1. Introduction. Abstract

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1 Angle beam method for detection of textural features in steel sheet A. Duijster 1, A. Volker 1, M. Stolzenberg 2 1 TNO, The Netherlands, arno.duijster@tno.nl 2 Salzgitter Mannesmann Forschung GmbH, Germany, m.stolzenberg@sz.szmf.de Abstract Texture is an important characteristic of sheet metal for forming complicated shapes accurately and reproducibly in one production step. Typical applications are automotive components. Moreover, texture is an important property for electro-steel. Currently texture is measured from samples taken from production material and analysed by XRD and/or EBSD. The existing methods do give a very complete image of the texture but are time consuming and hence expensive and lead to the loss of the produced material. This paper presents a new method using ultrasonic wedge transducers for inline texture analysis. Characteristic features are observed by Fourier transform the first ultrasonic signal that is recorded in transmission. The origin of the observed shoulders in the frequency spectrum is explained by numerical simulation. Moreover, the simulations demonstrate the sensitivity to textural features. Application of the method is demonstrated on several samples of the different steel types used in the Product Uniformity Control (PUC) project. The different textures in the samples express themselves in the location and the relative amplitude of the characteristic shoulders pattern in the frequency domain. A major advantage of the method is that it is very quick and can be applied inline. 1. Introduction Textures in steel sheets have a strong influence on the electrical, magnetical and mechanical properties of the material. In electro-steel e.g. the direction of grains and therefore the texture is important for the guidance of the magnetic field and eddy currents, and has to be properly adjusted. Mechanical properties are of importance especially in sheet forming processes. Soft low carbon steel grades were used mainly in applications, where a high degree of formability is important. Main focus lies on automotive industry, where complex parts have to be formed from sheets in thickness ranges below 0.8 mm. A favorable texture would be the {111}-texture, with a preferred material flow within the sheet plane and a strong resistance against material flow in thickness direction. This kind of texture is characterized by a high part of the so called gamma fiber, where the grains are oriented in a way that their {111}-plane is parallel to the rolling plane. The texture can be reached by thermal treatment of the sheet material, e.g. within a continuous annealing line. The influence of texture on the forming capabilities are well known (1), so the optimization of deep drawing capabilities by avoiding local reduction of thickness and earing has to be done by adjusting a {111}-texture. Presently the control of the textural state will be done by X-Ray Diffraction (XRD) or Electron Back Scatter Diffraction (EBSD) methods. If the texture has to be controlled during sheet production, non-destructive methods have to be applied. Experiments to determine the r-value, elastical constants and textural quantities have been done several years ago in laboratory experiments with EMATs (2)(3). In this paper, ultrasonic methods Creative Commons CC-BY-NC licence

2 with conventional piezo probes using higher frequencies were tested for the determination of textural features at low carbon steel sheets with different final treatments and resulting textural states. The examinations were carried out at cold strip taken as rolled from the SZFG cold rolling mill (sample WH). Cold rolled material (IF steel grade DX56D+Z) was annealed with two different annealing cycles (samples V1 and V2) in the annealing simulator. Additionally a sample from a deliverable steel sheet was taken at the end of the galvanizing line (sample FV). The material processing in the production line included finally skin passing with 0.9%. The annealing cycles were carried out for the first sample in a way similar to the annealing cycles in the hot dip galvanizing line (V1). V2 was annealed with a time-temperature cycle known to generate sharp textures and a high amount of gamma fiber. The samples V1 and V2 were not skin passed after annealing to minimize the influence of the dislocations on the X-ray diffraction (XRD) and NDT examinations. 2. Measurement approach using angle probes For the determination of elastic properties of material, ultrasonic shear waves are well suited, because they are polarized, so there is a fixed relation between moving direction of the particles and the travelling direction. Direction dependent properties of the material show up very well in the propagation of these kind of waves. Relations between the propagation of shear waves and elastic constants and orientation density function (ODF) are very well documented in literature. The easiest way to produce shear waves is the use of conventional angle probes with piezo transducers. Probes with an incidence angle of 35 are selected because in the {111}- texture the {110}-planes of the cubic unit cells are oriented near this angle related to the normal ([111]) direction. Important quantities of ultrasound measured in the experiments are sound speed, attenuation, angular dependency and frequency behavior. The transversal waves are generated with a standard probe head with a frequency of 4 MHz. In case of material with a thickness comparable to the wavelength the sound speed can be determined using resonances. In thin material, the reflected waves superimpose and propagate only if the thickness is a whole-numbered multiple of half of the wavelength. The frequency content was analyzed with FFT and gave a characteristic resonance frequency determined by the nominal frequency and the bandwidth of the used transducer. Measurements of ultrasound spectra were performed at all the samples, with directions varying in steps of 15 from the rolling direction (RD, 0 ) to the transverse direction (TD, 90 ). The data were recorded with an oscilloscope and the spectra calculated with FFT. Figure 1 shows the normalized spectra of the samples recorded in angular steps of 15 related to the RD. The spectra of the single sample states are varying in shape. The spectra of the cold rolled sample (WH) show several superimposed frequency maxima developing differently between RD and TD whereas the spectra of the hot dip galvanized and finally skin passed sample (FV) exhibits nearly no changes. Sample V1 shows a continuously changing spectrum between 0 and 90 with a strong change at 45. Finally, the spectrum of sample V2 shows a continuous development of changes between 0 and 75 and a strong change at 90. From the center frequencies of the spectra the sound speed has been derived. 2

