Analysis of the influence of crack in coke on the fracture

Homogenization method and s-version FEM are proposed to estimate the strength of coke in the view of its microstructure. It is important for improvement of permeability in a blast furnace to estimate the condition for making high-strength coke by evaluating its strength. To evaluate the strength of brittle materials with complex microstructual geometry such as coke, it is required to develop analytical procedures that can consider microscopic fractures. Stress intensity factor considering influence of microscopic cracks and inclusions can be estimated by using homogenization method and s-version FEM. To evaluate the strength of macroscopic base, we use homogenization method and estimate the stress intensity factor. Then the influence of the crack distribution on the stress intensity factor is considerd. The stress intensity factor is estimated in the case when inclusions exist. On the other hand, s-version FEM is used to estimate the stress intensity factor of macrocracks that are a principal factor of coke's brittle fracture considering the influence of microstructure. Numerical results calculated by those two methods are in good agreement with analytical result, and the performances of these methods are verified. When the Young's modulus of includes is higher than that of the matrix, the stress intensity factor of the microcrack decreases and increases in case inclusions locate ahead of the microcrack-tip and aback of the microcrack-tip, respectively. Macrocrack will propagate easily when microcracks lay ahead of macrocrack, and it will be hard for macrocrack to propagate when microcrack lay aback of macrocrack.