Article Article
A Framework for Computational Nondestructive Evaluation of Degraded Composites with Microscale Discontinuities

Ultrasonic nondestructive evaluation (NDE) of composites is performed to detect and quantify material damages. The estimation of degraded material properties is not generally performed using NDE. However, if successfully done, it has the potential to illuminate the progressive failure models for estimation of composite failure and predict remaining useful life more accurately. It could be done through multiple experiments with controlled degraded material properties due to microscale discontinuities to understand the signals and use that understanding for estimation of equivalent material properties. However, it is not practical to perform all the possible experiments with various damage scenarios and geometries. An alternate way is to obtain a physics-based under-standing of the perturbation of the ultrasonic wavefield. Through virtual experiments, signals could be evaluated in the presence of microscale discontinuities compared to the pristine materials as fast as possible. In this paper, a framework with computational NDE (CNDE) is proposed to visualize the effect of microscale discontinuities on an ultra-sonic wavefield to generate a database to compute the ultrasonic wavefield in degraded composites. The framework will help clarify the effect of micro discontinuities on the ultrasonic probing energy. Distributed point source method (DPSM) is a newly developed CNDE approach used herein to boost computational efficiency, which requires elastody-namic Green’s function in the material. Materials with micro discontinuities show the effect on the Green’s function and thus they affect the computed ultrasonic wavefield in CNDE. To obtain the degraded material properties for the CNDE, representative volume elements (RVEs) are studied to understand the effect of distributed discontinuities on the effective constitutive properties. Finally, the acquired effective properties were utilized to calculate perturbed Green’s function and consequently, the affected CNDE response. With the available technology at this time, it is challenging to validate a high-frequency NDE problem in the time domain; however, frequency domain results are presented in this paper and the effect of microscale discontinuities is enumerated.

References

Bakhvalov, N.S., and G. Panasenko, 1989, Homogenisation: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Materials, Springer, New York, NY.

Ballisti, R., and C. Hafner, 1983, “The Multiple Multipole Method (MMP) in Electro and Magnetostatic Problems,” IEEE Transactions on Magnetics, Vol. 19 No. 6, pp. 2367–2370.

Banerjee, S., and S. Shrestha, 2018, “Numerical Modeling of Ultrasonic Wave Propagation in Composites,” Computational and Experimental Methods in Structures: Structural Health Monitoring for Advanced Composite Structures, Vol. 8, pp. 93–124.

Banerjee, S., and T. Kundu, 2006a, “Symmetric and Anti-Symmetric Rayleigh-Lamb Modes in Sinusoidally Corrugated Waveguides: An Analyt-ical Approach,” International Journal of Solids and Structures, Vol. 43, No. 21, pp. 6551–6567.

Banerjee, S., and T. Kundu, 2006b, “Elastic Wave Propagation in Sinu-soidally Corrugated Waveguides,” The Journal of the Acoustical Society of America, Vol. 119, No. 4, pp. 2006–2017.

Banerjee, S., and T. Kundu, 2007b, “Advanced Application of Distributed Point Source Method - Ultrasonic Field Modeling in Solid media,” in DPSM for Modeling Engineering Problems, John Wiley & Sons, Hoboken, New Jersey, Ch. 4.

Banerjee, S., and T. Kundu, 2007a, “Ultrasonic Field Modeling in Plates Immersed in Fluids,” International Journal of Solids and Structures, Vol. 44, No. 18–19, pp. 6013–6029.

Banerjee, S., and T. Kundu, 2008a, “Semi-Analytical Modeling of Ultra-sonic Fields in Solids with Internal Anomalies Immersed in a Fluid,” Wave Motion, Vol. 45, No. 5, pp. 581–595.

Banerjee, S., and T. Kundu, 2008b, “Elastic Wave Field Computation in Multilayered Nonplanar Solid Structures: A Mesh-Free Semianalytical Approach,” The Journal of Acoustical Society of America, Vol. 123, No. 3,  pp. 1371–1382.

