MECHANICAL BEHAVIOUR OF A ULTRA-HIGH PERFORMANCE FIBRE REINFORCED CEMENT COMPOSITE SUBMITTED TO IMPACT LOADING CONDITIONS

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1 MECHANICAL BEHAVIOUR OF A ULTRA-HIGH PERFORMANCE FIBRE REINFORCED CEMENT COMPOSITE SUBMITTED TO IMPACT LOADING CONDITIONS Pierre Rossi and Edouard Parant Laboratoire Central des Ponts et Chaussées, Paris, France Abstract The multi-scales fibre reinforcement of this cement composite is characterized by the gradual and continuous activation of the various fibres scales until the peak strength. The studied material can be modelled as an elasto-plastic one with positive work hardening in tension. In order to cover a large range of loading rate, two dynamic tests are carried out using two four points bending test device on thin slabs: an hydraulic press and a block bar device. Results indicates that the modulus of rupture increases by 25 percent in the range of quasi-static loading rate [1.25x GPa/s], and that strength is quadrupled for loading rate superior to 500 GPa/s. Results indicate that this new material is more sensitive to the loading rate effects than all others cement materials. The direct tensile strength increases by about 1.5 MPa/log 10 unit under quasi-static loading. Keywords: cement composite, impact; multiscale fibre reinforcement; stress rate effects, ultra-high performance, steel fibres. 1. INTRODUCTION For a few years, the Laboratoire Central des Ponts et Chaussées (LCPC) has worked on the development of new cement composites. These materials are the direct implementation of the "Multi-Scale Fibre Reinforcement Concept" developed by Rossi [1], [2]. The idea is to mix short fibres with longer fibres in order to intervene at the same time on the material scale (increase of the tensile strength) and on the structure scale (increase

2 of the bearing capacity and the ductility). A Multi-Scale Fibre Reinforced Cement Composite (MSFRCC) is then obtained called CEMTEC multiscale. This MSFRCC contains 11% per volume of fibres. Three dimensions of steel fibre have been chosen. The present paper is on an experimental research related to this MSFRCC behaviour under different loading rates. 2. EXPERIMENTAL PROGRAM This article deals with the bending behaviour under different deflection rates of a representative structural element of slab. Two different testing devices are used. By this way, it is possible to cover a large range of stress rate. These two experimental procedures are: - On one hand, the quasi-static bending tests are performed using a conventional press, equipped with a servo control (1.25x10-4 to 1.35 GPa/s). - On the other hand, the bending tests are performed using a block bar device for loadings much faster (50 to 700 GPa/s). 3. MATERIAL MIX DESIGN AND EXPERIMENTAL SET-UP 3.1 Mix design The studied composite is distinguished from the other high-performance fibre reinforced cement composite (HPFRCC) by a very high strength (more than 20 MPa) and a strain hardening behaviour in uniaxial tension. This result is the combination of two factors: first, a very high performance matrix (i-e, very compact) and secondly, a strongly proportioned multi-scale fibre reinforcement (11 % of steel fibres). The composition of LCPC-MSFRCC is given in Table 1. Table 1: Mix design for MSFRCC Raw Materials OPC Sand Silica Fume Superplastizer Total Water Proportioning Mixing kg/m kg/m kg/m 3 44 kg/m kg/m 3 Steel Fiber Silica fume/cement Sand/Cement Total Water/Binder 858 kg/m 3 0,255 Superplat/Binder 1,02 % 0.49 Density

3 3.2 Specimens casting and dimensions Concerning the casting, the specimens are cast flat in three successive layers and are vibrated during the casting on a mobile plate. For the experimental setting, specimens have a 600 mm length, a 200 mm width and a 40 mm thickness. The maximum fibre length of the material being 20 mm (twisted steel fibre), the 200 mm width of the specimen allows an orthotropic orientation of the fibres. These specimen dimensions make them representative of those existing in a structural element like slab. The specimens were placed in a drying oven at 90 c during 4 days, 48 hours after their release from the mould. Finally, for each specimen, the upper face was dressed to obtain a constant thickness and inertia. 3.3 Quasi-static test Tests are carried out at three imposed displacement rate of the jack. During these bending tests, the distance between the lower supports is 420 mm and, between the higher supports is 140 mm. One used a special extensometer to measure the net deflection of the neutral axis in the direction of load application [3]; placed on the specimens, it is designed to eliminate parasitic displacements of the specimen supports due to concrete crushing. A second linear variable displacement transducer (LVDT) is placed parallel to the bottom face, on the level of the tended fibre, in the zone of constant moment. It is used to measure the maximal tensile strain. Because of the limited flow rate of the hydraulic pump, we test three deflection rates equal to: - v S = 3.3 x 10-3 mm.s -1, jack displacement rate relative to a quasi-static test, - v M = 3.3 x 10-1 mm.s -1, middle jack displacement rate, - v H = 3.34 x 10 1 mm.s -1, maximum jack displacement rate. 3.4 Impact test For higher loading rates, we use a block-bar device designed and developed by the Laboratoire Mécanique Matériaux Structures of Lyon University (L2MS-France) [4]. This equipment looks like the Hopkinson bars; the measurement of the efforts going through the thin slab is given by a measuring bar (called outgoing bar) instrumented with strain-gauges bridge suitably laid out. Loading is carried out directly by an impactor (no entering bars); the wave propagation cannot thus be represented any more by a compressive plane wave train. The stress and strain stated in the specimen are very heterogeneous during the test. But the goal of this study is only to calculate the modulus of rupture of each thin slab tested. A bending device, created for this study, was intercalated between the measuring bar and the impactor. It is composed of two trimmers, which reproduce the experimental conditions of the quasi-static test (even spacing between lower and higher supports). The general diagram is pointed out in figure Measuring set-up The block-bar device is instrumented to measure the following information:

