Study on Impact Resistance of Alkali-Activated Slag Cementitious Material with Steel Fiber

Abstract

Alkali-activated slag cementitious materials (AASCMs) use alkaline activators to activate blast furnace slag and waste slag to replace traditional Portland cement, which can reduce CO₂ emissions. An impact resistance test and scanning electron microscopy (SEM) microscopic performance analysis of alkali-activated slag cementitious material specimens with four different steel-fiber contents are performed. The effects of steel-fiber volume content and strain rate on the dynamic elastic modulus E_d, dynamic compressive strength σ_d, dynamic peak compressive strain ε_c, and energy absorption of the AASCM-SS are studied. The results indicate that the dynamic elastic modulus E_d, dynamic compressive strength σ_d, and energy absorption of the AASCM-SS increase with the increase of strain rate, and the dynamic peak compressive strain ε_c decreases with the increase of strain rate. The dynamic elastic modulus E_d, dynamic compressive strength σ_d, and dynamic peak compressive strain ε_c of the SS-AASCM increase first and then decrease with the increase of steel-fiber content. When the steel-fiber content is 0.5%, the σ_d and ε_c of the AASCM-SS are the highest, increased by 9.9% and 19.3%. The energy absorption of AASCM-SS increases with the increase of steel-fiber content. A dynamic constitutive model of the FR-AASCM considering the influence of damage, strain rate, and steel-fiber volume fraction is established. The proposed constitutive model is in acceptable agreement with the experimental AASCM-SS dynamic stress–strain curve, and the correlation coefficient is 0.91.

1. Introduction

Global production of Ordinary Portland Cement has exceeded 4 billion tons per year [1]. This large cement production accounts for 7–8% of global anthropogenic CO₂ emissions [2]. One approach to reducing global greenhouse gas emissions from the construction industry is to customize and adapt alternative cementitious materials. AASCM has a fast setting speed, high strength, and acceptable fire resistance. Studies have demonstrated that the initial setting time and final setting times of AASCM are 4–7 min and 35–45 min, respectively, which are considerably less than those of ordinary concrete (38–45 min and 6–8 h) [3,4]. When the water–binder ratio is 0.4–0.6, the compressive strength of AASCM can reach 56–82 MPa [5] and the flexural strength can reach 4.92–7.59 MPa [6], which is higher than that of ordinary concrete with the same water–binder ratio. The compressive strength is 32–45 MPa and flexural strength is 3.2–5 MPa [7]. In addition, the high-temperature resistance of AASCM is significantly better than that of ordinary concrete. The compressive strength of AASCM does not decrease after a 600 °C temperature, whereas the compressive strength of ordinary concrete decreases rapidly after 200 °C, and its compressive strength at 1200 °C is only 17% of that at room temperature [8]. Slag cement effectively reduced autoclave expansions from 6.6 and 6.8% to only 0.14 and 0.15%, far more than would be expected by dilution [9]. Compared with traditional Portland cement, AASCM exhibits greater shrinkage and is easier to crack. Studies have indicated that the self-shrinkage rate of AASCM can reach 3500 με, and the self-shrinkage of alkali slag cementitious materials is 3–6 times that of ordinary Portland cement [10]. Steel fibers are typically added to AASCM to form steel-fiber-toughened AASCM to improve its ductility and reduce shrinkage. The equal strength cementitious concrete quality loss rate after high temperatures is 28~37%, better than ordinary concrete at 35~48% [11,12].

