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.

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... t is suggested that each of the classical failure criteria can be unified by the present ellipse criterion depending on the difference of the ratio 0 = 0 . The deformation and fracture behavior of various structural materials or matter, such as metals, ceramics, intermetallics, rock, soil, concrete, etc., has been investigated for more than 200 years, and many important theories or rules were proposed and well developed. For brittle materials, for example, ceramics, intermetallics, rock, soil, and concrete, their yield and failure often occur simultaneously due to lack of plasticity or working hardening ability. Among the failure criteria available, there are four classical ones, which have been widely used for the yield or failure of brittle materials, as summarized in some textbooks [1-4]. As illustrated in Figs. 1(a) and 1(b), when one applies a tensile stress T to a specimen, the normal stress and the shear stress on any shear plane can be expressed as PRL 94, 094301 (2005) P H Y S I C A L