PSI - Issue 4

J. Maierhofer et al. / Procedia Structural Integrity 4 (2017) 19–26

24

J. Maierhofer/ Structural Integrity Procedia 00 (2017) 000–000

6

Fig. 4 shows that for long cracks and small scale yielding conditions a compressive overload has almost no influence on the crack propagation rate, whereas a tensile overload leads, after a very short acceleration (only for a few microns, see Bichler and Pippan (2007)), to a significant drop in the crack propagation rate (see for example Skorupa (1999)). Several experiments with different overload ratios K max,OL / K max showed that overloads higher than 1.1 times the primary load amplitude already show a measurable influence on the crack propagation rate (Fig. 5). A thorough description of the crack growth behavior after an overload would require an exact description of the change of crack closure in the transition regime. This is a cumbersome task, and only possible for the contribution of the change of the plasticity induced crack closure. For the change of roughness induced and oxide induced crack closure not well known assumptions have to be introduced. Hence here for simplicity only an empirical approximation is used.

Fig. 5. Crack retardation due to single tensile overloads.

To describe approximately the crack retardation due to overloads in a computational model, a modified Willenborg-Gallagher-Hughes model (see Willenborg et al. (1971) and Gallagher and Hughes (1974)) is suggested. The overload influenced zone ( ) OL 0 max,OL OL OL p K Z L K − ∆ ⋅ = (3) depends on the size of the overload; the parameters L OL and p OL are determined by statistical regression, whereas ∆ K 0 is the fatigue crack growth threshold at R = 0. Furthermore, a fictitious residual stress intensity factor due to overload induced residual stresses in front of the crack tip is calculated by

2 1

    

    

   ∆ 1 Z

 −  

a

K

K

K

= −Φ ⋅

⋅ −

(4)

res,OL

max,OL

max

OL

Finally, similarly to the consideration of residual stresses, the crack retardation can be estimated on the basis of the corresponding local effective stress ratio

max K K K K + + min

res,OL res,OL

R

=

.

(5)

eff