A Quasi-2D Exploration of Mixed-Mode Fracture Propagation in Concrete Semi-Circular Chevron-Notched Disks
Abstract
:1. Introduction
2. Experimental and Numerical Methods
2.1. Specification of Concrete SCCND
2.2. SCB Tests for Concrete SCCND
2.3. Numerical Simulation of SCB Tests
2.4. Methods for Fracture Analysis
3. Results and Discussion
3.1. Maximum Failure Load
3.2. Chevron-Notch and Fracturing Angles
3.3. Stress Distributions in SCCND by FRANC2D
3.4. Fracturing in SCCND Simulated by FRANC2D
3.5. CMOD Determined by SCB Tests
3.6. SIF and Fracture Toughness
3.7. Limitations and Prospects
4. Summary and Concluding Remarks
- Concrete SCB tests with SCCND specimens with a sharp notch tip are reliable and robust for studying mixed-mode (types I and II) fracture propagation in concrete because of their reliable results and relatively small standard deviations of all testing variables.
- The maximum failure load (Pmax) increases with increasing inclination angle (β).
- The fracture propagation angle (θ) also increases with increasing β, and the phenomenon of wing fractures can be observed.
- As powerful software for linear elastic fracture mechanics, FRANC2D can successfully simulate SCB tests with the same loading conditions in terms of fracture propagation in SCCND specimens.
- Despite the fact that the compressive normal stress concentrations in the SCCND specimen are adjacent to the three loading points, most variations of the normal stress distributions occur around the prefabricated chevron notch.
- With increasing β, the tensile stress concentration around the notch tip moves toward the upper face of the notch, and the compressive stress concentration forms at the notch tip to turn the tensile loading mode into the shearing one.
- The stress distributions along the upper and lower faces of the chevron notch can be produced by FRANC2D for quantitative analysis, and this stress analysis also verifies the previous findings about stress-distribution variations.
- The tensile mode (type I) can be generated when β = 0–30° because the CMOD increases, indicating the crack opening under tensile loading. In contrast, the mixed mode (types I and II) becomes more evident for β = 45–70°, with the CMOD decreasing, indicating the crack closing under both tensile and shearing loading conditions.
- The FPZ can be found for β = 0–30° but not for β = 45–70°, which basically agrees with the CCNBD tests simulated in a previous numerical study.
- The tensile SIF decreases monotonically with increasing β, whereas the shear SIF increases from zero for β = 0° to a peak value for β = 45–60° and then decreases when β is increased to 70°.
- Four fracture criteria—MTS, G, GMTS, and EMTSN—were examined against the experimental results. The GMTS and EMTSN criteria outperform the MTS and G ones. In particular, compared with the experimental results, the newly developed EMTSN criterion characterizes most precisely the critical fracture toughness of both tensile and shearing (KIc and KIIc).
- There is a linear relationship between CMOD and KI for concrete SCB tests. However, because it has been examined for both asphalt and concrete, it deserves further investigation for other brittle materials.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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β | Pmax [kN] | Group 1 | Group 2 | Group 3 | Mean | STD |
---|---|---|---|---|---|---|
0° | First half CCNBD | 0.687 | 0.211 | 0.529 | 0.483 | 0.232 |
Second half CCNBD | 0.767 | 0.141 | 0.563 | |||
30° | First half CCNBD | 0.663 | 0.520 | 0.193 | 0.571 | 0.182 |
Second half CCNBD | 0.746 | 0.670 | 0.632 | |||
45° | First half CCNBD | – | 0.740 | 0.888 | 0.867 | 0.098 |
Second half CCNBD | – | 0.830 | 1.010 | |||
60° | First half CCNBD | – | – | 1.011 | 1.112 | 0.101 |
Second half CCNBD | – | – | 1.213 | |||
70° | First half CCNBD | – | 1.185 | – | 0.983 | 0.203 |
Second half CCNBD | – | 0.780 | – |
β | Fracture Propagation Angle (θ) | ||||
---|---|---|---|---|---|
Group 1 | Group 2 | Group 3 | Mean | STD | |
0° | 0–10° | 0–5° | 2–5° | 4° | 3° |
30° | 30–45° | 55–68° | 5–15° | 36° | 22° |
45° | – | 38–57° | 55–65° | 54° | 10° |
60° | – | – | 78–80° | 79° | 1° |
70° | – | 44–96° | 80–96° | 79° | 21° |
β | 0° | 30° | 45° | 60° | 70° |
---|---|---|---|---|---|
θ (FRANC2D) | 2° | 56° | 85° | 95° | 107° |
θ (Experiment) | 2° | 55° | 65° | 80° | 96° |
β | [] | Group 1 | Group 2 | Group 3 | Mean | STD |
---|---|---|---|---|---|---|
0° | First half CCNBD | 0.376 | 0.116 | 0.290 | 0.265 | 0.127 |
Second half CCNBD | 0.420 | 0.077 | 0.308 | |||
30° | First half CCNBD | 0.231 | 0.181 | 0.067 | 0.199 | 0.063 |
Second half CCNBD | 0.260 | 0.233 | 0.220 | |||
45° | First half CCNBD | – | 0.151 | 0.181 | 0.177 | 0.020 |
Second half CCNBD | – | 0.170 | 0.206 | |||
60° | First half CCNBD | – | – | 0.119 | 0.131 | 0.012 |
Second half CCNBD | – | – | 0.142 | |||
70° | First half CCNBD | – | 0.082 | – | 0.068 | 0.014 |
Second half CCNBD | – | 0.054 | – |
β | [] | Group 1 | Group 2 | Group 3 | Mean | STD |
---|---|---|---|---|---|---|
0° | First half CCNBD | 0.000 | 0.000 | 0.000 | 0.00 | 0.00 |
Second half CCNBD | 0.000 | 0.000 | 0.000 | |||
30° | First half CCNBD | 0.086 | 0.068 | 0.025 | 0.074 | 0.024 |
Second half CCNBD | 0.097 | 0.087 | 0.082 | |||
45° | First half CCNBD | – | 0.084 | 0.100 | 0.098 | 0.011 |
Second half CCNBD | – | 0.094 | 0.114 | |||
60° | First half CCNBD | – | – | 0.088 | 0.097 | 0.009 |
Second half CCNBD | – | – | 0.105 | |||
70° | First half CCNBD | – | 0.072 | – | 0.060 | 0.012 |
Second half CCNBD | – | 0.047 | – |
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Lu, X.; Yan, G. A Quasi-2D Exploration of Mixed-Mode Fracture Propagation in Concrete Semi-Circular Chevron-Notched Disks. Buildings 2023, 13, 2633. https://doi.org/10.3390/buildings13102633
Lu X, Yan G. A Quasi-2D Exploration of Mixed-Mode Fracture Propagation in Concrete Semi-Circular Chevron-Notched Disks. Buildings. 2023; 13(10):2633. https://doi.org/10.3390/buildings13102633
Chicago/Turabian StyleLu, Xiaoqing, and Guanxi Yan. 2023. "A Quasi-2D Exploration of Mixed-Mode Fracture Propagation in Concrete Semi-Circular Chevron-Notched Disks" Buildings 13, no. 10: 2633. https://doi.org/10.3390/buildings13102633