Acta Polytechnica CTU Proceedings doi:10.14311/APP.2019.25.0001 Acta Polytechnica CTU Proceedings 25:1–5, 2019 © Czech Technical University in Prague, 2019 available online at https://ojs.cvut.cz/ojs/index.php/app EVALUATION OF HOPKINSON BAR EXPERIMENTS USING MULTIPLE DIGITAL IMAGE CORRELATION SOFTWARE TOOLS Marcel Adornaa,∗, Stefan Bronderb, Jan Faltaa, Petr Zlámal a, Tomáš Fílaa a Czech Technical University in Prague, Faculty of Transportation Sciences, Department of Mechanics and Materials, Konviktská 20, 120 00 Prague, Czech Republic b Universität des Saarlandes, Institute of Applied Mechanics, Campus A4.2, 66123 Saarbrücken, Germany ∗ corresponding author: adorna@fd.cvut.cz Abstract. Three different tools for Digital Image Correlation (DIC) were used for evaluation of dynamic experiments performed using custom Open Hopkinson Pressure Bar (OHPB) apparatus. High strain-rate measurements were performed on specimens of advanced cellular materials with predefined structure and negative Poisson’s ratio. Low impedance polymethyl methacrylate (PMMA) bars instrumented with foil strain-gauges were used for dynamic loading of the specimens. Experiments were observed using a pair of high-speed cameras for imaging of loading process in sufficient quality. Custom developed evaluation DIC tool implemented in Matlab, open-source Matlab tool (NCorr) and commercial DIC software (ISTRA 4D) were all used for evaluation of image sequences recorded by high-speed cameras. Comparison of results obtained using all three different DIC tools and results of complementary strain-gauge measurement are shown in this paper. Verification of reliability of custom made DIC software tool is presented. Keywords: Digital Image Correlation, Hopkinson Bar, impact loading, high-speed imaging. 1. Introduction Digital Image Correlation (DIC) is a well established method used for contactless assessment of full-field maps of displacement and strain on the surface of the deformed specimen. It shows a great promise for evaluation of high strain-rate experiments performed using Hopkinson Bar experimental device with speci- mens of geometrically complex structures [1]. In this study, three different DIC software tools were used for evaluation of direct impact Open Hopkin- son Presure Bar (OHPB) experiments performed on specimens of advanced materials with predefined struc- ture and negative Poisson’s ratio (so called auxetic structures). The compared DIC softwares were: i) custom developed DIC tool implemented in Matlab [2], ii) open-source Matlab tool NCorr [3] and iii) commercial DIC software ISTRA 4D. Full-field DIC analysis of the specimens surfaces was performed us- ing all three software tools with similar parameters settings. Obtained results were compared visually and quantitatively. Results were also compared with com- plementary strain-gauge measurement. Correlation of single nodal point of the specimen structure was also performed and influence of correlation coefficient was discussed. 2. Materials and methods 2.1. Specimens The specimens geometry was based on a periodical assembly of 3 × 3 × 3 re-entrant honeycomb auxetic unit cells. The specimens were printed using the Pro Jet HD3000 3D printer (3D Systems, Rock Hill, USA) from the UV curable polymer VisiJet EX200 at the highest available printing resolution (656 × 656 × 800 DPI). This polymeric core samples were dip coated with a thin layer of carbon and an electrodepostion of nanocrystalline nickel (Ni) was subsequently car- ried out, resulting in a homogeneous layer of nickle (coating thickness of approx. 60 µm and 120 µm) within the whole structure. Finally the core poly- mer structure was melted out of the specimens using pyrosis at approx. 1000 °C. For more information regarding the used specimens manufacturing process see [4]. The specimens of the 3D printed nickle coated structures are shown in Fig. 1. The overall sample dimensions (selected specifically to suit the dimen- sions of the OHPB apparatus) of the specimens were approximately 13 × 13 × 19 mm. 2.2. Digital Image Correlation High-speed imaging enables to capture the deforma- tion process of the OHPB tests in a suitable quality (sufficient number of images with small changes be- tween them can be captured during experiment) for evaluation using optical methods. DIC method en- ables for the evaluation of strain fields on the surface of geometrically complex structures by tracking of a vir- tual pattern selected in the sequence of images where the displacements are to be evaluated. Each point of the virtual pattern is subsequently tracked through the whole captured image sequence. The tracking algorithm is based on subsets of pixels which are de- fined as an area with specific pixel dimensions formed 1 https://doi.org/10.14311/APP.2019.25.0001 https://ojs.cvut.cz/ojs/index.php/app M. Adorna, S. Bronder, J. Falta et al. Acta Polytechnica CTU Proceedings Figure 1. Specimens of 3D printed nickle coated structure (left) and the uncoated structure (right) around the individual correlation point (Fig. 2). As the specimen is deformed, the reference pattern is deformed as well in the image sequence. The new position of the deformed subset is determined based on the extreme value of a correlation coefficient calcu- lated using the selected criterion. Note, that not the whole area of the deformed picture is searched, but only an offset area, which reduce the computational complexity. Figure 2. Parameters of the Digital Image Correla- tion, M - subset dimension, K - offset dimension, N - grid spacing 2.2.1. Custom DIC Matlab tool In our department, a custom developed DIC Matlab tool is commonly used for evaluation of various ex- periments. It is based on the Lucas-Kanade tracking technique, the correlation coefficients are estimated during a two-step procedure, first at the pixel level and second at sub-pixel level to determine the dis- placement with a higher precision. At the pixel level, the sum-squared difference (SSD) criterion is used whereas at the sub-pixel level the Lucas-Kanade al- gorithm based on the zero-normalised SSD (ZNSSD) criterion is used [5]. 