Abstract
In the present paper, ultrasonic testing of composite materials for aeronautical applications with intra-laminar cracks is investigated experimentally and by numerical simulations. For this purpose, different specimens were used. An ideal specimen without any crack and two specimens with cracks synthetically generated.
The experimental measurements were done with normal piezoelectric longitudinal and surface wave ultrasonic transducers in Pulse Echo and Trough Transmission configuration. For better interpretation of the received signals, wave propagation in the cross section of the rail was modelled numerically using a FEM code which was adapted to the special testing situation. The simulations are in good agreement with the experimental results for all specimens dealt with.
This activity is a part of our contribution at BRITE EURAM "INDUCE - Advanced Integrated NDT Concepts for Unified Life-Cicle".
Introduction
One of the primary challenges of the aeronautical industry is the tireless adaptation of increasing quality levels to costs and cycles reduction imperatives. This challenge - common to other industrial sectors such as energy, medical and transportation in general - can be met, among other things, by the adoption of Unified Life-Cycle Engineering concepts that merge aspects of concurrent engineering and total quality management around the design.
To make this objective feasible, INDUCE is fundamentally centred on:
The modelling of the items involved in the nondestructive inspections (materials, defects, structure excitation, response of equipment) and of their mutual interactions.
The development of advanced non-destructive techniques and analysis methodologies
The development of tools for integration among different techniques and of NDT modelling with CAD systems.
The simulation of US technique of analysis by means of a numerical model, can supply an important support for the laboratories in which this type of control are come true experimentally. The simulation allows verifying the reliability of some inspection techniques, in particular it allows to optimise the parameters that concurs in the control, (p.e. the frequency of the ultrasonic beam). It moreover allows to optimise the setting of the testing line.
With the numerical model, knowing the technical characteristics of the transducer, we can preview which are the defects that experimental inspection should find.
All these preliminary considerations would concur to strongly reduce the operating costs and to optimise the human and instrumental resources.
The numerical model has been implemented using a FEM code interpreted from ANSYS program, while the study of the ultrasonic pulse and its frequency spectrum have been realised by means of the Matlab program. We reproduce a non-destructive testing by ultrasounds, simulating the Pulse Echo technique as well as the Through Transmission technique.
Numerical Model
Fig 1: The simulated pulse load and its frequency spectrum.
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The propagation of an ultrasonic beam has been simulated in various means of propagation, isotropic as well as anisotropic, also in presence of defects. They have been simulated several prototypes of the model that differ for the means property and the characteristics of the ultrasonic pulse. The simpler prototype consists in the simulation of the propagation of a pressure pulsing in an homogenous and isotropic means. Particularly interesting is the model of the propagation of an ultrasonic beam in a laminated composite. The numerical model of the ultrasonic pulse has been come true (see figure 1), realising a pressure wave with a profile and one frequency spectrum with similar characteristics to those of the beam generated from the real transducers.
In order to carry out a verification on the reliability of the result supplied from the model, it has been constructed ad hoc a test specimen in laminated composite to carry out of the experimental verifications (see fig.2).
The specimens has been realised overlapping 17 ply of the thickness of 0,125 mm; each ply has made by carbon fibres in polymer resin with following lamination sequence:
[0/45/90/-45/0/45/90/-45/0/45/90/45/0/-45/90/45/0]
There are present some insert of Teflon at different thickness, as is shown in the fig.2.
Fig 2: Test Specimen used for the validation of the model |
The modelling of this material has been executed ply per ply. The elastic property of each ply was calculated using the micromechanics formulas.
Fig 3: Grid simulation of the specimen.
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In order to reproduce the propagation of the ultrasonic pulse in composite material it has been made an Transient Analysis (Time History). The ultrasonic pulse has been simulated as dynamic load of pressure. In the reality, when inspection is made using the Pulse Echo technique and longitudinal waves, the transducer is placed perpendicular to the surface of the specimen, a part of the ultrasonic beam generated propagates inside the material, while another part is reflected, following the Snell law. The same effect have a discontinuity that the residual beam can find during its propagation inside the thickness. The signal that come back to the transducer is transformed in an electrical pulse that is shown by the oscilloscope. Studying the time history of these signal it is possible to determinate the structural integrity of the materials.
In the simulation the point of the specimen where the beam impact is represented by the element on which the dynamic load is applied, while in order to find the pulse that it returns on the transducer, it reads the acceleration of the nodes of the element in correspondence of the point in which the presence of the transducer is simulated.
Result and Experimental Validation
In order to carry out a validation of the result reliability supplied from the model, it is compared the result coming from an inspection executed in Pulse Echo on a real specimen, and the result supplied by the numerical model. In the figure 4 we show the result of a inspection made with an ultrasonic beam with frequency of 5 MHz. In particular in the image show the signal coming from the transducer placed in correspondence of a insert of Teflon and having a section of 5x5 mm and of 0.025 mm of thickness, situated 5 ply under the surface.
Fig 4: Pulse Echo inspection: results coming from specimen.
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Fig 5: Output coming from the FEM simulation
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Fig 6: Representation of the stress in the z direction at 1 msec from the Entry Echo.
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The figure 5, instead, show the output of the numerical model. The acceleration of a node of the element affected by the ultrasonic beam is a parameter that can reproduce qualitatively the signal received by the transducer (see figure 5). Also the stress is a significative parameter to monitorate in the beam propagation direction, in order to reproduce the physic of the problem.
In order to supply a three-dimensional visualisation of the propagation of the ultrasonic beam inside the specimen, in figure 6 we show the stress in the z direction, in an area of the specimen mainly involved in the propagation. This figure show the stress situation 1msec after the Entry Echo.
Limit of the model
The limit of the model is that in order to realise the simulation of the propagation of an ultrasonic wave in a material, is necessary to discretise the dominion of propagation (that is continuum) in finite elements. In order to have a realistic reproduction of the wave propagation the discretisation of the dominion have to be at least 20 elements per wavelength. This means that for the simulation of the ultrasonic beam propagation with characteristic frequency of 5 MHz, it is necessary to use a grid with more than 104 elements.
That involves calculation times very high!
10 elements/wavelength in the space and 0.02 msec as step integration well reproduce the propagation. With these parameters the time of calculation for a HP 9000 735 is approximately 10 hours and the used memory in order to store the result of the analysis 500 Mb.
Points of Force
A point of force of this model is the good versatility that concur to easily modify the thickness of specimen, the dimensions of the defect (p.e. the thickness of the delamination), the frequency and the intensity of the ultrasonic beam. But an important aspect is the possibility to simulate the propagation in laminated composites with an arbitrary number of ply and fibres oriented in whichever direction.
Conclusion
The comparison between the result that the models have supplied and the values that was expected from theoretical considerations, has allowed us to conclude that the numerical model has a coherent behaviour with physics of the considered problems. For the validation we have made a campaign of test using ultrasounds with characteristic frequency of 5MHz, on a specimen in laminated. Then we have compared the result obtained from the experimental tests and the result obtained from the numerical model. The result are in perfect agreement.
About the method to determine a coefficient of attenuation of the material to give at model, the result can supply a good forecast of what a test should determine in a US control in laboratory. This concurs to use the model in the aim that us were fixed.
Moreover, with few modifications on the simulation of the ultrasonic beam and on the ways to find the output, we will made, in the near future, an evolution of the study in the direction of simulate other kind of inspection using transversal and surface waves.
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Fig 6: Representation of the stress in the z direction at 1 msec from the Entry Echo.