4 - The load supported by specimen (using measurements of the strain-gauges bridge glued onto the outgoing bar). - The deflection at midspan with a transducer connected to a conditioner. - The speed of the projectile at the impact time, by using an optical measurement. All signals are collected by differential amplifiers and sampled at the rate of 20 khz. They are synchronized: the projectile gives the "signal", when it passes in front of the optical measurement. That starts the measurement. 3.6 Loading rate In this study, our interest is to test several loading rates. For that,. Three kinds of contact were used: either steel against steel contact, or an absorber-absorber contact, or a steel-absorber contact. It is thus possible to reduce by thirty the stress rate. Figure 1: Impact test machine - general view and schema of the four points bending device placed between projectile and measuring bar. 4. EXPERIMENTAL RESULTS 4.1 Loading rate measurements The quasi-static tests are performed at imposed displacement rate of jack; the required variable is either a strain speed, or a stress speed. Since it is delicate to estimate

5 the strains increase in constant moment zone on the block-bar device, the loading rate is used for the analysis of quasi-static and dynamic tests. For quasi-static tests, the setting is controlled perfectly. One decides to calculate the loading rates on the linear part of the equivalent tensile stress-time curve, a domain where the specimen behaviour is pseudo-elastic. Furthermore, the loading rate decreases slowly. A checking for each test makes possible to control the good agreement between estimated and measured loading rate. These values are given below: - v S = 1.25 x 10-4 GPa/s, loading rate relative to quasi-static test, - v M = 1.25 x 10-2 GPa/s, intermediate loading rate, - v H = 1.35 x 10 0 GPa/s, maximum loading rate. The loading rate measurements are more difficult for the tests performed with the block-bars device. Indeed, according to the choice done on the values for the beginning and the end of the loading ramp, the loading rate can vary in a ratio of three for the same test (the duration of loading varies between 500 µs and 2 ms). So, the loading rate is estimated from a linear regression (method of least squares), rather than other methods. The loading rates vary thus between 50 and 700 GPa/s for all tests with the block-bar device. 4.2 Quasi-static test results For each speed range v L, v M and v H, nine thin slabs, which were fabricated with the MSFRCC, are tested. Figure 2 presents the characteristic curves (which integrate dispersion) relative to the composite for each loading rate. The characteristic curves are obtained using a method developed in a precedent study [5]. Increases of strength with the loading rate is presented in figure 3 and expressed as uniaxial tensile stress. It is determined by a back-analysis approach using elasto-plastic models for MSFRCC behaviour. We can make the following reports: - The average modulus of rupture of the MSFRCC and the corresponding strain increase with the jack displacement rate, as attempt. - The scattering on the equivalent tensile stress-strain curves relating to MSFRCC decreases when the displacement rate increase. The C.O.V. starts at 15.5 percent for the lower loading rate, v L and falls to 3.7 percent for the maximum loading rate, v H. The reports thus made, one can propose the following comments: - The loading rate effects in the domain of quasi-static speed, i.e. without the inertial phenomena, leads to a mechanical homogenisation of the MSFRCC. - Since the strain corresponding to the modulus of rupture increases with the loading rate, that implicates that the loading rate improves creation of cracks, as shown figure 4, and in consequence the ductility of the composite.

