Schematic description of: (a) Softening and hardening behavior of UHPFRC in uniaxial tension; (b) Corresponding load-deflection response under three point bending.

Contexts in source publication

Context 1

... with strain-softening ones, a strain-hardening material is considered to be more excellent with respect to mechanical performance. Nevertheless, due to the obvious distinction between the behavior of bending and uniaxial tension, strain-softening behavior in uniaxial tension can result in a deflection hardening response in bending, as shown in Figure 1. Due to bridge effect of fiber, the load-deflection response of UHPFRC prisms is significantly different with non-fiber-reinforced concrete, which always tends to brittle bending failure. ...

Context 2

... mean cube strengths for series 1 and series 2 are determined to be 176 and 172 MPa, respectively. The details of the two series and the essential parameters used in the inverse analysis are listed in Table 4. Figure 10 depicts the comparison of the tensile σ-ε curve back-calculated by the proposed method with the uniaxial tensile test results and the correlation between the calculated and measured load-deflection responses for series 1 and series 2. Figure 10a shows a σ-ε curve calculated by the analysis method is in good agreement with the direct tensile test results of series 1. However, the predicted tensile strength is slightly higher than the test result for series 2 due to the underestimation of elastic modulus, as shown in the inset of Figure 10c, and the higher scatter of experimental load-deflection responses, as illustrated in Figure 10d. ...

Context 3

... mean cube strengths for series 1 and series 2 are determined to be 176 and 172 MPa, respectively. The details of the two series and the essential parameters used in the inverse analysis are listed in Table 4. Figure 10 depicts the comparison of the tensile σ-ε curve back-calculated by the proposed method with the uniaxial tensile test results and the correlation between the calculated and measured load-deflection responses for series 1 and series 2. Figure 10a shows a σ-ε curve calculated by the analysis method is in good agreement with the direct tensile test results of series 1. However, the predicted tensile strength is slightly higher than the test result for series 2 due to the underestimation of elastic modulus, as shown in the inset of Figure 10c, and the higher scatter of experimental load-deflection responses, as illustrated in Figure 10d. ...

Context 4

... details of the two series and the essential parameters used in the inverse analysis are listed in Table 4. Figure 10 depicts the comparison of the tensile σ-ε curve back-calculated by the proposed method with the uniaxial tensile test results and the correlation between the calculated and measured load-deflection responses for series 1 and series 2. Figure 10a shows a σ-ε curve calculated by the analysis method is in good agreement with the direct tensile test results of series 1. However, the predicted tensile strength is slightly higher than the test result for series 2 due to the underestimation of elastic modulus, as shown in the inset of Figure 10c, and the higher scatter of experimental load-deflection responses, as illustrated in Figure 10d. In addition, since no experimental data are available for the deflection larger than 4mm, the stress-strain curve calculated by the inverse analysis is incomplete for series 2. The maximum compressive strain obtained by using Equation (5) is 2.01 × 10 −3 , which is only half of the ultimate compressive strain. ...

Context 5

... details of the two series and the essential parameters used in the inverse analysis are listed in Table 4. Figure 10 depicts the comparison of the tensile σ-ε curve back-calculated by the proposed method with the uniaxial tensile test results and the correlation between the calculated and measured load-deflection responses for series 1 and series 2. Figure 10a shows a σ-ε curve calculated by the analysis method is in good agreement with the direct tensile test results of series 1. However, the predicted tensile strength is slightly higher than the test result for series 2 due to the underestimation of elastic modulus, as shown in the inset of Figure 10c, and the higher scatter of experimental load-deflection responses, as illustrated in Figure 10d. In addition, since no experimental data are available for the deflection larger than 4mm, the stress-strain curve calculated by the inverse analysis is incomplete for series 2. The maximum compressive strain obtained by using Equation (5) is 2.01 × 10 −3 , which is only half of the ultimate compressive strain. ...

Context 6

... both the primitive and bilinear softening curves suggested by Yoo et al. [33] were converted into the tensile σ-ε curve depending on a reference length of 100 mm. The comparisons of the predicted tensile σ-ε curves obtained from the proposed inverse analysis with the analysis of Yoo et al. [33] are presented in Figure 11. The maximum tensile strain 6.5% corresponding to the cracking opening of 6.5 mm in accordance with the fiber length limit is obtained from the proposed analysis method. ...

Context 7

... stress-strain response obtained from the proposed method provides the best fit of the primitive softening curve for UH-V 1 , UH-V 2 , and UH-V 3 . A slight deviation between the proposed analysis and the primitive analysis result for UH-V 4 , as shown in Figure 11g, is mainly due to the intrinsic scatter of the experimental load-deflection responses at a high strength level and the low disperse degree of the fiber. The first cracking tensile strength with an approximate value of 10MPa is obtained by the proposed method for all specimens. ...

Context 8

... the verification results indicate that the proposed method can be used for predicting the postcracking tensile behavior of UHPFRC. Figure 11. Comparison of inverse analysis results with primitive and bilinear softening curves for each group reported in Ref. [33]: (a) σ-ε curves for UH-V1; (b) L-δ responses for UH-V1; (c) σ-ε curves for UH-V2; (d) L-δ responses for UH-V2; (e) σ-ε curves for UH-V3; (f) L-δ responses for UH-V3; (g) σ-ε curves for UH-V4; (h) L-δ responses for UH-V4. ...

Context 9

... bending test results shown in Figure 3 and the parameters listed in Table 1 were used for the inverse analysis. The tensile stress-strain curves of the UHPFRC with different fiber volume fractions were well predicted by using the proposed method to fit the load-deflection responses, as shown in Figure 12a. Additionally, the correlations between calculated load-deflection response and that obtained from the notched 3PBT were depicted in Figure 12b. ...

