1. Introduction
Concrete has the advantages of high compressive strength, low cost, and easy availability of materials, and it has become a widely used building material. However, due to the brittle failure, low tensile strength, and poor crack resistance of concrete, its application in engineering is limited. To improve the above shortcomings of concrete, researchers incorporated various fibres into concrete to made fibre-reinforced concrete (FRC). Although FRC mixed with steel fibre, carbon fibre, glass fibre, and so on improves the toughness of concrete to a certain extent, the strain-softening phenomenon shown in the tensile process causes limited improvement in the ultimate tensile strength and tensile strain [
1]. To improve the performance of FRC and meet the demand for FRC with strain-hardening ability, Naaman et al. [
2] conducted a lot of research on the damage morphology of the matrix. It was found that the matrix damage morphology depends on the fibre length, aspect ratio, volume fraction, spatial distribution, and pullout behaviour of the fibre, as well as the properties of the matrix. This also prompted researchers to come to a new understanding of FRC. Based on the previous research results, in 1987, Naaman [
3] first defined the conditions leading to strain-hardening behaviour and multiseam cracking of FRC in tension, which provided an important basis for subsequent research. Based on a micromechanical model, Li [
4] proposed the design concept of FRC with strain-hardening characteristics by reasonably controlling the properties of the fibre and the matrix and the interface parameters of fibre/matrix. On this basis, an ECC with higher tensile strength and tensile strain was successfully prepared [
5,
6,
7,
8]. ECCs are prepared using cement mortar as the matrix, fine quartz sand as the aggregate, and a certain amount of soft fibre (usually PVA fibre or PE fibre). The ultimate tensile strains of ECCs are 3~12%, which are several hundred times those of ordinary cementitious materials; additionally, the damage shows multiple obvious cracking patterns, and the cracks can all be maintained at approximately 60 μm [
9,
10,
11]. It can be concluded that ECCs have good toughness and meet the requirements of complex toughness, crack resistance, and durability.
PE fibres have high tensile strength and modulus of elasticity values and are suitable for acidic, alkaline, and high-temperature environments, making them particularly useful for producing ECCs. Li [
5], based on the theory of ECC preparation, selected PE fibre to prepare a PE-fibre-reinforced ECC with excellent flexural toughness and flexural properties.
Wang [
12] investigated the effects of PE fibres with different volume fractions (0%, 1%, 1.5%, and 2%) on the macroscopic and microscopic properties of ECCs. When the PE fibre content in the ECC reaches 1%, the ECC shows strain hardening and multiple seam cracking, and on the microscopic level, as the PE fibre content increases, the bridging properties of its ECC fibre and matrix show a trend of first increasing and then decreasing.
Liu [
13] conducted mechanical property tests on high- and early-strength cementitious composites (HE-ECCs) mixed with steel–PE fibres and investigated the effects of ultrafine fly ash and rubber particles on the properties. The test results show that partial replacement of PE fibres with steel fibres or ultrafine fly ash can improve the compressive strength and tensile modulus values of HE-ECC mixes. In terms of microstructure, ultrafine fly ash significantly improves the fracture toughness and physical adhesion strength between the PE fibres and the matrix.
Xia [
14] investigated the effects of four different fine aggregates on the mechanical properties of HE-ECCs. The results showed that the different types of fine aggregates have little effect on the fluidity of PE-ECCs but have a relatively great effect on the compressive strength, uniaxial tensile strength, and ultimate tensile strain.
Yi [
15] found that the slip-hardening parameter (β) of ultrahigh-strength ultrahigh-ductility cementitious composites (UHS-UHDCCs) is closely related to the inclination angle of PE fibres, and an increase in the inclination angle of PE fibres leads to an increase in β. A fine-scale mechanical model of single-PE-fibre pullout has been proposed and defined as physical debonding. The results show that the pullout load-displacement curve and single-crack stress–tension curve of a single PE fibre verify the accuracy of the proposed UHS-UHDCC fine-scale mechanical model.
A foundation of ECC research is the micromechanical model. The micromechanical model of ECCs is focused on microstructural and microscopic phenomena [
5,
16]. The damage of cement matrix composites starts from the microscopic scale [
17,
18,
19], where many cracks are generated in the microstructure; stress concentration occurs at the cracks. These small and irregular cracks develop and accumulate rapidly, and when the cracks reach saturation, macroscopic main cracks can be observed; eventually, the main cracks crack completely, leading to the destruction of the material. The fibres commonly used are in millimetre sizes; thus, the fibres have difficulty addressing the microscopic-size shortcomings of concrete. However, with the gradual maturity of micromaterial and nanomaterial research, the application of micromaterials and nanomaterials blended with macroscopic fibres in cementitious composites can solve this problem [
20,
21,
22,
23].