6 From the figure 3, it is interesting to determine the analytical expressions connecting the strength to stress rate for the quasi-static domain, by using a back-analysis approach. Indeed, only this domain corresponds to an intrinsic material behaviour [6]. The following relations are obtained: These relation is a line with slope equal to 1.5 MPa/u.log 10. It should be mentioned that this slope, which characterizes the sensitivity to the stress rate effects, is much higher than what is known in the literature for other cementitious materials. For cementitious matrix, including ultra high performance matrix, the slope is equal to 0,7 MPa/u.log [7], whereas for the HPFRCC such as the DUCTAL, the slope is equal to 0,8 MPa/u.log 10 [8], [9]. This very great sensitivity to the stress rate effects of this MSFRCC can be related only to the presence of fibres, and more precisely to the very many matrix-fibre interfaces. 80 Equivalent tensile stress [MPa] V L, caract V H, caract V M, caract Strain [x 10-3 ] Figure 2: Equivalent tensile stress-strain characteristic curves - three quasi-static impact velocity v L, v M, v H on MSFRCC.

7 35 Uniaxial tensile stress [MPa] E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 Stress rate [GPa/s] Figure 3: Stress rate sensitivity plots for MSFRCC (a) (b) Figure 4: Visible crack patterns for quasi-static and dynamic stress rates - a) speed 1.35 GPa/s - b) speed 500 GPa/s.

8 4.3 Impact test results The modulus of rupture is calculated arbitrarily according to the assumptions of strength of materials starting from the maximum force obtained during the test. In figure 5 are gathered the results relating to the two different experimental devices. These are explained in term of modulus of rupture for each stress rate. 250 Modulus of Rupture [MPa] DOMAIN 1 DOMAIN 2 0 1E-5 1E-3 1E-1 1E+1 1E+3 Stress rate [GPa/s] Figure 5: Stress rate sensitivity plots for MSFRCC - Modulus of rupture-stress rate for the whole range of impact velocity: 1.25x GPa/s. 5. CONCLUSIONS In this article is presented an experimental study relative to the stress rate dependence of mechanical behaviour of a multi-scale fibre reinforced cement composite. The range of loading rate studied goes from the domain of quasi-static tests (stress rate between 1.25x10-4 to 1.35 GPa/s), to the domain of dynamic tests (stress rate between 50 and 700 GPa/s). It appears that the studied MSFRCC is very sensitive to the stress rate effects, much more than all other known cementitious materials. Thus, the slope of the linear relation, which connects it uniaxial tensile strength to the stress rate is equal to 1.5 MPa/u.log, whereas for other cementitious materials, this slope is at the maximum 0.8 MPa/u.log. This stress rate effect also induces: - A mechanical homogenisation of the material properties. The dispersion on the modulus of rupture decreases with the stress rate, - A light increase of the Young modulus with the stress rate,

9 - An increase of the material ductility as long as the stress rate does not introduce inertial effects; and a reduction in this ductility for dynamic tests which generates important inertial forces within material. REFERENCES [1] Rossi, P., Acker, P., and Malier, Y., "Effect of steel fibres at two stages: the material and the structure". Materials and Structures, 20, (1987). [2] Rossi, P., "High performance multi-modal fibre reinforced cement composite (HPMFRCC): the LCPC experience," ACI Materials Journal,, 94 (6), (1997). [3] Boulay, C. and Colson, A., "A concrete extensometer eliminating the influence of transverse strains on the measurement of longitudinal strains", Materials and Structure, 14, (1981). [4] Jacquelin, E. and Hamelin, P., "Block-bar device for energy absorption analysis". Mechanical System and Signal Processing, 15 (3), (2001). [5] Rossi, P., Arca, A., Parant, E., Fakhri, P. "Bending and compressive behaviours of a new cement composite". Cement and Concrete Research, 35, (2005). [6] Rossi, P., "Strain rate effects in concrete structures: the LCPC experience". Materials and Structures, hors série, (1997). [7] Toutlemonde, F. and Rossi, P.,. "Are high performance concretes (HPC) suitable in case of high-rate dynamic loading?, proceedings of the 4 th Int. Symp. on the utilization of high strength / high performance concretes, BHP'96, F. de Larrard & R. Lacroix eds, LCPC- Presses de l'enpc, Paris, may 1996, (1996). [8] Toutlemonde, F. and Rossi, P., (1999). Discussion about article 95-M73 / in n November- December 1998 ACI Materials Journal, p. 735 "Review of strain rate effects for concrete in tension", by L.J. Malvar & C.A. Ross, published in ACI Materials Journal, 1999, 96 (5), (sept.- oct.). [9] Toutlemonde, F., Boulay, C., Sercombe, J., Le Maou, F., Renwez, S. and Adeline, R.. "Characterisation of Reactive Powder Concrete (RPC) in direct tension at medium to high loading rates", CONcrete under Severe Conditions II, CONSEC 98, TromsØ, Norway (1998).