Figure 1.
Sketch of test specimen (unit: mm)
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July
2022, 15(7): 1669-1683.
doi: 10.3934/dcdss.2021161
A novel bond stress-slip model for 3-D printed concretes
| 1. | School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an, China |
| 2. | School of Science, Xi'an University of Architecture and Technology, Xi'an, China |
| 3. | Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran |
| 4. | Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran |
This paper considers the 3D printing process as a discontinuous control system and gives a simple and coherent bond stress-slip model for a new and intelligent building 3-D printed concrete. The previous models focused on either the maximal stress or the maximal slip, however, the novel model uses an energy approach by the dimension analysis, so that the main factors affecting the bond stress-slip relationship can be clearly revealed, mainly including the concrete's properties (its porous structure and its strength), the steel bar's properties (its printing direction, its strength, its surface roughness and its geometrical property) and the printing process. It is confirmed that the proposed model, similar to the constitutive relationship in elasticity, plays a key role in concrete mechanics, and it can conveniently explain the observed phenomena from the experiment.
Keywords:
Reinforced concrete,
bond stress,
slip,
uniaxial tensile test,
energy factor,
optimization,
3D printing technology.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C35.
Citation:
Chun-Hui He, Shu-Hua Liu, Chao Liu, Hamid Mohammad-Sedighi. A novel bond stress-slip model for 3-D printed concretes. Discrete and Continuous Dynamical Systems - S,
2022, 15
(7)
: 1669-1683.
doi: 10.3934/dcdss.2021161
![]()
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Seeing with a single scale is always unbelieving: From magic to two-scale fractal, Thermal Science, 25 (2021), 1217-1219.
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A new proof of the dual optimization problem and its application to the optimal material distribution of sic/graphene composite, Reports in Mechanical Engineering, 1 (2020), 187-191.
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New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle, Thermal Science, 24 (2020), 659-681.
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J.-H. He and Y. O. El-Dib,
Homotopy perturbation method for Fangzhu oscillator, J. Mathematical Chemistry, 58 (2020), 2245-2253.
doi: 10.1007/s10910-020-01167-6. |
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J.-H. He and Y. O. El-Dib,
Homotopy perturbation method with three expansions for Helmholtz-Fangzhu oscillator, Internat. J. Modern Phys. B, 35 (2021), 2150244.
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doi: 10.1155/2012/328570. |
| [22] |
M. Hoseini Asl and J. Jafari Fesharaki,
3d optimization of gear train layout using particle swarm optimization algorithm, Journal of Applied and Computational Mechanics, 6 (2020), 823-840.
|
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X. Hu, G. Peng, D. Niu, X. Wu and L. Zhang,
Bond behavior between deformed steel bars and cementitious grout, Construction and Building Materials, 262 (2020), 120810.
doi: 10.1016/j.conbuildmat.2020.120810. |
| [24] |
M. Islam, A. Sadaf, M. R. Gómez, D. Mager, J. G. Korvink and A. D. Lantada,
Carbon fiber/microlattice 3d hybrid architecture as multi-scale scaffold for tissue engineering, Materials Science and Engineering: C, 126 (2021), 112140.
doi: 10.1016/j.msec.2021.112140. |
| [25] |
O. Leibovich and D. Z. Yankelevsky,
Nonlinear features of the bond-slip ascending branch, J. Materials in Civil Engineering, 32 (2020), 04020279.
doi: 10.1061/(ASCE)MT.1943-5533.0003368. |
| [26] |
T. Li, H. Zhu, Q. Wang, J. Li and T. Wu,
Experimental study on the enhancement of additional ribs to the bond performance of FRP bars in concrete, Construction and Building Materials, 185 (2018), 545-554.
doi: 10.1016/j.conbuildmat.2018.06.198. |
| [27] |
X.-X. Li, D. Tian and J.-H. He,
High energy surface as a receptor in electrospinning: A good switch for hydrophobicity to hydrophilicity, Thermal Science, 25 (2021), 2205-2212.
doi: 10.2298/TSCI191120107L. |
| [28] |
H. Liu, J. Yang and X. Wang,
Bond behavior between BFRP bar and recycled aggregate concrete reinforced with basalt fiber, Construction and Building Materials, 135 (2017), 477-483.
doi: 10.1016/j.conbuildmat.2016.12.161. |
| [29] |
W.-J. Meng, H.-X. Liu, G.-J. Liu, X.-Q. Kong and X.-Z. Wang,
Bond-slip constitutive relation between bfrp bar and basalt fiber recycled-aggregate concrete, KSCE Journal of Civil Engineering, 20 (2016), 1996-2006.
doi: 10.1007/s12205-015-0350-z. |
| [30] |
J. Patdiya and B. Kandasubramanian, Progress in 4d printing of stimuli responsive materials, Polymer-Plastics Technology and Materials, (2021), 1–39. |
| [31] |
A. Pavlovic and C. Fragassa,
Geometry optimization by fem simulation of the automatic changing gear, Reports in Mechanical Engineering, 1 (2020), 199-205.
