ISO/TR 13086-3:2018
(Main)Gas cylinders — Guidance for design of composite cylinders — Part 3: Calculation of stress ratios
Gas cylinders — Guidance for design of composite cylinders — Part 3: Calculation of stress ratios
This document addresses the topic of calculation of stress ratios when analyzing filament wound composite cylinders. This document is applicable to cylinders of Types 2, 3, and 4. The calculation of stress ratios supports the development and revision of standards for fibre reinforced composite pressurized cylinders.
Bouteilles à gaz — Recommandations pour la conception des bouteilles en matière composite — Partie 3: Titre manque
General Information
Standards Content (Sample)
TECHNICAL ISO/TR
REPORT 13086-3
First edition
2018-09
Gas cylinders — Guidance for design
of composite cylinders —
Part 3:
Calculation of stress ratios
Bouteilles à gaz — Recommandations pour la conception des
bouteilles en matière composite —
Reference number
ISO/TR 13086-3:2018(E)
©
ISO 2018
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ISO/TR 13086-3:2018(E)
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ISO/TR 13086-3:2018(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Background . 1
5 Stress ratio determination . 2
6 Stress ratio development and calculation . 2
6.1 General . 2
6.2 Use of pressure ratios . 4
6.3 Type 4 evaluation with hybrid construction . 4
6.4 Analysis of Type 2 and Type 3 designs . 5
6.5 Direct measurements methods .14
6.6 Design limits .15
6.7 Test methods .15
7 Verification and validation .16
8 Conclusions .16
Annex A (informative) Examples of direct measurement methods .17
Bibliography .23
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ISO/TR 13086-3:2018(E)
Foreword
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bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).
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.org/iso/foreword .html.
This document was prepared by Technical Committee ISO/TC 58, Gas cylinders, Subcommittee SC 3,
Cylinder design.
A list of all parts in the ISO 13086 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/members .html.
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TECHNICAL REPORT ISO/TR 13086-3:2018(E)
Gas cylinders — Guidance for design of composite
cylinders —
Part 3:
Calculation of stress ratios
1 Scope
This document addresses the topic of calculation of stress ratios when analyzing filament wound
composite cylinders. This document is applicable to cylinders of Types 2, 3, and 4. The calculation
of stress ratios supports the development and revision of standards for fibre reinforced composite
pressurized cylinders.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http: //www .electropedia .org/
— ISO Online browsing platform: available at https: //www .iso .org/obp
4 Background
Stress rupture, also known as static fatigue, is the broadly defined mechanism where a material
fails under sustained static load. Stress ratio, the ratio of maximum fibre stress at minimum cylinder
design burst pressure divided by the maximum fibre stress at cylinder working pressure, allowing
assessment of the likelihood of stress rupture of the reinforcing fibres. Other performance may be
affected by the amount of fibre on the part, as reflected by the stress ratio, but there are other means to
accomplish improvements in other performance areas (e.g. drop, impact, gunfire, flaw resistance), and
performance testing is a better means to assess other performance factors. It is assumed that a time-
based relationship between the applied static load and the breakdown of the material can be defined.
The goal of defining a mathematical relationship between applied stress and time to failure is to make
accurate predictions of the material’s performance for safe use. In the simplest of terms, the greater the
sustained load, the sooner the occurrence of failure (stress rupture). A full and accurate understanding
of the material’s working stress state in service is imperative in order to assure that the stress ratios
are calculated accurately, and therefore the reliability of the cylinder in service is known.
Burst ratios and stress ratios are theoretically the same for Type 4 cylinders with a single structural
reinforcing fibre, but not for Type 2 or Type 3 cylinders due to the effect of autofrettage. While use of a burst
ratio for Type 2 and Type 3 cylinders is normally conservative, poor design and autofrettage practice may
cause higher stress in the reinforcing fibre, causing premature failure by rupture. This unsafe condition
can result when using non-traditional materials, very thick liner and/or thin composite materials, and/
or high autofrettage pressures. Some amount of calculation is also required for Type 4 cylinders using
hybrid construction, which is the use of more than one structural reinforcing fibre (see 6.3).
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5 Stress ratio determination
Stress ratios can be determined by a burst ratio in some cases, and in all cases by analysis, where
material properties and dimensions are known, and where the analysis is compared with strain and
deflection measurements to confirm its accuracy. Stress ratios may also be determined by strain or
deflection measurements. Validity of analysis or measurements should be established in all cases,
particularly given the need to address safety concerns. Analysis and validation is easiest when the
cylinder is assumed to fail in the cylindrical section, and not in the dome section. Burst location can
be confirmed through burst testing, and the assumption is confirmed if at least a majority of the
bursts initiate in the cylinder. In the event all failures initiate in the dome, additional validation may be
required.
