PSI - Issue 2_A

Alessandro P Fantilli et al. / Procedia Structural Integrity 2 (2016) 2857–2864 A.P. Fantilli, A. Gorino, B. Chiaia / Structural Integrity Procedia 00 (2016) 000–000

2862

6

Table 1. Properties of the ideal FRC-RDP.

f c (MPa)

L f / 

V f (%)

P cr* (kN)

P u (kN)

V f,min (%)

Group

Panel

DI

v

0.30 0.50 0.70 0.50 0.70 0.90 0.80 1.20 1.60 0.40 0.60 0.80 0.50 0.80 1.10 0.90 1.30 1.70 0.50 0.70 0.90 0.50 0.90 1.30 0.80 1.40 2.00

24.95 26.33 27.99 25.74 26.99 28.34 26.46 28.48 30.74 34.16 35.66 37.14 34.30 36.23 38.29 35.70 37.78 39.87 41.59 42.92 44.62 41.24 43.56 46.37 42.02 45.07 48.48

16.44 24.59 33.60 19.59 25.99 32.64 20.88 29.66 39.15 24.25 35.02 46.00 23.11 35.24 47.82 27.20 38.35 49.89 33.76 46.32 59.16 26.25 45.03 64.51 27.88 47.00 67.12

-0.34 -0.07 0.20 -0.24 -0.04 0.15 -0.21 0.04 0.27 -0.29 -0.02 0.24 -0.33 -0.03 0.25 -0.24 0.02 0.25 -0.19 0.08 0.33 -0.36 0.03 0.39 -0.34 0.04 0.38

0.54 0.91 1.27 0.67 0.94 1.21 0.70 1.05 1.40 0.65 0.97 1.30 0.60 0.96 1.31 0.70 1.01 1.32 0.78 1.09 1.40 0.57 1.02 1.48 0.59 1.04 1.48

C30_A80_1 C30_A80_2 C30_A80_3 C30_A60_1 C30_A60_2 C30_A60_3 C30_A40_1 C30_A40_2 C30_A40_3 C45_A80_1 C45_A80_2 C45_A80_3 C45_A60_1 C45_A60_2 C45_A60_3 C45_A40_1 C45_A40_2 C45_A40_3 C60_A80_1 C60_A80_2 C60_A80_3 C60_A60_1 C60_A60_2 C60_A60_3 C60_A40_1 C60_A40_2 C60_A40_3

0.55

80

1

0.74

2

30

60

1.14

3

40

0.62

80

4

0.84

45

5

60

1.28

6

40

0.64

80

7

0.88

60

8

60

1.35

9

40

For each group of 3 homogeneous plates, a linear relationship between DI and V f is attained (Fig.6c). Thus, the values of V f,min , detected with the intersection between the line DI - V f and the axis DI = 0 , are reported in Table 1. If the normalized reinforcement ratio v = V f / V f,min is introduced (Fig.7a), the existence of a linear function DI - v can be argued for all the FRC-RDP. This line passes through the point v = 1 , DI = 0 and has a slope of 0.8 . In other words, for all the groups of FRC-RDP, the evaluation of the ductility index can be performed by means of the following general equation:   0.8 1 DI v    (12)

Fig. 6. – FRC-RDP of group 5: (a)-(b) load vs. deflection curves of two panels; (c) ductility index vs. fiber volume fraction diagram.