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NDT Modeling tools applied to the aeronautic industry: examples in CIVA
Frederic REVERDY 1, Nicolas DOMINGUEZ
2
1 CEA-LIST, 18 rue Marius Terce, 31025 Toulouse, France
Phone: +33 561168875, e-mail: [email protected] 2 EADS IW; 18 rue Marius Terce, 31025 Toulouse, France; E-mail: [email protected]
Abstract
Modern production of structural parts in the aeronautic industry is characterized by mechanically optimized
structures that can be complicated to inspect due to complex geometries and complex composite materials.
Developing NDT procedures is thus more challenging and could become costly without tools to help NDT
design and performances prediction. Simulation is a major asset to help engineers to evaluate existing
procedures, define new methods, perform analysis of non-trivial NDT data and train operators. CIVA is a
software platform that offers simulation tools for major NDT techniques [1]. For ultrasonic inspection CEA-
LIST has developed semi-analytical tools that have the advantages of high computational efficiency (fast
calculations) and easiness in use by non-specialists. Nevertheless, based on specific physical hypothesis their
domain of applicability is limited; for example carbon fiber reinforced composites have a well-defined periodic
microstructure that generates a patterned background noise that cannot be represented by semi-analytical models.
Full numerical schemes such as finite element (FEM) or finite difference in time domain (FDTD) are more
suitable to compute ultrasonic wave propagation in complex materials such as composite but require more
computational efforts, as well as expertise from users. Hybrid methods couple semi-analytical solutions and
numerical computations in limited spatial domains to handle complex cases with high computation
performances. In CIVA we have integrated hybrid models that couple the semi-analytical methods developed at
CEA to FDTD modelling developed at Airbus Group Innovations. In this paper we give some examples of the
semi-analytical methods developed at CEA for the inspection of composite materials. We then show some
extension of these methods to curved surfaces using Dynamic Ray Tracing models. Finally, we show the current
state of the hybrid models integrated in CIVA applied to the inspection of curved surface and ply waviness.
Keywords: Modeling, CIVA, Composite
1. Introduction
Fiber reinforced composites are steadily gaining importance in aeronautic applications (20%
mass of A380, 50% mass of A350 & Boeing 787…), and the importance of NonDestructive
Testing (NDT) for these materials is a major step in the manufacturing process (from 15% to
25% manufacturing time dedicated to NDT). The complexity of composite geometries leads
to an increasing need for adapted ultrasonic NDT methods. One way to address those
problems is to use simulation tools to optimize the procedures used for the inspection of those
structures.
According to the various problems (complex geometries, homogeneous or heterogeneous
structures…) different modelling strategies can be used: semi-analytical, pure numerical or
hybrid (mixing semi-analytical and numerical codes). Semi-analytical (mostly, integral
techniques) methods offer high computation performances within their validity range but
cannot offer the versatility of pure numerical techniques (FEM, FDTD…). The latest require
more computational efforts, as well as expertise from users. In this paper we present semi-
analytical tools developed within CIVA that allow to handle some NDT configurations
applied to composite structure. We also present hybrid methods that couple semi-analytical
solutions and numerical computations to handle more complex cases with high computation
performances.
2. Ray based theory and homogenization
2.1 Beam propagation in CIVA
The ultrasonic beam field radiated by a probe can be simulated in CIVA by using a semi-
analytical method based on the synthesis of the impulse response function. This model
assumes that the beam may be obtained by summing the contributions of individual sources
distributed along the surface of the probe. These elementary contributions are calculated using
the “pencil method” [2]. Once all contributions have been evaluated, the impulse response is
calculated and convoluted with the waveform of the probe. For phased-array probes, a phase
shift is applied to each individual contribution according to the time delay applied to each
element of the probe. This formulation allows to take account arbitrary waveforms and
arbitrary delay laws without the need of new calculations. This method is valid for
homogeneous and heterogeneous structures, isotropic and anisotropic materials, canonical
geometries and complex shapes.
