the original version of the model, was assumed to be proportional to q, inverse proportional to v, and proportional to the mean diffusional path, (D/f)1/2, respectively. This yields expressions for the functions, : C f q1 a a (2a) 2 2 1 b b C K E fv (2b) 2 2 1/2 1/2 c c C K E f D (2c) Ca, Cb, and Cc are dimensionless constants. In order to identify the ranges of K and f, where a certain step is the slowest one, the above expressions are equated to one another. In a double-logarithmic f-K plot the resulting power-law equations between K and f are represented by straight lines. These lines separate the regions in the f-K plane, where the respective steps are rate controlling. The lines defined by the conditions =1 bound these regions against the region outside, where no environmental effect is present. In order to obtain a graphical representation of the „rate-control map“, frequency, f, and stress intensity factor range, K, have to be normalized by the model parameters, fS and KS. Furthermore, a particular base, b, of the logarithm has to be introduced: 1 1/5 2 c 1 2 b 4 a Sf C q C v C D (3a) 2 1/10 2 c 1 b 3 a SK E C q C v C D (3b) b=Caq/fS (3c) The resulting rate-control map is presented in Fig. 1. If in a fatigue crack growth test (at varying K and/or f) one of the lines in Fig. 1 is crossed, a transition in the crack growth behaviour is expected. Such transitions have indeed been observed in [1]. By fitting individual lines of the map to the measured locations of the corresponding transitions the model parameters fS, KS, and b, have been estimated. The physical quantities characterizing the individual rate-controlling steps can then be calculated via Eqs. 3. In this way the general model, Eqs. 1 or 2, can be applied to a particular material, if the model assumptions are prooved to be valid.
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