Interference Effect Between a Parabolic Notch and a Screw Dislocation in Piezoelectric Quasicrystals - Yuanyuan Gao; Guanting Liu; Chengyan Wang; Junjie Fan (Crystals)
This study investigates the coupling mechanism between a parabolic notch and dislocations in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) based on the theory of complex variable functions. By applying perturbation techniques and the Cauchy integral, analytical solutions for complex potentials are derived, yielding closed-form expressions for the phonon–phason stress field and electric displacement field. Numerical examples reveal several key findings: significant stress concentration occurs at the notch root, accompanied by suppression of electric displacement; interference patterns between dislocation cores and notch-induced stress singularities are identified; the J-integral quantifies distance-dependent forces, size effects, and angular force distributions reflecting notch symmetry; and the energy-driven dislocation slip toward free surfaces leads to the formation of dislocation-free zones. These results provide new insights into electromechanical fracture mechanisms in quasicrystals.