Saurabh GUPTA and Prabhu RAJAGOPAL *

Transcription

1 8 th International Symposium on NDT in Aerospace, November 3-5, 2016 More info about this article: Interaction of Fundamental Symmetric Lamb Mode with Delaminations in Composite Plate Structures Saurabh GUPTA and Prabhu RAJAGOPAL * Center for Non-Destructive Evaluation and Department of Mechanical Engineering, IIT Madras, Chennai , T.N., India * Corresponding author: prajagopal@iitm.ac.in Abstract This paper addresses a gap in the literature on the 3-dimensional scattering of the fundamental symmetric Lamb mode from delimitations in composite plates. We study the scattering of low-frequency Lamb mode from a delamination in a stiffened 4-ply CFRP composite plate with 0/0/0/0 ply orientation. This work uses three dimensional finite element simulations. The FE simulated in-plane displacement contour obtained from the simulations represents wave propagation in the unidirectional composite laminate and includes complex wave interaction at the delamination region. Far field scattering coefficients for the Lamb mode are plotted as a function of circumferential position around the delamination. Results show that the delamination size has less influence on Lamb wave scattering in the low-frequency where the mode is non-dispersive. Further analysis was done using two-dimensional FE simulation for different ply-layup orientations with Lamb mode. This study shows that ply-layup orientation and through-thickness delamination location in fiber composite laminate have a significant influence on Lamb mode interaction. This work will be useful for practical Lamb wave based inspection of composite plate structures. Keywords: Composites, Finite element analysis, Guided Lamb wave. 1. Introduction Recent investigations of aircraft and space construction techniques have explored the use of composite materials because of their high strength to weight ratio and thermal stability. Composites are made of fibres of different materials in order to increase or decrease the strength of the composite laminate in the required direction. The damages in composites are more critical than metals and their detection is difficult due to the anisotropic nature of the composite laminates. Delamination is one of them and it is the most common defect in composite laminates. In delamination, adjacent surfaces called laminae separate from each other without any obvious visual evidence on the surface. This results in significant loss of strength or stiffness of composite laminate. Therefore, analyzing the effect of delamination and detecting it non-destructively has become a subject of considerable interest. Ultrasonic Lamb waves offer a convenient approach to evaluate composite laminates because they can propagate over a long distance even in materials with a high attenuation ratio and thus a broad area can be quickly examined [1]. Wave propagation in layered anisotropic media is more complex than isotropic materials [1-3]. This makes the detection of defects and scattering analysis difficult in anisotropic materials. Due to the complex wave interaction that occurs when hidden delamination damage is present, extensive research has been carried out on guided wave delamination detection methodologies [3-6]. Authors reported that guided Lamb mode shows less attenuation compare to other modes when it propagates through the laminated composite structures [3,4]. Quantitatively, delamination can be detected in cross ply composite laminates using guided Lamb ( ) wave velocity [4]. It is important to analyze the scattered energy in arbitrary directions for characterizing the delaminations. In this context, a scattering study was done using SDP technique (Scattering

2 directivity pattern) with guided Lamb waves in CFRP quasi-isotropic composite laminate [5]. The results obtained in this study show that scattering amplitude depends upon size as well as through-thickness location of delamination. When guided waves propagate in a delaminated composite structure, multiple reflections can occur within and around the delamination [6-8]. A similar kind of study was done using fundamental symmetric Lamb mode to detect a delamination at various ply-interfaces in a quasi-isotropic composite laminate [9], and a linear relationship was observed between the attenuation of the Lamb mode and the degree of the impact damage. The previously mentioned studies provided an insight to the fundamental physical phenomena of guided Lamb wave interaction at a delamination. They show that guided Lamb mode can successfully used for damage detection and characterization in composite laminates. In this study, we analyzed the scattering coefficients, for 4-ply unidirectional CFRP composite laminate, at the monitoring points taken around the delamination by using fundamental symmetric Lamb mode. It shows that delamination size does not influence on scattering significantly. Furtherr analysis was conducted for 4-ply symmetric and non- ply-layup symmetric composite laminates using two-dimension FE simulation with different orientations [(0/90)] S, [(0/45)] S, [(0/90)] 2, [(0/45/-45/0)], [(0/90/45/-45)] using Lamb mode. These studies show that lamb mode has less influence on delamination size but it strongly depends upon ply-layup orientations and through-thickness delamination location. Reflection coefficients were calculated for all cases studied. This research will be useful for practical Lamb wave based inspection of composite plate structures. 2. 3D FE Simulations of Delaminated Composite Laminates A 3D FE method was used to simulate a 4- ply (0/0/0/0) orientation quasi-isotropic composite laminate with square delamination between ply 2&3 as shown in Fig. 1. A commercial finite element package [10] was used to generate the geometry and perform the meshing operation. A schematicc diagram of the configuration used in the FE simulations is shown in Fig 1. Each lamina is modelled using eight-node 3D reduced integration solid brick elements with hourglass control in which each node has three degrees of freedom. The property of each lamina is given in Table1. Square shaped delaminations in terms of the wavelength (λ S0 ) was modeled at the centre of the composite plate. TABLE 1. Elastic properties of CFRP composite lamina ( ) ( ) ( ) ( ) ( ) ( ) ρ(kg/m 3 ) FIGURE.1. Schematic diagram of the configuration used in FE simulations

