PSI - Issue 25

Corrado Groth et al. / Procedia Structural Integrity 25 (2020) 136–148 C. Groth et al. / Structural Integrity Procedia 00 (2019) 000–000

140

5

Fig. 1: Left: geometry nomenclature; right: circular notched bar.

growth, that have to be imposed to the nodes of crack front, by means of mesh morphing. In particular the local increment ∆ a i of the i − th node, is calculated using a Euler integration algorithm (Paris and Erdogan (1963)) based on the Paris-Erdogan law (Equation 8).

C ∆ K

m

da dN =

(8)

In which C and m are material properties. Making use of the e ff ective Stress Intensity Factors (SIFs), extracted from the j − th Finite Element Analysis (FEA), and defining a starting value for ∆ a max , it is possible to evaluate the growth increment of each node of the front normalized with respect to ∆ K ( j ) max :

( j ) i ( j ) max

=

∆ K

m

( j ) i

( j ) max

∆ a

(9)

∆ a

∆ K

In addition, the maximum crack growth increment ∆ a ( j )

max , with the corresponding maximum SIFs ∆ K ( j )

max are intro

duced in the following formula for the evaluation of the loading cycles:

( j ) max

∆ a

∆ N j =

(10)

( j ) max

C ∆ K

m

3. Applications

3.1. 2 DoF notched bar

Proposed workflow is first implemented, as shown by Biancolini et al. (2018), in Ansys R Workbench TM for a simple circular notched bar, employing the same geometry explored by Carpinteri et al. (2003) in their work.