Behavior of steel fiber–reinforced high-strength concrete at medium strain rate

Abstract

Impact compression experiments for the steel fiber–reinforced high-strength concrete (SFRHSC) at medium strain rate were conducted using the split Hopkinson press bar (SHPB) testing method. The volume fractions of steel fibers of SFRHSC were between 0 and 3%. The experimental results showed that, when the strain rate increased from threshold value to 90 s^-1, the maximum stress of SFRHSC increased about 30%, the elastic modulus of SFRHSC increased about 50%, and the increase in the peak strain of SFRHSC was 2-3 times of that in the matrix specimen. The strength and toughness of the matrix were improved remarkably because of the superposition effect of the aggregate high-strength matrix and steel fiber high-strength matrix. As a result, under impact loading, cracks developed in the SFRHSC specimen, but the overall shape of the specimen remained virtually unchanged. However, under similar impact loading, the matrix specimens were almost broken into small pieces.

Keywords

steel fiber–reinforced high-strength concrete (SFRHSC) / high strain rates / split Hopkinson press bar (SHPB) / strain rate hardening effects

Introduction

The use of high-strength concrete (HSC) is becoming more common; however, the higher the strength of HSC, the higher the material brittleness. Therefore, it is important to enhance the ductility of HSC, and one possible direction is to use a steel fiber–reinforced kind, called steel fiber–reinforced high-strength concrete (SFRHSC). The static behavior of SFRHSC has been studied more, while its dynamic behavior has been studied less. The latter is very important for proper design and analysis of structures to ensure that they can resist dynamic loads such as earthquakes, accidental impact, or explosions. The early experimental data on concrete under impact loading were almost obtained with a pendulum test and drop-weight tests [1]; however, there are more gaps among different results [2-6]. Of course, one of the factors is the heterogeneous nature of concrete, but the main reason is the possible imprecision of the loading and measuring devices.

Another kind of equipment for performing impact experiments is the split Hopkinson press bar (SHPB), which offers more accurate measurement of materials’ behavior under impact loading. The technique is based on the theory of one-dimensional wave propagation in an elastic bar. The split-bar configuration was developed by Kolsky [7] following the original introduction by Hopkinson [8] and a comprehensive study by Davies [9]. The early small-diameter SHPB (e.g., 10 mm) is commonly used for testing metal or macromolecule polymers, and the large-diameter SHPB (diameter larger than 30 mm) has become more and more popular for the study of the dynamic behavior of concrete since the 1980s [10-13].

In this paper, the high-velocity impact test on SFRHSC was conducted using the SHPB experimental technique. Three series of SFRHSC were used: C100V₀, C100V₂, C100V₃, with a steel fiber volume fraction (V_f) of 0, 2%, and 3%, respectively. The primary objective of this study is to enhance the understanding of the response of SFRHSC to high strain rate impact. The expected results of the study are the determination of dynamic material properties and failure mechanisms of SFRHSC.

Test method

Constituent material

Graded 525 Ordinary Portland Cement supplied by Jiangnan Cement Factory, Nanjing, China, was used, complying with Chinese Standard GB175-92, similar to ASTM C150 type II cement.

Graded I fly ash and silicon ash were used for mineral admixtures to replace partial cement. The former was supplied by Zhenjing Kedian Fly Ash Development Co., Ltd., Jiangsu Province, China, and the later was supplied by Zunyi Iron Alloy Factory, Guizhou Province, China,. The quantity of reactive SiO₂ and the specific area of the silica fume are 94.48% and 24 m²/g, respectively.

Paddle-end steel fiber 30 mm in length and 0.6 mm in diameter was supplied by Ganzhou Lifa Metalwork Co., Ltd., of Jiangxi Province, China, and the fiber length (l_f), diameter (d_f), and aspect ratio (l_f/d_f) were 20 mm, 0.5 mm, and 40, respectively.

The fine aggregate used was river sand with a fineness modulus of 2.8.

The coarse aggregate used was basaltic macadam, with a continuous grading (5-10 mm) and a maximum size of 10 mm.

The water used was drinking-water, wih a pH value of 7.

A naphthalene high-quality water-reducing additive called “JM-B” was supplied by the Institute of Jiangsu Construction Science and Technology, China.