2.2 Anisotropic stratified structures
When dealing with the propagation of ultrasonic waves in composite materials one has to take
into account the anisotropic nature of the material but also the attenuation. Considering the
typical diameter of fibers (7 μm), the typical fiber volume fraction (65%) and the typical
frequency range of ultrasonic testing, the wavelength scale is such that viscosity, multiple-
scattering and their possible coupling appear as a homogeneous global phenomenon. A model
was developed in CIVA to predict the wave propagation and attenuation in unidirectional
fiber reinforced composite materials [3].
Many composite structures are made by stacking several unidirectional layers of various
orientations to obtain structural strengths in various directions. The pencil method described
earlier is a semi-analytical method that grows in complexity (and computation time) with the
number of reflexions/conversions for a given configuration. Composite materials are stratified
structures in nature that can lead to important computation times when using these models.
One way to simplify the problem is to use homogenization by replacing the layered structure
by a homogeneous anisotropic effective medium. A Ray theory Based Homogenization
method (RBH) was developed and is available in CIVA [4]. It aims at obtaining the effective
stiffness constants of a group of anisotropic layers.
Figure 1 : Ray theory Based Homogenization: the follow-up of the energy path in one pattern (left) leads to an average energy direction AB=De supposed to be that in the homogenized equivalent
material
The RBH method is carried out by following the energy ray paths inside each ply of the
composite leading to an average energy direction (direction AB) as shown in the previous
figure. An associated effective transmission factor is calculated to take into account the inner
refraction phenomena and a relationship between phase and energy directions leads to the
geometrical construction of an overall slowness surface that describes the anisotropic
homogeneous medium. Finally an optimization method is applied to obtain the associated
effective stiffness tensor, which in turn can be used in the simulations. This homogenization
process was applied to the inspection of a composite part that displays a slope in the middle of
the component as indicated in the following figure. Measurements of the beam field were
made in transmission for four positions along the component and compared to simulation.
Figure 2 : Beam field measurements and simulations in transmission for four positions along a composite component with a slope
The comparison between simulation and experimental results show a pretty good correlation
in terms of beam field deviation, spot size but also amplitude distribution across the beam
spot
2.3 Curved composite structures
In the case of complex geometries, the only way to model beam propagation with the semi-
analytical tools is to divide the component into a set of homogeneous sub-sections with a
local disorientation. On top of being cumbersome, this approximation leads to some
numerical artefacts due to the presence of fictive interfaces. To deal with these geometries the
ray-based model was extended to calculate the beam propagation in curved composites
without the need of discretization [5-6]. This model is based on the evaluation of the ray
trajectories and travel-times and the computation of the amplitude of a ray tube during the
propagation. The evaluation of the ray-paths and travel-time is done solving an eikonal
equation and the Christoffel equation using an iterative scheme. For each step of the
calculation, perturbations of the position of the ray and its slowness are simultaneously
evaluated. To describe the conservation of the energy inside the ray tube and compute the
amplitude of a ray tube, the transport equation is solved along a ray in an anisotropic
inhomogeneous medium.
We apply this model to the beam field calculation in a curved composite part. We compare
the simulation obtained for a curved part with an isotropic material (a), a component divided
into a set of ten anisotropic homogeneous sub-sections with a local disorientation (b) and the
model explained in this part for which we have a continuous anisotropy that follows the
curvature (c).
(a)
(b)
(c)
Figure 3 : Beam field calculation for a curved component with isotropic constants (a), anisotropic homogeneous sub-sections with a local disorientation (b) and continuous anisotropy (c).
In the top figures, it is possible to see the orientation of the anisotropy (indicated by the blue
arrows) for each sub-section for case b and to see the gradient of anisotropic properties (the
red arrow indicates the local direction of the anisotropy for the position of the cursor).
