Analytical evaluation of the transverse displacement at the tip of a semi-infinite crack in an elastic plate

•Analytical approach for evaluating transverse displacements in an angular sector.•Application to a semi-infinite crack subjected to mode I loading.•The SIF is determined from of the transverse displacement near the crack tip. In this paper, a general approach is developed for evaluating the transve...

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Bibliographic Details
Published in:Theoretical and applied fracture mechanics 2018-02, Vol.93, p.288-292
Main Authors: Kotousov, A., Khanna, A., Bun, S.
Format: Article
Language:English
Subjects:
Cracks
Elastic plates
Elasticity
Finite element method
First-order plate theory
Fracture mechanics
Plane problem of elasticity
Plate theory
Plate thickness effect
Wedge geometry
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Summary:•Analytical approach for evaluating transverse displacements in an angular sector.•Application to a semi-infinite crack subjected to mode I loading.•The SIF is determined from of the transverse displacement near the crack tip. In this paper, a general approach is developed for evaluating the transverse displacements in an angular sector. The problem is investigated within the first order plate theory, which can be considered as an elementary extension of the classical plane theories of elasticity. Based on this approach, a new analytical solution for a semi-infinite crack subjected to mode I loading is obtained and this solution is verified against previous three-dimensional Finite Element studies. This approach can also be useful in the analysis of other problems, which can be reduced to a modified Helmholtz (or Yukawa) equation in an angular sector.
ISSN:0167-8442
1872-7638
DOI:10.1016/j.tafmec.2017.09.011