PSI - Issue 12

Francesco Giorgetti et al. / Procedia Structural Integrity 12 (2018) 471–478 Giorgetti et al. / Structural Integrity Procedia 00 (2018) 000–000

474

4

The mesh morphing technique imposes a displacement field to a selected group of nodes. It is possible to enclose a limited number of nodes for the morphing action, namely those of the desired zones of the mesh, imposing a null movement to the nodes that wrap the a ff ected area. It is well said that the outcome of the morphing operation and the preservation of mesh quality depend on the skill of the user that performs the task.

2.2. Crack Propagation

The propagation of a crack with a Multiple Degrees of Freedom (MDOF) model is a complex task and di ff erent mathematical aspects need to be managed. The first topic concerns the values of displacement, related to the flaw 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 4).

C ∆ K

m

da dN =

(4)

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

∆ a

(5)

∆ K

Fig. 1. (a) Crack front normal and growth direction; (b) Modulus and direction of the growth of crack front.