Cohesive Zone Interpretations of Phase-Field Fracture Models

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Unlike micromechanics failure models that have a well-defined crack path, phase-field fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization length-scale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent crack-tip cohesive zone laws representing a phase-field fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I K-field loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened traction-separation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steady-state toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phase-field parameters and process zone characteristics in the material.

Original languageEnglish (US)
Article number121005
JournalJournal of Applied Mechanics, Transactions ASME
Issue number12
StatePublished - Dec 2022


  • cohesive zone law
  • constitutive modeling of materials
  • crack growth
  • finite element method
  • flow and fracture
  • micromechanics
  • phase-field fracture
  • process zone

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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