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Nonlinear Ultrasonic Materials State Awareness Monitoring

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

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  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

  2. 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

  3. 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

  4. Experimental Setup – Longitudinal Waves Barnard, et al. (JNDE, 1997)

  5. Experimental Procedure – Pulse Inversion Ohara, et al. (QNDE, 2004) and Kim, Qu, and Jacobs (JASA, 2006)

  6. 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)

  7. 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)

  8. 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)

  9. Nonlinear Lamb Waves – Dispersion Relationships Deng, et al. (Appl. Phys. Lett., 2005)

  10. 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

  11. Lamb Waves – Experimental Results Monotonic loading Low-cycle fatigue Aluminum 1100 Pruell, Kim, Qu and Jacobs (Appl. Phys. Lett., 2007)

  12. 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

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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:

  19. 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

  20. Comparison low cycle fatigue IN100 ~0.2Nf Strain controlled to 110% yield

  21. 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 .

  22. 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

  23. 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.

  24. 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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