Unified Tensile Fracture Criterion

We find that the classical failure criteria, i.e., maximum normal stress criterion, Tresca criterion, Mohr-Coulomb criterion, and von Mises criterion, cannot satisfactorily explain the tensile fracture behavior of the bulk metallic glass (BMG) materials. For a better description, we propose an ellipse criterion as a new failure criterion to unify the four classical criteria above and apply it to exemplarily describe the tensile fracture behavior of BMGs as well as a variety of other materials. It is suggested that each of the classical failure criteria can be unified by the present ellipse criterion depending on the difference of the ratio $\alpha ={\tau }_0/{\sigma }_0$.

Figure 1

(a) Illustration of a tensile specimen and shear plane and (b) distribution of normal stress $\sigma$ and shear stress $\tau$ on any shear plane of a tensile specimen. Schematic illustration of tensile failure based on (c) maximum normal stress criterion at ${\sigma }_0<2{\tau }_0$ and ${\theta }_T=90°$, (d) Tresca criterion at ${\sigma }_0>2{\tau }_0$ and ${\theta }_T=45°$, (e) Mohr-Coulomb criterion at $45°<{\theta }_T<90°$, and (f) von Mises criterion at ${\theta }_T=60°$.

Figure 2

Schematic illustration of the ellipse criterion at different conditions: (a) $\alpha ={\tau }_0/{\sigma }_o\to 0$ or ${\sigma }_o\to \infty$ and ${\theta }_T\approx 45°$; (b) $0<\alpha ={\tau }_0/{\sigma }_o<\sqrt{2}/2$ and $45°<{\theta }_T<90°$; (c) $\alpha ={\tau }_0/{\sigma }_o\ge \sqrt{2}/2$ and ${\theta }_T=90°$.

Figure 3

Dependence of tensile fracture strength ${\sigma }_T$ and tensile shear fracture angle ${\theta }_T$ on the ratio $\alpha ={\tau }_0/{\sigma }_o$ according to the ellipse criterion. In a different range of $\alpha ={\tau }_0/{\sigma }_o$, each of the four classical failure criteria can be unified by the present ellipse criterion.