Study on Dynamic Splitting Properties of S-PP Hybrid Fiber Concrete after High Temperatures

Abstract

To study the dynamic tensile mechanical properties of steel polypropylene hybrid fiber reinforced concrete (SP-HFRC) after high temperature, split Hopkinson pressure bar (SHPB) dynamic splitting tests were carried out, and the optimal fiber content combination was obtained. With the plain concrete (PC) as the control, the effects of fiber addition on energy dissipation and failure forms of concrete specimens after high temperatures were analyzed. LS-DYNA software was used to simulate the dynamic splitting test. The results show that the splitting strength of specimens increases first and then deteriorates with the increase of temperature. After high temperatures, HFRC has a positive and negative fiber hybrid effect. Among the studied fiber mixture combinations, S1PP0.2 (1 vol% steel fiber + 0.2 vol% polypropylene fiber) concrete has the best splitting resistance. Compared with PC, the splitting strength increases by 106.8% at 25 °C and 128.2% at 800 °C. From the perspective of energy, we can conclude that adding hybrid fiber can significantly improve the dynamic splitting and tensile toughness of concrete after high temperatures, and defining damage variables can better characterize the damage degree of concrete. PC cracks seriously after high temperatures, while S1PP0.2 concrete cracks but does not disperse at 800 °C, showing ductile failure characteristics. By modifying some parameters of the HJC model, the state of high-temperature concrete mechanical properties can be better characterized after deterioration. The simulated failure process shows an excellent agreement with the experimental results.

1. Introduction

Concrete is a brittle material with low tensile strength. During the service life of concrete buildings, tensile cracking failure is more frequent than compression failure [1]. In the case of fire and explosion, the degradation of the splitting and pulling performance of concrete members by high temperature and load coupling is more significant, which greatly reduces the safety performance of concrete buildings. Therefore, it is not only of great theoretical and practical significance to study the dynamic splitting tension characteristics of concrete after high temperatures, but also a fundamental problem to be solved in building fire safety [2,3].

To improve the comprehensive performance of concrete, engineering through the incorporation of the appropriate amount of fiber to improve the resistance to high-temperature burst performance, seismic performance, and durability of concrete structures, has become one of the main ways of concrete modification research [4,5,6]. Steel fiber reinforced concrete is the most widely used, and its impact resistance is significantly improved compared with other fiber reinforced concrete. However, it still has the disadvantages of high cost, easy corrosion, poor anti-burst effect, and so on. To overcome the above defects, researchers mixed steel fibers with high melting points and high elastic modulus with another low melting point and high ductility fiber into concrete for performance research. The purpose is to optimize the combination of the excellent properties of the fibers with different constitutive properties to meet the specific requirements of engineering construction [7,8]. Polypropylene fiber has a low melting point, which will melt and form pores under high temperatures. High-temperature water vapor in concrete can be discharged through the pores, which can effectively prevent the occurrence of the high-temperature burst phenomenon [9] to improve the fire resistance of concrete. At the same time, the anti-permeability is improved so that the mobility of water, chloride ions, and air in concrete is reduced. To delay the deterioration of steel material performance [10], the performance of the steel and concrete can play a better “positive hybrid effect”. Some progress has been made in the modification of steel-polypropylene hybrid fiber concrete. Xu [11] analyzed the influence law of tensile strength and strain rate of steel polypropylene hybrid fiber concrete (SP-HFRC) with different fiber content and length diameter ratio and believed that steel fiber increased the peak tensile strength, while polypropylene fiber mainly increased the residual strength after the peak. The damage degree of concrete could be significantly improved after mixing. Wu [12] systematically analyzed the strengthening and toughening mechanism of steel polypropylene hybrid fibers from the macro- and micro-scales and believed that steel fibers and polypropylene fibers could play a role in cracking resistance at different structural levels and loading stages, produce positive synergistic effects, and significantly improve the splitting tensile strength and flexural strength of self-compacting lightweight aggregate concrete. Some researchers have also considered the impact of a high-temperature environment. Compared with plain concrete, they have studied the improvement of the mechanical properties of SP-HFRC after high temperatures. Abadel [13] believed that concrete with only steel fiber is prone to burst after high temperature treatment and adding an appropriate volume fraction of steel fiber and polypropylene fiber can significantly improve the fracture performance and burst resistance of the concrete after high temperatures. Ding [14] studied the influence of the mixed-use of steel and polypropylene fibers of different specifications on the pore pressure of concrete and believed that adding fine polypropylene fibers could effectively reduce the pore pressure of concrete, improve the spalling phenomenon, and improve the high-temperature burst resistance. Researchers at home and abroad have conducted many experimental studies on the tensile properties of SP-HFRC. Still, the research conditions are mainly in the range of low strain rate. The current uniaxial tensile strength design specifications for concrete structures are based on common strain rate conditions, which cannot meet the requirements of resisting high strain rate loads caused by explosion and impact. It is not safe to take it as the strength reference value of building components. Meanwhile, it is found that there are few reports on the tensile properties of SP-HFRC under the coupling effect of impact load and temperature caused by fire and explosion. It is necessary to further study the dynamic splitting tensile properties of SP-HFRC under impact load after high temperature.

