applied fracture mechanics

216Applied Fracture MechanicsB1 B B 21,2B 2,2B1,3 B 2,3 b2 b3 0,B1,1 B 2,1B1,1 B 2,1B1,1 B 2,1 BB1B 31,2B 3,2B1,3 B 3,3 b2 b3 0.B1,1 B 3,1B1,1 B 3,1B1,1 B 3,1 (28)what gives 2 equations of the general form:Ck bC2 2, kbC3 3, k0k 2,3.(29)- eliminating b2hence:C2C C33,2C 3,3 b3 0,C2,2 C 2,3C2,2 C 2,3 (30) B1 B 2B1B 3B1,1 B 2,1B1,1 B 3,1 C2C B 3 1,2B 2,2B1,2 B 3,2CB2,2C 2,3 1,1B 2,1B1,1 B 3,1b3 .C3,2 C3,3 B1,3 B2,3 B1,3 B3,3 C2,2 C 2,3 B1,1 B 2,1B1,1 B 3,1 B1,2 B 2,2B1,2 B 3,2 B1,1 B 2,1 B1,1 B 3,1 (31)Hence, coefficient b2 can be calculated from one of the formulae (29); secondly, coefficient b1from one of equations (27), and finally, coefficient b0 from one of equations (25).The in this way found coefficients of the NASGRO equation enable approximation of curvesda/dN-K from Fig. 9 to the form shown in Fig. 10a. Considerable improvement in thetheoretical (analytical) description for the whole range of plotted curves is evident.Both criteria (15) and (20) have also some disadvantage consisting in that if theapproximating value is much smaller than the approximated value yi (i.e. by 3, 5, 7 ordersof magnitude) or simply close to zero then the component of the sum S and S* is close to thesquared value yi (in case of (15)) or to 1 (in case of (20)), independently of how these twovalues differ from each other.Obviously, it is important whether the approximation and behavior of the approximatingcurve near value yi at the level of e.g. 10 -6 and lower (i.e. for strongly decreasing valueswithin the “threshold” range of the graph) take place at the level of 10 -8 , 10 -12 or 10 -20 (what isnot hard to achieve for curves showing strong vertical courses on graphs plotted with the