Banerjee, S., S. Das, T. Kundu, and D. Placko, 2009, “Controlled Space Radiation Concept for Mesh-Free Semi-Analytical Technique to Model Wave Fields in Complex Geometries,” Ultrasonics, Vol. 48, No. 8, pp. 615–622.

Banerjee, S., T. Kundu, and N.A. Alnuaimi, 2007, “DPSM Technique for Ultrasonic Field Modelling Near Fluid-Solid Interface,” Ultrasonics, Vol. 46, No. 3, pp. 235–250.

Berger, H., S. Kari, U. Gabbert, R. Rodriguez-Ramos, R. Guinovart, J.A. Otero, and J. Bravo-Castillero, 2005, “An Analytical and Numerical Approach for Calculating Effective Material Coefficients of Piezoelectric Fiber Composites,” International Journal of Solids and Structures, Vol. 42, No. 21–22, pp. 5692–5714.

Bouchon, M., and F.J. Sánchez-Sesma, 2007, “Boundary Integral Equations and Boundary Elements Methods in Elastodynamics,” Advances in Geophysics, Vol. 48, pp. 157–189.

Burridge, R., 1971, “Lamb’s Problem for an Anisotropic Half-Space,” The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 24, No. 1,  pp. 81–98.

Every, A.G., and K.Y. Kim, 1996, “Determination of Elastic Constants of Anisotropic Solids from Elastodynamic Green’s Functions,” Ultrasonics, Vol. 34, No. 2–5, pp. 471–472.

Glushkov, E., N. Glushkova, and A. Eremin, 2011, “Forced Wave Propaga-tion and Energy Distribution in Anisotropic Laminate Composites,” The Journal of the Acoustical Society of America, Vol. 129, No. 5, pp. 2923–2934.

Hafner, C., 1985, “MMP Calculations of Guided Waves,” IEEE Transac-tions on Magnetics, Vol. 21, No. 6, pp. 2310–2312.

Imhof, M.G., 2004, “Computing the Elastic Scattering from Inclusions Using the Multiple Multipoles Method in Three Dimensions,” Geophysical Journal International, Vol. 156, No. 2, pp. 287–296.

Kraut, E.A., 1963, “Advances in the Theory of Anisotropic Elastic Wave Propagation,” Reviews of Geophysics, Vol. 1, No. 3, pp. 401–448.

Krowne, C.M., 1984, “Fourier Transformed Matrix Method of Finding Propagation Characteristics of Complex Anisotropic Layered Media,” IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 12, pp. 1617–1625.

Leckey, C.A.C., M.D. Rogge, and F.R. Parker, 2014, “Guided Waves in Anisotropic and Quasi-Isotropic Aerospace Composites: Three- Dimensional Simulation and Experiment,” Ultrasonics, Vol. 54, No. 1,  pp. 385–394.

Lenglet, E., A.-C. Hladky-Hennion, and J.-C. Debus, 2003, “Numerical Homogenization Techniques Applied to Piezoelectric Composites,” The Journal of the Acoustical Society of America, Vol. 113, No. 2, pp. 826–833.

Medeiros, R. de, M.E. Moreno, F.D. Marques, and V. Tita, 2012, “Effective Properties Evaluation for Smart Composite Materials,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 34, no. spe,  pp. 362–370.

Michalski, K.A., and J.R. Mosig, 1997, “Multilayered Media Green’s Functions in Integral Equation Formulations,” IEEE Transactions on Antennas and Propagation, Vol. 45, No. 3, pp. 508–519.

Moll, J., C. Rezk-Salama, R.T. Schulte, T. Klinkert, C.-P. Fritzen, and A. Kolb, 2011, “Interactive Simulation and Visualization of Lamb Wave Prop-agation in Isotropic and Anisotropic Structures,” Journal of Physics: Confer-ence Series, Vol. 305, No.1, doi: 10.1088/1742-6596/305/1/012095.