For the static tensile test of concrete, because the direct tensile test is difficult to operate, the indirect test method is usually used to measure the tensile properties. The most commonly used is the Brazilian disc test, also known as the splitting tensile test [15]. The dynamic splitting test is based on the static Brazilian disc theory. It uses an SHPB device to obtain the dynamic tensile strength of brittle materials such as concrete under high strain rate. During the loading process, stress concentration is easy to occur at both ends of the specimen, resulting in crushing failure, which will make the measurement results inaccurate. To make the test simple and avoid the unreasonable mode of failure of the force application point first in the loading process, researchers have improved the dynamic splitting test by using the methods of flattened Brazilian disc [16] and cushion [17] which have been better applied.

This paper plans to carry out dynamic splitting tests at different temperature levels (25 °C, 100 °C, 200 °C, 400 °C, 600 °C, and 800 °C) for SP-HFRC with six different fiber dosage combinations. Taking splitting strength as a measurement standard, this paper studies the change rule of the fiber hybrid effect after high temperatures obtain the optimal fiber dosage combination and sets PC as the control group test. The influence of temperature on dynamic splitting damage of concrete is analyzed from the perspective of dissipative energy. At the same time, the damage variable of dynamic splitting damage of SP-HFRC after high temperatures is defined based on dissipative energy. Combined with physical experiments and numerical analysis methods, the influence of high temperature on the failure forms of SP-HFRC and PC is further analyzed to provide a theoretical basis for the safety evaluation, repair, and reconstruction of tensile failure of SP-HFRC materials after high temperature.

2. Test Materials and Methods

2.1. Specimen Processing Process

Raw materials include Yunnan Yiliang Portland cement, coarse and fine aggregates, fly ash, steel fiber and polypropylene fiber, polycarboxylate water reducer, and water. See

Table 1. Performance and technical indexes of main raw materials.

Material Type	Density (kg/m3)	SiO2 (%)	Al2O3 (%)	CaO (%)	MgO (%)	Fe2O3 (%)	SO3 (%)	LOI (%)
Cement	2930	7.21	—	30.5	3.13	2.21	1.93	2.96
Fly ash	2550	45.1	24.2	5.6	1.72	3.58	2.1	4.7

for performance indexes of cement and fly ash. See

Table 2. Fiber performance index.

Fiber Type	Diameter $\left(\mathsf{\mu }\mathbf{m}\right)$	Length (mm)	Density (kg/m3)	Elastic Modulus (GPa)	Tensile Strength (MPa)	Ultimate Elongation (%)
Steel fiber	1000	35	7850	202	1000	2.6
Polypropylene fiber	48	12	910	4.8	500	15

for fiber type and performance index, and see Figure 1 for a physical drawing. See

Table 3. Mixing proportions of the concrete specimens.

Cement (kg/m3)	Water (kg/m3)	Sand (kg/m3)	Stone (kg/m3)	Fly Ash (kg/m3)	Water Reducer (kg/m3)
463	185	541	1261	93	2.25

for the mix proportion of the benchmark group in this test. It was prepared according to CECS 13:2009 “Standard for test methods of fiber concrete”. Adding too much fiber into concrete will affect the fiber bonding ability and mechanical properties of the concrete. Referring to the previous research results [18], this paper selects low fiber content concrete to study the mechanical properties. Three kinds of steel fibers with different volume contents are set, and the volume contents are 0.5%, 1%, and 1.5%, respectively. Polypropylene fiber is set with two different volume admixtures, which are 0.2% and 0.4%, respectively. Pour the fiber concrete mixture into the steel formwork, take cores, cut, and grind into cylindrical specimens with the size of $\mathsf{\Phi }50 \mathrm{mm}\times 40 \mathrm{mm}$ after standard curing for 28 days.

Use the KRX-17B box-type resistance furnace (Figure 2) to heat the processed test pieces. To make the test piece heat evenly and ensure that the test piece can accurately reach the set temperature, the cylindrical concrete test piece is placed upside down in parallel for one layer, and there is a surplus gap between the test pieces to improve the heating area of the test piece. According to the previous research results and experience of the research group and consulting references [19,20], the heating temperature gradient was determined as 25 °C, 100 °C, 200 °C, 400 °C, 600 °C, and 800 °C, and each temperature group had three specimens. The average value of the research results was taken. Set the average heating rate of the resistance furnace at 5 °C/min, and maintain the constant temperature for 2 h after reaching the conditions of the rated temperature group. The temperature rise curve is shown in Figure 3.

