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 30 th June, 2010 Built Environment Division Engineering for Maintenance System Lab Hokkaido University

Transcript of Development of constitutive laws of ... - eng.hokudai.ac.jp€¦ · Mechanical behavior of this...

Page 1: Development of constitutive laws of ... - eng.hokudai.ac.jp€¦ · Mechanical behavior of this material ….. Static loading Cyclic loading Tension and compression. Location 1 Location

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

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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:

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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

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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).

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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:

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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

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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

Page 8: Development of constitutive laws of ... - eng.hokudai.ac.jp€¦ · Mechanical behavior of this material ….. Static loading Cyclic loading Tension and compression. Location 1 Location

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

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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)

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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

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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

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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

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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

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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

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Thank you for your

attention !