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V. T. Pinto, L. A. Oliveira Rocha, C. Fragassa, E. Domingues Dos Santos and L. A. Isoldi,
Multiobjective geometric analysis of stiffened plates under bending through constructal design method, Journal of Applied and Computational Mechanics, 6 (2020), 1438-1449.
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Xolography for linear volumetric 3d, Printing Nature, 588 (2020), 620-624.
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M. Rossi, C. Calderini and S. Lagomarsino,
Experimental testing of the seismic in-plane displacement capacity of masonry cross vaults through a scale model, Bulletin of Earthquake Engineering, 14 (2016), 261-281.
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Comparison of advanced methods for picking path optimization: Case study of dual-zone warehouse, Int J. Simul Model, 19 (2020), 410-421.
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H. M. Sedighi and K. H. Shirazi,
Using homotopy analysis method to determine profile for disk cam by means of optimization of dissipated energy, International Review of Mechanical Engineering, 5 (2011), 941-946.
|
| [37] |
D. Shen, X. Shi, H. Zhang, X. Duan and G. Jiang,
Experimental study of early-age bond behavior between high strength concrete and steel bars using a pull-out test, Construction and Building Materials, 113 (2016), 653-663.
doi: 10.1016/j.conbuildmat.2016.03.094. |
| [38] |
J. Song, W. Wang, S. Su, X. Ding, Q. Luo and C. Quan,
Experimental study on the bond-slip performance between concrete and a corrugated steel plate with studs, Engineering Structures, 224 (2020), 111195.
doi: 10.1016/j.engstruct.2020.111195. |
| [39] |
J. Sun, J. Xiao, Z. Li and X. Feng,
Experimental study on the thermal performance of a 3d printed concrete prototype building, Energy and Buildings, 241 (2021), 110965.
doi: 10.1016/j.enbuild.2021.110965. |
| [40] |
X. Sun, C. Gao and H. Wang,
Bond performance between BFRP bars and 3D printed concrete, Construction and Building Materials, 269 (2021), 121325.
doi: 10.1016/j.conbuildmat.2020.121325. |
| [41] |
S. Troha, Ž. Vrcan, D. Karaivanov and M. Isametova,
The selection of optimal reversible two-speed planetary gear trains for machine tool gearboxes, Facta Universitatis, Series: Mechanical Engineering, 18 (2020), 121-134.
|
| [42] |
H. Wang, J. Chen, X. Sun and C. Gao,
Bonding performance between steel wire rope and 3d printed cement-based composites, Journal of Building Structures (in Chinese), 42 (2021), 1-7.
doi: 10.14006/j.jzjgxb.2019.0410. |
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K.-L. Wang, Effect of fangzhu's nanoscale surface morphology on water collection, Mathematical Methods in the Applied Sciences, 2020.
doi: 10.1002/mma.6569. |
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L. Wu, W. Yang, Y. Sun, Q. Kang and Z. Wan,
Experimental study on the influencing factors of the adhesive property between printed concrete and rebar, Industrial Construction (in Chinese), 262 (2020), 32-38.
doi: 10.13204/j.gyjzG20011603. |
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W. Xu, G. Wu et al., Experimental study on the bond behavior between sand spraying frp bars and concrete, Industrial Construction (in Chinese), (2009), 118–121. |
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C. Yang and S. Qi, Experimental study on the bond performance between bfrp bars and coral concrete, Engineering Mechanics (in Chinese), 35. |
| [47] |
Q. Yuan, Z. Li, D. Zhou, T. Huang, H. Huang, D. Jiao and C. Shi,
A feasible method for measuring the buildability of fresh 3d printing mortar, Construction and Building Materials, 227 (2019), 116600.
doi: 10.1016/j.conbuildmat.2019.07.326. |
| [48] |
Z. Zheng, M. Zhang and Z. Liu,
Investigation on evaluating the printable height and dimensional stability of food extrusion-based 3d printed foods, Journal of Food Engineering, 306 (2021), 110636.
doi: 10.1016/j.jfoodeng.2021.110636. |
| [49] |
Y.-T. Zuo and H.-J. Liu,
Fractal approach to mechanical and electrical properties of graphene/sic composites, Facta Universitatis, Series: Mechanical Engineering, 19 (2021), 271-284.