2.2. Dynamic Splitting Test

This test was completed by $\mathsf{\Phi }50 \mathrm{mm}$ SHPB test device (Figure 4), which is composed of a launching power device, incident bar, transmission bar, absorption bar, and dynamic strain test system. The bar is made of a high-strength alloy with a density of 7850 kg/m³, an elastic modulus of 210 GPa, a Poisson’s ratio of 0.3, a longitudinal wave velocity of 5173 m/s, an incident bar length of 2 m, and a transmission bar length of 2 m. In the test, a spindle-shaped bullet is used to generate a half-sine loading wave. Regarding the impact load effect caused by the explosion, the impact speed is selected as 6.6 m/s, and the average strain rate of the specimen is around 102 s⁻¹.

The dynamic splitting test follows the static elastic mechanics theory in terms of splitting strength. Brittle materials such as concrete are in a central two-way tensile compressive stress state under impact load. Most failure forms of the samples meet the conditions for the center of the flattened Brazilian disc to crack so that the splitting strength can be used as its tensile strength [21]. To ensure the central crack initiation condition required by the test as much as possible, according to the requirements of document [22], the loading angle of the platform is controlled by the cushions to satisfy the requirement ($2a\ge {20}^{\mathrm{o}}$). This method also improves the phenomenon of stress concentration at the loading part. The picture of specimen installation is shown in Figure 5. The force on the flattened Brazilian disc is shown in Figure 6, and the calculation formula of the central tensile stress of the specimen is as follows.

$${\sigma }_{st,d}=n\frac{2F(t)}{\pi dh}$$

(1)

where $F(t)$ represents the force at both ends of the test piece, $d$ represents the diameter of the test piece, $h$ represents the thickness of the test piece, $n$ represents the correlation coefficient of loading angle, the loading angle of this test is 22°, and $n$ is taken as 0.95.

The test process is based on the assumption of one-dimensional stress and uniformity. After the bullet hits the incident bar, the incident wave will propagate along the bar, and the transmitted wave and reflected wave will be generated when encountering the Brazilian disc specimen. The incident wave, reflected wave, and transmitted wave on the bar are collected by pasting strain gauges on the incident bar and transmission bar and combining them with the super dynamic strain gauge. According to the force reaction theorem, the force on both ends of the test piece can be expressed as Equation (2).

$$F\left(t\right)=\frac{\pi D^2}{8}E\left({\epsilon }_i\left(t\right)+{\epsilon }_r(t)+{\epsilon }_t(t)\right)$$

(2)

where ${\epsilon }_i$, ${\epsilon }_r$, and ${\epsilon }_t$ represent the strain of the incident wave, reflected wave, and transmitted wave, respectively, $D$ represents the diameter of the pressure bar, and $E$ represents the elastic modulus of the pressure bar.

To sum up, the dynamic splitting strength of concrete specimens can be expressed as Equation (3).

$$f_{st,d}=1.9\frac{F{\left(t\right)}_{\max }}{\pi dh}$$

(3)

where $f_{st,d}$ represents the dynamic splitting strength of concrete specimens, and $F{\left(t\right)}_{\max }$ represents the maximum load acting on both ends of the specimen.

2.3. Calculation of Dissipated Energy

The process of tensile failure of concrete structures affected by high temperature (fire) after dynamic disturbance is also the conversion of energy. Analyzing the failure of concrete materials from the energy perspective can better reflect the damage evolution law of specimens under different working conditions. According to the characteristics of the dynamic splitting test, the dissipated energy is closely related to the tensile damage of materials, which can be used as the toughness evaluation index of concrete materials [23]. Based on the law of energy conservation [24], the dynamic splitting tensile toughness of the material is further analyzed from the perspective of energy dissipation. The energy carried by the incident wave, reflected wave, and transmitted wave in the whole impact process and the energy dissipated by the failure of the specimen can be obtained from Equations (4)–(7), and the dissipated energy density is $w_d$, which is calculated from Equation (8).

$$W_i(t)=C_0{A}_b{E}_b{\displaystyle {\int }_0^T\stackrel{2}{{\epsilon }_i(t)}}dt$$

(4)

$$W_r(t)=C_0{A}_b{E}_b{\displaystyle {\int }_0^T\stackrel{2}{{\epsilon }_r(t)}}dt$$

