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Unveiling 3D Deformations in Polymer Composites by Coupled Micro X-Ray Computed Tomography and Volumetric Digital Image Correlation

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Abstract

A new method combining micro-X-ray computed tomography (μXCT) and volumetric digital image correlation (V-DIC) in conjunction with in-situ mechanical testing was used to probe three-dimensional (3D) deformation behavior in a friction stir blind rivet (FSBR) joint of carbon fiber reinforced polymer (CFRP) composite. Intrinsic microstructural features such as fibers, pores and metal inclusions enabled accurate volumetric strain calculation of dense fiber reinforced polymer composites using V-DIC without the need for high-contrast additives. Deformation calculated with V-DIC was employed to determine variation of local mechanical properties within the FSBR altered stir-zone microstructure. Unique deformation mechanisms such as internal interfacial shear and microstructure-dependent local buckling were observed in situ. The obtained 3D microscale strain maps revealed that the deformation behavior in joint-affected zones was fundamentally different from that of the bulk composite. Combined μXCT and V-DIC were shown to be effective for understanding 3D microscale deformations in composites.

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Notes

  1. The form of g(z) is obtained from the analogous one-dimensional problem for eccentrically loaded column buckling.

  2. Libraries are available on GitHub for download: https://github.com/bpcroom/XCT-Processing

  3. Using two-sample Kolmogorov-Smirnov tests. Due to extremely large sample sizes (Nstir = 18,000, Nbulk = 88,000) and clearly different distributions, p values were incalculably small, less than p = 10−300 .

  4. Confidence margin represents ± 1 standard deviation.

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Acknowledgments

This material is based upon work supported by the National Science Foundation (NSF) Graduate Research Fellowship Program under Grant No. 1315231, NSF Civil, Mechanical and Manufacturing Innovation Grant No. 1363468, 1358673 and 1418696, and Ford Motor Company Research and Advanced Engineering.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Virginia, 122 Engineer’s Way, Charlottesville, VA, 22903, USA

    B. Croom & X. Li

  2. Department of Mechanical Engineering, University of Hawaii at Manoa, 2540 Dole Street, Honolulu, HI, 96822, USA

    W.-M. Wang & J. Li

Authors
  1. B. Croom
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  2. W.-M. Wang
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  3. J. Li
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  4. X. Li
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Corresponding authors

Correspondence to J. Li or X. Li.

Appendix

Appendix

A. Mechanical Testing of Carbon Fiber Reinforced Polymer

To ascertain mechanical properties, ASTM D695 [25] compression tests were performed on samples with height of 11.6 mm and cross section of 13 mm × 3 mm excised from bulk CFRP material identical to that used in the FSBR specimens (Fig. 14). While flexural properties are commonly used for fiber composites, it was believed that data derived from compression tests would more accurately reflect the loading behavior observed in this experiment. A total of four specimens was used, with each specimen continuously compressed until onset of buckling. Due to the specimen’s limited size, non-contacting digital image correlation was selected to measure axial deformation. A random speckle pattern was applied to the CFRP surface using black spray paint on a matte white base coat to produce speckles with sizes ranging from 0.07 mm to 0.25 mm. Images were periodically captured throughout the compression tests with a CMOS digital camera and high magnification 135 mm lens; image resolution was 41 pixels/mm. Strain was measured with commercial two-dimensional digital image correlation software (Vic-2D, Correlated Solutions, Inc.) using 35 × 35 pixel subset size and spacing of 15 pixels between subsets. The linear regions of each stress–strain curve (approximately 0.0025 mm/mm to 0.01 mm/mm; varied slightly with specimen) were analyzed to determine elastic modulus and Poisson’s ratio using strains calculated at approximately 900 subsets from each specimen. By this means, a compressive stiffness of 8.8 ± 0.5 GPa and Poisson’s ratio of 0.37 were determined.

Fig. 14
figure 14

Determination of DIC compressive stiffness via digital image correlation. (a) Representative image used in DIC analysis with inset showing detail of speckle pattern. (b) Calculated stiffness of CFRP materials, with each color in the stress–strain curve representing results from one of four samples. Scale bar: 10 mm

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B. SEM Composition Analysis

EDS analysis was used to determine the composition of metal inclusions observed in the stir zone. It was found that the most prominent peak for the small inclusions (Fig. 15; green circle) was zinc, and for the large inclusion (purple square) was aluminum. The likely provenance of these materials was the zinc coating on the steel rivet and the aluminum workpiece.

Fig. 15
figure 15

Composition of metal inclusions within the stir zone, determined with EDS. Inclusions in green circle were determined to be zinc, while inclusion in purple square was determined to be aluminum. Scale bar: 50 μm

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C. Intensity Correction of Image Reconstruction

By sampling intensities (i.e., grayscale value of a pixel) in bulk material regions of each reconstructed image, it was shown that intensity variation in each image was systematic (Fig. 16). This conclusion is supported by several findings:

Fig. 16
figure 16

(a) Average bulk material intensity as a function of Z coordinate for several loading cases. (b) Fiber volume calculation before intensity correction. (c) Fiber volume calculation after intensity correction. Scale bars in (b) and (c): 250 μm

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  • The intensity peaks were located in identical locations for each image.

  • The specimen experienced large deformation and rigid body displacement (i.e., elevating the loading stage) between images, so variation cannot be attributed to material variation.

  • Analysis of both specimen and reference radiographs did not demonstrate this variation, so variation cannot be attributed to source or sensor defects; rather, it must have been an artifact of the reconstruction algorithm.

  • Adjustment of beam-hardening correction factors did not correct this variation.

  • The bow-shaped trend in average intensity is likely due to vignetting, for which flat-field correction is an accepted and commonly used correction technique.

The systematic variation was corrected by subtracting a Gaussian-smoothed average of the calculated intensities (shown as thick black line in Fig. 16a) from each reconstructed tomographic image. This enabled accurate intensity-based segmentation of the tomographic images; for comparison, calculated fiber volume is shown in Fig. 16(b-c) with and without intensity correction.

D. Accuracy of Image Segmentation

  1. a)

    Plot of fiber diameter vs. thresholded size

Certainly, fiber volume and fiber orientation calculations are highly sensitive to fiber dimensions; for this reason μXCT and SEM images were compared to verify that the thresholded μXCT images produced realistic fiber dimensions. Fig. 17 compares fiber diameters measured with scanning electron microscopy and thresholded images, and suggests that the thresholded fibers have reasonably accurate dimensions.

Fig. 17
figure 17

Comparison of CFRP fiber diameters in (a) SEM image and (b) thresholded XCT scan. Scale bars: 20 μm

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  1. b)

    SEM fiber volume vs. μXCT fiber volume

A baseline measurement for fiber volume was determined from scanning electron image. Intensity gradients were removed by second-order surface fitting for each region, and the flattened image was thresholded to distinguish fibers and matrix. Calculations in Fig. 18 revealed much higher fiber volume in the spin-affected zones than in the bulk material; these measurements closely correspond with the μXCT calculations presented in “Volume fraction analysis” section.

Fig. 18
figure 18

Fiber volume calculation for different CFRP zones using scanning electron image. From left to right: Thresholded images and fiber volume for (left) interior spin-affected zone, (center) exterior spin-affected zone, and (right) bulk material. Scale bar: 100 μm

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Croom, B., Wang, WM., Li, J. et al. Unveiling 3D Deformations in Polymer Composites by Coupled Micro X-Ray Computed Tomography and Volumetric Digital Image Correlation. Exp Mech 56, 999–1016 (2016). https://doi.org/10.1007/s11340-016-0140-7

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