Fracture instability and limit strength condition in structures with re-entrant corners

When considering a structural element with a re-entrant corner, the experimental analysis shows how the fracture strength increases with the angle of the corner. Thus, the strength increases with a decrease of the mass of the structure, in contrast to what we are used to observe in different kind of collapses, e.g., plasticity. To predict this behaviour, a non-local theory, basically based on the Novozhilov’s hypothesis of existence of a fracture quantum, is herein presented. Theoretical predictions for the strength of finite structures (e.g., finite plates under tension or beams under bending) by varying both angle and relative depth of the corner are presented: accordingly, simple formulas, useful in the design of such structures, are provided. The theory is then compared with experimental and numerical results, showing a relevant agreement.