Experimental study on direct tensile behaviour of UHPFRC under high strain-rates

Construction and Building Materials 218 (2019) 667–680

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Experimental study on direct tensile behaviour of UHPFRC under high strain-rates Ezio Cadoni a,⇑, Daniele Forni a, Emmanuel Bonnet b, Svatopluk Dobrusky b a b

DynaMat Laboratory, University of Applied Sciences of Southern Switzerland, Campus SUPSI-Trevano, 6952 Canobbio, Switzerland R&D LafargeHolcim, 38291 Saint-Quentin Fallavier, France

h i g h l i g h t s
Experimental study on the dynamic direct tensile behaviour of various UHPFRCs.
The three matrixes showed significant strain rate sensitivity in direct tension.
The results on UHPFRC highlighted strain-hardening behaviour in dynamics.
Using dog-bone-shaped specimen the multi-cracking process has been detected.

a r t i c l e

i n f o

Article history: Received 7 January 2019 Received in revised form 11 April 2019 Accepted 24 May 2019

Keywords: Ultra High Performance Fibre-Reinforced Concrete Tensile strength High strain-rates Split Hopkinson Tensile Bar Impact

a b s t r a c t An experimental investigation was carried out to characterise the direct tensile behaviour at high strain rate of various UHPFRC mix designs (150, 170 and 210 MPa) with various dosages of fibres. The mechanical characterisation at high strain-rate was performed by means of two split Hopkinson tension bar devices and one Hydro-Pneumatic Machine that are installed at the DynaMat Laboratory of the University of Applied Sciences and Arts of Southern Switzerland in Lugano. The direct tensile tests of different UHPFRCs were performed on cylindrical notched specimens of H/D = 1 with 20 mm and 60 mm in diameter (notch/radius = 0.20) and on dog-bone-shaped specimens. The results highlighted different strain rate sensitivities of the materials. Higher dynamic increase factor was registered for the matrix with special thermal curing respect to those cured as usual. Important increment of strength was obtained for the matrix where sand was partially replaced by Silica Fume. These results are the base for better understanding the dynamic mechanical behaviour that will be obtained by further tests on Ultra High Performance Fibre-Reinforced Concretes (other DuctalÒ mixes). Such data will provide designers better and more relevant properties of these materials useful for designing protective structures. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays, modern architecture as well as structural engineering require advanced materials to enhance both the service life and the load carrying capacities, as well as reducing as much as possible the environmental impact. The cementitious based materials are among the most promising solutions that today better answer to these needs. Since the eighties research efforts have been oriented towards obtaining higher and higher strength, in reducing the water/binder ratio and decreasing the aggregates’ size, resulting very compact materials with outstanding properties. Furthermore, with the addition of fibre reinforcement these materials

⇑ Corresponding author. E-mail address: [email protected] (E. Cadoni). https://doi.org/10.1016/j.conbuildmat.2019.05.152 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

gain in ductility giving high performances in terms of toughness, strength capacity and durability. Currently, with the term Ultra-High Performance FibreReinforced Concrete (UHPFRC) are identified the cementitious composite materials combining a cement-based matrix with a low water-to-cement ratio and reinforcing fibres, exhibiting as a result outstanding compressive strength (P150 MPa), high durability, as well as enhanced aesthetic aspects. These characteristics are the reasons why the use of UHPFRC in construction is constantly growing worldwide. After the first applications, which were concentrated in footbridges and pre-cast elements, nowadays the use is being expanded to rehabilitation and refurbishment of deteriorating concrete bridges, high rise buildings, protective defence constructions, offshore structures, and façades. An impressive example of the potentiality of UHPFRC is represented by the Musée

