Crack extension and arrest in contact stress fields

Sudden crack extension and arrest is observed when indenters are pressed into the surface of brittle materials. The energetics of this system are examined. Crack extension is defined by a condition of decreased free energy (after A. A. Griffith) and crack arrest is defined by a condition of increased free energy with a further increase in crack size. The analysis shows that the critical stress required for crack extension depends on the dimension of the stress field and other factors, viz., crack size and material properties, usually associated with Griffith's fracture equation. The dependence on the dimension of the stress field explains Auerbach's empirical law which shows that the apparent strength of a brittle material increases with the decreasing size of the contact stress field. Experimental observations for hot-pressed Si₃N₄ and SiC are presented to examine this size effect and its predicted relation to material properties.