(5)

$$W_{\mathrm{t}}(t)=C_0{A}_b{E}_b{\displaystyle {\int }_0^T\stackrel{2}{{\epsilon }_t(t)}}dt$$

(6)

$$W_s(t)=W_i(t)-W_r(t)-W_t(t)$$

(7)

$$w_d=\frac{W_{s,\max }}{V_c}$$

(8)

where $W_s(t)$ represents the energy dissipated by the specimen, $W_i(t)$ represents the incident wave energy, $W_r(t)$ represents the reflected wave energy, $W_t(t)$ represents the transmitted wave energy, $C_0$ represents the wave velocity of bar, $A_b$ and $E_b$, respectively, represent the cross-sectional area and the elastic modulus of the Hopkinson pressure bar, $T$ represents any time, $W_{s,\max }$ represents the total dissipated energy, and $V_c$ represents the volume of the concrete specimen.

It can be seen from Equation (9) that the loading strain rate $\dot{\epsilon }$ is related to the dynamic splitting strength $f_{st,d}$ and dynamic elastic modulus $E_d$, while the dynamic elastic modulus of the material is difficult to measure. To avoid the influence of the strain rate error on the analysis process, this paper uses the incident wave energy change rate ${\dot{e}}_i$ to measure the change law of the dissipated energy of concrete materials, and the formula is shown in Equation (10).

$$\dot{\epsilon }=\frac{f_{st,d}}{\tau E_d}$$

(9)

$${\dot{e}}_i=\frac{W_{i,\max }}{t_i}$$

(10)

where $\tau$ represents the time interval from zero to peak of transmission strain, $W_{i,\max }$ represents the value after the incident energy is stabilized, and $t_i$ represents the duration of the incident wave.

3. Experimental Results and Analysis

3.1. Experimental Results

The average of the three data measured in the test is the final test result. The data results of the dynamic splitting test are shown in

Table 4. Summary of experimental results.

Temperature (°C)	Fiber Content (%)	${\mathit{f}}_{\mathit{s}\mathit{t},\mathit{d}}$ (MPa)	Temperature (°C)	Fiber Content (%)	${\mathit{f}}_{\mathit{s}\mathit{t},\mathit{d}}$ (MPa)
25	PC	7.20	100	PC	7.77
	S0.5PP0.2	12.13		S0.5PP0.2	14.05
	S1PP0.2	14.89		S1PP0.2	16.38
	S1.5PP0.2	13.52		S1.5PP0.2	14.55
	S0.5PP0.4	11.42		S0.5PP0.4	12.53
	S1PP0.4	10.81		S1PP0.4	11.37
	S1.5PP0.4	10.17		S1.5PP0.4	10.41
200	PC	8.16	400	PC	6.05
	S0.5PP0.2	14.52		S0.5PP0.2	11.81
	S1PP0.2	16.93		S1PP0.2	12.95
	S1.5PP0.2	15.13		S1.5PP0.2	12.44
	S0.5PP0.4	13.32		S0.5PP0.4	10.51
	S1PP0.4	8.52		S1PP0.4	5.73
	S1.5PP0.4	8.20		S1.5PP0.4	5.41
600	PC	4.14	800	PC	2.55
	S0.5PP0.2	7.73		S0.5PP0.2	5.12
	S1PP0.2	8.39		S1PP0.2	5.82
	S1.5PP0.2	8.06		S1.5PP0.2	5.51
	S0.5PP0.4	7.28		S0.5PP0.4	4.60
	S1PP0.4	4.33		S1PP0.4	2.20
	S1.5PP0.4	3.87		S1.5PP0.4	1.84

Note: “PC” refers to plain concrete; “S” refers to steel fiber; “PP” refers to polypropylene fiber; and the number next refer to the percentage of volume content.

.

