The scale- or the size-dependence of mechanical strength in many brittle materials appears to follow a ‘universal law,’ of the form: strength proportional as:L^-n or V^-n, where n is a number, L is the length and V is the volume of the specimen or structure. Broadly known as the “size-effect” in geology, civil engineering, mining and materials science, this behavior determines the strength of large structures such as ice sheets, rock formations, coal pillars in mines and concrete beams and columns in civil infrastructure. As of now, there is no reliable scientific basis or theory to explain the size effect or for determining a reliable value of ‘n’. This has been the missing link in strength of materials for nearly a century since the Griffith’s crack theory Here, we show that the change in net-section strain energy, due an initial crack in a structure, and its dissipation within a crack layer of finite thickness, leads to the necessary and sufficient physical basis to explain the size-dependence of strength as L^-0.5. Further, size-independence of strength is explained simultaneously when the crack layer volume approaches the specimen volume.
EXTENDED ABSTRACT