13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure1. Typical load versus plastic displacement curves for static and growing cracks 2.2. Plastic factor of front face compact tension Following the similar route for deriving the LLD-based J equation, this section formulates an incremental CMOD-based (Crack Mouth Open Displacement) J estimation. A total CMOD, V, is separated into an elastic component el V and a plastic component pl V . As such, the total J can be decomposed into an elastic component el J and a plastic component pl J , as show in Eq 1. The el J is defined in Eq 2, whereas the pl J is determined by 0 pl pl V V V V pl pl A J PdV Bb Bb η η = = ∫ (11) where Vη is the plastic factor of front face compact tension, pl VA is the area under the measured pl P V− curve. Without loss of generality, it is assumed the ratio of pl V and pl Δ is a function of a/W [19] ( ) / pl pl V a W λ = Δ (12) Substitution Eq 12 into Eq 11 gives ( ) pl pl pl 0 0 = = pl pl V V J Pd Pd Bb Bb η η λ λ Δ Δ Δ Δ ∫ ∫ (13) From Eqs 3, 11, 12 and 13, three equivalent expressions for this new plastic factor are obtained ( ) pl pl / pl V pl V V A a W A η λ η Δ Δ = = = Δ (14) Since pl J is now the function of pl V and a, its complete differential is obtained as
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