Crack-Tip Stress Concentration and Structure Size in Nonlinear Structured Materials

We revisit the standard elastic-plastic fracture theory developed by Hutchinson, Rice, and Rosengren (HRR) and reproduce, by a simple scaling argument, the stress singularity around the crack tip derived by HRR. From the singular behavior thus reconfirmed, we propose a general scaling relation which guarantees an effect similar to the tip-blunting effect: the maximum stress at the crack tip in a structured material can be reduced by increasing the structure size. This proposed relation is explicitly confirmed by numerical calculations performed for a coarse-grained lattice model, and leads to general scaling relations for fracture surface energy and to a possible reinforcement of cellular solids due to the pores.