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: frederic.reverdy@cea.fr 2 EADS IW; 18 rue Marius Terce, 31025 Toulouse, France; E-mail: nicolas.dominguez@eads.net

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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