At present, research on steel-fiber-toughened AASCM has focused primarily on static performance; a considerable amount of research has been performed on its elastic modulus, compressive strength, flexural strength, and stress–strain relationship. Jin L [13] studied the static mechanical properties of steel-fiber-reinforced high-performance concrete. The results indicated that the introduction of steel fibers significantly improves the tensile strength, splitting tensile strength, and flexural strength of the steel-fiber-reinforced high-strength concrete. Steel fiber can effectively reduce the loss of modulus of elasticity of concrete after fire, and the modulus of elasticity of steel-fiber concrete after 600 °C is 17.2–26.9% higher than that of non-fiber concrete [14], so the fire-resistant properties of steel fiber and AASCM can be matched with each other. Yang and Luo [15,16] demonstrated that steel fibers have a higher elastic modulus than concrete matrices, and that the incorporation of steel fibers can enhance the elastic modulus of concrete. In addition, a large number of scholars have studied the static mechanical properties of steel-fiber-reinforced concrete [16,17]. The results have indicated that steel fibers can significantly improve the tensile flexural and compressive strengths of concrete. This is because the steel fibers have a bridging role in the matrix and inhibit the extension of cracks [18]. The volume content of steel fibers has a significant effect on the mechanical properties of concrete. When the steel-fiber content is 1.0–2.0%, the enhancement is the most apparent. Therefore, steel fibers have been widely used in the study of the static mechanical properties of AASCM [13,14,16,17].

Although the static mechanical properties of steel fibers in AASCM are abundant, there are limited studies on their dynamic mechanical properties, which reduces their application in structural engineering. Fiber-modified concrete has better tensile properties, crack resistance and toughness than ordinary concrete, and exhibits excellent mechanical properties under dynamic impact loading [19,20]. Therefore, the dynamic properties of steel-fiber-toughened AASCM were studied in this paper. The Hopkinson bar impact tests of steel fiber toughened AASCM with four different contents (0%, 0.5%, 1.0%, 1.5%) are performed. The effects of the strain rate and steel-fiber volume content on the dynamic compressive strength, dynamic elastic modulus, dynamic peak compressive strain, and energy absorption of AASCM are analyzed. The dynamic stress–strain curves of the steel-fiber-toughened AASCM are compared with those of existing models. The effects of the steel-fiber content and distribution on the impact resistance of AASCM are analyzed using scanning electron microscopy (SEM).

2. Test Survey

2.1. Experimental Design

The materials used in the test are as follows. Granulated blast furnace slag was selected; the specific surface area of the material was 440 m²/kg, specific gravity was 2.45, and average particle size was 2.4 μm. The composition is listed in

Table 1. Chemical composition of granulated blast furnace slag.

Component	CaO	SiO2	Al2O3	MgO	Fe2O3	Miscellaneous
Content/%	41.17	33.94	13.16	7.28	0.66	3.79

. Natural river sand with a fineness modulus of 2.6 and bulk density of 2480 kg/m³ was selected as fine aggregate. Steel fibers were provided by Suzhou Shiweikang Metal Products Co. Ltd. In Suzhou, China; the detailed parameters are listed in

Table 2. Performance index of steel fiber.

Density (kg/m3)	Diameter (µm)	Length (mm)	Tensile Strength (MPa)	Elastic Modulus (GPa)
7800	210	12	2969	200

; The alkali activator was made of liquid sodium silicate in (Figure 1b) and solid sodium hydroxide in (Figure 1c). Four kinds of steel-fiber contents (0%, 0.5%, 1.0%, 1.5%) were designed for the experiment; the mixtures are listed in

Table 3. Experimental design.

Groups	Vf (%)	Size (mm)	Mineral Fines (kg/m3)	Sodium Silicate (kg/m3)	Sodium Hydroxide (kg/m3)	Water (kg/m3)	River Sand (kg/m3)	Trial Amount
1	0	Φ75 × 36.5	625	164	27.8	152	833	6
2	0.5	Φ75 × 36.5	625	164	27.8	152	833	6
3	1.0	Φ75 × 36.5	625	164	27.8	152	833	6
4	1.5	Φ75 × 36.5	625	164	27.8	152	833	6

. In attempt to weaken the effect of uneven fiber distribution on the test results, the specimens were vibrated for 20–30 s after casting. The dimensions of the specimens were Φ75 mm × 37.5 mm.

