Assessment of Methods to Derive Tensile Properties of Ultra-High-Performance Fiber-Reinforced Cementitious Composites
Abstract
:1. Introduction
2. Materials and Methods
2.1. UHPC
2.2. Fiber Reinforcement
2.3. UHPFRC
2.4. Splitting Tensile Tests
2.4.1. Test Specimens
2.4.2. Test Setup
2.5. Uniaxial Tensile Tests
2.5.1. Drilling Direction
2.5.2. Test Specimens
2.5.3. Test Setups
2.5.4. Testing Program
2.6. Flexural Tests on Prismatic Elements
2.6.1. Test Specimens
2.6.2. Test Setup
2.7. Flexural Tests on Thin Plates
2.7.1. Test Specimens
2.7.2. Test Setup
2.8. Compression Tests
2.8.1. Test Specimens
2.8.2. Test Setup
2.9. Modulus of Elasticity Tests
2.9.1. Test Specimens
2.9.2. Test Setup
3. Results
3.1. Splitting Tensile Tests
3.2. Uniaxial Tensile Tests
3.3. Flexural Tests on Prismatic Elements
3.4. Flexural Tests on Thin Plates
3.5. Compressive Strength
3.6. Modulus of Elasticity
4. Discussion
4.1. Discussion on the Splitting Tensile Tests
4.2. Discussion on the Uniaxial Tensile Tests
4.2.1. Matrix Tensile Strength
4.2.2. Residual Tensile Strength and Dissipated Energy
4.2.3. Effect of the Test Setup
4.2.4. Effect of Notching
4.2.5. Effect of the Fiber Content
4.2.6. Fiber Orientation and Distribution
4.2.7. Crack Opening at Zero Tensile Resistance
4.3. Discussion on the Flexural Tests
4.3.1. Determination of the Matrix Tensile Strength
4.3.2. Comparison with the Uniaxial Tests
4.3.3. Determination of the Tensile Strain
4.3.4. Comparison with Simplified Models
4.3.5. Crack Opening–Deflection Relationship
4.4. Discussion on the Compression Tests
4.5. The Constitutive Law Derived
5. Conclusions
- The study demonstrated that the splitting tensile test can provide a reliable estimation of the matrix tensile strength, both for UHPC without fibers and for UHPFRC with low fiber content. Furthermore, the conversion factor between the uniaxial and splitting tensile strengths should be taken as at least 1.0.
- An investigation of the various test setups revealed that Setup I yielded unreliable results for the matrix tensile strength. In contrast, Setup II yielded matrix strength values around 10 MPa. Other experiments, such as the uniaxial tensile test using Setup III and flexural tests and splitting tensile tests, yielded strength values around 8 MPa.
- Upon examination of the post-cracking behavior of the uniaxial tensile tests, it becomes evident that there is a considerable disparity between the experimental results. The difference between the minimum and maximum strength values reached a factor of 10, while for the energy absorption capacity, it was approximately 5. The results of the flexural tests also showed a significant variation, but much smaller: the extreme results were generally within a range of 20–30%, although occasionally the difference was close to 40%. The results also indicated that for excellent post-cracking behavior, it is not enough to have an excellent strength value, but it is also necessary to maintain this high value over a wider cracking range.
- The findings indicated that the significance of the test setup in the post-cracking phase of the uniaxial tensile tests was comparatively less pronounced. However, the influence of fiber orientation and fiber distribution emerged as a dominant factor, and the precise way in which the fresh mix is poured is of critical importance.
- The uniaxial tensile tests have demonstrated the practical limitations associated with specimens without notches. Moreover, the approximately 30% reduction in the cross-sectional area achieved with a 4 mm notch has been found to be insufficient to reliably influence crack location. Consequently, a cross-sectional reduction of approximately 50% achieved with a 6.5 mm notch was identified as a more suitable solution.
- The flexural experiments suggest that the scale factor for the conversion between the matrix flexural tensile strength and uniaxial tensile strength might be increased, at least for the experiments investigated. Furthermore, for flexural tests on thin plates, the proposed value of 1.0 for the scale factor overestimates the matrix tensile strength, but the value determined by inverse analysis is a satisfactory approximation.
- A comparison of the direct and indirect tensile experiments investigated revealed that in the range of small crack widths, the derived tensile stress–crack opening curves have different characteristics, yet yielded comparable outcomes from a practical standpoint. the investigated simplified tensile laws developed for fiber-reinforced NSC, especially the DAfStb’s multi-linear approach, appeared to be applicable to UHPFRC as well.
