Journal article
Crack solutions and weight functions for plane problems in three-dimensional quasicrystals
Publication Details
Authors: | Gao, Y.; Ricoeur, A.; Zhang, L.; Yang, L. |
Publisher: | Springer Science Business Media |
Publication year: | 2014 |
Journal: | Archive of Applied Mechanics |
Pages range : | 1103-1115 |
Volume number: | 84 |
Start page: | 1103 |
End page: | 1115 |
Number of pages: | 13 |
ISSN: | 0939-1533 |
DOI-Link der Erstveröffentlichung: |
Abstract
The plane problems of an elliptic hole and a crack in three-dimensional quasicrystals subject to far-field loadings are studied. The generalized Stroh formalism is adopted here, and the explicit solutions for the coupled fields are obtained in the closed form. When the elliptic hole reduces to a crack, the analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The crack theory of quasicrystals, including the determination of the field intensity factors, crack opening displacements, crack tip energy release rates and so on, is a prerequisite. Applying Betti's theorem of reciprocity, the weight functions for a quasicrystal body with a crack are derived. The weight functions provide a means of calculating the intensity factors for the crack when both phonon and phason point forces are imposed at arbitrary locations.
The plane problems of an elliptic hole and a crack in three-dimensional quasicrystals subject to far-field loadings are studied. The generalized Stroh formalism is adopted here, and the explicit solutions for the coupled fields are obtained in the closed form. When the elliptic hole reduces to a crack, the analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The crack theory of quasicrystals, including the determination of the field intensity factors, crack opening displacements, crack tip energy release rates and so on, is a prerequisite. Applying Betti's theorem of reciprocity, the weight functions for a quasicrystal body with a crack are derived. The weight functions provide a means of calculating the intensity factors for the crack when both phonon and phason point forces are imposed at arbitrary locations.
Keywords
Crack, Crack weight function, Elliptic hole, Energy release rate, Field intensity factor, Three-dimensional quasicrystal