2.2. SHPB Test

The impact test device was a Φ75 mm split Hopkinson pressure bar, as indicated in Figure 2. The specimen was placed between the incident and transmission bars; strain gauges were placed on the incident and transmission bars. A compressive-stress pulse was generated by the impactor. First, the impact pulse was transmitted to the incident rod and collected using a strain gauge. Then, the impact pulse penetrated the incident rod and acted on the AASCM specimen between the incident and transmission rods. Finally, part of the shock pulse was transmitted to the transmission rod through the sample; the impact velocity was set to 50–110 s⁻¹, with a set of tests every 10 s⁻¹. The other part was reflected back to the incident rod.

3. Result and Discussion

3.1. Impact Failure Mode of AASCMs

The AASCM specimens after the impact test failure are displayed in Figure 3. From Figure 3a, it can be observed that steel fibers can significantly improve the impact resistance of AASCM, and the higher the steel-fiber content, the stronger the impact resistance of the AASCM. In the case of low impact rate (less than 80 s⁻¹), the undoped fiber specimens were completely broken after the test. The addition of steel fibers improves the impact resistance of the AASCM specimens. With the increase of steel-fiber content from zero to 1.5%, the AASCM specimens change from complete “crushing” to “partial crushing”, and then to “slight cracking”. The elastic modulus and tensile strength of the steel fibers are considerably higher than those of the AASCM. The elastic modulus of steel fibers is 7–14 times that of AASCM [21] and the tensile strength is 80–140 times that of AASCM [22,23,24]. High-strength steel fibers can increase the integrity of the specimen structure, strengthen the bonding between AASCM materials, effectively inhibit the development of cracks, and improve the ability of AASCM to resist impact. Therefore, steel fibers can effectively inhibit the failure of AASCM materials under impact loads.

The effect of the impact rate on the impact resistance of AASCM is displayed in Figure 3b–e. It can be observed that when the steel-fiber content is 0–1.5%, as the impact rate increases from 30 s⁻¹ to 120 s⁻¹, the failure mode of AASCM specimens demonstrates a change of “basic integrity—slight rupture—small part rupture—most rupture-complete rupture”. The higher the impact rate, the higher the impact load and energy of the specimen and the more serious the damage to the specimen.

3.2. Dynamic Elastic Modulus

Dynamic elastic modulus is an important index for measuring the impact resistance of AASCM. In the Hopkinson test, the dynamic elastic modulus E_d of AASCM is characterized by the slope of the peak stress 40% and peak stress 60%; its calculation is displayed in Equation (1).

$$E_{\mathrm{d}}={\displaystyle \frac{{\sigma }_1-{\sigma }_2}{{\epsilon }_1-{\epsilon }_2}}$$

(1)

where σ₁ is the peak stress of 60% and ε₁ is the dynamic strain corresponding to σ₁. σ₂ is the peak stress of 40% and ε₂ is the dynamic strain corresponding to σ₂.

3.2.1. Effect of Strain Rate on Dynamic Elastic Modulus

To study the influence of strain rate on dynamic elastic modulus, the development law of dynamic elastic modulus E_d of AASCM specimens under different strain rates was analyzed when the steel-fiber content was 0–1.5%, as indicated in Figure 4. It can be observed that except for the specimen with a steel-fiber content of 1.5% and loading rate of 60–80 s⁻¹, the overall dynamic elastic modulus of the remaining AASCM specimens increases with the increase of strain rate. When the loading rate increases from 50–60 s⁻¹ to 100–110 s⁻¹, the dynamic elastic modulus E_d of the AASCM specimens increases from 27–40 GPa to 80–88 GPa, an increase of 66–162.2%. The effect of the strain rate on the dynamic elastic modulus of the AASCM specimens is similar to that of ordinary concrete and recycled concrete. Studies have demonstrated that when the loading rate increases from 39.9 s⁻¹ to 90.6 s⁻¹, the dynamic elastic modulus of ordinary concrete increases by 63.6% [25]. This is because an increase in the strain rate leads to an increase in the microcrack propagation speed in AASCM; however, the propagation speed of the stress pulse continues to be higher than that of the microcrack development speed. Therefore, a strain delay phenomenon occurs in AASCM under dynamic impact and the peak strain growth rate slows, thereby increasing the dynamic elastic modulus of the material.

