Mixed-mode crack tip loading and crack deflection in 1D quasicrystals

Abstract

Quasicrystals (QC) are a new class of materials besides crystals and amorphous solids and have aroused much attention of researchers since they were discovered. This paper presents a generalized fracture theory including the J-integral and crack closure integrals, relations between J 1 , J 2 and the stress intensity factors as well as the implementation of the near-tip stress and displacement solutions of 1D QC. Different crack deflection criteria, i.e. the J-integral and maximum circumferential stress criteria are investigated for mixed-mode loading conditions accounting for phononphason coupling. One focus is on the influence of phason stress intensity factors on crack deflection angles. Keywords quasicrystal • crack deflection • mixed-mode loading • fracture quantities • J-integral

Numerical crack path prediction under mixed-mode loading in 1D quasicrystals

“…By this means, the coupling constants cited from [37] are more or less hypothetical values, since there isn't any experimental evidence for their correctness. By adopting such constants (R 1 /C 1111 = 0.47%) in previous work [26], it was noticed that the selected QC shows a very weak coupling effect. Moreover, only small phason SIFs could be induced at the crack tip by mechanical loading because phason loading cannot be applied physically.…”

“…The second energy rate is rather an auxiliary quantity, which may be useful e.g. in numerical fracture analysis [31], in particular in connection with the J-integral [26].…”

“…The problem of crack growth in QCs has been treated on the nanoscale by a molecular dynamics approach [25]. Crack deflection in QCs is handled within a continuum mechanical framework [26], where different crack tip loading quantities, i.e. J-integral, energy release rate and stress intensity factors are related to each other and exploited with respect to crack deflection criteria.…”

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

“…Path-independent integral in fracture mechanics of quasicrystals has been derived to evaluate the fracture parameters in QCs with the atomic arrangement quasiperiodic in one-, two-or three-direction, and the relation between stress intensity factors and energy release rate was discussed [16]. Crack path prediction and crack deflection in 1D quasicrystals were investigated theoretically within a quasi-static framework [17]. By using the generalized Almansi's theorem and the Schmidt method, the non-local solution of a mode-I crack in a 1D QC has been studied [18].…”

Static response of functionally graded multilayered one-dimensional quasicrystal cylindrical shells

“…In comparison with crystals, QCs hold 5-, 8-, 10- or 12-fold rotational symmetry. The one-, two-, three-dimensional (3D) QCs are utilized to describe the projection of the periodic lattice of higher dimensional mathematical space to physical space [10]. One-dimensional (1D) QCs refer to a 3D structure with an atomic arrangement being periodic in one plane and quasiperiodic in the direction perpendicular to that plane [11].…”