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Sensitivity of in-Plane Strain Measurement to Calibration Parameter for out-of-Plane Specimen Rotations

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Abstract

In practice, out-of-plane motions usually are not avoidable during experiments. Since 2D–DIC measurements are vulnerable to parasitic deformations due to out-of-plane specimen motions, three-dimensional digital image correlation (StereoDIC or 3D–DIC) oftentimes is employed. The StereoDIC method is known to be capable of accurate deformation measurements for specimens subjected to general three-dimensional motions, including out-of-plane rotations and displacements. As a result, there has been limited study of the deformation measurements obtained when using StereoDIC to measure the displacement and strain fields for a specimen subjected only to out-of-plane rotation. To assess the accuracy of strain measurements obtained using stereovision systems and StereoDIC when a specimen undergoes appreciable out of plane rotation, rigid body out-of-plane rotation experiments are performed in the range −400 ≤ θ ≤ 400 using a two-camera stereovision system. Results indicate that (a) for what would normally be considered “small angle” calibration processes, the measured normal strain in the foreshortened specimen direction due to specimen rotation increases in a non-linear manner with rotation angle, with measurement errors exceeding ±1400με and (b) for what would normally be considered “large angle” calibration processes, the magnitude of the errors in the strain are reduced to ±300με. To theoretically assess the effect of calibration parameters on the measurements, two separate analyses are performed. First, theoretical strains due to out-of-plane rigid body rotation are determined using a pinhole camera model to project a series of three-dimensional object points into the image plane using large angle calibration parameters and then re-project the corresponding sensor plane coordinates back into the plane using small angle calibration parameters. Secondly, the entire imaging process is also simulated in order to remove experimental error sources and to further validate the theory. Results from both approaches confirmed the same strain error trends as the experimental strain measurements, providing confidence that the source of the errors is the calibration process. Finally, variance based sensitivity analyses show that inaccuracy in the calibrated stereo angle parameter is the most significant factor affecting the accuracy of the measured strain.

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Notes

  1. The model used in this study does not include image distortion parameters (e.g. radial, tangential), which can be included if needed for a specific imaging configuration.

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Acknowledgements

The authors are grateful for the financial support from SPARC Graduate Research Grant Program, University of South Carolina, under grant numbers # 15540-17-43825 and the Department of Mechanical Engineering, University of South Carolina, through a Teaching Assistantship.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA

    F. Yasmeen, M.A. Sutton & S. Rajan

  2. Department of Materials Engineering, University of Leuven, Leuven, Belgium

    R. Balcaen & D. Debruyne

  3. Correlated Solutions Incorporated, 121 Dutchman Blvd, Irmo, SC, 29063, USA

    H.W. Schreier

Authors
  1. F. Yasmeen
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  2. R. Balcaen
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  3. M.A. Sutton
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  4. D. Debruyne
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  5. S. Rajan
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  6. H.W. Schreier
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Corresponding author

Correspondence to F. Yasmeen.

Appendix 1

Appendix 1

Fig. 14
figure 14

Typical U, V, W displacement contours obtained using VIC-3D for large angle calibrated (LAC) stereo pair for out-of-plane rotation. (a) θ = 200; (b) θ = 400; (c) θ = 00; (d) θ =  − 200; (e) θ =  − 400; All units in mm

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Fig. 15
figure 15

Typical U, V, W displacement contours obtained using VIC-3D for small angle calibrated (SAC) stereo pair for out-of-plane rotation (a) θ = 200, (b) θ = 400, (c) θ = 00; (d) θ =  − 200; (e) θ =  − 400. All units in mm

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Fig. 16
figure 16

Typical U, V, W displacement fields obtained using VIC-3D along line L0 for (a) LAC (b) SAC stereo pair for out-of-plane rotation θ =  − 400 (line L0 is presented in Fig. 6, Fig. 14 and Fig. 15)

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Fig. 17
figure 17

Typical U, V, W displacement fields obtained using VIC-3D along line L0 for (a) LAC (b) SAC stereo pair for out-of-plane rotation θ = 400 (line L0 is presented in Fig. 6, Fig. 14 and Fig. 15)

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Yasmeen, F., Balcaen, R., Sutton, M. et al. Sensitivity of in-Plane Strain Measurement to Calibration Parameter for out-of-Plane Specimen Rotations. Exp Mech 58, 1115–1132 (2018). https://doi.org/10.1007/s11340-017-0370-3

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