Looking at the bottom figures we clearly see a difference when we choose isotropic properties
in terms of beam size. Discretizing the curvature into sub-sections with local anisotropy
requires drawing the CAD file and assigning at each sub-section the proper material
orientation. We see that the beam field is closer to the continuous case but a discretization in
ten sub-sections is not enough.
If we look at the amplitude distribution of the field at mid-plane (Figure 4) we see that
choosing an isotropic material leads to a big decrease in amplitude (~16dB) as well as a bad
representation of the width of the field. Discretizing the curvature into a ten sub-section leads
to a better representation of the beam field but still the amplitude is not well predicted (~2dB)
and artifacts are visible on each side of the main lobe.
Figure 4 : Amplitude distribution at mid plane for the continuous model (black line), discretized code (blue dotted line) and isotropic material (red line)
This new model allows to deal with complex composite parts as long as a cartography of the
anisotropic properties is given to the model.
3. Hybrid models
The models described previously are semi-analytical models that take advantage of
homogenization schemes to calculate the beam field in anisotropic structures and its
interaction with defects. While semi-analytical tools offer the advantage of fast calculations
they cannot always represent the complexity of phenomena encountered in the inspection of
composite structures. Carbon fibers reinforced composites have a well-defined periodic
microstructure, which is known to generate a patterned background noise for ultrasonic
inspections. Micrographic analyses have shown that plies of pre-preg materials are separated
by thin layers of resin, which constitute an acoustical impedance mismatch and therefore a
source of scattering. The combination of a regular ply pattern with the resin scattering
explains the structural noise when the bandwidth of the probe is appropriate. To tackle those
problems Airbus Group Innovations has developed a full numerical software based on Finite
Differences in Time Domain (FDTD) [7]. This code can model all the FCFRP and resin layers
thus the structural noise but at the expense of computation time.
A hybrid model that couple the semi-analytical methods described before to the FDTD
modelling developed at Airbus Group Innovations was developed and integrated in CIVA.
This analytical/numerical approach allows to combine the advantages of both methods while
minimizing their inconveniences. The FDTD is used in a restricted area surrounding the
component; the boundaries are in the coupling medium as close to the surface as possible to
minimize the FDTD calculation in the fluid. The semi-analytical code is used to predict the
incident field at the boundaries of this restricted area. Using the reciprocity principle or
decomposition techniques (considering independent forward and backward processes) it is
possible to calculate the pressure received by the probe after propagation in the FDTD area.
3.1 Graphic User Interface
A dedicated interface was developed in CIVA to define stratified structures and use the hybrid
code. Complex parts can be defined using a piecewise description; which describes the neutral
axis of the component. After defining the thickness above and below the neutral axis, the
number of plies, the presence of a resin layer between each ply the component is drawn as
shown in Figure 5. Using the anisotropic properties of the material for a flat composite the
code calculates and displays the local anisotropy at each point in the complex component.
This local orientation of the anisotropy is communicated to the FDTD code for calculation of
the strains and displacements at each time step. The user can modify the characteristics of
each ply or epoxy layer (stiffness or thickness) independently and analyze for example the
influence of the lack of periodicity on the signal.
Figure 5 : Graphic user interface for the hybrid model
3.2 Validation for the structural noise
The first validation of the hybrid model is to analyze the amplitude of the structural noise and
backwall echo obtained on flat composite sample with two transducers operating at different
central frequencies. The sample is a Pre-preg stack made of T700/M21 material composed of
28 plies. The thickness of each ply is assumed to be 0.259mm including a 15 µm epoxy layer.
The two transducers have a diameter of 6 mm and a nominal central frequency of 3.5 and 5
MHz, respectively. Since the most important parameters for the structural noise are the central
frequency and the bandwidth of the transducer these two parameters in the model have been
adjusted to fit the experimental frontwall echo. The model doesn’t take into account
attenuation due to viscoelasticity in the matrix. It is possible to simulate attenuation in post-
processing by applying a sliding window over the signal. Although this is not fully
satisfactory for highly damped material, the considered composite material displays a
dispersion (velocity variation with frequency) low enough to be neglected. The
superimposition of the experimental and simulated signals is shown in Figure 6 for the bothj
transducers.
