Physical differences between models of an infinitesimal crack at a V-notch edge and a crack emanating from a V-notch tip along with their approximate solutions

Existing theoretical methods for solving the stress intensity factors (SIFs) of a cracked V-notch plane are products of highly sophisticated mathematical analyses and are therefore, challenging for engineers to study, derive, and reproduce. Based on our extension of the dimensional analysis, or the 'geometry parameter method', we investigated a V-notched edge of a semi-infinite plate with a crack at the notch tip; the differences between the SIFs of an infinitesimal crack at the tip and cracks emanating in a half plate were presented, and examined. By using superposition and fitting, practicable yet simple, explicit, and closed-form approximations were achieved. Influences affecting the plastic zone were also investigated. The study proved useful, providing various insights that may help practising engineers to establish quick estimation of SIFs.