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Title: Optimized Actuator/Sensor Combinations for Structural Health Monitoring: Simulation and Experimental Validation Authors:
R. Sridaran Venkat 1 C. Boller 1 Nitin. B. Ravi 2 N. Chakraborty 2 G.S. Kamalakar 2 Kishorkumar Ukirde 2 D. R. Mahapatra 2
1
Chair of Non-Destructive Testing and Quality Assurance (LZfPQ), Saarland University, Saarbrücken/Germany 2 Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012 India PAPER DEADLINE: **May 15, 2015** PAPER LENGTH: **8 PAGES MAXIMUM **
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ABSTRACT Improved structural integrity of engineering structures is one of the key features of having a reliable Structural Health Monitoring (SHM) system with regard to Damage Tolerant Design (DTD). Modelling of damage, its predictive analysis as well as numerical simulations to model wave propagation in case of ultrasonic based guided wave methods are possible using commercial Finite Element Methods (FEM) based software. Such software are computationally intensive and lack major importance on SHM aspects such as probability of damage analysis with respect to DTD and actuatorsensor optimization with respect to NDT methods. Bridging both the DTD and NDT simulations in a single simulation package can aid better understanding of the various physical processes involved in the SHM domain. In this paper, we propose a study on an experimental panel where Probability of Damage (POD) analysis is performed and using the information of the damage location and the mesh created to perform such analysis, a guided wave simulation is performed to optimize the actuator-sensor locations so that the sensors mounted can capture the signal carrying the signature of the defect present in the component. An experimental study is performed to validate the simulation results. The simulation tools to be used will be commercial or close to commercialization which are currently made available through a simulation platform developed under the Indo-German INDEUS project.
_____________________________ R. Sridaran Venkat, LZfPQ, Saarland University, Saarbrücken, Germany C. Boller, LZfPQ, Saarland University, Saarbrücken, Germany,
[email protected] Nitin. B. Ravi, Dept. Aerospace Engineering, IISc, Bangalore N. Chakraborty, Dept. Aerospace Engineering, IISc, Bangalore G.S. Kamalakar, Dept. Aerospace Engineering, IISc, Bangalore Kishorkumar Ukirde, Dept. Aerospace Engineering, IISc, Bangalore D. R. Mahapatra, Dept. Aerospace Engineering, IISc, Bangalore
INTRODUCTION Increasing awarenesss of ageing of structures resulted in the scientific community to develop new inspection paradigms which can reliably monitor the growth of damages present in those structures and predict their remaining life. Structural Health Monitoring (SHM) with the aid of Non-destructive Testing (NDT) methods as a system replaces time-consuming inspection techniques to provide information about the current state of the structure under service. Interestingly, this information conveys existence of damages if present, their locations and their severities. In the recent years, there has been lot of research activities in the development of real-time structural health monitoring systems using Guided waves. The objective of any SHM system is to aid the Damage Tolerant Design (DTD) philosophy by successfully monitoring the damage growth until it reaches the threshold that is defined by fracture mechanics so that the entire structure may it be an aircraft or bridge or building can be effectively and safely utilised throughout its life span. The current situation in SHM domain demands for full-scale simulation which requires following aspects to be integrated: 1. Tools and plug-ins for modeling the geometry of the structure under monitoring. 2. Simulating the crack initiation and propagation due to the actual service loading conditions in order to provide the information on probable damage locations. 3. With the knowledge of the damage locations, the system requires efficient methods to simulate the Guided waves into the structure to design the actuatorsensor configurations for successfully capturing the damage information. DAMAGE TOLERANT DESIGN APPROACH AND NDE Cracks are common in aircraft structures due to various loading scenarios. In order to predict the damage in the structure before failure, the fatigue life calculations are done to justify the reliability during service and to determine the inspection threshold. Consider a stiffened panel with sensors mounted which is an embodiment of a fuselage of an aircraft (Figure 1). Cracks can develop on the component at different locations due to various forces acting on the component. While the location of the crack can be predicted using structural loads and POD map for various fatigue, it becomes important to rapidly and quickly inspect the component to detect the crack before catastrophic failure could occur. A fatigue analysis was performed for the stiffened panel for various crack lengths and for a constant amplitude load. The probable locations of damages are predicted using FE simulation. The indicated location of damage from