Failure criteria: Old wines in new bottles?

•A closed form solution of the size effect problem is presented.•Size effect is caused by different behavior of mechanical properties of core and surface.•The connection of size effect and volume–surface strain energy is demonstrated. Aim of the present work is to communicate a part of the experience gathered by the first author after 40 years of involvement in Fracture Mechanics and Failure of Materials in general, through close collaboration with his colleagues. From this point of view, a few prerequisites for the, say, correct formation of a failure criterion are considered. For example, are of equal validity deductive and inductive approaches? Furthermore, some common characteristics of existing failure criteria are discussed and their effect on the quality and the general applicability of failure criteria is presented. For example, how and why does geometry affect failure predictions? Do cracks or other singularities require a special treatment? Is the characterization of materials through usual constitutive equations adequate? In a more practical level, the necessity of introducing as more as possible stress/strain components in the formation of a failure criterion is emphasized, driving directly to strain energy density (SED) considerations. The deterministic requirement of “cause-effect” demands available (i.e. elastic) SED, excluding plastic work, and, consequently, plastic strains from the formation of any criterion. Considering the only two mechanisms of storing SED in materials (volume-lengths and shape-angles changes of the elementary volume), we arrive into a dilemma regarding the “behavior” of the SED parts been spent for volume or shape changes. In case they are collaborative, their sum (i.e. the total elastic SED) is adequate to describe failure. Contrarily, in case of competitive behavior, each SED component has its-own importance and must be traced separately. Finally, existing groups of criteria are commented and some conclusions are presented.