- The study investigated the relationship between the deflection and crack opening, as well as the deflection and strain values in flexural experiments. The relationships obtained for typical UHPFRC mixtures and the given test setup and test specimen geometry were found to be invariant with respect to the material composition utilized or the type and quantity of steel fibers employed. The presented expressions are straightforward to employ in practice on mean values of at least six experiments and permit the derivation of crack openings and elongations on the tensile side from measurements of mid-field deflections alone, rather than complicated and unclear elongation (crack or strain) measurements. The crack opening and strain values thus obtained from the deflection can be utilized either directly or as input to inverse analysis to derive the constitutive law (uniaxial stress–strain relationship).
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Test Series | Direction | Test Setup | Fiber Content | Number of Specimens |
---|---|---|---|---|
Series 1 | H | Setup I | 2 vol% | 6 |
V | 6 | |||
L | 3 | |||
Series 2 | H | Setup II | 12 | |
V | 11 | |||
L | 8 | |||
Series 3 | H | Setup III | 1 vol% | 12 |
V | 12 | |||
L | 7 | |||
Series 4 | H | 2 vol% | 11 | |
V | 11 | |||
L | 8 |
Fiber Content [vol%] | Splitting Tensile Strength [MPa] | Mean [MPa] | Standard Deviation [MPa] | Coefficient of Variation [%] |
---|---|---|---|---|
0 | 9.56 | 7.87 | 0.96 | 12.2 |
6.74 | ||||
7.96 | ||||
6.99 | ||||
7.43 | ||||
8.53 | ||||
1 1 | 8.34 | 8.07 | 0.79 | 9.8 |
8.88 | ||||
7.00 | ||||
1 2 | 13.21 | 14.08 | 1.02 | 7.3 |
13.51 | ||||
15.51 | ||||
2 | 16.23 | 16.15 | 1.20 | 7.4 |
14.65 | ||||
17.57 |
Test Series | Direction | Mean of fct | Median of fct | St. Deviation of fct | Min. of fct | Max. of fct |
---|---|---|---|---|---|---|
Series 1 | H | 3.87 | 3.79 | 1.16 | 2.05 | 5.43 |
V | 6.54 | 7.31 | 1.75 | 3.28 | 8.10 | |
L | 4.20 | 4.28 | 0.95 | 3.00 | 5.33 | |
Series 2 | H | 9.99 | 10.03 | 0.58 | 8.92 | 11.17 |
V | 9.71 | 9.67 | 1.00 | 7.54 | 11.11 | |
L | 9.63 | 9.45 | 0.57 | 8.77 | 10.57 | |
Series 3 | H | 8.00 | 7.86 | 1.15 | 6.12 | 10.59 |
V | 7.56 | 7.44 | 0.74 | 6.60 | 9.43 | |
L | 8.37 | 8.43 | 1.08 | 6.72 | 9.69 | |
Series 4 | H | 7.92 | 7.69 | 0.96 | 6.59 | 9.31 |
V | 7.68 | 7.71 | 1.07 | 6.11 | 9.65 | |
L | 8.00 | 8.11 | 0.99 | 6.52 | 9.36 |
Test Series | Direction | Mean of fcf | Median of fcf | St. Deviation of fcf | Min. of fcf | Max. of fcf |
---|---|---|---|---|---|---|
Series 1 | H | 3.38 | 3.50 | 1.40 | 1.00 | 5.11 |
V | 6.53 | 6.55 | 1.16 | 4.45 | 8.12 | |
L | 5.87 | 5.58 | 1.52 | 4.18 | 7.86 | |
Series 2 | H | 7.44 | 8.59 | 3.05 | 0.90 | 11.11 |
V | 4.23 | 3.68 | 2.43 | 1.11 | 8.47 | |
L | 2.51 | 2.58 | 1.25 | 0.76 | 4.64 | |
Series 3 | H | 6.34 | 5.80 | 2.75 | 1.80 | 9.94 |
