Fracture Behavior of Crack-Damaged Concrete Beams Reinforced with Ultra-High-Performance Concrete Layers
Abstract
:1. Introduction
- a.
- There needs to be deeper investigation into the fracture toughness of U+NC beams.
- b.
- Quantitative formulas for calculating the ductility of U+NC are absent.
- c.
- Interfacial bond–slip properties are less often considered in simulations (mostly treated as a perfect connection or a constant is specified).
2. Methods
2.1. Double-K Fracture Criterion
- (1)
- SNC
- (2)
- U+SNC
2.2. XFEM Crack Tip Processing Theory
- (1)
- XFEM crack tip processing theory
- (2)
- XFEM case validation
3. Finite Element Modeling of U+SNC
3.1. Geometric Model
3.2. Interface Model
3.3. XFEM Model
3.4. Workflows
4. Analysis of Results
4.1. Crack Extension Process
4.2. Effect of UHPC Layer Thickness on Fracture Performance of U+SNC Beams
4.3. Effect of Crack Height Ratio on Fracture Toughness of Reinforced Beams
4.4. Effect of VSF on Fracture Toughness of U+SNC
5. Results and Outlook
- (1)
- The XFEM method can accurately and reliably predict the crack extension trend and fracture parameters of materials;
- (2)
- The load-carrying capacity and toughness of the UHPC significantly increased with d, and the optimal d was 20 mm, allowing for the combined effects of self-weight of U+SNC and gain cost of the UHPC layer;
- (3)
- With a constant d, increasing a/h results in a modest improvement in the structural fracture performance of U+SNC;
- (4)
- As VSF increases, the U+SNC beam exhibits a smoother crack extension phase and higher toughness and flexural properties, where the best are achieved at a VSF of 3%.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Full Name | Abbreviation |
Ultra-high-performance concrete | UHPC |
Finite element method | FEM |
Crack mouth opening displacement | CMOD |
Steel fiber | SF |
UHPC-reinforced single-notched concrete beam | U+SNC |
Extended finite element method | XFEM |
Critical CMOD | CMODc |
Crack height ratio | a/h |
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Ref. | Size/(mm) | Thickness of UHPC/(mm) | Software | The Constitutive Relationship |
---|---|---|---|---|
[4] | 1600 × 140 × 230 | 30 | Abaqus | CDP |
[7] | 2200 × 150 × 250 | 50 | Atena | SBETA |
[8] | 2200 × 150 × 200 | 30/50/70 | Atena | SBETA |
[9] | 1500 × 100 × 200 | 10 | Abaqus | CDP |
[20] | 3000 × 250 × 400 | 40/80 | Msc | Macgegor |
[21] | 3200 × 2000 × 280 | 50 | Msc | MacGegor |
[22] | 1600 × 150 × 250 | 50 | Atena | SBETA |
Materials | Density/ ) | Elastic Modulus/ (GPa) | Poisson’s Ratio | Ultimate Tensile Strength/ (MPa) | Rupture Energy/ (N/m) |
---|---|---|---|---|---|
NC | 2400 | 28.3 | 0.2 | 3.8 | 43.4 |
Rebar | 7800 | 174 | 0.3 | - | - |
Specimen | /(kN) | Errors | CMOD/(mm) | Errors |
---|---|---|---|---|
