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A Novel Approach for the Determination of Surface Tilt Angles in Two-Dimensional Digital Image Correlation Experiments

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A Correction to this article was published on 27 December 2019

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Abstract

Two-dimensional digital image correlation (2D-DIC) is increasingly being used in a wide variety of applications. This technique is capable of measuring the in-plane deformations and strains of planner surfaces. A basic condition for using this technique is having the camera to observe the target surface perpendicularly. If the camera is not perpendicular to the surface, errors will be introduced in the measured displacements and strains. Small amounts of camera misalignment can easily go undetected during the initial setting of the experimental setup. In this paper, a novel approach for verifying the perpendicularity of the camera with respect to the target surface in 2D-DIC experiments is introduced. If the camera is not perpendicular to the surface, the tilt angles about both of the two in-plane axes can be calculated using this novel approach. A simple in-plane rigid-body-translation of the specimen in any of the two in-plane directions (horizontal or vertical direction relative to the camera image), is used for detecting camera non-perpendicularity and calculating the tilt angle(s). This approach uses the normal and shear strain errors, induced in DIC results due to camera non-perpendicularity, to determine the surface tilt angle(s), if any is present. The tilt angle(s) are calculated using simple analytical equations that are developed based on the pinhole camera model. The proposed approach is validated using experiments performed while the target surface is tilted at angles ranging from 0.5° to 4°. The experimental results show that this approach is able to confidently detect camera misalignment for tilt angles of 1° or larger and the tilt angles can be calculated with less than 0.3° error.

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Change history

  • 27 December 2019

    The original article has been corrected on the line “These two parameters are the average…” and on Eqs. 19, 20, 21 and 23.

References

  1. Sutton M, Wolters W, Peters W, Ranson W, McNeill S (1983) Determination of displacement using an improved digital correlation method. Image Vis Comput 1:133–139

    Article  Google Scholar 

  2. Sutton M, McNeill S, Helm J, Chao Y (2000) Advances in two-dimensional and three-dimensional computer vision. In: Rastogi P (ed) Topics in applied physics, vol 77. Springer, Berlin, pp 323–372

    Google Scholar 

  3. Sutton M, Orteu J, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Springer, New York

    Google Scholar 

  4. Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001 (17pp)

    Article  Google Scholar 

  5. Orteu J (2009) 3-D computer vision in experimental mechanics. Opt Lasers Eng 47:282–291

    Article  Google Scholar 

  6. Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties–a review. Strain 42:69–80

    Article  Google Scholar 

  7. Feng D, Feng M (2016) Vision-based multipoint displacement measurement for structural health monitoring. Struct Control Health Monit 23:876–890

    Article  Google Scholar 

  8. Helfrick M, Niezrecki C, Avitabile P, Schmidt T (2011) 3D digital image correlation methods for full-field vibration measurement. Mech Syst Signal Process 25:917–927

    Article  Google Scholar 

  9. Hijazi A, Yardi N, Madhavan V (2004) Determination of forming limit curves using 3D digital image correlation and in-situ observation. Proceedings of the International SAMPE Symposium and Exhibition, Long Beach, CA, pp. 16–20

  10. Liljenhjerte J, Upadhyaya P, Kumar S (2016) Hyperelastic strain measurements and constitutive parameters identification of 3d printed soft polymers by image processing. Additive Manufact 11:40–48

    Article  Google Scholar 

  11. Caminero M, Lopez-Pedrosa M, Pinna C (2013) And Soutis. C. Damage monitoring and analysis of composite laminates with an open hole and adhesively bonded repairs using digital image correlation. Compos Part B 53:76–91

    Article  Google Scholar 

  12. Eshtayeh M, Hijazi A, Hrairi M (2015) Nondestructive evaluation of welded joints using digital image correlation. J Nondestruct Eval 34:37

    Article  Google Scholar 

  13. Libertiaux V, Pascon F, Cescotto S (2011) Experimental verification of brain tissue incompressibility using digital image correlation. J Mech Behav Biomed Mater 4:1177–1185

    Article  Google Scholar 

  14. Soltani A, Curtze S, Lahti J, Järvelä K, Laurikka J, Hokka M, Kuokkala V (2018) Digital Image Correlation Study of the Deformation and Functioning of the Human Heart during Open-Heart Surgery. In Mechanics of Biological Systems, Materials and other topics in Experimental and Applied Mechanics, Springer: Cham 4: 19–27

