Journal of Jilin University(Engineering and Technology Edition) ›› 2019, Vol. 49 ›› Issue (4): 1144-1152.doi: 10.13229/j.cnki.jdxbgxb20180020

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Determination of fracture toughness and softening traction⁃separation law of polypropylene fiber reinforced concrete

Ning⁃hui LIANG1,2(),Qing⁃xu MIAO1,2,Xin⁃rong LIU1,2,Ji⁃fei DAI3,Zu⁃liang ZHONG1,2   

  1. 1. School of Civil Engineering, Chongqing University, Chongqing 400045, China
    2. National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas, Chongqing 400045, China
    3. China Construction Infrastructure Co, Ltd, Beijing 100044, China
  • Received:2018-01-08 Online:2019-07-01 Published:2019-07-16

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Abstract:

The three?point bending test was carried out on concrete notched beams with different amount of coarse and fine polypropylene(PP) fibers. Based on the double?K fracture theory, the influence of mixing method of PP fibers with different sizes on the fracture toughness and failure mechanism were discussed.The real cohesive toughness, the increment of initiation toughness and the bridge connection toughness were gained by the quantitative relationship between the initiation toughness, the unstable toughness and the cohesive toughness. In addition, The theoretical cohesive toughness was calculated from three kinds of ordinary concrete bilinear softening constitutive curves, which was compared with the real cohesive toughness to determine the bilinear softening traction?separation law of PFRC, which was suitable for different PP fiber incorporation conditions. The results show that PFRC has higher initiation toughness, unstable toughness and fracture energy compared with plain concrete. The enhancement effect of bridge connection toughness from bridging stress is very significant when 2 or 3 sizes of PP fibers are mixed. The 3 sizes of PP fibers play the role of bridging at different stages of crack propagation, and it serves a well function of toughening and strengthening. The bilinear softening traction?separation law proposed by Xu and Reinhardt is well applicable for PFRC when the correction coefficient is 6.

Key words: civil engineering, polypropylene fiber reinforced concrete, double?K fracture model, bilinear softening traction?separation law

CLC Number: 

  • TU528

Fig.1

Distribution of critical cohesive stress on fictitious crack zone"

Fig.2

Bilinear softening traction?separation law"

Table 1

Physical and mechanical properties of"

参 数 FF1 FF2 CF1
直径/mm 0.026 0.100 0.800
长度/mm 19 19 50
抗拉强度/MPa 641 322 706
弹性模量/GPa 4.5 4.9 7.4
断裂伸长率/% 40 15 10
密度/(g·cm-3) 0.91 0.91 0.95
推荐掺量/(kg·m-3) 0.9 0.9 6.0

Table 2

Amount of polypropylene fiber for different specimens"

试件编号 纤维种类 纤维掺量/(kg·m-3)
A0 无 0
A1 FF1 0.9
A2 FF2 0.9
A3 CF1 6.0
A4 FF1+CF1 0.6+5.4
A5 FF1+CF1 0.9+5.1
A6 FF1+CF1 1.2+4.8
A7 FF2+CF1 0.6+5.4
A8 FF2+CF1 0.9+5.1
A9 FF2+CF1 1.2+4.8
A10 FF1+FF2+CF1 0.45+0.45+5.1
A11 FF1+FF2+CF1 0.6+0.6+4.8

Fig.3

"

Table 3

Calculated results of double?K fracture parameters and fracture energy"

试件

编号

 CMOD c/μm C T O D c /μm P inl/N

K I c i n i

/(MPa·m1/2)

 P m a x /N a c/mm

K I c u n

/(MPa·m1/2)

G f

/(N·m-1)
A0 39.9 10 1665 0.561 2017 57 0.869 104.7
A1 48.1 13 1943 0.654 2441 59 1.133 147.6
A2 42.5 12 1503 0.506 1929 61 0.960 113.3
A3 51.1 15 1807 0.608 2265 61 1.132 403.1
A4 51.2 16 1727 0.582 2243 62 1.120 537.9
A5 58.8 21 1850 0.623 2457 63 1.336 562.0
A6 54.7 18 1752 0.590 2276 64 1.285 535.0
A7 54.8 18 1797 0.605 2351 63 1.287 480.7
A8 56.5 19 1755 0.591 2284 64 1.282 544.2
A9 47.2 16 1627 0.548 2177 64 1.272 433.6
A10 44.9 18 1983 0.670 2552 63 1.356 537.7
A11 57.3 20 1930 0.650 2580 64 1.454 608.8

Table 4

Increment of initiation toughness and bridge connection toughness of polypropylene fiber"

试件编号 K I c c s Δ K I c i n i s
A0 0 0
A1 0.171 0.093
A2 0.146 -0.055
A3 0.216 0.047
A4 0.230 0.021
A5 0.405 0.062
A6 0.387 0.029
A7 0.374 0.044
A8 0.383 0.030
A9 0.416 -0.013
A10 0.378 0.109
A11 0.496 0.089

Table 5

Comparison between K I c , T c and K I c , E c "