Context 10

... tensile stress-strain curves of the UHPFRC with different fiber volume fractions were well predicted by using the proposed method to fit the load-deflection responses, as shown in Figure 12a. Additionally, the correlations between calculated load-deflection response and that obtained from the notched 3PBT were depicted in Figure 12b. As shown in inset of Figure 12a, the postcracking tensile strength exhibits an approximately proportional behavior to the fiber volume fraction, whereas the first cracking tensile strength was insensitive to the fiber volume fraction, and it was primarily determined by the matrix strength. ...

Context 11

... the correlations between calculated load-deflection response and that obtained from the notched 3PBT were depicted in Figure 12b. As shown in inset of Figure 12a, the postcracking tensile strength exhibits an approximately proportional behavior to the fiber volume fraction, whereas the first cracking tensile strength was insensitive to the fiber volume fraction, and it was primarily determined by the matrix strength. In addition, the ultimate tensile strain was also seldom affected by the amount of fiber, which is mainly influenced by the fiber length and orientation. ...

Context 12

... a strain-softening UHPFRC with deflection-hardening behavior in bending, the deflection corresponding to the bending strength was insensitive to the fiber volume fraction. As shown in Figure 12a, due to the fiber bridging, the strain-softening part of tensile stress-strain response contributes to the load-carrying capacity and nonlinear energy dissipation. When subjected to bending stresses, the post-peak response in the tensile regions contributes to the load-carrying capacity in the softening observed in the deflection response of the UHPFRC prisms with the fiber content of 0.5%. ...

Context 13

... subjected to bending stresses, the post-peak response in the tensile regions contributes to the load-carrying capacity in the softening observed in the deflection response of the UHPFRC prisms with the fiber content of 0.5%. However, if the volume fraction of the fibers is larger than 0.75%, as shown in Figure 12b, the stiffness contribution of the cracked zone may result in loads in excess of the first cracking point and is defined as deflection hardening. Therefore, the stiffness of the cracked zone in the tensile regions contributes to the increased capacity in bending at large deflection levels. ...

Context 14

... it is essential to make a balance between the handiness and the accuracy of the proposed method. Figure 13 shows the effect of the number of segments on the accuracy of the proposed inverse method. The overestimation of the calculated postcracking strength is reduced from 9.6% to 0.6% compared to experimental result, with the number of segments increased from three to eight. ...

Context 15

... overestimation of the calculated postcracking strength is reduced from 9.6% to 0.6% compared to experimental result, with the number of segments increased from three to eight. Furthermore, the modulus of the strain-hardening stage is improved with increasing the number of segments, as shown in the inset of Figure 13a. When n is equal to 5, the corresponding overestimation is under 4%, which is precise enough for the structural design and quality control of the strain-hardening UHPFRC. ...

Context 16

... order to investigate the influence of the notch-to-depth ratio, the load-deflection responses are simulated for series 1 with a notch depth of 0, 12.5, 25, and 50 mm at the midspan of the beam specimens that which result in a ratio a/d of 0, 0.08, 0.16, and 0.33, respectively. Figure 14a demonstrates the effect of the ratio a/d on the load-deflection response of series 1. It is observed that the peak load decreases sharply, and the curve becomes smooth with an increasing notch-to-depth ratio. ...

Context 17

... is observed that the peak load decreases sharply, and the curve becomes smooth with an increasing notch-to-depth ratio. As shown in the inset of Figure 14a, the load at LOP is inversely proportional to the notch-to-depth ratio because UHPFRC is more prone to cracking failure with the increase of that ratio. Furthermore, Figure 14b depicts the bending stress-deflection curves of series 1 with different notch-to-depth ratios. ...

Context 18

... shown in the inset of Figure 14a, the load at LOP is inversely proportional to the notch-to-depth ratio because UHPFRC is more prone to cracking failure with the increase of that ratio. Furthermore, Figure 14b depicts the bending stress-deflection curves of series 1 with different notch-to-depth ratios. The bending stress was calculated by using Equation (1). ...

Context 19

... bending stress was calculated by using Equation (1). The bending strength is slightly affected by the notch-to-depth ratio, and softening occurs more slowly with an increasing notch-to-depth ratio, as shown in Figure 14b. This is due to the distance between the top of the specimen and the tip of the notch, which reduces with the increase of the notch-to-depth ratio, leading to a lower first cracking load. ...

Context 20

... for the postcracking strength study, the bending tensile strength and ductility were expressed as the normalized M−φ response, which is irrelevant to specimen size and first cracking tensile strength. Figure 15a demonstrates the tensile constitutive model with the normalized postcracking strength (β 2 ) varied from 0.25 to 1.25 and the corresponding normalized transition strain α 2 = 10, simulating a range of strain-softening response of the UHPFRC with a low fiber volume fraction, to the strain-hardening response of the UHPFRC with a high fiber volume fraction. Figure 15b illustrates that the normalized M−φ relationship is highly sensitive to variations in the material parameter β 2 , as it significantly influences the peak and post-peak response. ...

Context 21

... 15a demonstrates the tensile constitutive model with the normalized postcracking strength (β 2 ) varied from 0.25 to 1.25 and the corresponding normalized transition strain α 2 = 10, simulating a range of strain-softening response of the UHPFRC with a low fiber volume fraction, to the strain-hardening response of the UHPFRC with a high fiber volume fraction. Figure 15b illustrates that the normalized M−φ relationship is highly sensitive to variations in the material parameter β 2 , as it significantly influences the peak and post-peak response. It is important to remark that the bending tensile strength and ductility are improved as the normalized postcracking strength changes from 0.25 to 1.25, and a significant deflection hardening response occurs when β 2 is larger than 0.75. ...