EFIT Simulations for Ultrasonic NDE
Renי Marklein, Karl-Jצrg Langenberg, Klaus Mayer
(University of Kassel, Department of Electrical and Computer Engineering, Electromagnetic Field
Theory, Wilhelmshצher Allee 71, D-34121 Kassel, Germany)
(firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,
Paper presented at the 8th ECNDT, Barcelona, June 2002
This contribution presents numerical modelling results for typical piezoelectric transducers
and non-destructive testing situations. Starting from the transducer modelling of straight-beam and angle-beam probes up to the simulation of the time of flight diffraction (TOFD)
technique and the long-long-trans (LLT) technique, results are given as A-scans and time domain snapshots of the ultrasonic wavefield, which provide an excellent way to interpret
the pulse signature shown in the A-scan.
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. EFIT, the
Elastodynamic Finite Integration Technique, starts with the elastodynamic governing
equations in integral form. This means that EFIT simulates the nature of ultrasonic waves
without any approximations. EFIT discretizes the basic field equations uniquely on a
staggered grid; a pertinent code has been implemented for widely arbitrary inhomogeneous
and/or anisotropic materials. Details are given for instance by R. Marklein (1). In the
present contribution EFIT is applied to simulate the radiation field of various piezoelectric
transducers: longitudinal vertical, longitudinal 70°, subsurface longitudinal wave and shear
45° probes. This clarifies the physical understanding of the generated wavefield of such
transducers. In a second step, these radiation fields are scattered by various canonical
defects: idealized planar cracks with different orientation to the incident beam. That way, a
test bed for the TOFD and/or the LLT technique is provided. The resulting crack tip signal
amplitudes, as they appear in the A-scans, are compared to those of method of moment
modelling. Scanning the transducer(s) results in B-scans, and again, EFIT simulations
provide an excellent tool for their interpretation.
EFIT simulations for ultrasonic NDE
EFIT is a simulation tool which relies on the direct discretization of the governing
equations of elastodynamics; i. e. Newton-Cauchy’s equation of motion and the equation
of deformation rate (see reference (1)). All field quantities are function of position and
time. In the following we present several simulations where we study the ultrasonic wave
generation, propagation, and reception in detail. The time-domain snapshots displayed in
the figures below can be composed to “wave movies” and played with Windows Media
Player or Quick Time Player, which is extremely useful for multimedia presentations. The
wave movies visualize the dynamic behavior of the ultrasonic wavefield which is very
helpful for the understanding of the ultrasonic wave propagation. Some words to the
notation of the different wave types: if we consider plane ultrasonic waves in solids, we
find mainly two different wave types which travel with different velocities: the one with
the highest velocity arrives first and is therefore called primary (P) wave, the other is then
called (S) secondary wave. The polarization acts as a second criterion and this is usually
used in NDT, like longitudinal (L) and transversal (T) or short “long” and “trans” or
pressure (P) and shear (S). And even further, if we introduce a reference plane, we can
differentiate between shear vertical (SV) and shear horizontal (SH) polarization. In this
paper we focus on the 2-D P-SV case only. Our standard model pulse is a raised cosine
pulse with two cycles (RC2) as shown in figure 1. The carrier frequency f0 is amplitude
modulated with the envelope containing two oscillations. Parameters of the impulse are the
frequency f0, the cycle length T0 and the total pulse duration T.
Fig 1: Time history of the raised
cosine pulse with two cycles: RC2(t). The carrier frequency is f0=1/T0
and T is the pulse duration. Here T=2T0.
Different straight-beam and angle-beam probes
Fig 2: EFIT time-domain snapshots of the ultrasonic wavefield generated by a
longitudinal vertical straight-beam probe. The position and size of the probe is
indicated by the black bar. Displayed is the magnitude of the particle velocity |v| at
three different time points t1, t2 and t3 with |
t1 < t2 < t3.
Figure 2 presents the first 2-D EFIT result for an ultrasonic wavefield generated by a long
vertical probe with an RC2 pulse as the stimulus. The nearly plane pressure wavefront (P)
of the aperture, the concentrically pressure waves (Pl, Pr) and shear waves (Sl, Sr) emitted
from the edges of the aperture, Rayleigh surface waves (Rl, Rr) and the lateral head waves
(Hl, Hr) are clearly observed. Figure 3 displays time-domain snapshots for different
ultrasonic probes in the 2-D pressure-shear vertical (P-SV) case. The main features are
clearly observed. For instance, figure 3c shows the wavefield of a longitudinal 70° angle beam probe, where beside the pressure wavefront (P) the mode-converted shear wavefront
(S) is visible.
