The Krajcinovic approach to model size dependent fracture in quasi-brittle solids

• Published in: Mechanics of materials 2014-04, Vol.71, p.21-33
• Main Authors: Rinaldi, Antonio, Mastilovic, Sreten
• Format: Article
• Language: English
• Subjects: Communities; Crack initiation; Crack propagation; Damage; Damage tolerance; Failure; Fractal analysis; Fractal theory; Fracture mechanics; Scaling laws; Size effects; Statistical damage mechanics; Stems; Strength scaling
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2014.01.005

•The “Krajcinovic approach” tackles fracture sample-size effects by a novel fractal scheme.•The method consists of the nested application of the Family–Vicsek scaling laws.•The damage parameter turns scaling laws into engineering constitutive relationships.•The method rationale apply to all real quasi-brittle structural and material systems. The failure in “quasibrittle” microstructural systems, occurring with no early warning, is a debated problem of great practical importance for the structural engineering community. Available models do not fully account for typical sample-size effects observed in fracture initiation and propagation. The Krajcinovic approach (K-approach) proposed here stems from a posthumous interpretation of Krajcinovic’s original ideas and offers a new route to tackle such effects by means of an advanced fractal scheme, which consists of the sequential application of the Family–Vicsek scaling laws for the number of damage events n(ε;L) in the fracture initiation and propagation regimes separately. The procedure is developed and explained in the context of an established lattice models under static tensile testing. Average simulation data for any outer-size L – here ranging from 24 to 192 – is shown to scale nicely by this method, throughout the entire damage process. The proper definition of the damage parameter D allows deploying the deduced scaling laws to deduce the actual stress vs. strain relationship applicable in engineering. The discussion extends with no prejudice to data from real experiments, provided that all necessary information is gathered and all underlying assumptions hold true. The approach shall appeal per se also to the larger scientific community of physicists and mathematicians involved in statistical mechanics and random network failure.