Detect of defect in carbon epoxy materials, Ingegneria aerospaziale

S

2

S S

1 S

3 S

4 t

t t t t

1 2 3 4

–

Fig. 2.7 The signal of a thermic wave at a generic point x of the image

1

If the system records images with a frequency related to the frequency of modulation of the

excitation source (for example four images in a loop with values S at t , S at t and so on),

1 1 2 2

it’s possible to obtain the following data of

distributed at the same distance in a modulation cycle,

“magnitude” and “phase” of the object:

   

2 2

M [ S ( x ) S ( x )] [ S ( x ) S ( x )] (3.6)

3 1 1 1 4 1 2 1



S ( x ) S ( x )

  3 1 1 1 (3.7)

arctan 

S ( x ) S ( x )

4 1 2 1

where:

 M (magnitude) is the vector sum of the amplitude of direct and reflected wave;

 ϕ (phase) is the difference between the phases of direct and incident wave.

Beside, the signal measured in the point x is obtained by combining radiation emitted by the object

1

and radiation reflected by environment warm objects.

Therefore we may say that:

measured signal = object’s radiation + environment radiation reflected



ε ε) (3.8)

S = i S + (1 S Reflection’s

Measured Thermal wave

where:

ε is emissivity

i is external lighting factor

Substituting equation (3.8) into equations (3.6) and (3.7) we respectively have:

14

 

2

   

   

      

M iS ( x ) (

1 ) S ( x ) iS ( x ) (

1 ) S ( x )

   

3 ,

Tw 3 ,Re fl 1

,

Tw 1

,Re fl (3.9)

2

  

   

2 2

M i S ( x ) S ( x )

 

3 ,

Tw 1

,

Tw   



 i S ( x ) S ( x )

S ( x ) S ( x )  

 3 ,

Tw 1

,

Tw

  

3 1

arctg arctg

   



S ( x ) S ( x ) i S ( x ) S ( x )

 

4 2 4 ,

Tw 2 ,

Tw (3.10)



S ( x ) S ( x )

 3 ,

Tw 1

,

Tw

arctg 

S ( x ) S ( x )

4 ,

Tw 2 ,

Tw 

In general the signal of the thermal wave is influenced by emissivity , by the excitement intensity I

apart the reflection that can vary depending on the object position.

Equations (3.9) and (3.10) show that amplitude and phase images, got with the lock-in technique,

enjoy many important properties not present in images obtained with other thermographic analysis:

 being possible to consider external reflections constant during measurement (S =S ),

3,Refl 1,Refl

every additive component of the signal disappear; this fact shows that magnitude and phase

images obtained with lock-in system are independent from external reflections;

 from external uneven lighting and from object’s

single phase image is also independent

emissivity as well as from external reflections.

method’s theoretical analysis allows to predict field’s depth, which depends on thermal

Lock-in the

. 

diffusion’s length heat transfer’s general

An expression for may be obtained by solving the

differential equation for a harmonic excitation that, in one-dimensional case, leads to the following

expression:  c

 

x c



 

2 k

T ( x , t ) T e cos( t x )

o 2 k

where:

 3

is density [Kg/m ];

c is specific conductivity [J/Kg K]

k is conductivity [W/m K]

 = 2 is pulse [rad/s]

 2

= kc is thermal diffusivity [m /s]

Thermal wave’s amplitude, that attenuates itself with an exponential law, reduces to (1/e), that is

:

37% of its original strength, when x = 15

2

k

  (3.11)

 c ,

shows that thermal diffusion’s length as well as wave’s amplitude

The expression (3.11)

 c

 x 

, depends not only on material’s specific parameters (k,

2 k

T e , c) but also on modulation

o 

frequency ( ). This last link is more evident if the expression (3.11) is rewritten as follows:



  (3.12)

 f

the thermal diffusion’s length,

In Tab. 3.1 there are many values of for various materials and

frequencies.

The presence of a defect is underlined through the phase difference between integrated zone and

lacked one or through amplitude difference; results are shown as phase and/or amplitude images.

About amplitude image, the field of depth is equal to thermal diffusion’s length, while for the phase

image it is about 1,8 times that length because of substantial non sensitivity to external factors.

material limits object’s solvable dimension in a measure as

However, thermal wave spread through

.

greater as diffusion’s length Therefore, since spread is more evident at low frequencies, spatial

resolution reduces when we observe material’s deeper layers.

MATERIAL 1 Hz 0.47 Hz 0.12 Hz 0.03 Hz

5.6 8.2 16 32

Aluminum 0.52 0.76 1.5 3.0

Alumina Al O

2 3 6.46 9.42 18.65 37.30

Copper 1.18 1.72 3.41 6.81

Steel 18/8 Cr/Ni 0.76 1.11 2.19 4.39

Steel 2% W 1.6 2.3 4.6 9.2

Titanium 0.526 0.767 1.52 3.04

Glass 0.2 0.29 0.58 1.15

PVC 0.149 0.217 0.43 0.86

Teflon 0.8 1.17 2.31 4.62

Parall. carboresin 0.375 0.547 1.08 2.17

Orthog. carboresin 0.232 0.338 0.67 1.34

Parall. fiberglass 0.22 0.32 0.62 1.3

Water

– Thermal diffusion’s length

Tab. 2.1 in millimeters for various modulation frequencies.

