PSI - Issue 13

Rodrygo Figueiredo Moço et al. / Procedia Structural Integrity 13 (2018) 1915–1923 Rodrygo F. Moço, Fábio G. Cavalcante and Gustavo H. B. Donato / Structural Integrity Procedia 00 (2018) 000–000

1918

4

2.5E-8

3.8

C Mean Values

(a)

(b)

m Mean Values

3.6

2.0E-8

3.4

1.5E-8

3.2

1.0E-8

3.0

Coefficient - C

Exponent - m

5.0E-9

2.8

2.6

0.0E+0

-1

2

5

8

11

14

17

-1

2

5

8

11

14

17

%Prestrain

%Prestrain

(a) (b) Fig. 2. C and m parameters representing, respectively, (a) the position of da/dN vs. ΔK evolution and (b) its slope .

2. Finite element models and numerical procedures To assess the effects of plastic prestrain on FCG of pipes and pressure vessels, it was necessary to develop refined Finite Element (FE) models to reproduce UOE and calendering processes (see Fig. 3) – the main objective was to obtain the strain distributions along the material’s thickness and angular position after the UOE or calendaring forming processes, which were modeled using the dynamic explicit FE method. Similar approach can be found in Henryk (2007). The models were built using plane strain 4 node elements (CPE4R) with ABAQUS 2013 software in order to obtain the corresponding strain levels generated during the forming process. The models covered all the UOE and calendaring processes steps – in the case of UOE (see Fig. 3a), it included initial crimping, U and O forming and an internal mechanical expansion (E). The pipe dimensions simulated are 48” diameter and 1” thickness. Symmetry conditions were applied, which means that only half of the pipe was simulated and, due to the results of convergence analysis, only 5 elements were used through the thickness of the pipe as can be seen in the detail of the same figure. The calendaring simulation presents very similar features.

(a) (b) Fig. 3. (a) UOE process simulation with symmetry conditions and five elements through the thickness of the pipe; (b) calendaring simulation. After the prestrain profiles in realistic applications were obtained, FCG could be calculated using a Matlab 2014 routine, which analyses every element along the thickness and angular position of the pipe; the following procedures