3.2.2. Influence of Steel-Fiber Content on Dynamic Elastic Modulus

To study the influence of the steel-fiber content on the dynamic elastic modulus, the development law of the dynamic elastic modulus E_d of AASCM specimens with different steel-fiber contents was analyzed when the loading rate was 50–110 s⁻¹, as indicated in Figure 5. Except for the individual specimens, the dynamic elastic modulus of the AASCM specimens is 27–82 Gpa, which is considerably higher than the static elastic modulus of AASCM (21–36 Gpa) [26]. It can be observed that the elastic modulus of AASCMs can be improved by adding an appropriate amount of steel fiber (1%). When the strain rate is 50–110 s⁻¹, the dynamic elastic modulus of the AASCM specimens increases by 65.6–173.7% compared with that of the non-fiber AASCM specimens. The main reason why an appropriate amount of steel fibers can improve the dynamic elastic modulus of AASCM specimens is that steel fibers are high-modulus fibers. The addition of steel fiber not only improves the elastic modulus of the AASCM, but also enhances the dynamic compressive strength of the AASCM, reduces the deformation of materials, and improves the dynamic elastic modulus of the AASCM.

In addition, at each loading rate, the incorporation of excess steel fibers reduces the dynamic elastic modulus E_d of the AASCM specimens. Compared with the steel fiber content of 1%, the steel-fiber content of 1.5% reduces the dynamic elastic modulus of AASCM specimens by 97.8–162.2%. This is because when the steel-fiber content is overly high, the gap between the steel fiber and cementitious material increases, and the nonuniformity of the AASCM increases. The increase in the nonuniformity of the AASCM degrades its mechanical properties, thus reducing its dynamic elastic modulus of AASCM [27]. And excessive fibers can agglomerate or form voids within the cementitious material, a phenomenon specifically reflected in Section 5. At each loading rate, the low dosage of steel fibers also reduced the dynamic elastic modulus of the AASCM specimens E_d. A steel-fiber content of 0.5% reduced the dynamic elastic modulus of the AASCM specimens by 59.7~72.9% as compared to the AASCM without fiber dosage. It was due to the 0.5% steel-fiber doped specimen is the first production of the doped fiber specimen, mixing is not sufficient to cause uneven distribution of steel fibers, which in turn affected the mechanical properties of the specimen.

3.3. Dynamic Compressive Strength

3.3.1. Effect of Strain Rate on Dynamic Compressive Strength

To study the effect of strain rate on dynamic compressive strength, the variation of dynamic compressive strength σ_d of AASCM specimens with strain rate was analyzed under the loading rate of 50–110 s⁻¹ when the steel-fiber content was 0–1.5%, as indicated in Figure 6. The overall dynamic compressive strength of the AASCM specimens increases with an increase in the strain rate. With an increase in strain rate from 50–60 s⁻¹ to 100–110 s⁻¹, the dynamic compressive strength of the AASCM increases by 2.4–44%. The effect of the strain rate on the dynamic compressive strength of the AASCM specimens is similar to that of ordinary and recycled concrete. Studies have indicated that when the loading rate increases from 51 s⁻¹ to 90 s⁻¹, the dynamic peak compressive strain of ordinary concrete increases by 20.8% [28]. There are two main reasons for the increase in the overall dynamic compressive strength of AASCM specimens with the increase in strain rate. First, the specimen is under confining pressure. The higher the strain rate, the more evident the confining pressure effect, which leads to an increase in the dynamic compressive strength of the AASCM under a high strain rate [29]. Secondly, the greater the strain rate, the greater the impact energy of the specimen and the more microcracks in the material that must consume energy. The specimen cannot suddenly accumulate sufficient microcracks in a short time to consume the energy generated by the impact. It can only consume energy by increasing the strength and elastic deformation, thereby increasing the dynamic compressive strength of the specimen [30].

