Cohesive zone size of microcracks in brittle materials

Consideration of cohesive microcracks in continuum micromechanics is a challenging task since a lot of applications (such as, e.g., estimation of the stiffness of a microcracked solid) require a priori knowledge of the size of the cohesive zone. The latter, however, can be determined analytically only for the special case of Barenblatt–Dugdale cracks, i.e. for cracks with spatially constant cohesive tractions. Herein, we deal with the general case of spatially non-constant cohesive tractions: Generalizing the Barenblatt–Dugdale approach, we consider that each crack is surrounded by a plane annular cohesive zone characterized by a constitutive softening law (introduced as a power law) relating the vector of cohesive tractions to the displacement discontinuity. The size of this cohesive zone is then estimated using the theorem of minimum potential energy, based on a class of kinematically admissible displacement fields.