An energy-based fracture criterion for quasi-brittle crack propagation in micropolar continuum: Analytical and numerical study

The present study provides closed-form expressions of propagation (kinking) angles by generalizing maximum energy release rate criterion in linear elastic fracture mechanics (LEFM) within micropolar theory of elasticity to address the in-plane, brittle crack prop- agation phenomenon in size-dependent materials with the presence of particle rotations. The accuracy and limitations of the derived formulation is checked by manually de- tecting the peak point of the energy release rate (ERR) through repetitive numerical simulations performed for arbitrary orientations of infinitesimal branch crack, modelled via magnifying the corresponding region with proper boundary conditions. In both ap- proaches (analytical and numerical), the basic fracture parameters (i.e. stress and couple- stress intensity factors at the main or infinitesimal branch tip) are attained with the aid of micropolar/extended-FEM (micropolar/XFEM) model. Through the parametric study, performed for numerous material properties and load- ing conditions, it is revealed that, as non-locality increases, the variation of propagation angle with the mode mixity ratio substantially diverges from that in Cauchy continuum. It is manifested as a change in the trend of angle-mode mixity ratio curve, and domi- nated by the stress related intensity factors in the absence of non-singular terms. Having a branch orientation approaching to crack’s axis with increased non-locality indicates the practical importance of resorting to non-classical theories for materials with scale effects such as particulate composites, masonry walls, rock-like assemblages, etc. follow- ing their disposition to fracture type failure. Moreover, the proposed fracture criterion enables crack propagation simulations within the framework of LEFM by integrating the formulation into a numerical method.