Figure 1: Cracks under indentation (a) of median type or half-penny crack (type M) and (b) type
Concretes |
S s |
Cs |
g1 |
Materials (kg/m3) g2 Lp Sf |
w |
Sp |
w/b |
w/c |
fresh properties |
||||
SCC1 368 |
570 |
243 |
328 |
492 |
100 |
32 |
187 |
8 |
0.41 |
0.51 |
730 |
0.90 |
8.0 |
SCC2 368 |
570 |
243 |
328 |
492 |
100 |
32 |
178 |
8 |
0.39 |
0.48 |
720 |
0.87 |
8.4 |
SCC3 368 |
570 |
243 |
328 |
492 |
100 |
32 |
169 |
8 |
0.37 |
0.46 |
705 |
0.86 |
9.2 |
SCC4 368 |
570 |
243 |
328 |
492 |
100 |
32 |
160 |
8 |
0.35 |
0.43 |
695 |
0.84 |
10.4 |
SCC5 368 |
570 |
243 |
328 |
492 |
100 |
32 |
151 |
8 |
0.33 |
0.41 |
675 |
0.81 |
11.7 |
NVC1 400 |
570 |
243 |
379 |
567 |
/ |
/ |
214 |
/ |
0.53 |
0.53 |
/ |
/ |
/ |
NVC4 400 |
570 |
243 |
379 |
567 |
/ |
/ |
144 |
13, |
2 0.36 |
0.36 |
/ |
/ |
/ |
EFNARC / |
/ |
/ |
/ |
/ |
/ |
|
/ |
/ |
/ |
/ |
650–800 |
> 0,8 |
(8-14) |
Table 1:Compositions and fresh properties of the mixtures
concrete Matrix |
SCC1 |
SCC2 |
SCC3 |
SCC4 |
SCC5 |
NVC1 |
NVC4 |
w/b ratio |
0.41 |
0.39 |
0.37 |
0.35 |
0.33 |
0.53 |
0.36 |
w/c ratio |
0.51 |
0.48 |
0.46 |
0.43 |
0.41 |
0.53 |
0.36 |
fc28, cyl. (MPa) |
36.7 |
41.3 |
46.5 |
54.3 |
61.7 |
36.4 |
53.6 |
E(GPa) |
28.3 |
34.5 |
42.4 |
47.9 |
51.8 |
34.9 |
49.2 |
Slope of C3/2 = f (P) |
36.29 |
34.47 |
32.56 |
30.40 |
28.71 |
34,62 |
29.74 |
KICM MPa.m1/2 |
2.27 |
2.39 |
2.53 |
2.71 |
2.87 |
2,38 |
2,77 |
Table 2:Fracture parameters and other mechanical properties.
Research program |
Material |
Proposed empirical relation |
Beygy et al. [46] |
SCC |
KIC = -57.57 (w/c) + 67.01 |
Propcopski and Langier [43] |
Gravel concrete without silica fume |
KIC = -157.95 (w/c) + 162.66 |
Ince et al. [47] |
NVC |
KIC = 142 / (9.6)1.5x w/c |
Karamloo M. et al. [48] |
SCCL |
KIC = - 99.197 (w/c) + 63.827 R2 = 0.981 |
Test results (of current study) |
SCC |
KIC = - 7.6 (w/b) + 5.366 R2 = 0,9945 |
Test results (of current study) |
SCC |
KIC = - 6,046 (w/c) + 5,322 R2 = 0,9877 |
(SCLC): Self-Compacting Lightweight Concrete
Table 3:Proposed empirical relations in the literature for SCC, NVC and other types of concrete
KIC fracture toughness calculations based on: |
Concrete |
SCC4 |
SCC5 |
NVC4 |
1- Literature results |
fc28,cyl (MPa) |
53,9 ± 7,9 |
65,0 ± 8,3 |
53,4 ± 2,3 |
*Hillerborg Approach (3PBTests) [51]. |
KIC (MPa.m1/2) |
3,85 |
4,21 |
4,54 |
* Anderson Approach (3PBTests) [52]. |
KIC (Mpa.m1/2) |
1,23 |
1,43 |
1,78 |
2- Results of the current study |
fc28,cyl (MPa) |
54,3 ± 2,2 |
61,7 ± 3,0 |
53,6 ± 1,6 |
* Grairia Approach (IITests). |
KIC (MPam1/2) |
2,71 |
2,87 |
2,77 |
Table 4: Comparison of the results of toughness (KIC) with the literature.
Concrete type |
SCC1 |
NVC1 |
SCC4 |
NVC4 |
fc 28, cyl (MPa) |
36.7 |
36.4 |
54.3 |
53.6 |
KIC (MPa.m1/2) |
2.27 |
2.38 |
2.71 |
2.77 |
E (GPa) |
28.3 |
34.9 |
47.9 |
49.2 |
Resistance class fc28, cyl (MPa) |
37 |
54 |
||
Resistance class fc28, cub (MPa) |
40 |
60 |
||
Performance of KIC (NVC) / KIC (SCC) (%) |
4.85 |
2.21 |
Table 5: Comparison of the performance of NVC fracture parameters compared to those of SCC with the same compressive strength:
Figure 1: Cracks under indentation (a) of median type or half-penny crack (type M) and (b) type
Figure2: Schematic view of the indented surface (top view) and the cross section (section view) of Vickers indentation cracking system.
Figure 3: Samples of SCC and NVC for Instrumented Indentation Tests
Figure 4: instrumented indentation test set-up: (a) General view of the macro indenter Zwick and
(b).zoom on the two cells of observation and indentation.
Figure 5: a) Schematic illustration of an instrumented indentation test on of the specimen face), b) The
dimensions associated to the crack length and diagonal indent measurements and c) The C3/2 = f (P)
and a.l1/2 = f(P) graphs with their respective slopes, used to calculate the corresponding fracture
toughness values kIC in both modes (M and P) and this for the material studied by Pertuz et al.[30]:
Sintered tungsten carbide WC - WTi.
Figure 6: Photographs of the SCC4 specimen: a) Indentation test sample, b) Enlarged view of the zone to be indented prior to the test and c) Enlarged view of the area indented after the test: cracking on the surface of the SCC4 matrix after loading at 800N.
Figure 7: Load–displacement curves obtained for SCC4 mix (w/c = 0.43, w/b = 0.35) under 800 N loading.
Figure 8: Crack length of the indent as a function of the indentation load obtained for SCC4 (w/b = 0.35).
Figure 9: Variation in fracture toughness KIC versus water-to-binder ratio (w / b).
Figure 10: Fracture toughness versus w/c ratio for different types of concrete.
Figure 11: Variation in fracture toughness KIC versus compressive strength (fc28).
Figure 12: Fracture parameter (KIC) comparison between SCC and NVC with similar compressive strength.
Tables at a glance
Figures at a glance