doi: 10.22190/FUME201212003Z. |
show all references
References:
| [1] |
Q. T. Ain and J.-H. He,
On two-scale dimension and its applications, Thermal Science, 23 (2019), 1707-1712.
doi: 10.2298/TSCI190408138A. |
| [2] |
A. M. Ali, L. Dieng and R. Masmoudi, Experimental, analytical and numerical assessment of the bond-slip behaviour in concrete-filled-frp tubes, Engineering Structures, 225 (2020) 111254.
doi: 10.1016/j.engstruct.2020.111254. |
| [3] |
L. Bai, J. Yu, M. Zhang and T. Zhou,
Experimental study on the bond behavior between H-shaped steel and engineered cementitious composites, Construction and Building Materials, 196 (2019), 214-232.
doi: 10.1016/j.conbuildmat.2018.11.117. |
| [4] |
B. Baz, G. Aouad and S. Remond,
Effect of the printing method and mortar's workability on pull-out strength of 3d printed elements, Construction and Building Materials, 230 (2020), 117002.
doi: 10.1016/j.conbuildmat.2019.117002. |
| [5] |
S. Chu and A. Kwan,
A new bond model for reinforcing bars in steel fibre reinforced concrete, Cement and Concrete Composites, 104 (2019), 103405.
doi: 10.1016/j.cemconcomp.2019.103405. |
| [6] |
A. Elias-Zuniga, L. M. Palacios-Pineda, O. Martinez-Romero and D. Olvera Trejo, Dynamics response of the forced fangzhu fractal device for water collection from air, Fractals, 29 (2021).
doi: 10.1142/S0218348X21501863. |
| [7] |
M. Emadi, H. Beheshti and M. Heidari-Rarani,
Multi-objective optimization of hybrid aluminum–composite tube under axial crushing, International Journal of Applied Mechanics, 12 (2020), 2050042.
doi: 10.1142/S1758825120500428. |
| [8] |
J. A. Estrada-Díaz, D. Olvera-Trejo, A. Elías-Zúñiga and O. Martínez-Romero,
A mathematical dimensionless model for electrohydrodynamics, Results in Physics, 25 (2021), 104256.
|
| [9] |
P. Feng, X. Meng, J.-F. Chen and L. Ye,
Mechanical properties of structures 3d printed with cementitious powders, Construction and Building Materials, 93 (2015), 486-497.
doi: 10.1016/j.conbuildmat.2015.05.132. |
| [10] |
C. Fragassa and P. E. Minak, Mechanical characterisation of photopolymer resins for rapid prototyping, Proceedings of the 27th Danubia-Adria Symposium on Advances in Experimental Mechanics, DAS, 22-25 Sept., Wroclaw. Code 125161 (2010) 55–56. |
| [11] |
R. García-Alvarado, G. Moroni-Orellana and P. Banda-Pérez,
Architectural evaluation of 3d-printed buildings, Buildings, 11 (2021), 254.
doi: 10.3390/buildings11060254. |
| [12] |
R. F. Ghachi, W. I. Alnahhal, O. Abdeljaber, J. Renno, A. Tahidul Haque, J. Shim and A. Aref, Optimization of viscoelastic metamaterials for vibration attenuation properties, International Journal of Applied Mechanics, 12 (2020).
doi: 10.1142/S1758825120501161. |
| [13] |
M. Hassan, B. Benmokrane, A. ElSafty and A. Fam,
Bond durability of basalt-fiber-reinforced-polymer (bfrp) bars embedded in concrete in aggressive environments, Composites Part B: Engineering, 106 (2016), 262-272.
doi: 10.1016/j.compositesb.2016.09.039. |
| [14] |
C.-H. He, J.-H. He and H. M. Sedighi, Fangzhu: An ancient chinese nanotechnology for water collection from air: History, mathematical insight, promises, and challenges, Mathematical Methods in the Applied Sciences, 2020.
doi: 10.1002/mma.6384. |
| [15] |
C.-H. He, C. Liu, J.-H. He, A. H. Shirazi and H. Mohammad-Sedighi,
Passive atmospheric water harvesting utilizing an ancient chinese ink slab, Facta Universitatis, Series: Mechanical Engineering, 19 (2021), 229-239.
doi: 10.22190/FUME201203001H. |
| [16] |
J.-H. He,
Seeing with a single scale is always unbelieving: From magic to two-scale fractal, Thermal Science, 25 (2021), 1217-1219.
