Figure 1: Normalized double-logarithmic rate-control map [1] Extension of the Original Formalism As a single rate-controlling step was assumed, the model outlined above is not able to predict crack growth rates in the vicinity of the bounds of the rate-control map. In order to take into account the simultaneous operation of more than one rate-controlling step the damage ratio is considered the analogue of the spring constants (or conductivities) in a series of springs (or electric resistors). The resulting model reads: ref e da/dN da/dN (4a) c b a 1/ 1/ 1/ 1 1 (4b) The process-competition model for the crack growth mechanisms in the aggressive and in the reference environment applied to obtain the ratecontrol map is substituted by the superposition model represented by the first plus sign in Eq. 4b. The functions a, b, and c can be replaced by the expressions given in Eqs. 2, if the corresponding assumptions are justified. Using the constants obtained by the fit performed in [1] for the Al alloy 6013 T6 a 3D representation of Eq. 4b is obtained (Fig. 2). -5 -4 -3 -2 -1 0 1 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 log b (f/f S ) log b (K/K S ) 1 2 3 4 4 4 A B C S 1 q-controlled field 2 v-controlled field 3 D-controlled field 4 no effect of environment
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