A Modeling Platform for Ultrasonic Immersion Testing of Polycrystalline Materials with Flaws

Transcription

1 11th European Conference on Non-Destructive Testing (ECNDT 2014), October 6-10, 2014, Prague, Czech Republic A Modeling Platform for Ultrasonic Immersion Testing of Polycrystalline Materials with Flaws Frank SCHUBERT Fraunhofer Institute for Ceramic Technologies and Systems, Branch Materials Diagnostics (IKTS-MD); Dresden, Germany; Phone: , Fax: ; frank.schubert@ikts-md.fraunhofer.de Abstract A numerical wave-physical modeling platform for ultrasonic immersion testing based on the Elastodynamic Finite Integration Technique (EFIT) is presented. Besides the characteristics of the transducer like diameter, focal length, frequency, pulse form, tilting angle etc., the platform is able to model the most important flaw geometries like cracks, notches, flat bottom holes, voids, inclusions, delaminations etc. Moreover, complex polycrystalline microstructures based on random isometric and textured Voronoi tessellations can be included and their frequency-dependent influence on the wave field can be studied. Numerical results of typical immersion testing applications are presented in terms of time-resolved wave front snapshots and pulse-echo A- Scans. These findings are briefly discussed and compared to experimental data. Keywords: Ultrasonic testing (UT), modeling and simulation, polycrystalline microstructure, immersion testing, elastodynamic finite integration technique (EFIT) 1. Introduction Ultrasonic immersion testing with conventional focused and unfocused transducers represents one of the most important measurement set-ups in nondestructive testing. In order to optimize the relevant UT configuration for specific materials and flaws a detailed understanding of the interaction between ultrasonic waves and specimen is essential. This includes the excited wave field in water, reflection and transmission at the interface, mode conversion between pressure and shear waves, shortening of the focal length in solids, interaction with the microstructure of the material, interaction with defects, reflections at the back wall including multiple reflections between top surface and back wall as well as the propagation path back to the transducer. Most of these aspects are in general guided by wave physics. This is of particular importance if the dominant wavelengths of the ultrasonic pulse are comparable to the lateral size of the flaw and/or the grain size of the microstructure. In the following sections an advanced numerical modeling platform for ultrasonic immersion testing of polycrystalline materials with flaws based on the Elastodynamic Finite Integration Technique (EFIT, [1]) is presented. Besides the characteristics of the transducer like diameter, focal length, frequency, pulse form, tilting angle etc., the platform is able to model the most important flaw geometries like cracks, notches, flat bottom holes, voids, inclusions, delaminations etc. Moreover, complex polycrystalline microstructures based on random isometric and textured Voronoi tessellations can be included and their frequency-dependent influence on the wave field can be studied. The modeling platform includes 2-D, 3-D and axisymmetric 2.5-D solver that can be used according to the specific application and available computing power. Exemplary numerical results of typical immersion testing applications are presented in terms of time-resolved wave front snapshots and pulse-echo A-Scans. A brief discussion and first qualitative comparisons with known experimental findings are also given.

2 2. Examples of application 2.1 Homogeneous plate with unfocused transducer In the first example shown in Fig. 1 a basic set-up for ultrasonic pulse-echo immersion testing was simulated. It consists of an unfocused transducer placed in water and a homogeneous and isotropic titanium plate located in a certain adjustable distance from the transducer. In the wave front snapshots the temporal evolution of the absolute value of the particle velocity vector is shown. For reasons of a better presentation this value is increased by a factor of 4 inside the titanium plate. In the pictures one can see how the initial P wave is transmitted and reflected at the water/metal interface (surface echo, ) and how the transmitted pulse is reflected at the back wall of the plate (back wall echo, BE). The wave front snapshots display the wave propagation until the surface echo reaches the transducer. In the corresponding A- Scan the complete time window of the simulation is shown. It comprises the period until the second back wall echo has been detected. In the A-Scan in Fig. 1 (top right) the strong surface echo and the first two back wall echoes can be clearly identified. Model 1 can also be calculated by the 2.5-D EFIT solver in order to solve the axisymmetric 3-D problem. 2.2 Homogeneous plate with focused transducer In the second example demonstrated in Fig. 2 a focused transducer was used instead of an unfocused transducer as in example 1. The focal distance in water was chosen in such a way that the effective focus inside the titanium plate is located approximately 10 mm below the top surface of the plate. Due to the focused wave field all existing echoes in the A-Scan are smaller than in Fig. 1. Between first and second back wall echo a small shear wave contribution from the back wall reflection is visible. The existence of this mode conversion effect is supported by the corresponding wave front snapshots. It is significantly stronger than in the unfocused case from Fig. 1. Similar to model 1, model 2 can also be calculated by the 2.5-D EFIT solver in order to solve the corresponding axisymmetric 3-D problem. 2.3 Homogeneous plate with focused transducer and flat bottom hole In model 3 shown in Fig. 3 a flat bottom hole () was added. Its diameter corresponds to the P wavelength in titanium. The is modelled with stress-free boundary conditions. Due to the specific focal length of the transducer used in the simulation, the is hit optimally by the P wave pulse. This leads to a strong significant echo in the corresponding A-Scan while the echoes of the back wall are reduced. Between the two back wall echoes further secondary echoes are also visible. They are caused by multiple reflection and mode conversion of the echo between the top surfaces of the plate and the, respectively. Model 3 can be calculated by the 2.5-D EFIT solver for 3-D axisymmetric problems as well. 2.4 Coarse-grained polycrystalline plate with focused transducer and flat bottom hole In Fig. 4 the homogeneous titanium model was replaced by a coarse-grained polycrystalline model based on a random isometric Voronoi tessellation. In this model the elastic properties of each grain and their orientations are fluctuating around a certain mean value. In this context the grains can be modelled by locally isotropic or anisotropic material parameters. As can be seen from the snapshots and the corresponding A-Scan the heterogeneous microstructure leads to a strong scattering of the P wave by the grains and thus, to a significant frequencydependent attenuation of the echo. The back wall echo is no longer existing. Moreover, the typical backscatter noise is also visible. Its strength depends on the effective impedance