Moreno, M.E., V. Tita, and F.D. Marques, 2009, “Finite Element Analysis Applied to Evaluation of Effective Material Coefficients for Piezoelectric Fiber Composites,” Brazilian Symposium on Aerospace Engineering & Applications, São Paulo, Brazil.

Newberry, B.P., and R.B. Thompson, 1989, “A Paraxial Theory for the Propagation of Ultrasonic Beams in Anisotropic Solids,” The Journal of the Acoustical Society of America, Vol. 85, No. 6, pp. 2290–2300.

Payton, R.C., 1983, Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff Publishers, Hague, Netherlands, Vol. 4.

Placko, D. and T. Kundu, 2001, “Theoretical Study of Magnetic and Ultra-sonic Sensors: Dependence of Magnetic Potential and Acoustic Pressure on the Sensor Geometry,” 6th Annual International Symposium on NDE for Health Monitoring and Diagnostics, Newport Beach, California.

Placko, D., and T. Kundu, 2007, DPSM for Modeling Engineering Problems, John Wiley & Sons, Hoboken, NJ.

Placko, D., T. Kundu, and R. Ahmad, 2002, “Theoretical Computation of Acoustic Pressure Generated by Ultrasonic Sensors in the Presence of an Interface,” NDE for Health Monitoring and Diagnostics, San Diego, CA.

Pointer, T., E. Liu, and J.A. Hudson, 1998, “Numerical Modelling of Seismic Waves Scattered by Hydrofractures: Application of the Indirect Boundary Element Method,” Geophysical Journal International, Vol. 135, No. 1, pp. 289–03.

Qin, R.-S., Y. Xiao, and H. Lan, 2014, “Numerical Simulation of Effective Properties of 3D Piezoelectric Composites,” Journal of Engineering, Vol. 2014, Article ID: 824806.

Rahani, E.K., and T. Kundu, 2011, “Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) Modifications to DPSM for Ultrasonic Field Modeling,” Ultrasonics, Vol. 51, No. 5, pp. 625–631.

Rajamohan, C., and J. Raamachandran, 1999, “Bending of Anisotropic Plates by Charge Simulation Method,” Advances in Engineering Software, Vol. 30, No. 5, pp. 369–373.

Sánchez-Sesma, F.J., and M. Campillo, 1991, “Diffraction of P, SV and Rayleigh Waves by Topographic Features: A Boundary Integral Formula-tion,” Bulletin of the Seismological Society of America, Vol. 81, No. 6, pp. 2234–2253.

Sánchez-Sesma, F.J., and M. Campillo, 1993, “Topographic Effects for Incident P, SV and Rayleigh Waves,” Tectonophysics, Vol. 218, No 1–3,  pp. 113–125.

Shaw, R.P., 1979, “Boundary Integral Equation Methods Applied to Wave Problems,” in Developments in Boundary Element Methods, edited by P.K. Banerjee and R. Butterfield, Applied Science Publishers, London, England, pp. 121–153.

Shrestha, S., 2017, “Computational Wave Field Modeling using Sequential Mapping of Poly-Crepitus Green’s Function in Anisotropic Media,” (Doctoral Dissertation), https://scholarcommons.sc.edu/etd/4419/.

Shrestha, S., and S. Banerjee, 2016, “DPSM Modeling of Wave Propagation in Anisotropic Half Space,” American Society for Composites: Thirty-First Technical Conference, Williamsburg, VA.

Shrestha, S., and S. Banerjee, 2017, “Computational Wave Field Modeling in Anisotropic Plate,” SPIE Smart Structures and Materials + Nondestruc-tive Evaluation and Health Monitoring, Portland, OR.

Shrestha, S., and S. Banerjee, 2018, “Virtual Nondestructive Evaluation for Anisotropic Plates Using Symmetry Informed Sequential Mapping of Anisotropic Green’s Function (SISMAG),” Ultrasonics, Vol. 88, pp. 51–63.

