Presentation of the Master Thesis of Edoardo Pompa. A joint study of Fusion for Energy and University of Rome "Tor Vergata" with the support of RBF Morph for mesh morphing technology. In the framework of the RBF4CRACKS research project. Mesh morphing is used to adapt a crack onto a target shape and to evolve crack shape according to local driving force.

1. CRACK PROPAGATION ANALYSIS OF ITER VACUUM
VESSEL PORT STUB WITH RADIAL BASIS FUNCTIONS
MESH MORPHING
Università degli studi di Roma “Tor Vergata”
Facoltà di Ingegneria
Corso di laurea in Ingegneria Meccanica
Elaborato di laurea magistrale
Candidato:
Edoardo Pompa
Correlatori:
Dott. Ing. Gabriele D’Amico
Dott. Ing. Stefano Porziani
Relatore:
Prof. Ing. Marco E. Biancolini

2. Development and application of a new method to evaluate the crack shape
evolution during cyclic loadings by the usage of Finite Elements Analysis in
conjunction with mesh morphing, which allows a fast arrangement of the existing
mesh to a new configuration.
Objective:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa

3. ➢ The ITER project
➢ Fatigue crack growth
➢ Description of an innovative procedure
➢ Validation with literature reference
➢ Application to Vacuum Vessel port stub
➢ Conclusions
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa
Summary:

5. The ITER project
International Thermonuclear Experimental Reactor
5"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa
International Nuclear Fusion R&D
project (China, EU, India, Japan,
Korea, Russia, USA).
Experimental Tokamak Nuclear
Fusion Reactor being built
in Cadarache (France).
Demonstrate that Fusion is a
valuable source of energy
Study “burning” plasma
Test key technologies
ITER Machine (under construction in Cadarache, southern France)
ITER will be the first fusion device (tokamak) designed to produce a ten-fold
return on energy (500 MW of fusion power from 50 MW of input power).

6. The ITER project
Tokamak: russian acronym for «toroidal chamber with magnetic coils»
Nuclear reaction from the stars reproduced on the earth:
➢ Extreme temperatures (150M °C)
➢ Strong magnetic fields (12 T)
Heat coming from the reaction can be
collected and used to produce energy.
Tokamak and nuclear fusion:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 6
D + T ➔ 4He + n + 17.58 MeV
ITER Machine

7. The ITER project
Sealed steel, torus shaped vacuum chamber housing the plasma, made
by 9 toroidal sectors (40⁰ each)
Key functions of the component:
➢ First containment barrier against radiation and heat
➢ Provides and assures high quality vacuum
➢ Participates in removing the heat
➢ Support for in-vessel components
The Vacuum Vessel:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 7
• RCC-MR code foresees a complete inspection of
the component via non-destructive Examination
(NDE) to ensure the absence of critical defects.
• Where not accessible (but also to determine the
minimum safe dimension of the flaw), RCC-MR
code gives useful guidelines for verification of the
design through Fracture Mechanics analyses.
VV 40⁰ sector
VV 320⁰ view

9. Fatigue crack growth
With the advent of Finite Element Analysis, models for the crack shape evolution have been
developed. They can be divided in two macro categories:
• Two degrees of freedom models: assuming a pre-defined crack shape it studies the
growth of two key points of the crack front.
Not suitable for irregular crack shapes, significant crack shape changes, out-of-plane
propagation, or complex loading scenarios.
Crack shape evolution:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 9

10. Fatigue crack growth
With the advent of Finite Element Analysis, models for the crack shape evolution have been
developed. They can be divided in two macro categories:
• Multiple degrees of freedom models: divides the crack front into a set of points and
defines the crack shape by connecting the points through cubic splines or simply through
polygonal lines.
More precise crack shapes and fracture parameters. It has been used in more complex
situations, ranging from simple in-plane propagation to mixed-mode loading.
Crack shape evolution:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 10

