PSI - Issue 48

Štěpán Major / Procedia Structural Integrity 48 (2023) 230 – 237 Major / Structural Integrity Procedia 00 (2019) 000 – 000

234

5

marked as the fracture plane in the center of the weld. The crack growth itself is simulated using the modified Paris-Erdogan equation for the initiation phase and an equation for the growth phase, see Navaro (2011). The stress-strain characteristics needed to calculate the instantaneous value of Δ K are determined using the FEM model, see Fig. 2.

Fig. 2. (a) global view on FEM model of the welded sample; (b) sub-model of the elliptical crack in the center of which there is an inclusion.

In FEM model is necessarily use sub-modelling. For calculation was assumed that the material can be characterized by linear elastic deformation. Number of cycles N i in the initiation stage of fracture process can be calculated by equation:

f a

da

  , N FS a N FS  ( ) Tot i



(8)



n

C K 

a PE

where a is the length of the crack, or one of the half-axis, see Fig.1. Variable ΔK is the stress intensity factor at the crack tip. Constants C PE and n are determined experimentally for the given material. The letters FS indicate the so called damage parameter based on the fatigue criterion proposed by Fatemi and Socie. The damage parameter is given by the equation:

  

   







1  

(9)

FS

k

max

max



2



y

In this equation, Δγ max is the shear strain increment in the plane where it has maximum value, k is a constant that is obtained from the fatigue tests, σ max is the normal stress perpendicular to the plane where is the maximum shear strain, and σ y is the yield strength. Second stage of crack growth can be described the growth law in this form:

    

    

n

    

    

1 2

f



 

f

da dN

a

(10)

, th Long n C K K       PE

0 0 a a l     f f f

The following quantities occur in this equation: the ΔK th,Long is the growth threshold for long cracks (thus the th in the index comes from the first letters of the word threshold), f is a power parameter, l 0 is the average distance to the first microstructural barrier and a 0 is the El Haddad parameter. The influence of the increasing concentration of hydrogen in the cavity is included in the calculation so that the calculated local parameters of the stress tensor are corrected by the value of the hydrostatic pressure of hydrogen in the cavity.