simulation drives the NDE inspection like ultrasonic simulation where sensors can be mounted near the location of probable damage to quickly identify and monitor the defect. Seven ‘L’ shaped stiffeners of 25.4mm x 38.1mm x 2mm dimensions are riveted to a panel of 1224mm x 1215mm x 2mm dimensions using 5mm rivets and is considered as a test sample. The stiffeners are provided to support the skin and to prevent bending of skin in ‘Z’ direction. One end of the panel is constrained for 6 degrees of freedom (DOF) and on other end, a 21 KN in-plane pressure is applied. The stress analysis is carried out for healthy panel as well as for panels with various crack lengths. The cracks are introduced at rivet location in the center of the panel on the center stiffener. The stress contour is shown in the Figure 2 for various crack lengths. It can be observed from the contours that for undamaged panel (Figure 2a) the maximum stress arises around the rivet hole and these are prone areas for crack initiation.
Figure 1. Stiffened Panel with crack showing loading conditions and sensors mounted for rapid inspection
As crack length increases, stress at crack tip also increases. There are other probable locations where crack can initiate and grow.
a
b
c
d
Figure 2.Stress contours for various crack length
FATIGUE ANALYSIS Generally, the response of structure or component is the starting point for any type of fatigue analysis, which is usually presented in stress or strain time history. If response time history is made up of constant amplitude stress or strain cycles then the fatigue design can be executed by referring to typical S-N curve. When the response time history is iregular with time, then rainflow cycle counting is used to decompose the irregular time history into equivalent stress block loading. The number of cycles in each block is generally recorded as stress-exceedance histogram. This can be used in appropriate damage model to estimate the fatigue life. The probability of damage is detected by performing fatigue analysis for different crack lengths as seen in Figure 3. The stiffened panel is subjected to dynamic loading .The initial crack length was set at 50mm and stress and fatigue analysis was carried out for different crack lengths up to 340mm which is a damage tolerant criteria. The residual strength is then calculated for different crack lengths as shown in Figure 4a.
a
b
c
d
Figure 3.Probability of damage (POD) for various crack length
PROBABILITY OF DAMAGE AND FATIGUE CUMULATIVE LIFE Fatigue life evaluation of mechanical components under complex loading conditions is of great importance to optimize structural design and improve inspection and maintenance procedures. Fatigue damage were estimated by Palmgren-Miner rule. The Miner law is adopted and the damage D is expressed as follows [2] n (1) D i N fi Where N fi is the cycle count at the time of failure under axial loading and is obtained from S-N curve of the material, and ni is the actual cycle count at the adequate stress level. Figure 4b shows the variation in POD with accumulative life of the component.
(a) (b) Figure 4. (a) Residual strength of stiffened panel and (b) Life curve of component
As aircraft undergoes varying stress levels, multiple cracks can occur on the component. Detecting the damages for multiple cracks is difficult through manual inspection. Simulation data can help in identifying multiple damage locations and simulation of NDE inspection can aid in optimizing the inspection process. DEVELOPMENT OF 3D LAMB WAVE SIMULATIONS Ray tracing based method is employed to simulate the propagation of the lamb wave within the material. Ray tracing assumes that the energy emitted from the source is divided into discrete elements called rays whose propagation and interaction with features such as edges and damages inside the material is governed by Snell’s law of reflection and refraction. Propagation of rays in three dimensional medium using propagation of sound wave in air has been discussed in literature [3]. Different ray tracing methods in various media have also been studied [4-12]. To study the effect of the crack and holes on the guided wave generated on the panel, two piezo-electric
sensors, one acting as an actuator and other as sensor operating in pitch catch mode, were placed between two stiffeners equidistant with respect to the crack. Two additional sensors along the line of actuator were placed in the area adjacent to the stiffener line adjacent to the stiffener containing the crack. The sensor locations were strategically located to capture any signal packet containing the signature of the crack and the holes. The schematic of section of the test panel with sensor locations is shown in Figure 1. The simulation was performed on the panel with 50mm crack. By classical methods, a set of rays can be represented by an equation of a line originating from a point, which is given by
x xs d
(2)
where x is a coordinate on a ray originating from xs whose direction vector is given by d and α is distance between original and new point. Consider ray r⃗inc , incident on a surface at an angle θ with a surface normal N as shown in Figure 5.
