applied fracture mechanics

Good Practice for Fatigue Crack Growth Curves Description 2213.4. Regression of dependences in the NASGRO equationApproximation of curves da/dN-K substantially depends on preset values of parameters Kcand Kth. Hence, it is very important whether they can be determined on the grounds of thetest data only (if they cover the whole range of the curve, i.e. 10 -7 through 10 -2 mm/cycle,which is not always easy to reach), or whether they need any other method/way to bedetermined, e.g. formula (2), functional dependences of the type Kth = f(R) and Kc = f(R), orthe above-mentioned extrapolation. The above-discussed results of extrapolationcorrespond to the case when both the parameters show constant values for all theapproximated curves. The plots for the test data show, however, that they depend on thestress ratio R – for each of nine experimentally gained curves parameters Kth,i and Kc,i canbe estimated and the data gained can then be used to determine dependences Kth = f(R) andKc = f(R), including coefficients for equation (2).Formulae (2) and (2a) are special cases of a general formula of the following form: a 21R1A0KthK0 aa 0 1 f 1CCthR.(33)Having re-arranged this formula, the following is arrived at:1 a 2 1R1A0 1R1A0 0 tha a 01 f 1f log K log K Clog C Rlogth(34)and then:1R1A01 a logK 1th 2log log K0 Cloga a 0f 1R1A0CthRlog 1 f (35)which can be described with the linear-regression equation as: 1R1A0where FR ( ) log, 1 f y m mFR ( ) mRFR ( ),(36)0 1 2and the corrected value of the threshold range of the stress intensity factor is: a y log 1Kth 2log .a a 0