Chapter 3 Tensile B ehaviour and Failure Mechanism of the
3.4 Failure process of the crossing point .1 Load-displacement Curves
Figure 3.18 shows load-displacement curves of all specimens. It is important to note that for the specimen CR8@100-3, the displacement couldn't be obtained well, as shown in Figure 3.18(d).
60
50
40
- 30
ct 0
`-20
10
0 0
60
50
40
30 Ct 0
`-.120
10
0
2 4 6 8 10
Displacement (mm)
(a) CR5@50
12 14
0 510
Displacement (mm) (b) CR5 @ 100
Figure 3.18(1) Load-displacement curves
15
60—
50
40
-30 -
0
10-
0.
0
60
50
40
30
czt 0
`-20
10
0
510
Displacement (mm) (c) CR8@50
15
0
510
Displacement (mm) (d) CR8@100
Figure 3.18(2) Load-displacement curves
44
15
60
50
40
30 ct 0 '-20
10
0
CR13@100-1 CR13@100-2 CR13@100-3
0 510
Displacement (mm)
15
(e) CR13@100
Figure 3.18(3) Load-displacement curves
3.4.2 Failure Mechanism of the Crossing Point
It is known that the CFRP grid is manufactured by several layers of vertical bars and horizontal bars by pressing and adhesion. The mutual action exists between the horizontal layer and the vertical layer in the crossing point of the CFRP grid. When the tensile load of the vertical bar reaches some critical value, the mutual action between the horizontal layer and vertical layer in the crossing point began to be destroyed. After this critical point, slip between the horizontal layer and vertical layer generated. And the slip increases with the increasing of the tensile load. Accordingly, under the tensile load, the displacement of the vertical bar includes the elastic deformation of the vertical bar and the slip between the horizontal layer and the vertical layer. At last, the crossing point couldn't bear more load for the loss of slid stability.
Based on the analysis of failure process and the characteristics of load-displacement curves as above, the simplified linear model was proposed, as shown in Eq. (3-2) and Figure 3.19.
F = KS (3-2)
F: tensile load; S:
crossing point.
displacement of the vertical bar; K: tensile resistant rigidity of the
C73 0 c N
Fu
0Su
Displacement (S) Figure 3.19 Simplified model of failure process
For this simplified model, main mechanical parameters are shown in Table 3.7.
Compared with the test pull-out distance as shown in Table 3.5, it shows that the peak displacement is a little huger than the test pull-out distance. This is because the simplified model considers the tensile deformation of the vertical bar and the slip between the vertical layer and the horizontal layer comprehensively, while the test pull-out distance is just the slip value between the vertical layer and the horizontal layer. For the high elastic
modulus (105MPa) of CFRP grid, it is clarified that the tensile deformation of the vertical bar is rather small, and the slip between the horizontal bar and the vertical bar in crossing point is the dominant deformation.
Table 3.7 Main mechanical parameters of simplified model for different CFRP grids
Type Anti-slid rigidity/K (kN/mm)
Maximum tensile load/F,,, (kN)
Peak displacement
Su/(mm)
CR5@50 0.982 11.2 11.4
CR5 @ 100 1.017 12.0 11.8
CR8@50 1.504 17.0 11.3
CR8@100 1.537 18.6 12.1
CR13@100 3.674 48.5 13.2
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3.5 Tensile mechanical model of the crossin g point 3.5.1 Simplified method of the crossing point
The analysis above shows that the tensile failure of the crossing point is caused by the loss of slid stability between the horizontal bar and the vertical bar. But for the manufacture method of the CFRP grid, the structural characteristic of the crossing point is rather complicated. Several layers of CFRP bars cross and intersect in the crossing point.
In order to reveal the failure mechanism and tensile bearing characteristic of the crossing point intuitively, take no account of the multi-layer characteristic of the horizontal bar and vertical bar in the crossing point. Suppose only single layer of horizontal bar and vertical bar existing. And the tensile behavior of the crossing point is reflected by the interface behavior between the horizontal bar and the vertical bar. For the different simplified method of the interface between the horizontal bar and the vertical bar, two mechanical models were proposed as below.
3.5.2 Elastic Layer Model (ELM) (1) Basic assumptions
The elastic layer was adopted to simulate the interface between the horizontal bar and the vertical bar. The sketch of elastic layer model is shown in Figure 3.20. Basic assumptions of elastic layer model are shown as below.
(a) Take no account of the tensile deformation of the vertical bar under tensile load.
(b) All the tensile behavior of the crossing point is equivalent to the tensile behavior of the elastic layer. The break of the crossing point is reflected by the brittle fracture of the elastic layer.
(c) Bond strength between the elastic layer and the CFRP grid is infinity, which means that it couldn't occur the bond failure under tensile load.