Fig 3: Time-domain EFIT ultrasonic transducer modeling in the 2-D pressureshear
vertical (P-SV) case: a) longitudinal 0° wave transducer; b) longitudinal 30°
wave transducer; c) longitudinal 70° wave transducer; d) subsurface longitudinal
wave transducer; e) shear 45° wave transducer; f) Rayleigh wave transducer.
Scattering by an inclined crack
Figure 4 shows the geometry of an inclined crack which is illuminated by the wavefield of
a longitudinal vertical probe. The received A-scan in non-rectified high-frequency (HF)
form is given in figure 5a, where the essential crack tip echoes (Pct, Pcb) are identified and
indicated in the time-domain snapshots in figure 5b. Due to the stair stepped approximation
of the original flat crack in the discrete EFIT grid system several echoes arrive between
these signals, which are indicated in the A-scan as noise. In figure 5c a reference solution
using the method of moments is presented. The two crack tip echoes are indicated and the
amplitude of the echoes coincides with the prediction in figure 5a.
Fig 4: LLT geometry for the 2-D EFIT simulation. The black bar indicates the
position of the 2 MHz long straight-beam probe. P=L is the incident longitudinal
wave; Pct=Lct is the diffracted echo from the top tip and Pcb=Lcb is the diffracted
echo from the bottom tip of the inclined crack.
c) Method of moments solution
5: 2-D EFIT simulation of the
LLT technique: a) A-scan in highfrequency
form; b) EFIT timedomain
snapshots of the magnitude
of the particle velocity vector, the
dash-dotted circles indicate
characteristic of the cylindrical
pressure wavefront from the top and bottom crack tip (Pct and Pcb); c)
reference solution using methods of
moments (MoM) for the free-space
case and plane pressure illumination.
Figure 6 and 7 display 2-D EFIT results for the LLT technique applied to a solid test
specimen with a vertical flat crack. The LLT echo as the dominant signal is indicated in the
A-scan and time-domain snapshots. Beside this main pulse two smaller echoes are received
at the probe. The origins of these echoes are indicated in the snapshots.
Fig 6: LLT geometry for the 2-D EFIT simulation. The black bar indicates the
position of two angle-beam probes, a 2 MHz 30° longitudinal angle-beam probe and a
2 MHz 62° transversal angle-beam probe.
Fig 7: 2-D EFIT simulation of the LLT technique: a) A-scan in high-frequency
form and b) EFIT time-domain snapshots of the magnitude of the particle velocity
vector. The dash-dotted lines indicate the characteristic of the received echoes.
Figure 8, 9, 10 and 11 display 2-D EFIT results for the TOFD technique. Here we study in
figure 8 and 9 the vectorial elastic case compared to the scalar acoustic case given in figure
10 and 11. Figure 9a displays the A-scan for the elastic case. The first two echoes (Pr, Pl)
are generated by the longitudinal wave from the right and left edge of the emitter. The
important echoes (Pct, Pcb) from the top and bottom crack tip are indicated in the A-scan
and the snapshots. Figure 11 shows comparable results for the scalar acoustic case, where
the echo from the top crack tip is much larger as in the elastic case (see figure 9a).
Fig 8: TOFD geometry for the 2-D EFIT simulation. The black bars indicate the
position of two angle-beam 45° long 2 MHz probes.
9: 2-D EFIT simulation of the TOFD technique: a) A-scan in high-frequency
form and b) time-domain snapshots of the magnitude of the particle velocity vector.
The dash-dotted circles indicate the characteristic of the crack tip echoes.
Fig 10: TOFD geometry for the 2-D EFIT simulation. The solid material is treated
as a scalar acoustic medium with the parameters indicated in the figure. The black
bars indicate the position of two angle-beam 45° long 2 MHz probes.
11: 2-D EFIT simulation of the TOFD technique for the scalar acoustic case:
a) A-scan in high-frequency form and b) time-domain snapshots of the magnitude of
the particle velocity vector. The dash-dotted circles indicate the characteristics of the
crack tip echoes.
EFIT has been applied to a wide set of real-life problems. Here we have presented only
some selected examples. Further results can be found in the literature, for instance in
reference (1) and references therein and our website www.tet.e-technik.uni-kassel.de.
- R. Marklein, Numerical Methods for the Modeling of Acoustic, Electromagnetic,
Elastic and Piezoelectric Wave Propagation Problems in the Time Domain Based on
the Finite Integration Technique, Shaker Verlag, Aachen, Germany, 1997, (available
from http://www.shaker.de), (in German).