A model for differential estimation of 3D thermal propagation by finite difference

Andrés David Restrepo Girón, Humberto Loaiza Correa

Abstract


In this paper, a new mathematical model based on finite difference discretization of the Fourier’s 3D heat propagation model, is shown. From this one, a new technique is proposed to detect flaws in composite thin layers, under evaluation by a Pulsed Active Thermography experiment. The discrete model defined is easily adaptable to a spatial filter structure, which can be applied to the infrared sequence of images acquired from that thermography experiment, to obtain a better contrast between possible internal flaws and sound regions of material. The performance of the technique proposed is evaluated using artificial thermal sequences generated by ThermoCalc6L, software that is able to compute dynamic thermal distributions in anisotropic layered solids, simulating defects and different excitation sets. Results show that this technique offers a better contrast between defect and background thermal information, than other common technique like Differential Absolute Contrast (DAC), and it runs faster than the classic 3D thermal filtering method.

Keywords


Active thermography; pulsed thermography; thermal propagation; thermal contrast; spatial filter

References


Benítez, H; Ibarra, C.; Bendada, A.; Maldague, X.; Loaiza, H.; Caicedo, E. (2006). Modified Differential Absolute Contrast Using Thermal Quadrupoles for the Nondestructive Testing of Finite Thickness Specimens by Infrared Thermography. En IEEE Canadian Conference on Electrical and Computer Engineering [CCECE’2006], Ottawa, Canada. Washington, D.C: IEEE Computer Society

Benítez, H.; Loaiza, H.; Caicedo, E. (2011). Termografía Activa Pulsada en Inspección de Materiales. Técnicas Avanzadas de Procesado [Colección de Ciencias Físicas, Exactas y Naturales, (1ª ed.)]. Cali, Colombia: Universidad del Valle / Pontificia Universidad Javeriana de Cali

Department of Defense. (2002). Ceramic Matrix Composites. Composite Materials Handbook, Volume 5. Washington, D.C.: Autor

Grinzato, E.; Bison, P.G.; Marinettti, S.; Vavilov, V. (2000). Thermal NDE enhanced by 3D numerical modeling applied to works of art. 15th World Conference on Non-Destructive Testing. 15-21 October 2000 in Rome. Proceedings. Recuperado de http://www.ndt.net/article/wcndt00/papers/idn909/idn909.htm

IATA - International Air Transport Association. (2009). A global approach to reducing aviation emissions. First stop: carbon-neutral growth from 2020. Suiza: Autor.

Ibarra, C. (2005). Quantitative Subsurface Defect Evaluation by Pulsed Phase Thermography: Depth Retrieval with the Phase [Tesis Doctoral]. Facultad de Ciencias e Ingeniería, Universidad Laval. Quebec, Canadá

X. Maldague (Ed. Tech.), & P. Moore (Ed.). (2001). Infrared and Thermal Testing. Nondestructive Testing Handbook, Volumen 3 (3a ed.). Columbus, OH: ASNT

Meola, C.; Carlomagno, G.; Giorleo, G. (2004). Using infrared thermography to analyze substrate and adhesive effects in bonded structures. Journal of Adhesion Science and Technology, 18(6), 617-634

Snell Jr, J. R.; Spring, R. W. (2007, Octubre 2). Infrared Thermography Advances. Recuperado de http://www.ndtmag.com/Articles/Feature_Article/BNP_GUID_9-5-2006_A_10000000000000179212

Ozimek, J. (2006). The Boeing Company [ponencia en JP Morgan Airline, Aerospace and Airfreight Conference, New Yor, NY, Febrero de 2006]. Recuperado de http://www.docstoc.com.lax.llnw-trials.com/docs/3754071/The-Boeing-Company-JP-Morgan-Airline-Aerospace-and-Airfreight-

Pohl, J. (1998). Ultrasonic Inspection of Adaptive CFRP-Structures. NDT Database & Journal,, Vol.3, No.9, septiembre de 1998. Recuperado en febrero, 2012 de http://www.ndt.net/article/ecndt98/aero/015/015.htm

Tadeu, A., & Simões, N. (2005). Fundamental solutions for transient heat transfer by conduction and convection in an unbounded, half-space, slab and layered media in the frequency domain. Engineering Analysis with Boundary Elements, 29(12), 1130-1142

Tadeu, A.; Simões, N. (2006). Three-dimensional fundamental solutions for transient heat transfer by conduction in an unbounded medium, half-space, slab and layered media. Engineering Analysis with Boundary Elements, 30(5), 338-349

Tadeu, A.; Simões, N. (2007). Conduction and convection phenomena through a slab with thermal heterogeneities. Applied Mathematical Modelling, 31(7), 1444-1459.

Valdés, M.; Inamura, M.; Valera, J.; Yao L. (2006). Multidimensional filtering approaches for pre-processing thermal images. En Multidimensional System Signal Processing, 17(4), 299-325




DOI: http://dx.doi.org/10.18046/syt.v10i21.1193

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