Crack-tip fields of an anti-plane crack in micropolar elastic solids

Due to the existence of microstructures involving characteristic length scales, micropolar materials such as bones, rocks and foam materials usually have complex fracture behaviors. The near-tip fields of an anti-plane crack in micropolar media and the local cracking modes, however, remain unclear. In this paper, the Williams asymptotic solutions of the near-tip fields of an anti-plane crack in micropolar elasticity are derived. A force stress intensity factor (FSIF) and two couple stress intensity factors (CSIFs) are the key fracture parameters characterizing the anti-plane crack-tip fields. And the energy release rate for an anti-plane crack is similar to the Rice's J -integral for classical continua. Then, six crack modes are introduced for a three-dimensional micropolar solid, i.e., three global modes controlled by the FSIFs and three local modes controlled by the CSIFs. Different from classical isotropic elasticity, a material constant appears in the singular terms of the crack-tip force stress and couple stress fields of isotropic micropolar materials. In addition, there are six constant terms in the asymptotic solutions of the crack-tip fields, i.e., three constant force stresses and tree constant couple stresses similar to the T-stress in classical fracture mechanics. Sequentially, the J -integral for three-dimensional micropolar solids is expressed concisely by the FSIFs and CSIFs. It can be observed that the CSIFs normalized by the torsion and bending characteristic lengths are dimensionally equivalent to the FSIFs. This work provides a theoretical basis for studying the fracture performance and crack propagation criterion of micropolar materials.