El ensayo de doble punzonamiento con cuña para la...

El ensayo de doble punzonamiento con cuña para la caracterizaciòn del comportamiento a tracciòn del HRF Liberato Ferrara Politecnico di Milano, Italy

EXPERIENCIAS INTERNACIONALES DEL HORMIGON REFORZADO CO FIBRAS

Barcelona, 21 de marzo de 2013

FR(SC)C: an intelligent material

shear-flow induced fiber orientation

Netwonian fluid

free surface flowvelocity/drag force

profileresultant drag force

on flow-through fibers:

fiber orientation effect

MOULD

high yield stress fluid

free surface flow

(e.g. FRC casting)per

per

velocity/drag force

profile (extended plug flow)resultant drag force


fiber drag effect

MOULD

low yield stress/low viscosity

fluid free surface flow

(e.g. FRSCC casting)per

per

velocity/drag force profile

(limited plug flow - low gradient)resultant drag force


limited fiber orientation effect

MOULD

low yield stress-high viscosity

fluid free surface flow

(e.g. FRSCC casting)per

per

velocity/drag force profile

(limited plug flow - high gradient)resultant drag force


fiber orientation effect

MOULD

Fibers can be aligned along the direction of the casting flow

Identification of material properties as a function of flow induced fiber alignment: which test?

Direct tension tests?

Not easy to be properly performed

Bending tests?

Need for back analysis


3 Point Bending Test … … Wedge Splitting Test


Direct Tension Test

(rotating platens)

di Prisco et al., Materials and Structures, 2013

Identification of material properties as a function of flow induced fiber alignment: Double Edge Wedge Splitting test


0 4 8 12 16 20

applied vertical load P (kN)

0

4

8

12

16

20

mea

sure

d t

rans

vers

e lo

ad F

SP (k

N)

y = 0.89 x


friction effects

Ferrara et al., Materials and Structures, 2011


calibration

Constituent Quantity (kg/m3)

Cement 600

Slag 500

Sand 0-2 mm 982

Water 200

Superplasticizer 33 (lt/m3)

Steel fibers (lf = 13 mm; df = 0.16 mm) 100



calibration

Slump flow V-funnel L-box U-box J-ring



calibration: achieving fiber orientation

slab casting

flow induced

fiber alignment

slab cutting

DEWS testing

?

Magnetic inductance associated to the flux

LV = LV0 + Lfibers

Matrix contribution LV0

Fiber contribution Lfibers

Assess local concentration and orientation of fibers


calibration: monitoring (ND) fiber orientation

Magnetic method




Magnetic method


Faifer et al., Sensors, 2013

preferential fiber

alignment

perform M measurements

rotate by 2 /m at once

Directions of maximum inductance

Self compactability – flow induced fiber alignment

0 50 100

nominal fiber content (kg/m3)

0

5

10

15

20

25

Lav

era

ge (

H)

y = 0.18 x (R2 = 0.988)

average of Laverage

Calibration

Quantitative assessment of local unhomogeneities in fiber

dispersion




Magnetic method

preferential fiber

alignment

perform M measurements

rotate by 2 /m at once



Magnetic method


Faifer et al., Sensors, 2013

1

2

3

4

5

6

7

8

9

10

11

12

13

15

16

17

18

ND = 110.5

ND = 101.8D = 119.1

14

ND = 100.8 ND = 111.7

ND = 108.7D = 109.5

ND = 110.5

ND = 103.5D = 107.8

ND = 100D = 101.9

ND = 106.6D = 109.9

ND = 103.6D = 106.7

ND = 105.7D = 105.6

ND = 99.5D = 99.4

ND = 93.7D = 98.2

ND = 79.4D = 85

ND = 94.2

ND = 97.5 ND = 88.7

ND = 75.9



calibration

slab casting

flow induced

fiber alignment

slab cutting

DEWS testing



calibration

0 1 2 3 4 5

COD (mm)

0

2

4

6

8

10

N (

N/m

m2)

unfavorable flow-induced fiber alignment

favorable flow-induced fiber alignment

H2

H1

S

The same material exhibits either a

strain hardening

Or

strain softening

tensile behaviour

whether tested parallel or orthogonal to flow induced

fiber alignment



calibration

0 1 2 3 4 5

COD (mm)

0

2

4

6

8

10

N (

N/m

m2)

unfavorable flow-induced fiber alignment

favorable flow-induced fiber alignment

H2

H1

S

Multiple cracking



a proposal: strain softening material

st

ress

strain = COD/helement

plain matrix(as from MC2010)

0.5/hel 2.5/hel

fFT ,2 .5

fFt

0.9fFt

0.015%

fFT,0.5



a proposal: strain hardening material

stre

ss

strain = peak +(COD-CODpeak)/helement

peak + 0.5/hel

0.9fFt

fFT ,peak

fFT , peak+0.5

CODpeak

LCOD

peak + 2.5/hel

strain = COD/LCOD

peak =

fFT, peak+2.5

Same opening of the localized crack as for

strain softening



finite element validation

Crush-Crack damage model



finite element validation and mesh independence

0 1 2 3 4

COD (mm)

0

2

4

6

8

10

(M

Pa)

exp.

num.

