Size effect on toughness induced by crack close to free surface

Abstract This study explains from the fracture mechanics principles that the common size effect observed in fracture toughness and energy measurements of many engineering materials including concrete, fiber reinforced composites and even coarse-grained ceramics are in fact similar to what has been observed in the well-studied elastic–plastic fracture of metals. The conditions required for measurements of the material constant, the plane strain fracture toughness KIC, of metals are akin to those required to avoid such a size effect on the fracture toughness and energy of concrete and other composites. Using the common yield strength and plain strain fracture toughness criteria a reference crack length a∗ is defined in this study, which is then used to introduce a simple asymptotic function. The asymptotic analysis shows that the size effect on fracture toughness and energy of a heterogeneous material such as concrete will be inevitable if the relative crack measured by the crack ratio a/a ∗ or the remaining ligament ratio W−a /a ∗ is too close to one. This relative crack needs to be around 10 or even higher to avoid the size effect influence. Experimental results and previous models are compared with the current asymptotic analysis.