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High-Accuracy, High-Efficiency Compensation Method in Two-Dimensional Digital Image Correlation

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Abstract

When measuring plate specimen deformations, traditional two-dimensional (2D) digital image correlation (DIC) often leads to insufficiently accurate results due to out-of-plane motion of the specimen during the measurement. To remove the effects of out-of-plane motion, a compensation method for 2D DIC has been developed by researchers. The method markedly improves 2D DIC measurement accuracy. However, two problems with this compensation method remain to be solved: (1) the compensation-method coefficient matrices are affected by experimental noise and correlation errors, and (2) the coefficient matrices are singular when the specimen deformations are small enough, especially when the specimens remain static. For these reasons, an improved compensation method is proposed in this paper. The proposed method adds an extra single-camera calibration step to determine the distortion parameters so that the coefficient matrices are not affected by deformed images and the compensation results become more stable. To ensure measurement efficiency, virtual extensometers are taken as an example to compare the two compensation methods. Static experiments have been carried out to analyze the effects caused by different measurement parameters. Tensile experiments indicate that the improved compensation method leads to highly accurate results that not only are comparable with those of three-dimensional (3D) DIC, but that also agree with the results measured by a strain gauge. A video extensometer with a high accuracy of 5 μ ε at a rate of 28 fps has been developed as well.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11332010, 51271174, 11372300, 11472266 and 11428206).

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Authors and Affiliations

  1. CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230027, China

    X. Xu, Q. Zhang, Y. Su, Y. Cai, W. Xue, Z. Gao, Y. Xue, Z. Lv & S. Fu

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  1. X. Xu
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  2. Q. Zhang
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  3. Y. Su
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Correspondence to Q. Zhang.

Appendix:

Appendix:

Comparison Between 3D Results with and Without Asymmetry

To study the differences between the results measured by the 3D DIC setup with and without asymmetry, four cameras were used to perform the confirmatory experiment. As shown in Fig. 16(a), the angles between the four cameras and the sample’s orthonormal direction were −10, 0, 10, and 20 degrees respectively. The first (from left to right) and third cameras had a 3D DIC setup, whereas the other two cameras had another. The two 3D DIC setups were both calibrated. Each DIC setup used hardware to ensure synchronization. However, synchronization of the two DIC setups was maintained by comparing the acquisition times. The extensometer was focused on the reference image captured by the second camera, and a correlation method was used to locate matching positions on the other three reference images. The line strains measured by the two setups are depicted in Fig. 16(b). Their absolute errors are shown in Fig. 16(c). It is clear that the results measured by 3D DIC with and without asymmetry show slight differences (RMS = 7.7 μ ε).

Fig. 16
figure 16

Comparison between 3D results with and without asymmetry. (a) Experimental setup and results. (b) Line strains measured by 3D DIC with and without asymmetry. (c) Absolute error between line strains

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Compensations for the Entire DIC area of Interest

As studied in Ref. [15], compensations for the entire DIC area of interest have been performed, as shown in Fig. 17. Here, the sample was mainly rotated along the y-direction, with other smaller motions. The full-field displacements u and v are shown in Fig. 17(a) and (b) respectively. Ideally, the displacements would all be the same. The displacements measured by 2D DIC do not satisfy this condition. However, the displacements measured by the C0 and C1 compensation methods do agree with the ideal condition. Note that the displacements measured by the two compensation methods show slight differences due to different compensation parameters. The statistical results are shown in Table 3. The results illustrate that both the C0 and C1 methods can improve the measurement accuracy of 2D DIC, but that the C1 compensation method leads to more accurate results.

Fig. 17
figure 17

Compensations for the entire DIC area of interest. (a) Displacement u and (b) displacement v

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Table 3 Statistical results for displacements u and v (Unit: pixel)
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Xu, X., Zhang, Q., Su, Y. et al. High-Accuracy, High-Efficiency Compensation Method in Two-Dimensional Digital Image Correlation. Exp Mech 57, 831–846 (2017). https://doi.org/10.1007/s11340-017-0274-2

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  • DOI: https://doi.org/10.1007/s11340-017-0274-2

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