doi: 10.2298/TSCI2102217H. |
| [17] |
J.-H. He,
A new proof of the dual optimization problem and its application to the optimal material distribution of sic/graphene composite, Reports in Mechanical Engineering, 1 (2020), 187-191.
doi: 10.31181/rme200101187h. |
| [18] |
J.-H. He and Q.-T. Ain,
New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle, Thermal Science, 24 (2020), 659-681.
doi: 10.2298/TSCI200127065H. |
| [19] |
J.-H. He and Y. O. El-Dib,
Homotopy perturbation method for Fangzhu oscillator, J. Mathematical Chemistry, 58 (2020), 2245-2253.
doi: 10.1007/s10910-020-01167-6. |
| [20] |
J.-H. He and Y. O. El-Dib,
Homotopy perturbation method with three expansions for Helmholtz-Fangzhu oscillator, Internat. J. Modern Phys. B, 35 (2021), 2150244.
doi: 10.1142/S0217979221502441. |
| [21] |
S. Hong and S.-K. Park, Uniaxial bond stress-slip relationship of reinforcing bars in concrete, Advances in Materials Science and Engineering, 2012 (2012).
doi: 10.1155/2012/328570. |
| [22] |
M. Hoseini Asl and J. Jafari Fesharaki,
3d optimization of gear train layout using particle swarm optimization algorithm, Journal of Applied and Computational Mechanics, 6 (2020), 823-840.
|
| [23] |
X. Hu, G. Peng, D. Niu, X. Wu and L. Zhang,
Bond behavior between deformed steel bars and cementitious grout, Construction and Building Materials, 262 (2020), 120810.
doi: 10.1016/j.conbuildmat.2020.120810. |
| [24] |
M. Islam, A. Sadaf, M. R. Gómez, D. Mager, J. G. Korvink and A. D. Lantada,
Carbon fiber/microlattice 3d hybrid architecture as multi-scale scaffold for tissue engineering, Materials Science and Engineering: C, 126 (2021), 112140.
doi: 10.1016/j.msec.2021.112140. |
| [25] |
O. Leibovich and D. Z. Yankelevsky,
Nonlinear features of the bond-slip ascending branch, J. Materials in Civil Engineering, 32 (2020), 04020279.
doi: 10.1061/(ASCE)MT.1943-5533.0003368. |
| [26] |
T. Li, H. Zhu, Q. Wang, J. Li and T. Wu,
Experimental study on the enhancement of additional ribs to the bond performance of FRP bars in concrete, Construction and Building Materials, 185 (2018), 545-554.
doi: 10.1016/j.conbuildmat.2018.06.198. |
| [27] |
X.-X. Li, D. Tian and J.-H. He,
High energy surface as a receptor in electrospinning: A good switch for hydrophobicity to hydrophilicity, Thermal Science, 25 (2021), 2205-2212.
doi: 10.2298/TSCI191120107L. |
| [28] |
H. Liu, J. Yang and X. Wang,
Bond behavior between BFRP bar and recycled aggregate concrete reinforced with basalt fiber, Construction and Building Materials, 135 (2017), 477-483.
doi: 10.1016/j.conbuildmat.2016.12.161. |
| [29] |
W.-J. Meng, H.-X. Liu, G.-J. Liu, X.-Q. Kong and X.-Z. Wang,
Bond-slip constitutive relation between bfrp bar and basalt fiber recycled-aggregate concrete, KSCE Journal of Civil Engineering, 20 (2016), 1996-2006.
doi: 10.1007/s12205-015-0350-z. |
| [30] |
J. Patdiya and B. Kandasubramanian, Progress in 4d printing of stimuli responsive materials, Polymer-Plastics Technology and Materials, (2021), 1–39. |
| [31] |
A. Pavlovic and C. Fragassa,
Geometry optimization by fem simulation of the automatic changing gear, Reports in Mechanical Engineering, 1 (2020), 199-205.
doi: 10.31181/rme200101199p. |
| [32] |
V. T. Pinto, L. A. Oliveira Rocha, C. Fragassa, E. Domingues Dos Santos and L. A. Isoldi,
Multiobjective geometric analysis of stiffened plates under bending through constructal design method, Journal of Applied and Computational Mechanics, 6 (2020), 1438-1449.
|
| [33] |
M. Regehly, Y. Garmshausen, M. Reuter, N. F. König, E. Israel, D. P. Kelly, C.-Y. Chou, K. Koch, B. Asfari and S. Hecht,
Xolography for linear volumetric 3d, Printing Nature, 588 (2020), 620-624.
|
| [34] |
M. Rossi, C. Calderini and S. Lagomarsino,
Experimental testing of the seismic in-plane displacement capacity of masonry cross vaults through a scale model, Bulletin of Earthquake Engineering, 14 (2016), 261-281.