Figure 6 : Superimposition of the experimental signal with the FDTD code for a transducer at 3.5 MHz left) and 5 MHz (right)
One can see that simulation shows a pretty good prediction of the amplitude and time of flight
of the backwall. The model predicts also relatively well the amplitude of the structural noise
for both the 3.5 MHz (absence of structural noise) and 5 MHz probes. It is thus possible to use
this model to predict the Signal-to-Noise ratio and thus the possibility of detecting small
delaminations in the presence of structural noise. We then looked at the inspection of
reference block with various thicknesses and various Flat-Bottomed Holes (FBH). We
compare the signals obtained for each thickness with a linear-phased array probe at 5 MHz.
Similarly to the results presented before we adjust the central frequency and bandwidth of the
transducer to fit the frontwall echo.
Figure 7 : Reference block with various thicknesses and comparisons between experimental and simulated signals obtained for various thicknesses.
We can see that the amplitude of the structural noise is well predicted. We notice a difference
in terms of time of flight especially for the thicker steps of the block. This is due to the fact
that the model doesn’t take into account dispersion (the velocity is assumed to be constant
with frequency) while we know that the composite acts as low-pass filter and we should
expect slower velocities for thicker material. The amplitude of the backwall echo is relatively
well predicted; the difference observed between the experimental and simulated signals is
within the variation of amplitude measured on the experimental cscan.
It is also possible to perform mechanical or electronic scans with the hybrid model; the code
loops through all positions. This is where the use of a hybrid model makes sense where we
repeat several calculations that would take a long time with a pure numerical code. The
following shows an example of bscan obtained across a 6-mm FBH. We clearly see the echo
reflected off the top of the FBH, the frontwall and backwall echoes.
Figure 8 : Mechanical bscan obtained over a 6-mm FBH
3.2 Ply waviness
Finally since numeric models can handle complex problems we added the possibility to define
ply waviness defects. The defect is defined in the hybrid code as a Gaussian modulation of
various plies within the thickness of the sample. This modulation leads to an increase of the
thickness of some plies and a compression for others. It is possible to combine several defects
to model more complex ply waviness observed in reality.
As a first result we tried to simulate the response of a ply waviness observed in one composite
panel. A micrography of the waviness is shown in the following figure; we can see clearly a
strong waviness right at the surface, which impacts also the volume of the composite. To
represent this waviness we used two defects in the hybrid code: one with a strong modulation
close to the surface and another one with a smoother variation. One can see that in reality the
strong waviness propagates across the thickness with a small angle and also starts right at the
second ply, which is not possible yet with the current description entered in the code. The
transducer used is the same 5-MHz linear phased array used for the inspection of the reference
block. The electronic bscan obtained is shown in Figure 9. One can see a big variation of the
structural noise with an increase of energy right in the center of the waviness.
Figure 9 : Ply waviness observed in a composite panel, its representation in the hybrid code and the bscan obtained
Experimental validations will be carried on several samples containing ply waviness to see if
the model predicts correctly the variation introduced by such defects.
4. Conclusions
The complexity of composite geometries leads to an increasing need for adapted ultrasonic
NDT methods. This is why we have developed simulation tools adapted to the inspection of
such structures. Homogenization algorithms have been implemented for both plane and
curved structures to be able to use semi-analytical models that allow fast computation times.
These models allow calculation of beam field and interaction with various defects in 3D. To
deal with structural noise and ply waviness we have implemented a hybrid model in 2D that
combines the fast time computation of semi-analytical codes in areas where the geometry is
simple with the efficiency of numeric codes in areas with complexities. The next steps are to
validate this hybrid model for more cases and to implement it in 3D.
References
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