Crack Paths 2012

obtained by three methods: Mitchell model [22], C O F Amodel and experimental

values [20]. To estimate V'f, C O F Amodel (V’f= 0.965Vu+343) has slightly improved

the results: error (V’f) = 0.107 against 0.109 to Mitchell [22]. Figure 2 shows the results

on H'f coefficient determined by Manson's Universal Slopes model [26, 27], C O F A

model and experimental values [20]. For the estimation of H'f, C O F Amodel improve

here significantly the results: error (H'f) = 0.5856 against 0.655 obtained by Manson's

Universal Slopes [26, 27].

Note that the estimation of H'f remains difficult for ε'f≥ 0.4 (Figure 3). This deficiency

can be reduced if the model takes into account the Brinell hardness (BHN)[3, 5, 12].To

this purpose, we introduce into C O F Amodel a regularization parameter R which depends on B H Nand which is computed as follows: R = m * (BHN) n.

Figure 4. The influence of regularization parameter R

Figure 3. Comparison between experimental values of H’f and those obta ned wi h C O F Aand MU-Slop

on ε'f

The formula for modelling the fatigue ductility coefficient becomes:

0.09

0.53

V§ ·

0.0130

0.155

u

'

0 . 1 B H N

H

H

f

f

E ¨ ¸ © ¹

Final Model

W enote that the curve of H'f coefficients estimated by C O F Amodel follows the shape

of the curve of H'f coefficients determined experimentally (Figure 4).

R parameter has allowed us to minimize the error in estimating the coefficient H'f (error

(H'f) = 0.5647). This has significantly improved the estimated coefficient H'f with respect

to the estimation given by the models discussed above.

The C O F Amodel equations are finally:

H

H

0.0130

0.09

u E ¨ ¸ © ¹ V § ·

0.1

'

0.155

V

0.0965 343 u V

u

B H N

'

f

0.53

f

f

872