0
x<
Horizontal bar
Vertical bar /
Elastic layer
Figure 3.20 Sketch of elastic layer model
(2) Main mechanical parameters of Elastic Layer Model
In order to analyze conveniently, suppose the thickness of the elastic layer be equal to 1 mm. Peak deformation of elastic layer under tensile load could be calculated by Eq.(3-3) as below.
S =6ul_
u E1
Ful w x 1 x E1
Ful
-wEl (3-3)
S..: ultimate tensile deformation of the elastic layer;
F1: ultimate tensile load;
w: width of the elastic layer, which is equal to the width of CFRP grid;
O: ultimate tensile stress of the elastic layer;
Et: elastic modulus of the elastic layer;
1: length of the elastic layer.
Based on the simplified model of failure process as shown in Figure 3.20, according to the principle of equivalent tensile deformation, equations could be established as below.
FuFul
K wE1 (3-4)
K =wEl
l (3-5)
Generally, the width of the elastic layer is equal to the length of the elastic layer and both are equal to the width of CFRP grid. Accordingly, Eq.(3-5) could be expressed by Eq.(3-6).
E1 = K(3-6)
Based on the assumption, the failure principle of the crossing point is that the elastic layer reaches the ultimate tensile strain. As shown in Eq.(3-7).
E_~tu=F. tu
L.,lwEl (3-7)
F1: ultimate tensile load , as shown in Table 3.4;
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w: width of the elastic layer, which is equal to the width of CFRP grid and could be obtained by multiple measurements;
Et: elastic modulus of the elastic layer, which could be obtained by Eq. (3-6), as shown in Table 3.8.
Main mechanical parameters of elastic layer model are shown in Table 3.8.
Table 3.8 Main mechanical parameters of elastic layer model
Type of CFRP grid
Elastic modulus/El
(MPa)
Width / w (mm)
Thickness
It (mm) Ultimate strain En, /( Ps )
CR5@50 982 6
1
1.9x 106
CR5@ 100 1017 8 1.5X106
CR8@50 1504 8 1.4x 106
CR8@ 100 1537 7 1.7x 106
CR13@100 3674 9 1.5X106
3.5.3 Spring Model (SM) (1) Basic assumptions
The spring was adopted to simulate the interface between the horizontal bar and the vertical bar. The sketch of spring model is shown in Figure 3.21. Basic assumptions of the spring model are shown as below.
(a) Take no account of the tensile deformation of the vertical bar.
(b) All the tensile behavior of the crossing point is equivalent to the tensile behavior of the spring which are set on the interface between the horizontal bar and vertical bar.
The horizontal spring was used to simulate the compressive behavior among the vertical laminates and horizontal laminates. The vertical spring was used to simulate the slide between the horizontal bar and vertical bar. The break of the crossing point is reflected by the elastic brittle fracture of the vertical spring.
•
Horizontal spring
/ •
Vertical spring
• •
Figure 3.21 Sketch of spring model
(2) Main mechanical parameters of Spring Model
Suppose the number of vertical springs is n. Based on Hooke's law,
F = nkS
(3-8)F: tensile load; k: rigidity coefficient of spring;
S: tensile deformation of spring, which is equal to the test p in Table 3.5.
ull-out distance, as shown
Combined with Eq.(3-2),
nk = K
(3-9)k=K
n
(3-10)
In Eq. (3-10), K: tensile resistant rigidity of the crossing point, as shown in Table 3.7. Main mechanical parameters of the spring model are shown in Table 3.9.
Table 3.9 Main mechanical parameters of spring model Type of CFRP grid Rigidity coefficient /k
(kN/mm)
Ultimate displacement Su/(mm)
CR5@50 0.982/n 10.3
CR5 @ 100 1.017/n 11.0
CR8@50 1.504/n 10.0
CR8 @ 100 1.537/n 11.0
CR13@100 3.674/n 12.3
Based on the elastic layer model (ELM) and spring model (SM) as shown above, the tensile failure mechanism could be revealed from the mechanical perspective intuitively.
Besides, these mechanical models could be used in the calculation and numerical simulation of the strengthened concrete structures by using CFRP grid.
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3.6 Tensile behavior of multi pie crossing points in CFRP grid
3.6.1 Introduction
In order to investigate the bond behavior between the strengthening material and the existing concrete structures, a lot of pull-out tests were conducted in the past. The relative experimental results were introduced in Chapter 2. According to the literature review, it was found that four failure modes can be observed [3-2H3-8]: (1) removing of the mortar;
(2) splitting; (3) pull-out failure of the CFRP grid; (4) fracture of the CFRP grid.
