Nonlinear Ultrasonic Materials State Awareness Monitoring
1 / 24

Nonlinear Ultrasonic Materials State Awareness Monitoring - PowerPoint PPT Presentation

  • Uploaded on

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Nonlinear Ultrasonic Materials State Awareness Monitoring' - hans

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Slide1 l.jpg

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

Slide2 l.jpg

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

Slide3 l.jpg

increasing input voltage



Measurement Principle


Yost and Cantrell (IEEE, 1997)





Determination of acoustic nonlinearity parameter

Slide4 l.jpg

Experimental Setup – Longitudinal Waves

Barnard, et al. (JNDE, 1997)

Slide5 l.jpg

Experimental Procedure – Pulse Inversion

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

Slide6 l.jpg

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)

Slide7 l.jpg

Experimental Results – Low-Cycle Fatigue

Normalize to undamaged  to account for variability in initial microstructure

105% Yield


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)

Slide8 l.jpg

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)

Slide9 l.jpg

Nonlinear Lamb Waves – Dispersion Relationships

Deng, et al. (Appl. Phys. Lett., 2005)

Slide10 l.jpg

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

Slide11 l.jpg

Lamb Waves – Experimental Results

Monotonic loading

Low-cycle fatigue

Aluminum 1100

Pruell, Kim, Qu and Jacobs (Appl. Phys. Lett., 2007)

Slide12 l.jpg

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


Crystal plasticity

Third order elastic (TOE)


Slide13 l.jpg

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.

Slide14 l.jpg

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.

Slide15 l.jpg




Dislocation Dipoles/Precipitates


rd= dislocation (dipole) density

h = dipole height


r= radius of precipitates

d = lattice misfit parameter between the

precipitate and the matrix (coherency)

n = Poisson’s ratio

fp = volume fraction of precipitates

Slide16 l.jpg


Penny-Shaped Cracks




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.

Slide17 l.jpg


during Fatigue,


(Dislocation motions)

Change in 2nd & 3rd order elastic



in Grains:

Residual Stress

Plastic Strain

Material Nonlinearity


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.

Slide18 l.jpg

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:

Slide19 l.jpg

Fatigue life,

Predicted Material Nonlinearity



  • 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


Slide20 l.jpg

Comparison low cycle fatigue IN100


Strain controlled to 110% yield

Slide21 l.jpg

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 .

Slide22 l.jpg

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

Slide23 l.jpg

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.

Slide24 l.jpg


  • Thanks to:

  • Jin-Yeon Kim,

  • Jan Hermann,

  • Christian Bermes,

  • Christoph Pruell

  • Jerrol W. Littles,

  • DARPA,

  • DAAD,

  • Pratt and Whitney,

  • NSF