimen. The different value from load cell B is due to the inertia effect of grip and the insufficient length of transmitter bar (load cell B) to avoid the influence of the reflected stress wave. Thus, it is concluded that the pure material response of the specimen cannot be obtained by using the stress histories at load cell A and load cell B in the system in Fig. 3.

3. How to obtain pure material response at high strain rates

To find a way to obtain a pure material response at high strain rates, both cases 1 and 2 were investigated as shown in Fig. 8. Case 1 utilizes the identical geometry of the specimen at static rate, and the specimen is con-nected with a hinged grip system to the load cells as

(a) Wave propagation in energy bar

(b) Generation of impulse on load frame

(c) Failure of specimen

Fig. 5 Simulation results with load frame.

Fig. 7 First wave front of stress histories from load cells A and B.

(a) Case 1: set-up with two grips

(b) Case 2: set-up with only one grip Fig. 8 Cases for numerical analysis to obtain pure mate-rial response under high rate loading.

Fig. 6 Equivalent stress histories of specimen estimated from load cells A and B with different positions.


shown in Fig. 8a. However, the specimen in case 2 is connected to the load frame with a hinged grip system and directly to a transmitter bar as shown in Fig. 8b. The transmitter bar in case 2 has a section as a specimen to eliminate any effect of dispersion on the signal from load cell B in the transmitter bar. The length of the transmitter bar was also carefully determined to elimi-nate the influence of the reflected stress wave on the measured stress history. Since the duration of incident wave has not been determined yet in this case, the cal-culation would be based on the propagation time relation between the second incident wave front and the first reflection wave front. Firstly, the first wave front travels through specimen and comes to the load cell B with the time T1. Then, this wave continues propagate to the support and reflect to load cell B with total time T2. At load cell B position, in order to obtain only pure first wave front without reflect wave, the condition is the second wave front comes right after the time of first wave front reflect to load cell B. In other words, T1 is equal or smaller than T2. Therefore, the transmitter bar length of 320 mm is obtained. The calculation in detail as follows:

The material of specimen is assigned in simulation with an assumption of linear elastic plastic behavior where elastic modulus Ec is 60000 MPa and plastic hardening modulus is ( ) ( )14 9 0.006 0.00015p

cE = − − = 854.7 MPa.

In other hand, the wave propagation velocities in specimen will depend on the stage of material. It is

4804c c cC E ρ= ≈ m/s for elastic stage and is 573p p

c c cC E ρ= ≈ m/s for plastic stage. Identically, the wave propagation velocity in transmitter bar (in elastic stage only) is 4993bar bar barC E ρ= ≈ m/s.

If we choose the position to place the load cell B is 50 mm from the connector then the distance that the wave front propagates through specimen to load cell B is S = 200 + 50 = 250 mm.

The condition to the wave at load cell B does not meet the reflected wave from support is the time of the second wave propagates in distance S must be smaller than the time of first wave propagates from load cell B to support and reflect to load cell B. Call X is the dis-tance from load cell B to support, this condition means:

0.2 0.05 24804 573 4993 4993

X+ < ⋅

+ (2)

Solving this inequation, X is larger than 117 mm was obtained. With this result, the authors chose the length of transmitter bar is 320 mm that satisfied the require-ment.

In case 2, the stress wave through the specimen propagates to the transmitter bar. Thus, the stress history measured from the transmitter bar purely reflects the material characteristics of the specimen. The equivalent stress histories of the specimen from load cells A and B are illustrated in Fig. 9: load cell A gives a very high

value for peak stress at 32 MPa while load cell B pro-vides 12 MPa. Load cell B in case 2 provides more rea-sonable stress value than that in case 1, i.e., peak value from load cell B in case 2 approximates 14 MPa as-signed maximum tensile strength of the material.

Figure 10 shows the estimated stress versus strain curve in case 2. To establish the curve, the “measured” stress of the specimen in Fig. 10 is obtained from the solid element at the position of the load cell B in Fig. 8b, while the “measured” strain is obtained from the dis-placements of two nodes in the specimen with 200 mm gauge length. The stress versus strain response from the numerical simulation in case 2 is well matched with the assigned stress versus strain curve as shown in Fig. 10.

