Study of mixed mode I/II cohesive zone models of different rank coals

Jianfeng Yang, Haojie Lian, Vinh Phu Nguyen

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15 Citations (Scopus)


The present work studies the Park–Paulino–Roesler (PPR) model, a unified potential-based cohesive zone model (CZM), for mixed mode I/II fractures in different rank coals, including weakly caking coals, fat coals and anthracite, by using disk-shaped compact tension (DC(T)) tests and punch-through shear (PTS) tests. The PTS experiments show that with the increase in coal rank, the initial shear stiffness and shear peak loads grow and the maximum tangential crack opening displacement (δt) decreases gradually. Additionally, the post-peak softening curve tends to have a linear shape, and the shear crack surface is rougher and more tortuous for the lower rank coals. The mode II fracture energy (Φt) was evaluated by calculating the area under the shear load–displacement curves. Φt is remarkably higher than mode I fracture energy (Φn) for the same coal rank, and the average value of Φt decreases from 145.54 J/m2 to 70.11 J/m2 as the coal rank of the specimens increases from weakly caking coals to anthracite. In order to verify the obtained PPR CZMs, mixed mode I/II single-edge notched beam (SENB) tests were performed and the experimental results are in good agreement with the numerical simulation. Moreover, we conducted SENB tests with different-size specimens, and the established PPR CZM model demonstrated its ability of describing the size effect of the mixed mode I/II fracture in coals.

Original languageEnglish
Article number107611
Number of pages16
JournalEngineering Fracture Mechanics
Publication statusPublished - 1 Apr 2021


  • Coal ranks
  • Cohesive zone model
  • Crack propagation
  • Punch-through shear tests
  • Size effect

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