Experimental Study on Tensile Behavior of Cement Paste, Mortar and Concrete under High Strain Rates

Transcription

1 1268 Vol.30 No.6 CHEN Xudong et al: Experimental Study on Tensile Behavior of Cement... DOI /s Experimental Study on Tensile Behavior of Cement Paste, Mortar and Concrete under High Strain Rates CHEN Xudong, SHAO Yu, XU Lingyu, CHEN Chen (College of Civil and Transportation Engineering, Hohai University, Nanjing , China) Abstract: Effects of the strain rate on cement paste, mortar and concrete were studied. A modified SHPB testing technique with flattened Brazilian disc (FBD) specimen was developed to measure the dynamic tensile stress-strain curve of materials. A pulse-shaped split Hopkinson pressure bar (SHPB) was employed to determine the dynamic tensile mechanical responses and failure behavior of materials under valid dynamic testing conditions. Quasi-static experiments were conducted to study material strain rate sensitivity. Strain rate sensitivity of the materials was measured in terms of the stress-strain curve, elastic modulus, tensile strength and critical strain at peak stress. Empirical relations between dynamic increase factor (DIF) and the material properties were derived and presented. Key words: tensile behavior; cement-based materials; experimental study; split Hopkinson pressure bar 1 Introduction Shelters used by the military to protect personnel and equipment from conventional weaponry attacks are typically constructed of massive slabs. Therefore, the investigation of concrete s response to highamplitude, short duration, impulse loads is an important consideration in protective construction design and analysis [1]. To model the response in the laboratory requires that the environment must reflect the type of confinement, magnitude of stress change, and the time scale of loading anticipated in the field [2]. The Split Hopkinson Pressure Bar (SHPB) technique [3] can produce the required environments in the laboratory. During the past several years researchers have demonstrated that the SHPB technique can determine the dynamic, high stress and strain rate of concrete [4]. Although the conditions of the experiment have Wuhan University of Technology and SpringerVerlag Berlin Heidelberg 2015 (Received: Sep. 20, 2014; Accepted: Nov. 18, 2014) CHEN Xudong( 陈徐东 ):Ph D; cxdong1985@hotmail. com Funded by the National Natural Science Foundation of China (No ) and the Natural Science Foundation of Jiangsu Province (No. BK ) been restrictive (eg, conditions of uniaxial strain), this technique has significantly extended the stress and strain rate regimes over which dynamic material properties can be investigated. Because of experimental difficulties in direct tensile tests, indirect methods are used as convenient alternatives to measure the tensile strength of concrete [5,6]. These include, for example, the Brazilian disc test [7], the four points bending tests [8], and the three points bending test [9]. These indirect methods are much easier and less extensive in experimentation than direct methods, and they have thus been widely used in laboratory experiments. Among these indirect methods, because of convenient specimen preparation and experimental implementation, the Brazilian disc test is the most popular for tensile strength in civil engineering. The Brazilian disc test has also been extended to dynamic tensile strengths for concrete and rocks [10-14], by the use of the split Hopkinson pressure bar (SHPB). The primary objective of this research was to enhance the understanding of the response of cement paste, mortar and concrete to high strain rates loading. The anticipated results of the study are determination of dynamic material properties, failure mechanisms, and crack patterns for failure in tension.

