Mechanical Properties of Concrete Reinforced with AR-Glass Fibers T. Desai*, R. Shah*, A. Peled+, and B. Mobasher* * Dept of Civil and Env. Eng., Arizona State Univ., Tempe, AZ, USA + Structural Eng. Dept., Ben Gurion University, Beer Sheva, Israel
7th International Conference on Brittle-Matrix Composites, BMC-7 Warsaw, Poland, October 13-15th, 2003
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Scope of Presentation
Reinforcing Mechanisms Filament Winding Processing Experimental Program Theoretical aspect of Composite Laminates Results and Discussions Conclusions
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AR Glass Fiber Types
Two types of AR Glass fibers, HP and HD were used. Source: VETROTEX, Cem-FIL, SAINT-GOBAIN chopped strand form.
High dispersion (HD) AR-Glass fibers
disperse thoroughly throughout the mixtures. controlling and prevention of early shrinkage plastic cracking.
High performance (HP) AR-Glass fibers
maintain the bundle characteristics throughout the mixing and casting, increase concrete's flexural strength, ductility, toughness.
Fiber
Length mm
Diameter Micron
Tensile Strength MPa
Elastic Modulus GPa
Ultimate Elongation %
Density g/cm3
Glass (AR)
6,12,24
12
150-380
70
1.5-3.5
2.5
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Toughening Due to Fiber Bridging
Fiber Debonding and pullout Closing Pressure Crack face stiffness Stress Intensity reduction Crack closure
2 COD f = E'
a
a
P* (U) K IP
a0
af
K IF dd F ac f
K I = P*(U)g(1, a0
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)d a
Introduction to R-Curves Rm
Green’s function Approach: lb
K b ( lb ) G( a, x )s b ( x )dx
Rm + n1 R
0
Rm + n2 R Rm + n 2 R Rm + n2 R
G(a,x) = green’s function a = crack length lb = bridging zone length sb = bridging stress
Potential Energy Approach: lb
du Rb 2 s b ( u ) dx dx 0
R Rm
Rm + n1 R
Rm + n2 R
u(x) =
crack opening profile
a
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Formulation of Theoretical R-Curves
Notch Sensitivity a+a = 0 b
1 LEFM 1 Quasi Brittle Materials
Failure Conditions, Stable and unstable crack growth
G, R
(2) critical R G R G, 0 a a (1) stable R G R G , Critical Condition a a a 0 a a ac =a0+a = a You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
Mix Formulation Dry weight per m3
Type #1, Kg
Type #2, Kg
Cementitious materials (Cement + flyash,fa/C=0.1)
876
341
20-10 mm Aggregates
460
600
10-5 mm Aggregates
300
388
Fine Aggregates
578
751
Water/Cement Ratio
0.4
0.55
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Mixtures Matrix MIX ID
Control HP6_10 HP12_10 HP24_10 HP612_10 HP624_10 HP1224_10 HP61224_10 HP1224_20 HP12_20 HD12_20
Fiber Length
Vf
Compression Test
Flexure Test
mm
Kg/m3
Age of Curing
Age of Curing
3 days 7 days 28 days * 2 2 2 2 2 2 2 2 2
28 days 3 3 3 3 3 3 3 3 3 3
NA NA 6 10 12 10 24 10 6,12 10 6,24 10 12,24 10 6,12,24 10 12,24 20 12 20 12
20
-
-
-
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3
Scope of Work
Comparison of fiber dispersion characteristics.
Effect of fiber volume fraction and length
Dosage of high dispersion (HD) fibers = 0.6, 5, and 20 Kg/m3. Dosage of high performance (HP) fibers = 5, 10, and 20 Kg/m3. HP fibers = 6, 12, 24, 40 mm HD fibers = 12 , 24 mm
Effect of Fiber in a Hybrid length
various lengths of fibers, at 10 Kg/m3
HP6-12 HP6-24 HP12-24 HP6-12-24
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Closed-Loop Compression Tests
A 450 KN closed-loop controlled testing machine. two LVDTs measured the axial strain from a special ring type fixture Three replicate compression cylinders 76.2x152 mm long. Gage length 64 mm. A chain type fixture with an extensometer was used to measure the transverse strain. The axial mode controlled the prepeak-microcracking phase. The circumferential displacement controlled post-peak response.