3.3.2. Effect of Steel-Fiber Content on Dynamic Compressive Strength

To study the effect of steel-fiber content on dynamic compressive strength, the variation of dynamic compressive strength σ_d of AASCM specimens with steel-fiber content under 50–110 s⁻¹ loading rate was analyzed, as displayed in Figure 7. It can be observed that an increase in the steel-fiber content does not effectively improve the dynamic compressive strength of the AASCM at a strain rate of 50–80 s⁻¹. Compared with the undoped fiber specimen, a steel-fiber content of 0.5% only increases the dynamic compressive strength of AASCM by 0.9–4.5%. The main reason why the incorporation of steel fibers does not effectively improve the dynamic compressive strength of AASCM specimens is that under the condition of a low strain rate, the impact energy of the specimens is small, the impact load action time is long, and the specimens have sufficient time to gather enough microcracks to consume the energy generated by the impact; therefore, the increase in the dynamic compressive strength of the specimens is not apparent.

It can also be observed from Figure 7 that steel fiber can effectively improve the dynamic compressive strength of AASCM when the strain rate is 80–110 s⁻¹. Compared with the specimens without fibers, the dynamic compressive strengths of AASCMs with fiber contents of 0.5%, 1.0%, and 1.5% increase by 9.9%, 14.3%, and 14.7%, respectively. The higher the strain rate, the more evident the effect of the steel-fiber content on the dynamic compressive strength of the AASCM. This is because the elastic modulus of the steel fiber is higher than that of the AASCM; under a high strain rate, the steel fiber bears part of the energy and the proportion of the energy increases, which limits the elastic deformation ability of the AASCM [31].

3.4. Dynamic Peak Compressive Strain

3.4.1. Effect of Strain Rate on Dynamic Peak Compressive Strain

To study the influence of strain rate on dynamic peak compressive strain, the development law of dynamic peak compressive strain ε_c of AASCM specimens under different strain rates was analyzed when the steel-fiber content was 0–1.5%. The results are displayed in Figure 8. The overall dynamic peak compressive strain of the AASCM specimens decreases with an increase in the strain rate, except for the specimens without steel fibers and with a loading rate of 60–80 s⁻¹. When the loading rate increases from 50–60 s⁻¹ to 100–110 s⁻¹, the dynamic peak compressive strain ε_c of the AASCM specimens decreases by 13.2–49.3%. Studies have demonstrated that when the loading rate increases from 55 s⁻¹ to 108 s⁻¹, the dynamic peak compressive strain of ordinary concrete decreases by 52% [32]. The effect of the strain rate on the dynamic peak compressive strain of the AASCM specimens is similar to that of ordinary and recycled concrete. This is because the peak compressive stress of the steel-fiber AASCM is positively correlated with the strain rate; therefore, the strength of the specimen increases with an increase in strain rate, the ability of the AASCM to resist failure increases, and the deformation of the specimen decreases gradually.

3.4.2. Effect of Steel-Fiber Content on Dynamic Peak Compressive Strain

In order to study the influence of steel-fiber content on dynamic peak compressive strain, the development law of dynamic peak compressive strain ε_c of AASCM specimens with different steel-fiber contents was analyzed when the loading rate was 50–110 s⁻¹. The results are displayed in Figure 9. It can be observed that except for individual specimens, the dynamic peak strain of the AASCM specimens is 3500–8000 με, which is considerably higher than the static peak compressive strain of AASCM (1400–2300 με) [33]. It can also be observed that an appropriate amount of steel fiber (0.5%) can increase the dynamic compressive strain of AASCM specimens at each loading strain rate; the increase ratio is 1.2–127.7%. There are two main reasons why an appropriate amount of steel fibers can improve the dynamic peak compressive strain of AASCM specimens. First, under an impact load, steel fibers can inhibit the development and extension of transverse cracks in the specimens, thereby increasing the longitudinal deformation capacity of the specimens and improving the dynamic peak compressive strain. Secondly, under an impact load, the steel fiber has the characteristics of high strength and high elastic modulus, which allows the steel fiber to effectively share part of the impact energy and improve the dynamic compressive strain of the specimen.