3.2. Dynamic Splitting Strength

Dynamic splitting strength is the change of dynamic splitting strength of concrete with different fiber content combinations with temperature shown in Figure 7. It can be seen from the figure that under the same incident wave energy change rate, the splitting strength of SP-HFRC and PC increases first and then decreases with the increase of temperature. The temperature strengthening threshold temperature of S1PP0.4 (1 vol% steel fiber + 0.4 vol% polypropylene fiber) and S1.5PP0.4 concrete is around 100 °C, and the temperature strengthening threshold temperature of concrete with other fiber content is around 200 °C. At the same time, it is found that SP-HFRC shows a positive hybrid effect at room temperature, and its dynamic splitting strength is higher than that of PC. After 200 °C, the splitting strength of S1PP0.4 and S1.5PP0.4 concrete is gradually lower than that of PC, showing a negative hybrid effect. S1PP0.2 concrete has the best splitting performance among the fiber content combinations studied. Compared with PC, the splitting strength at 25 °C is increased by 106.8%, and the splitting strength at 800 °C is increased by 128.2%. At 200 °C, the dynamic splitting strength of S1PP0.2 concrete reaches a maximum of 16.93 MPa. Cause analysis: the mixed steel fiber and polypropylene fiber are randomly distributed in the micro-cracks in the concrete to prevent the occurrence of connected cracks, which significantly weakens the tensile stress causing damage to enhance the impact resistance and splitting tensile resistance of concrete. For steel fibers, the bond strength between the hydration products of cement and steel fibers gradually increases before 200 °C. The splitting performance is improved, the temperature continues to rise, the hydration products of concrete have different degrees of thermal decomposition, the concrete structure becomes loose, and the splitting performance gradually decreases. The melting point of polypropylene fiber is 165 °C. Before reaching the melting point temperature, polypropylene fiber is closely connected with the internal aggregate, giving full play to the role of crack resistance and toughening. It has an apparent strengthening effect on the splitting strength of concrete. After reaching the melting point temperature, the polypropylene fiber melts, fills the pores between the aggregates, and the compactness of the matrix is practical. The pores formed by melting are conducive to the discharge of high-temperature water vapor in the concrete, effectively improving the internal pressure environment, thereby improving the splitting performance and burst resistance of the material. When the volume content of polypropylene fiber is 0.4%, more pores are produced after melting. After being subjected to impact load, more cracks are generated through pore connectivity, and the splitting performance is seriously degraded, thus showing a negative hybrid effect.

3.3. Analysis of Damage Variables Based on Dissipative Energy

The typical energy variation of a specimen with time in a dynamic splitting test is shown in Figure 8. The incident energy, reflected energy, and dissipated energy increase gradually with time until they become stable. The incident and reflected energy are enormous, the dissipated energy is small, and the transmitted energy is minimal, which is close to a parallel line. Due to the influence of the loading mode, the contact area between the specimen and the bar is small, resulting in most of the energy being reflected, and a small part of the energy being transferred to the transmission bar. While the stress wave passes through the concrete specimen, the energy of the stress wave is continuously consumed. The specimen gradually absorbs energy, causing internal damage and eventually destruction. Due to the small conversion of heat energy, the kinetic energy and other energy consumption can be ignored. The total dissipated energy is the energy consumed by the dynamic loading failure of the specimen [25].

To avoid lengthy space, to achieve the research purpose, only S1PP0.2 concrete and PC with the best splitting performance can be used for energy analysis. Figure 9 shows the time history curve of dynamic splitting dissipation energy of PC and S1PP0.2 concrete in different temperature groups. It can be seen from the figure that the dynamic splitting dissipation energy of concrete materials increases first and then decreases with the increase of temperature. Compared with PC, the energy dissipation effect of S1PP0.2 concrete at the same temperature is significantly improved, and the variation law of HFRC dissipation energy and splitting strength with temperature is consistent.

Introducing damage variables into concrete materials can better study the deformation and failure characteristics of materials. In the constitutive relationship, the accompanying variable of damage variable, namely the damage propagation force, refers to the energy dissipation density, so it is more meaningful to define the damage variable from the perspective of energy dissipation. According to the energy point of view, concrete material deforms after being subjected to impact load, and the bearing capacity of the material gradually decreases in this process. That is, the constitutive energy of the material also decreases. It is more reasonable to define damage in combination with the relationship between material performance degradation and energy dissipation. Based on the previous research results [26], $E_{\varsigma }$ is defined as the constitutive energy of the material, $E_{\lambda }$ as the deformation energy, and $D_o$ as the damage variable.

$$E_{\varsigma }=E_{\lambda }+w_d$$

(11)

$$D_o=w_d/E_{\varsigma }$$

(12)

where $w_d$ represents the dissipative energy density. $E_{\varsigma }$ can be obtained by calculating the area surrounded by dynamic splitting stress and strain.

$$E_{\varsigma }={\displaystyle \int {\sigma }_T}d{\epsilon }_T$$

(13)

Table 5. Changes of damage variables at different temperatures.

