### Abstract

Path-independent integrals are successfully utilized for accurate evaluation of fracture parameters in crystalic materials, where atomic arrangement is periodic. In quasicrystals (QC) the atomic arrangement is quasiperiodic in one-, two- or three-directions. The 2-d elastic problem for quasicrystal is described by coupled governing equations for phonon and phason displacements. Conservation laws for quasicrystals are utilized to derive path-independent integrals for cracks. The relation between the energy release and stress intensity factor for a crack under the mode I is given for decagonal QCs. The path-independent integral formulation is valid also for cracks in QCs with continuously varying material properties.

Original language | English |
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Pages (from-to) | 61-71 |

Number of pages | 11 |

Journal | Engineering Fracture Mechanics |

Volume | 140 |

DOIs | |

State | Published - May 1 2015 |

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### Keywords

- Bak's model
- Decagonal quasicrystals
- Elastodynamics
- Energy balance
- Intensity factors
- Path-independent integral
- Phason
- Phonon

### Cite this

*Engineering Fracture Mechanics*,

*140*, 61-71. https://doi.org/10.1016/j.engfracmech.2015.03.039