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Sample Environment School 2015
Thin walled pressure vessel design
Robert Done MIMechE
ISIS Project design Engineer
Thin walled pressure
vessel design
 General Stress-Strain.
 Vessel design.
 Materials.
 Sealing.
 Safety.
Thin walled pressure vessel design
General Stress-Strain
General Stress-Strain
Stress:
• The ability of a mechanical component
to withstand load depends upon its
dimensions.
• The cross-sectional area over which the
load is distributed determines the
stress.
Load
Stress =
Area
General Stress-Strain
Stress:
• The direct stress may be tensile (Load is
a pull) or compressive (Load is a push).
• Failure will depend on the direction of
the load.
General Stress-Strain
Strain:
• A mechanical component under load
experiences a change in shape.
• Under tensile load, the component’s
length with be extended.
• The component is said to be strained.
Change in length
Strain =
Original length
x
ε=
l
General Stress-Strain
Modulus of elasticity:
• If the extension or compression of a
component disappears on removal of the load,
the material is said to be elastic.
• The strain is directly proportional to the
applied stress.
Stress
= CONSTANT = E
Strain
σ
=E
ε
General Stress-Strain
• Thin walled pressure vessel.
Tensile forces
P
P
• Yield pressure and burst pressure are
effectively the same in thin walled vessels.
General Stress-Strain
Elastic limit;
•
•
Material limits – Stress-extension diagram
General design limits the stress to below the yield point
UTS
Work-hardening region
Yield
Stress
Elastic region
Elastic
Extension
Uniform Plastic
Extension
Extension
Necking
Thin walled pressure vessel design
Pressure vessel design
Vessel Design
• All pressure vessel designs are covered
by the Pressure Equipment Directive
(PED).
• This states that pressure vessels must:
 Be safe
 Meet essential safety requirements
covering design, manufacture and
testing
 Satisfy appropriate conformity
assessment procedures
Vessel Design
Vessel Design
• Working pressure = Required value
• Design pressure = 1.1 x WP for relief
valve
• Design pressure = 1.4 x WP for bursting
disc
• Test pressure = 1.25 x DP
Vessel Design
• Thin walled cylinder calculations.
• Wall thickness t < 1/10th of the radius.
• Stress can be considered uniform
throughout the thickness of the wall.
Hoop stress = σ H
pr
=
t
Vessel Design
• In addition to the hoop stress, an
additional longitudinal (Axial) stress
exists.
pr
Longitudinal stress = σ A =
2t
Vessel Design
• If the vessel has an internal vacuum,
additional collapse conditions need to
be considered.
• These are based on the ratio of wall
thickness, diameter and length.
Vessel Design
• The external forces on vacuum vessels
can be enormous.
E ×e×ε
Pm =
R
Vessel Design
• The geometry of the vessel needs to be
considered in the design process.
• The vessel may have to be rectangular
in section.
• It may be of an annular construction.
Vessel Design
• It will be necessary to assess:
 The flanges and the bolts
 The end wall thickness
 Ports
 Thin windows
1.8 mm
Vessel Design
• Various examples
Thin walled pressure vessel design
Materials
Materials
• The emphasis in neutron scattering is to
have a minimal amount of structural
material in the direct line of neutrons.
• The higher the strength of a pressure
vessel material, the smaller the wall
thickness.
• High-strength materials tend to be
alloys, often with neutron absorbing
additives.
Materials
• Further requirements will be imposed
by cryogenic and elevated temperatures.
• At low temperatures, metals become
stronger but become more brittle.
• At high temperatures, deformation is by
‘Creep’.
Materials
• Grain size and orientation of materials
become important.
• Impurities generated in mechanical
processing.
• Fracture toughness if the vessel is
subjected to cyclic loadings.
• Corrosive environments.
Materials
• 7075 grade aluminium alloy.
• Stainless steel for hydrogen use.
• Vanadium for high temperature
applications.
• Titanium alloys.
• Niobium for extreme temperature
applications.
Thin walled pressure vessel design
Sealing
Sealing
• Standard seal arrangements such as polymer o-rings
and soft-material gaskets such as PTFE only work to a
defined pressure limit.
• The limit is described by the seal’s ability to resist the
pressure force with a balancing clamping force.
• Pressure = Force x Area
• Once the seal is displaced by the pressure force, a
pressure leak occurs.
• The limit tends to be that of material strength.
Sealing
• Various materials can be used to make a
suitable pressure/vacuum seal.
Sealing
• Indium wire is very often used for applications where
cryogenic sealing is required.
• The metal is very soft, malleable and easily fusible.
• It is so soft that it can be easily cut with a knife.
• Joints can be made by simply overlapping the two ends of the
seal
• It remains relatively soft even at Liquid Helium temperatures.
• It has a melting point around 156 ºC which limits its elevated
temperature use.
Sealing
• Gold wire is used for applications where elevated temperature
sealing is required.
• The metal is very soft, malleable and ductile.
• The two ends of the seal must be welded together –
specialised process.
• Even though it is malleable, a significant force is required to
make the seal – flange and bolt designs need to take this into
consideration.
• Gold is also chemically inert, making it suitable where
chemical reactions are present within the pressure vessel.
• It has a melting point around 1064 ºC making it ideal for
elevated temperature use – gold is an expensive material.
Sealing
• Spring energised seals are often used where higher pressures
and temperatures are required.
• The plastic deformation of the outer jacket of the seal is
initially made by its own reactive force from the elastic core
composed of a close-wound helical spring.
• Further deformation occurs when the C shaped seal is
pressurised, forcing the jacket to yield and fill the flange
sealing groove.
• The seals can be made from aluminium, silver, copper,
tantalum, stainless steel, titanium and inconel.
Thin walled pressure vessel design
Safety
Safety
• Working with any pressure system demands respect of
the associated hazards.
• Pressure systems have considerable amounts of stored
potential energy.
• It is the total energy of a system that is important.
• Total energy is the product of pressure and volume.
1 litre at 1000 bar
= 1000 bar litre.
1000 litre at 1 bar
= 1000 bar litre.
Safety
• Material data and test certificates should be obtained.
• Tensile test samples prepared of any non-standard
materials.
• Stress calculations, finite element analysis (FEA).
• Circuit volumes should be kept to a minimum.
Safety
• Protect all systems from the event of overpressurisation with a safety relief device.
• Bursting disc or relief valves.
• Some systems may need registration and assessment by
third-party bodies.
Thin walled pressure vessel design
Summary
Thin walled pressure vessel design
 General stress-strain
o Stress/Strain = Constant = E
o Yield pressure and burst pressure are effectively the same
 Vessel design
o Hoop & longitudinal stress
o Collapse pressure for vacuum vessels
 Materials
o A range of materials are available – depends on the
application
o Low neutron scattering is preferred
Thin walled pressure vessel design
 Sealing
o Polymer O rings – PTFE
o Indium wire – gold wire – energised seals
 Safety
o Total energy of the system
o Design to a recognised code
Thin walled pressure vessel design
Discussion