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des Civilisations de l’Éurope et de la Méditerranée (MuCEM) in Marseille [1] or by the Jean Bouin rugby stadium in Paris [2]. In UHPFRC the amount of fibres (P2% per volume) is significantly higher than for ordinary fibre-reinforced concrete (FRC, 0.5% per volume) which brings interesting properties from a structural perspective. In fact, such an amount of fibre reinforcement produces an enhancement of both the tensile strength and ductility. This permits the replacement of all or part of the traditional reinforcement (rebar) usually present in reinforced concrete elements. Furthermore, the fibre addition improves the energy absorption capacity of these materials through the enhanced capability to continue to transfer stresses after the first cracking. As a result, the structural response to impact loading can be sensitively improved and the risk of debris ejection, caused by spalling in the case of blast, is reduced. UHPFRCs are commonly classified as a function of their tensile behaviour in strain-softening and strain-hardening materials depending on whether the stress increases or decreases after the first cracking. In the first case the fibres’ contribution is only limited to continue to transfer forces across the crack by means of fibre bridging, avoiding brittle failure, and leading to a gradual post-peak strength decrement. In the second case the UHPFRC is able to continue to increase the tensile capacity due to the multiple cracking phenomenon and a favourable fibres’ orientation that provides a large dissipation of energy. The presence of a high content of fibres may enhance the tensile strength beyond the matrix strength but this is conditioned by the shape of the fibres as well as by their distribution and orientation [3–6]. It should be pointed out that the classification of UHPFRC as ‘‘softening” or ‘‘hardening” fails when it behaves as ‘‘hardening” in a bending test but not in a direct tensile test. Because of the influence of size and shape of the specimens as well as fibre orientation this classification should be considered to be more a structural rather than a material characteristic. From the economics point of view, despite the higher initial cost (at least five times more [7]) with respect to conventional concrete, UHPFRC materials possess many interesting aspects in terms of sustainability. In fact, the advantages in their use could be easily demonstrated by performing a life cycle cost analysis. It has been shown that the life cycle cost of a structure (for example a bridge) made with UHPFRC is lower than the same structure made with standard concrete [8]. From the environmental point of view the use of UHPFRC can be considered as a possible way to mitigate the CO2 emissions that cause global warming and climate change compared to normal concrete (an interesting application can be found in [9], where it has been used in façade systems to enhance the building energy performance). Dong et al. [10] demonstrated that the use of UHPFRC in structures gives a significant benefit in terms of sustainability. In fact, they estimated a reduction of CO2 emissions of around 48% compared with traditional concrete structures, due the reduced need bar repairs. For particular infrastructures, such as bridges, the use of UHPFRC can offer a sustainability solution with a reduction of the equivalent annual cost and a longer service life with respect to other structural solutions (e.g., traditional reinforced concrete or steel bridges). A part of these economic and environmental aspects the reasons for the extended use of UHPFRC reside in their outstanding mechanical characteristics, for example the large dissipation of energy together with ultra-high strength makes these materials an excellent choice for protective structures. Indeed, many research teams have started to suggest protective solutions made of UHPFRC for impact [11,12], blast [13–15], as well as close charge [16–18] loadings. In parallel numerical studies have been performed, for example on the tensile behaviour of UHPFRCs with different fibre contents [19] or on the simulation of panels under blast loading [20,21].

Thomas and Sorensen in a review of the tensile behaviour of UHPFRC [22] concluded that the strain rate sensitivity is similar to that of conventional concrete up to intermediate strain rates while it is higher at high strain rates. The Dynamic Increase Factor (DIF) is typically lower for UHPFRC than for concrete. The strain rate sensitivity has been found not to depend on fibre volume content, fibre shape and aspect ratio, or compressive strength. The modulus of elasticity of UHPFRC in tension is not strain rate sensitive up to strain rates of the order of 101 s1 . Park et al. [23] studied the effect of blending macro- and micro fibres on the tensile stress-strain response of Ultra High Performance Hybrid Fibre Reinforced Concrete (UHP-HFRC). Another review on mechanical properties of UHPFRCs can be found in [24,25] both for quasistatic and impact loadings. The strain hardening properties of UHPFRC under direct tensile loading were reported in [26,27]. The strain rate dependency of the UHPFRC properties under tension was reported in [28] at low and intermediate regime (from 104 to 101 s1 ). Tensile strength, energy absorption capacity, strain capacity and elastic modulus increase with increasing fibre volume content. The tensile behaviour (strain rate range between 14:3 s1 and 214:8 s1 ) was investigated by Wu et al. [4] who conducted a series of spalling tests on UHPFRC specimens with three fibre volume contents (0%, 1%, 2%) and two types (micro-straight, hooked) of steel fibres. They observed high strain rate sensitivity for dynamic tensile behaviour, in particular for the matrix. The dynamic spalling strength increased with increasing fibre volume content and was reduced with increasing the critical time to fracture. The micro-straight steel fibres behaved slightly better than the hooked ones. The influence of steel fibre reinforcements (micro-straight and twisted steel fibres) on dynamic strength (compressive and split tensile strength) was reported in [6]. The test results showed a higher loading rate sensitivity for micro-straight steel fibres with respect to the twisted ones. The increase of fibre volume fraction as well as aspect ratio and fibre length positively influence the dynamic strength. In compression the effects of fibre volume content and strain rate on UHPFRC have been evaluated by several authors [29–32]. Other aspects related to the tensile behaviour are still under investigation such as the crack propagation speed [33,34], the tensile fatigue behaviour of UHPFRC [35] or the dynamic pull-out behaviour [36]. With the intention of providing a new experimental data set on the direct tensile behaviour of UHPFRC materials at high strain rate, in this study three different matrixes with two fibre volume contents (2% and 3.25%), for both notched and un-notched specimens, were investigated. The paper is organised in the following sections: (i) research significance, (ii) materials and specimens, (iii) experimental set-ups for high strain rate testing, (iv) experimental results and discussion, (v) conclusions. 2. Research significance The design of special structures using UHPFRCs which may be subjected to severe dynamic loadings requires a comprehensive knowledge of their mechanical properties of these materials that govern their structural response. Despite the studies performed in recent years, many questions are still open and require comprehensive investigation both experimentally and numerically as well as specific standards. One open issue is the dynamic behaviour in direct tension. Because of the lack of experimental data, the effects of fibre reinforcement (geometry, aspect ratio, fibre volume content, etc.), on the effect of strain rate on mechanical properties are not completely well-understood. The aim of this paper is to

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provide insights and information that will help with the understanding of these phenomena.

