Rayleigh Wave Interaction and Mode Conversion in a Delamination

Transcription

1 Rayleigh Wave Interaction and Mode Conversion in a Delamination Sunil Kishore Chakrapani a, Vinay Dayal, a and Jamie Dunt b a Department of Aerospace Engineering & Center for NDE, Iowa State University, Ames, b Department of Aerospace Engineering, Iowa State University, Ames, Iowa, Abstract. The interaction of Rayleigh waves with a delamination in a fiber reinforced composite plate was analyzed in the present work. Rayleigh waves interacting with delamination, mode convert into Lamb waves in the delamination zone. These guided Lamb modes have the capability to mode convert back into Rayleigh modes when they interact with the edge of the delamination. Unidirectional glass/epoxy laminate with delamination of known size was fabricated and tested using air-coupled ultrasonics. Finite element models were developed to understand the various mode conversions. Experimental and numerical A-Scans, mode velocities were used to identify each mode. A good correlation between experimental and numerical results was observed. Keywords: Nonlinear, Composites, Nonlinear Elastic Wave Spectroscopy PACS: Dc, Ba, Gf, Zx INTRODUCTION Damage detection in composites has been of focus since the advent of composites. Macro-scale damage like delamination can be very difficult to detect in very thick composites. As the use of composite for fabricating large structures keep increasing, detecting damage in such structures becomes very vital. Use of conventional ultrasonic techniques for damage detection becomes difficult due to attenuation by multiple layers at higher frequencies. Recent studies [1] has shown that Rayleigh waves can be effectively used to detect sub-surface defects. These waves are generated using air coupled ultrasonics operating at relatively low frequencies, i.e. <1MHz, therefore the wave does not suffer attenuation and has a longer wavelength. Since Rayleigh wave sensitivity is a function of its wavelength, a longer wavelength would help in inspecting thicker structures. Stress wave interaction with delamination has been of considerable interest. Some of the primary work in the field of stress wave interaction with delaminations was performed by B. A. Auld and M. Tan [2] who predicted the reflection of Lamb modes from vertical delaminations. Later, S. Rokhlin [3] studied the Lamb mode diffraction in different delaminations placed at the mid-plane. N. Guo and P. Cawley [4] have published the work on the interaction of the fundamental S 0 Lamb mode with delamination in a cross-ply laminate at different depths. Ramadas et. al. [5] showed the mode conversions which occur when the fundamental anti-symmetric and symmetric modes interact with delamination using finite element techniques. Further G. Shkerdin and C. Glorieux [6] used modal decomposition technique to show the various Lamb mode conversions in a plate with delamination. Numerical models were created to study multi-mode interaction and mode generations. Rayleigh to Lamb conversions were also given special attention. The present study deals with the interaction of a Rayleigh wave with delamination. The primary Rayleigh wave upon interacting with the leading edge (wave propagating from left to right as described in later sections) of the delamination, mode converts into the fundamental Lamb modes in the upper section of the delamination. The Lamb mode interacts with the trailing edge of the delamination to reconvert back into a Rayleigh wave. Finite element models were used to capture this phenomenon and unidirectional glass/epoxy laminate with delaminations were fabricated to validate the theoretical models. The sample was designed so that only the fundamental Lamb mode can be excited in the delamination. This approach makes it easier for the experimental-theoretical correlation. EXPERIMENTAL SETUP AND SAMPLE PREPARATION All experiments were carried out on a 30mm unidirectional laminate. A delamination was created by placing a film of release film in between dry fiber layers. Vacuum assisted resin transfer molding (VARTM) was used to cure

