Asymptotic analysis of fracture propagation in materials with rotating particles

• A small-scale Cosserat continuum to model cracks in materials with microrotations.
• It is asymptotics of small Cosserat characteristic lengths.
• An example of such materials is given by particulate materials.
• A unified crack growth criterion for Mode I and II cracks.
• It explains the observed in-plane growth of shear fractures.

Cosserat continuum for particulate materials has characteristic lengths commensurate with small particle sizes leading to small-scale Cosserat continuum – an asymptotics intermediate between the characteristic length and the crack length. We show that the main asymptotic term can be obtained from the classical crack problem by finding rotations from the displacements and, using the Cosserat constitutive equations finding the moment stresses. We obtained that Mode I, II stress singularities are the same in classical continuum; the moment stress has a stronger singularity (power 3/2). Bond bending and breakage caused by relative particle rotations constitutes the dominant mechanism of crack propagation.