Fracture mechanics analysis of auxetic chiral materials

Abstract

Auxetic materials sometimes exhibit extremely high strength, stiffness and toughness, such as limpet tooth. The toughening mechanism of such materials is still not completely clear. This paper first theoretically derives the crack-tip asymptotic fields of a planar auxetic chiral solid. It can be found that the planar auxetic chiral solid has three crack modes, i.e., the opening mode governed by the mode I force stress intensity factor (FSIF), the sliding mode governed by the mode-II FSIF and the local bending mode governed by the couple stress intensity factor (CSIF), and these crack modes are generally coupled with each other. The microstructural auxeticity induces asymmetric distributions of the angular functions in the mode I and mode II cracks. Local bending deformation is likely to induce the occurrence of stepped crack paths in auxetic chiral materials observed experimentally in available literature. Then, a new interaction integral (I-integral) method is established to decouple the mode-I FSIF, the mode-II FSIF and the CSIF. The proposed I-integral has two extra superiorities over the J-integral: (i) it does not require the derivatives of material parameters; (ii) it is domain-independent for material interfaces, which is theoretically proved and numerically validated. With these two features, the proposed I-integral becomes a powerful tool in decoupling the FSIFs and CSIF for nonhomogeneous and multi-interface auxetic chiral materials. Numerical simulations on the fracture of limpet teeth indicate that the tensile-torsional coupling deformation of microstructures can reduce the risk of mode I fracture of auxetic chiral materials. The chirality angle affects both the FSIFs and CSIFs significantly.