H2

H1

S

0 1 2 3 4

COD (mm)

0

2

4

6

8

10

(M

Pa)

experimental

num - hel = 2.67 mm

num - hel = 2.0 mm

num - hel = 1.33 mm



finite element validation: uncoupling of principal stresses

CODcracking COD = 0.5 mm CODpeak = 0.75 mm

CODpeak + 0.25 mm

CODpeak + 1.25 mm

COD = 4 mm

Principal compressive stresses follow same “softening trend as tensile (unlikely in

Brazilian test)




-2 0 20

20

40

60

80

100

liga

men

t(c

oord

inat

e in

mm

)

0 2 4 6 8 10

principal stresses (MPa)

CODcracking = 0.05 mm

COD = 0.5 mm

CODpeak = 0.75 mm

CODpeak + 0.25 mm = 1 mm

CODpeak +1.25 mm = 2.0 mm

COD = 4mm (e.o.c.)

compressive tensile

Strain hardening material




-1 0 10

20

40

60

80

100

liga

men

t(c

oord

inat

e in

mm

)

0 1 2 3 4

principal stresses (MPa)


COD = 0.05 mm

COD = 0.25 mm

COD = 1.25 mm

COD = 2.0 mm

COD = 3.1 mm (e.o.c.)

compressive tensile

Strain softening material



finite element validation: principal strain evolution


0 10 20

x (mm)

1

2


COD = 0.5 mm

CODpeak = 0.75 mm

CODpeak + 0.5 mm

CODpeak + 2.5 mm

COD = 4.0 mm (e.o.c.)

0 10 20

x (mm)

0

1

2

-20 -10 00

0.1

0.2

0.3

-20 -10 00

0.01

0.02

0.03

pre-peak zoom

pre-peak zoom





0

20

40

60

80

100

liga

men

t(c

oord

inat

e in

mm

)

0 0.4 0.8 1.2 1.6 2


COD = 0.5 mm

CODpeak = 0.75 mm

CODpeak + 0.5 mm = 1.25 mm

CODpeak +2.5 mm = 3.25 mm

COD = 4 mm (e.o.c.)





0 10 20

x (mm)

0.5

1

CODcracking = peak = 0.03 mm

COD = 0.05 mm

COD = 0.5 mm

COD = 1.5 mm

COD = 2.5 mm

COD = 3.1 mm (e.o.c.)

0 10 20

x (mm)

0

0.1

0.2

-20 -10 00

0.2

0.4

-20 -10 00

0.001

0.002

pre-peak zoom

pre-peak zoom





0

20

40

60

80

100

ligam

ent

(coo

rdin

ate

in m

m)

0 1 2 3 4 5

CODcracking=peak = 0.03 mm

COD = 0.05 mm

COD = 0.5 mm

COD = 1.5 mm

COD = 2.5 mm

COD = 3.1 mm (e.o.c.)



finite element validation: damage evolution


Strain hardening materials

COD = 0.5 mm

CODpeak = 0.75 mm

CODpeak + 0.5 mm

CODpeak + 1.25 mm

CODpeak + 3.25 mm





Strain softening materials






0 2 4 6 8 10

COD (mm)

0

10

20

30

N (

N/m

m2)

beam L1

beam L2

beam T2

beam T1


500 mm - 20 in.

150 mm - 6 in.

450 mm - 18 in.

200 mm - 8 in.

A

A sect. A-A

150 mm

6 in.

30 mm - 1.2 in7 mm

Identification of material properties as a function of flow induced fiber alignment: 4-point bending tests

b

eam

T2

beam

T1

50 150150150 500

beam L2

beam L1

150

150

150

50

casting

direction

supposed flow lines

T1-BT2-B

T1-AT2-A L1-A

L2-AL2-B

L1-B

Slab A

COD

Str

ess

wI

0.1 mm

fIf

N,peak

wpeak

w1

w2

wi

localized crackmultiple cracking

w1 = (3-5 wI – wpeak h/lCOD) + wpeak

w2 = (0.02h 20% – wpeak h/lCOD) + wpeak

wi = ( h 20% – wpeak h/lCOD) + wpeak

h specimen depth (30 mm)

lCOD COD measurement length

(200 mm)



