In order to better match the multi-level structural characteristics and multi-scale fracture process of cementitious composite, multi-scale hybrid fiber-reinforced strain hardening cementitious composite (MsHySHCC) was designed by adding hooked steel fiber and calcium carbonate (CaCO_{3}) whisker into conventional polyvinyl alcohol (PVA) fiber-reinforced SHCC. Compressive properties of PVA-SHCC and MsHySHCC were evaluated experimentally. The results indicate that the designed MsHySHCC had a better compressive performance than that of PVA-SHCC. Moderately partially substituted PVA fibers by steela fiber and CaCO_{3} whisker enhanced the compressive parameters, however, further substitution of PVA fibers by increasing the content of CaCO_{3} whisker didn’t bring a higher promotion. Two kinds of semi-theoretical compression constitutive models were developed from the perspective of damage mechanics theory and geometrical mathematical description, respectively. It was found that both of the proposed models can be applied to predict the uniaxial compressive stress-strain relationships of PVA-SHCC and MsHySHCCs.

Con el fin de combinar de la mejor forma posible las características estructurales de compuestos base cemento a varios niveles y su proceso de fractura a múltiples escalas, se diseñó un compuesto híbrido de base cemento de endurecimiento por deformación reforzado con fibras (MsHySHCC), añadiendo fibra de acero en forma de gancho y fibra de carbonato de calcio (CaCO_{3}) en SHCC reforzado con fibra de alcohol polivinílico convencional (PVA). Se evaluaron las propiedades a compresión de PVA-SHCC y MsHySHCC. Los resultados indican que el MsHySHCC diseñado tuvo un mejor rendimiento a compresión que el de PVA-SHCC. Las fibras de PVA sustituidas parcialmente por fibra de acero y de CaCO_{3} mejoraron los parámetros de compresión, sin embargo, una mayor sustitución de las fibras de PVA no causó una mejora al aumentar el contenido de fibras de CaCO_{3}. Se desarrollaron dos tipos de modelos constitutivos de compresión semi-teóricos desde la perspectiva de la teoría de la mecánica del daño y la descripción matemática geométrica, respectivamente. Se encontró que ambos modelos propuestos se pueden aplicar para predecir las relaciones de tensión-deformación a compresión uniaxial de PVA-SHCC y MsHySHCCs

Strain hardening cementitious composite (SHCC) has attracted wide attention in the field of civil engineering because of its ultra-high ductility and obvious characteristics of multiple cracking (

To solve the cost issue, fiber hybridization method is usually employed (

Recently, as a novel cheap microfiber, calcium carbonate (CaCO_{3}) whisker (CW) was introduced to improve the mechanical properties of PVA-SHCC and hybrid SF/PVA-SHCC on microscopic scale level. Therefore, a new type of hybrid fiber reinforced SHCC, which is named multi-scale hybrid fiber reinforced strain hardening cementitious composite (MsHySHCC), was designed (

Ma et al. (

To PVA-SHCC and MsHySHCC, the fully understand of their compressive properties and compression constitutive model is the important precondition to promote their widely application in structural design. Therefore, many scholars have evaluated the compressive properties and tried to describe the compressive constitutive relationship of SHCC and hybrid fiber reinforced SHCC from an empirical or theoretical perspective. Ding et al. (

Yun (

From the discussions on the previous literatures, it can be found that the effects of SF-PVA hybrid fibers and SF-PVA-CW multiscale hybrid fibers on the compressive behavior of SHCC are not fully understood, and even sometimes obtained contrary conclusions in previous literatures. Moreover, the studies on the theoretical compressive constitutive models are still very limited. Although some scholars have modified the Lemaitre’s damage model to describe the compression constitutive relationship of normal concrete, these existing concrete damage constitutive models are not applicable to hybrid fiber-reinforced cementitious composite, especially for hybrid fiber reinforced SHCC and MsHySHCC. Therefore, a further experimental and theoretical investigation on the compressive behavior of hybrid fiber reinforced SHCC is still needed.

In this paper, a kind of MsHySHCC was designed by adding hooked steel fiber and CaCO_{3} whisker into conventional PVA-SHCC. Compressive properties of PVA-SHCC and designed MsHySHCC were evaluated experimentally. The effect of steel fiber, PVA fiber and CaCO_{3} whisker on the compressive stress, compressive strain and compressive toughness was discussed. Based on the experimental results, a damage constitutive model and a geometrical mathematical model were proposed. Through the analysis in this paper, an in-depth understanding for compressive behavior of PVA-SHCC and MsHySHCC will be given, which is of great significance for their large-scale structural engineering applications in the future.

