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Corrosion Induced Cracking: Analytical and Non-Linear Fracture mechanics Modelling. OSTRAVA 10-02-2005 Institute of Structural Mechanics Faculty of Civil Engineering University of Technology, Brno Florentina Pernica, Drahomír Novák. Introduction. - PowerPoint PPT Presentation
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1
Corrosion Induced Cracking: Analytical and Non-Linear Fracture
mechanics Modelling
OSTRAVA
10-02-2005
Institute of Structural Mechanics
Faculty of Civil Engineering
University of Technology, Brno
Florentina Pernica, Drahomír Novák
2
Introduction• The aim: to develop NLFM computational model
for the corrosion induced cracking and compare the results with one obtained from analytical model.
• Computational model that was prepared using software ATENA 2D.
• Analytical model for corrosion induced cracking in RC structures.
3
Analytical model for corrosion
• The deterioration mechanism: corrosion of reinforcement.
• Two processes may lead to depassivation of steel:
- carbonatio of concrete - chloride ingress.
• An analytical model for corrosion induced cracking in RC structures has been derived based on the concepts of fracture mechanics and smeared cracks.
4
Analytical model
ef
t
αc
αc
sc E
πbf
b/aνa/bν
tπdw
2
11
4
c
sefr
ν(t)ab(t)ab
)d(D
tdEaσP
22
22
0
1
2
2
5
Analytical model
0
2
4
6
8
10
12
14
16
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7
Crack Width (mm)
Pres
sure
(MPa
)0
0,1
0,2
0,3
0,4
0,5
0,6
0 2 4 6 8 10
Time (year)
Cra
ck W
idth
(m
m)
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10
Time (year)
Pres
sure
(MPa
)
6
• Was done using software ATENA 2D based on non-linear fracture mechanics.
• Was developed mainly for the realistic simulation of RC structures, realistic modelling of cracking in quasi-brittle materials.
• The corrosion problem was solved as 2D plane stain.
The computational model
7
Modelling of the entire concrete circle: mesh, boundaries conditions and applying shrinkage
Evolution of cracks at peak load
Alternative 1
Concrete E(Gpa)
ft
(MPa)
fc
(MPa)
Gf
(MN/m)3D
NonLinCementitious 2
3.032E+04
2.3
-23
4E-05
8
Alternative 2
1
2
Concrete E(Gpa)
ft
(MPa)
fc
(MPa)
Gf
(MN/m)3D
NonLinCementitious 2
3.032E+04
2.3
-23
4E-05
0
2
4
6
8
10
12
14
16
18
20
0 0,2 0,4 0,6 0,8
Crack width (mm)
Str
ess
(MP
a)
ATENA 2D Ft=2 MPa
ATENA 2D Ft=2,31 MPA
Analytical model
Quarter of concrete circle1- the values of stress were taken2-the values of crack width were measured
Graphs stress vs. crack width
9
Alternative 3
Concrete E(Gpa)
ft
(MPa)
fc
(MPa)
Gf
(MN/m)
3D NonLinCementitious 2
3.032E+04
2.3
-23
4E-05
3D NonLinCementitious 2
weaker
2.5E+04
1.8
-18
1.5e-05
1
Evolution of cracks in first steps Evolution of cracks at peak load 0
2
4
6
8
10
12
0 0,1 0,2 0,3 0,4 0,5 0,6
Crack width (mm)
Str
ess
(MP
a)
Atena 2D
Analytical model
10
Conclusions
• FEM computational model was developed.
• The trends of stress vs. crack width curves of both experimental and numerical results were similar.
• The differences: due to insufficient previous material parameters calibration and due to comparing linear with non-linear solution.