Transcript Slide 1
Nonlinear Ultrasonic Materials State
Awareness Monitoring
Laurence J. Jacobs and Jianmin Qu
G. W. Woodruff School of Mechanical Engineering
College of Engineering
Georgia Institute of Technology
Atlanta, GA 30332 USA
February 20, 2008
Prognosis Workshop
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Linear vs. Nonlinear Ultrasonics
Linear Ultrasonics: Detection of Flaws/Discontinuities
• Characterize stiffness/density related properties
• Linear UT Scattering, dispersion (guided waves), attenuation
• Detect geometric and material discontinuities (cracks, voids,
inclusions, etc.)
• Used primarily at the later stage of component fatigue life
Nonlinear Ultrasonics: Characterization of Distributed Damage
• Characterize strength related properties
• Nonlinear UT (e.g., higher order harmonics)
• Detect accumulated damage (dislocations, PSB, microplasticity)
• Can be used in the early stage of component fatigue life
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Measurement Principle
Yost and Cantrell (IEEE, 1997)
u(0,t)=Aosin(wt)
Specimen
h
u(x,t)=A1sin(wt-kx)
+A2sin[2(wt-kx)]
Determination of acoustic nonlinearity parameter
A2
A12
cl : longitudin al wave speed
f : frequency
h : Propagatio n distance (specimen thickness )
A1 : Absolute amplitude of the fundamenta l
3
A2 : Absolute amplitude of the second harmonic
Experimental Setup – Longitudinal Waves
Pulser
(50 )
: Trig
: Low Volt signal
: High Volt signal
: Parallel
50
load
calibration
Voltage Probe
Function
Generator
Current Probe
Fluid
coupling
Receiver
Toneburst
Sync
out
Fatigue
load
High-Power
Gated
Amplifier
Ch 3 Ch 2 Ch 1
Transmitter
GPIB
High-volt out
4 dB
Pad
50
term
Oscilloscope
Ch 4
40 dB
Pad
Computer
Barnard, et al. (JNDE, 1997)
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Experimental Procedure – Pulse Inversion
20
Un-inverted
3
Inverted
0.10
Fundamental
Fundamental Amplitude
10
2nd harmonic signal
5
1st echo
0
-5
-10
0.08
2
0.06
2nd harmonic
0.04
1
0.02
-15
-20
1.0
0
2.0
3.0
time (sec)
4.0
5.0
0.00
0
5
10
15
Frequency (MHz)
Ohara, et al. (QNDE, 2004) and Kim, Qu, and Jacobs (JASA, 2006)
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2nd Harmonic Amplitude
Amplitude (Volts)
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Experimental Results – Monotonic Loading
•Calibrate/verify procedure on borosilicate and fused silica
•Validate repeatability of interrupted tests on monotonic
loaded IN100 specimen
Acoustic nonlinearity parameter,
50
Kim, Qu and Jacobs (JASA, 2006)
45
40
35
30
25
20
undamaged 125% yield
Strain= 0.07463
135% yield
0.1066
Stress & Strain
145% yield
0.1377
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Experimental Results – Low-Cycle Fatigue
Normalized nonlinearity parameter, /0
Normalize to undamaged to account for variability in initial microstructure
1.6
105% Yield
1.5
1.4
IN100
1.3
1.2
Specimen #1
Specimen #2
Specimen #3
Best fit
1.1
1.0
0
20
40
60
80
100
Fatigue life (%)
Kim, Qu and Jacobs (JASA, 2006) also note similar results by Nagy (Ultrasonics,
1998), Frouin, et al. (J. Mat. Res, 1999), and Cantrell and Yost (Int. J. Fatigue, 2001)
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3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
undamaged 115% yield
Strain=0.04816
125% yield 135% yield 145% yield
0.07463
0.1066
0.1377
Applied Stress & Strain
Normalized acoustic nonlinearity, /0
Normalized acoustic nonlinearity, /undamage
Rayleigh Waves – Experimental Results
1.8
Rayleigh wave measurement (Specimen #1)
Rayleigh wave measurement (Specimen #2)
Best fit of longitudinal wave measurement results
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0
10
20
30
40
50
60
70
80
90 100
Fatigue life (%)
Monotonic loading
Low-cycle fatigue
IN100 with comparison to longitudinal wave results
Hermann, Kim, Qu and Jacobs (JAP, 2006) and note similar results by Barnard, et
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al (QNDE, 2003) and Blackshire, et al. (QNDE, 2003)
Nonlinear Lamb Waves – Dispersion Relationships
Deng, et al. (Appl. Phys. Lett., 2005)
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Lamb Waves – Cumulative Nonlinearity
Bermes, Kim, Qu and Jacobs (Appl. Phys. Lett., 2007)
Measured slope 1100 is 0.0001167; Measured slope of 6061 is 0.00004594;
Ratio is 2.541
Absolute of 1100 is 12.0; Absolute of 6061 is 5.67; Ratio is 2.12
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Lamb Waves – Experimental Results
Monotonic loading
Low-cycle fatigue
Aluminum 1100
Pruell, Kim, Qu and Jacobs (Appl. Phys. Lett., 2007)
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Sources of and How It Relates to Fatigue Damage in Metallic Materials
Physics/microstructure based.
Nonlinear
Parameter
Discrete
Dislocations
Residual
Plasticity
Lattice Anharmonicity
F ( a0 ) 0
a0
F (a ) 0
Deformation of crystal lattice, even within the
elastic range, is not ideally linear. This slight
deviation from linearity yields
V (a )
e
a
2Ead
C111
C11
where C111 is the third order elastic constant
(TOE), and C11 is the (second order) elastic
constant.
