Specimen boundary induced size effect on quasi‐brittle fracture

Abstract

A simple asymptotic analysis dealing with the influence of specimen boundaries on quasi‐brittle fracture of brittle heterogenous materials is presented. The influence of crack‐length/specimen‐size ratio (α‐ratio) on fracture behaviour of finite‐sized specimens has been quantitatively determined by the asymptotic boundary effect model. Different to the common size effect study relying on two scaling parameters that can only be determined by curve‐fitting to experimental results, the present boundary effect model is able to predict the quasi‐brittle fracture behaviour using two fundamental material properties: the tensile strength f_t and fracture toughness K_IC. f_t and K_IC can be determined separately following the standard strength and fracture toughness tests, or estimated from the available data in the literature for most commonly‐used materials. Alternatively, f_t and K_IC can be determined indirectly from quasi‐brittle fracture results using the boundary effect model so that the stringent tensile and fracture toughness tests can be replaced by the simple quasi‐brittle fracture tests. The boundary effect model shows the two scaling parameters used in the size effect study are α‐ratio dependent, and can only be taken as experimental constants for geometrically similar specimens of one single α‐ratio. Furthermore, un‐notched specimens containing small natural flaws have also been considered by the boundary effect model through linking the micro‐flaws to equivalent shallow notches with a near zero α‐ratio. As a result, both notched and un‐notched specimens can be analysed by the same boundary effect relationship.