Spies, M., 1999, “Transducer Field Modeling in Anisotropic Media by Superposition of Gaussian Base Functions,” The Journal of the Acoustical Society of America, Vol. 105, No. 2, pp. 633–638.

Sun, C.T., and R.S. Vaidya, 1996, “Prediction of Composite Properties from a Representative Volume Element,” Composites Science and Tech-nology, Vol. 56, No. 2, pp. 171–179.

Swaminathan, S., and S. Ghosh, 2006, “Statistically Equivalent Representa-tive Volume Elements for Unidirectional Composite Microstructures:  Part II-with Interfacial Debonding,” Journal of Composite Materials, Vol. 40, No. 7, pp. 605–621.

Swaminathan, S., S. Ghosh, and N.J. Pagano, 2006, “Statistically Equivalent Representative Volume Elements for Unidirectional Composite Microstructures: Part I-Without damage,” Journal of Composite Materials, Vol. 40, No. 7, pp. 583–604.

Tavaf, V., M. Saadatzi, and S. Banerjee, 2019, “Quantification of Degraded Constitutive Coefficients of Composites in the Presence of Distributed Defects,” Journal of Composite Materials, Vol. 53, No. 18, pp. 2517–2529.

Tavaf, V., M. Saadatzi, S. Shrestha, and S. Banerjee, 2018a, “Effect of Multi-scale Precursor Damage on Wave Propagation through Modulated Consti-tutive Properties of Composite Materials,” SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, Denver, CO.

Tavaf, V., M. Saadatzi, S. Shrestha, and S. Banerjee, 2018b, “Quantification of Material Degradation and its Behavior of Elastodynamic Green’s Function for Computational Wave Field Modeling in Composites,” Materials Today Communications, Vol. 17, pp. 402–412.

Wada, Y., T. Kundu, and K. Nakamura, 2014, “Mesh-Free Distributed Point Source Method for Modeling Viscous Fluid Motion Between Disks Vibrating at Ultrasonic Frequency,” The Journal of the Acoustical Society of America, Vol. 136, No. 2, pp. 466–474.

Wang, C.-Y., and J.D. Achenbach, 1992, “A New Look at 2-D Time-Domain Elastodynamic Green’s Functions for General Anisotropic Solids,” Wave Motion, Vol. 16, No. 4, pp. 389–405.

Wang, C.-Y., and J.D. Achenbach, 1993, “A New Method to Obtain 3-D Green’s Functions for Anisotropic Solids,” Wave Motion, Vol. 18, No. 3,  pp. 273–289.

Weilinger Associates, 2009, “Finite Element Analysis of Propagating Elastic Waves” (report based on software package), Weilinger Associates Inc., New York, NY.  

Wen, J.J., and M.A. Breazeale, 1988, “A Diffraction Beam Field Expressed as the Superposition of Gaussian Beams,” Journal of the Acoustical Society of America, Vol. 83, No. 5, pp. 1752–1756.

Willis, J., 1991, “Inclusions and Cracks in Constrained Anisotropic Media,” Modern Theory of Anisotropic Elasticity and Applications, pp. 87–102.

Willis, J.R., 1973, “Self-Similar Problems in Elastodynamics,” Philosophical Transactions of the Royal Society of London, Series A, Mathematical, Physical and Engineering Sciences, Vol. 274, No. 1240, pp. 435–491. 

Yeatts, F.R., 1984, “Elastic Radiation from a Point Force in an Anisotropic Medium,” Physical Review B, Vol. 29, No. 4, pp. 1674–1684.

Zhao, X., and Rose, J.L., 2003, “Boundary Element Modeling for Defect Characterization Potential in a Wave Guide,” International Journal of Solids and Structures, Vol. 40, No. 11, pp. 2645–2658.

Metrics
Usage Shares
Total Views
159 Page Views
Total Shares
0 Tweets
159
0 PDF Downloads
0
0 Facebook Shares
Total Usage
159