Nonlinear Ultrasonic Materials State Awareness Monitoring
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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. Linear vs. Nonlinear Ultrasonics.

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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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increasing input voltage

A2

A12

Measurement Principle

u(0,t)=Aosin(wt)

Yost and Cantrell (IEEE, 1997)

Specimen

u(x,t)=A1sin(wt-kx)

+A2sin[2(wt-kx)]

h

Determination of acoustic nonlinearity parameter


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Experimental Setup – Longitudinal Waves

Barnard, et al. (JNDE, 1997)


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Experimental Procedure – Pulse Inversion

Ohara, et al. (QNDE, 2004) and Kim, Qu, and Jacobs (JASA, 2006)


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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

Kim, Qu and Jacobs (JASA, 2006)


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Experimental Results – Low-Cycle Fatigue

Normalize to undamaged  to account for variability in initial microstructure

105% Yield

IN100

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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Rayleigh Waves – Experimental Results

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 al (QNDE, 2003) and Blackshire, et al. (QNDE, 2003)


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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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Nonlinear Parameter b

Residual Plasticity

Sources of b and How It Relates to Fatigue Damage in Metallic Materials

Physics/microstructure based.

Discrete Dislocations

Relate b to plastic strain

(phenomenological)

Crystal plasticity

Third order elastic (TOE)

constants


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Lattice Anharmonicity

Deformation of crystal lattice, even within the elastic range, is not ideally linear. This slight deviation from linearity yields

where C111 is the third order elastic constant (TOE), and C11 is the (second order) elastic constant.

For single crystal Ni

Granato, A. V. and Lucke, K. (1956), J. Appl. Phys. 27: 583-593.


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Dislocation Monopoles

A dislocation loop with length L pinned at both ends subjected to harmonic excitation

b = Burgers vector

Im{e} – attenuation; Re{e} – higher order harmonics

rm = dislocation (monopole) density

G = shear modulus

W= Schmid factor

  • Hikata, A., Chick, B. B. and Elbaum, C. (1965), J. Appl. Phys. 36: 229-236.

  • Hikata, A. and Elbaum, C. (1966), Phys. Rev. 144 469 -477.

  • Hikata, A., Sewell, F. A. and Elbdum, C. (1966), Phys. Rev. 151: 442-449.

  • Cantrell, J. H. (2004), Proc. Roy. Soc. Lond. A 460: 757-780.


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h

precipitate

dislocation

Dislocation Dipoles/Precipitates

Dipoles

rd= dislocation (dipole) density

h = dipole height

Precipitates

r= radius of precipitates

d = lattice misfit parameter between the

precipitate and the matrix (coherency)

n = Poisson’s ratio

fp = volume fraction of precipitates


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Microcracks

Penny-Shaped Cracks

t

t

a

fc = crack density (# of crack per unit volume)

a = average crack radius

l = crack surface roughness

  • Cantrell, J. H. (2004), Proc. Roy. Soc. Lond. A 460: 757-780.


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Deformation

during Fatigue,

Creep

(Dislocation motions)

Change in 2nd & 3rd order elastic

constants

Plasticity

in Grains:

Residual Stress

Plastic Strain

Material Nonlinearity

bC(3)/C(2)

Nonlinear Acoustic Measurements b

Plasticity Simulation

Plasticity and b

Before fatigue

After N cycles

plastically deformed grains

Kim, J. Y., Qu, J., Jacobs, L. J., Littles, J. W. and Savage, M. F. (2006), J. Nondestructive Evaluation 25: 28 - 36.


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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

Output Data:


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Fatigue life,

Predicted Material Nonlinearity

Wave

propagation

  • 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

loading


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Comparison low cycle fatigue IN100

~0.2Nf

Strain controlled to 110% yield


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Third Order Elastic Constants (TOE) and b

For isotropic nonlinear materials: l, m,n

  • 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 .


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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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