F (a )
Fmax
For single crystal Ni
a
C11 240GPa
C111 1630GPa
e 6.8
Granato, A. V. and Lucke, K. (1956), J. Appl. Phys. 27: 583-593.
Dislocation Monopoles
iwt
y
y( x)e
L
x
A dislocation loop with length L pinned at both ends
subjected to harmonic excitation
b L
b = Burgers vector
y ( x)iwt dx
0
L
Im{} – attenuation; Re{} – higher order harmonics
m = dislocation (monopole) density
G = shear modulus
= Schmid factor
24 m L4 C112
m
3 2
5
Gb
• Hikata, A., Chick, B. B. and Elbaum, C. (1965), J. Appl. Phys. 36: 229236.
• Hikata, A. and Elbaum, C. (1966), Phys. Rev. 144 469 -477.
• Hikata, A., Sewell, F. A. and Elbdum, C. (1966), Phys. Rev. 151: 442449.
• Cantrell, J. H. (2004), Proc. Roy. Soc. Lond. A 460: 757-780.
Dislocation Dipoles/Precipitates
Dipoles
h
16 2 d h3(1 )2 C112
d
G 2b
d = dislocation (dipole) density
h = dipole height
Precipitates
precipitate
dislocation
p
205m2 r 4 (1 )C112
G 2b2 (1 ) f p1 3
r = radius of precipitates
= lattice misfit parameter between the
precipitate and the matrix (coherency)
= Poisson’s ratio
fp = volume fraction of precipitates
Microcracks
Penny-Shaped Cracks
c
a
32000 f c a 5 (1 )3 (1 ) 2 G 2 2
7 G (8a 3 f c (1 2 ) 5) 20a (1 )
4 f c L2b(1 ) 2 G 2 2
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2
fc = crack density (# of crack per unit volume)
a = average crack radius
= crack surface roughness
• Cantrell, J. H. (2004), Proc. Roy. Soc. Lond. A 460: 757-780.
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Plasticity and
Before fatigue
After N cycles
C(N2) 1 C(N2) C(N2) (E p , σres )
C(N3) 1 C(N3) C(N3) (E p , σres )
plastically deformed
grains
Deformation
during Fatigue,
Creep
(Dislocation
motions)
Plasticity
in Grains:
Residual Stress
Plastic Strain
Plasticity
Simulation
Change in
2nd & 3rd
order
elastic
constants
Material
Nonlinearity
C(3)/C(2)
Nonlinear Acoustic
Measurements
Kim, J. Y., Qu, J., Jacobs, L. J., Littles, J. W. and Savage, M. F. (2006),
J. Nondestructive Evaluation 25: 28 - 36.
An Example
(FEM Simulations were conducted by Dr. McDowell’s group)
IN100; max = 0.1% yield strain; R=0.05; 18x18x18 mesh; 216 grains; ran 10 cycles
Saturation of plastic strain
Inelastic Strain Contour
-0.0004
p
Plastic Strain ( 11)
0.0000
-0.0008
-0.0012
After 1 cycle
After 5 cycles
After 10 cycles
-0.0016
10
i
Output Data: Eijp IK
15
20
25
30
Grain Number
35
40
Predicted Material Nonlinearity
50
45
Wave
propagation
40
p
Threshold Initial Plastic Strain (Ex )
= 0.08 %
= 0.06 %
= 0.04 %
35
30
0.0
0.2
0.4
0.6
0.8
1.0
Fatigue life,N/Nf
•
loading
•
Grains that have initial (after 10 cycles) strain above the
threshold strain are assumed to accumulate plastic strain
Residual stress is assumed to be constant after 10 cycles
Specimen #1
50
44
42
45
40
Beta
Comparison low cycle fatigue IN100
40
38
36
30
0.0
~0.2Nf
p
Threshold Initial Plastic Strain (Ex )
= 0.08 %
= 0.06 %
= 0.04 %
35
0.2
0.4
0.6
0.8
1.0
34
Position 1
Position 2
Position 3
Position 4
32
0
5000
N/Nf
Strain controlled to 110% yield
10000
15000
Cycles
20000
25000
Third Order Elastic Constants (TOE) and
For isotropic nonlinear materials: l, m, n
ux Acos(kL x wt ) A2 (2m l )Fx cos[2(kL x wt )]
uy B cos(kT x wt ) ABmG sin[2(kT x wt )]
• Other waves (Rayleigh, Lamb, etc) are combinations of ux
and uy.
• Shear wave by itself does not produce 2nd order harmonics.
• Shear wave does produce 2nd order harmonics in the
presence of longitudinal waves.
• Such interaction is a challenge/opportunity to obtain TOE
• TOE can be related to plasticity .
Summary and Conclusions
• Significant increase in the acoustic nonlinearity parameter,
associated with the high plasticity of low cycle fatigue
• The acoustic nonlinearity parameter, can be used to
quantitatively characterize the damage state of a specimen at the
early stages of fatigue
• Potential to use measured versus fatigue life data to potentially
serve as a master curve for life prediction based on nonlinear
ultrasound
• Sensitivity versus selectivity: potential to distinguish the different
mechanisms of damage
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Next Step
• Is there a simplified universal relationship that
can relate the different measurements and
betas?
• Experimental evidence shows that changes in
nonlinear parameters are intrinsic to the
material, in spite of having 3 different
nonlinear parameters.
• We hypothesize that the procedure can be
simplified by introducing a universal
“normalization” parameter.
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Acknowledgements
Thanks to:
•Jin-Yeon Kim,
•Jan Hermann,
•Christian Bermes,
•Christoph Pruell
•Jerrol W. Littles,
•DARPA,
•DAAD,
•Pratt and Whitney,
•NSF
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