2 Journal of Wuhan University of Technology-Mater. Sci. Ed. Dec Experimental 2.1 Materials and sample preparation ASTM type I cement was used in the production of paste, mortar and concrete specimens. A common water-cement ratio of 0.45 was used for cement paste. For mortar, the fine aggregate was river sand consisting mainly of quartz, with 10 percent feldspar. The gradation test showed that the particle size of the sand was continuously distributed within the range of mm with 80% of sand. The water-cement ratio of 0.45 was also used for cement mortar. The concrete was mixed in the proportion of 1:2:4 (cement: sand: coarse aggregate) by weight with a water-cement ratio of 0.45, using gravel of 9 mm maximum size. The standard specimens were cast in steel molds with dimensions of 150 mm 150 mm 550 mm. Following casting, the specimens were covered with a plastic membrane to prevent the moisture from evaporating. The specimens were de-moulded after 24 h, and then moist-cured in a water tank. After curing for 90 days, the specimens were cored from the standard specimens. The geometry of a flattered Brazilian disc (FBD) specimen was used in this investigation, with radius D=74 mm, thickness of t=30 mm, and loading angle of 2a=20 o. 2.2 Quasi-static Brazilian test The Quasi-static Brazilian test was carried out in a conventional testing machine. This measurement was used as a control variable, with a monotonic increase of 10-5 s -1 ; it was fitted to reach the maximum load of a time from 2 to 3 min. During the test, the applied load and the strain were recorded continuously at a rate of 3 data per second. The stress at the center of the specimen is given by [15] : (1) where, Y is the non-dimensional stress, which is related to the loading angle; and P is the applied load (kn). When 2a=0, Y=1. This case corresponds to the original Brazilian disc. For a given value of 2a, Y can be calibrated through finite-element analysis [15]. In our case 2a=20 o, and Y was calibrated to be Fig.1 shows the stress-strain behavior of cement paste, mortar and concrete under quasi-static loading. 2.3 Split Hopkinson pressure bar (SHPB) The conventional SHBP analysis is based on the mechanics of the longitudinal elastic wave propagation in cylindrical bars. According to the theory of the elastic wave propagation, stress and particle velocity of a longitudinal stress wave can be accurately determined from the associated strain measured by strain gauges. Furthermore, it is assumed that these quantities are not only known at the measuring points in the middle of pressure bars but also at any other places in the pressure bars, because signals at one location can be obtained from signals measured at another place according to one-dimensional stress wave theory. Thus, the transmitted wave can be shifted to the output barspecimen interface to obtain the force and velocity, whereas the input force and velocity can be determined via incident and reflected waves shifted to the input barspecimen interface. Forces and velocities at both faces of the sample are then given by the following [16,17] : (2) where, P 1, P 2, V input, and V output are the forces and particle velocities at the interfaces, respectively; S B, E and C 0 are respectively the cross-sectional area, Young s modulus and the longitudinal wave speed in the pressure bars; e i (t), e r (t), and e t (t) are the strain signals at the bar-specimen interface. Signals from the strain gauges were captured by an oscilloscope. A typical set of incident, reflect, and transmitted waves recorded by the oscilloscope is shown in Fig.2. The pulse shaping technique [18-20] (Frew et al 2001; Frew 2002; Lu and Li 2010a) was applied by sticking a pulse shaper on the impact end of the incident bar to prevent the sudden hit by the striker bar. After impact of the striker bar, with the plastic deformation of the pulse shaper, the increase rate of the incident pulses reached its peak value at nearly the same time. In this study, a piece of copper was selected

3 1270 Vol.30 No.6 CHEN Xudong et al: Experimental Study on Tensile Behavior of Cement... end sharply increases with increasing strain rate and reaches failure strength before perforation of the main crack. Thus, damage on the loaded end continually expands, leading to further damage. Finally, a failure surface forms, leading to local damage. and inserted between the striker bar and incident bar to achieve the stress equilibrium in the experiment. The diameter of shaper discs is 1.5 mm and the overall thickness is 0.8 mm. In order to perform the tensile splitting experiments under high strain rate loading, SHPB was used in the Brazilian configuration. In this paper, Eq.(1) is also used for calculating the indirect tensile stress of materials under dynamic loading. A regime of approximately linear variation was observed in the strain over time, the slope of this region is determined from a least-squares fit as strain rate. The corresponding striker velocities are 5, 10, 15, 20, 25, and 30 m/s. 3 Results and discussion 3.1 Failure mode Typical failure patterns of the mortar specimens under different strain rates are shown in Fig.3. The main crack orientation was parallel to the impact direction and axial crack divided the specimen into at least two pieces. There are three kinds of typical failure patterns of concrete specimens under dynamic loading. When the strain rate was low, the specimen broke into two roughly symmetrical halves (Fig.3(a)). As strain rate increased, triangular partial mechanical damage started to appear on the loaded end of the specimen and the damaged area increased with increasing strain rate (Figs.3(b) and 3(c)). This can be explained as follows. In the process of pouring and curing, damage (including tiny voids and cracks) is produced in specimen. When subjected to dynamic loading, owing to the loading condition and the flat form on the loaded end of the specimen, internal damage to the specimen occurs before other damage; this damage expands along the compressed direction and, finally, axial damage perforates and merges, and a main crack forms. In addition, compressive stress applied to the loaded 3.2 Stress-strain behavior The stress-strain curves of cement paste, mortar and concrete under impact velocity of 20 m/s are shown in Fig.3. Results indicate that the mechanical behavior of cement-based materials depends on the strain rate and the stress-strain curves at high strain rates are generally higher than that at lower rates, indicating a stiffening behavior as strain rate increases within these rates.