Material Type	T (°C)	${\dot{\mathit{e}}}_{\mathit{i}}$ (MJ/s)	${\mathit{W}}_{\mathit{s},\mathbf{max}}$ (J)	${\mathit{w}}_{\mathit{d}}$ (104 J/m3)	${\mathit{E}}_{\mathit{\varsigma }}$ (104 J/m3)	${\mathit{D}}_{\mathit{o}}$ (–)
PC	25	0.64	37.23	47.43	319.60	0.1484
	100	0.63	39.22	49.96	335.77	0.1488
	200	0.67	42.33	53.92	366.81	0.1470
	400	0.61	36.01	45.87	307.91	0.1490
	600	0.62	30.46	38.80	245.10	0.1583
	800	0.59	23.48	29.91	174.71	0.1712
S1PP0.2	25	0.62	45.91	58.49	1160.43	0.0504
	100	0.65	50.19	63.94	1329.36	0.0481
	200	0.61	54.05	68.85	1509.83	0.0456
	400	0.66	45.11	57.46	1134.41	0.0507
	600	0.58	37.76	48.10	837.98	0.0574
	800	0.63	30.91	39.38	576.52	0.0683

shows the relevant parameters of constitutive energy, dissipated energy density, and damage variables during the dynamic splitting process of PC and S1PP0.2 concrete under different temperature groups. It can be seen that the constitutive energy level of S1PP0.2 concrete is significantly higher than that of PC, and the constitutive energy is the highest at 200 °C. At the same time, it is found that the dissipative energy density of PC at 400 °C is similar to that of S1PP0.2 concrete at 600 °C, but the difference in constitutive energy is significant. According to the test failure diagram, the former is more serious, indicating that S1PP0.2 concrete contains high releasable internal energy, which can be released through reflected and transmitted waves, showing toughness characteristics, which are closely related to the addition of steel fiber and polypropylene fiber. Most of the constitutive energy of PC is used for deformation and crack propagation, resulting in more serious damage [27]. It can be seen from the change law of the damage variable that with the increase of temperature, the value of the damage variable decreases slowly and then increases, indicating that there is a temperature strengthening effect before 200 °C, and the damage degree does not change significantly at this stage. From 400 °C to 800 °C, the value of the damage variable increases significantly, indicating that higher temperature seriously degrades the overall performance of concrete. In S1PP0.2 concrete, the level of the concrete damage variable is significantly lower than that of PC. Comparing the damage diagrams under different temperatures, it is concluded that the greater the value of the damage variable, the greater the damage and damage degree of concrete. In conclusion, from the perspective of energy analysis, it can be seen that adding an appropriate amount of steel polypropylene fiber can improve the dynamic splitting tensile toughness of concrete after high temperatures, and the damage degree of concrete under different states can be better characterized by defining the damage variable.

3.4. Characteristics of Stress–Strain Curve

Figure 10 shows the splitting tensile stress–strain curves of PC and S1PP0.2 concrete at different temperature groups. It can be seen that when the temperature is low, there are two obvious peak points in the curve, and there are valley points between the peak points, showing the “double peak” feature, which gradually disappears when the temperature is high. The bimodal phenomenon can also be explained from the perspective of energy, indicating that there is a transitional change process of energy in the propagation of stress waves in concrete specimens under dynamic impact [28]. Still, the difference is that the first peak stress of PC is less than the second peak stress, and the first peak stress of S1PP0.2 concrete is greater than the second peak stress. The reason for the different “bimodal” trend is that adding hybrid fibers improves the toughness of concrete materials, changing its energy consumption characteristics, and the attenuation degree of stress wave in S1PP0.2 concrete is significant. The energy consumption effect of S1PP0.2 concrete is greater than that of PC. After 600 °C, the overall performance of concrete materials is seriously degraded, the toughness characteristics disappear, and the stress–strain curve shows that it directly enters the unloading stage from the elastic stage.

3.5. Splitting Failure Form

The dynamic splitting failure forms of concrete after treatment at different temperature groups are shown in Figure 11 and Figure 12. From the comparison of the two groups of diagrams, it can be concluded that the failure mode of PC and S1PP0.2 concrete specimens is generally split into two halves from the middle along the radial centerline, showing a tensile failure mode. The specimen shows an inverted triangle failure area in the contact part between the two end faces of the incident bar and the transmission bar, and the damage degree of the two end faces is different. The damage degree of the end face in contact with the incident bar is greater than that of the transmission bar. With the increase of temperature, the crushing area of the triangle area at both ends increases significantly.

However, the failure forms of the two concrete specimens are different due to the differences in mechanical properties. The failure form of PC from 25 °C to 200 °C is to destroy two halves along the diameter direction. From 400 °C to 800 °C, the deterioration degree of PC gradually increases, and the damage form changes from fragmentation into blocks to crushing damage. The damage forms of S1PP0.2 concrete under different temperatures are the same, and the damage is relatively more serious with the increase of temperature. Before the temperature reaches the melting point of polypropylene fiber, steel fiber and polypropylene fiber jointly improve the splitting performance of the specimen, and the crushing area on the surface of the specimen is very minimal, which is still a whole. The temperature continues to rise, and the polypropylene fiber melts, which improves the high-temperature vapor environment inside the concrete. At the same time, the steel fiber can prevent crack propagation and delay damage development. Although the specimen has obvious cracks along the diameter direction, the damage degree is significantly reduced compared with PC. At 800 °C, the specimen is still stuck together as a whole, showing the form of a crack without scattering. The results show that adding an appropriate amount of steel polypropylene fiber into concrete can significantly improve the dynamic tensile properties of concrete after high temperatures.