3. Materials and specimens Several DuctalÒ products were used in this study. Three compressive strengths (150 MPa, 170 MPa and 210 MPa) were obtained by using three different matrices A, B and C respectively. The main difference between the matrices is that Matrix A has no pozzolanic material, Matrix B uses 150–200 kg of Silica Fume as a replacement for sand, and Matrix C is made of the same premix as Matrix B but cured for 48 h at 90 °C and 100% R.H. after demolding (24 h). For the matrixes A and B two volumetric dosages (2% and 3.25%) of steel fibres were analysed. High carbon straight fibres, 14 mm long with a 0.20 mm diameter (aspect ratio lf =df equal to 70) with a tensile strength of 2500 MPa, were used. The mix proportions of the UHPFRC are collected in Table 1. In total, 45 notched cylinders of £20 mm/20 mm, 55 notched cylinders of £60 mm/60 mm and 18 dog-bone-shaped unnotched specimens were prepared (Fig. 1). The £20 mm cylinders were drilled out of 200/300/40 mm cast slabs (15 samples per a slab) whereas the £60 mm cylinders were drilled out of 100/100/400 mm prisms (3 samples per a prism). The notches were made after drilling to a depth of 20% of the cylinder diameters. The notch was required to favour stable crack propagation in a single section and to permit analysis how fibre pull-out contributes to the post-peak behaviour. The dog-bone-shaped specimens were cylinders with the extremities of 60 mm in diameter tapered, with radius of 37.5 mm, in the central part with gauge length of 50 mm and diameter of 30 mm (see Fig. 1c). The samples were cast and cured at LafargeHolcim Research Center in

France in laboratory conditions. The pouring of the slabs was performed from the middle when there were no fibres whereas the pouring of the prisms was done from one side to keep the same fibre orientation (the samples were drilled out along the length/ pouring). Quasi-static mechanical properties of the various DuctalÒ classes were tested at LafargeHolcim Research Center on at least 6 samples for each property according to NF P 18-470. Table 2 shows mean compressive strength (f cm ), mean tensile strength (f ct;m ) derived from a bending test reduced by a coefficient (Eq. (D.1) [37]), and mean tensile post-peak resistance (f ctfm ) measured at 0.3 mm crack opening. 4. Experimental set-ups for high strain-rate testing The dynamic response of these of materials at high strain-rates was obtained by means of two Split Hopkinson Tensile Bar (SHTB) devices installed in the DynaMat Laboratory of the University of Applied Sciences of Southern Switzerland. They are able to generate a well controlled and repeatable loading pulse in terms of rise time, amplitude and duration, giving rise to the propagation of uniaxial elastic plane stress wave [38] and by following the method developed by [39–41] it is possible to obtain accurate measurements. The SHTB devices used in this research are based on that developed in the seventies by Albertini and Montagnani [42,43], detailed description can be found in [5]. The specimens having a diameter of 20 mm have been tested in the SHTB device consisting of two circular aluminium bars with a diameter of 20 mm, having a length of 3 and 6 m acting as input bar u and output bar w, respectively (see Fig. 2). Notched specimens x are glued to the input and output bars by means of

Table 1 Mix proportion of the various UHPFRC DuctalÒ products. DuctalÒ product

150–2%

150–3.25%

170–2%

170–3.25%

210–2%

Premix Powder [kg/m3] Fibres [kg/m3] Water [kg/m3] Superplasticizer [kg/m3]

A 2200 156 158 25

A 2170 253 155 25

B 2170 156 158 35

B 2140 253 155 35

C 2170 156 158 35

Curing

standard

standard

standard

standard

heat curing

Fig. 1. Specimens: (a) notched cylinder 20 mm in diameter; (b) notched cylinder 60 mm in diameter; (c) dog-bone-shaped specimen.

Table 2 Quasi-static mechanical properties of the various DuctalÒ products Material

f cm [MPa]

Ec [GPa]

f ct;m [MPa]

f ctfm [MPa] (2.00%)

f ctfm [MPa] (3.25%)

Matrix A Matrix B Matrix C

150 170 210

55 60 60

8.3 11.0 10.5

8.9 10.2 12.4

12.8 11.4 –

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a bi-component epoxy resin having a tensile strength of 30 MPa (see Fig. 7).The pulse is generated by means of pretensioning a high strength steel bar (C85 with Rm =1256 MPa, according to European Standard EN10204). The pretensioned bar s has a diameter of 12 mm (so as to have the same acoustical impedance as the aluminium bars) and a length of 6 m. It is directly screwed to the aluminium input bar at one end and is also connected to the hydraulic actuator r. The dynamic test is performed by storing elastic energy in the pretensioned bar which is blocked at one end (near the connection with the input bar) by the blocking device t and pulled by the hydraulic actuator (600 kN maximum load) at the other end. When the fragile bolt fails in the blocking device the system is subjected to a tensile mechanical pulse of 2.4 ms duration with a linear loading rate during the rise time, which propagates along the input and output bars causing fracture of the specimen. The length of the pretensioned bar and of the output bar is the

same (6 m). The pretensioned bar has to be long enough to generate a tensile pulse ensuring a constant strain-rate deformation to the specimen and to permit the complete pull-out process [5,44] in the case of fiber-reinforcement. The output bar is required to be sufficiently long to allow specimen deformation without any wave superposition coming from the free end of the bar. The incident and reflected pulses are recorded by the strain gauge station v while the transmitted pulse is recorded at the strain gauge station in the output bar w. The displacement of the two specimen ends are recorded by an electro-optical extensometer y and the test is also followed by a fast video camera z. All data are recorded using a transient recorder 10 s. For testing the specimens having a diameter of 60 mm (i.e. the notched cylinder and the dog-bone-shaped specimens) a second SHTB (see 3) was used that has different bar dimension (3 m in length and 60 mm diameter).