2 the epoxy and fibers. Once cured the release film was pried open to mimic a true delamination.. The delamination dimensions are 50mm (L) x 50mm (W) x 1.4mm (T). The chosen thickness of the delamination can only generate the fundamental Lamb modes, i.e. A 0 and S 0. The experimental setup consists of a pair of air coupled ultrasound transducers supplied by Ultran. A square wave pulse at 200 khz from 5077 pulser-receiver was used as the excitation source. An auxiliary amplifier supplying 40dB was used to improve the signal to noise ratio. A 12 bit digitizer was used to capture waveforms and store it in the computer. Figure 1 shows a schematic of the setup used. FIGURE 1: Schematic of the experimental setup along with delamination at the edge of the sample. NUMERICAL MODEL To confirm the experimental findings and understand the various mode conversions, a finite element model was created. A half space with layered media was modeled using 8 node, 2D, plane strain elements. The composite properties listed in TABLE 1 was used for modeling purpose. A delamination was created using the zero-volume method as described in earlier work [4,5]. Wave propagation analysis was performed using a 200 khz tone burst with hanning window. A nodal excitation was given in the form of out-of-plane displacement. A-Scans were extracted from various locations of the model to compare with the experimental results. The delamination considered in the FEM model is shown in Figure 2. FIGURE 2: Finite element model of a half-space with delamination.

3 TABLE 1: Mechanical properties of the laminate. Property Value E x GPa E y 6.90 GPa E z 6.90 GPa ν xy ν yz ν xz G xy 3.06 GPa G xz 3.33 GPa G yz GPa ρ 1990 Kg/m 3 RESULTS The analysis can be split into 3 sections as shown in Figure 3. Section 1 is a layered half space where only Rayleigh wave generation is possible. Section 2 can be split into Section 2a which is the region above the delamination and Section 2b which is the layered half-space below the delamination. Section 3 is the half-space following the trailing edge of the delamination. Each of these sections are analyzed in detail. FIGURE 3: Schematic of the different sections considered for analysis. To be consistent with some of the previous work [6, 7] and for clarity of presentation, each of the newly generated modes is given a different name. The primary excited mode is mentioned first, and the subsequent generated modes are listed from left to right. The current mode is the one which is mentioned last. Subscript generally denotes the mode type, although for Rayleigh waves it is simply used to distinguish between Rayleigh modes in different sections. For example, R 1A 0 denotes the fundamental A 0 mode generated from the primary Rayleigh wave. This naming convention is consistent with previous published work. [6, 7] Section 1 The section is a layered half-space, where Rayleigh waves can propagation. Since there is no delamination, there is no discontinuity and hence only Rayleigh wave can exists. The propagation will be equivalent to that of a defect free plate. To experimentally obtain the Rayleigh modes, the air coupled transducers were orientated at 14 degrees. This was done by optimizing for maximum amplitude. The numerically simulated and experimentally measured response is shown in Figure 4.

4 FIGURE 4. A-Scans extracted from Section 1 showing the primary Rayleigh wave. (a) Numerical response, (b) experimentally measured response. Section 2 This section can be split into the region above the delamination, which is a layered thin plate with stress free boundary conditions and region below the delamination which is a layered half-space. Section 2.a This section encompasses the entire delamination, i.e. the leading edge and the trailing edge of the delamination. Since this section is a thin plate, the Rayleigh wave has a tendency to mode convert into a Lamb wave. The incoming Rayleigh wave R 1 from Section 1, interacts with the leading edge of the delamination and mode converts into the antisymmetric mode R 1A 0 and symmetric mode R 1S 0. Since the Rayleigh wave has a higher out-of-plane component, large portion of the incident energy is converted into the anti-symmetric mode which has a high out-of-plane component. The numerically simulated and experimentally measured responses are shown in Figure 5. Multiple reflections at the trailing edge of the delamination is possible, but it is not the focus of this research. FIGURE 5: A-Scans extracted from Section 2a showing the mode converted Lamb wave R1A0 and R1S0. (a) Numerical response, (b) experimentally measured response.

5 FIGURE 6. Results from Section 2b showing the Rayleigh mode R1R2. (a) Numerical response, (b) out-of-plane displacement normalized to one wavelength. FIGURE 7: A-Scans extracted from Section 3 showing the mode converted Rayleigh waves R1R2R3 and R1A0R4. Notice R1A0R4 arrives later in time than R1R2R3. (a) Numerical response, (b) experimentally measured response. Section 2.b This section is region below the delamination which is a layered half-space. Hence only Rayleigh wave propagation is possible in this region. The incoming Rayleigh wave, R 1, interacts with the leading edge of the delamination to spilt the energy into section 2.b producing R 1R 2. This mode is not a new mode, but a continued propagation of R 1. But for clarity s sake it is presented with a new name. Since this mode is buried under the delamination, it can only be picked up in the numerical simulation. It is not possible to receive it experimentally. Hence to confirm the mode, the out-of-plane displacement is plotted along with the numerically obtained A-Scan in Figure 6.

