Fractal dimension-based fine-scale damage law for uniaxial compression test of 3D printed steel slag cementitious materials

Purpose: In order to deeply explore the damage morphology, crack extension and interlayer relationship of 3D printed steel slag cementitious materials, with the change of fractal dimension of materials before and after uniaxial compression as the focus of the study, using CT image technology to obtain two-dimensional images loaded with up to 90% of the predicted damage load, extracting microscopic damage cracks with the help of image processing software, and based on the theory of fractal geometry, the fractal dimension is used to reveal the extension law of cracks in the interlayer. The relationship between fractal dimension and crack characteristics was established.

In this study, a high-resolution X-ray scanner was used to acquire CT scan images of 3D printed specimens. The first CT scan was performed before the specimen was loaded; then it was loaded to 90% of the expected peak load at a rate of 0.1 mm/min, held for 30 minutes and a second CT scan was performed. During the scanning period, gray-scale cross-section images were acquired along the loading direction. The box dimension method was used for crack fractal dimension calculation to quantitatively characterize the non-homogeneity and complexity of the pore structure of the 3D printed specimens. The specific calculation steps of fractal dimension are as follows: a square box with side length r is used to cover the pore image, the number of boxes containing pores is counted, the operation is repeated by decreasing the side length, and the counting stops when the side length reaches the pixels of the picture, and the curve is finally plotted, and the absolute value of the slope of the straight line is the fractal dimension of the pore structure. In this study, we used the three-dimensional visualization software AVIZO and the Image J, an image processing software, for the reconstruction and analysis work of CT images. The crack images in RGB mode were binarized, with white (value 1) denoting cracks and black (value 0) denoting undamaged steel slag cementitious materials, and then the fractal dimension of the cracked area was calculated using the binarized data.

The stress-strain curves under uniaxial compression of the 3D printed specimens are similar to those of the cast specimens, both including rising and falling sections. Compared with the cast specimens, the peak stresses and strains of the 3D printed specimens were smaller than those of the cast specimens, and the descending section of the 3D printed specimens was steeper, and the damaged specimens showed more brittle behavior. In order to evaluate the distribution pattern of cracks inside the 3D printed steel slag cementitious materials, the CT scanned slices were subjected to crack extraction, and the crack area of each slice was calculated separately, and finally the crack fraction of each slice was obtained; the cracks were not uniformly distributed in the cross section, which presented a large crack fraction of the middle, which reached about 10%, and the crack fractions at both ends were lower than that of the middle. In the specimen, ultra-long cracks dominate, especially obvious in the interlayer, with mostly short cracks at the top and bottom, and the crack area distribution is consistent with the crack fraction. It shows that the 3D printed interlayer promotes the formation of long and ultra-long cracks, and exacerbates the specimen deterioration. The cracks develop centrally in the interlayer region of the specimen, leading to an increase in the crack fraction, which is dominated by the main crack, and several longitudinal and oblique cracks are separated from time to time, and the fractal dimension increases by 0.94%, 4.27%, 3.39%, 6.40%, 2.81%, and 1.35%, respectively, relative to the unloaded preloading. The change rule of fractal dimension is consistent with the distribution of pores and cracks described earlier, reflecting that the interlayer pores are an important reason for deepening the crack extension. The fractal dimension of the CT scan image can well reflect the law of crack extension, i.e., the larger the fractal dimension is, the more the cracks are, and the more the crack extension is enriched. The linear correlation between fractal dimension and crack fraction and crack area is high, which indicates that fractal dimension can visually characterize the size of the crack area, and the correlation between crack length (width) and fractal dimension is relatively weak and non-linearly increasing, with a partial linear decrease.Conclusion: Compared with the traditional cast specimens, the strength of 3D printed specimens in uniaxial compression tests was significantly reduced. The stress-strain curves of 3D printed specimens were steeper in the descending stage, showing brittle characteristics. In the CT image analysis before uniaxial compression, it was found that the interlayer porosity of the 3D printed specimen was 2.63%, and the pore distribution and pore size distribution showed obvious peaks in the interlayer region, and there was an obvious correlation between the porosity and pore size distribution. The CT images after uniaxial compression showed that the crack fraction, crack width and crack length in the interlayer were significantly higher than those in other parts, and a large number of long cracks appeared, indicating that the interlayer structure led to the significant deterioration of the specimen, which further verified its brittle properties. Characterization of cracks by fractal dimension revealed that the linear correlation between fractal dimension and crack fraction and crack area was high, and the correlation with crack length (width) was relatively weak. In the interlayer region, the fractal dimension of cracks is larger, reflecting the fractal expansion pattern of cracks in this region.