3 (a) Sample WH (b) Sample FV (c) Sample V1 (d) Sample V2 Figure 1. Normalised FFT spectra of ultrasonic transversal waves under 35 to the normal of the rolling plane a) sample WH, cold rolled, b) sample FV, hot dip galvanised, c) sample V1 and d) sample V2, recorded from RD to TD in steps of Modelling ultrasonic wave propagation To simulate the wave propagation for the geometry described in the previous paragraph, the elastic wave equation is solved numerically using a 2D rotated staggered grid finite difference scheme. The implementation is capable of modelling elastic waves in a heterogeneous anisotropic medium. In this case the model consists of two 35 shear wave wedges, simulating Krautkramer MWB35N transducers operating at 4 MHz. The external boundaries of the wedges are absorbing, thereby avoiding reflections inside the wedge. The signal that is transmitted from the transducer is selected to match the signal in the data sheet for this type of transducer (4). Between these wedges, a 1.6 mm thick steel plate is modelled (see Figure 2). The top and bottom steel boundaries outside the wedges are modelled as stress free boundaries. The sides of the plate are made absorbing as well. The elastic properties of the steel are described by the two Lamé parameters λ and μ, a parameter c which is a measure of the elastic anisotropy of the individual crystallites and the W 400, W 420 and W 440 parameters, which are the crystallographic orientation distribution coefficients (ODC) (5). These coefficients express the amount of steel texture. The elastic constants are defined as C 11 = λ + 2μ + ( 12 2cπ ( ( ], (1) C 22 = λ + 2μ + ( 12 2cπ ( ( ], (2) 3

4 C 33 = λ + 2μ + ( 32 2cπ2 ) W , (3) C 44 = μ ( 16 2cπ ( ], (4) C 55 = μ ( 16 2cπ ( ], (5) C 66 = μ + ( 4 2cπ W 440 ], (6) C 23 = λ ( 16 2cπ ( ], (7) C 13 = λ ( 16 2cπ ( ], (8) C 12 = λ + ( 4 2cπ W 440 ], (9) showing the relationships between the aforementioned parameters. In the simulation, the two wedge transducers are rotated around their vertical axis with an interval of 15, comparable to the experimental setup. The output of the simulation consists of snaps shots of the wave field and the wave field measured by the recording transducer. Figure 2. Model geometry consisting of two 35 shear wave Plexiglas wedges with transducers, on both sides of a 1.6 mm thick steel plate. 4. Relation between texture and observed frequency spectra Figure 3 shows an example snap shot of the wave field at 7.3 s in the simulation. Three wave fronts are distinguishable that are more or less parallel with the receiving transducer aperture. The arrival time difference between these waves is quite small, such that in the recorded wave field these appear as one arrival. It is important to understand where these three arrivals originate from. A schematic drawing is shown in Figure 4, showing the individual arrivals. From these three signals, the first and strongest arrival is the direct wave from the transmitter to the receiver (incoming at an angle of 29 ). In the wedges, this wave is a compressional wave and in the steel the wave is a shear wave. The second arrival originates from the head wave that is excited at the wedge-steel interface of the transmitting receiver. The head wave travels at an angle of roughly 32. Once this wave reaches the steel-receiver wedge interface, it generates a compressional wave in the 4