4. Numerical Simulation

4.1. Establishment of Numerical Model

With the development of computer technology, numerical analysis of tests with finite element software has become an essential means to study the internal damage and dynamic characteristics of concrete. The phenomenon of the dynamic splitting test shows that under a high strain rate, the concrete will produce triangular failure areas at both ends, mainly caused by the serious stress concentration at the end of the sample. To better observe the stress propagation process, the LS-DYNA finite element software simulates the dynamic splitting test of concrete SHPB. The model establishment (Figure 13) is mainly composed of four parts: concrete specimen, incident bar, transmission bar, and bullet, and solid164 entity unit type is selected. Bullet, incident bar, and transmission bar are made of linear elastic materials, and concrete materials are made of the HJC constitutive model. The contact algorithm is defined according to the experimental situation: automatic surface-to-surface contact is adopted between the bullet and the incident bar, and surface-to-surface erosion contact is adopted between the bar and the specimen. The displacement and rotation of the bar are constrained according to the experimental conditions, and the non-reflective boundary is defined at the end of the transmission bar to prevent the reflection of non-physical waves from affecting the calculation results. They are using the maximum principal strain failure criterion in erosion from keywords *MAT_ADD_EROSION to define the failure of concrete specimens under dynamic splitting.

4.2. HJC Model Parameters of High Temperature Concrete

The HJC constitutive model is a mechanical constitutive model very suitable for studying dynamic mechanical properties of concrete, which can accurately reflect the change law of mechanical properties of concrete under dynamic impact [29]. The yield surface equation considers the effects of the damage factor, hydrostatic pressure state, and strain rate, and the nonlinear relationship can be expressed as Equation (14).

$${\sigma }^{\ast }=\left[A\left(1-D\right)+B{P}^{\ast N}\right]\left(1+C\ln {\dot{\epsilon }}^{\ast }\right)$$

(14)

where ${\sigma }^{\ast }$ represents the normalized equivalent strength, $P^{\ast }$ represents the normalized pressure, ${\dot{\epsilon }}^{\ast }$ represents the normalized true strain rate obtained by dividing the true strain rate $\dot{\epsilon }$ by the reference strain rate ${\dot{\epsilon }}_0$, $A$ represents the normalized cohesive strength, $B$ represents the normalized pressure hardening coefficient, $C$ represents the strain rate influence coefficient, $N$ represents the pressure hardening coefficient, and $D$ represents the damage factor.

The damage factor is obtained from the accumulation of equivalent plastic strain and plastic volumetric strain. The damage evolution can be expressed as Equation (15).

$$D={\displaystyle \sum \frac{\Delta {\epsilon }_p+\Delta u_p}{D_1{\left(P^{\ast }+T^{\ast }\right)}^{D_2}}}$$

(15)

where $D$ represents the damage factor, $D_1$, $D_2$ are the damage coefficient, $\Delta {\epsilon }_p$, $\Delta u_p$ are equivalent plastic strain and corresponding volumetric strain, and $T^{\ast }$ represents the normalized maximum tensile stress obtained by dividing the maximum tensile strength by the static compressive strength.

The model contains 21 parameters, including basic mechanical parameters: $f_c$, $\rho$, $G$, and $T$, strain rate effect parameter: C, and ${\dot{\epsilon }}_0$, failure type parameter: FS, yield surface parameters: A, B, N, and $S_{\max }$, damage parameters: $D_1$, $D_2$, and $E_{f\min }$, and equation of state parameters: $K_1$, $K_2$, $K_3$, $p_c$, ${\mu }_c$, $p_l$, and ${\mu }_l$. Since there is no change in heat during the impact splitting tensile test after high temperature, the damage caused by temperature to the concrete specimen directly changes the physical and mechanical properties. The damage caused by high temperature to the concrete specimen can be characterized by the changing of material model parameters [30]. The basic mechanical parameters of the specimen after normal temperature and high temperature are obtained from the static test. Other parameters are obtained from the empirical values and appropriate methods in the literature [31,32]. To achieve the purpose of the test comparison, the concrete at normal temperature and 800 °C is selected for the simulation study of dynamic tensile properties. The partial parameters of the model are shown in

Table 6. Parameters of the concrete HJC material model.

