  Ever since its publication, the Griffith theory is the most widely used
criterion for estimating the ideal strength and fracture strength of materials
depending on whether the materials contain cracks or not. A Griffith strength
limit of ~E/9 is the upper bound for ideal strengths of materials. With the
improved quality of fabricated samples and the power of computational modeling,
people have recently reported the possibility of exceeding the ideal strength
predicted by the Griffith theory. In this study, a new strength criterion was
established based on the stable analysis of thermodynamical systems; then
first-principles density functional theory (DFT) is used to study the ideal
strength of four materials (diamond, c-BN, Cu, and CeO2) under uniaxial tensile
loading along the [100], [110], and [111] low-index crystallographic
directions. By comparing the ideal strengths between DFT results and the
Griffith theory, it is found that the Griffith theory fails in all the four
materials. Further analysis of the fracture mechanism demonstrates that the
failure of the Griffith theory is because the ideal strength point does not
correspond to creating of new surfaces, which is against the Griffith
assumption that the crack intrinsically exists all the time; the failure point
corresponds to the crack at the start of propagation.