11. Fatigue crack growth
There are different techniques also for the crack update:
• Remeshing techniques: after the evaluation of the crack advance defines a complete
new three-dimensional mesh in which the computed new crack front is incorporated.
➢ High quality mesh
➢ Long computational time
• Mesh morphing techniques: the update of the mesh can be achieved moving the
nodes of a baseline configuration.
➢ Reduced computational time
➢ Possibility to automatize the process
➢ Problems of mesh degeneration
Mesh update:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 11

13. Method developed in ANSYS Workbench environment.
Multiple degrees of freedom model with mesh update through morphing.
➢ Crack shape evolution analysis-and-update procedure:
Base
Mesh
Crack growth
parameters
New
Mesh
Description of an innovative procedure
Method workflow:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 13
Static
analysis
Mesh
morphing

14. Description of an innovative procedure
Morphing implemented in ANSYS Mechanical through RBF Morph ACT extension.
Radial Basis Functions for the displacement field generation from user imposed
displacements.
The following setup has been adopted for the crack shape evolution:
Morphing setup:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 14

15. Description of an innovative procedure
MAPDL Commands introduced in the Solution tree.
Direction and entity of increments are evaluated in such way:
• Entity of increments: numerical algorithm based on Paris law. Evaluation of each node
increment starting from a maximum increment imposed by user.
Crack advance evaluation:
∆𝑎𝑖
(𝑗)
= 𝐶 ∆K 𝑖
(𝑗) 𝑚
∆𝑁(𝑗)
∆𝑁(𝑗)
=
∆𝑎 𝑚𝑎𝑥
(𝑗)
𝐶 ∆K 𝑚𝑎𝑥
(𝑗) 𝑚
∆𝑎 𝑚𝑎𝑥
(𝑗)
∆K 𝑚𝑎𝑥
(𝑗)
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 15

16. Description of an innovative procedure
MAPDL Commands introduced in the Solution tree.
Direction and entity of increments are evaluated in such way:
• Directions: calculated at each node as weighted average of each segment normal
appertaining on the front and adjacent to the node, in relation to their length.
Crack advance evaluation:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 16
𝑁𝑛 =
𝑁𝑠𝑖 ∗ 𝐿𝑠𝑖 + 𝑁𝑠𝑖+1 ∗ 𝐿𝑠𝑖+1
𝐿𝑠𝑖 + 𝐿𝑠𝑖+1

17. Description of an innovative procedure
MAPDL Commands introduced in the Solution tree.
Direction and entity of increments are evaluated in such way:
Observation: crack tip triaxiality and transition between plane stress and plane strain state
has been taken into account by the use of a constraint factor.
Crack advance evaluation:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 17
𝑇𝑧 =
σzz
(σxx + σyy)
E’ =
E
(1 − υ 𝑇𝑧)

18. Description of an innovative procedure
First benchmark: sensitivity to the variation of the maximum crack growth increment.
Smooth bar with semielliptical crack under cyclic traction:
∆𝑎 𝑚𝑎𝑥
(𝑗)
in range 0.1 - 0.3 mm/cycle
Same shape evolution, even for higher increments.
Sensitivity analyses:
0,5
0,55
0,6
0,65
0,7
0,75
0,8
0,08 0,13 0,18 0,23 0,28
a/b
a/d
da = 0.1 mm/cycle
da = 0.2 mm/cycle
da = 0.3 mm/cycle
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 18

20. Validation with literature reference
Lin and Smith numerical model for the crack shape evolution tested on smooth and
notched bars. Caspers experimental results are also included.
Smooth bar, semielliptical crack:
• a0/d = 0.1 , a0/b0 = 0.45 ;
• a0/d = 0.1 , a0/b0 = 0.54 ;
• a0/d = 0.1 , a0/b0 = 0.6 ;
Notched bar, semielliptical crack:
• Notch ratio: r/D = 0.1;
• Crack parameters: a0/D = 0.1; a0/c0 = 0.6;
References:
M. Caspers, C. Mattheck and D. Munz, “Propagation of surface cracks in notched and unnotched rods”
X. B. Lin, R. A. Smith, “Fatigue Growth Simulation for Cracks in Notched and Unnotched Round Bars”
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 20

