Cracking at later ages can be an effect of different causes. External restraints can play an important role in crack formation [24]. Other influences are sulfate attack, alkali-silica reaction, corrosion, differences in settlement, structural cracking due to corrosion of the reinforcements and/or overstressing the construction, tension cracking due to bending and thermally-induced cracking due to temperature changes, amongst others. One of the major cracking problems, i.e., pitting and spalling, is due to freeze-thawing. Due to the volume increase of water due to freezing, water inside the pore structure and cracks will start to expand, leading to stresses in the concrete material. One way of counteracting such volume increase is the use of an air entrainer. However, for transportation, this admixture is not stable. The trick is that a certain pore structure is created so that there is no scaling.
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The formed cracks are aesthetically unappealing. In addition, the overall public perception when seeing cracks is that the structure has failed or is about to fail. However, when the crack is not structural, not too wide and is not leaking water, it can commonly be accepted. Therefore, one should engineer the material in such a way that is it acceptable for all parties.
When the crack is ideally sealed from further ingress, less deteriorating mechanisms may occur. The ingress of water for example could induce steel corrosion, frost attack, chemical attack and internal expansion, endangering the durability of a structure. Due to the (partial) prevention of this water movement, a more durable and sustainable material is designed. The sealing of a crack can be monitored by means of studying the (water) permeability. Due to their swelling capacity, upon contact with fluids, SAPs may cause a decrease in permeability of cracked cementitious materials as the swelling action is physically sealing the crack. Lee et al. [146,147,148] and Snoeck et al. [56,78,144] investigated the incorporation of SAP in concrete in order to obtain self-sealing properties. When liquids enter a crack, SAP particles along the crack faces will swell and block the crack. This is reflected in a decrease of water permeability through a crack. When a water head is imposed, the SAPs are able to withstand water movement, as studied and visualized by means of neutron radiography [56,144,149]. In Figure 6 the crack sealing capability of SAPs is shown. The top of the figure shows a cracked specimen and an imposed water head of 20 mm. It is clear that the water level decreases as a function of time. On the other hand, in the lower part of the figure, an analogous specimen but now containing SAPs is shown. As the SAPs swell, they seal the crack and the water head is maintained in time.
SAPs are able to stimulate and promote the precipitation of healing products in a crack, as was visualized by means of X-ray computed microtomography, redrafted after [190] ( 2016 Elsevier). Legend: grey concrete and pores, red crack, blue macro pores with superabsorbent polymers and yellow formed healing products after being stored for four weeks in a relative humidity of 60% (RH = 60%), more than 90% (RH > 90%) or in wet/dry cycles (1 h in water and 23 h in standard laboratory conditions) (wet/dry).
The SAPs, as one of the promising paths for self-healing, were also applied in a real-scale concrete element (150 mm 250 mm 3000 mm) [145]. Several beams were made, with and without self-healing properties. Based on the measured crack width reduction over time, it was shown that best crack healing was obtained when superabsorbent polymers were added to the mixture.
For a deeper understanding of the functional behavior of energy materials, it is necessary to investigate their microstructure, e.g., via imaging techniques like scanning electron microscopy (SEM). However, active materials are often heterogeneous, necessitating quantification of features over large volumes to achieve representativity which often requires reduced resolution for large fields of view. Cracks within Li-ion electrode particles are an example of fine features, representative quantification of which requires large volumes of tens of particles. To overcome the trade-off between the imaged volume of the material and the resolution achieved, we deploy generative adversarial networks (GAN), namely SRGANs, to super-resolve SEM images of cracked cathode materials. A quantitative analysis indicates that SRGANs outperform various other networks for crack detection within aged cathode particles. This makes GANs viable for performing super-resolution on microscopy images for mitigating the trade-off between resolution and field of view, thus enabling representative quantification of fine features.
Since the SEM image data considered in the present paper depicts differently aged/cracked cathode particles, this dataset will serve as the basis for investigating the influence of aging parameters on the crack formation within cathode particles in future studies. Therefore, in the present paper, we additionally study to what extent super-resolution supports the analysis of crack formation. More precisely, we segment the cracks within super-resolved image data which we compare to cracks determined from high-resolution images. We observe a significant improvement for crack segmentation results when using super-resolved images in comparison to upsampled low-resolution images, see the discussion section for more details. This indicates that super-resolving SEM image data of cathode materials can significantly support the analysis of battery aging processes. Moreover, super-resolution using machine learning methods is not limited to SEM image data of cathode materials. The networks discussed in the present paper could easily be deployed onto image data obtained by different measurement techniques like, for example, atomic force microscopy50.
