ABSTRACT
C = G + Qdqpi/Bda (2a) = Gfr + wpl/Bda = D (2b) In Eqn.2b, sub fr denotes that it has been dissipated in what in lefm is seen as 'fracture'. The terminology Qdqpi in Eqn.2a implies a driving force whilst Wpj in Eqn.2b, though numerically equal, is a dissipation. The form dqpj/da invites the concept of 'crack opening angle' (COA), but since it is based on a global displacement, it may or may not be identifiable with a local 'crack-tip opening angle', (CTOA). Thus attention passes to crack opening angle with satisfaction of energy dissipation rate through Eqn.2, rather than opening displacement. 2.3 The local CTOA The physical picture used, [4], is that of Wnuk, [9], where a final crack opening stretch, 8t, occurs in the micro-ligament between the current tip and the void ahead of it, at fixed crack length. Once the ligament has fractured, the CTOA can be formed as
a = 6t/d (3) where d is the spacing of the inclusions around which the dominant micro-voids are grown. An increment of crack growth, da, does not tend to a limit of zero but to the finite quantity, d. In a two dimensional model, these events must be represented as distinct steps in growth with d(Aa) -> d. In a three dimensional body the steps are averaged across the thickness and would not normally be seen on the macro-scale.