It can also be observed from Figure 9 that the incorporation of excessive steel fibers will reduce the dynamic peak compressive strain ε_c of the AASCM specimens at each loading rate. Compared with the steel-fiber content of 0.5%, the steel-fiber contents of 1% and 1.5% reduce the dynamic peak compressive strain of AASCM specimens by 64.9–121.9% and 48–121.6%, respectively. The initial and final setting times of the AASCM specimens are considerably smaller than those of ordinary concrete. The incorporation of steel fibers reduces the working performance of AASCM, making steel fibers more prone to clustering in AASCM than in ordinary concrete. The internal defects of the material increase and the brittleness increases under the impact load, which in turn reduces the dynamic peak compressive strain of the AASCM specimens.

3.5. Energy Absorption

3.5.1. Energy Absorption and Calculation

Energy absorption is another important index for measuring the impact resistance of AASCM and reflects the ability of the material to absorb energy during the period from loading to failure. The energy absorption capacity of a material can be obtained by integrating the stress–strain curve [34]. The equation is as follows:

$$W={\int }_0^{\epsilon }\sigma \left(\epsilon \right)d\epsilon ,$$

(2)

where σ(ε) is the dynamic stress–strain curve of the specimen and ε is the dynamic limit strain of the curve.

3.5.2. Effect of Strain Rate on Energy Absorption

To study the effect of strain rate on the impact toughness of AASCM, the development law of energy absorption W of AASCM specimens under different strain rates was analyzed when the steel-fiber content was 0–1.5%. The results are displayed in Figure 10. It can be observed that the impact toughness of the AASCM increases with an increase in the strain rate. When the loading rate increases from 50–60 s⁻¹ to 100–110 s⁻¹, the impact toughness of AASCM increases by 9.4–153%. The effect of strain rate on the impact toughness of AASCM is similar to that of ordinary concrete and recycled concrete. Studies have indicated that when the loading rate increases from 65 s⁻¹ to 90 s⁻¹, the impact toughness of ordinary concrete increases by 51% [33]. This is because at low strain rates, the specimen is not completely ruptured, and the reflection and transmission of energy are high, thereby reducing the energy absorbed by the specimen [34]. With an increase in the strain rate, the damage to the specimen is aggravated; however, the impact time is shortened, the crack development time is limited, more energy is used for the generation of microcracks, and the generation of cracks requires more energy than the development, resulting in the improvement of the AASCM impact toughness [35,36,37].

3.5.3. Effect of Steel Fiber Content on Energy Absorption

To study the effect of steel-fiber content on the impact toughness of AASCM, the development law of the energy absorption W of AASCM specimens with different steel-fiber contents was analyzed at a loading rate of 50–110 s⁻¹. The results are displayed in Figure 11. It can be observed that steel fibers can improve the impact toughness of the AASCM specimens as a whole, except for the specimens with a loading rate of 50–60 s⁻¹ and steel-fiber content of 1%. The main reason for this is that the steel fiber is closely connected to the AASCM and bears the main impact force at the microcracks of the material; more energy is required to pull out the steel fibers during the AASCM failure process [35].

It can also be observed that the impact toughness of the AASCM increases with an increase in the steel-fiber content at high strain rates. When the strain rate is 80–110 s⁻¹, the energy absorption capacities of AASCM with fiber contents of 0.5%, 1.0%, and 1.5% are 45.2%, 55.5%, and 73.1% higher than that of non-fiber AASCM, respectively. This is because the specimen is completely broken at a high strain rate, and the reflection and transmission of energy are extremely low. The tensile, pull-out, and fracture properties of the steel fibers are particularly important for inhibiting the generation and development of microcracks. Therefore, the greater the fiber volume content, the stronger the energy absorption capacity [38], which is consistent with the conclusions of Zhang [36].

4. Dynamic Constitutive Model of Steel-Fiber Reinforced Alkali Slag Cementitious Material

Domestic and foreign scholars have conducted research on the constitutive model of concrete and have obtained several conclusions. In this study, two types of dynamic stress–strain constitutive models of concrete were considered and evaluated, as indicated in

Table 4. Dynamic constitutive model of concrete.

