Modeling of failure in cement based angle ply laminates Barzin Mobasher Department of Civil and Environmental Engineering Arizona State University Tempe, Arizona, 85287-5306 The American Ceramic Society 101st Annual Meeting April 25-28, 1999 - Indianapolis, IN.
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Outline of presentation
Introduction Development and mechanical properties of angle ply laminates Mechanical properties of angle ply and sandwich laminates Failure characteristics Micro-mechanical modeling
Fracture mechanics composite materials laminate theory
Conclusions
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Toughening Due to Fiber Bridging Determination of Bend over point
Modeling steps and requirements: Fiber debonding and pullout response Closing Pressure formulation for a single isolated crack Crack face stiffness Stress Intensity reduction toughening and strength of lamina enhancements
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BOP, distributed cracking, and CDS state BOP Distributed Cracking leading to Characteristic damage state Determination of Bend Over point using Fracture Mechanics approach Determination of lamina failure using composite mechanics approach
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Cracking in Tensile Specimens-1
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Cracking in Tensile Specimens-2
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Delamination and shear failure criteria are needed Shear failure mechanism in a unidirectional specimen
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Lightweight concrete sandwich laminates 25
Pumice
concrete, unreinforced core
Specimen 1 Specimen 2
Stress(N/mm^2)
20
Specimen 3
15
10
5
0
0
2
4
Deflection (mm)
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6
Coupled problem of matrix and interface crack growth
Fiber Pullout Closing Pressure Formulation Toughening of Matrix
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Failure Criteria for Lamina Cracking
Bridging effect of fibers s
m
K Ic = K I - K I
L* (x)
f x a
CODc = CODm - COD f
KI
f
ac
= P * (U) g(1, ) d a a 0
2 COD f = E'
a
a
a0 a f
P * (U) K IP
Fiber debonding in the wake region
K IF d d F
F P* (U,x)
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g =K I (x)
FEM model for uniaxial Tension Specimen
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Toughening of the Matrix in terms of KI required for crack growth 100
E = 210 GPa f
due to applied load
E = 30 GPa m
1/2
80
= 0.3
I
K , MPa-mm
f
= 0.18 m
60
K = 35.66 MPa mm Ic
40
CTOD = 0.02 mm
composite
c
L = 15 mm f
20
due to fibers 0
r = 0.1 mm
FEM R-Curve Model
f
V = 5% f
20
22
24
26
Crack Length, mm
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1/2
Effect of interfacial shear strength E = 200 GPa
25
f
E = 28 GPa f
L = 20 mm r = 0.15 mm V = 5%
Crack Length, mm
24 23
f
a = 19.05 mm 0
22 21 No Fiber
20
q = 5.5 N/mm y
q = 2.5 N/mm y
0.000
0.001
0.002 0.003 COD/2, mm
0.004
0.005
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Effect of fiber volume fraction K = 35.66 MPa mm
25
1/2
Ic
CTOD = 0.012 mm c
f
24
E = 28 GPa m
L = 20 mm f
r = 0.15 mm
23
Steel Fiber
f
v = 12%
q = 2.5 N/mm y
a = 19.05 mm
22
0
21 V = 0%
20
f
Initial crack tip
V = 5% f
V = 15% f
0.000
0.001
0.002
0.003
COD/2, mm
0.004
0.005
Applied Load/Thickness, N/mm
Crack Length, mm
E = 200 GPa
f
60
v = 10% f
v = 5% f
40 K = 35.66 MPa mm
1/2
Ic
CTOD = 0.012 mm c
E = 200000 MPa
20
f
E = 28000 MPa m
q = 5.5 N/mm v = 0% f
y
L = 20 mm r = 0.15 mm
0 0.00
0.05
0.10
Deflection, mm You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
0.15
0.20
Modeling of SFRC 200 due to applied load
160 E = 210 GPa f
1/2
E = 30 GPa f
120
= 0.18 m
K = 35.66 MPa mm
1/2
Ic
CTOD = 0.02 mm
composite
80
c
L = 15 mm
I
K , MPa-mm
m
= 0.3
f
r = 0.1 mm f
V = 5%
due to fibers
40
f
FEM R-Curve Model
0
20
30
40
Crack Length, mm You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
50
Incremental Approach Piecewise linear approach: ΔN ΔM
A B
B
D
0 Δε Δκ
N or M
For uniaxial loads only in a symmetric lamina (B=0) : ΔN A Δε 0
For Bending only in a symmetric lamina (B=0) : ΔM D Δ You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
e or d
Computations Within a load step Compute overall stiffness Calculate the strains, stresses, curvature, and elongation
Check for the failure in the components of the lamina using th e fracture Mechanics approach. update the lamina properties
Initialize all the geometrical and historical parameters for each lamina. Then, update the stresses with imposed forces added in this increment
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Check for the failure of the entire lamina using Tsai-Wu Theory update the structure
Tsai-Wu Failure Criterion R F11 F2 2 F111 2 F22 2 2 2F12 1 2 F66 6 2 F44 4 2 F55 5 2
If R<1 safe if R 1, failure of the lamina
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Material Property to Yield surface Parameters (in MPa)
t1 := 50
F1 :=
t2 := 10 c1 := 15 c2 := 15
12 := 5 13 := 5
23 := 8
F2 := F12 :=
-7 150 1
30 -1
225000
F11 := F22 :=
1 750 1 150
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F66 := F55 :=
1 64 1
25 1 F44 := 25
Failure Surface 7
1
1
1 1 2 2 R := 150 1 30 2 750 1 150 2 112500 1 2
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Cross Ply Laminates 30
ply failure in 0 lamina
Stress, MPa
20
First ply failure in 90 lamina
first ply failure in 0 lamina
10 matrix cracking in 0 lamina matrix cracking in 90 lamina 0 0.000
0.004
0/90/0 0.008 Strain, mm/mm
0.012
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0.016
Flexural Prediction 40
Flexural Sress(MPa)
cracking of zero lamina
30 Theoretical Result
0/90/90/0
20 Matrix cracking in 90 ply
10
0 0.0
Matrix cracking in Zero ply
2.0 4.0 Deflection (mm)
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6.0
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