Fig. 2. Experimental set-up for high strain-rate testing of notched cylinder specimens with 20 mm diameter: 1-hydraulic actuator; 2-pretensioned bar; 3-blocking device; 4input bar; 5-strain gauge station; 6-output bar; 7-specimen; 8-electro-optical extensometer; 9-fast video camera; 10-transient recorder.

Fig. 3. Experimental set-up for high strain-rate testing of notched cylinder specimens with 60 mm diameter and dog-bone-shaped specimens: 1-hydraulic actuator; 2pretensioned bar; 3-blocking device; 4-input bar; 5-strain gauge station; 6-output bar; 7-specimen; 8-electro-optical extensometer; 9-fast video camera; 10-transient recorder.

E. Cadoni et al. / Construction and Building Materials 218 (2019) 667–680

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The pulse propagates with the velocity C 0 of the elastic wave with its shape remaining constant. When the incident pulse I reaches the specimen, part of it R is reflected by the specimen whereas another part T passes through the specimen propagating into the output bar. In Fig. 4 are depicted the signals coming from the input and output strain gauges in the case of 20 mm unreinforced specimens. The input strain gauge measures the superposition of the incident and reflected pulses (I þ R ) while the output strain gauge measures the transmitted (T ) pulse. The signals of the input and output strain gauges for the case of 60 mm fiber-reinforced specimens are shown in Figs. 5 and 6, respectively. By applying the one-dimensional elastic plane stress wave propagation theory [38] the stress (1), the strain (2) and the strain-rate (3) versus time within the specimen can be evaluated as:

Fig. 6. Transmitted pulse in the fibre-reinforced specimen 60 mm in diameter.

rðtÞ ¼ E0 

Fig. 4. Incident, reflected and transmitted pulses in the unreinforced specimen 20 mm in diameter.

Fig. 5. Incident and reflected pulses in the fibre-reinforced specimen 60 mm in diameter.

A0  T ðtÞ A Z

t

ðtÞ ¼ 

2C 0 L

_ ðtÞ ¼ 

2C 0  R ðtÞ L

0

R ðtÞ

ð1Þ

ð2Þ

ð3Þ

where E0 is the Young’s modulus of the bars, A0 is the cross section of the input and output bars, A is the cross section of the specimen within the gauge length L; C 0 is the bar elastic wave speed, T and R are the transmitted and reflected pulses, respectively. Direct measurements of the displacements were carried out by means of an electro-optical Extensometer H.-D. Rudolph GmbH (Model 200XR). This apparatus contactless measures the motion of two black-and-white edges (targets) on UHPFRC samples: one in the input and another in the output part, before and after the notch as shown in Fig. 7.

Fig. 7. Un-reinforced matrix specimen after test.

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Fig. 10. Behaviour of UHPFRC in tension.

Fig. 8. Stress versus displacement curve of UHPFRC in tension (Matrix B).

occurs, dpc is the displacement corresponding to the post-peak strength (normally named fibre efficiency). Finally, the value df is the maximum displacement that causes pull-out of the fibres and coincides to the half fibre length. 5.1. Dynamic tensile behaviour of the three matrixes

Fig. 9. Comparison between stress and strain rate versus time curves of UHPFRC in tension.

5. Experimental results and discussion An experimental study of the direct tensile behaviour of UHPFRC under high strain rate has been carried out through the study of the three matrixes and four fibre-reinforced mixes using notched and dog-bone-shaped specimens. In Fig. 10 are depicted the typical stress versus displacement curves of the matrix (curve 0) and two UHPFRCs having a volume content of fibre <2% (curve 1) and P2% (curve 2). The UHPFRC can be classified as:
strain-hardening when rpr P rcr
strain-softening when rpc < rcr . where rcr is the first peak stress corresponding to the cracking process, rpc is the post-peak strength. The value dcr represents the displacement corresponding to the matrix strength, d0 represents the value when the separation of the matrix specimen into two halves

