Plate-like structures made of composite materials are becoming increasingly common in aerospace industry, ground transportation, civil engineering, etc. They are often over-designed to compensate for a lack of efficient techniques for evaluating the initial integrity of the mechanical structures and/or for a reliable monitoring of damage and aging.
Established ultrasonic techniques for Quantitative Non-Destructive Evaluation (QNDE) rely on a wide variety of different wave propagation mechanisms. In particular, Rayleigh waves (RW) are used to detect subsurface flaws in thick plates, while Lamb Waves (LW) are by far the most used in thin plates inspection, since they can explore the entire thickness of the plate and propagate a long distance without appreciable attenuation. However, LW testing is generally complicated by the coexistence of at least two modes at any given frequency and by the strongly dispersive nature of these modes at high frequency. Furthermore, a single and pure Lamb mode may generate a variety of other modes either by interacting with a surface or subsurface flaw or by crossing the interface between two materials of different impedance . As a consequence the output signal becomes richer, but often very difficult to interpret and a detailed physical analysis of the propagation mechanism may be of great interest[2-3].
Given the wave frequency, thickness and physical properties of the plate material, we simulate, using the Local Interaction Simulation Approach (LISA) [5-8], the interaction of LW's with various kinds of defects. Simulations can be performed not only to suggest new experiments but also to provide an interpretation of existent experimental results. A comparison between experimental and simulated results may be very instructive and is certainly of interest.
In particular, in the framework of the European project DAMASCOS (Damage Assessment in Smart Composite Structures), we are interested in simulating damage phenomena in composite materials in order to optimize the interrogation frequency and use of propagating modes.
RESULTS AND DISCUSSION
In the present contribution we simulate the propagation of LW's through a composite plate (3 mm thick) initially intact and then damaged by a passing-by hole of diameter ranging from 1 to 10 mm. This simple, well defined defect geometry was chosen in order to validate our method and obtain a quantitative comparison with experimental results in a controlled and reproducible case. The material sample considered is a Carbon Fiber Reinforced Plastic (CFRP) plate. The ultrasonic source/sensor configuration is schematized in Figure 1. The experimental results considered for the comparison were produced within the DAMASCOS partnership, in particular by INSA Laboratoires of Lyon, France, and University of Valenciennes (VA), France.
Fig 1: |
In Figures 2a, 2b and 2c we present snapshots at a fixed time (t = 126 m s) of the out-of-plane displacement components of the LW propagating in the plate in the cases of 1, 4 and 10 mm holes, respectively. In these plots both the faster S0 and the A0 modes are visible. The S0 mode is seen already reflected back from the edge of the specimen. The interference pattern caused by the defect is clearly visible. However, in order to quantitatively highlight the differences between the faulted and reference (unfaulted) cases, we show, in Figure 3a, 3b, 3c, the "signature" of the hole, i.e. the difference between the displacement maps of the damaged and undamaged case. Note that the amplitude range in the grayness scales is (-0.01,0.01) in the upper plot, (-0.1,0.06) in the middle plot and (-0.15,-0.08) in the bottom plot. Thus, as expected, the greater the hole diameter, the greater its signature.
Fig 2a: ||
Fig 2: Map of the out-of-plane component of the displacement at the time t = 126 ms. From top to bottom: plate with a hole of ø = 1, 4, 10 mm, respectively.||Figure 3: "Signature" of the defect. From top to bottom: plate with a hole of Æ = 1, 4, 10 mm, respectively. Notice the difference in the grayness scales. |
Figure 4 shows the comparison between the S0 signals at the receiver obtained from our simulations (continuous line) and INSA experimental data (dotted line) for the unfaulted plate (upper plot) and for the plate with the 10 mm-hole (lower plot). We can observe a good quantitative agreement between synthetic and experimental results.
Fig 4: Temporal signals at the receiver: comparison between our simulations (continuous line) and INSA experimental data (dotted line) for the unfaulted plate (upper plot) and for the plate with the 10 mm-hole (lower plot).|
The S0 Lamb mode spectrum amplitude maximum and time shift versus hole diameter are shown in Figure 5, displaying a quantitative comparison between simulation (continuous line) and experimental results (INSA: dotted line; VA: dashed line). (By courtesy of Thomas Monnier.)
|Fig 5: S0 Lamb mode Spectrum Amplitude Maximum and Time Shift versus hole diameter (continuous line: simulations; dotted line: INSA; dashed line: VA) in GRP. By courtesy of Thomas Monnier.|
This work was supported by the European Community through a Brite EuRam Grant (project No BE-97.4213 ''DAMASCOS''), and by the INFM Parallel Computing Initiative. In addition, the authors wish to thank Drs. T. Monnier (INSA Laboratoires, Lyon, France) and S. Grondel (University of Valenciennes, France) for allowing us to include here their experimental results and for fruitful discussions.
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