M0 | 6.253 | 2% | 0.0536 | / |
L0 | 6.103 | — | ||
M1 | 6.681 | 4% | 0.0605 | 3% |
L1 | 6.434 | 0.0588 | ||
M2 | 8.801 | 9% | 0.0953 | 11% |
L2 | 8.043 | 0.0858 | ||
M4 | 11.533 | 13% | 0.0875 | 14% |
L4 | 10.231 | 0.0770 |
Material Type | Density/ ) | Elastic Modulus/ (GPa) | Poisson’s Ratio | Ultimate Tensile Strength/ (MPa) | Rupture Energy/ (N/m) |
---|---|---|---|---|---|
Concrete | 2400 | 31.50 | 0.167 | 1.65 | 102.8 |
UHPC | 2600 | 42.45 | 0.19 | 8.1 | 781.7 |
Feature Parameters | Numerical Factor |
---|---|
) | 1358 |
20,358 | |
5.63 | |
(mm) | 0.241 |
Stabilization | 0.001 |
Friction coefficient | 1.44 |
Spec. No. | U-10 | U-15 | U-20 | U-25 | |
---|---|---|---|---|---|
Parameter | |||||
Fini/(kN) | 7.684 | 15.154 | 20.283 | 21.362 | |
Fmax/(kN) | 11.812 | 16.629 | 21.791 | 28.297 | |
Fini/Fmax | 0.651 | 0.911 | 0.931 | 0.755 | |
1.487 | 2.599 | 3.365 | 3.534 | ||
/ | 2.481 | 3.350 | 4.277 | 6.403 | |
/ | −0.965 | −1.444 | −1.924 | −2.278 | |
/ | −1.232 | −1.856 | −2.481 | −3.695 | |
/ | 0.522 | 1.155 | 1.441 | 1.255 | |
/ | 1.250 | 1.494 | 1.796 | 2.709 |
Spec. No. | U20-4 | U20-3 | U20-2 | U20-1 | |
---|---|---|---|---|---|
Parameter | |||||
Fini/(kN) | 20.283 | 21.588 | 23.076 | 24.014 | |
Fmax/(kN) | 21.791 | 23.151 | 24.703 | 25.667 | |
Fini/Fmax | 0.931 | 0.932 | 0.934 | 0.936 | |
7.572 | 2.731 | 2.240 | 1.674 | ||
/ | 2.646 | 3.831 | 3.851 | 3.256 | |
/ | −1.924 | −1.462 | −1.146 | −1.059 | |
/ | −2.481 | −2.113 | −2.015 | −1.737 | |
/ | 1.441 | 1.269 | 1.094 | 0.615 | |
/ | 1.796 | 1.718 | 1.836 | 1.519 |
Spec. No. | U20-S0 | U20-S1 | U20-S2 | U20-S3 | |
---|---|---|---|---|---|
Parameter | |||||
Fini(kN) | 20.283 | 37.025 | 45.945 | 62.419 | |
Fmax(kN) | 21.791 | 41.881 | 53.495 | 71.381 | |
Fini/Fmax | 0.931 | 0.884 | 0.859 | 0.874 | |
3.365 | 5.838 | 7.156 | 9.590 | ||
4.277 | 8.923 | 11.937 | 16.181 | ||
−1.924 | −4.141 | −4.973 | −5.608 | ||
−2.481 | −7.051 | −9.398 | −11.619 | ||
1.441 | 1.697 | 2.183 | 3.982 | ||
1.796 | 1.872 | 2.540 | 4.562 |
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Guo, Z.; Tao, X.; Xiao, Z.; Chen, H.; Li, X.; Luo, J. Fracture Behavior of Crack-Damaged Concrete Beams Reinforced with Ultra-High-Performance Concrete Layers. J. Compos. Sci. 2024, 8, 355. https://doi.org/10.3390/jcs8090355
Guo Z, Tao X, Xiao Z, Chen H, Li X, Luo J. Fracture Behavior of Crack-Damaged Concrete Beams Reinforced with Ultra-High-Performance Concrete Layers. Journal of Composites Science. 2024; 8(9):355. https://doi.org/10.3390/jcs8090355
Chicago/Turabian StyleGuo, Zenghui, Xuejun Tao, Zhengwei Xiao, Hui Chen, Xixi Li, and Jianlin Luo. 2024. "Fracture Behavior of Crack-Damaged Concrete Beams Reinforced with Ultra-High-Performance Concrete Layers" Journal of Composites Science 8, no. 9: 355. https://doi.org/10.3390/jcs8090355