Finite Element Modeling and Multiphysics Simulation of Air Coupled Ultrasonic with Time Domain Analysis

This paper describes the finite element modelling of air coupled ultrasonic using multiphysics approach. In the model, the two different physics domains were coupled to each other at the interface by using proper boundary conditions for each domain. The simulation result shows that, ultrasonic waves generated in plate structure are leaked to the air medium by creating the pressure wave. The time domain analysis for guided wave in a steel plate with surrounded air demonstrates the presence of the leaky Ao and So modes in air. The simulated result for air coupled ultrasonic was also observed for composite section. Introduction Ultrasonic Testing (UT) [1] is an important Non Destructive Evaluation (NDE) [2] method for inspection of structural materials and components for presence of various kinds of flaws. Conventionally, ultrasonic tests are performed with the help of contact probes. However with the advancement of automation, non contact ultrasonic inspection [3] gained popularity because of its capability to integrate with the automated scanning systems with continuous scanning. Air coupled ultrasonic [4] methods are utilised in various application areas in view of the faster scanning. Understanding of ultrasonic wave propagation and its capability for flaw detection is an important aspect for proper evaluation of wave characteristics for characterisation of material or detection of flaws. This paper describes the two dimensional Finite Element Method (FEM) [5] model for simulation of air coupled ultrasonic. The air coupled ultrasonic is modelled with two different materials namely air and other materials like steel or composites. Different physics are applicable within two different material domains. Hence this multi-physics [6] model required coupling of dependent variables (within two material domains) at the interface. This paper describes in detail regarding the modelling of air coupled ultrasonic. Air coupled ultrasonic In case air coupled ultrasonic, the ultrasonic wave is generated by ultrasonic transducer, and is propagated through air and then gets incident on the material domain. The ultrasonic wave then propagates through the material under inspection which in turn interacts with the flaws and then comes out of the material to the air medium. The transmitted / refracted / reflected signal from the specimen is then detected mostly by another air coupled transducer. The sound wave propagation in air is the physics of acoustics whereas the waves in solid are the physics dealing with generation and propagation of stress wave. In case of waves in air, the physics about the pressure acoustics where the ultrasonic energy passes through the medium of air through pressure waves by transferring the energy by displacement of particles in air. The ultrasonic wave property depends on the properties like pressure, M or e In fo a t O pe n A cc es s D at ab as e w w w .n dt .n et /? id = 15 19 4 temperature, Gas constant of the medium etc. In case of sound wave generated and propagated in solids, the ultrasonic energy is transferred by propagation of stress waves. The sound wave properties depend on the properties of material in which it propagates. The property of the elastic wave in solid depends on the elastic constants of the material under test. So leaving aside the generation of ultrasonic, the propagation and interaction of air coupled ultrasonic basically involves two physical domains, one being air and another is solid material. Finite Element modelling with multiphysics domains The modelling and simulation of ultrasonic wave propagation gives better insights for understanding of wave propagation and its interaction with flaws for their detection. Modelling of ultrasonic propagation is very widely being carried out by Finite Element Method with generation and propagation in single solid media. In that case, a single physical domain remains valid for the complete modelling and simulation of wave generation and propagation. The modelling of ultrasonic wave propagation in the case of air coupled ultrasonic needs to be done separately in two different regions as two different physics are involved for the solution. Hence the air coupled ultrasonic is a multiphysics problem. In case of multiphysics modelling problem, the problem has to be solved in two different physical domains and the continuity of parameters at the common boundary is to be addressed. The boundary conditions at the common boundary are the key to the solution of multiphysics modelling problem. The boundary condition obviously depends on the physics involved in two domains. Modelling of Air coupled ultrasonic In the modelling and simulation of the air coupled ultrasonic problems, there are two domains namely air and solid and there is an interface between two domains. The Finite Element Modelling and simulation of air coupled ultrasonic was carried out with commercially available analysis software COMSOL. To demonstrate the modelling and simulation of air coupled ultrasonic, a case of ultrasonic guided wave in a plate structure was considered. Figure 1 shows the model geometry of the case where a steel plate of 3 mm thickness and length of 300 mm was shown to be surrounded by air of thickness of 10 mm. The air was considered on one side of the model because of computational reason. Figure 1: Model Geometry for modeling and simulation of air coupled ultrasonic The top region is given as air domain and the bottom plate structure is considered as the solid domain. The setting of parameters for the domain and for the interface is as mentioned below. Domain – Air