5 Figure 3. On the left, a snapshot of the wavefield at 7.3 µs in the simulation. Both wedges are shown (edges marked with a light blue line), and the steel sheet in between (edges marked with a pink line). On the right, the transmitted signal in blue, and the recorded signal in red, in the full simulation time. Four wavefronts are identified in the left figure, and their corresponding peaks in the recorded signal. Overlapping wavefronts lead to an interference pattern. Figure 4. Schematic overview of the main wave paths in the wedges and the steel plate. P stands for compression waves, S for shear waves, and H for head waves. The arrows denote mode conversions. Note that the (green) head wave is a wave travelling along the steel surface, continuously radiating into the steel plate, although only one path is shown. wedge. The third echo originates from the first multiple reflection in the steel plate, again arriving with an angle of 29. This signal is already quite weak and is therefore less important for the further analysis. Since these three waves overlap at their arrival, the generate an interference pattern, showing high and low values, respectively corresponding with constructive and destructive interference. The interference patterns depend on the amplitudes and time shifts of the three incoming waves. This can be related to the texture of the steel. Due to anisotropy in the medium, the sound speed is directiondependent, leading to varying delays in arrival times of the three waves. As a result, the interference pattern changes. 5

6 5. Modelling results Li and Thompson used four groups of ODCs in their numerical simulations, two groups (I and II) corresponding to relatively strong textures and two groups (III and IV) corresponding to relatively weak textures (5). Variations of these four textures have been used in the finite difference simulations, obtained at the seven measurement directions in Figure 1. The four textures as used here are not related to a realistic steel sample. Note that neither the elastic constants nor the ODC parameters of the experimental samples are known, so that the experimental results cannot be reproduced realistically in simulations. The resulting frequency spectra from the recorded signals are shown in Figure 5. Although the experimental spectra cannot be compared to the spectra from the simulations, a comparable trend can be observed. Some of these spectra are continuously changing or have subtle variations, some show large increasing or decreasing maxima and minima while rotating the wedges over 90. These spectra prove that the variations as observed in experiments can be attributed to the anisotropy in the medium. Figure 5. Frequency spectra of four textures, computed at 7 different measurement directions, identical to the directions in Figure 1. Next to the spectra, the parameters are displayed which are used to compute the elastic constants with equations (1)-(9). 6. Experimental results Figure 6 shows the ODF for three of the four samples, measured by XRD and the sound speed of the transversal waves for the different samples determined from the FFT spectra. Figure 6a-c show ODF sections at φ 2 =45 for three of the four samples examined. The hot dip galvanized material (FV) exhibits a texture with a weak alpha and gamma fiber and a sound speed with no remarkably changes over the whole angular range between RD and TD (Figure 6d). Sample V1 annealed according to the process in the galvanizing line shows a more pronounced texture than the sample FV. Especially the gamma fiber is stronger and the ODF in the region of the alpha fiber (φ 1 near 0 ) shows differences for the angle Φ between 0 and 70. Also in the region of the gamma fiber (Φ near 55 ) minor differences are visible. The sound speed of the shear waves shows a difference between 6