References	Constitutive Model	Scope of Application
Al-Salloum [35]	$\mathsf{\sigma }={\displaystyle \frac{AX+(B-1)X^2}{1+\left(A-2\right)X+B{X}^2}}{\sigma }_{\mathrm{d}}$ $\mathrm{A}=2.318\mathrm{s}\mathrm{i}\mathrm{n}(0.0086{\dot{\epsilon }}_{\mathrm{c}}+0.1436)$ $\mathrm{B}=0.595+0.5095\cos \left(0.01865{\dot{\epsilon }}_{\mathrm{c}}\right)+0.1386\mathrm{s}\mathrm{i}\mathrm{n}\left(0.01865{\dot{\epsilon }}_{\mathrm{c}}\right)$ $\mathrm{X}={\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{c}}}}$ ${\epsilon }_{\mathrm{c}}=0.0008{{\dot{\epsilon }}_{\mathrm{c}}}^3-0.5{{\dot{\epsilon }}_{\mathrm{c}}}^2+96{\dot{\epsilon }}_{\mathrm{c}}-1580$	Ordinary concrete
Hou [16]	$\mathsf{\sigma }=E_{\mathrm{d}}\epsilon \left[\left(1-C\right)+C(1-D)\right]$ $D=1-\mathrm{e}\mathrm{x}\mathrm{p}[-{\left({\displaystyle \frac{\epsilon }{F}}\right)}^n]$ $n=-0.56+3V_f+\left(0.35-2V_f\right)ln{\dot{\epsilon }}_c$ $F=0.0062+0.3{V_f}^{1.7}-0.00167\left(0.1+V_f\right)ln{\dot{\epsilon }}_{\mathrm{c}}$ $C=0.977-1.4V_f+\left(0.004+0.25V_f\right)ln{\dot{\epsilon }}_c$	Fiber-reinforced concrete $(0\% \le V_f \le 5.0\%)$
This paper proposes	$\mathsf{\sigma }={\displaystyle \frac{AX+(B-1)X^2}{1+\left(A-2\right)X+B{X}^2}}{\sigma }_{\mathrm{d}}$ $\mathrm{X}={\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{c}}}}$ $\mathrm{A}=-1.96968+0.19855{\dot{\epsilon }}_{\mathrm{c}} -$$913.96781V_f -$$0.0017{\dot{\epsilon }}_{{\mathrm{c}}^2}$$+ 52101.53203V_{f^2}$ $\mathrm{B}=1.38152-0.0392{\dot{\epsilon }}_{\mathrm{c}}$$+ 273.72326V_f$$+ 0.0002963{\dot{\epsilon }}_{{\mathrm{c}}^2}$$-$$11912.45192V_{f^2}$	Steel-fiber toughened alkali slag cementitious material

Note: F, n, C, A, and B are the material parameters, σ_d is the dynamic peak compressive strain, and ε_c is the damage factor.

. Al-Salloum et al. [39] established a dynamic constitutive model of concrete based on the test results, mainly considering the influence of the dynamic strain rate and peak compressive strain on the model. In addition, Hou et al. [40] introduced parameters to represent the influence of residual strength, proposed a relationship between the parameters, dynamic strain rate, and fiber volume content, and established a constitutive model of fiber-reinforced concrete. Figure 12 compares the experimental values of the dynamic stress–strain relationship for the Al-Salloum model, Hou model, and steel-fiber-reinforced AASCM. The Hou model predicts worse results at low fiber admixture due to its use of Reactive Powder Concrete, which has a higher modulus of elasticity [41]. The change trend of the Al-Salloum model curve is similar to the dynamic stress–strain curve of the steel-fiber-reinforced AASCM. Therefore, the Al-Salloum model can better predict the dynamic stress–strain curve of Al-Salloum than the Hou model.

The parameters were modified based on the Al-Salloum concrete model. The parameters are modified. The modified steel-fiber-toughened AASCM dynamic stress–strain model is presented in Table 4. The dynamic stress–strain relationship of the steel-fiber-reinforced AASCM was compared with that of the modified Al-Salloum model, as indicated in Figure 13. The stress–strain curve of the steel-fiber-toughened AASCM fits well with the modified FR-AASCM curve; the correlation coefficient between the modified equation and measured data is 0.91.

