Model I cohesive zone models of different rank coals

The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals and anthracite, through disk-shaped compact tension tests. Firstly, the experiments show that with the coal rank rising, the critical crack separation displacements and the degrees of the nonlinearity of the softening function decline gradually. By fitting the experimental data with the four commonly used cohesive zone models including the power law, the exponential law, the bilinear law and the linear law, the best-fitted model for each rank of coals was identified and the corresponding parameters were found. Secondly, to arrive at a general CZM formulation for the different rank coals, Karihaloo's polynomial law was employed, which also gave better fit to the experimental data compared with the aforementioned four CZMs. After obtaining the CZM for coals, fracture energy was evaluated which is equal to the area under the softening curve. With the increase of the coal rank, the fracture energy reduces but its coefficient of variation increases. Thirdly, the geometric characteristics of fractures in different rank coals are studied. The lower rank coals have more tortuous crack propagation paths and larger roughness coefficients, whereas the higher rank coals possess wider average fracture apertures. Lastly, in order to further test the applicability of the obtained cohesion-separation laws, we implemented the Karihaloo's polynomial CZM and the bilinear CZM into the cohesive elements of ABAQUS (R) using the user-subroutine VUMAT, and thereby simulated the crack propagation in single-edge notched beams made of weakly caking coals, fat coals, and meager-lean coals, respectively. It is found that the numerical results based on Karihaloo's polynomial CZM have a better agreement with the experimental data than the bilinear CZM.