1    The geometric stress-concentration factor K_{t} is found from the equation in Figure 4-36:

K_t=A\left(\frac{r}{d}\right)^b          (a)

where A and b are given in the same figure as a function of the D/d ratio, which is 2 / 1.8 = 1.111. For this ratio, A = 1.014 7 and b = –0.217 9, giving

K_t=1.0147\left(\frac{0.25}{1.8}\right)^{-0.2179}=1.56          (b)

2    The notch sensitivity q of the material can be found by using the Neuber factor \sqrt{a} from Figure 6-35 and Tables 6-6 to 6-8 in combination with equation 6.13 (p. 345), or by reading q directly from Figure 6-36. We will do the former. The Neuber factor from Table 6-6 for S_{ut} = 100 kpsi is 0.062. Note that this is the square root of a:

q=\frac{1}{1+\frac{\sqrt{a}}{\sqrt{r}}}        (6.13)

q=\frac{1}{1+\frac{\sqrt{a}}{\sqrt{r}}}=\frac{1}{1+\frac{0.062}{\sqrt{0.25}}}=0.89          (c)

3    The fatigue stress-concentration factor can now be found from equation 6.11b (p. 343):

K_f=1+q\left(K_t-1\right)         (6.11b)

K_f=1+q\left(K_t-1\right)=1+0.89(1.56-1)=1.50          (d)

4    The files EX06-03 are on the CD-ROM.