NUMERICAL SIMULATION OF WAVE PROPAGATION IN WELD JOINTS INCLUDING A FLAW

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3^ème Conférence Internationale sur

le Soudage, le CND et l’Industrie des Matériaux et Alliages (IC-WNDT-MI’12) Oran du 26 au 28 Novembre 2012, http://www.csc.dz/ic-wndt-mi12/index.php 27

NUMERICAL SIMULATION OF WAVE PROPAGATION IN WELD JOINTS INCLUDING A FLAW

Morad Grimes, Sofiane Haddad and Toufik Benkedidah

Jijel University, Electronics department grimes_morad@yahoo.fr

Abstract :

In this study, the process of wave propagation in weld joints including a flaw was simulated using elastic finite-difference time-domain (FDTD) method and a digitized cross-section photograph of actual test object as input data. In order to distinguish the different elements constituting the experiment (transducer, wedge of a probe, test object), different colors are assigned to these different materials. Each color contains information on material parameters, such as the velocity of longitudinal and transversal waves, and the material density.

Keywords : simulation, FDTD method, ultrasonic, weld joints.

1 Introduction

Simulation tools in non-destructive testing with ultrasound deserve more and more attention on behalf of their capability to produce real-life synthetic data; these data are of significant help in the interpretation of recorded A- and/or B-scans.

Several simulation methods for calculating ultrasonic fields in solids have been reported, for example, the finite element method (FEM), boundary element method (BEM), elastodynamic finite integration technique (EFIT) and finite-difference time-domain (FDTD) method. In this work, We are interested in the FDTD method because of the simplicity of the scheme.

2 Elastic FDTD method

The followings are the governing equations of two-dimensional elastic FDTD method for the isotropic medium related to x-y direction [1] :

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 

2 2

x xx xy

y xy yy

xx x y

yy y x

xy x y

v

t x y

v

t x y

v v

t x y

v v

t y x

v v

t y x

 



 



   

 

   

 

   

   

  

  

  

   

   

  

   

  

   

    

     



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where vx and vy are the particle velocities components, xx and yy the normal stress components in the direction x and y, respectively, xy is the shear stress components on the x-y plane,  is the medium density, and λ and μ are the first and second Lamé coefficients, respectively.

3 Input data

An example of a cross-section photograph is shown in figure 1. The photograph shows butt weld joints including a flaw. The thickness of the steel plate is 20 mm.

Figure 1. An example of a digitized cross-section photograph of a test object.

In order to simulate the ultrasonic propagation in our test object, input data are required, in particular realistic geometry of test object. In our simulation, the geometry of the wedge of a probe, the piezoelectric transducer, the test object and the flaw is determined by a digital image of our configuration and then processed to a color bitmap image which has same pixel size as a grid of the FDTD [2].

In the bitmap image as shown in figure 2, red, green, blue and white represent the different materials, the piezoelectric transducer, the wedge, the test object and the flaw, respectively.

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Figure 2. Processed image for input data of FDTD method.

The material constants of test object are given in table 1 :

Table – Parameters of test object.

Color Vl(m/s) Vs(m/s) 

Red - - -

Green 2700 1400 1170

Blue 5900 3200 7700

White - - -

4 FDTD Simulation results

Ultrasonic fields obtained by the FDTD method using the shape file and the parameter table are shown in figure 3.

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Figure 3. Time snapshots of shear wave propagation in test object.

5

Conclusions

A time domain simulation tool for the ultrasonic wave propagation in was developed using the combined method of the FDTD and the image-based modeling. In perspectives, we are now extending this shear wave simulation to three-dimensional and check the validity of the simulation technique by an experiment.

References

[1] J. Virieux, "P-SV wave propagation in heterogeneous media: Velocity-stress finite difference method", Geophysics, Vol. 51, pp.889-901, 1986.

[2] K. NAKAHATA, A large scale simulation of ultrasonic wave propagation in concrete using parallelized EFIT", Journal of Solid Mechanics and Materials Engineering, Vol. 2, pp.1462-1469, 2008.

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

x 10^-5 -0.6

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

Amplitude [V]

Time [S]