5. Micro-Analysis

The microstructure of the steel fibers in the AASCMs is displayed in Figure 13. It can be observed that the disordered distribution of steel fibers in AASCM forms a three-dimensional support network [42]. The support generated by steel fibers can prevent the segregation and settlement of aggregates and enhance the mechanical properties of AASCMs [34]. The tendency of cracks to localize along specific paths can be prevented by other mechanisms, such as crack deflection or crack branching, thus increasing the effective crack path for stress release and improving mechanical properties. Simultaneously, the material produces cracks perpendicular to the length of the steel fiber after impact. It can be observed that the steel fibers bridge both sides of the crack. At this point, the steel fibers can have a bridging role [43,44,45]. Through the bonding force between steel fibers and the cementitious material, crack development is inhibited and the ability of the material to resist deformation is enhanced, thereby enhancing the impact resistance of the AASCM. In addition, it can be observed from Figure 14 that with an increase in the steel-fiber volume content, the number of microcracks and crack width of the specimen gradually decrease, which explains why with an increase in steel-fiber content, the damage degree of the AASCM specimen decreases. However, excessive steel fibers cause fiber agglomeration [26] (Figure 14b), which leads to a decrease in the density of the AASCM and an increase in porosity, which ultimately leads to a decrease in the mechanical properties (the dynamic elastic modulus E_d, dynamic compressive strength σ_d, and dynamic peak compressive strain ε_c) of the AASCM.

6. Conclusions

In this study, four types of steel-fiber volume content AASCM impact resistance tests were conducted with the strain rate and steel-fiber content as independent variables. The effects of different variables on the dynamic elastic modulus, dynamic compressive strength, dynamic peak compressive strain, and energy absorption of the AASCMs were analyzed. The main conclusions are as follows.

(1)

The dynamic elastic modulus and dynamic compressive strength of the AASCMs increases with the increase of the strain rate. Steel fibers can improve the dynamic elastic modulus and dynamic compressive of AASCMs. The dynamic elastic modulus of AASCMs can be increased by 65.6–173.7%, and increase the dynamic compressive strength of AASCMs by 2.4–44% by adding a 1.0% volume fraction of steel fiber.

(2)

The dynamic peak compressive strain of AASCMs without steel fiber is the greatest at a strain rate of 60–80 s⁻¹. An appropriate amount of steel fibers can improve the dynamic peak compressive strain of the AASCMs. With an increase in steel-fiber volume content, the dynamic peak compressive strain of AASCMs increases first and then decreases, reaching a maximum at 0.5% content.

(3)

The energy absorption capacity of AASCMs increases with the increase the strain rate. Steel fibers can significantly improve the impact toughness of AASCMs. At high strain rates, the larger the fiber volume content, the stronger the energy absorption capacity of AASCMs; the steel fiber can increase the energy absorption capacity of AASCMs by 9.4–153%.

(4)

The existing constitutive model has a high prediction accuracy for the FR-AASCM stress–strain curve; and the correlation coefficient was greater than 0.85. A dynamic constitutive model of the FR-AASCM was established based on the Al-Salloum model with a correlation coefficient was 0.91.

(5)

Through SEM microanalysis, it was found that with an increase in the steel-fiber volume content, the number of microcracks generated after the specimen is destroyed decreases, the width of the microcracks decreases, and the degree of damage gradually decreases, thereby improving the impact resistance of the AASCMs.

(6)

In addition, the work can be also extended under several directions in the future. First, introduce hybrid fiber systems (e.g., a mix of steel and synthetic fibers) may further optimize both ductility and energy absorption of AASCMs. Second, the combination of Split Hopkinson Pressure Bar test and soundness test can be considered to explore the delayed expansion resistance of the AASCM. Finally, the toughening efficiency of steel fibers can be further improved by controlling the orientation of steel fibers in AASCMs through the magnetic field orientation method, and the effect of the setting speed of AASCMs on the orientation of fibers can be explored.