applied fracture mechanics

214Applied Fracture Mechanics da 1 f Kth K maxlog logC n log K p log 1 q log 1 ,dN 1 RK K c and can be presented in the following general way:(21)y b 0 b 1 f 1 b 2 f 2 b 3 f 3 .(22)Coefficients bi are directly connected with C, n, p and q (b0=log(C), b1=n, b2=p, b3=-q), whereasfunctions fi depend on K and R and include all the remaining coefficients of the NASGROequation. Coefficients bi of the approximating equation are calculated from the minimumcondition of the equation (20), i.e.: n b0 b1 f1, ib2 f2, ib3 f3,iyiyS bb i1i kk 1,2,3,4.This leads to the following system of equations:k2 0(23)nSb0 b1 f1, ib2 f2, ib3 f3,iyi 1 2 0,b0i1y i yinSb0 b1 f1, ib2 f2, ib3 f3, iyi f 1 2 0,b1i1y i yinSb0 b1 f1, ib2 f2, ib3 f3, iyi f 2 2 0,b 2 i1 y i yinSb0 b1 f1, ib2 f2, ib3 f3, iyi f 3 2 0.b 3 i1y i yiIt is a system of 4 linear equations with 4 unknowns bi, which after transformation takes aform:(24)f f fn b b b bn n n n n1 11, i 2, i 3, i 0 2 1 2 2 2 30,2i1yi i1yi i1 yi i1 yi i1yin 2f n n n n1, if1, if1, if1, if2, if1, if3,i 0 2 1 2 2 2 32i1 yi i1 yi i1 yi i1 yi i1yin f n n2, if2, if1, ifn 22, if n2, if2, if3,i 0 2 1b2 2 b3i1 y2 2i i1 yi i1yii1 yii1yin 2f n n n n3, if3, if1, if3, if2, if3, if3,i 0 2 1 2 2 2 32i1 yi i1 yi i1 yi i1 yi i1yin b b b b0,n b b 0,n b b b b0.(25)