Raw materials for mortar matrix used in this study were ordinary Portland cement P·O 42.5, Class-I fly ash, fine quartz sand (particle size 100-210 μm, mean size 150 μm) and water. The ratio of cement, quartz sand and fly ash was 1:1.8:4, and the water to binder ratio was 0.34. The amount of superplasticizer (polycarboxylic acid type, water reducing ratio 28.3%) was 0.5 wt.% of binder content. The multiscale hybrid fiber system was composed of steel fiber, PVA fiber and CaCO_{3} whisker. Their basic information was shown in

Groups | Specification | Steel fiber (SF) /% | PVA fiber (PVA) /% | CaCO_{3} whisker (CW) /% |
---|---|---|---|---|

Control-1 | Matrix | 0 | 0 | 0 |

Control-2 | CW1 | 0 | 0 | 1 |

Control-3 | CW2 | 0 | 0 | 2 |

PVA-SHCC | PVA2 | 0 | 2 | 0 |

MsHySHCC-1 | SF0.25PVA1.75CW1 | 0.25 | 1.75 | 1 |

MsHySHCC-2 | SF0.5PVA1.5CW1 | 0.5 | 1.5 | 1 |

MsHySHCC-3 | SF0.75PVA1.25CW1 | 0.75 | 1.25 | 1 |

MsHySHCC-4 | SF0.25PVA1.5CW2 | 0.25 | 1.5 | 2 |

MsHySHCC-5 | SF0.5PVA1.25CW2 | 0.5 | 1.25 | 2 |

MsHySHCC-6 | SF0.75PVA1CW2 | 0.75 | 1 | 2 |

Before compressive test, the tensile stress-strain curves were experimentally obtained to verify whether the designed MsHySHCCs can achieve strain-hardening behavior. Typical tensile stress-strain curves are shown in

The mixing, preparation and curing processes of compression specimens are shown in ^{o}C and a humidity of 95%, and were kept there for 28 days. To ensure the accuracy of the experimental results, for each design mix 6 specimens were casted.

Uniaxial compression test was carried out using an electro-hydraulic servo material testing machine. The loading method was the displacement control with a rate of 0.2 mm/min. The loading instrument for the compression test is shown in

In order to evaluate the compressive properties (compressive strength, compressive peak strain and compressive toughness) more accurately, the Weibull distribution method was employed in this study. The standard Weibull distribution equation can be expressed as

Where _{0} is the characteristic strength (also called scale parameter);

According to _{0}, respectively. Taking the compressive strength of PVA-SHCC group as an example, its linear fitting curves and probability distributions are illustrated in _{0} is 37.1. As illustrated in

_{
a
} and lateral deformation _{
l
} of specimen at 0.85 times peak stress. From _{
a
} and _{
l
} values of all the designed MsHySHCCs in

An in-depth analysis of _{3} whisker has higher cracking control ability than PVA fiber, and a high content of steel fiber means a better anti-deformability, as have been widely discussed by previous literatures (_{3} whisker can’t effectively improve the compressive behavior of SHCC (see MsHySHCC-4, MsHySHCC-5 and MsHySHCC-6). This implies that the macro fibers (e.g. steel fiber and PVA fiber) have stronger cracking control ability than that of micro fiber (e.g. CaCO_{3} whisker).

Typical compressive stress-strain curves of control groups, PVA-SHCC and MsHySHCCs are shown in

Compared to mortar matrix without whiskers, the introduction of CaCO_{3} whisker improves the compressive behavior due to the micro reinforcing mechanisms, such as whisker pullout, whisker bridging and crack deflection, as shown in

All the pre-peak curves are linear and elastic until about 40-60% of the peak, then the curves deviate from linear stage and become increasingly nonlinear up to the peak stress. Compared to PVA-SHCC, the ascending slop of MsHySHCCs increases slightly due to the high elastic modulus of steel fiber and CaCO_{3} whisker. In the descending stage, the MsHySHCCs has a relative higher residual stress value than that of PVA-SHCC due to the addition of hooked steel fibers and CaCO_{3} whiskers, which can provide a better bridging effect than mono PVA fibers.

Partially substituted PVA fibers by steel fibers and CaCO_{3} whiskers increased the compressive strength, as can be seen from _{3} whisker can improve the compactness of composite and the micro reinforcing mechanisms presented in

With the increase of steel fiber and CaCO_{3} whisker content, the descending stage becomes plumper, yielding higher residual load bearing capacity. This is because the steel fiber and CaCO_{3} whisker used in this study are rigid fiber with very high elastic modulus and stiffness. They can well hinder the growth and propagation of cracks, thus providing a significant improvement effect on residual load bearing capacity. Inversely, PVA fiber is a kind of flexible synthetic fiber, and its influence on the residual load bearing capacity is weaker than that of steel fiber and CaCO_{3} whisker.

(a) whisker pullout; (b) whisker bridging; (c) crack deflection

Based on the compressive stress-strain curves in _{3} whisker increases the compressive strength and compressive peak strain owing to the micro-mechanism in _{3} whisker improves the compressive strength but decreases the compressive peak strain. Increasing whisker content can further improve the compressive strength, although the content of PVA fiber is further decreased. The compressive peak strain of PVA-SHCC and MsHySHCCs ranges from 3200 to 4100 με. The compressive peak strain of MsHySHCCs is smaller than that of PVA-SHCC, which implies that the MsHySHCCs have a higher elastic modulus, because the peak stress of MsHySHCCs is larger than that of PVA-SHCC. Furthermore, it seems that there is little correlation between the peak strain and the content of steel fibers or CaCO_{3} whiskers.

