A study was conducted to investigate the influence of nucleation of the chains of nanoscopic grains near the vertexes of cracks on the crack resistance of nanocrystalline ceramics. The consideration of the energy characteristics of the nucleation of nanoscopic grain chains near the crack tip was excluded from the investigation and the influence of the nucleated nanograins on the crack resistance of the nanocrystalline materials was considered. The structure of a two-dimensional section of a nanocrystalline sample with a plane type I crack with length l was assumed to be invariable along axis z, which was perpendicular to the figure plane. This assumption allowed researchers to simplify the mathematical analysis of the stated problem reducing it to the consideration of the two-dimensional structure.
Morozov, N. F., Ovid'Ko, I. A., & Skiba, N. V. (2013). Influence of nucleation of the chains of nanoscopic grains near the vertexes of cracks on the crack resistance of nanocrystalline ceramics. Doklady Physics, (6), 249-252. https://doi.org/10.1134/S1028335813060049