16

3 Experimental investigation

Tests have been carried on in the DIAS (Dipartimento di Ingegneria Aerospaziale) Gasdynamics

Laboratory.

3.1 Description of samples

Several CFRP samples were analyzed, which were fabricated at C.I.R.A. (Centro Italiano Ricerche

Aerospaziali) have been analyzed through non destructive control by lockin thermography. During

the production process, the samples have been divided into 4 types as shown in Table 3.1

The samples tested in this thesis work are of different stacking sequence and are simply named: P1,

P2, P3 and P4; details are collected in table 3.1.

Type Stacking sequence N° plies

P1 [0°] 24

P2 [90°] 24

P3 [45°/-45°] 24

s

P4 [45/0/-45/90/45/0/-45/90//90/-45/0/45/90/-45/0/45] 32

–

Tab 3.1 .

Samples type with relative stacking sequence and number of plies

In particular, samples were fabricated using a material made up of plies of unidirectional pre-preg

M21/IM7 supplied by HEXCEL, that represented the base element for plies composite manufacture

by the Hand Lay-up technique. This pre-preg is cut to obtain plies of 10cm x 5cm.

For each of this type individuated by the sequence of plies it is carried out another differentiation of

the productive process through the different pressure used during the curing cycle. The pressure

percentages are: 100%, 50%, 25% and 0%. This work wants to observe how fiber orientation effects

porosity distribution and defect detection as well.

During the manufacturing process inside each samples, in the half part, as sketched in Fig.3.1, is put

a Teflon disk 20 mm in diameter and 0,0625 mm thickness, to simulate delamination.

Fig. 3.1- Sample sketch

The thermographic analysis is carried out with lock-in thermography in reflection, or better the

infrared camera frames the same side of the sample that the lamp stimulates thermally, or in

transmission for which the camera views the side opposite to heating.

17

The analyzed samples show a rough side, resulting to be the one in contact with the bag during the

be named respectively “rough side” and

manufacturing step, and a smooth side. Both sides will

“smooth side”.

3.2 Testing procedure

The used instrumentation include (Fig. 3.2):

 Thermacam FLIR SC6000

 Frequency Modulator

 Halogen lamp of 500 W;

 Computer ;

 Software to process data IrNDT (1.7.0.0);

 CFRP sample.

The test campaign starts analyzing the samples at 100% of pressure, and goes on analyzing the

other samples at the lower curing pressure. Each sample has been analyzed from both smooth and

rough sides. It is to underline that the smooth side mostly created troubles because of reflections

from the surrounding during the lab test.

Considering an average value of for the thermal diffusivity, from the

relationship:

it is possible to estimate the frequency value: 18

3.3 IrNDT (1.7.0.0)

The software used is the IrNDT, which was developed by Automation Technology.

This software is made up of a modular structure; each module corresponds to a different kind of

analysis. In this work is used the Lock-in thermography module. This module allows the user too

personalize several parameters for both the acquisition of images and the analysis of them.

Fig 3.2- Initial screen of IrNDT

Figure 3.2 shows the initial screen of the program, once selected the lock-in module. As can be

seen, on the left side (Fig. 3.3) are customizable parameters for image acquisition:

 Stimulation thermal or lock-in frequency;

 Acquisition duration;

 Acquisition frame rate; 19

–

Fig. 3.3 Acquisition parameters

On the right side (Fig. 3.4), instead, it is possible to set parameters that concern the analysis of the

sequence of image obtained:

 type of representation of the results (image Phase or amplitude);

 Number of images to be included in the analysis;

 Method of data processing (Harmonic Approximation frequency or Single Discrete Fourier

Transform);

 Phase correction Fig. 3.4 - Parameters of image analysis

The three parameters related to the acquisition of the images are easy to understand, while the three

on the analysis deserve further details.

The first parameter allows choosing between phase or amplitude image. For our analysis we

selected phase images, since these are not affected by uneven lighting, reflections from outside or

from changes in emissivity of the object. 20

The second parameter allows selection of the images to be used in the elaboration process.

There are two processing methods, which can be selected. One is the Harmonic Approximation that

is the classic method used in lock-in thermography. The other method Single frequency DFT,

however, uses the discrete Fourier transform, which allows to change the domain from time to

frequency, in order to derive the values of phase and amplitude. Also in this case, we decided to

apply the same criterion for the entire survey, using the Single frequency DFT method. This choice

was made also in consideration of the research carried out by F.J. Madruga, who shows that the

DFT method provides a better signal over noise ratio and that, contrary to the classical one, does not

give rise to the formation of the so-called Bad Pixels (pixels of abnormal color).

The command Phase Correction, finally, allows to set the reference phase in order to increase the<