3 Figure 2 shows the theoretical phase velocity dispersion curve for a (0/0/0/0) degree orientation CFRP composite laminate in the 0 o propagation direction calculated using Disperse [11]. The dispersion results for unidirectional laminate show thatt fundamental symmetric Lamb mode and the anti-symmetric Lamb mode A 0 exist at the low frequencythickness. How to Use this Template (Second Level (Use the Microsoft Word template style: Heading 2) Heading) A 0 FIGURE 2. Phase velocity dispersion curves for the [0/0] S quasi-isotropic composite laminate (CFRP) at 0 o propagation direction Figure 3 presents typical contour snapshots of FE simulated in-plane displacement magnitude of the [0/0/0/0] degree fiber orientation of CFRP composite laminate. Figure 3(a) shows an instant soon (42µs) after the excitation in which the Lamb wave is generated. Figure 3(b) shows waves scattered by the square shaped delamination. FIGURE.3. Typical snapshots contour of total in-plane displacement for the [0/0/0/0] degree fiber orientations composite laminate at the different time instances. (a) soon after excitation and (b) shortly after Lamb wave interaction with a 0.5λ S0 square delamination located between second and third lamina 3. 2D FE Simulations of Delaminated Composite Laminates A 2D FE method was used to simulate a 4- ply [(0/90)] S, [(0/45)] S, [(0/90/0/90)], [(0/45/- 45/0)], [(0/90/45/-45)] orientation quasi-isotropic composite laminate. A delamination was introduced between the first and second lamina (for remaining cases 2-3 interface delamination and 3-4 interface delamination) with an axis-span of d/λ S0, and distance of L from its left tip to the left beam end as shown in Fig. 4. Monitoring points were taken in far field (more than 5λ S0 ) for all the cases studied. A commercial finite element package [9] was used to generate the geometry and perform the meshing operation. The dispersion results,

4 presented in Fig. 5, for cross-ply composite laminates shows that either the fundamental symmetric Lamb mode or the anti-symmetric Lamb mode A 0 exists at the working. E FIGURE.4. Schematic diagram of the configuration used in 2D-FE A 0 A 0 (a) (b) Higher order modes (c) (d) FIGURE.5. Dispersion curves for various ply-layups (a) [(0/90)] S (b) [(0/90)] 2 (c) [(0/45)] S (d) [(0/45/-45/0)] 4. Results & Discussion Figure 6 represents typical contour snapshots of FE simulated in-plane displacement of the [0/0/0/0] degree orientation quasi-isotropic composite laminate. Various stagess of the wave defect interaction can be seen, ncluding effects such as mode trapping in the delamination. In order to quantify the phenomenon, a scattering coefficient was obtained as the spectral ratio of

5 scattered to incident signal amplitude. Figure 7 shows the scattering ratio for the different monitoring positions and for the various delamination sizes in an overlay plot D FE Simulation Results Energy trapped within delamination FIGURE.6. Snapshots of the contour of total displacement magnitude from 3D FE simulation of Lamb wave interaction with a square delamination 4-ply composite laminate of size (a) λ S0 (b) 0.75 λ S0 (c) 0.5 λ S0 (d) 0.25 λ S0 FIGURE.7.Scattering coefficient of Lamb incident at square delamination of 4 different dimensions (0.25λ S0, 0.5λ S0, 0.75λ S0, λ S0 ) located between second and third lamina in a 4-ply composite laminate Overall, the results show that very little wave energy is reflected from the delamination, for all sizes studied. The 3D wave scattering results show that the delamination size does not influence scattering. Hence, subsequent models are 2D. The calculation cases and 2D FE results shown in Figs. 8, 9 and 10 are listed in Table 2.