doi: 10.1007/s10518-015-9815-1. |
| [35] |
J. Sebo and J. Busa Jr,
Comparison of advanced methods for picking path optimization: Case study of dual-zone warehouse, Int J. Simul Model, 19 (2020), 410-421.
doi: 10.2507/IJSIMM19-3-521. |
| [36] |
H. M. Sedighi and K. H. Shirazi,
Using homotopy analysis method to determine profile for disk cam by means of optimization of dissipated energy, International Review of Mechanical Engineering, 5 (2011), 941-946.
|
| [37] |
D. Shen, X. Shi, H. Zhang, X. Duan and G. Jiang,
Experimental study of early-age bond behavior between high strength concrete and steel bars using a pull-out test, Construction and Building Materials, 113 (2016), 653-663.
doi: 10.1016/j.conbuildmat.2016.03.094. |
| [38] |
J. Song, W. Wang, S. Su, X. Ding, Q. Luo and C. Quan,
Experimental study on the bond-slip performance between concrete and a corrugated steel plate with studs, Engineering Structures, 224 (2020), 111195.
doi: 10.1016/j.engstruct.2020.111195. |
| [39] |
J. Sun, J. Xiao, Z. Li and X. Feng,
Experimental study on the thermal performance of a 3d printed concrete prototype building, Energy and Buildings, 241 (2021), 110965.
doi: 10.1016/j.enbuild.2021.110965. |
| [40] |
X. Sun, C. Gao and H. Wang,
Bond performance between BFRP bars and 3D printed concrete, Construction and Building Materials, 269 (2021), 121325.
doi: 10.1016/j.conbuildmat.2020.121325. |
| [41] |
S. Troha, Ž. Vrcan, D. Karaivanov and M. Isametova,
The selection of optimal reversible two-speed planetary gear trains for machine tool gearboxes, Facta Universitatis, Series: Mechanical Engineering, 18 (2020), 121-134.
|
| [42] |
H. Wang, J. Chen, X. Sun and C. Gao,
Bonding performance between steel wire rope and 3d printed cement-based composites, Journal of Building Structures (in Chinese), 42 (2021), 1-7.
doi: 10.14006/j.jzjgxb.2019.0410. |
| [43] |
K.-L. Wang, Effect of fangzhu's nanoscale surface morphology on water collection, Mathematical Methods in the Applied Sciences, 2020.
doi: 10.1002/mma.6569. |
| [44] |
L. Wu, W. Yang, Y. Sun, Q. Kang and Z. Wan,
Experimental study on the influencing factors of the adhesive property between printed concrete and rebar, Industrial Construction (in Chinese), 262 (2020), 32-38.
doi: 10.13204/j.gyjzG20011603. |
| [45] |
W. Xu, G. Wu et al., Experimental study on the bond behavior between sand spraying frp bars and concrete, Industrial Construction (in Chinese), (2009), 118–121. |
| [46] |
C. Yang and S. Qi, Experimental study on the bond performance between bfrp bars and coral concrete, Engineering Mechanics (in Chinese), 35. |
| [47] |
Q. Yuan, Z. Li, D. Zhou, T. Huang, H. Huang, D. Jiao and C. Shi,
A feasible method for measuring the buildability of fresh 3d printing mortar, Construction and Building Materials, 227 (2019), 116600.
doi: 10.1016/j.conbuildmat.2019.07.326. |
| [48] |
Z. Zheng, M. Zhang and Z. Liu,
Investigation on evaluating the printable height and dimensional stability of food extrusion-based 3d printed foods, Journal of Food Engineering, 306 (2021), 110636.
doi: 10.1016/j.jfoodeng.2021.110636. |
| [49] |
Y.-T. Zuo and H.-J. Liu,
Fractal approach to mechanical and electrical properties of graphene/sic composites, Facta Universitatis, Series: Mechanical Engineering, 19 (2021), 271-284.
doi: 10.22190/FUME201212003Z. |
Figure 2.
Cubic specimen
Figure 3.
Test loading device
Figure 4.
Damaged shape of specimen (The main damage of the specimen is the split failure, and the pull-out failure mainly occurred in the specimens with the 45 printing direction) (a) Herringbone splitting (b) In-line splitting (c) Pull out
Figure 5.
Bond stress-slip relationship
Figure 6.
Printing direction
Table 1.