The dynamic behaviour of the three matrixes has been investigated using uniaxial tensile tests on notched cylindrical specimens in a wide range of strain rates. In particular, the specimens having a diameter of 20 mm have been tested in the intermediate regime of strain rate by using the Hydro-Pneumatic Machine (see detailed description in [44]) with a stress rate of about 300 MPa/s and by a Split Hopkinson Tensile Bar (described in Section 4) with two pre-load levels in the pretensioned bar of 18 kN and 30 kN corresponding to a nominal stress rate of 600 and 900 GPa/s, respectively. The results of high strain-rate tests for specimens with a diameter of 20 mm are given in Table 3 where are reported the values and standard deviations of the stress-rate r_ , measured in the stress vs. time curve (from the output strain gauge station, see Fig. 9), the tensile strength of the matrix rcr and corresponding strain cr and displacement dcr , two times in correspondence of the peak stress (tcr ) and the end of the test (t u ), the displacement measured (du ), finally the fracture energy Gf and total energy W t . Fig. 11 shows the evolution of the tensile strength as a function of the stress rate. The results are compared with those obtained for an equivalent UHPFRC matrix [5]. Matrix A highlights an increment of the tensile strength from the intermediate regime to the higher regime of 36%, whilst Matrix B and Matrix C give an enhancement of 67% and 61%, respectively. These matrixes have a behaviour similar to conventional concrete [38,45,46] even if lower DIFs are shown. The dynamic tensile strength increases with a decrease in the fracture time as shown in Fig. 14. The fracture time can be useful for an interpretation of the rate effects of fracture of UHPFRC based on the structural-temporal approach [47]. The strain rate, obtained during dynamic tests of UHPFRC with a SHTB, is not constant because of the loading process. In the case of metallic or ductile materials, where the plastic zone is well defined, the stain-rate is obtained as an average of the strain-rate value (by applying Eq. (3)) to the above-mentioned zone. For UHPFRC as well as for other cementitious materials, or in the general case of brittle materials, the strain rate is generally measured when the maximum value of the strength is reached [48], as shown in

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E. Cadoni et al. / Construction and Building Materials 218 (2019) 667–680 Table 3 Material properties of three matrixes at high strain-rate regime with specimen of 20 mm diameter.

r_

rcr

cr

[GPa/s]

[MPa]

[%]

tcr [ls]

tu [ls]

dcr [mm]

du [mm]

Gf [J/m2]

Wt [J/m2]

Matrix A

683 (±53) 818 (±135)

19.90 (±1.46) 20.38 (±2.34)

0.043 (±0.013) 0.058 (±0.008)

46 (±4) 42 (±3)

59 (±7) 52 (±3)

0.008 (±0.003) 0.012 (±0.002)

0.028 (±0.008) 0.045 (±0.004)

211 (±69) 345 (±34)

334 (±98) 510 (±48)

Matrix B

526 (±84) 989 (±50)

19.94 (±1.56) 20.78 (±0.44)

0.047 (±0.012) 0.045 (±0.014)

53 (±2) 36 (±1)

67 (±3) 47 (±1)

0.009 (±0.002) 0.011 (±0.003)

0.025 (±0.006) 0.047 (±0.004)

159 (±43) 366 (±20)

292 (±66) 535 (±35)

Matrix C

489 (±76) 586 (±162) 872 (±137)

19.76 (±0.39) 21.81 (±2.25) 24.20 (±1.92)

0.062 (±0.010) 0.062 (±0.024) 0.053 (±0.014)

77 (±4) 54 (±6) 45 (±3)

88 (±4) 68 (±7) 56 (±2)

0.012 (±0.002) 0.012 (±0.005) 0.011 (±0.003)

0.028 (±0.001) 0.036 (±0.010) 0.038 (±0.014)

160 (±22) 255 (±85) 334 (±114)

328 (±19) 419 (±127) 502 (±147)

Material

As a consequence, the stress rate is considered constant as 395 GPa/s. During the initial transient of a dynamic test, the equilibrium between the two faces of the specimen is not guaranteed. By using Eqs. (5) and (6) is possible to calculate the loads at the interfaces between the specimen and the input (1) and output (2) bars.

F 1 ðtÞ ¼ A0  C 0 ½I ðtÞ þ R ðtÞ

ð5Þ

F 2 ðtÞ ¼ A0  C 0 T ðtÞ

ð6Þ

Fig. 12 shows F 1 and F 2 as a function of time. In the first 30 ls is evident that equilibrium is not reached. After 5 reverberations, equilibrium is reached (between 30 and 50 microseconds). The function RðtÞ defined by Eq. (7) [49] in this region is lower than 3%.

     DFðtÞ   ¼ 2  F 1 ðtÞ  F 2 ðtÞ RðtÞ ¼    F av g F 1 ðtÞ þ F 2 

ð7Þ

The displacement of the two specimens’ ends were calculated by using the following Eqs. (8)–(10):

Z d1 ðtÞ ¼ C 0 0

t

½I ðsÞ  R ðsÞds

ð8Þ

Fig. 11. Stress versus stress rate evolution of the three matrixes.

Fig. 9. In the elastic zone the strain rate can be evaluated as indicated in Eq. (4):

_ ¼

r_ E

ð4Þ

These values have been reported in Table 3. The stress versus displacement curve depicted in Fig. 8 shows three main characteristic branches: 1. a linearly increasing branch which can be taken as elastic, characterised by an elastic modulus and by the elastic limit (zone I); 2. a strain hardening branch where the stress increases nonlinearly with strain up to the ultimate tensile stress (zone II); 3. a softening branch where load decreases non-linearly with displacement, corresponding to fracture propagation through the specimen cross-section (zone III). Observing Fig. 4, where the signals obtained during a dynamic test with a SHTB are shown, some important information can be obtained such as the rise time in the input pulse, that is 78 ls.

Fig. 12. Load versus time curves obtained by using Eqs. (5) and (6) their average.