6 TABLE 2. Calculation cases and results in this study Cases Incident wave [(0/90)] S [(0/90)] 2 [(0/45)] S [(0/45/-45/0)] [(0/90/45/-45)] Reflected wave Delamination location 1-2 interface 2-3 interface None Small Medium, dispersive None None None Multiple 3-4 interface Multiple reflections Small Small, more dispersive Figure 8 shows the A scans of in-plane displacement of [(0/90) S ] & [(0/90)] 2 ply lay-ups. Figure 9(a), (b) & Fig. 10 shows reflection coefficients for Lamb mode incidence. In-plane lamb wave mode was excited at the source point x=zero, by exciting all the nodes through the thickness, in +x direction as shown in Fig. 4. reflection coefficients were observed when the delamination was located in the 1-2 and 3-4 interfaces Fig. 9(a), (b) for ply lay-ups [(0/90)] S, [(0/90)] 2, [(0/45)] S, [(0/45/-45/0)] vanishing when the delamination is at the mid plane D FE Simulation Results (a) (b) (c) (d)

7 Observe multiple reflections (e) (f) FIGURE.8. In-plane displacements with through-thickness location of delaminations between layers 1&2, 2&3, and 3&4 for CFRP composite laminate (a), (b), (c) for ply lay-up [(0/90) S ] respectively & (d), (e), (f) for ply layup [(0/90) 2 ] respectively (a) (b) FIGURE.9. (a), (b) Reflection coefficients for ply lay-ups [(0/90)] S, [(0/90)] 2, [(0/45)] S, [(0/45/-45/0)] upon incident of Lamb mode. reflections at the delamination (mid-plane interface) can be observed for the fully non-symmetric composite laminate [(0/90/45/-45)] as shown in Fig. 10. Multiple reflections were observed within and around the delamination due to discontinuity in Lamb mode propagation, at the entry and exit of the delamination. The detailed physics of this phenomena is studied in more detail. Reflection at mid plane FIGURE.10. Reflection coefficient for ply lay- up [(0/90/45/-45)] upon incident of Lamb mode

8 5. Conclusions FE simulations were conducted for 4-ply unidirectional and cross ply CFRP composite laminates. The 3-dimensional scattering describes that there is less influence of delamination size upon Lamb mode interaction. For all cases studied, 2D FE simulation results show that the reflection coefficient strongly depends upon ply-layup orientation and through-thickness delamination location. This study shows that it is difficult to detect the delamination when it is present at the mid plane of the composite laminate for all the cases except [(0/90/45/-45)] ply-layup orientation with incident of Lamb mode. Multiple reflections were observed at non-symmetric delamination location site in the received signal with Lamb mode. The outcome of this study will be helpful for study of interaction of guided Lamb modes with delaminations in laminated composites with varying ply-layups. References 1. A. Raghavan and C. E. S. Cesnik, Shock Vib. Digest, 39, (2007). 2. P. Rajagopal and M. J. S. Lowe, J. Acoust. Soc. Am, 124, (2008). 3. N. Guo and P. Cawley, J. Acoust. Soc. Am, 94, 2240 (1993). 4. N. Toyama, J. Noda and T. Okabe Composite Science and Technology, 63, (2003). 5. C. Ng and M. Vedit, J. Acoust. Soc. Am, 129, (2010). 6. T. Hayashi and K. Kawashima, Ultrasonics, 40, (2002). 7. R. S Panda, P. Rajagopal and K. Balasubramaniam, An Approach for Defect Visualization and Identification in Composite Plate Structures Using Air-Coupled Guided Ultrasound, in Review of Progress in Quantitative Nondestructive Evaluation, (American Institute of Physics 1650, Melville, NY, 2015), pp Z. Su, L. Ye and Y. Lu, J. Sound Vib, 295, (2006). 9. Birt. E. A, NDT and Condition Monitoring, 40, (1998). 10. See for ABAQUS Analysis User s Manual, Version ; accessed 28 July DISPERSE user's manual, version (2001).