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.
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