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Z

t

d2 ðtÞ ¼ C 0 0

T ðsÞds Z

t

dðtÞ ¼ 2  C 0 0

R ðsÞds

ð9Þ

ð10Þ

where C 0 is the elastic wave velocity, I ; R and T are the incident, reflected and transmitted pulses, respectively. Furthermore, the displacements were directly measured by using the optical extensometer. In Fig. 13 the three curves are depicted as a function of time. Only the first part (between 40 and 60 ls) the displacements calculated are slightly higher than the measured. It can be stated that, also in the case of displacement the use of the reflected pulse for the determination of the displacement can be admitted without committing an important error. 5.2. Notched cylindrical specimens It is particularly important for UHPFRC to optimise the dynamic testing conditions for an accurate measurement of all branches of the stress-strain (or displacement) curves. When the matrix strength is achieved, a relatively long softening (or hardening) branch corresponding to the fracturing and fibre pull-out processes occur. In order to concentrate the fracturing process in a predetermined zone and to avoid multiple cracks which complicate the analysis of the pull-out process, notched specimens were used. Whatever the precise deformation mechanism involved, the elastic limit of the linear branch of the stress-strain curve of a UHPFRC corresponds to the passage from predominantly linear elastic to predominantly non-linear plastic deformation mode. The overall elastic strain rate, just before the elastic limit and the nominal plastic strain rate just after the elastic limit, should be nearly equal. However at the elastic limit, while the elastic strain will and must be homogeneously distributed over the specimen gauge length, the initial non-linear plastic strain will be confined to one or more restricted regions within the specimen gauge length because it takes some time to spread over the whole gauge length, with the consequence that the definition of an overall plastic strain rate near the elastic limit is impossible. In fact, in the regions of localised non-linear plastic strain of the specimen gauge length

Fig. 13. Comparison between displacement versus time curves directly measured or obtained by equations.

Fig. 14. Tensile strength versus fracture time.

the plastic strain rate will be very high while outside it will be very low, arriving at a stable value only after some time. In Fig. 15 the stress and strain rate versus time is shown. The strain rate is calculated by using Eq. (3). The strain rate at the end of the elastic branch was 3:05 s1 while the value obtained by using Eq. (4) was 3:02 s1 . At the maximum tensile strength the strain rate is 15:8 s1 . This increase is due to the decrease of stiffness in the hardening stage. After this point the strain rate is no longer definable because of the fibre pull-out process. A comparison between 6 mix designs, Matrix A and Matrix B with three volumetric dosage of steel fibres (0%, 2.00% and 3.25%), has been performed by using notched specimens (60 mm in diameter), to analyse how the fibres are able to favour stable propagation, under the same initial condition of preloading in the pretensioned bar (60 kN) that leads to a stress rate of 180 GPa/ s. The notched specimens were equipped with two black and white

Fig. 15. Stress versus stress rate of the three matrixes.

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E. Cadoni et al. / Construction and Building Materials 218 (2019) 667–680 Table 4 Material properties of three matrixes at high strain-rate regime with specimen of 60 mm diameter.

r_

rcr

cr

[GPa/s]

[MPa]

[%]

tcr [ls]

tu [ls]

dcr [mm]

du [mm]

Gf [J/m2]

Wt [J/m2]

Matrix A

143 (±44)

7.94 (±0.48)

0.02112 (±0.00002)

90 (±26)

123 (±36)

0.005 (±0.000)

0.013 (±0.002)

31 (±7)

57 (±10)

Matrix B

176 (±7)

8.64 (±0.30)

0.01725 (±0.00001)

74 (±4)

100 (±5)

0.004 (±0.000)

0.010 (±0.000)

30 (±1)

53 (±4)

Matrix C

174 (±10)

9.00 (±0.62)

0.01557 (±0.00002)

76 (±5)

102 (±3)

0.003 (±0.000)

0.009 (±0.001)

26 (±1)

47 (±1)

Material

Table 5 Material properties of the six UHPFRC with 2 and 3.25% fiber reinforcing at high strain-rate regime for specimens of 60 mm diameter.

r_ [GPa/s]

[MPa]

t cr [ls]

dcr [mm]

W cr [J/m2]

[MPa]

t pc [ls]

dpc [mm]

W pc [J/m2]

Matrix A 2%

187 (±11)

12.7 (±0.3)

95 (±5)

0.005 (±0.002)

48.5 (±16.9)

13.5 (±1.2)

266 (±25)

0.151 (±0.012)

1855 (±304)

Matrix A 3.25%

186 (±12)

13.6 (±0.3)

117 (±23)

0.009 (±0.005)

100.2 (±64.6)

21.3 (±4.4)

324 (±47)

0.110 (±0.027)

1944 (±467)

Matrix B 2%

172 (21)

11.4 (±1.3)

92 (±2)

0.007 (±0.001)

55.7 (±7.4)

12.2 (±1.0)

232 (±6)

0.122 (±0.009)

1335 (±37)

185 (±5)

13.0 (±1.5)

109 (±17)

0.008 (±0.003)

81.7 (±45.0)

15.1 (±2.6)

240 (±25)

0.096 (±0.011)

1266 (±229)

Material

Matrix B 3.25%

rcr

rpc

targets before and after the notch for local displacement measurement with the optical-electronic displacement transducer. The notch depth ratio was kept constant at 0.20. At least three reliable results were obtained for each mix. To highlight the fibre reinforcement effect, the two matrixes with the same geometry were tested at the same condition of the fibre-reinforced specimens and the results are shown in Table 4. The results on fibre reinforced materials (2.00% and 3.25%) are shown in Table 5, where beside the values measured in the case of matrixes the post-peak behaviour has been described by means of the post-peak stress rpc and the corresponding displacement dpc , and the energy measured as area under the stress versus displacement curve in correspondence with rcr ; W cr , and in correspondence with rpc ; W pc .