Mixture proportions

The mix proportions and static compressive strengths for the materials used in these experiments are presented in Table 1. C100V₀, C100V₂, and C100V₃ denote that the V_f of SFRHSC is 0, 2%, and 3% respectively. The specimens for impact testing were 35 mm in diameter and 70 mm in length, and 24 specimens were cast for each mixture proportion. In the preparation of the specimen, care was taken to ensure that the two faces were parallel. The cross sections of the concrete specimen are shown in Fig. 1.

Test apparatus

A 74-mm-diameter SHPB was used for this program, and the setup is outlined in Fig. 2. The SHPB consists of four basic parts: a striker bar (projectile), input bar, output bar, and a short specimen, which is placed between the input and output bar. The projectile from the gas gun is forced under pressure out of a barrel impinging on the input bar, and the impact at the free end of the input bar develops a compressive longitudinal incident wave ϵ_i(t). Once this wave reaches the interface of the input bar and specimen, a part of it, ϵ_r(t), is reflected, whereas another part goes through the specimen and develops in the output bar the transmitted wave ϵ_t(t). These three waves are recorded by strain gauges attached at the middle of the input and output bars. There are two fundamental postulates for the SHPB test: 1) one-dimensional elastic stress wave theory is valid in pressure bars; 2) stress and strain states within the specimen are uniaxial and uniform. Based on these assumptions, the stress, strain, and strain rate of the specimen in the SHPB can be represented respectively as

\sigma (t)=(A_e{E}_e/2A_s)[{ϵ}_i(t)+{ϵ}_r(t)+{ϵ}_t(t)],

ϵ(t)=(C_{\mathrm{e}}/L_{\mathrm{s}}){\displaystyle {\int }_{\mathrm{0}}^t[{ϵ}_{\mathrm{i}}(t)-{ϵ}_{\mathrm{r}}(t)-{ϵ}_{\mathrm{t}}(t)]\mathrm{d}t,}

\dot{ϵ}=(C_{\mathrm{e}}/L_{\mathrm{s}})[{ϵ}_{\mathrm{i}}(t)-{ϵ}_{\mathrm{r}}(t)-{ϵ}_{\mathrm{t}}(t)],

where E_e, C_e, and A_e are the elastic modulus, longitudinal wave velocity, and cross-sectional area of the input or output bars, respectively. A_s and L_s are the cross-sectional area and length of the specimen, respectively. Compressive strain is taken as positive. From the above information, the dynamic stress-strain relationship for a specific strain rate may be ascertained.

An absorbing bar was positioned at the far end and in contact with the output bar during the test. This served to absorb the stress wave that travels along the output bar, thus avoiding reflection back into the output bar. A buffer was mounted on the platform to attenuate the impact of the absorbing bar.

A pair of laser beams was used to measure the velocity of projectile. The velocity of projectile is raised when the pressure of gas increases; thus, the strain rate of the specimen increases. However, the velocities of the projectile are slightly different at the same gas pressure, and the strain rate of the specimen may not be a specified value and only is controlled to a range at about the specified value.

Results and discussion

The dynamic stress-strain curves of SFRHSC are presented in Fig. 3. The values of strain rate, dynamic compressive strength, and peak strain of SFRHSC are shown in Table 2. Fig. 4 shows the photo of specimens after failure at a strain rate of about 70 s^-1.

Effect of strain rate on dynamic behavior of SFRHSC

The experimental results show that the strain rate of 40-42 s^-1 is a threshold value, and when the strain rate is lower than the threshold value, the dynamic compressive strengths of SFRHSC are lower than their static compressive strengths and slowly increase with the increase of the strain rate; SFRHSC exhibits a significant strength increase when the strain rate is higher than the threshold value. That is to say, SFRHSCs are rate-sensitive materials, and the critical strain rate is about 40-42 s^-1.

The strain rate hardening effect can be explained as follows:

First, concrete fractures and disintegrates due to the development of micro-cracks inside the specimen once the stress reaches fracture strength, and the crack opening energy is much more than that of the crack extension. The higher the impact velocity, the more the crack opening, and the more kinetic energy is absorbed. The failure strength of concrete then increases.