Main chemical components of cementitious materials wt. %
| Component | Na |
MgO | Al |
SiO |
P |
SO |
Cl | K |
FeO |
TiO |
SrO |
| Cement | 0.08 | 0.65 | 4.65 | 20.9 | 0.12 | 2.65 | 0.05 | 0.87 | 65.00 | 3.23 | 0.22 |
| Component | Na |
MgO | Al |
SiO |
P |
SO |
Cl | K |
FeO |
TiO |
SrO |
| Cement | 0.08 | 0.65 | 4.65 | 20.9 | 0.12 | 2.65 | 0.05 | 0.87 | 65.00 | 3.23 | 0.22 |
Table 2.
Mix ratio of 3D printed concrete (wt. %)
| Water-cement ratio | cement | Early Strength Agent | Sand | Fly ash | Silica Fume | Cellulase | PVA | Water reducing agent |
| 0.3 | 26.6% | 2.66% | 66.46% | 2.68% | 1.34% | 0.027% | 0.0225% | 0.186% |
| Water-cement ratio | cement | Early Strength Agent | Sand | Fly ash | Silica Fume | Cellulase | PVA | Water reducing agent |
| 0.3 | 26.6% | 2.66% | 66.46% | 2.68% | 1.34% | 0.027% | 0.0225% | 0.186% |
Table 3.
Mechanical properties of the casted and printed concretes
| Samples | Compressive strength | |
| Casted concrete | 50.2 MPa | |
| Printed concrete | X-direction | 37.7 MPa |
| Y-direction | 42.9 MPa | |
| Z-direction | 40.0 MPa | |
| Samples | Compressive strength | |
| Casted concrete | 50.2 MPa | |
| Printed concrete | X-direction | 37.7 MPa |
| Y-direction | 42.9 MPa | |
| Z-direction | 40.0 MPa | |
Table 4.
Mechanical properties of steel bars
| Rebar type | Diameter (mm) | Yield Strength (MPa) | Ultimate strength (MPa) | Strain | Elastic Modulus (MPa) |
| HRB400 | 10 | 330 | 400 | 14% | 2.00 |
| Rebar type | Diameter (mm) | Yield Strength (MPa) | Ultimate strength (MPa) | Strain | Elastic Modulus (MPa) |
| HRB400 | 10 | 330 | 400 | 14% | 2.00 |
Table 5.
Pull-out test results of 3D printed concrete
| Samples | Rebar type | $\tau_\text{max}$ (MPa) | $s_\text{max}$ (mm) | $\tau_\text{max}s_\text{max}$ (MPa$^{*}$mm) | Average (MPa$^{*}$mm) | |
| Our group | Casted sample | HRB400 | 10.13 | 0.933 | 9.4512 | 9.4512 |
| Parallelly printed samples | 8.75 | 0.93 | 8.1375 | 8.1375 | ||
| Vertically printed samples | 8.22 | 0.99 | 8.1378 | 8.1378 | ||
| Inclined printed samples with 45° | 6.15 | 0.80 | 4.92 | 4.92 | ||
| Ref. [40] | Casted samples | BFRP Unsmooth bar | 26.57 | 0.54 | 14.3478 | 16.7413 |
| 28.17 | 0.59 | 16.6203 | ||||
| 28.74 | 0.67 | 19.2558 | ||||
| BFRP Smooth bar | 23.94 | 1.35 | 19.36953 | 22.86019 | ||
| 25.71 | 1.42 | 23.60083 | ||||
| 24.82 | 1.33 | 25.61021 | ||||
| Parallelly printed samples | BFRP Unsmooth bar | 22.81 | 0.49 | 11.1769 | 12.37963 | |
| 24.27 | 0.56 | 13.5912 | ||||
| 23.79 | 0.52 | 12.3708 | ||||
| BFRP Smooth bar | 21.35 | 1.29 | 14.4182 | 16.80665 | ||
| 22.79 | 1.32 | 17.94038 | ||||
| 21.42 | 1.46 | 18.06137 | ||||
| Vertically printed samples | BFRP Unsmooth bar | 20.48 | 0.52 | 10.6496 | 10.47707 | |
| 20.65 | 0.48 | 9.912 | ||||
| 19.41 | 0.56 | 10.8696 | ||||
| BFRP Smooth bar | 13.51 | 1.01 | 10.7561 | 12.68027 | ||