试件编号 K I c , T c K I c , E c （Petersson) K I c , E c （CEB?FIP Model Code 1990) K I c , E c （徐世烺和Reinhardt)
λ=5 λ=6 λ=7 λ=8 λ=9 λ=10
∑ i = 1 11 η i 0.601 0.594 0.274 0.149 0.161 0.220 0.279 0.305
A0?1 0.287 0.479 0.344 0.328 0.299 0.283 0.272 0.265 0.260
A0?2 0.335 0.510 0.366 0.348 0.317 0.299 0.288 0.280 0.274
A0?3 0.304 0.415 0.298 0.283 0.259 0.245 0.236 0.230 0.225
η 0 0.08 0.004 0.002 0.0025 0.005 0.007 0.009 0.010
A1?1 0.489 0.525 0.523 0.494 0.445 0.442 0.431 0.419 0.411
A1?2 0.523 0.622 0.620 0.587 0.532 0.529 0.508 0.493 0.483
A1?3 0.424 0.538 0.536 0.506 0.460 0.458 0.441 0.429 0.420
η 1 0.024 0.023 0.011 0.003 0.003 0.0038 0.006 0.008
A2?1 0.588 0.730 0.725 0.692 0.624 0.619 0.594 0.577 0.564
A2?2 0.419 0.630 0.627 0.596 0.540 0.536 0.515 0.501 0.490
A2?3 0.355 0.555 0.552 0.524 0.475 0.474 0.456 0.443 0.434
η 2 0.105 0.101 0.07 0.031 0.029 0.02 0.015 0.012
A3?1 0.493 0.547 0.546 0.509 0.461 0.458 0.441 0.428 0.419
A3?2 0.549 0.837 0.836 0.773 0.692 0.689 0.653 0.631 0.616
A3?3 0.526 0.678 0.677 0.630 0.568 0.563 0.539 0.523 0.512
η 3 0.109 0.108 0.06 0.023 0.02 0.013 0.011 0.01
A4?1 0.517 0.617 0.616 0.571 0.516 0.512 0.491 0.476 0.466
A4?2 0.931 1.06 1.05 0.972 0.863 0.848 0.807 0.779 0.759
A4?3 0.405 0.632 0.632 0.585 0.527 0.523 0.501 0.486 0.475
η 4 0.077 0.051 0.037 0.019 0.021 0.025 0.031 0.037
A5?1 0.791 0.803 0.802 0.743 0.667 0.658 0.630 0.610 0.595
A5?2 0.628 0.771 0.770 0.712 0.639 0.632 0.604 0.586 0.571
A5?3 - - - - - - - - -
η 5 0.020 0.020 0.009 0.015 0.017 0.026 0.031 0.041
A6?1 0.649 0.759 0.757 0.701 0.630 0.623 0.596 0.578 0.564
A6?2 0.740 0.893 0.892 0.823 0.735 0.724 0.691 0.668 0.651
A6?3 0.695 0.845 0.843 0.781 0.699 0.689 0.659 0.638 0.622
η 6 0.058 0.057 0.017 0.0004 0.0001 0.006 0.013 0.02
A7?1 0.713 0.828 0.828 0.763 0.683 0.673 0.644 0.623 0.607
A7?2 0.836 0.960 0.958 0.885 0.788 0.776 0.740 0.715 0.697
A7?3 0.681 0.783 0.781 0.726 0.652 0.644 0.616 0.598 0.583
η 7 0.040 0.038 0.007 0.004 0.007 0.018 0.03 0.04
A8?1 0.805 1.038 1.037 0.952 0.846 0.831 0.791 0.764 0.744
A8?2 0.628 0.741 0.739 0.687 0.617 0.611 0.585 0.567 0.553
A8?3 0.691 0.833 0.832 0.768 0.687 0.678 0.648 0.627 0.612
η 8 0.087 0.086 0.031 0.002 0.001 0.004 0.009 0.016
A9?1 0.541 0.677 0.676 0.630 0.568 0.563 0.540 0.523 0.512
A9?2 0.794 0.943 0.942 0.868 0.773 0.761 0.726 0.701 0.683
A9?3 0.724 0.880 0.879 0.811 0.725 0.715 0.682 0.660 0.643
η 9 0.065 0.064 0.021 0.001 0.0016 0.006 0.013 0.019
A10?1 0.716 0.767 0.766 0.708 0.635 0.628 0.610 0.582 0.568
A10?2 0.783 0.864 0.863 0.797 0.713 0.703 0.671 0.650 0.633
A10?3 0.688 0.755 0.754 0.699 0.627 0.621 0.594 0.576 0.562
η 10 0.014 0.013 0.0004 0.015 0.019 0.034 0.048 0.06
A11?1 0.789 0.774 0.773 0.716 0.643 0.635 0.608 0.589 0.575
A11?2 0.806 0.848 0.847 0.781 0.699 0.689 0.659 0.637 0.621
A11?3 - - - - - - - - -
η 11 0.002 0.002 0.006 0.032 0.037 0.054 0.068 0.080
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