2.2.2. NCorr MAtlab tool Ncorr is an open source 2D DIC Matlab program, which implements several different correlation pro- cedures and criterions. However, for the evalua- tion of OHPB measurements, only one of the pro- cedures provided results comparable with our custom- developed Matlab tool. In this procedure the zero- normalized cross correlation criterion (ZNCC) in com- bination with the Gauss-Newton nonlinear iterative least squares method is used. 2.2.3. ISTRA4D ISTRA4D is a very robust commercial multi-camera DIC software. It implements many optimized correla- tion procedures, however the user is not able to select them manually and is therefore not in a full control of the correlation procedure. Correlation criteria and their inner parameters are not accessible or modifiable. Results obtained using ISTRA4D are compared with other software tools, however, precision and reliability of ISTRA4D software is not discussed in this paper. 2.3. Open Hopkinson Pressure Bar High strain-rate experiments with the auxetic speci- mens were performed using the OHPB direct impact apparatus [6]. In contrary to conventionally used Split Hopkinson Pressure Bar (SHPB) technique, in the OHPB no striker bar is used and instead an in- strumented incident bar is accelerated by a gas-gun system and directly hits a specimen mounted at the end of a transmission bar in the setup. In our OHPB setup, the incident bar is guided by a gas-gun barrel and by a low friction linear guidance system. This apparatus can be used to compress specimens to a considerably high strain. Moreover, as both the inci- dent and the transmission bar are instrumented with strain-gauges, it is possible to evaluate the data from both contact faces of the mounted specimen. Due to a low mechanical impedance of the tested spec- imens, the polymethyl-methacrylate (PMMA) bars with diameter of 20 mm were used. Both incident and transmission bar had a length of 1750 mm. One measurement point was placed on the incident bar, two measuring points were placed on the transmis- sion bar. All measuring points were equipped with two pairs of strain-gauges (one pair semiconductor and one pair foil strain-gauges) in Wheatstone half- bridge arrangement. For this study, only data from foil strain-gauges 3/120 LY61 (HBM, Germany) with 3 mm active length were used since semiconductor strain-gauges exhibited non-linear behaviour in larger deformations and had a significantly reduced lifetime. The experiments were observed using a pair of syn- chronised high-speed camera Fastcam SA-Z (Photron, Japan) with resolution of 256 × 168 px at approx. 252 kfps. Sufficient illumination of the specimen sur- face was achieved using a pair of high intensity LED lights (Constellation 60, Veritas, USA). Note, that only one of the two cameras observed the surface of measured sample and its close proximity. Record from the second camera was not used for evaluation in this study but only for general inspection of the experi- ment. Overview of the used experimental setup and the basic principle of OHPB are shown in Fig. 3. 2 vol. 25/2019 Evaluation of Hopkinson Bar Experiments using multiple DIC tools Figure 3. Principle of OHPB method with schematic of high speed camera used for DIC evaluation (left), Hopkinson Bar experimental setup with a pair o high-speed cameras (right) 3. DIC tools comparison 3.1. Full-field DIC comparison A virtual grid of 22 × 14 (columns × rows) correlation points was created to cover the area of the specimens surface and the ends of the measuring bars on the high-speed camera images. The same parameters of DIC evaluation were set for all three compared softwares: subset size M = 23 px, offset size K = 33 px, grid spacing N = 4 px. Evolution of the full-field in-plane displacement of the representative auxetic specimen with 60 µm layer of coating deformed using the OHPB apparatus and evaluated using the DIC by all three correlation softwares is shown in Fig. 6. Correlation of high-speed camera images was possible only up to the 100th image in the sequence which corresponds to approx. 0.15-0.2 overall strain (35 px of subset displacement). For higher displacement, NCorr provides distorted results due to low value of correlation coefficient and loss of correlation points. ISTRA4D and custom DIC tool results are reliable up to 130th image (approx. 