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Effects of Various Shape Functions and Subset Size in Local Deformation Measurements Using DIC

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Abstract

The digital image correlation (DIC) method obtains comparable results with strain gauges and its reliability and accuracy are commonly accepted in the measurement of affine deformations. However, in engineering measurements, there are always substantial local deformations with high strain gradients, such as the Portevin-Le Chatelier (PLC) shear bands, deformations near gaps, and crack tips. In these situations, strain gauges are restricted because the results within the contact areas are smoothed. Although the DIC method can be employed to measure these local deformations, the calculation parameters (e.g., the order of the shape functions, and template size) seriously impact the results. By analyzing PLC shear bands with different gradients in tensile tests and simulated bands, the deep mechanism on how shape functions and templates impact on the accuracy of DIC results is established. This study also demonstrates that second-order shape functions are more suitable than first-order shape functions to describe local deformations. The theory that the results of second-order shape functions are reliable and accurate when the relative error between first- and second-order shape functions is less than 10 %, is proposed. In addition, improving the spatial resolution and the acquisition frequency is proposed, and proved to achieve reliable results.

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Acknowledgments

This work was supported by the National Basic Research Program of China (2011CB302105), and the National Natural Science Foundation of China (Grant Nos. 11372300, 11332010, 51271174, 11127201, 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

    Xiaohai Xu, Yong Su, Yulong Cai, Teng Cheng & Qingchuan Zhang

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  1. Xiaohai Xu
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  2. Yong Su
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  3. Yulong Cai
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  4. Teng Cheng
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  5. Qingchuan Zhang
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Corresponding author

Correspondence to Qingchuan Zhang.

Appendix: Influence of Variable Sizes of Speckles

Appendix: Influence of Variable Sizes of Speckles

To discover how they influence the results, speckles with variable sizes were employed and a typical deformation (a = 0.01 and c = 11 pixels) was applied. The sizes of the speckles satisfied a normal distribution with μ = 2.5 and σ = 1/3 so the sizes of 99.7 % speckles were located between 1.5 and 3.5 pixels.

Figure 17 shows that variable sizes of speckles scarcely cause any difference compared with speckles with a fixed 2.5-pixel radius. The two types of speckles produced nearly the same results regardless of the order of the shape functions.

Fig. 17
figure 17

Influence of variable sizes of speckles

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The simulations are highly dependent on the speckles, and simulated speckles are quite different from spray spots. Results with simulated speckles and spray spots employed in the simulations are presented in Fig. 18 to illustrate the difference. Figure 18(a) indicates the reference speckle image with simulated speckles and with spray spots shown in Fig. 18(b). Figure 18(c) shows the displacement errors calculated using different shape functions with the simulated speckles, and spray spots, respectively (The displacements were imposed by equation (8) while a = 0.01 and c = 11 pixels). There were interpolation errors (of about 0.004 pixels) outside the band when spray spots were employed. However, the tendency was the same regardless of the type of speckles used and the strain curves were little different (shown in Fig. 18(d)).

Fig. 18
figure 18

Difference between simulated speckles and spray spots. Reference image with simulated speckles a and spray spots b. c Displacement errors. d Strain curves

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Xu, X., Su, Y., Cai, Y. et al. Effects of Various Shape Functions and Subset Size in Local Deformation Measurements Using DIC. Exp Mech 55, 1575–1590 (2015). https://doi.org/10.1007/s11340-015-0054-9

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  • DOI: https://doi.org/10.1007/s11340-015-0054-9

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