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HP12, Vf=10 Kg/m3
Stress, MPa
Comparison of Axial and Circumferential Stress-Strains 28 Days 7 Days 3 Days
40
30 W/C = 0.4
20
10
0.01
0.008 0.006 0.004 0.002 Circumferential Strain, mm/mm
0
0.0005 0.001 0.0015 0.002 0.0025 0.003
Axial Strain, mm/mm
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Comparison of Axial and Circumferential Stress-Strains 28 Days 7 Days 3 Days
30
Stress, MPa
25 20 15 10 5 0 0.01
V f = 10 Kg/m3
HP12-24 0.008
0.006
0.004
0.002
Circumferential Strain, mm/mm
0
W/C = 0.4
0.0005 0.001 0.0015 0.002 0.0025 0.003
Axial Strain, mm/mm
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Effect of Curing Duration on Compression Response-Effect of Volume Fraction
Vf = 10 Kg/m3
30
W/C = 0.4 20
10
Vf = 20 Kg/m3
40
Stress, MPa
Stress, MPa
40
28 Days 7 Days 3 Days
28 Days 7 Days 3 Days
30
W/C = 0.4
20
10
HP12
HP12 0
0
0.002
0.004
0.006
0.008
Circumferential Strain, mm/mm
0.01
0
0
0.002
0.004
0.006
0.008
Circumferential Strain, mm/mm
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0.01
Effect of Fiber Volume Fraction on Compression Response 40
40
V f = 10 Kg/m3
Vf = 5 Kg/m3 Vf = 10 Kg/m3
30 Vf = 20 Kg/m 3
W/C = 0.4
20
V f = 10 Kg/m3
30
Vf = 20 Kg/m3
Stress, MPa
Stress, MPa
Vf = 20 Kg/m3
20 W/C = 0.4
Vf = 5 Kg/m 3 W/C = 0.55
10
10 HP1210_28 HP1220_28
HP12_7
0
0
0.002
0.004
0.006
0.008
Circumferential Strain, mm/mm
0.01
0
0
0.002
0.004
0.006
0.008
Circumferential Strain, mm/mm
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0.01
Comparison of HP and HD fibers 40 28 Days 7 Days w/c = 0.55 Vf = 0.6 Kg/m3
28 days 7 days
30 Stress, MPa
Stress, MPa
30
40
20
10
w/c = 0.55 Vf = 5 Kg/m3
20
10 HP12mm ARGlass fibers
HD12mm 0 0.000
0.004 0.008 Circumferential Strain, mm/mm
0.012
0 0.000
0.004 0.008 Circumferential Strain, mm/mm
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0.012
Effect of Fiber Length on Compression Response Mix
40
type II
Stress, MPa
30
20
10
0 0.000
w/c = 0.55 Vf = 5 Kg/m3
HP40 mm HP12 mm 0.002 0.004 0.006 0.008 Circumferential Strain, mm/mm
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0.010
Closed-Loop Flexure Tests
89 KN closed-loop controlled testing machine. one LVDT measured the deflection of the beam. Three replicate flexural prisms 100x100x368 mm in dimensions. Notch length of 12 mm. A crack mouth opening gage was used as the control parameter.
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Effect of Fiber Volume Fraction on Flexural Response Control
0.04 2500
10 Kg/m3 20 Kg/m3
2000
8 Load, KN
W/C = 0.4
8
0.03
Age = 28 Days
6
HP12
HP 12mm W/C = 0.4
4
4
1500
Vf = 20 Kg/m3
Vf =10 Kg/m3
Control
2
1000 500
Age = 28 Days
0
0
0
0.2
0.4
0.6
0.8
Crack Mouth opening Displacement, mm
1
0 0
0.2
0.4
0.6
CMOD, mm
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0.8
1
Load, lbs
10
Load, KN
0
Vf = 20 Kg/m 3 Vf = 10 Kg/m 3 Vf = 5 Kg/m3 Control
12
CMOD, in 0.01 0.02
Comparison of HP and HD fibers 8000 28 days 7 days 3 days
6000
w/c = 0.55 Vf = 0.6 Kg/m3
4000 HD24mm AntiCrack Glass fibers
2000
Load, N
Load, N
6000
8000 w/c = 0.55 Vf = 5 Kg/m3
28 days 7 days 3 days
4000
2000 HP40mm AntiCrack Glass fibers
0 0.0
0.2 0.4 CMOD, mm
0.6
0 0.0
0.2
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0.4 CMOD, mm
0.6
0.8
Comparison of HD and HP types 12 Control HD12 HP12
10
Vf = 20 Kg/m3
Load, KN
8
W/C = 0.4
6
Age = 28 Days
4 2 0
0
0.1
0.2
0.3
0.4
0.5
0.6
CMOD, mm
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Effect of Fiber Length Distribution on The Flexural Strength and Toughness 30
30
Fiber Volume Fraction= 10 Kg/m3
24
24 mm 12-24 mm
18 6-24 mm 6-12-24 mm 12 mm
12
6-12 mm
6
0 800
6 mm
Mean Fiber Length, mm
Mean Fiber Length, mm
Fiber Volume Fraction= 10 Kg/m 3
24 mm
20
12-24 mm 6-12-24 mm 6-24 mm 12 mm
10
6-12 mm 6 mm Control
Control
0 1200 1600 2000 Maximum Load, lbs
2400
0
4
8 12 Toughness, lbs-in
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16
20
Discussion of Test results
effect of fiber volume fraction on the strength and ductility An increase in volume fraction of fibers:
the strength is increased not much increase in the toughness for concrete with higher fibers content. contribution of the fibers in the post peak region of the high volume fraction is not as much as the case with the lower volume fraction. Due to the higher strength, a higher magnitude of energy is released, and resulting in strengthening but with added brittleness since the fibers are unable to absorb the energy released as the specimen enters the post peak response for higher volume fraction of fibers.