V | 5.35 | 5.16 | 2.36 | 2.51 | 8.81 | |
L | 2.62 | 1.96 | 1.46 | 1.07 | 5.06 | |
Series 4 | H | 7.44 | 5.46 | 5.47 | 1.88 | 16.23 |
V | 5.28 | 5.05 | 3.17 | 1.52 | 10.65 | |
L | 3.33 | 3.02 | 1.44 | 1.10 | 6.18 |
Test Series | Direction | Mean of Wf,2 | Median of Wf,2 | St. Deviation of Wf,2 | Min. of Wf,2 | Max. of Wf,2 |
---|---|---|---|---|---|---|
Series 1 | H | 5.31 | 5.54 | 1.51 | 2.98 | 7.71 |
V | 9.14 | 8.54 | 1.39 | 7.94 | 11.85 | |
L | 7.91 | 7.58 | 0.61 | 7.39 | 8.76 | |
Series 2 | H | 11.98 | 12.38 | 3.83 | 5.59 | 17.82 |
V | 8.55 | 8.03 | 2.65 | 5.07 | 12.09 | |
L | 6.05 | 6.57 | 1.93 | 2.32 | 8.93 | |
Series 3 | H | 9.72 | 9.43 | 3.54 | 3.30 | 14.93 |
V | 8.25 | 7.66 | 3.02 | 4.31 | 14.61 | |
L | 5.43 | 4.37 | 1.89 | 3.81 | 8.13 | |
Series 4 | H | 9.22 | 8.38 | 4.34 | 3.66 | 16.66 |
V | 8.09 | 7.80 | 4.03 | 3.58 | 15.64 | |
L | 6.26 | 6.47 | 1.73 | 3.92 | 9.36 |
Test Series | Direction | Mean of Wf,3 | Median of Wf,3 | St. Deviation of Wf,3 | Min. of Wf,3 | Max. of Wf,3 |
---|---|---|---|---|---|---|
Series 1 | H | 6.67 | 7.02 | 1.90 | 3.50 | 9.51 |
V | 10.96 | 10.13 | 1.71 | 10.03 | 14.38 | |
L | 10.11 | 10.16 | 0.58 | 9.37 | 10.80 | |
Series 2 | H | 15.07 | 15.68 | 5.00 | 6.34 | 22.73 |
V | 10.82 | 10.13 | 3.28 | 6.37 | 15.34 | |
L | 7.51 | 7.97 | 2.49 | 2.79 | 11.40 | |
Series 3 | H | 12.44 | 11.69 | 4.71 | 4.28 | 19.67 |
V | 10.77 | 10.16 | 4.03 | 5.45 | 19.61 | |
L | 6.79 | 5.25 | 0.00 | 8.13 | 8.13 | |
Series 4 | H | 11.44 | 10.89 | 4.97 | 4.95 | 20.08 |
V | 10.40 | 10.19 | 5.30 | 4.59 | 20.39 | |
L | 8.16 | 8.50 | 2.45 | 5.08 | 12.45 |
Fiber Content | Number of Specimens | Mean of fc | Median of fc | St. Deviation of fc | Min. of fc | Max. of fc |
---|---|---|---|---|---|---|
0 vol% | 12 | 154.3 | 154.0 | 3.44 | 148.1 | 160.4 |
1 vol% | 10 | 167.8 | 167.1 | 5.24 | 160.5 | 176.8 |
2 vol% | 6 | 172.5 | 172.4 | 6.77 | 163.0 | 182.8 |
Fiber Content | Number of Specimens | Mean of fc | Median of fc | St. Deviation of fc | Min. of fc | Max. of fc |
---|---|---|---|---|---|---|
1 vol% | 5 | 187.1 | 185.6 | 4.75 | 182.0 | 194.2 |
2 vol% | 5 | 189.1 | 190.9 | 6.31 | 181.7 | 197.4 |
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Mészöly, T.; Randl, N. Assessment of Methods to Derive Tensile Properties of Ultra-High-Performance Fiber-Reinforced Cementitious Composites. Materials 2024, 17, 3259. https://doi.org/10.3390/ma17133259
Mészöly T, Randl N. Assessment of Methods to Derive Tensile Properties of Ultra-High-Performance Fiber-Reinforced Cementitious Composites. Materials. 2024; 17(13):3259. https://doi.org/10.3390/ma17133259
Chicago/Turabian StyleMészöly, Tamás, and Norbert Randl. 2024. "Assessment of Methods to Derive Tensile Properties of Ultra-High-Performance Fiber-Reinforced Cementitious Composites" Materials 17, no. 13: 3259. https://doi.org/10.3390/ma17133259