3 mismatch between adjacent grains. Model 4 can also be used in the frame of full 3-D calculations based on a 3-D Voronoi tessellation. However, in this case the computational effort is large and the maximum frequencies of the initial pulse are limited to a few MHz in order to keep the model small enough for calculations on conventional PCs. 2.5 Fine-grained polycrystalline plate with focused transducer and flat bottom hole In Fig. 5 the mean size of the grains was decreased by a factor of 3 while their elastic properties remained constant. In this case the attenuation of the echo is expected to be smaller than in coarse-grained microstructures. This result was in fact confirmed by a couple of 2-D simulations with varying grain size and is also visible in Fig. 5 where the echo is slightly larger than in Fig. 4 and the first back wall echo is visible again. These findings demonstrate that even 2-D simulations are able to reproduce real experimental results, at least qualitatively. For a detailed quantitative comparison full 3-D simulations are necessary. 2.6 Coarse-grained polycrystalline plate with tilted focused transducer and flat bottom hole In Fig. 6 the transducer was tilted by 3 in order to demonstrate the propagation of an inclined wave field. In this case the dominant part of the pulse no longer hits the and therefore, no significant echo is visible in the corresponding A-Scan. Nevertheless, small inclination angles of less than 1-2 are interesting if the angular backscatter characteristic of microstructure and defect are different from each other and can be separated. Similar to models 4 and 5, also model 6 can be treated by the full 3-D EFIT solver. 2.7 Texturized polycrystalline plate with focused transducer and flat bottom hole In many practical applications a rolled microstructure needs to be investigated. For this purpose a textured Voronoi tessellation as shown in Fig. 7 can be used as material model. It is well known from experimental data that in this case the backscatter noise is strongly enhanced and thus, the identification of defect echoes is hindered. The wave front snapshots and the corresponding A-Scan in Fig. 7 fully support these findings. This textured model can also calculated by the 3-D EFIT solver. Conclusions and Outlook In this paper an advanced modelling platform for ultrasonic immersion testing was presented. It includes 2-D and 3-D models, focused, unfocused and tilted transducers, phased arrays (not shown here), homogeneous and heterogeneous polycrystalline microstructures incl. texture, locally isotropic and anisotropic grains, as well as flat bottom holes, cross holes, voids, notches, spherical inclusions and many other types of scatterers. In the future quantitative comparisons with experiments and analytical models [2] are intended. References 1. F. Schubert, Numerical time-domain modeling of linear and nonlinear ultrasonic wave propagation using finite integration techniques Theory and applications, Ultrasonics 42, , S. Hirsekorn. Calculation of Ultrasonic Scattering Waves in Polycrystals via the Ensemble Averaged Equation of Motion of the Material, International Congress on Ultrasonics, Singapore, May 2-5, 2013.

4 Transducer 1 st BE 2 nd BE : Surface echo Figure 1. 2-D EFIT simulation of ultrasonic immersion testing of a homogeneous and isotropic titanium plate without defects using a non-focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 2.5-D EFIT solver.

5 st 1 BE 2nd BE : Surface echo Figure 2. 2-D EFIT simulation of ultrasonic immersion testing of a homogeneous and isotropic titanium plate without defects using a focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 2.5-D EFIT solver.

6 BE BE : Surface echo : Flat bottom hole Figure 3. 2-D EFIT simulation of ultrasonic immersion testing of a homogeneous and isotropic titanium plate including a flat bottom hole () using a focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 2.5-D EFIT solver.

7 BE : Surface echo : Flat bottom hole Figure 4. 2-D EFIT simulation of ultrasonic immersion testing of a coarse-grained polycrystalline titanium plate including a flat bottom hole () using a focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 3-D EFIT solver.

8 BE : Surface echo : Flat bottom hole Figure 5. 2-D EFIT simulation of ultrasonic immersion testing of a fine-grained polycrystalline titanium plate including a flat bottom hole () using a focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 3-D EFIT solver.

9 : Surface echo : Flat bottom hole Figure 6. 2-D EFIT simulation of ultrasonic immersion testing of a polycrystalline titanium plate including a flat bottom hole () using a tilted focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 3-D EFIT solver.

10 : Surface echo : Flat bottom hole BS: Backscatter BS Figure 7. 2-D EFIT simulation of ultrasonic immersion testing of a textured polycrystalline titanium plate including a flat bottom hole () using a focused transducer. Top left: discrete EFIT model; top right: A-Scan integrated over the transducer aperture; remaining pictures: time snapshots of the absolute value of the particle velocity vector until arrival of the surface echo. This model can also be calculated by the 3-D EFIT solver.