In this domain the pressure acoustics physics is active. The dependent variable in the domain is pressure (p). The transient analysis (time domain analysis) was considered for getting solution. The meshing was generated according to the lowest wavelength available in the ultrasonic signal. Time steps were also evaluated by following CFL criteria. Lagrange quadratic element types are used for the simulation. Except in the common boundaries with solid, the boundary conditions were taken as impedance boundary condition to avoid unnecessary reflections from the outer boundaries which create confusion for understanding of the propagated desired signal. Air was considered as the medium with density value of 1.23 kg/m and velocity of sound in the medium as 343 m/s. Domain – Solid In this domain, plane strain condition is considered because of the given plate size with u & v as the dependent variables. In this case also Lagrange type elements were used with transient analysis. For the purpose of modelling, steel is chosen as the solid medium with standard material properties of steel as the input parameters for the model. The free boundary conditions were chosen for the boundaries other than the common boundary. The free boundary condition will ensure the plate as the wave guide and the ultrasonic guided wave will be generated under specific excitation. Common boundary between two physics domain (Interface) The boundary conditions at the common boundaries of regions with different physics are the key for the modelling and simulation of multiphysics problem. At the interface, both physics has to be coupled. At the interface, the acoustic pressure wave needs to be coupled to solid boundary. To achieve this, the boundary load F on the solid is to be defined as F = -nsp Where p is the acoustic pressure wave of fluid medium and ns is the outward pointing unit normal vector seen form inside the solid domain. This boundary condition ensures the coupling of acoustic pressure wave in fluid domain to solid domain. The response of the solid also needs to be coupled back to the acoustics domain. For this, the normal acceleration of the interface of fluid domain is made equal to that of the solid structure. This ensures the coupling of normal acceleration of solid structure to the fluid domain. Simulation of air coupled ultrasonic In this case the initial ultrasonic excitation was given directly on to the steel plate. The asymmetric excitation was given from the left hand side of the steel plate. The three cycles 200 KHz cosine signal operated with hanning window as shown in figure 2 is used as the initial excitation signal. Figure 2: Initial excitation signal used for generating guided wave The asymmetric excitation signal of 200 KHz on the steel plate generates both So and Ao mode. The So and Ao modes get leaked to air thorough the interface. The leaky wave from the steel media generates the pressure wave in the air medium. Figure 2 shows simulation result of the leaky guided wave in the 2D surface plot at 30 μs. Figure 3: 2D surface plot shows the leaky guided wave in air from steel plate The low amplitude intensity signal is the Ao mode where as the high amplitude signal is the So mode which leaked from the steel plate. The corresponding 2D surface plate for steel plate is shown in figure 4. Figure 4: 2D surface plot indicating the Ao and So mode in the steel plate (Solid domain) Figure 5 shows the 2D surface plot for the signal at 54 μs. The plot indicates the further separation of both modes as time progresses because of different group velocities of two modes. Figure 5: 2D surface plot shows the Ao and So mode at latter stage of time The A-scan signal as observed by the detector placed at the middle of the geometry is shown in figure 6. Figure 6: A-scan signal observed in air domain Both the So mode and the Ao modes are clearly seen when observed in the air domain. The difference in amplitude is also observed in the detected signal. After successful modeling and simulation of air coupled ultrasonic with the simple plate structure, a complicated structure of composite section was undertaken for simulation with multiphysics problem. The structure was excited from the left hand side. The 2D surface plot of the simulated result for the air coupled ultrasonic through multiphysics simulation is shown in figure 7. Figure 7: 2D surface plot of the air domain indicating the pressure wave with presence of signals for different guided modes ConclusionThe modeling and simulation of air coupled ultrasonic is successfully carried out withtwo-dimensional Finite Element Model. The simulation with multiphysics approach wasutilized for solving two different physics in two different domains. Two domains representingdifferent physics problems were coupled at the interface by coupling the variables by givingproper boundary conditions. Different ultrasonic guided modes generated in solid domainwere correctly observed through the pressure acoustics signal created in the air domain. References[1] Dale Ensminger and Leonanrd J Bond, “ Ultrasonics: Fundamentals, Technologies andApplications”, 3 Edition, CRC Press, Taylor & Francis Group, 2012[2] C Hellier, M Shakinovsky, “Handbook of Non Destructive Evaluation”, Second Edition,Mc Graw Hill, 2012[3] Robert E Green Jr, “Non Contact Ultrasonic techniques”, Ultrasonics, 42(1-9), April2004, p9-16[4] Grandia WA et al, “NDE Applications of Air Coupled Transducer”, IEEE UltrasonicsSymposium, 1995, p697-709[5] Bikash Ghose et al, “Two Dimensional FEM Simulation of Ultrasonic Wave Propagationin Isotropic Solid Media using COMSOL”, COMSOL Conference 2010, Bangalore, India[6] COMSOL User’s Guide, Version 3.5a, COMSOL AB, 2008