Second, the lateral confinement causes the dynamic strength enhancement of concrete with an increase in strain rate. The lateral confinement comes from both the contact surface restriction and the lateral inertia during the rapid compression. The stress response of concrete is hydrostatic stress dependent, and the compressive strength of concrete can be largely enhanced by the lateral confinement [14].

In additional, similar to Brace [15], Janach [16] and Glenn [17] interpreted the strain rate effect on rocks. The increase in the dynamic compressive strength of concrete may come from a result of the transition from a uniaxial stress state to a uniaxial strain state. In the SHPB test, the stress state in the concrete specimen is not entirely uniaxial, especially at a high strain rate. The radial strain is confined strongly, as if the material were in three-dimensionnal compression, and therefore, the compressive strength increases.

Effect of steel fiber on dynamic behavior of SFRHSC

As in a static or quasi-static state, steel fiber also played an important role in strengthening and toughening of SFRHSC at a high strain rate. As shown in Fig. 5, when the strain rates increase from about 40 s^-1 to 90-95 s^-1, the compressive strength for three series of concrete rise, and the magnitude of the rise is in the order C100V₃>C100V₂>C100V₀, which illustrates that the strain rate hardening effect becomes stronger with the incorporation of steel fibers. SFRHSC exhibits relatively excellent ductility at a high strain rate. As shown in Fig. 3, the descending portions of the stress-strain curves of the SFRHSC are much flatter than those of the matrix concrete. According to Fig. 6, it is observed that a sharp increase in the area enclosed by stress-strain curves of SFRHSC, and the higher V_f, the quicker the areas increase, which indicates that the SFRHSC has a great ability to absorb kinetic energy. During the very transient impact event, the initiation and propagation of cracks in the SFRHSC specimen were restrained by the steel fibers, causing higher compressive strength and toughness of the material.

Failure pattern of SFRHSC specimen at a high strain rate

The experimental results show that the SFRHSC specimen is damaged relatively slightly in contrast to a matrix concrete specimen at the same or approximate strain rate (>40 s^-1). Three series of concrete specimens after failure at a strain rate of about 70 s^-1 are shown in Fig. 4. The matrix concrete specimen is crushed up completely, but the SFRHSC specimens remain their integrity. These failure patterns of SFRHSC can be taken as the strengthening and toughening caused by steel fibers. On the other hand, the failure patterns can be interpreted at the point of stress wave. The tension strength of concrete is much lower than its compressive strength, and in the SHPB test, the stress wave is reflected as tension at the lateral portion of the specimen, which causes the tension damage of the concrete specimen. As for the SFRHSCs, their randomly distributed short fibers form networks to a certain extent, which could withstand tension damage. As a result, the destruction of the SFRHSC specimen is much slighter than that of the matrix concrete specimen at the same or approximate strain rate.

Conclusions

1) SFRHSC is a rate-sensitive material, and the critical strain rate is about 40-42 s^-1. When the strain rate is lower than the critical strain rate, the dynamic compressive strength of SFRHSC is lower than its static compressive strength and increases slowly with an increase in strain rate, and SFRHSC exhibits a significant strain rate hardening effect, that is, the strength increases after the strain rate becomes higher than the critical strain rate.

2) Steel fibers play an important role in the strengthening and toughening of SFRHSC at a high strain rate. The strain rate hardening effect becomes stronger with the incorporation of steel fibers, and the magnitude of the compressive strength rise is in the order C100V₃>C100V₂>C100V₀ when the strain rates increase from about 40 s^-1 to 90-95 s^-1. SFRHSC exhibits relatively excellent ductility at a high strain rate, the descending portions of the stress-strain curves of the SFRHSC are much flatter than those of matrix concrete, and the areas enclosed by stress-strain curves of SFRHSC increase more sharply than those of matrix concrete increase. The higher V_f, the quicker the areas increase.

3) SFRHSC exhibits excellent failure patterns at a high strain rate, and the SFRHSC specimen is damaged relatively slightly in contrast to a matrix concrete specimen at the same or the approximate strain rate (>40 s^-1). The SFRHSC specimen retains its integrity at the strain rate at which the matrix concrete specimens are crushed up completely.

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