4 Journal of Wuhan University of Technology-Mater. Sci. Ed. Dec following equations: For cement paste: 3.3 Dynamic increase factor (DIF) (6) For mortar: (7) For concrete: (8) The dynamic increase factor (DIF) was defined as the ratio of the dynamic tensile strength to the corresponding quasi-static tensile strength and was widely adopted to evaluate the strain rate effect of materials[21]. The relationship of DIF of cement paste, mortar and concrete versus strain rates is presented in Fig.4. In this study, it is also found that the DIF of cement paste is larger than that of mortar and concrete. A simple constitutive model was obtained as shown in the following equations: For cement paste: (3) For mortar: 3.5 Critical strain (4) For concrete: (5) 3.4 Elastic modulus The elastic modulus is a parameter to describe the elastic characteristic of cement-based materials. And there are different expressions for elastic modulus. The secant modulus of concrete is generally considered to increase with strain rate [22]. But when referring to the initial modulus, views are different from the researchers. Some think that it increases with strain rate[23], while some contend that slight variations in the initial tangent modulus are observed[20]. In the present paper, the elastic modulus is defined as E=(sb-sa)/(ebea), where a and b correspond to the 40% and 60% of the peak stress, respectively. Fig.5 depicts the elastic modulus of materials at various strain rates. It could be found that the stiffness is almost linearly increased with the strain rate. The relationship between the elastic modulus and strain rate could be fitted with the Critical strain is defined as the strain when the stress reaches the peak. Bischoff and Perry [21] summarized a wide range of concretes of various static strength and strain rate, showing that the significant increases in critical strain were sometimes observed during impact loading, although these increases were generally less than those observed for strength. Fig.6 depicts a tendency that the critical strain increases with the strain rates. From Fig.6 it can be found that the critical strain of cement paste, mortar and concrete are

5 1272 Vol.30 No.6 CHEN Xudong et al: Experimental Study on Tensile Behavior of Cement... in the same regime under dynamic loading. According to Bischoff and Perry [21], the extent of cracking required for failure increases with the strain rate. The increased critical strain may also be explained by the lateral confinement which results in the formation of significant amounts of microcracks, but prevents the formation of macrocracks. The criticals strains of cement paste, mortar and concrete were proposed and that of concrete was defined by the following formula using data regression technique. For cement paste, mortar or concrete: (9) 3.6 Energy dissipation In order to study the change in the mechanical properties of cement paste, mortar and concrete under a dynamic load from an energy perspective, the incident pulse energy W i (t), reflective pulse energy W r (t) and transmitted pulse energy W t (t) can be defined as: can be expressed as: For cement paste: For mortar: For concrete: (16) (17) (18) (10) The average incident pulse energy rate be defined as [24] : (11) (12) can (13) where, T is the incident pulse duration. Based on the principle of energy conservation, the dissipated energies of materials can be obtained from (14) (15) After analysing the characteristics of the dynamic test, it is known that W s (t) was directly related to material damage evolution. Study of the relationship between W smax and can thus effectively reflect the dynamic properties of materials under different loading conditions. As shown in Fig.7, the correlation between W s,max and was obvious; the equations of the curves The correlation relationship reflects the mechanical performance that tensile behavior of cement-based materials enhanced with an increase in incident pulse energy rate. This is consistent with the changing regularities of strength and deformation, and can also confirm the accuracy of the changing rules from another point of view. In addition, for concretelike materials, more attention should be paid to energy absorption capacity because it can be considered as synthetic exhibitor of strength and deformation properties. 4 Conclusions A modified SHPB testing technique with flattened Brazilian disc (FBD) specimen was developed to measure the dynamic tensile stress-strain curve of cement paste, mortar and concrete. A pulse shaping technique was used to achieve dynamic force balance on both ends of the specimen. Test results show that the dynamic tensile strength, elastic modulus, dynamic increase factor (DIF) and critical strain increase with strain rate. Empirical formulae of mechanical properties of cement paste, mortar and concrete with respect to

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