  15. Sutton M, Li N, Joy D, Reynolds A, Li X (2007) Scanning electron microscopy for quantitative small and large deformation measurements part I: SEM imaging at magnifications from 200 to 10,000. Exp Mech 47:775–787

    Article  Google Scholar 

  16. Kirugulige M, Hareesh S, Tippur V, Denney T (2007) Measurement of transient deformations using digital image correlation method and high-speed photography: application to dynamic fracture. Appl Opt 46:5083–5096

    Article  Google Scholar 

  17. Hijazi A, Madhavan V (2008) A novel ultra-high speed camera for digital image processing applications. Meas Sci Technol 19:085503

    Article  Google Scholar 

  18. Luo P, Chao Y, Sutton M, Peters W (1993) Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision. Exp Mech 33:123–132

    Article  Google Scholar 

  19. Hijazi A, Kähler C (2017) Contribution of the imaging system components in the overall error of the two-dimensional digital image correlation technique. J Test Eval 45:369–384

    Article  Google Scholar 

  20. Haddadi H, Belhabib S (2008) Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Opt Lasers Eng 46:185–196

    Article  Google Scholar 

  21. Bornert M et al (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech 49:353–370

    Article  Google Scholar 

  22. Chu T, Ranson W, Sutton M, Peters W (1984) Applications of digital-image-correlation techniques to experimental mechanics. Exp Mech 25:232–244

    Article  Google Scholar 

  23. Sutton M, Yan J, Tiwari V, Schreier H, Orteu J (2008) The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt Lasers Eng 46:746–757

    Article  Google Scholar 

  24. Pan B, Yu L, Wu D (2013) High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification. Exp Mech 53:1719–1733

    Article  Google Scholar 

  25. Pan B, Yu L, Wu D (2013) High-accuracy 2D digital image correlation measurements using low-cost imaging lenses: implementation of a generalized compensation method. Meas Sci Technol 25:025001

    Article  Google Scholar 

  26. Siddiqui M (2015) Towards eliminating the displacement Bias due to out-of-plane motion in 2D inverse problems: a case of general rigid-body motion. Strain 51:55–70

    Article  Google Scholar 

  27. Badaloni M, Lava P, Rossi M, Chiappini G, Debruyne D (2016) Out-of-plane motion evaluation and correction in 2D DIC. Adv Optic Methods Experiment Mech, Springer: Cham, Vol. 3, pp. 181–187

    Chapter  Google Scholar 

  28. Meng L, Jin G, Yao X (2006) Errors caused by misalignment of the optical camera axis and the object surface in the DSCM. J Tsinghua Univ: Sci Technol 46:1930–1932

    Google Scholar 

  29. Lava P, Coppieters S, Wang Y, Van-Houtte P, Debruyne D (2011) Error estimation in measuring strain fields with DIC on planar sheet metal specimens with a non-perpendicular camera alignment. Opt Lasers Eng 49:57–65

    Article  Google Scholar 

  30. Hijazi A, Friedl A, Kähler C (2011) Influence of camera’s optical axis non-perpendicularity on measurement accuracy of two-dimensional digital image correlation. JJMIE 5:373–382

    Google Scholar 

  31. MatchID-2D manual: < www.MatchID.org >

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Acknowledgements

The experiments were done in the Metrology laboratory of the Mechanical Engineering Department at King Abdul-Aziz University.

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Authors and Affiliations

  1. Department of Mechanical Engineering, German Jordanian University, Amman, Jordan

    A. L. Hijazi

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  1. A. L. Hijazi
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Correspondence to A. L. Hijazi.

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Exemplary speckle pattern image files with 2° camera tilt angle are available online.

The original version of this article was revised: corrected on the line “These two parameters are the average…” and on equations 19,20,21 and 23.

Electronic supplementary material

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Exemplary speckle pattern image files with 2° camera tilt angle (RAR 1731 kb)

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Hijazi, A.L. A Novel Approach for the Determination of Surface Tilt Angles in Two-Dimensional Digital Image Correlation Experiments. Exp Mech 60, 267–282 (2020). https://doi.org/10.1007/s11340-019-00554-8

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