Justification of the Small Process Zone Case of the Two Extremes Procedure for Quantifying Fracture Initiation at a Blunt Flaw

With the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture as a basis, the author is involved in a wide-ranging research programme, the objective being to extend the sharp crack fracture mechanics methodology to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a blunt flaw fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) or any characteristic dimension of a configuration other than the root radius ρ. This relation gives the critical elastic flaw-tip peak stress σ_pcr, and has been derived using a two extremes procedure, whereby the separate solutions for small and large s/ρ are blended together so as to give a single relation that is valid for the complete spectrum of s/ρ values. The small s/ρ solution was obtained by inputting the stress field in the immediate vicinity of the flaw root into an analysis of the behaviour of a process zone at a planar surface. This paper provides formal justification for this small s/ρ procedure.