Fracture size effects from disordered lattice models

• Published in: International journal of fracture Vol. 154; no. 1-2; pp. 51 - 59
• Main Authors: Alava, Mikko J., Nukala, Phani K. V. V., Zapperi, Stefano
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2008; Springer; Springer Nature B.V
• Subjects: Automotive Engineering; Brittle materials; Characterization and Evaluation of Materials; Chemistry and Materials Science; Civil Engineering; Classical Mechanics; Computer simulation; Crack propagation; Crossovers; Exact sciences and technology; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fracture strength; Fundamental areas of phenomenology (including applications); Materials Science; Mechanical Engineering; Original Paper; Physics; Scaling laws; Size effects; Solid mechanics; Static elasticity (thermoelasticity...); Stress concentration; Structural and continuum mechanics; Fracture; Statistical models; Disorder; Size effect; Notch; Stress concentration; Averaging method; Statistical analysis; Disordered system; Probabilistic approach; Rupture; Mechanical properties; Brittle material; Statistical models .Disorder; Modeling; Random fuse model; Scaling law; Lattice model; Rupture strength
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-008-9306-3

We study size effects in the fracture strength of notched quasi-brittle materials using numerical simulations of lattice models for fracture. In particular, we consider the random fuse model, the random spring model and the random beam model, which all give similar results. These allow us to establish and understand the crossover between a regime controlled by disorder-induced statistical effects and a stress-concentration controlled regime ruled by fracture mechanics. The crossover is described by a scaling law that accounts for the presence of fracture process zone which we quantify by averaging over several disordered configurations of the model. The models can be used to study the development of the fracture process zone as the load is increased and to express this in terms of crack resistance (R-curve).