7 (a) FV (b) V1 (c) V2 (d) Figure 6. ODF with φ 2 =45 for the samples (a) FV, (b) V1 and (c) V2, and in (d) the sound speed from FFT spectra for the samples WH, FV, V1 and V2. RD and TD. Between 0 and 45 the speed does not change noticeably, a minimum lies at 60 followed by an increase to the highest value at TD. Sample V2 had a strong gamma fiber nearly symmetrical to Φ=50 and two maxima at Φ=50, φ 1 =5, and Φ=54, φ 1 =50. The sound speed shows a more symmetric behavior, a continuous decrease to a minimum at about 45 and then a continuous increase to TD, higher than the value at RD. A relation of the measured sound speeds to the ODF can be found as follows (6). Due to the specific propagation angle of 35 to the ND and rotation of the sound direction from 0 to 90 to RD (φ 1 ) the sound propagates parallel to a {100}-plane of the crystallites oriented according to the gamma fiber. For the cold rolled material no ODF was recorded. The sound speed from 0 to 90 to RD shows an increase from about 60 to 90 corresponding to the anisotropy in grain shape due to rolling (Figure 6d). Due to a weak intensity of the ODF (Figure 6a), in the FV sample only minor changes of the sound speed can be found as a function of angle to RD (Figure 6d). The somewhat more intense ODF of sample V1 (fig. 6b) shows a weak alpha fiber (Φ: 0-90, φ 1 0 ) and only small differences along the gamma fiber (Φ 50, φ 1 :0-90 ). At about φ 1 =0 a shallow maximum of the <110>{111} (<110> show in RD) orientations shows up. In the angular dependency of sound speed a minimum at about 60 to RD can be found. This corresponds to the sound propagation near the <110> direction of the crystallites found in the <110>{111} orientation. In sample V2 a large gamma fiber in one main orientation can be found, most of the crystallites are oriented in <110> {111} at about Φ 50, φ 1 :0 and 60 of the ODF (Figure 6c). In the maximum orientation the sound propagates at about 0 and 90 to RD 7

8 near a <100> direction and at about 45 near a <110> direction of the crystallites. From calculations using the elastically constants of iron it is found that the sound speed in <100> direction is higher than in <110> directions, according to the findings our experiments with a maximum at 0 and a minimum at about 45 (Figure 6d). Longitudinal ultrasound or pressure waves were applied in ND at the samples FV, V1 and V2. The sound speed was determined using the resonance method. A comparison of V1 and V2 shows, that V2 has a higher speed than V1 at nearly comparable grain sizes and microstructures. The reason is the higher number of crystallites oriented in {111} texture in V2 compared to V1, so due to the higher orientation sound speed should be higher. 7. Conclusion The method in this paper shows the influence of texture on the propagation of ultrasonic waves in steel for different measurement orientations. The used measurement setup focuses on the propagation of shear waves in steel, and the recorded signal appears to be an interference pattern of mainly three shear waves: a primary shear wave induced by the induced compressional wave hitting the surface of the steel plate, a wave induced by a head wave travelling along the surface of the steel plate, and an internal reflection of the primary shear wave. The measured interference pattern depends on the orientation of the steel sample (leading to slightly varying sound speeds), as observed in measurements and explained by simulations. Features of this angular dependency of the sound speed could be related to crystallographic orientations. As a result, the proposed approach can be used as a fingerprint method for the identification of a certain types of textures. Acknowledgements The research leading to these results has received funding from the European Union s Research Fund for Coal and Steel (RFCS) research programme under grant agreement nr. RFSR-CT References 1. D. Raabe, in: W. Dahl, Eigenschaften und Anwendungen von Stählen, Band 1: Grundlagen, Verlag der Augustinus Buchhandlung, Aachen, A.V. Clark, R.B. Thompson, Y. Li, R.C. Reno, G.V. Blessing, D.V. Mitrakovic, R.E. Schramm, and D. Matlock, Ultrasonic measurement of sheet steel texture and formability: Comparison with neutron diffraction and mechanical measurements, Research in Nondestructive Evaluation, volume 2, issue 4, pages , Forouraghi, K., Ultrasonic measurement of drawability (r-values) of low carbon steel sheets, Diss. Iowa State University, General Electric, Ultrasonic Transducers For Flaw Detection and Sizing, [accessed January 2018] 5. Y. Li, and R.B. Thompson, Effects of dispersion on the inference of metal texture from S0 plate mode measurements. Part I. Evaluation of dispersion correction methods, Journal of the Acoustical Society of America, volume 91, issue 3, pages , D. Raabe, F. Roters, Simulation on the influence of Texture on Earing in Steel using the Texture Component Crystal Plasticity FEM; Scientific Report Max-Planck- Institut für Eisenforschung 2003/2004, S