Development of constitutive laws of ... - eng.hokudai.ac.jp€¦ · Mechanical behavior of this...
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Development of constitutive laws of
High Performance Fiber Reinforced
Mortar under Tension and Compression
Mamun Mohammed Abdullah Al
Maintenance System Engineering Lab
Doctoral First Year Student
30th June, 2010
Built Environment Division
Engineering for Maintenance System Lab
Hokkaido University
Background of the study
Detail concept of the σ-w model
Determine the parameter of the model
Comparison of Experimental result
Next plan.
Outline of today’s presentation:
Background of the study:
High Performance Fiber Reinforced Cementitous Composite
High strength
More ductility
High fluidity
(High Performance Fiber Reinforced Mortar)HPFRM
Toughness
Durability Stiffness
Thermal resistance
Mechanical behavior of this
material …..
Static loading
Cyclic loading
Tension and compression. Location 1 Location 2 Location 3
Flow direction
* Test data by Grunewald (2004)
Previous
research…
• It is reported that orientation and number of fiber are the two most influential factors
to define the mechanical behavior of HPFRM
• It is reported that orientation and number of fiber vary from place to place
Proposed tension softening model:
σw= [{∑Pi (w).η} / A]N
i= 1
Where,
P i(w) = The pullout force generated by an individual
fiber I, at any crack width w
η = The orientation coefficient
N = No. of fiber in crack plane
αi = The inclination angle of fiber
η = ∑ COSαi
N
i= 1
1N
• The input of this model like no. of fiber (N), and inclination angle (αi)
are variable ( For any volume fraction and any casting direction).
• Very flexible to adapt for any kinds of fiber( Straight fiber, Hooked
fiber and so on).
HPFRM Member
Vf
Mean
Vf
Sta
nd
ard
Dev
iati
on
α
Slo
pe,
m
Pro
bab
ilit
y
No. of fiber
Su
b a
rea
Nf / Unit area
Transform
P(x) =1
σ √2πe-(x-μ) 2/ (2σ 2)
α
Av:
An
gle
Vf
Slo
pe,
m
ηφ = ∑ COSφ1
Ni
N
Microscopic analysis
Fiber slip
Pu
llou
t
forc
e
Str
ess
Crack width
Parameter 1
Parameter 3Parameter 2
σ = (P × Nf × ηφ) / A
5/16
Detail of modeling:
Parameter No1:Determine mean and STD of Nf
0
1
2
3
0 25 50 75 100
Slo
pe,
m
Angle, Degree
Slope for different μ
MaximumMinimumAverage
0
1
2
3
0 25 50 75 100
Slo
pe
Angle, Degree
Slope for different σ
Maximum
Minimum
Average
μ= m1 Vf σ= m2 Vf
Fibers
3 mm2
mm
Microscopic analysis Empirically (μ, σ )
Steel fiber in HPFRM Scatter
0
0.1
0.2
0.3
0 5 10 15
Pro
ba
bil
ity
No. of fiber
Normal distribution of fiber
0 Deg:(1.5%)
45 Deg:(1.5%)
90 Deg:(1.5%)
0
100
200
300
400
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Su
b a
rea
, m
m2
No. of fiber per mm2
Sub area vs No. of fiber /mm2
0 Deg: (1.5%)
45 Deg: (1.5%)
90 deg: (1.5%)
P(x) =1
σ √2πe-(x-μ) 2/ (2σ 2)
Sub area = Probability × Area of the
specimen
Transform
Mean (μ) and STD (σ)
Volume of fiber (Vf)
Casting direction (αcasting)
Distribution of fiber (Nf):
Accuracy of Nf Value of per small division
φ = m3 × αcasting + C
Parameter no.2:Inclination angle of fiber(φ):
0
0.1
0.2
0.3
0 0.5 1 1.5 2
Slo
pe,
m
Fiber volume, %
Slope (reg:)
0
10
20
30
40
0 0.5 1 1.5 2
Va
lue
of
C
Fiber volume, %
C value (Reg:)
ηφ = ∑ COSi=1
N
φInclination angle (φ)
Casting direction (αcasting) Volume of fiber (Vf)
Inclination of fiber Only average value
Parameter no.3:Pullout response of single fiber
2 4 6 8 100
10
20
30
40
Embdeed length, mm
Pu
llo
ut
forc
e, N
Average pullout response pullout response
Markovich et.al. 2005
Straight fiber: 13/0.2
Str
ess
Crack width
σ = (P × Nf × ηφ) / A
Parameter 1: No. of fiber (Nf)
Parameter 2: Orientation angle(ηφ)Parameter 3: Pullout force of fiber (P)
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a
Experiment 1 Average Maximum
Minimum Experiment 2
L0.5%, 0 Degree
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a Experiment 1 Average Maximum Minimum Experiment 2
L0.5%, 45 Degree
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a
Experiment 1 Average Maximum
Minimum Experiment 2
L0.5%, 90 Degree
Comparison of tensile softening of HPFRM:
90° 0°
Flow direction
Load direction
2 4 6 8
1
2
3
4
5
6
7
8
0
Crack width, mm
Str
ess,
MP
a
Experiment 1 Average Maximum
Minimum Experiment 2
L1.0%, 0 Degree
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a
Experiment Average Maximum Minimum
L1.0%, 45 Degree
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a
Experiment Average Maximum Minimum
L1.0%, 90 Degree
90° 0°
Flow direction
Load direction
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a
L1.5%,0 Degree Experiment Average Maximum Minimum
0 2 4 6 80
2
4
6
8
Experiment Average Maximum Minimum
L1.5%, 45 Degree
Crack width, mm
Str
ess,
MP
a
2 4 6 8
2
4
6
8
0
Crack width, mm
Str
ess,
MP
a
L1.5%, 90 Degree
Experiment 1 Average Maximum
Minimum Experiment 2
90° 0°
Flow direction
Load direction
• The proposed model shows very good agreement with
experimental results
1 2 3 4 5
5
10
15
20
0
Crack width , mm
Str
ess,
MP
a
L 2.0%, 0 Degree Experiment Average Maximum
Minimum
Comparison of tensile behavior with other researcher:
Markovich et.al.
Vf: 2%
L/d: 13/0.2
Casting direction : 0 degree
• Shows very good agreement of the proposed model
Near future plan:
July 2010 August 2010 September 2010
Task 1
Pullout test of
single fiber
(Pilot test).
Task 2
Pullout test (Static and cyclic)
Prepare next experimental plan
Evaluation
TaskTime
Thank you for your
attention !