Molecular dynamics study on atomic elastic stiffness at mode I crack tip in Si: Precursor instability in their eigenvalue before crack propagation

• We discuss the onset of crack propagation by the atomic elastic stiffness in Si Tersoff potential.
• We find the precursor instability in the 1st eigenvalue of the stiffness matrix.
• The eigenvector indicates mode I, II and III cracking for (0 1 0), (1 1 0) and (1 1 1) cracks.
• We also find the stress concentrated area has higher stiffness than that in perfect lattice.
• The area may prevent dislocation emission and give brittle character to Si.

We performed molecular dynamics simulations on the [0 0 1](0 1 0), [0 0 1](1 1 0) and [1¯ 1¯ 2](1 1 1) mode I through cracks in Si, and discussed the unstable crack propagation based on the determinant and eigenvalue of the atomic elastic stiffness (AES), Bijα, under the finite temperature of 300 K. Two significant findings are obtained; the one is the existence of extremely high detBijα atoms, or “highly stable” zone, at the crack tip although the tip surface actually has negative detBijα atoms. The other finding is the precursor instability of the 1st eigenvalue of [Bijα]{Δεj}=ηα{Δεj}. Although there is a little difference in the responses of the [0 0 1](0 1 0), [0 0 1](1 1 0) and [1¯ 1¯ 2](1 1 1) cracks, extremely negative eigenvalue of ηα(1)ηα(1) is observed before the unstable crack propagation. The corresponding eigenvector shows large positive Δε2Δε2 (crack opening or mode I) in the [0 0 1](0 1 0) crack, large negative Δε1Δε1 (intrusion in the x-direction or mode II) in the [0 0 1](1 1 0) crack and large Δε5Δε5 (shear in the zx   or mode III) in the [1¯ 1¯ 2](1 1 1) crack. However, the fracture process in the later stage is rather complicated so that the final fracture mode is not correspond to these instability mode.

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