Thus, this technique is expected to have a plethora of applications in materials science and particularly Li-ion electrode characterization where understanding the distributions of small components and features such as conductive carbon, cracks, and unwanted deposits are critical to understanding the performance and degradation of cells.
In the previous section, we investigated the performance of super-resolution results obtained by the trained networks by direct comparison to the grayscale high-resolution images. Recall, that the SEM image data considered in the present paper depicts differently aged cathode particles where the aging leads to cracks within the particles. Thus, for investigating the influence of aging on the crack formation, the cracks have to be identified reliably from SEM image data. Therefore, in this section we investigate how super-resolution of low-resolution SEM image data improves subsequent procedures for the crack segmentation.
High-resolution image IHR (a) and the corresponding segmentation map SHR computed from IHR (b) where black color indicates the background, gray color the cracks and white color the particles. The corresponding segmentation map \(\widehatS_\rmHR\) computed from the upsampled low-resolution image (c) and from the images super-resolved by SRGAN (d), SRResNet2 (e), and CinCGAN (f). All figures use the same length scale.
In order to quantify the similarity between cracks \(\widehatC_\rmHR\) determined from super-resolution/upsampled images and the ground truth CHR we consider the Jaccard index which is given by
Additionally, we investigate how well quantities for characterizing crack formation in particles can be estimated using super-resolved image data. More precisely, we compute the specific crack density ρ from the segmented high-resolution image data which is given by
The values of \(\parallel f-\widehatf\parallel\) for probability densities of crack sizes determined from upsampled low-resolution images (as reference) and from super-resolution images computed by the trained networks U-NetGAN, SRResNet1, SRGAN, SRResNet2, and CinCGAN are listed in Table 3. Altogether, SRGAN performs best with respect to crack segmentation, see also the discussion provided in the next section.
Probability densities of area-equivalent diameters of cracks computed from high-resolution, upsampled low-resolution and super-resolved image data (a), and point-wise absolute errors with respect to the probability density f computed from high-resolution image data (b).
Overall Table 3 indicates that super-resolving image data can lead to a better segmentation of the crack phase within NMC particles from SEM data than simply upsampling low-resolution images. More precisely, the values of the Jaccard index listed in Table 3 indicate that the application of SRGAN leads to a significant improvement over upsampling of the low-resolution image using bilinear interpolation, i.e., the Jaccard index is 0.556 for the upsampling method, whereas the application of SRGAN leads to a Jaccard index of 0.679. Moreover, we observe that, with a relative error of 0.036, the specific crack density ρ can be reliably estimated using image data which has been super-resolved by SRGAN. In comparison to this, the relative error using upsampled low-resolution data is 0.136.
Furthermore, Fig. 5a shows that the crack size distribution determined from the upsampled low-resolution data is, in comparison to the distribution determined from high-resolution data, shifted to the right, where the point-wise absolute errors are visualized in Fig. 5b. This discrepancy between the size distributions of cracks determined from low-resolution and high-resolution data can be reduced by super-resolving the low-resolution data with SRGAN. More precisely, Fig. 5b shows that the point-wise absolute errors of the probability density \(\widehatf\) computed from super-resolved data obtained with SRGAN are close to 0. This is also reflected by the \(\parallel f-\widehatf\parallel\) values in Table 3. Overall, SRGAN outperforms the remaining networks considered in the present paper with respect to the segmentation of cracks. Further improvements of the results achieved with SRGAN could be obtained by considering further discriminators which distinguish between alternative representations (e.g., a representation in some feature space) of super-resolved and high-resolution images34. Note that the relatively poor result for the crack size distribution achieved by SRResNet2 can be attributed to noisy predictions of the network which affects the resulting segmentation, see Fig. 4e, f. More precisely, we observe that many cracks are wrongly fragmented into multiple regions, which significantly changes the crack size distribution. This indicates that, in order to perform an in-depth analysis of crack formation in NMC particles, SRResNet2 would require further calibration and/or additional post-processing steps would have to be performed on the images super-resolved by this network. Nevertheless, the super-resolution results achieved by SRGAN suggest that it might be well suited for further analyzes of crack formation in NMC particles. 2ff7e9595c
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