The Griffith barrier, initiation, and arrest energies by stable cracks

Abstract

We report on a new, cost-effective, and relatively simple experimental method to evaluate the Griffith barrier, initiation, and arrest energies in cracked brittle specimens under Mode-I conditions, by a stable crack propagation under displacement control conditions. Obreimoff's experiment inspired the new method, and thus we termed it the Obreimoff-inspired Coefficient of Thermal Expansion Mismatch (OCTEM) method. It includes inserting a 10 mm by diameter low angle conic aluminum pin into a perfectly matched conic hole in a rectangular thin precracked brittle specimen. Upon heating the assembly on top of an electrical heating stage, the thermal expansion coefficients mismatch between the aluminum pin and specimen generated sufficient deformation until the crack propagates stably. Silicon specimens, where the cracks propagated on the (110)[1$\overline{1}$0] low energy cleavage system, were used as a model material. Cracks propagated stably in cycles of initiation, propagation, and arrest. Measuring the specimens’ temperatures during the experiments and depicting the temporal crack lengths allowed us to evaluate a set of initiation and arrest energies using linear elastic, plane stress, and contact problems with friction finite element analysis. The cleavage energy decreased as crack length grew in a stable propagation, similar to what we observed in unstable cracks. We show the importance of the gradient of the strain energy release rate (SERR), $\overline{\Theta }$ dG₀/da, on the cleavage energies. Finally, we compared the cleavage energy at initiation vs. $\overline{\Theta }$ for stable and unstable conditions.