The document summarizes a study of cracks that form at the point where the diameter changes in rear plugs manufactured for hyperbaric equipment. Finite element modeling showed stress concentrations form at this point under pressure. Residual tensile stresses remain after each cycle and can reach 620 MPa. This fatigue causes cracking over time. However, the simulations show cracks stop growing once they pass into a compressive stress area, reaching only 9mm, so the cracking does not affect safety.

1. NC HYPERBARIC S.A.
Condado de Treviño, 6.
09001 BURGOS – ESPAÑA
Tel.: 34-947 47 38 74
Fax: 34-947 47 35 31
www.nchyperbaric.com
Rear plug crack study
We realised a long time ago that the rear plugs that we manufacture for our
HPP equipments suffer a crack at the point where the diameter changes. The following
report will show that this crack is not dangerous.
We have modelled the plug using a Finite Element Model (FEM) calculation. In
the following figure the part shape can be seen.
1
AREAS
MAY 16 2008
TYPE NUM 14:09:25
Zone to be
studied
Y
Z X
Figure 1.- Plug FEM model
The plug has been meshed properly to study the area where the plug changes
in diameter.
Figure 2.- Plug meshing detail

2. NC HYPERBARIC S.A.
Condado de Treviño, 6.
09001 BURGOS – ESPAÑA
Tel.: 34-947 47 38 74
Fax: 34-947 47 35 31
www.nchyperbaric.com
Once we pressurize the machine, there is a stress concentration in the studied
area. This stress concentration plastificates the material and produces tensile residual
stresses.
In the next picture we can see the stresses originated by the working pressure
at the point where the diameter changes in the rear plug (measured in MPA). The red
area is yielded (the yield limit is surpassed).
Figure 3.- Stresses at working pressure
After the cycle there are some residual stresses at the same point which can be
seen in the next picture.
Crack propagation path.
The line that joint MN and MX
Figure 4.- Residual tensile stresses
These residual stresses can reach 620 MPA after the rear plug is relaxed.

3. NC HYPERBARIC S.A.
Condado de Treviño, 6.
09001 BURGOS – ESPAÑA
Tel.: 34-947 47 38 74
Fax: 34-947 47 35 31
www.nchyperbaric.com
Because of this effect, the plug works, in that area, between compression (at
working pressure) and tensile stresses (at 0 bar). This way of working makes the plug
have a severe working condition in that small area that produces cracking. The fatigue
cycle of the surface is between a tensile stress of 620MPa and a compressive stress of
732 MPa.
Anyway, the affected area is a small one and once the crack surpasses the
“red” area, it goes into an area with compressive stresses which stops the crack.
We have simulated and calculated the crack propagation and in the following
figures can be observed the results:
- It is necessary only 10000 cycles to have a crack of 0,1mm.
- A very small initial crack of 0,075mm (could be the surface roughness)
makes the crack propagating.
- The crack grows up to 2 mm when the plug makes 45000 cycles.
- The crack reaches 4mm when doing 100000 cycles.
- The crack stops when reaching 9mm.
10000000
1000000
Number of Cyles
100000
10000
1000
0 2 4 6 8 10 12
a (mm), for an initial crack of 0.1 mm
Figure 5.- Crack grow calculation (initial crack of 0,1mm)

4. NC HYPERBARIC S.A.
Condado de Treviño, 6.
09001 BURGOS – ESPAÑA
Tel.: 34-947 47 38 74
Fax: 34-947 47 35 31
www.nchyperbaric.com
10000000
1000000
Number of Cycles
100000
10000
1000
0 2 4 6 8 10 12
a (mm), for an initial crack of 0.075 mm
Figure 6.- Crack grow calculation (initial crack of 0,075mm)
CONCLUSION
The crack appears in the plug at the point where the diameter changes,
but as it is demonstrated, the crack can start at very low number of cycles, but
after reaching about 1 mm, the crack grows very slowly, stopping when
reaching 9 mm.
The crack is not dangerous and does not affect safety.