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Fracture Testing of a LayeredFunctionally Graded Material
Mike HillDoug CarpenterZuhair MunirJeff Gibeling
University of California, Davis
Glaucio Paulino University of Illinois, Urbana-Champaign
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Outline
❏ Material◆ Ti/TiB functionally graded material
❏ KI - R fracture testing❏ Effect of precracking
◆ Three methods attempted
❏ Residual stress measurement❏ Correction of KI - R results for
residual stress
◆ Weight function◆ Superposition
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Material
❏ Manufactured by Cercom (Vista, CA)◆ Ti and TiB2 powders◆ Six
Ti/TiB2 mixtures
on CP Ti plate
❏ Processing
◆ Hot press (1578K, 13.8 MPa) ◆ Ti + TiB2 → TiB (little residual
TiB2)
❏ Ceramic/Metallic◆ Modulus range: 107 (Ti) to 313 (15Ti/85TiB)
GPa◆ Toughness range: 134 (Ti) to 6.5 (Pure TiB) MPa.m1/2
85 TiB / 15 TiCP Ti150 mm
≈17 mm
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❏ Standard SE(B) tests (E1820-96)◆ Nearly full thickness
samples◆ W = 13.6 to 14.7 mm
S ≈ 4 Wao ≈ 0.36 to 0.4 WB ≈ 0.5 W
❏ Crack driving from TiB-rich side❏ Optical crack length
measurement❏ Data reduction based on monolithic material❏ Results
for three precrack conditions
◆ No precrack, compression, reverse bending
R-curve Fracture Testing
CP Ti
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Fracture Testing - Precracking
❏ Precracking methods◆ Crack-tip in tension (metals)
● Uncontrollable crack growth (pop-in)
◆ Uniform compression (ceramics)● High loads required to
initiate crack
● Global modulus changed 33%● Damage: Yielding of Ti,
Debonding
of TiB in Ti matrix, Microcracking of TiB
◆ Reverse bending● Controllable crack growth,
no modulus change
❏ Effect on toughness?
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Fracture Testing - Results
❏ Rising R-curve
❏ Precracking affects toughness◆ Uniform compression ! 40%
lower◆ Early failure of sample without precrack
0
5
10
15
20
25
30
35
0.3 0.4 0.5 0.6 0.7 0.8
Axial Compression (FGM4)No precrack (FGM5a)Reverse Bend
(FGM6)
Km
ea
s (M
Pa.
m1
/2)
a/W
5 / 6
4 / 5
3 / 4 5 / 6
4 / 5
3 / 4
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Toughening Mechanisms
❏ Intrinsic (crack-tip) toughening❏ Crack branching and
bridging
(Layer 6, TiB in Ti matrix)
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Residual Stress
❏ FGM contains residual stress (RS)❏ Remove RS effect from KI -
R measurement
◆ Measure residual stress through thickness◆ Use weight function
to find KRS◆ Use superposition to find material toughness
Kmaterial ≈ Kmeasured + KRS❏ Measure RS using the compliance
method
◆ Slot incrementally◆ Measure strain release◆ Back-calculate to
find RS
center ofgage
2.4 mm(0.096 in)
x
y
TiB rich
CP Ti
a
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Compliance Method
❏ Assumes elastic stress release◆ Released strain a function of
residual stress
❏ Express unknown RS in Legendre basis◆
◆ Strain can be found for known stress (FEM)◆ Find strain for
basis functions using FEM◆
◆ Include property variation for FGM
❏ Find basis amplitudes from measured strain◆
σ RS i ii m
x A P x( ) ( ),
==∑
2
C aij i P xj≡ =ε σ( ) ( )
A C C CT T= ( )−1 ε
center ofgage
2.4 mm(0.096 in)
x
y
a
ε = CA
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Measured Residual Stress
❏ Measured Strain
❏ Strain Fit
❏ Residual Stress
-120
-100
-80
-60
-40
-20
0
20
-200
0
200
400
600
800
1000
1200
0 2 4 6 8 10 12 14
Gage1 (top)Fit (top)
Gage2 (bottom)Fit (Bottom)
To
p G
age
(µµµµεεεε )
Bo
ttom
Gag
e ( µµ µµεε εε)
Slot Depth, a (mm)
-80
-60
-40
-20
0
20
40
60
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
8-1 (10th)8-2 (8th)7-1 (10th)7-3 (8th)
Res
idu
al S
tres
s (M
Pa)
Normalized Slot Depth (x/t)
center ofgage
2.4 mm(0.096 in)
x
y
a
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Residual Stress Corrected R-curve
❏ KRS < 0 (toughness overestimated)
❏ Initial material toughness 35% lower
0
5
10
15
20
25
30
35
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.3 0.4 0.5 0.6 0.7
Kmeas (FGM6)
Kmaterial = Kmeas + KRS
KRS
Km
ea
s o
r K
ma
tl (
MP
a.m
1/2
)K
RS (M
Pa
.m1
/2)
a /W
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Conclusions
❏ Precracking method affects toughness◆ Tension fatigue
uncontrollable◆ Uniform compression damaging◆ Reverse bending
produced desired results
❏ FGM exhibits rising R-curve behavior◆ Intrinsic toughness◆
Crack branching◆ Crack bridging
❏ R-curve corrected for residual stress◆ Residual stress
measured, KRS computed◆ Superposition of KRS and Kmeasured◆ 34%
change in brittle region
