Fractal characterization of ceramic crack patterns after thermal shocks

Abstract

This work utilized a combination of experimental evidence and fractal geometric method to assess the effect of crack extension concerning the thermal shock on residual strength of ceramics. Sintered alumina (Al2O3) ceramic slabs were bundled and quenched in water under different thermal shock temperatures. The fractal dimension of thermal shock crack patterns on the interior surface and the cooled surface was calculated by the Box‐counting method. Fracture energy of a fractal pattern of microcracks in quasi‐brittle solids was employed to explain the relationship between crack length and fractal dimensions. The results show that if the crack propagation has the same crack length but a larger fractal dimension, it will absorb more fracture energy. The thermal shock crack patterns of Al2O3 ceramics with different grain sizes were analyzed, and the smaller grain size ceramic had a higher fractal dimension of crack patterns than the larger one.

Numerical Study of Thermal Shock Damage Mechanism of Polycrystalline Ceramics

“…For convenience, the macroscopic model will be named by its related grain size. The final crack patterns are shown in Supplementary Figure S1 in the supplementary file, which is similar to the reported experiment result (Qi and Meng, 2019). Many branches were observed and the crack eventually grew into a net structure.…”

Characterization of Ceramic Thermal Shock Cracks Based on the Multifractal Spectrum

“…By performing multifractal spectrum calculations on a large number of crack images and observing their chromaticity maps, it is found that the location, width, and bifurcation of the cracks affect the calculation results of the multifractal spectrum, which also verifies that even some minor features on the surface can be faithfully characterized by the multifractal. Based on the results of Qi [7], the fracture energy of microcrack fractal patterns in quasi-brittle solids can be used to explain the relationship between crack length and fractal dimension. If the crack propagation has the crack length but a larger fractal dimension, it will absorb more energy.…”

“…Li et al [6] constructed a fine-scale damage mechanics model to simulate the interaction between thermal impact cracks and prefabricated cracks, extending the study of the thermal impact damage mechanism of ceramics. While the mechanisms of crack generation and propagation have been studied above, Qi et al [7] investigated the effect of thermal shock-induced crack propagation on the residual strength of ceramics in terms of fractal geometry, calculated the fractal dimension of thermal shock cracks by the box-counting method, and explained the relationship between crack length and fractal dimension using the fractal energy of microcrack fractal patterns in quasi-brittle solids. Ricco et al [8] investigated the effect of microstructure and surface energy on subcritical crack propagation in microcrystalline glass and found that stress corrosion cracking in microcrystalline glass is due to a combination of surface energy and microstructural features.…”

Review about the Application of Fractal Theory in the Research of Packaging Materials

“…It was noted that the fractal dimensions were scattered within the scope of 1. 60 1.98, and the distribution was uneven. This indicated that the size and morphology of nanoparticles in the composite were different.…”

“…The fracture energy of microcracks with fractal in quasi brittle solids can explain the relationship between crack length and crack length. When the crack length is identical but the fractal dimension is larger, the fracture energy absorbed by the crack is greater [ 60 ]. Vukovic et al [ 61 ] described a new method for analyzing the microstructure properties of materials, which was used to predict the final properties of ceramics by fractal specialty programming in a fractal field simulator generating structure, grains, and pores.…”