Size Effects on Strength, Toughness, and Ductility

Abstract

Strain localization for slabs in tension and curvature localization for beams in flexure are associated with the fracture toughness of the material. Even if no initial cracks are supposed to exist in the sturcture, the concepts of fracture mechanics are applicable. Size‐scale and slenderness are demonstrated to have a fundamental influence on the global structure behavior, which can range from ductile to brittle when softening is taken into account. Whereas in classical plasticity and damage theory geometrically similar structures exhibit congruent behavior since only energy dissipation per unit volume is allowed, when energy dissipation per unit area is also considered (strain or curvature localization), the global brittleness becomes scale‐dependent. A limit analysis for beams in flexure is proposed, taking into account the cohesive forces developing between the two opposite crack surfaces. Such a simple approach shows a clear trend toward brittle behavior and catastrophic events for large size and slenderness. When snap‐back instability occurs, the softening load‐deflection curve exhibits a positive slope and its path becomes virtual. If the loading process is deflection‐controlled, the loading capacity of the beam will exhibit a discontinuity with a negative jump. Such results are confirmed by refined finite element investigation.