Figure 5. Determination of reflected ray component along the surface of hole approximated as line segments
The reflected ray component r ref is given by the following equation
r ref r inc (r inc .N ) N
(3)
Since the guided wave is modelled in isotropic medium, only the reflective component of the wave is considered. The magnitude of displacement of wave field at ray origin along with the direction is estimated at the beginning. The field is reevaluated when the ray interacts with boundary features, thereby incorporating the scattering properties of the boundary. The spherical losses due to ray propagation in the medium are also incorporated. The interaction of the ray with the boundary is studied by discretizing the edges of the boundary into finite line segments (Figure 5). The discretizing of the line segments is introduced by the meshing software during meshing of the geometry. The accuracy the scattering effects therefore depends on the size of the line segments. To study the effects of holes and the crack at various sensor locations, only finite set of rays are launched at the actuator. When the actuator is excited, the wave propagates in cylindrical manner. So it is assumed that the energy is distributed equally in all the directions. Therefore only a fraction of energy is considered along the ray path. An additional condition that only the rays which will reach the sensor after interaction with the boundary was imposed during simulation. This was done to identify the rays that will be incident on the sensor after reflection from the holes and the crack. For the signal to interact with various boundary features on the sample, it is important that the wavelength of the signal launched at the actuator match the dimensions of the features to be captured. Such a condition was also imposed during simulation.
RESULTS AND DISCUSSION The signal was simulated at 310 KHz for a 2mm thick Aluminum plate. Appropriate transfer function was used to convert the actuator signal into displacement field and appropriate scattering models for reflections from cracks and rivets was used at crack location and holes to model the signal. A receiver transfer function was used to convert the displacement field into voltage signal at the sensor. All the signals were unit normalized for comparison. To validate the simulated signal, signals were measured using data acquisition systems by mounting sensors at locations used in simulation model. Figure 6 shows the comparison between the signals generated through ray tracing model and actual signal measured by Sensor -3 using data acquisition system for a healthy and damaged sample. The difference observed in the present simulation are attributed to the approximation that scattering is only due to the rivet hole whereas, in actual and experimental case a large amount of scattering is observed which could be due to stiffener edges. Further detailed insight regarding this aspect will be reported in future investigations.
(a) (b) Figure 6. Comparison between signal generated through RTSFEM model and experimental signal measured at Sensor-3 on (a) sample with no crack, (b) sample with 50mm crack
Figure 7. Experimental validation using LDV.
To study the placement of actuator and sensor, a 3D Laser Doppler Vibrometer (LDV) was used to monitor the wave propagation in the damaged sample. It can be seen that a signal packet gets reflected due to crack (Figure 7e, 7f) and by placing a sensor at that
location, the packet reflected due to the crack will be captured at Sensor -1 (Ref. Figure 1). Figure 8 shows the signal captured using data acquisition system at Sensor-1 and Sensor-2. The effect of the crack is evident in Figure 8a.
