## __2016-Sustainable Industrial Processing Summit__

SIPS 2016 Volume 7: Yang Intl. Symp. / Multiscale Material Mechanics

Editors: | Kongoli F, Aifantis E, Wang H, Zhu T |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2016 |

Pages: | 190 pages |

ISBN: | 978-1-987820-48-5 |

ISSN: | 2291-1227 (**Metals and Materials Processing in a Clean Environment Series**) |

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## On singularities at an inclined crack tip terminating at the bi-material interface in a Reissner plate

**Zhaojun
Zhang**^{1};

^{1}DALIAN UNIVERSITY OF TECHNOLOGY, Dalian, China;

**Type of Paper:** Regular

**Id Paper:** 318

**Topic:** 1## Abstract:

In the framework of linear elasticity, singularities occur in domains with non-smooth boundaries. Particularly in fracture mechanics, the local stress field near stress concentrations is of interest. In this work, the internal force singularities at the tip of an arbitrarily inclined semi-infinite crack terminating at the interface of two dissimilar materials are investigated on the basis of Reissner¡¯s plate theory. Using the eigenfunction expansion method, the eigenequation of the corresponding problem is derived explicitly by directly solving the governing equations of Reissner¡¯s plate theory in terms of three generalized displacement components. The focus is on the calculation of the singularity order as a fundamental quantity in fracture mechanics. The singularity orders of the moments and shear force at the crack tip are determined by the dominant eigenvalues whose real parts lie between 0 and 1. The influences of the bi-material parameters and the crack inclination angle on the moment and shear force singularity orders are discussed in detail. Specially, the variations of the shear force singularity order with the bi-material parameter and the crack inclination angle are analyzed in mathematics. It is proved that the shear force singularity order is a completely monotonic function of the bi-material parameter and the inclination angle. Some numerical results are given in order to prove the validity of the present study.

## Keywords:

Mechanics; Surface;

## Cite this article as:

Zhang Z. On singularities at an inclined crack tip terminating at the bi-material interface in a Reissner plate. In: Kongoli F, Aifantis E, Wang H, Zhu T, editors. Sustainable Industrial Processing Summit SIPS 2016 Volume 7: Yang Intl. Symp. / Multiscale Material Mechanics. Volume 7. Montreal(Canada): FLOGEN Star Outreach. 2016. p. 131-132.