The delayed TR-NEWS allows to use the single focusing as a basis of amplitude modulation, to

create arbitrary wave envelope shapes in the focusing region. This could be used to introduce a

low-frequency component into the material by using high-frequency transmitter.

It was found that the reduction of the sidelobes in CFRP is still possible and effective by using

delayed TR-NEWS directly on the sidelobes: using a larger delay and smaller amplitude waves

tailored to directly arrive at the focusing point at the same time and magnitude as sidelobes

but in an opposite phase.

The future work in this subject will include the analysis of a local nonlinearity in the focusing

region using the proposed delayed TR-NEWS signal processing method. The FEM model can be

used to predict the probable size of a defect that could be detected with this method.

Abstract

Carbon Fibre Reinforced Polymer material with a contact gap defect is simulated by finite element method. The 2D simulation is based on a

simple laminate model of the anisotropic material layers. It is conducted in a 2D quarter space of simulated material with Lysmer and

Kuhlemeyer absorbing boundary conditions. The contact gap is included in the epoxy layer near the receiving transducer. It is modelled using

node-to-node contact algorithm. The Kuhn-Tucker normal contact conditions are satisfied by penalty plus Lagrangian multiplier method. Friction

effects are included using penalty method. The finite element dynamic wave propagation problem is solved explicitly by central difference

scheme using diagonalized mass and damping matrices. The simulation results are to be used to compare various non-destructive testing

methods meant for nonlinear defect detection, such as delayed Time Reversal - Nonlinear Elastic Wave Spectroscopy (TR-NEWS) and Pulse

Inversion. Using the simulation results, the interaction of the wave field with the defect inside the material can be closely examined to

investigate the benefits of advanced non-destructive testing methods.

Finite element simulation and delayed TR-NEWS analysis

of contact gap in carbon fibre composite Martin Lints1,2, Serge Dos Santos1and Andrus Salupere2

1 INSA Centre Val de Loire, Inserm U930 "Imagerie et Cerveau" , 3 rue de la Chocolaterie, CS23410, 41034 Blois France,

2Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia

martin.lints@cens.ioc.ee, serge.dossantos@insa-cvl.fr, salupere@ioc.ee

Original TR-NEWS signal processing can be used to focus the wave energy under

the receiving transducer or vibrometer of an ultrasonic Non-Destructive Testing

(NDT) setup. It is a promising method for evaluation of complex, dispersive and

nonlinear media because it relies on the internal reflections for the focusing

process of the wave energy into a specific spot in a certain time, therefore taking

advantage of the complex internal structure of the material. Such focused wave

has an improved signal-to-noise ratio, making it suitable for investigating

dispersive, chaotic or highly attenuating media. The investigation has been

carried out initially experimentally on bi-layered aluminium block, then on a CFRP

sample. The findings are studied further using Finite Element Method (FEM)

simulation of wave motion in a stochastic layer thickness laminate model of CFRP

block to examine the signal propagation and focusing inside the material.

TR - NEWS = Time Reversal - Nonlinear Elastic Wave Spectroscopy [1]

Nonlinear Time Reversal methods

http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.063902

Optimized excitation based on TR-NEWS approach for extraction of the

localized nonlinear signature in a complex chaotic medium : applied for

cryptography applications [5] (left) and applied for Non Destructive Testing

( NDT) applications (right) [4]

Fig 3: Experimental set-up

The physical interpretation of the cross-correlation function

Introduction

Conclusion

References

This work is supported by the Région Centre-Val de Loire (France) under the PLET project. This research has been conducted within the co-tutelle

Ph.D. studies of Martin Lints, between the Institute of Cybernetics at Tallinn University of Technology in Estonia and the Institut National des

Sciences Appliquées Centre Val de Loire at Blois, France. The laboratory visits have been funded by European Social Funds via Estonian Ministry of

Education and Research and Archimedes Foundation (30.1-9.3/287, 30.1-9.3/1137 and 16-3.4/1390) through DoRa and Kristjan Jaak Scholarship

programmes. This research is partly supported by Estonian Research Council (project IUT33-24)

Aknowledgments

1. Koen Van Den Abeele and Serge Dos Santos, Détection et localisation de microdégradation de ﾏatéヴiaux paヴ spectヴoscopie d’oﾐdes élastiケues ﾐoﾐ linéaires, 2006 , pp 18-28 http://www.bruit.fr/flipbook/AT45/files/assets/basic-html/page26.html

2. M. Lints, S. Dos Santos, A. Salupere, Solitary waves for Non-Destructive Testing applications: Delayed Nonlinear Time Reversal signal processing optimization, Wave Motion, Volume 71, pp. 101–112(2017) http://dx.doi.org/10.1016/j.wavemoti.2016.07.001

3. Matthew Frazier et al, Nonlinear Time Reversal in a Wave Chaotic System, Phys. Rev. Lett., 110, 063902 (2013)

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