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effects of length of fiber on flexural load and toughness
marginal effect on the flexural load capacity when increasing the length of fibers. significant decrease in the toughness with increasing the length of fibers. The decrease in toughness is around 40% from HP6 to HP24 mm. This behavior might be due to difference in the mode of failure of fibers. Shorter fibers fail mainly by fiber pullout whereas the longer fiber failed mainly by fiber fracture. Fiber fracture consumes less energy than fiber pullout.
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How Do We Estimate Bridging Tractions From The R-Curve Behavior of Composites?
Inverse Problem: Parameter optimization of stress-crack width response.
Input:
stress crack width relationship model R-Curve Theoretical formulation
Output: Simulation of Flexural load-deformation
Assume a generalized profile of bridging tractions (model assumption) Obtain Theoretical R-curves as a function of Crack Extension. Compute Load Deformation from the R-curves. Correlate closing pressure-crack length to energy in the process zone. Parameter Optimization through inverse solution.
Optimization: fit of experimental data with model estimation
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R-Curve parameters G, R Instability:
Quasi-brittle Material
Gc= Rc (dG/da)c = (dR/da)c
Brittle Material (LEFM)
a0
a
ac =a0+a = a
a Crack Extension 1 1 1 1 di 2 4 d2 a a d 0 0 R= 1 - 2 d1 a - a0
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2
i 1, 2
- d1
a - a0
d2
Sakai-Suzuki Model, 1994
Similar in Nature to Foote, Mai, Cotterell Model
s b
sb
sb
sb
x
x
crack
crack lb
lb
bridging zone ni
x q sb sb0 1 lb Plain Concrete You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
bridging zone x sb s lb FRC 0 b
q
nd
Methods of Solution- Approach I
Assume a two point criteria for failure.
Set up and solve 2 equations, for 2 unknowns, for c and
Stable crack growth length, c Energy release required for growth, R() Use Tension sw curve as failure criteria. Convert to material parameters, Gf, and u, or KIc, or CTODc Newton-Raphson Algorithm for nonlinear equation solution.
Compute Load deformation
Increment “a”, get R, set R=G, solve for P Use “a” get compliance, compute deformation. Compare load-deformation from material properties.
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Stress vs. Crack Opening Stress, MPa
6 5 4 3
q 0 x sb sb lb
nd
2 1
0 0
0.01
0.02
0.03
0.04
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0.05
0.06
u, mm
Stress vs. Position
0.06
6
0.05
5 Stress, MPa
Crack Opening, mm
Crack Opening vs. Position
0.04
x n ub (x) u ( ) lb 0 b
0.03
4
2
0.01
1
5
10
15 20 Position, mm
25
30
nd
3
0.02
0 0
x s b s lb 0 b
q
0
0
5
10
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15
20
Position, mm
25
30
0.14
7000
0.12
6000
0.1
5000
Load, N
R, N/mm
R-Curve- Load Deformation
4000
0.08
3000
0.06 0.04 0.02 0 10
1 = 0.0368 c = 3.057, R = 0.1332 Nmm (plateau) Closing Pressure, KI = 46.07MPa mm1/2 20
30
40
50
60
70
80
Crack Length, mm
90
100
2000 1000 00
0.02 0.04 0.06 0.08 0.1
CMOD, mm
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0.12 0.14 0.16
Effect of Tensile Strength
Specimen = 101.6x101.6x304.2 a0= 12.75 mm E = 25000 MPa n = 0.16 u = 0.06 mm ni = 1.5 up = 0.004 mm q = 0.5
Nominal Stress, MPa
6
f 't = 6 MPa 4 f 't = 5 MPa f 't = 4 MPa 2 f 't = 3 MPa
0
0
0.02 0.04 Crack opening, mm
0.06