(b) (b) Figure 8. Signal packets at Sensor-1 and Sensor-2
SENSOR OPTIMIZATION THROUGH FEM USING COMSOL Finite element method based COMSOL tool is used to simulate the Guided wave propagation into the structure. The objective of this method is to record the wave propagation at regular intervals with and without damage. The panel in Figure.1 is modeled in COMSOL and fine triangular mesh of 2mm is used. Courant Friedrichs Lewy (CFL) criteria must be satisfied in order to get the stability while solving PDEs and as a result minimum time step of 1μs is applied. Maximum element size is taken λ/12 mm. Structural mechanics module along with boundary load is applied on the actuators. The differential images of wave propagation of undamaged and damaged conditions reveal points of maximum constructive interferences and minimum destructive intereferences on the test object. Based on this condition, the piezo-patches can be placed on the structure under monitoring. Fig 9.1 and 9.2 show the Guided wave propagation at different time intervals and Fig 9.3 shows the corresponding differential images.
undamaged
damaged
crack undamaged
damaged
Fig 9.1 and 9.2 Wave propagation at 40μs and 60μs
40μs
crack 60μs
Fig 9.3 Differential images for 40 and 60μs
CONCLUSION A representative aircraft component was considered and, stress and fatigue analysis was performed to identify a potential crack location and POD. Using this information, guided wave simulation using ray tracing was performed to visualize signal at various sensor locations and experimental validation was performed. Laser Doppler Vibrometer was used to identify potential sensor locations to capture the signal reflected from crack. Guided wave propagation using FEM based COMSOL models described to see the differential images of the base signal and damaged signals during the wave propagation taken at regular intervals. This allows one to place the sensors at maximum intensity points due to the constructive interferences. The same technique can be adapted to validate the results from RT-SFEM approach and LDV data. ACKNOWLEDGEMENT The authors would like to acknowledge the financial support by Indo-German Science & Technology Center (IGSTC) for this work. They also acknowledge Rathod. for his scattering models, Ganesh K.G, for his help in experimentation using LDV, Mirko S. for his help on identifying samples, and support from IMA and TechM. REFERENCES S Ariduru, “Fatigue Life Calculation By Rainflow Cycle Counting Method" Stevan Maksimovic, "Fatigue Life Analysis of Aircraft Structural Components ", ScientificTechnical Review,Vol.LV,No.1,2005 3. Andrzej Kulowski, "Algorithmic Representation of the Ray Tracing Technique", Applied Acoustics, 18 (1985) 449-469 4. J.A. Ogilvy, "Ultrasonic beam profiles and beam propagation in an austenitic weld using a theoretical ray tracing model," Ultrasonics, 1986 Vol 24 November, 337-347. 5. J. A. Ogilvy, "A layered media model for ray propagation in anisotropic inhomogeneous materials", Appl. Math. Modelling, 1990, Vol. 14, May, 237-247. 6. J. A. Ogilvy, "Ultrasonic reflection properties of planar defects within austenitic welds", Ultrasonics 1988 Vol 26 November, 318-327. 7. Sanjeevareddy Kolkoori, Christian Hoehne, Jens Prager, Michael Rethmeier, Marc Kreutzbruck, "Quantitative Evaluation of Ultrasonic C-Scan Image in Acoustically Homogeneous and Layered Anisotropic Materials using Three Dimensional Ray Tracing Method", Ultrasonics, 54 (2014) 551–562. 8. J. A. Johnson, N. M. Carlson, and D.M. Tow, "Ray Trace Calculations of Ultrasonic Fields", Res Nondestr Eval, (1991) 3:27-39. 9. J. Sadler, R. Gr. Maev, "A ray technique to calculate reflected and transmitted waves", Ultrasonics, 48 (2008) 687–696. 10. M. Brigante, "On multiple scattering in acoustic media: A deterministic Ray Tracing method for random structures", Ultrasonics 53 (2013) 652–657. 11. V. Schmitz, F. Walte, S.V. Chakhlov, "3D ray tracing in austenite materials", NDT&E International, 32 (1999) 201–213. 12. Nitin B. Ravi, Vivek T. R, Nibir C, D.R Mahapatra, Ramanan Sridaran, Christian Boller, Proc. SPIE 9437, Structural Health Monitoring and Inspection of Advanced Materials, Aerospace and Civil Infrastructure 2015 1. 2.
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