Based on the analysis results of the crossing point in CFRP grid, it can be concluded that the pull-out failure of the CFRP grid in the past experiments was caused by the fracture of the crossing point in CFRP grid. But because in the past experiments the CFRP grid in the mortar was a piece of grid mesh with multiple crossing points and vertical bars.
Besides, cracks occurred in the mortar during the loading process. Preliminary analysis showed that these factors must influence the tensile behavior of the crossing point in CFRP grid. Accordingly, the tensile behavior of crossing point in CFRP grid was investigated furtherly based on past experimental results.
3.6.2 Tensile process of multiple crossing points in CFRP grid (1) Analysis method
Figure 3.22 shows a mechanical model of one crossing point in CFRP grid under tensile load. Two strains on the two sides of the crossing point were obtained. Under the tensile load, the horizontal bar bears the resistant action. It is easy to get the mechanical relationship between the strains on the two sides of the crossing point and the tensile load, as shown in Eq. (3-11).
(s1 —E2)E,A = F =T
(3-11)s , 62. : strains on the two sides of the crossing point in CFRP grid;
E, : elastic modulus of the CFRP grid;
A: cross sectional area of the CFRP grid;
T: tensile load;
F: resistant action of the horizontal bar;
Because the elastic modulus and cross sectional area can be regarded as the constant value of the CFRP grid. Accordingly, the Eq. (3-11) indicates that the strain difference on the two sides of the crossing point can be used to reflect the tensile resistant action of the horizontal bar. In other words, we can calculated the strain difference to analyze the tensile process of the crossing point in CFRP grid.
It was noted that the CFRP grid in the pull-out specimen is a piece of grid mesh
which was composed of multiple horizontal bars and vertical bars. The past research results showed that the strain on the horizontal bar were rather smaller than that on the vertical bar. And because the tensile load was applied on the middle vertical bar, the other vertical bars on the two sides didn't bear the load directly. Accordingly, the influences of the horizontal bars and other vertical bars on the strain difference on the two sides of crossing point which was used to reflect the tensile behavior of crossing point can be ignored. In other words, adopting the strain differences on the two sides of crossing points along the vertical bar to analyze the tensile behavior of the crossing point in these pull-out specimens is reasonable.
The specific analysis method is calculating the strain difference on the two sides of the crossing point along the vertical bar and then analyzing the changing process of strain differences based on the strain difference-load curves.
V
H T
ensile load (T)
Figure 3.22 Mechanical model of one crossing point in CFRP grid (2) Introduction of the specimens used to analyze the strain difference
As introduced in Chapter 2, a lots of pull-out specimens for the bond behavior between the CFRP grid-mortar and the existing concrete have been conducted. In this study, the latest past researches from Zhang [3-2] and Kikuchi [3-3] were selected to analyze the tensile behavior of the crossing point in CFRP grid.
According to the preliminary analysis of past experimental data, it was found that some strains on the two sides of the crossing point in CFRP grid were not acquired. Finally, 6 specimens were selected to analyze. The main information and experimental results were shown in Table 3.11.
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Table 3.11 Main information and experimental results of pull-out specimens
No.
Type of CFRP
grid
Grid interval
(mm)
Grid mesh
Thickness of mortar
(mm)
Surface condition
Compressive strength of
mortar (MPa)
Tensile strength
of mortar
(MPa)
Maximum load (kN)
Failure modes
Specimen number in reference
SD1 CR8 100 2x2
40
Sand blast without
primer
33.2 2.02 8.78 Removing
of mortar No.8
SD2 CR13 100 3x2 Sand
blast and primer
47.1 3.21
62.27 Splitting
of mortar No.1
SD3' CR13 100 3x2 69.63 Splitting
of mortar No.2
SD4 CR13 100 3x2
Sand blast without
primer
45.83 Splitting
of mortar No.3
SD5 CR8 50 4x4
Sand blast and
primer
34.72
Pull-out of CFRP
grid
No.4
SD6 CR8 100 2x2 28.12
Pull-out of CFRP
grid
No.5
* Specimen No.3 was loaded under cyclic loading.
(3) Analysis of the load-strain difference curves (a) Specimen SD 1
In order to avoid the confusion with the past researches, the same numbers of the strains were used when calculating the strain difference.
For specimen SD 1, strain differences on the two sides of crossing points CP1 and CP2 were calculated, respectively. Figure 3.23 shows the strain arrangement and calculated load-strain difference curves.
It was found that both of the two strain differences on the two crossing points increased with the increasing of tensile load, and the strain difference of the crossing point CP1 was larger than that of the crossing point CP2. This indicates that the borne tensile load of the crossing point CP1 is larger than that of CP2. This might be caused by the transfer mode of the tensile load along the vertical bar in the CFRP grid. Preliminary analysis showed that for the determined CFRP grid, the main influence factors on the transfer mode of the tensile load along the vertical bar is the damage condition of the mortar during the loading process. If the mortar under the crossing point fractured, the resistant capacity of horizontal bar in the crossing point would decrease and more tensile load would be transferred to other crossing point.