The stress versus time curves are presented in Figs. 16 and 17. Figs. 16 and 17 show that both materials (Matrix A and Matrix B) with the two fibre volume contents (2.00% and 3.25%) can be considered as strain hardening materials (for the two matrixes rpr P rcr for both fibre reinforcement percentages). Strain hardening is more visible in the stress versus displacement curves shown in Figs. 18 and 19. In the first 0.3 mm the materials assume an elastic-plastic and/or elastic-plastic with hardening behaviour. Quasi-static tests on specimens with diameter 60 mm have been carried out by means of an electro-mechanics universal machine. These results have been used to evaluate the DIF for the tensile strength. The values obtained were: 1.52 and 1.94 for un-reinforced matrix; 2.60 and 1.72 for the fibre volume content

Fig. 16. Stress versus time curves of notched cylinder specimens Matrix A.

Fig. 17. Stress versus time curves of notched cylinder specimens Matrix B.

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Fig. 18. Stress versus displacement curves of notched cylinder specimens Matrix A.

Fig. 20. Fiber influence on strength.

Fig. 21. Rise time of the incident pulse in the dynamic test on dog-bone-shaped specimen. Fig. 19. Stress versus displacement curves of notched cylinder specimens Matrix B.

of 2.00%, 1.97 and 1.86 for the 3.25% for Matrix A and Matrix B, respectively. It can be noted how the fibre reinforcement does not have a large influence on the DIF of the strength confirming the trend highlighted in [22]. That fibre reinforcement enhances the stress capacity of the material can be seen in Fig. 20 which shows the comparison between the tensile strength as a function of the fibre volume content on dynamic tests at high strain-rate as well as quasi-static tests. 5.3. Un-notched dog-bone-shaped specimens In order to observe the multi-cracking process and to evaluate the feasibility to catch such phenomena as fracture spacing and

strain hardening, 18 dog-bone-shaped specimens have been cast by using two selected mix designs: Matrix A (2.00%) and Matrix B (2.00%). These specimens have extremities of diameter 60 mm, the gauge length being 30 mm in diameter and 40 mm in length as described in Section 3. Five specimens for each materials were tested keeping the pre-load constant in the pretensioned bar as well as in the 60 mm diameter notched specimens testing. In order to obtain an accurate measurement of the linear part of the stress-strain curve the dog-bone-shaped specimen geometry must have: 1. a transverse cross-sectional area of the parts that connect to the incident and transmitted bars which must allow a bonding strength to the SHTB bars much higher than the specimen resistance;

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2. a minimum size, which must be a representative volume of material, for example, a few times the size of the UHPFRC components such as the fibres; 3. a gauge length in a state of homogeneous stress distribution in the presence of stress wave propagation, characteristic of impact testing.

Fig. 22. Comparison between stress versus displacement curves of Matrix A notched and un-notched specimens with fibre content 2.00%.

Fig. 23. Comparison between stress versus displacement curves of Matrix B notched and un-notched specimens with fibre content 2.00%.

To define the specimen geometry satisfying the above points 1., 2., 3., the geometry of the input and output bars of the large SHTB existing at DynaMat Laboratory (which was used for this dynamic testing programme of UHPFRC materials) was taken into account; the input and output bars are aluminium cylindrical bars of 60 mm diameter. The dynamic tension test of the UHPFRC specimens with the SHTB is performed by bonding the specimens to the input and output bars of 60 mm diameter by means of a bicomponent adhesive. In the case of UHPFRC materials its ultimate tensile strength can be hypothesised to be two-three times the quasi-static value, reaching then a value of about 30 MPa; this value of stress cannot be sustained by adhesives meaning that we cannot use a UHPFRC specimen of the gauge length of the same cross-section area as the input and output bars. Therefore it has been hypothesised that use of a specimen having a crosssectional area for the gauge length that is smaller than that of the bars must be used in order to bring the UHPFRC specimen ultimate resistance load to a value less than the bonding strength of the specimen to the bars. The cross-section area of the specimen gauge length is about 4 times smaller than the cross-section area of the bars so that the adhesive is submitted to a stress of about 7.5 MPa in corresponding

Fig. 24. Stress versus time curve with indication of the photos.

