Local lattice instability analysis on mode I crack tip in [formula omitted]-SiC: Characteristics in binary covalent crystal

Abstract

Local lattice instability analysis based on the atomic elastic stiffness (AES), Bijα=Δσiα/Δεj (i,j=1–6 in Voigt notation), is applied to mode I crack tip in covalent binary crystal β-SiC of Tersoff interatomic potential. The application limit of the AES is disclosed at the discontinuous local energy surface of disordered broken bonds in the discrete binary system; however, we also captured interesting results with the 1st eigenvalue ηα(1) of Bijα as follows, (1) the atomic stress of C atoms coincides with the stress singularity in the linear fracture mechanics, when the minimum eigenvalue of C atom shows the first sudden drop or the first instability, (2) but the crack doesn’t propagate nor there is no remarkable change in the stress–strain curve, (3) bond breaking and reconstruction occurs in the vicinity of crack tip at the second instability in the eigenvalue, (4) C atoms in the disordered configuration show extraordinary large negative eigenvalue (possibly due to discontinuity of energy surface), while Si atoms show third drop in the eigenvalue just before unstable crack propagation, (5) linear fracture mechanics fails to predict the stress singularity at the crack propagation, (6) the principal axes of the eigenvector of ηα(1)<0 atoms reveal the deformation mode for local slip and cracking on the multiple (111) planes in the unstable domain at the forefront of the propagating crack.