Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 2: Numerical method. (July 2017)

• Record Type: Journal Article
• Authors: Dang, HuaYang; Zhao, MingHao; Fan, CuiYing; Chen, ZengTao
• Is Part Of: Engineering fracture mechanics. Volume 180(2017)
• Page Start: 268
• Page End: 281
• Publication Date: 2017-07
• Subjects: One-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material -- Fundamental solution -- Constant triangular element -- Gaussian distribution function -- Elliptical interface crack -- Extended displacement discontinuity method -- Extended stress intensity factor -- Energy release rate; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2017.05.042
• Languages: English
• ISSNs: 0013-7944

Abstract

Highlights: Numerical method for interface crack in 1-D hexagonal quasicrystals is proposed. The fundamental solution for extended displacement discontinuities is obtained. The extended SIFs without oscillatory singularities are obtained. The method is applicable to interface cracks in other multifunctional materials. Abstract: The extended displacement discontinuity boundary integral equation and boundary element method are extended to analyze a three-dimensional (3D) arbitrarily shaped interface crack in a one-dimensional hexagonal, quasicrystal bi-material with both electric and thermal effects under combined phonon-phason-electric-thermal loadings. Based on the analogy with the analysis method for three-dimensional, transversely isotropic magnetoelectrothermoelastic bi-materials (Dang et al., in press) the numerical method is proposed for one-dimensional quasicrystal bi-materials. Firstly, the fundamental solutions for uniformly distributed, extended displacement discontinuities applied over a constant triangular element are obtained by integrating the fundamental solutions for unit-point extended displacement discontinuities given in Part 1 over the triangular area (Zhao et al., 2017). Secondly, in order to eliminate the oscillatory singularity near the crack front, the Delta function in the integral–differential equations is approximated by the Gaussian distribution function, and the Heaviside step function is replaced by the Error function accordingly. Thirdly, the extended stress intensity factors without oscillatory singularities and the energy release rate are all obtained in terms of the extended displacement discontinuities. At last, the extended displacement discontinuity boundary element method is proposed to validate the analytical solution. In the numerical simulation, the multi-physical behavior of an elliptical, interface crack is numerically simulated. The correctness of the proposed numerical method, the influence of the applied, combined phonon-phason-electric-thermal loadings, the material-mismatch, and the ellipticity ratio are all studied.