Underpinning of a simple blunt flaw fracture initiation relation

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 fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a Mode I fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius ρ. The relation gives the critical elastic flaw-tip peak stress σpcr, and has been derived using a “two-extremes” procedure, whereby the separate, and indeed exact, solutions for small and large s/ρ values are blended together to give an all-embracing relation that is valid for all s/ρ values. σpcr is expressed in terms of the process zone material parameters and geometrical parameters but, for a wide range of flaw geometry parameters, σpcr essentially depends on only one geometrical parameter: ρ. This paper provides underpinning for the general thrust of the “two-extremes” procedure by appealing to exact results for the complete spectrum of s/ρ values from analyses of appropriate Mode III models. Results obtained by applying the “two-extremes” procedure are shown to be in very good agreement with the exact results.