To validate the proposed method, additional simula-tions were carried out to investigate the effect of chang-ing the length of transmitter bar on the obtained stress versus strain response of the specimen in simulations. While the numerical models using different length of transmitter bar are illustrated in Fig. 11a, the stress ver-sus strain curves of the specimen estimated using from the different transmitter bars with various length are provided in Fig. 11b. Although the longer length of transmitter bar provided a result better matching with

Fig. 9 Stress histories obtained from both load cells A and B for the set-up of case 2.

Fig. 10 Stress-strain curve obtained from the set-up of case 2.


assigned curve, there is no significant difference re-gardless of the length of the transmitter bar. The ob-tained stress versus strain curve using the 320 mm length transmitter bar is not much different with the assigned one. Thus, based on these simulation results, case 2 with a transmitter bar length of 320 mm is able to measure pure material response of HPFRCC at high strain rates.

4. Proposed strain energy frame impact machine (SEFIM)

To further reduce the length of the system, an energy frame instead of an energy bar is proposed to store the elastic strain energy as illustrated in Fig. 12. The system with an energy frame not only makes the length of sys-tem shorter but also stores a much larger amount of elastic strain energy.

As illustrated in Fig. 12, the energy frame is directly connected to a pull bar through a coupler. Once the ten-sile load is applied at the pull bar, the whole system is stretched until the coupler fractures. When that happens, the energy frame storing large amount of elastic strain energy suddenly generates a high rate stress wave. Then, the stress wave propagates to the specimen through the hinged grip system and makes the specimen fail in ten-sion.

The stress history of the specimen is obtained from the strain gauges attached on the surfaces of transmitter bar while the strain history is estimated by tracking two individual points marked on the top surface of the specimen with the aid of a high speed camera system. Figure 13 shows the failure of the specimen in simula-tion.

The tensile stress versus strain curve of the specimen in Fig. 14 is obtained from a numerical simulation using the aforementioned method. The curve from simulation in Fig. 14 is closed to the assigned stress versus strain curve of the material. To simplify the simulation, the material model used did not considered softening part in the stress versus strain curves of the assumed material. It was focused on obtaining the hardening part of the assigned curve.

The capacity of coupler influences the strain rate of the system as shown in Fig. 15. A broad range of strain rate (20 to 80 s-1) can be produced by controlling the stress level in the energy frame at the point of strain

Fig. 12 Proposed strain energy frame impact machine (SEFIM).

Fig. 13 Failure of specimen in the proposed set-up.

Fig. 14 Assigned and obtained stress versus strain re-sponse of specimen from simulation.

(a) Case 2 with different lengths of transmitter bar

(b) Stress-strain curves of case 2

with different lengths of transmitter bar Fig. 11 Cases for numerical analysis to obtain pure mate-rial response under high rate loading.


energy release. Based on the numerical validation, a prototype of the

Strain Energy Frame Impact Machine (SEFIM) was built and applied to investigate the direct tensile behav-ior of HPFRCC at high strain rates as shown in Fig. 16.

5. Impact tests with strain energy frame impact machine (SEFIM)

A few impact tests were carried out using the prototype to verify all arguments discussed above. In addition, the tensile behavior of HPFRCC under static condition was investigated. Both maximum post cracking strength and strain capacity are mainly discussed although there are other tensile parameters, e.g., the number of cracks within gauge length, average crack spacing, and first cracking strength, describing the tensile behavior of HPFRCC. 5.1 Materials and specimens Both high strength steel hooked (H-) and twisted (T-) fibers were investigated using 2% fiber contents by vol-ume in a mortar with 81 MPa compressive strength. The geometry of specimen and test set-up is illustrated in Fig. 17a, while the static tensile behavior of HPFRCCs with those fibers is shown in Fig. 17b. However, the speci-men at high strain rates is prepared by cutting-off one bell-shaped end and then connecting it to a transmitter bar through the connector as shown in Fig. 18. The same size of specimen used in both the static and impact tests

eliminates any size effect in estimating the strain rate effects. As mentioned above, the ability to test large-sized specimens, which is a critical condition for investigating the behavior of HPFRCC, is one of main advantages of the proposed SEFIM. 5.2 Strain gauges and data acquisition (DAQ) The use of the strain gauge has become a standard tech-nique to measure the bar strains in Kolsky bar experi-ments. Two dynamic strain gauges are attached, in the prototype, at both sides of transmitter bar and at 50 mm from the connector to measure the stress history of the specimen. Their positions are similar to the ones in simulation. These strain gauges were then connected to a high speed DAQ.

Fig. 15 Strain rates according to the capacity of coupler.