(a) compressive strength and (b) compressive peak strain

Compressive toughness is used to evaluate the energy absorption capacity of PVA-SHCC and MsHySHCCs under compression loading, which is numerically equal to the area enclosed under the stress-strain curve, also called strain energy, as given in _{3} whiskers can’t further significantly increase the compressive toughness of MsHySHCCs, as shown in

Groups | Pre-peak strain energy /(N·mm/mm^{3}) |
Post-peak strain energy /(N·mm/mm^{3}) |
Total strain energy /(N·mm/mm^{3}) |
Relative toughness index |
---|---|---|---|---|

PVA-SHCC | 6.92 | 24.38 | 33.61 | 1.00 |

MsHySHCC-1 | 7.64 | 31.80 | 38.98 | 1.16 |

MsHySHCC-2 | 7.94 | 34.06 | 42.20 | 1.26 |

MsHySHCC-3 | 7.73 | 34.58 | 45.47 | 1.35 |

MsHySHCC-4 | 7.31 | 25.66 | 45.99 | 1.37 |

MsHySHCC-5 | 6.83 | 28.40 | 44.90 | 1.34 |

MsHySHCC-6 | 7.41 | 31.74 | 41.29 | 1.23 |

Based on the strain equivalent principle, previous literatures state that the compressive damage constitutive model of plain concrete can be expressed as

where _{
pk
} is the peak compressive strain;

where _{
pk
} is the compressive strength (peak compressive stress), MPa.

However, to fiber-reinforced cementitious composite, the addition of fibers improves the compressive toughness of cementitious composite, thus making the compressive stress-strain curves plumper. Therefore, a fiber reinforcing factor _{
v
} is employed in the above model to consider the effect of volume and geometrical characteristic of fibers (_{
v
} can be expressed as

where _{
i
} is the volume content of fiber _{
i
} is the length of fiber _{
i
} is the diameter of fiber _{
i
} is elastic modulus of fiber _{
sf
} is the elastic modulus of steel fiber, GPa, as shown in

To PVA-SHCC and MsHySHCCs, the post-peak load decreases more slowly and the energy absorption capacity is higher. In order to describe the post-peak stress-strain relationship more accurately, an energy method was employed in this paper to describe the post-peak strain behavior. According to Ou and Tsai’s study (

where _{
c
} is the energy absorption capacity of control mortar, which can be integrated through the stress-strain curves in _{
c
} can be defined as the area enclosed under the compressive stress-strain curve when the compressive strain is 0.015.

In this paper, the relationship between elastic modulus _{
v
} is shown in _{
v
} is shown in

The post-peak compressive stress-strain relationship of PVA-SHCC and MsHySHCCs can be expressed as

Where

Therefore, the compressive stress-strain relationship of PVA-SHCC and MsHySHCCs can be expressed as

Many current specifications have given the geometrical mathematical equations to describe the ascending and descending curves of compressive constitutive relationship of normal concrete, as presented in

where

Compared to normal concrete, PVA-SHCC and MsHySHCC will obtain a higher post-peak residual bearing capacity due to the addition of fibers. Therefore, the descending parameter _{
v
}. Based on the experimental results and regression analysis, the relationship between _{
v
}
_{
pk
} can be illustrated in

Compressive behaviors of multi-scale fiber reinforced strain hardening cementitious composite (MsHySHCC) were investigated experimentally in this paper. From this study, the following conclusions can be addressed.

The addition of CaCO_{3} whisker increased the compressive strength and toughness of mortar matrix by the micro-mechanism of whisker pull-out, whisker bridging and crack deflection, thus improved the compressive performance of MsHySHCC.

(2) The hybrid use of hooked steel fiber and CaCO_{3} whisker had higher cracking control ability than PVA fiber, and a high content of steel fiber means a better anti-deformability. Moderately partially substituted PVA fibers by steel fiber and CaCO_{3} whisker can enhance the compressive behaviors of PVA-SHCC. But excessive reduction of PVA fiber content will degrade the compressive performance of MsHySHCC.

(3) Based on the experimental data, a damage constitutive model and a geometrical mathematical model were proposed semi-theoretically. Through the comparison between experimental results and theoretical results calculated by these two models, it can be found that both of the models can well calculate and predict the compressive constitutive relationships of PVA-SHCC and MsHySHCC. The geometrical constitutive model is more concise, but the damage constitutive model can describe the damage and reinforcing mechanism to some extent.

The Natural Science Foundation of China (51908247) and the Opening Project of State Key Laboratory for GeoMechanics and Deep Underground Engineering (KFJJ202007) are gratefully acknowledged by the authors.

Conceptualization: C. Zhang. Funding acquisition: C. Zhang. Investigation: C. Zhang, Z. Yuan, Y. Shen. Methodology: Z. Yuan, Y. Shen. Validation: C. Zhang, Z. Yuan, Y. Shen. Roles/Writing, original draft: C. Zhang. Writing, review & editing: C. Zhang.

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