Table 6 Material properties of dog-bone-shaped specimens on UHPFRC with 2% fiber reinforcing at high strain-rate regime.

r_ [GPa/s]

[MPa]

t cr [%][ls]

dcr [mm]

W cr [J/m2]

[MPa]

tpc [ls]

dpc [mm]

W pc [J/m2]

Matrix A 2%

328 (±8)

22.2 (±2.8)

81 (±6)

0.011 (±0.002)

189.8 (±55.7)

15.1 (±2.5)

250 (±25)

0.227 (±0.049)

2831 (±581)

Matrix B 2%

335 (±12)

18.9 (±1.0)

73 (±3)

0.008 (±0.001)

119.4 (±16.4)

15.9 (±1.4)

256 (±59)

0.244 (±0.112)

3410 (±1622)

Material

rcr

rpc

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to the ultimate tensile dynamic strength of 30 MPa of a UHPFRC specimen; an adhesive strength of 7.5 MPa is an attainable value using the best commercial adhesives so that the dog-boneshaped specimen satisfies the requirement of the point 1 above. The size of the dog-bone-shaped specimen also allows the accommodation of fibre sizes used in practical applications, thus satisfying the requirement of the point 2 above. As described before the requirement of the point 3 above, concerning the homogeneous stress and strain distribution along the specimen gauge length, can be achieved by means of about 8 propagations inside the specimen of the stress waves reflected at the specimen-bars interfaces. Considering that the distance between the specimen-bars interfaces is 160 mm, that the gauge length is 40 mm and the propagation speed of the stress wave is about 4 km/s then the time needed by the stress wave to travel eight times between the interfaces of the gauge length is about 80 ls; therefore for the accurate measurement of the elastic limit with the MHB at a constant elastic strain rate the generation of a linear increasing loading pulse is needed having a rise time not shorter than 100 ls. By observing Fig. 21 it is possible to note that the linear increasing loading pulse has a rise time of 220 ls which is enough to obtain such a homogeneous distribution of strain.

The results for dog-bone-shaped specimen are collected in Table 6. 5.3.1. Multi-cracking process Multi-cracking is a failure process that occurs after the first peak as is well shown in Figs. 24 and 25. The high fibre content permits an increasing the loading capacity after the first stress-peak. In the case of the dog-bone-shaped specimen with 2.00% fibre volume content the first stress peak is higher than the post-peak stress (47% and 18% for matrix A and B, respectively). Pictures of the crack spacing are shown in Figs. 26 and 27 for matrixes A and B, respectively. The crack spacing seems to be proportional to the fibre length. Comparing the behaviour of notched specimens and dog-boneshaped specimens it is possible to observe in Figs. 22 and 23 how the notch influences the data dispersion and the first peak. It is necessary to remark that the stress rates are not exactly the same, in fact for the dog-bone-shaped specimens they are 328 GPa/s and 335 GPa/s while for the notched specimens they are 187 GPa/s and 172 GPa/s for matrix A and matrix B, respectively. Another problem is the different geometry, as the cross-section is around 48 mm in diameter for the notched specimen and 30 mm for the un-notched

Fig. 25. Photo sequence indicated in Fig. 24.

Fig. 26. Multi-cracking distribution on dog-bone-shaped specimen Matrix A with 2% fiber-reinforcement.

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Fig. 27. Multi-cracking distribution on dog-bone-shaped specimen Matrix B with 2% fiber-reinforcement.

specimens. This comparison is useful in order to observe the different behaviour of these fibre-reinforced materials in the presence of a unique crack respect to the presence of multi-cracking process.

Declaration of Competing Interest None Acknowledgements

6. Conclusions In this study the dynamic response of UHPFRC mixes under direct tension was experimentally investigated. Three different types of specimen were used to analyse the strain rate sensitivity of three matrixes (notched cylinders having H = D=20 mm), the effect of two fibre volume fraction contents (notched cylinders having H = D=60 mm) and the multi-cracking process (unnotched dog-bone-shaped specimens). The strain rate sensitivity of three different matrix was analysed for a wide range of strain rates by means of a Hydro-Pneumatic Machine and a Split Hopkinson Tensile Bar. By using the same initial condition in terms of pre-loading and input stress rate, two fibre volume contents were evaluated using cylindrical notched specimens. The comparison was carried out in terms of stress versus time and stress versus displacement curves. Based on the results of this experimental campaign on the dynamic direct tensile behaviour of UHPFRCs, the following conclusions can drawn:
The three matrixes showed in direct tension a significant sensitivity to the strain rate providing higher strength at higher regimes of stress rate.
The results for fibre reinforced UHPFRC highlighted strainhardening behaviour in dynamics. The observed hardening behaviour of these UHPFRC products is crucial for their outstanding energy dissipation.
In the case of un-notched specimen a higher first peak occurs before the multi-cracking process is developed.
The notched specimens showed a more uniform post-peak behaviour, contrarily to the un-notched ones where the dispersion is quite high depending on how the cracks are positioned and the fibres are distributed.
Matrix A showed higher strain-hardening capacities with respect to Matrix B, despite it having poorer mechanical characteristics.
The post-peak behaviour seems not to be strain rate sensitive with these fibre volume contents.
The use of dog-bone-shaped specimens has demonstrated the capability of such experimental techniques to catch the multicracking process and measuring the spacing of the cracks. These data will be the basis for the analysis of the results of further testing campaign that will be carried out on several Ductal classes. Future research will be addressed to continue to analyse the behaviour of un-notched specimen with higher fibre volume contents, and to use these results to calibrate different material models.

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