| 18.84 | 1.36 | 13.48032 | ||||
| 18.91 | 1.27 | 13.80439 | ||||
| Inclined printed samples with 45° | BFRP Unsmooth bar | 23.59 | 0.58 | 13.6822 | 12.42147 | |
| 22.58 | 0.49 | 11.0642 | ||||
| 22.76 | 0.55 | 12.518 | ||||
| BFRP Smooth bar | 15.46 | 1.37 | 18.74461 | 16.44966 | ||
| 20.07 | 1.25 | 13.83025 | ||||
| 21.94 | 1.34 | 16.77412 | ||||
| Samples | Rebar type | $\tau_\text{max}$ (MPa) | $s_\text{max}$ (mm) | $\tau_\text{max}s_\text{max}$ (MPa$^{*}$mm) | Average (MPa$^{*}$mm) | |
| Our group | Casted sample | HRB400 | 10.13 | 0.933 | 9.4512 | 9.4512 |
| Parallelly printed samples | 8.75 | 0.93 | 8.1375 | 8.1375 | ||
| Vertically printed samples | 8.22 | 0.99 | 8.1378 | 8.1378 | ||
| Inclined printed samples with 45° | 6.15 | 0.80 | 4.92 | 4.92 | ||
| Ref. [40] | Casted samples | BFRP Unsmooth bar | 26.57 | 0.54 | 14.3478 | 16.7413 |
| 28.17 | 0.59 | 16.6203 | ||||
| 28.74 | 0.67 | 19.2558 | ||||
| BFRP Smooth bar | 23.94 | 1.35 | 19.36953 | 22.86019 | ||
| 25.71 | 1.42 | 23.60083 | ||||
| 24.82 | 1.33 | 25.61021 | ||||
| Parallelly printed samples | BFRP Unsmooth bar | 22.81 | 0.49 | 11.1769 | 12.37963 | |
| 24.27 | 0.56 | 13.5912 | ||||
| 23.79 | 0.52 | 12.3708 | ||||
| BFRP Smooth bar | 21.35 | 1.29 | 14.4182 | 16.80665 | ||
| 22.79 | 1.32 | 17.94038 | ||||
| 21.42 | 1.46 | 18.06137 | ||||
| Vertically printed samples | BFRP Unsmooth bar | 20.48 | 0.52 | 10.6496 | 10.47707 | |
| 20.65 | 0.48 | 9.912 | ||||
| 19.41 | 0.56 | 10.8696 | ||||
| BFRP Smooth bar | 13.51 | 1.01 | 10.7561 | 12.68027 | ||
| 18.84 | 1.36 | 13.48032 | ||||
| 18.91 | 1.27 | 13.80439 | ||||
| Inclined printed samples with 45° | BFRP Unsmooth bar | 23.59 | 0.58 | 13.6822 | 12.42147 | |
| 22.58 | 0.49 | 11.0642 | ||||
| 22.76 | 0.55 | 12.518 | ||||
| BFRP Smooth bar | 15.46 | 1.37 | 18.74461 | 16.44966 | ||
| 20.07 | 1.25 | 13.83025 | ||||
| 21.94 | 1.34 | 16.77412 | ||||
Table 6.
Effects of bars property and concretes property on the bond stress-slip relationship
| Samples | D mm | $\tau_\text{max}$ MPa | $s_\text{max}$ mm | $\tau_\text{max}s_\text{max}$ MPa.mm | L mm | DL mm$^{2}$ | $\tau_\text{concrete}$ MPa | $\tau_\text{max}s_\text{max}$/ ($\tau_\text{concrete} L$) |
| Casted | 10.0 | 10.13 | 0.93 | 9.4512 | 60 | 600 | 50.2 | 0.003137848 |
| Parallelly | 8.75 | 0.93 | 8.1375 | 42.9 | 0.003161421 | |||
| Vertically | 8.22 | 0.99 | 8.1378 | 37.7 | 0.003597612 | |||
| Ref.[45] | 9.6 | 15.88 | 2.23 | 35.4124 | 48 | 461 | 37.7 | 0.019569187 |
| 10.4 | 18.56 | 1.68 | 31.1808 | 54 | 557 | 0.015444947 | ||
| Ref.[46] | 8.0 | 19.49 | 1.50 | 29.2350 | 40 | 320 | 36.3 | 0.020139846 |
| 12.0 | 17.75 | 3.14 | 55.7350 | 60 | 720 | 0.025597042 | ||
| 8.0 | 21.09 | 1.77 | 37.3293 | 20 | 160 | 0.051431937 | ||
| 12.0 | 20.27 | 2.30 | 46.6210 | 30 | 360 | 0.042822632 | ||