Cao [
24] added microscale CWs to cementitious composites and concluded that the resulting strengthening of the microstructure can inhibit the formation of microcracks, improve the fine pore structure, reduce the brittleness of cementitious materials, and improve their micromechanical properties.
Pan [
25] designed multiscale fibre-reinforced cementitious composites with PVA fibres and CWs; the experimental results show that for the ECC, the compressive strength is significantly increased and that the tensile strain hardening behaviour is improved when the CW volume fraction is 6%. Microstructural analysis shows that CWs and PVA fibres have good interactions at different sizes.
Muradyan [
26] studied the effects of different CNTs concentration (0.001, 0.01, 0.05, and 0.1 wt.%) on the compressive strengths of cement mortars. The results show that the 7 d strengths of the specimens increase by 13% and 19.5% with and without surfactant, respectively, and that the 28 d compressive strengths increase by 6.3% and 13.8%, respectively.
Liu [
27] incorporated 0%, 0.05%, 0.08%, 0.10%, 0.15%, 0.20%, and 0.30% mass replacement proportions of MWCNTs at water–cement ratios of 0.25, 0.3, 0.35, and 0.4. The experimental results show that under a fixed water–cement ratio, with increasing CNT doping, the compressive and flexural strengths of the cementitious composites first increase and then decrease. The bridging and filling effects of CNTs are observed by electron microscopy.
Chaipanich [
28] used scanning electron microscopy (SEM) and X-ray diffraction (XRD) analyses to study the microstructures and morphologies of carbon nanotube cement composites. The scanning electron microscopy images show good interactions between carbon nanotubes and the cement matrix. CNTs act as fine aggregates at the microscale/nanoscale, making their microstructures increasingly dense and robust. The microstructures and mechanical properties of the cement matrix composites are improved after the incorporation of carbon nanotubes.
Lin [
29] fabricated carbon-fibre-reinforced polymer (CFRP) matrix composite laminates containing conductive nanofillers composed of different mass fractions of carbon black (CB), CNTs, and mixed CB and CNTs. The lightning damage tolerance levels of CFRP matrix composite laminates containing conductive nanofillers were evaluated using simulated lightning tests. The results show that the addition of CB and CNTs can reduce the lightning damage degree of CFRP composites while damaging the bending performance.
Lampkin [
30] chose to use CNTs as an additive to create a conductive resin matrix to improve the conductivity, thereby reducing the damage and increasing the residual strength of the material. The results show that due to the limited size of the manufactured CFRP plate, the residual strength of the CFRP composite material under the lightning test is not ideal, but the addition of CNTs effectively improves the conductivity of the CFRP composite material and reduces the damage of the lightning strike to the CFRP composite material.
Wu [
31,
32] used hybrids of CWs and partial substitutions of PE fibres to study their effects on the tensile and compressive properties of engineering cement-based composites. Cao [
33] formed a new hybrid fibre system by adding steel fibres, PVA, and CWs and evaluated the flexural toughness. Li [
34] used PVA fibres, CNTs, and granulated blast furnace slag to modify the properties of ECCs. However, the above studies involve little research on three different scales of fibres and do not feature comparisons of the effects of three different fibres on the mechanical properties of ECCs; in addition, an optimised design scheme for the comprehensive performance of the experimental design is not provided. Therefore, we propose the construction of a multiscale fibre reinforcement system using nanoscale CNTs, microscale CWs, and millimetre-scale PE fibres to control the defects at different levels through multilevel fibres to generally improve the mechanical properties of highly ductile fibre-reinforced cementitious composites. In this paper, we use nanoscale CNTs, microscale CWs, and millimetre-scale PE fibres as external doping fibres to design the effects of single-factor doping on the strengths of ECC specimens with three different scales of fibres; additionally, we use the Box-Behnken regression model in Design Expert software to establish a regression model with compressive strength, flexural strength, and tensile strength serving as response values. Compressive strength, flexural strength and tensile strength are used as response values to analyse the interactions between the two factors on the response values; the prediction results are given to derive the optimal ratio that meets the response value requirements, which provides a reference for the multiobjective optimisation of the ECC mix proportion.