The experimental results showed that the specimen SD1 failure by the removing of the mortar. Combined with the load-strain difference curves, it can be concluded that the mortar didn't fractured severely during the loading process. Because if the mortar fractured severely, the transfer mode of the tensile load along the vertical bar would change significantly and this will cause the load-strain difference curves be rather irregular. Figure 3.24 shows the pattern of the mortar and CFRP grid after the failure of the specimen. It can be seen that there was no significant crack on the mortar. This demonstrated that the deduction above is reasonable. Experimental results showed that
the crossing point of this specimen SD1 didn't fractured and the control failure of this specimen is the interface bond failure between the CFRP grid-mortar and the concrete.
(a) Strain arrangement of specimen SD1
(b) Load-strain difference curves of specimen SD1
Figure 3.23 Strain arrangement and load-strain difference of specimen SD 1
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Figure 3.24 Pattern of the mortar and CFRP grid after failure of specimen SD1
(b) Specimens SD2, SD3, SD4
For Specimens SD2, SD3 and SD4, the dimensions and strain arrangements were same. Strain differences on the two sides of crossing points CP1, CP2 and CP3 were calculated, respectively. Figure 3.25 shows the strain arrangement and the calculated load-strain difference curves.
For specimen SD2, from the load-strain difference curves in Figure 3.25 (b), it can be found that:
1) The strain differences of the crossing point CP1 were small minus values. This means that the strains on the two sides of crossing point CP1 sere very close.
Analysis showed that this indicates that the crossing point CP1 nearly didn't bear the tensile load and the small minus value might be caused by the influence of
the extrusion of the mortar. This indicates that the mortar under the crossing point CP1 couldn't provide the enough support.
2) When the tensile load reached 23kN, the strain difference of the crossing point CP2 began to decrease. This indicated that the borne tensile load of the crossing
point CP2 began to decrease. It might be caused by the fracture of the mortar
near the crossing point CP2. Because the cracks on the mortar under crossing
point CP2 would weaken its support capacity. The load-strain difference curve showed that when the tensile load was about 40kN, the crossing point CP2 cannot bear the tensile load. This indicated that the mortar fractured severely.
3) With the increasing of the tensile load, the strain difference of crossing point CP3 kept increasing. Compared with the strain differences of other two crossing
points, it indicated that more and more tensile load of specimen SD2 was mainly
borne by the crossing point CP3 with the increasing of tensile load. This was
caused by change of the tensile load transfer mode along the vertical bar.
Figure 3.26 shows the failure photo of specimen SD2. It can be seen that the mortar fractured near the crossing points. And the mortar under the crossing point CP 1 fractured severely. This can explain why the crossing point CP1 nearly didn't bear the tensile load during the loading process.
For specimen SD3, the loading method was different with other specimens, which was loaded under the cyclic loading. From the load-strain difference curves in Figure 3.25
(b), it can be found that:
1) Similar with specimen SD2, the crossing point CP1 nearly didn't bear the tensile load during the loading process. This indicated that the mortar under the crossing point CP1 fractured severely.
2) For the cyclic loading method, the strain differences increased and decreased with the increasing and decreasing of the tensile load.
3) The borne tensile load of the crossing point CP2 was larger than that of the crossing point CP3. Compared with that of specimen SD3, in can be concluded
that the mortar near the crossing point CP2 of specimen SD3 didn't fracture more severe than that of specimen SD2. Figure 3.29 (b) shows the failure photo of specimen SD3.
For specimen SD4, from the load-strain difference curves in Figure 3.25 (c), it can be found that:
1) Similar with specimens SD2 and SD3, the crossing point CP1 nearly didn't bear the tensile load during the loading process. This indicated that the mortar under the crossing point CP 1 fractured severely.
2) Comparative of the load-strain difference curves corresponding to the crossing point CP2 and CP3 showed that before the maximum tensile load, the tensile
load was mainly borne by the crossing point CP2, while after the maximum load,
the borne load of the crossing point CP3 increased. This indicated that the
crossing point CP3 still borne the tensile load after the tensile load.
Figure 3.26 (c) shows the failure photo of specimen SD4. Compared with specimens SD2 and SD3, the fracture of mortar in specimen SD4 was lighter. This is because the maximum tensile load of specimen SD4 was much smaller than those of specimens SD2 and SD3 for the no use of primer. Accordingly, the borne tensile load of the crossing point in specimen SD4 was smaller than those of specimens SD2 and SD3. This caused that the borne load of mortar from the CFRP was smaller than those of specimens SD2 and SD3.
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