Fig. 16 Prototype of SEFIM (built at SeJong University in 2011).

a) Geometry of specimen and test set-up (Kim and Kang 2011)

b) Static response of HPFRCCs

Fig. 17 Static test and response of HPFRCCs with 2% fibers.

Fig. 18 Connection between specimen and transmitter bar.


5.3 High speed camera A high speed camera system is used to directly monitor the elongation of the specimen in high strain rates in the SEFIM while the Split Hopkinson Pressure Bar (SHPB) techniques use strain histories from both incident and transmitter bars to indirectly determine the strain histo-ries of specimen. The images of the specimen at high strain rates are recorded with a speed of 50,000 frames per second and stored in a computer system. The camera focused on two marked points of 100 mm distance, the gauge length of the specimen, as shown in Fig. 18. 5.4 Trigger system The data acquisition and the high speed camera are all connected to an optical trigger system located at both sides of coupler as shown in Fig. 16. The optical trigger system immediately generates a 5 voltage electrical signal once the coupler is broken. Then, both the DAQ and the high speed camera system start to record the event. By using this trigger system, the raw data from the DAQ and high speed camera can be synchronized. 6. Results and discussion

6.1 Strain history The elongation of specimen is obtained by using an im-age processing technique. The specimen images, during impact, which was captured by a high speed camera, consist of continuous and discontinuous deformations due to the formation of cracks and their propagations. The deformations between any two points within an image can be measured by means of the image matching technique relying on tracking two sequential images to estimate the relative motion of surface structures. By applying the tracking function of the two marked points in commercial image processing software, the elongation of the specimen during high rate loading is captured, and then the strain history is obtained by dividing the elon-gation with gauge length. Figure 19 shows the strain history obtained by this method.

6.2 Stress history Figure 20 shows the stress signal obtained from two strain gauges by multiplying with elastic modulus of the transmitter bar. The dotted and dashed curves are meas-ured stress histories from strain gauge 0 and 1, respec-tively, while the continuous curve is the averaged curve. The stress histories from the two strain gauges have opposite signs at the beginning of the history. The dif-ferent sign convention might result from a slight mis-alignment of transmitter bar, which causes confusion in the strain gauge measurements. However, the effect can be remedied by averaging the two stress histories. The averaged value represents the axial strain of transmitter bar and eventually provides a longitudinal axial stress history of the specimen (Fig. 20). The alignment of the transmitter bar and the position of the strain gauges should be carefully checked prior to testing.

6.3 Stress - strain curve The stress-strain curve is established by combining the stress history and the strain history as shown in Fig. 21. It should be also noticed that both stress and strain his-tories start at the same time as shown in Fig. 19 and Fig. 20. The strain hardening and multiple cracking behavior

Fig. 19 Strain history of HPFRCC with 2% H- fibers under impact, obtained from a high speed camera system.

Fig. 20 Stress history of HPFRCC with 2% H- fibers un-der impact.

Fig. 21 Stress versus strain curve of HPFRCC with 2% H- fibers under impact.


of HPFRCC is still valid at the high strain rates shown in Fig. 21 and Fig. 22, respectively. It is clear that HPFRCC, under high strain rate tensile load, still showed an initially elastic respond up to a certain stress level as static case. After reaching the first cracking strength, the tensile stress slightly increases up to the maximum tensile strength. The same trend was also reported by Fujikake et al. (2005) for RPC (Reactive Powder Concrete) reinforced with 2% short straight steel fibers in volume subjected to rapid loading.

As shown in Fig. 21, the strain at maximum stress (strain capacity) is 2.8% which is 4.7 times higher than that of static case (0.6%). This enhanced strain capacity at high strain rates was also reported by other research-ers including Cusatis (2011), Kormeling and Reinhardt (1987), Zhu et al. (2012). In addition, the enhancement of the strain capacity at high rates is partly from the reduced gauge length of the specimens for impact in comparison with that for static tests.

Thus, the advantages of HPFRCC including high ductility and energy absorption capacity are still valid even at high strain rates, at least at the strain rate of this test (45 s-1). The peak strain rate during the event is chosen as the strain rate level in this study.

In order to compare dynamic and static strength of material, the Dynamic Increase Factor (DIF) is normally estimated by calculating the ratio between the dynamic and static strength. The DIF of 2% H- fiber reinforced HPFRCC is estimated as 1.89. Thus, there is a clear increasing tendency in the tensile strength of HPFRCC as the strain rate increases. Until the strain rate reaches the seismic rate (0.1 s-1), the increasing tendency of the post cracking strength of HPFRCC was reported by re-searchers Kim et al. (2009), Douglas and Billington (2011). However, there are very few test results about HPFRCC beyond the seismic loading rate.