6 Section 3 The section following the trailing edge of the delamination, is another layered half-space which is equivalent to a defect free region. The R 1A 0 mode interacts with the T-E of the delamination and mode converts back into a Rayleigh wave R 1A 0R 4 since it is no longer a plate-like structure. The R 1S 0 cannot mode convert back since it has very little out-of-plane component. Hence its mode conversion efficiency is very less. This is consistent with the work performed by G. Shkerdin and C. Glorieux [6]. The Rayleigh wave R 1R 2 traveling under the delamination in Section 2.b interacts with the T-E and due to displacement continuity, it can continue to propagate as a Rayleigh mode on the surface; R 1R 2R 3. The experimentally measured and numerically simulated A-Scan responses are shown in Figure 7. DISCUSSIONS It can be noticed that R 1R 2R 3 arrives earlier than R 1A 0R 4. To understand this response a velocity analysis was performed at various section. Individual A-Scans were collected experimentally and numerically. Using the waveform overlap technique the difference in time of flight was measured. Knowing the distance of the propagation, the velocity was calculated. Further, analytical dispersion curves were plotted as shown in Figure 8. Table 2 shows a summary of the velocities of the various modes. FIGURE 8: Analytical dispersion curve for unidirectional glass/epoxy laminate. TABLE 2: Summary of velocities of the different modes. Mode Name Section Experimental Velocity m/s Numerical Velocity m/s Analytical Velocity m/s R R 1A 0 2.a R 1S 0 2.a R 1R 2 2.b R 1R 2R A 10% difference in velocity can be observed for all modes between the numerical and experimentally obtained data. This can be due to lower material properties or the lack of air coupling during the numerical simulation. But the values between various modes are consistent, i.e. all the Rayleigh modes, R 1, R 1R 2, R 1R 2R 3, R 1A 0R 4 travel with the same speed. This confirms that these are Rayleigh modes although they undergo mode conversions and propagate in different section. The speed of R 1A 0 and R 1S 0 matches very well with the numerically and analytically obtained velocities. It can be observed the R 1A 0 travels at a lower speed compared to R 1R 2. Hence their arrival times at the T- E of delamination will be different. Since R 1R 2 is faster than R 1A 0, it arrives first and can be seen in Figure.

7 CONCLUSIONS The main objective of this paper was to study the Rayleigh wave interaction with a delamination. A preliminary B-Scan showed amplitude and velocity changes over the delamination. Finite element model was developed to understand the mode conversions. The numerical model was validated by fabricating a composite sample with known delamination size and tested using air-coupled ultrasonics. It was observed that primary Rayleigh wave can interact with a delamination and mode convert into anti-symmetric modes. These modes can convert back into Rayleigh modes when they encounter a half-space. All the described mode conversions were supported with experimental and numerical evidence. This work can be used to effectively detect the delamination and also determine the depth of the delamination with the help of Lamb wave velocity. By measuring the speed of A 0 mode, the thickness of the delamination can be determined knowing the frequency. ACKNOWLEDGMENTS The authors wish to thank Daniel Barnard for many helpful discussions during the course of this research. REFERENCES 1. S. K. Chakrapani, V. Dayal, D. Barnard, Res Nondestr Eval, Vol.24 Issue 4. Pp (2013). 2. B. A. Auld and M. Tan, Ultrasonic Symp. Proc. (1977), pp S. Rokhlin, Int. Adv. Nondestr. Test. 6, (1979). 4. N. Guo and P. Cawley, J. Acoust. Soc. Am. Vol.94, 2240 (1993). 5. C. Ramadas, K. Balasubramaniam, M. Joshi, and C. V. Krishnamurthy, Smart Mater. Struct. 18, 1 7 (2009). 6. G. Shkerdin and C. Glorieux, J. Acoust. Soc. Am. Vol. 116, Issue 4, pp (2004). 7. D. J. Barnard, S. K. Chakrapani, V. Dayal, Review of Qualitative non-destructive evaluation (QNDE 2012), Vol 1511, pp (2013).