| Ref.[28] | 16.0 | 16.42 | 3.72 | 61.0517 | 80 | 1280 | 35.0 | 0.021804189 |
| 16.0 | 18.06 | 2.15 | 38.7929 | 80 | 1280 | 35.0 | 0.013854600 | |
| 16.0 | 11.11 | 3.47 | 38.5517 | 80 | 1280 | 42.5 | 0.011338735 | |
| 16.0 | 14.81 | 4.92 | 72.8652 | 80 | 1280 | 55.5 | 0.016411081 | |
| 16.0 | 17.36 | 2.67 | 46.3512 | 80 | 1280 | 60.9 | 0.009513793 | |
| Ref.[13] | 12.0 | 16.48 | 1.08 | 17.7984 | 60 | 720 | 30.0 | 0.009888000 |
| 12.0 | 20.43 | 1.50 | 30.6450 | 60 | 720 | 0.017025000 | ||
| 8.0 | 19.03 | 0.32 | 6.08960 | 40 | 320 | 0.005074667 | ||
| Ref.[29] | 10.0 | 20.00 | 0.91 | 18.2000 | 7.8 | 78.3 | 30 | 0.077479779 |
| 8.0 | 50.00 | 1.12 | 56.0000 | 19.5 | 156 | 20 | 0.143589744 | |
| 12.0 | 90.00 | 1.90 | 171.000 | 16.45 | 197.4 | 40 | 0.259878419 | |
| Ref.[26] | 10.0 | 13.52 | 3.20 | 43.2640 | 50 | 500 | 35.3 | 0.024512181 |
| 10.0 | 16.33 | 2.72 | 44.4176 | 100 | 1000 | 0.012582890 | ||
| 10.0 | 14.58 | 0.65 | 9.47700 | 150 | 1500 | 0.001789802 |
| Samples | D mm | $\tau_\text{max}$ MPa | $s_\text{max}$ mm | $\tau_\text{max}s_\text{max}$ MPa.mm | L mm | DL mm$^{2}$ | $\tau_\text{concrete}$ MPa | $\tau_\text{max}s_\text{max}$/ ($\tau_\text{concrete} L$) |
| Casted | 10.0 | 10.13 | 0.93 | 9.4512 | 60 | 600 | 50.2 | 0.003137848 |
| Parallelly | 8.75 | 0.93 | 8.1375 | 42.9 | 0.003161421 | |||
| Vertically | 8.22 | 0.99 | 8.1378 | 37.7 | 0.003597612 | |||
| Ref.[45] | 9.6 | 15.88 | 2.23 | 35.4124 | 48 | 461 | 37.7 | 0.019569187 |
| 10.4 | 18.56 | 1.68 | 31.1808 | 54 | 557 | 0.015444947 | ||
| Ref.[46] | 8.0 | 19.49 | 1.50 | 29.2350 | 40 | 320 | 36.3 | 0.020139846 |
| 12.0 | 17.75 | 3.14 | 55.7350 | 60 | 720 | 0.025597042 | ||
| 8.0 | 21.09 | 1.77 | 37.3293 | 20 | 160 | 0.051431937 | ||
| 12.0 | 20.27 | 2.30 | 46.6210 | 30 | 360 | 0.042822632 | ||
| Ref.[28] | 16.0 | 16.42 | 3.72 | 61.0517 | 80 | 1280 | 35.0 | 0.021804189 |
| 16.0 | 18.06 | 2.15 | 38.7929 | 80 | 1280 | 35.0 | 0.013854600 | |
| 16.0 | 11.11 | 3.47 | 38.5517 | 80 | 1280 | 42.5 | 0.011338735 | |
| 16.0 | 14.81 | 4.92 | 72.8652 | 80 | 1280 | 55.5 | 0.016411081 | |
| 16.0 | 17.36 | 2.67 | 46.3512 | 80 | 1280 | 60.9 | 0.009513793 | |
| Ref.[13] | 12.0 | 16.48 | 1.08 | 17.7984 | 60 | 720 | 30.0 | 0.009888000 |
| 12.0 | 20.43 | 1.50 | 30.6450 | 60 | 720 | 0.017025000 | ||
| 8.0 | 19.03 | 0.32 | 6.08960 | 40 | 320 | 0.005074667 | ||
| Ref.[29] | 10.0 | 20.00 | 0.91 | 18.2000 | 7.8 | 78.3 | 30 | 0.077479779 |
| 8.0 | 50.00 | 1.12 | 56.0000 | 19.5 | 156 | 20 | 0.143589744 | |
| 12.0 | 90.00 | 1.90 | 171.000 | 16.45 | 197.4 | 40 | 0.259878419 | |
| Ref.[26] | 10.0 | 13.52 | 3.20 | 43.2640 | 50 | 500 | 35.3 | 0.024512181 |
| 10.0 | 16.33 | 2.72 | 44.4176 | 100 | 1000 | 0.012582890 | ||
| 10.0 | 14.58 | 0.65 | 9.47700 | 150 | 1500 | 0.001789802 |
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