Characteristic Tensor for Evaluation of Singular Stress Field under Mixed-mode Loadings

A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius. It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters. Therefore, it can be used to estimate stress intensity factors (SIFs) for cracks of arbitrary shape subjected to multiaxial stress loads. A characteristic tensor can also be used to estimate SIFs for kinked cracks. This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters. Consequently, a single straight crack and a kinked crack of finite length existing in a two-dimensional, infinite isotropic elastic body in a plane stress state, were considered to investigate the properties of the characteristic tensor under mixed-mode loadings. To demonstrate the practical utility of the characteristic tensor, the stress distribution obtained through finite element analysis (FEA) was used to estimate mixed-mode SIFs, and the values of estimated SIFs were compared with those obtained using an analytical solution. Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values. This indicates that the proposed characteristic-tensor-based approach is effective in extracting features of singular stress fields at crack tips, and can be employed to estimate values of fracture-mechanics parameters, such as SIFs. Owing to its simplicity, the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios. The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.