Analytical Modeling of the Postcracking Response Observed in Hybrid Steel/Polypropylene Fiber-Reinforced Concrete
Abstract
:1. Introduction
2. Model Formulation
2.1. Constitutive Rules
2.2. Compatibility Equations
2.3. Equilibrium Equations
3. Summary of Experimental Results
- HySP-FRC-75-0, only including S fibers (S = 0.75% of the matrix);
- HySP-FRC-55-20, with 25% of the S fibers replaced by P fibers;
- HySP-FRC-37.5, with 50% of the S fibers replaced by P fibers;
- HySP-FRC-20-55, with 75% of the S fibers replaced by P fibers;
- HySP-FRC-0-75, only including P fibers (P = 0.75 % of the matrix).
- First crack strength (flf):
- Work capacity indices: U1 and U2 (energy absorption values) represent the areas under the vertical load (P)–CTOD curve in a representative range for the serviceability limit state (i.e., considering a CTOD ranging between CTOD0 and CTOD0+0.6) and for the ultimate state (i.e., considering a CTOD ranging between CTOD0+0.6 and CTOD0.6+3), respectively.
- Equivalent post-cracking strengths: The first one (feq(0–0.6)) is supposed to be significant for the serviceability limit state (evaluated as a function of the U1 parameter), whereas the second one (feq(0.6–3)) is rather relevant for the ultimate state (evaluated as a function of the U2 parameter).
- Ductility indices: D0 and D1 can be determined with the following equations:
4. Model Validation
5. Conclusions
- The proposed model is based on sufficiently general, yet analytically expressed, normal stress–crack opening relationships, which can potentially simulate the various possible responses observed in experimental tests on FRC specimens.
- The model parameters were identified for each mixture, and a very good agreement was obtained between the experimental results and the simulation output for all the HyFRC specimens considered in this study.
- Moreover, the parameters obtained for the normal stress–crack opening identified for the various HyFRC specimens exhibited a regular variability with respect to the fiber content and proportions of each specimen.
Author Contributions
Funding
Conflicts of Interest
References
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bi | ai | w |
---|---|---|
1 | ||
0 | 0 |
Mixtures | ft | α1 | w1 | α2 | w2 | α3 | w3 | w4 | E/s |
---|---|---|---|---|---|---|---|---|---|
[MPa] | - | [mm] | - | [mm] | - | [mm] | [mm] | [MPa/mm] | |
HySP-FRC-75-0 | 2.650 | 1.000 | 0.050 | 0.700 | 0.363 | 1.240 | 3.750 | 5.000 | 52.213 |
HySP-FRC-55-20 | 2.700 | 1.000 | 0.050 | 0.720 | 0.390 | 1.135 | 3.750 | 5.000 | 52.213 |
HySP-FRC-37.5 | 2.765 | 1.000 | 0.050 | 0.555 | 0.500 | 0.780 | 3.750 | 5.000 | 52.213 |
HySP-FRC-20-55 | 2.400 | 0.890 | 0.220 | 0.400 | 0.600 | 0.480 | 3.750 | 5.000 | 104.425 |
HySP-FRC-0-75 | 2.400 | 0.860 | 0.380 | 0.305 | 0.850 | 0.288 | 3.750 | 5.000 | 104.425 |
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Caggiano, A.; Pepe, M.; Xargay, H.; Martinelli, E. Analytical Modeling of the Postcracking Response Observed in Hybrid Steel/Polypropylene Fiber-Reinforced Concrete. Polymers 2020, 12, 1864. https://doi.org/10.3390/polym12091864
Caggiano A, Pepe M, Xargay H, Martinelli E. Analytical Modeling of the Postcracking Response Observed in Hybrid Steel/Polypropylene Fiber-Reinforced Concrete. Polymers. 2020; 12(9):1864. https://doi.org/10.3390/polym12091864
Chicago/Turabian StyleCaggiano, Antonio, Marco Pepe, Hernan Xargay, and Enzo Martinelli. 2020. "Analytical Modeling of the Postcracking Response Observed in Hybrid Steel/Polypropylene Fiber-Reinforced Concrete" Polymers 12, no. 9: 1864. https://doi.org/10.3390/polym12091864
APA StyleCaggiano, A., Pepe, M., Xargay, H., & Martinelli, E. (2020). Analytical Modeling of the Postcracking Response Observed in Hybrid Steel/Polypropylene Fiber-Reinforced Concrete. Polymers, 12(9), 1864. https://doi.org/10.3390/polym12091864