PSI - Issue 68

Chahboub Yassine et al. / Procedia Structural Integrity 68 (2025) 310–317 CHAHBOUB YASSINE/ Structural Integrity Procedia 00 (2025) 000–000

312

3

The voids growth rate is the sum of existing voids growth fg and the new voids nucleation fn, and the following equation presents it:

#

# # = +

(5)

! "

Where the components are further formulated as follows:

!"

!" #

# $

$ %& !

= " !" & ! = A

(6)

%

(7) (8)

#

#

$ ) /

% * ,

!" ! ! A %

&

' &

!"# $%& ('

'

=

#

+ -

(

&

(

"

.

%

#

!" #$ !

In which the volume plastic strain rate, S N is the voids nucleation mean quantity, fn is the volume ratio of the second phase particles (responsible for the voids nucleation), and Ꜫ N is the mean strain at the time of voids nucleation. So eight parameters have to be defined:

! " # $ % % % % % % % & ! " # $ $ % % # # # # & ! ! " =

The values of q 1 and q 2 are almost constant based on several studies related to the determination of GTN parameters for different parameters, as shown the below table1. q 1 =1, q 2 =1.5.

Table 1: Initial values of GTN parameters References q 1 q 2

E N

S N

f 0

f c

f n

f f

Material

Bauvineau et al.(1996)(48)

1.5

1

-

-

0.002

0.004

-

-

CMn Steel

Decamp

et

1.5

1

-

-

0.0023

0.004

-

0.225

CMn Steel

al.(1997)(49)

Schmitt

et

1.5

1

0.3

0.1

0

0.06

0.002

0.212

Ferritic base Steel CMn Steel

al.(1997)(50) Skallerud and Zhang .(1997)(51)

1.25

1

0.3

0.1

0.0003

0.026

0.006

0.15

2. Experiments and Simulations 2.1. GTN parameters prediction using the direct method.

The numerical simulation of the four-point bending test on pipes with through-wall fracture defect in Figure 1 was performed. One large-scale experiment FP1a was carried out on mock-ups made of ferritic pipes in the EDF four-point bending test facility, developed during the former STYLE project; see Moinereau et al. (2014). The GTN model was only applied in the localized region as seen from Figure 2(b). The dimensions of mock-up FP1 are given in the article by Moinereau et al. 2014.