Number	T (°C)	$\mathit{\rho }$ (kg/m3)	$\mathit{G}$	${\mathit{f}}_{\mathit{c}} \left(\mathbf{MPa}\right)$	${\mathit{f}}_{\mathit{t}} \left(\mathbf{MPa}\right)$	${\mathit{p}}_{\mathit{c}} \left(\mathbf{MPa}\right)$	${\mathit{\mu }}_{\mathit{c}}$	${\mathit{p}}_{\mathit{l}} \left(\mathbf{GPa}\right)$	${\mathit{\mu }}_{\mathit{l}}$
PC	25	2310	13.5	41.6	3.99	13.89	0.000760	0.81	0.100
	800	2181	2.75	14.8	2.38	4.93	0.000675	0.81	0.121
S1PP0.2	25	2430	21.3	53.2	4.52	17.73	0.000894	0.81	0.100
	800	2317	4.28	27	3.22	9	0.000812	0.81	0.116

.

4.3. Simulation Curve Verification

The strain data at the corresponding position is derived by LS-Prepost post-processing software. The three-wave method is used to process the data to obtain the dynamic splitting stress–strain curve of the specimen, which is compared with the experimental results, as shown in Figure 14.

It can be seen from the figure that the changing trend of the simulated curve and the experimental curve in the pre-peak stage is basically the same. There are differences in the characterization of the post-peak specimen failure stage, which is due to the failure criteria used in the simulation analysis to control the failure characterization of the failure degree of the unit, which is different from the actual failure in the form of expression. At the same time, it is found that the variation of splitting strength with the temperature of the simulated specimen is consistent with the experimental results, and it shows obvious strength degradation characteristics at 800 °C.

4.4. Simulating Splitting Failure Process

Figure 15 shows the failure process of PC and S1PP0.2 concrete simulated by a dynamic splitting test under normal temperature and 800 °C. The numerical simulation results show that the concrete specimen first produces the crack initiation point from the end face in contact with the incident bar. Then the crack begins to crack in the center. The crack is derived from the contact surface at both ends. It penetrates the middle of the specimen, the transmission end is crushed, and the incident end and transmission end gradually to form a triangular failure area. This result is due to the stress concentration at the two contact end faces. When the strong compressive stress wave is transmitted to this position, the area of the crushing area presents a triangular shape. The specimen breaks when the crushing area gradually expands to the diameter direction. At the same time, it is found that the damage degree of the concrete specimen in contact with the incident bar and the transmission bar is inconsistent, and the damage degree of the end surface in contact with the incident bar is greater than that of the transmission bar. Comparing the splitting failure process of PC and S1PP0.2 concrete, under normal temperature, the splitting failure crack of PC is long and wide, and the crack penetrates from the contact end face of the incident bar to the contact end face of the transmission bar. However, the destruction degree of S1PP0.2 concrete is not as serious as that of PC, and there is no penetrating crack. Under 800 °C, the damage crack of PC runs through and has the trend of deriving to the surrounding, and the damage is more serious. S1PP0.2 concrete has smaller main cracks and secondary cracks. The overall damage degree is lower than PC, and the two contact end faces still form triangular area damage. The failure results of LS-DYNA numerical simulation are matched with the experimental failure results, which shows that the modified HJC model effectively studies the dynamic tensile properties of concrete after high temperature. It can accurately reflect the change law of dynamic splitting tensile mechanical properties of concrete specimens during the impact process.

5. Conclusions

Under the change rate of incident wave energy, with the increase of temperature, the splitting strength of the specimen shows a trend of first strengthening and then deteriorating with the rise of temperature. After high temperatures, SP-HFRC has a positive and negative fiber hybrid effect. S1PP0.2 concrete has the best splitting resistance among the fiber content combinations studied. Compared with PC, the splitting strength at 25 °C is increased by 106.8%, and the splitting strength at 800 °C is increased by 128.2%.

From the perspective of energy analysis, it can be seen that adding an appropriate amount of steel polypropylene hybrid fiber can significantly improve the dynamic splitting tensile toughness of concrete after high temperatures. The greater the value of the damage variable, the greater the damage degree of the concrete specimen, indicating that the damage degree of concrete can be better characterized by defining the damage variable.

Before 200 °C, the failure mode of PC is to destroy two halves along the diameter direction. After 400 °C, the internal damage is gradually serious, the bearing capacity is reduced, and the failure mode of the test piece changes from fragmentation to crushing. In S1PP0.2 concrete, the failure forms of concrete at different temperature groups are the same. At 800 °C, it still shows the form of cracking but not dispersing, showing ductile failure characteristics.

The failure forms of numerical simulation are consistent with the experimental results, and the damage degree of S1PP0.2 concrete under the same temperature is significantly lower than that of PC, indicating that the state of high-temperature concrete after mechanical property degradation can be better characterized by modifying some parameters of HJC model.