PSI - Issue 13

Jean-Benoit Kopp et al. / Procedia Structural Integrity 13 (2018) 855–861

857

3

Author name / Structural Integrity Procedia 00 (2018) 000–000

VAL ISO > 2.16E+01 < 4.03E+01 > 7. 9 < 1.68E+04

VAL ISO > 2.16E+01 < 4.03E+01

VAL ISO > 7.19E 01 < 1.68E+04 3.29E+ 1.53E+05

VAL ISO > 2.16E+01 < 4.03E+01 3.29E+04 1.53E+05

1.53E+05 7.09E+03

1.53E+05 7.09E+03

3.29E+04 1.53E+03

1.53E+03 3.29E+02 7.09E+03 3.29E+04 1.53E+03

7.09E+03

1.53E+03 3.29E+02

71.

71

3.29E+02

3.29E+02

71.

71.

15.

15.

15.

15.

3.3

3.3

3.3

3.3

0.71

0.71

0.71

0.71

0.15

0.15

0.15

0.15

3.29E 02

3.29E 02

7.09E 03 3.29E 02

7.09E 03 3.29E 02

7.09E 03

AMPLITUDE DEFORMEE COM1P.O0SANTES VECTEURS FX FY FZ VAL ISO > 5.82E 01 < 2.06E+05 7.09E 03 VAL ISO > 2.16E+01 < 4.03E+01 5 82 2 6 5

VAL ISO > 1.13E+00 < 3.23E+05 AMPLITUDE DEFORMEE O1MP.O0SCANTESV ECTEURS FX FY FZ VAL ISO > 2.16E+01 < 4.03E+01 L O > 1.13 0 3 2 5

Wel. au pas 9 temps= 3.25000E 04

Wel. au pas 4 temps= 0.00000E+00

1.53E+05

1.53E+05

3.29E+02 7.09E+03 1.53E+03 3.29E+04 7.09E+03 3.29E+04 1.53E+05

3.29E+04 1.53E+ 5

7.09E+03 3.29E+04

1.53E+03

3.29E+02 7.09E+03

71. 1.53E+03

71. 1.53E+03

15.

15.

3.29E+02

3.29E+02

3.3

3.3

71.

71

0.71

0.71

0.15

0.15

15.

15.

3.29E 02

3.29E 02

3.3

3.3

7.09E 03

7.09E 03

0.71

0.71

AMPLITUDE DEFORMEE O1MP.O0SCANTESV ECTEURS FX FY FZ 3.29E 02 0.15

AMPLITUDE DEFORMEE O1MP.O0SCANTESV ECTEURS FX FY FZ 3.29E 02 0.15

Wel. au pas 14 temps= 6.50000E 04

Wel. au pas 19 temps= 9.75000E 04

7.09E 03

7.09E 03

Fig. 1. Isovalues of the elastic energy density during opening of a instantaneously fractured ring.

geometry. In the part 3.1, the numerical procedure is only used to analyse experimental data. The experience allows to access the crack path history (crack length as a function of time a ( t )) during RCP and the elastic energy stored in the structure before crack initiation and propagation. The numerical model allows to estimate the energy released by the structure to the material ( G ID ) to ensure RCP taking into account inertia e ff ects.

2.1. Finite element mesh

A model of an half pipe and plate are meshed. A linear elastic behaviour is considered for the material. The symmetry of the structure is used for fracturing. 8-nodes and 20-nodes cubes have been used. For a good compromise between accuracy and computation time, each element corresponds to an angle of 2 degrees. 3 layers of 8-nodes elements in the thickness of the shell give relatively accurate results equivalent to a single layer for 20-nodes elements (see here (Kopp et al., 2014a) to have more details).

2.2. Boundary conditions

Part of boundary conditions are taken to avoid rigid body displacements. The initial imposed null displacements along the crack path are then withdrawn to simulate the crack propagation. Two loading types are considered before the fracture in pipe structure. The first one considers imposed parallel displacements at the poles of the pipe with variable widths. The second one considers a uniform pressure inside the pipe.

2.3. Validation of the moving crack model

As presented here (Kopp et al., 2014a) the numerical procedure has been validated using the analytical solution of Broberg (Broberg, 1960).

2.4. Free frequencies of the fractured ring

It appears clearly that the opening speed of the fractured pipe influences considerably the dynamic energy release rate G Id . This can be explained by linking the free frequencies of the fractured pipe to the dynamic correction factors. A fractured ring is modelled to study the free frequencies of the fractured pipes (see Fig. 1). For the pressurized one, whatever the wall thickness, the free-frequencies of a fractured ring are more or less the same. For a pre-stressed one, the thinner the wall thickness is, the faster the opening velocity of the fractured ring is, and the more important the dynamic correction is.