21. Validation with literature reference
Good agreement with the experimental results.
All geometries converge asymptotically to a preferred pattern as they extend. (a/b = 0.75)
Smooth bar:
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5
a/b
a/d
0.54x0.1
0.6x0.1
0.45x0.1
Ref. 06x01
Ref. 1x01
Ref. 0.5x0.1
Ref. 0.47x0.1
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 21

22. Validation with literature reference
Good agreement with the experimental results.
The shape development is not affected significantly by the notch ratio, r/d, and loading.
Notched bar:
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0 0,1 0,2 0,3 0,4 0,5 0,6
a/b
a/d
Tension r/d = 0.1
Ref. Bending r/d = 0.05
Ref. Tension r/d = 0.05
Ref. Bending r/d = 0.2
Ref. Tension r/d = 0.2
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 22

24. Application to VV port stub
Local model of one Vacuum Vessel port stub.
Results from the multiple degree of freedom model compared with the two degrees of
freedom model used for the assessment.
The full load spectrum (combination of seismic, thermal, electro-magnetic events) has been
taken into account by the use of Miner rule for cumulative damage, defining an equivalent
cyclic load and number of cycles that produce the same damage in the flawed part.
The model:
24"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa

25. Application to VV port stub
The evolution of two initial semielliptical crack (estimated life of 7280 cycles) has been
studied.
Not a significant difference can be spotted from the comparison of the crack geometrical
parameters, since the crack shape changes during propagation are not significant.
Results:
10
11
12
13
14
15
16
17
18
8 9 10 11 12 13 14
Crackhalfwidthb[mm]
Crack depth a [mm]
Ref. 10x15
Ref. 10x12
10x15
10x12
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 25

26. Application to VV port stub
The evolution of two initial semielliptical crack (for 7280 cycles) has been studied.
Also the peak SIF and J integral shows a good agreement between the two models.
Results:
0,15
0,16
0,17
0,18
0,19
0,2
0,21
0,22
0,23
0,24
0,25
0,E+00 2,E+03 4,E+03 6,E+03 8,E+03
K/Kc
Cycles
0,15
0,16
0,17
0,18
0,19
0,2
0,21
0,22
0,23
0,24
0,25
0,E+00 2,E+03 4,E+03 6,E+03 8,E+03
J/Jc
Cycles
Ref.
10x15
Ref.
10x12
10x15
10x12
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 26

27. Application to VV port stub
The peculiarity of the multiple degrees of freedom model is clear when the entire crack is
considered. The crack modelled by the multiple DOF procedure develops a small
asymmetry with respect of the initial geometry.
Since the crack is close to the smoothed edge of the port stub, the fracture parameters
curves are not symmetric, and so are not the crack increments computed for each node.
This leads to a higher growth of the crack side close to the smoothed edge.
Results:
0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20
yaxis[mm]
x axis [mm]
Initial
shape
2 DOF
model
M DOF
model
0
1
2
3
4
5
6
7
8
9
10
0 10 20 30 40
Jint[kJ/m2]
crack front length [mm]
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 27

29. ➢ A new procedure for the prediction of crack shape evolution has been developed,
based on a multiple degrees of freedom model for the nodal crack front increments and on
mesh morphing for a quick rearrangement of the mesh.
➢ The method is in a good agreement with the reference results coming from other
MDOF models, as long as with experimental results.
➢ The method application shows the differences in the approximation introduced with
the 2DOF models.
Conclusions:
"Crack growth propagation analysis of ITER Vacuum Vessel port stub with RBF mesh morphing“ – Edoardo Pompa 29

30. Candidato:
Edoardo Pompa
Correlatori:
Dott. Ing. Gabriele D’Amico
Dott. Ing. Stefano Porziani
Relatore:
Prof. Ing. Marco E. Biancolini