f’t, MPa
6
5
4
3
1
0.0367
0.0279
0.02
0.013
c
3.057
3.221
3.427
3.67
R, Nmm
0.133
0.111
0.089
0.067
Gf, Nmm
0.133
0.111
0.089
0.067
KI, closing pressure
46.0
41.8
37.2
31.8
lb
K b ( lb ) G( a,x )sb ( x )dx 0
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Model Comparison 0.2
f 't = 6 MPa
0.16 f 't = 6 MPa
f 't = 5 MPa
f 't = 5 MPa
0.12
Load, N
Resistance Curve, Nmm
6000
f 't = 4 MPa 0.08
f 't = 4 MPa
4000
f 't = 3 MPa f 't = 3 MPa
2000
0.04
0
0
20
40 60 80 Crack Extension, mm
100
0
0
0.04
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0.08 0.12 CMOD, mm
0.16
0.2
Effect of Max Crack Opening 6
8000
wmax= 0.02, 0.04, 0.06, 0.08
wmax=0.02, 0.04, 0.06, 0.08 6000 Load, N
Stress, MPa
4 4000
2 2000
0
0
0.02
0.04 w, mm
0.06
0.08
0
0
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0.1 0.2 CMOD, mm
0.3
Parametric Study of Fiber Content 0.6
8000 Vf = 20 Kg/m3
6000 Load, N
R, N-mm
0.4 Vf = 10 Kg/m3
Vf = 20 Kg/m3
4000
0.2 2000 Vf = 10 Kg/m3
0
0
20
40
60
80
100
0
0
0.2
Crack Length, mm
Vf = 20 Kg/m3 1 = 0.1041, c = 3.55 R = 0.495 Nmm Closing Pressure K = 35.06 MPa mm1/2
0.4
0.6
0.8
CMOD, mm
Vf = 10 Kg/m3 1 = 0.0726, c =3.242 R = 0.293 Nmm Closing Pressure, K = 34.88 MPa mm1/2
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1
Theoretical Prediction of Load Deformation Response-Effect of Age on Flexural response 0.20
8000 3 days 28 days Model Prediction 3 Days Model Prediction 28 Days
4000
2000
0
0.16
R, N-mm
Load, N
6000
0.1
0.2 CMOD, mm
0.12
0.08
0.04
w/c = 0.55 V f = 0.6 Kg/m 3
0.0
Model Prediction 3 Days Model Prediction 28 Days
0.3
0.4
0.00 0.0
w/c = 0.55 V f = 0.6 Kg/m3
20.0
40.0 60.0 Crack Length, mm
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80.0
100.0
Comparison with Experimental Results-Case I 7000 HP1220_28 Model Fit
6000 5000
Load, N
Size = 101.6x101.6x457.2 a0= 12.75 mm E = 16000 MPa n = 0.17 u = 0.19 mm f’t = 5.0 MPa ni = 0.85 up = 0.004 mm q = 0.5 Gf = 0.495 Nmm
W/C = 0.4 Vf = 20 Kg/m3
4000 3000 2000 1000 0 0.0000
1 = 0.1041 c = 3.55, d1 = 1.89 , d2 = 0.546 R = 0.495 Nmm (plateau) Ki = 35.06 MPa mm^1/2
0.2000 0.4000 Crack Mouth Opening, mm
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Comparison with Experimental Results-Case II 7000 6000
HP1210_28 Model Fit
5000 Load, N
Specimen = 101.6x101.6x457.2 a0= 12.75 mm E = 20000 MPa n = 0.17 u = 0.11 mm f’t = 4.0 MPa ni = 0.46 up = 0.004 mm q = 0.5 Gf = 0.292 Nmm Kic= 76.51 MPa mm1/2
W/C = 0.4 Vf = 10 Kg/m3
4000 3000 2000 1000 0 0.0000
1 = 0.0726 c = 3.24, d1 = 1.87 , d2 = 0.51 R = 0.292 Nmm (plateau) Ki = 34.88 MPa mm1/2 0.1000 0.2000 Crack Mouth Opening, mm
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0.3000
Effect of fiber Volume fraction 12 V f=20 Kg/m3
10
Age = 28 Days
Vf=10 Kg/m3 20 Kg/m 3 Simulation 10 Kg/m 3 Simulation Control Simulation 20 Kg/m 3 Exp.
Load, KN
8 6
10 Kg/m 3 Exp. Control Exp.
4 Control
2
W/C = 0.4
HP12 AR Glass fibers
0
0
0.2
0.4
0.6
0.8
CMOD, mm You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
1
Conclusions The
stress crack width models can be used in conjunction with R-Curves to explain the prepeak nonlinear and post peak strain softening response obtained in flexural specimens. R-Curves combine the effect of material properties, geometry of the loading , and various stages of crack propagation and can be easily implemented computationally to include the nonlinear effects of stable crack growth. BMC-7 Warsaw, ‘03
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