0.25-0.3 overall strain, displacement of 45 px). Dynamic equilibrium was achieved during dynamic experiment as the sample was deformed uniformly on the both ends. 3.2. DIC and strain-gauge results comparison The stress-strain curves with strain calculated using the three DIC tools paired with the strain-gauge stress compared with the curve from conventional strain- gauge evaluation are shown in Fig. 4. DIC strain was for all software tools derived by tracking grid of correlation points created on the both edges of the deformed specimen. Stress-strain curves derived us- ing all correlation tools are in a very good agreement with the strain-gauge curve on both samples up to 0.16 of overall strain (100th image). For ISTRA4D software and our custom correlation tool it is possible to perform correlation up to 0.25 of overall strain. Differences of the DIC curves to strain-gauge curve after 0.25 is due to large deformations of the individ- ual cells of the tested structure resulting in a loss of correlation. Figure 4. Comparison of stress-strain diagrams with strain evaluated from strain-gauges and DIC tools 3.3. DIC single nodal point analysis To further investigate the process of correlation of the virtual grid, the correlation of a single grid point located in the node of the specimen structure was performed. Tracked point of the structure and its location during the deformation is shown in Fig. 7. Original location of the point is marked by the green cross, the red cross marks the location evaluated from our custom tool and the blue cross from NCorr. Note, that for relatively small displacement, the location provided by both software tools is identical (Frame 30). The displacement of the same nodal point through the image sequence is shown in Fig. 5. Figure 5. Displacement of single node point through image sequence 3 M. Adorna, S. Bronder, J. Falta et al. Acta Polytechnica CTU Proceedings Figure 6. Full-field DIC analysis, OHPB measurement of auxetic structure: displacement in pixel, Custom DIC tool (top), NCorr (middle), ISTRA4D (bottom); note, that ISTRA4D uses different color range Figure 7. Single correlation point tracking, original point position (green), custom DIC tool (red), NCrorr (blue) It is shown, that both the custom developed DIC tool and NCorr track the nodal point reliably up to the 80th frame in the sequence. After that, the reliability of custom made software is much better. This is also illustrated by the graph shown in Fig. 8, which shows the correlation coefficient mean value across all the correlation points in virtual grid. It is shown, that although the correlation criterions are different, the drop of correlation coefficient in NCorr software is much larger through the image sequence than in custom developed DIC tool. 4. Conclusion OHPB measuring device with low impedance PMMA bars was successfully used for dynamic testing of the nickle coated 3D printed specimens of auxetic struc- ture. Three different DIC tools were used for eval- uation high-speed camera record of representative experiment. The results derived from all three soft- ware tools were compared and were found to be in a good agreement with the complementary strain-gauge Figure 8. Correlation coefficient of compared DIC tools measurement. The results from NCorr open-source tool were reliable up to 16 % of deformation, the re- sults from custom DIC tool and commercial ISTRA4D software were reliable up to 25% of deformation. Sin- gle nodal point analysis was carried out for further proving that our custom developed DIC software tool 4 vol. 25/2019 Evaluation of Hopkinson Bar Experiments using multiple DIC tools is not only comparable with other software tools but provides even more reliable results. It was shown that both, the OHPB and the DIC are suitable tools for advanced characterization of nickle coated auxetic structures under high strain-rate loading. Acknowledgements The research was supported by the Czech Science Foun- dation (project no. 19-23675S) and the internal grants of the Czech Technical University in Prague (projects no. SGS18/153/OHK2/2T/16 and SGS18/154/OHK2/2T/16). All the financial support is gratefully acknowledged. References [1] T. Fíla, P. Koudelka, P. Zlámal, et al. Strain dependency of poisson’s ratio of sls printed auxetic lattices subjected to quasi static and dynamic compressive loading, 2019. doi:10.1002/adem.201900204. [2] I. Jandejsek, J. Valach, D. Vavřík. Optimization and calibration of digital image correlation method, 2010. [3] J. Blaber, B. Adair, A. Antoniou. Ncorr: Open-source 2d digital image correlation matlab software. Experimental Mechanics 55(6):1105–1122, 2015. doi:10.1007/s11340-015-0009-1. [4] A. Jung, M. Weinmann, H. Natter. Electroforming and Electrodeposition on Complex 3D Geometries: Special Requirements and New Methods, pp. 941–970. Springer International Publishing, 2016. doi:10.1007/978-3-319-15266-0_46. [5] B. D. Lucas, T. Kanade. An iterative image registration technique with an application to stereo vision. In Proceedings of the 7th International Joint Conference on Artificial Intelligence - Volume 2, pp. 674–679. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1981. [6] R. A. Govender, R. J. Curry. The “open” hopkinson pressure bar: Towards addressing force equilibrium in specimens with non-uniform deformation. Journal of Dynamic Behavior of Materials 2(1):43–49, 2016. doi:10.1007/s40870-015-0042-2. 5 https://doi.org/10.1002/adem.201900204 https://doi.org/10.1007/s11340-015-0009-1 https://doi.org/10.1007/978-3-319-15266-0_46 https://doi.org/10.1007/s40870-015-0042-2 Acta Polytechnica CTU Proceedings 25:1–5, 2019 1 Introduction 2 Materials and methods 2.1 Specimens 2.2 Digital Image Correlation 2.2.1 Custom DIC Matlab tool 2.2.2 NCorr MAtlab tool 2.2.3 ISTRA4D 2.3 Open Hopkinson Pressure Bar 3 DIC tools comparison 3.1 Full-field DIC comparison 3.2 DIC and strain-gauge results comparison 3.3 DIC single nodal point analysis 4 Conclusion Acknowledgements References