Based on the results of this test and Kim et al. (2009),

the DIF of HPFRCC with 2% H- fiber versus strain rate from low to high was drawn together in Fig. 23. Clearly, this figure reveals a behavior similar to that experienced in the case of brittle ceramic materials, like concrete. In the case of concrete, in fact, DIF for tensile strength dependence on the strain rate level in logarithmic scale presents two different slops for medium strain rate and high strain rate and the variation of the gradient is lo-cated at about 1 s-1. In the present case, a two-segment trend-line was also drawn, display a knee located at seismic strain rate. Actually, in order to predict a dy-namic tensile strength at a given strain rate level starting from static range, the CEB (1993) formulation was usu-ally used. But unfortunately, this formulation is only used for concrete not for HPFRCC. A suitable formula-tion can be applied for HPFRCC is also a research ob-ject of authors in future. Therefore, the dynamic behav-ior of HPFRCC at high strain rates needs to be further investigated. In addition, the effect of fiber types, matrix types on DIF at different strain rate will be investigated as a future subject of research.

Further, the specimen with 2% T- fiber was also tested at high strain rate using the prototype. However, the specimen with 2% T- fiber was not completely fractured into two separate parts as shown in Fig. 24, while the specimen with 2% H- fiber showed clear failure by us-ing couplers with the same capacity. This result can be explained by two reasons. The first reason is the low capacity of the coupler; a coupler with higher capacity should be used for testing of HPFRCC with 2% T- fibers. The other reason for the result is that the HPFRCC with 2% T- fiber produces a higher rate sensitivity, i.e., the peak stress recorded during impact test is 31.2MPa, while the static strength of the specimen is 14.12 MPa (DIF is 2.21). Although the specimen with 2% T- fibers did not completely fail, the specimen did show multiple cracks and an enhancement of post cracking strength as shown in Fig. 24 and Fig. 25. The higher DIF for T- fiber indicated the fact that the rate sensitivity of HPFRCC is influenced by the types of fiber.

a) 2% (H-) fibers reinforced specimen

b) 1% (T-) fibers reinforced specimen

Fig. 22 Multiple micro cracks of HPFRCCs.

Fig. 23 DIF of HPFRCC with 2% H- fibers versus strain rate ranging from low to high rate.


7. Summary and conclusions

A new impact test set-up for HPFRCC called SEFIM, a modified version of SEITS, is proposed. The proposed system can be used for testing large-sized specimens of HPFRCC and can easily control strain rates by changing the material of energy frame or by changing the capacity of couplers. The proposed system has three clear ad-vantages over the original SEITS: 1) the proposed system is less influenced from the gravity effect; 2) the proposed system can store larger amount of elastic strain energy since using an energy frame instead of an energy bar; and, 3) the proposed system can deliver a high rate tensile

stress wave to one specimen without any eccentricity. Numerical simulations have been performed to 1)

validate the proposed system with an energy frame; 2) estimate the possible strain rate range; and 3) find a way to obtain a pure material response at high strain rates. The information presented indicates that the proposed system with an energy frame provides broad range of strain rates from 20 to 80 s-1.

Based on the obtained results of the proposed system, a prototype has been built and the tensile stress-strain response of HPFRCC at high strain rates was tested by using the prototype of SEFIM. For the measurement of tensile stress – strain response of specimens at high strain rates, a high speed camera system is applied to obtain the deformation history of specimen while two dynamic strain gauges are attached at both sides of transmitter bar to capture the stress signal. There is a significant enhancement of both strength and strain ca-pacity in the behavior HPFRCC at high strain rates, al-though the dynamic enhancement is quite different ac-cording to the types of fiber.

Acknowledgment The research described herein was sponsored by Basic Science Research Program (2010-0003161) from the National Research Foundation (NRF) of Korea and by the human resource development (20104010100520) from the Korea Institute of Energy Technology Evalua-tion and Planning. The authors are grateful to the spon-sors for the financial support. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors. References Bindiganavile, V., Banthia, N. and Aarup, B., (2002).

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Fig. 24 Multiple micro cracks of HPFRCC with 2% T- fibers under impact, captured by normal camera after testing.


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Documents

Strain Energy Frame Impact Machine (SEFIM)