Defects play a significant role on the gross mechanical behaviour of the structure is spite of their localized character. It becomes especially critical for composites which are inherently more prone to have flaws as a result of matrix-inclusion interfaces. As understanding corresponding fracture mechanism is important for their efficient applications, the present study is devoted on investigating in-plane, quasi-brittle crack propagation phenomenon of composites following the principles of linear elastic fracture mechanics (LEFM). As materials possessing heterogeneities of significant size and texture indicates the presence of scale parameters, the medium should be modelled within the framework of non-classical (non-local) theories, while in this particular case, micropolar theory of elasticity is utilized following its ability in describing the overall mechanical behaviour of materials with presence of particle rotations. The analytical expressions of kinking (propagation) angles are derived by generalizing maximum energy release rate criterion into micropolar solids, and then implemented into the developed combined micropolar/extended finite element method (XFEM) model. The strong dependency between evaluation of crack growth and the level of non-locality is demonstrated considering various benchmark problems with different crack orientations and loading/boundary conditions to study Mode I (crack opening), and Mode II (crack shearing) and mixed mode (Mode I+II) cases. All these efforts highlight the importance of microstructure on the macroscopic crack path.