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Characteristic Tensor for Evaluation of Singular Stress Field Under Mixed-Mode Loadings

Kei Saito1, 2, *, Tei Hirashima1, Ninshu Ma2, *, Hidekazu Murakawa2

1 JSOL Corporation, 2-5-24 Harumi, Chuo-ku, Tokyo, 104-0053, Japan.
2 Osaka University, 11-1 Mihogaoka, Ibaraki, Osaka, 567-0047, Japan.

* Corresponding Authors: Kei Saito. Email: email;
   Ninshu Ma. Email:

Computer Modeling in Engineering & Sciences 2020, 122(2), 415-432.


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 twodimensional, 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 characteristictensor-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.


Cite This Article

Saito, K., Hirashima, T., Ma, N., Murakawa, H. (2020). Characteristic Tensor for Evaluation of Singular Stress Field Under Mixed-Mode Loadings. CMES-Computer Modeling in Engineering & Sciences, 122(2), 415–432.


cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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