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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

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2 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 Linear vs. Nonlinear Ultrasonics

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3 Measurement Principle Specimen u(0,t)=A o sin( t) h u(x,t)=A 1 sin( t-kx) +A 2 sin[2( t-kx)] Determination of acoustic nonlinearity parameter A2A2 A12A12 increasing input voltage Yost and Cantrell (IEEE, 1997)

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

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

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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)

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7 Experimental Results – Low-Cycle Fatigue 105% Yield Normalize to undamaged to account for variability in initial microstructure 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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8 Rayleigh Waves – Experimental Results Monotonic loadingLow-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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9 Nonlinear Lamb Waves – Dispersion Relationships Deng, et al. (Appl. Phys. Lett., 2005)

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10 Lamb Waves – Cumulative Nonlinearity 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 Bermes, Kim, Qu and Jacobs (Appl. Phys. Lett., 2007)

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11 Lamb Waves – Experimental Results Aluminum 1100 Monotonic loading Low-cycle fatigue 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 Residual Plasticity Discrete Dislocations Nonlinear Parameter Physics/microstructure based. Relate 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 C 111 is the third order elastic constant (TOE), and C 11 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 Im{ } – attenuation; Re{ } – higher order harmonics m = dislocation (monopole) density G = shear modulus = Schmid factor b = Burgers vector 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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Dislocation Dipoles/Precipitates h d = dislocation (dipole) density h = dipole height Precipitates r = radius of precipitates = lattice misfit parameter between the precipitate and the matrix (coherency) = Poisson’s ratio f p = volume fraction of precipitates dislocation precipitate Dipoles

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Microcracks Penny-Shaped Cracks a f c = 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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Before fatigueAfter N cycles Plasticity and plastically deformed grains Deformation during Fatigue, Creep (Dislocation motions) Plasticity in Grains: Residual Stress Plastic Strain Change in 2 nd & 3 rd order elastic constants Material Nonlinearity C (3) /C (2) Plasticity Simulation 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.

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An Example (FEM Simulations were conducted by Dr. McDowell’s group) Inelastic Strain Contour Output Data: IN100; max = 0.1% yield strain; R=0.05; 18x18x18 mesh; 216 grains; ran 10 cycles Saturation of plastic strain

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loading 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 Predicted Material Nonlinearity Fatigue life,

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~0.2N f Strain controlled to 110% yield Comparison low cycle fatigue IN100

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Third Order Elastic Constants (TOE) and For isotropic nonlinear materials: l, m, n Other waves (Rayleigh, Lamb, etc) are combinations of u x and u y. Shear wave by itself does not produce 2 nd order harmonics. Shear wave does produce 2 nd 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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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

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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.

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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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