0.9 fIf/

N,peak/ 1

peak = CMODpeak

lCOD

arctg Ec

25+2h0.7

2h0.7

Ec = 22000 (fc/10)0.3 = 43600 N/mm2

for fc = 96 N/mm2

= 2.16 (for h = 30 mm)

M = N,peak bh2/6

peakpeak

0.9fIf/

xx

crack opening w

N, peak

0.02 h

1 feq,2

2 feq, wu

wu = 0.10 h

0.10

M = feq (0.1h) bh2/6(0.02)

peak

Compression

force0.02

(0.10)

1

M = feq2 bh2/6

(0.02)0.02

peak

x x



0 2 4 6

COD (mm)

0

2

4

6

8

10

(N

/mm

2)

DEWS L1/2-B

DEWS T1/T2-B

DEWS T1/T2-A

DEWS L1/L2-A

Slab A

beam

T2

beam

T1

50 150150150 500

beam L2

beam L1

150

150

150

50

casting

direction

supposed flow lines

T1-BT2-B

T1-AT2-A L1-A

L2-AL2-B

L1-B

Slab A

Identification of material properties as a function of flow induced fiber alignment: DEWS tests




in plane rotations

0 5 10 15 20

in plane rotation - front (°)

0

0.5

1

P/P m

ax

Slab ADEWS L1-B

DEWS T1-B

DEWS L1-A

DEWS T1-A

top-center

top-bottom

0 5 10 15 20

in plane rotation - rear (°)

0

0.5

1

P/P m

ax

Slab ADEWS L1-B

DEWS T1-B

DEWS L1-A

DEWS T1-A

top-center

top-bottom



Out of plane rotations

0 1 2 3 4

out of plane rotation - bottom (°)

0

0.5

1

P/P m

ax

Slab ADEWS L1-B

DEWS T1-B

DEWS L1-A

DEWS T1-A

0 1 2 3 4

out of plane rotation - mid (°)

0

0.5

1

P/P m

ax

Slab ADEWS L1-B

DEWS T1-B

DEWS L1-A

DEWS T1-A

0 1 2 3 4

out of plane rotation - top (°)

0

0.5

1

P/P m

ax

Slab ADEWS L1-B

DEWS T1-B

DEWS L1-A

DEWS T1-A

0 0.002 0.004 0.006 0.008 0.01

strain

0

4

8

12

16

(N/m

m2)

beams L1/2

slab A

arctg Ec

DEWS L1/2-B

DEWS T1/2-B

0.6 3

crack opening w (mm)

0

4

8

12

16

(N/m

m2)

0 3 6 9

beams L1/2

slab A

DEWS L1/2-B

DEWS T1/2-B

Identification of material properties as a function of flow induced fiber alignment: 4pb vs. DEWS tests


0.2 0.4 0.6 0.8orientation density

(vertical to the fracture surface)

0

5

10

15

4pb (

N/m

m2)

peak = 0.25 + 21.6x (R2 = 0.937)

0.02h = 1.94 + 6.4x (R2 = 0.785)

0.10h = 1.37 + 3.0x (R2 = 0.940)

0.2 0.4 0.6 0.8orientation density

(vertical to the fracture surface)

0

5

10

15

DE

WS (

N/m

m2)

peak = 0.6 + 11.7x (R2 = 0.745)

0.01h = 0.4 + 10.4x (R2 = 0.805)

0.05h = 0.8 + 3.0x (R2 = 0.745)

Identification of material properties as a function of flow induced fiber alignment: 4pb vs. DEWS tests


Concluding remarks

Double Edge Wedge Splitting test suitable to identify, with no need for back analysis, the tensile cosntitutive

behaviour of FRCs performing and indirect test

Compact specimen geometry and dimensions: suitable for identifying fiber orientation dependant behaviour

Test methodology has been demonstrated capable to discriminate between strain softening and hardening

materials

size effect …?

Thank you for your attention!

Fiber dispersion and orientation

Hardened state behaviour Fresh state behaviour

Understanding the performance: from material to

structure

Fiber dispersion and orientation

Hardened state behaviour Fresh state behaviour

Modelling the performance: from material to

structure

fibres

velocity profile drag forces orientating effect

fibres


fibres


Tailoring the performance: from material to

structure

B

A

Lc

vLL

lwsR

iw

0 10 20 30

curvature (1/mm*105)

0

1

2

3

4

Mom

ent

(kN

m)

0 200 400 600

curvature (1/in) *105

0

2

4

Mom

ent (ft kips)

Mu,exp = 2.2 kNm = 3 ft kips

Mcr,exp = 1.7 kNm = 2.3 ft kips

= 0.23

orientation density

= 0.35

= 0.55

= 0.63

dashed line - CNR-DT204

solid line - proposed approach

experiments

rheology

fiber monitoring

casting and processing

1 kN m moment at mid span

1 kN/m distributed load

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