6 Stress ratio development and calculation
6.1 General
Stress ratio is defined as the stress in the material at ultimate load (burst pressure) divided by the
stress in the material at the rated load (or nominal use pressure). Stress ratio is developed using the
nominal burst pressure for the cylinders used in the test studies, but is often applied to the minimum
design burst pressure to add a degree of conservatism, given that the coefficient of variation of burst
pressure for a production batch of cylinders may be different than the coefficient of variation of burst
pressure for the test study cylinders. Stress ratio is used in stress rupture analysis in the same manner
as stress range is used in cyclic fatigue analysis to help set the reference conditions for the performance
predictions.
Maximumfibrestressatspecifiedminimumdesignbursttpressure
Stressratio=
Maximumfibrestressatworkingpressure
As provided in numerous technical papers in composite design, stress rupture resistance is developed
on testing of individual strands or composite cylinders which are held to various percentages of their
[1] to [8]
average ultimate strength. These studies look to the intrinsic properties of the material to
evaluate degradation rates from specific loads. Presentation of stress rupture has many formats but
it always includes the stress ratio (or load fraction) and time to failure at the reference stress state as
[9]
shown in Figure 1 .
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Key
X time, hours
Y load fraction of median strength
Figure 1 — Carbon composite stress rupture chart
In addition, the nearly perfectly linear strain response of fibre composites under load provides another
opportunity to limit the complexity of the stress rupture analysis. The linear stress-strain curve for
carbon fibre is displayed in Figure 2. The material does not display a yield point so stress rupture
curves as exampled in Figure 1 can accurately predict the material’s response across wide ranges of
applied stress. This response is typical for nearly all fibre reinforced composite materials and vessel
types. This allows significant reduction of the complexity of the fatigue predictions at least as it relates
to the individual fibres in the laminate itself. The basic assumption in any analysis of composites is that
the reinforcement fibres dominate the viscoelastic response of the material. For resins with significant
creep under load or credited for stress ratio compliance their stress rupture properties will also be
evaluated in a comprehensive stress rupture analysis.
Different levels of difficulty are encountered in composite pressure vessel design when evaluating the
actual stress state of a reinforcement. A common issue in all designs is to resolve the laminate stiffness
in the fabricated cylinder in the principle directions. This is typically well estimated using classical
lamination theory (macro-mechanics) coupled with a suitable micro-mechanics approach, e.g. rule of
mixtures. In lamination theory, the local angle of the fibre reinforcement has a direct bearing on the
stiffness of the laminate as shown in Figure 3.
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Key
X strain (%)
Y stress (Mpa)
[10]
Figure 2 — Typical stress-strain curves of carbon fibre composites at 0° and 90°
Key
prediction
baseline data
verification data
X orientation angle (degree)
Y stiffness (GPa)
Figure 3 — Laminate stiffness vs. fibre angle
6.2 Use of pressure ratios
For cylinders with a non-load-sharing liner (Type 4) and with a single reinforcement fibre type, the
materials have elastic behavior, and there is no bending in the cylinder section. The burst ratio is
defined as the pressure at burst, divided by the working pressure, and is equal to the stress ratio.
Burstpressure
Burstratio==StressratioforType 44withonlyonematerial
Workingpressure
6.3 Type 4 evaluation with hybrid construction
In Type 4 designs that are hybridized with multiple fibres of different classifications (e.g. carbon, glass,
aramid), additional calculations will be applied to verify the proper stress ratio in the design. Hybrids
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may include using one material in each layer, and changing materials between layers, and it may include
co-mingled fibres in a winding band. When evaluating co-mingled fibres, the strain in the fibre direction
will be the same for each fibre in the band. Consideration will also be given to load share from external
protection layers.
The stress in each reinforcement will be checked. Examples of hybridized cylinders are those
constructed with both carbon and glass fibres where the glass may or may not be used for stress ratio
compliance. A load sharing hybrid is one in which both fibres meet their required stress ratio at working
pressure. A non-loadsharing hybrid is one in which the primary fibre was able to meet its stress ratio
requirements if the secondary fibre was removed.
If the secondary fibre is considered non-structural its load share at burst will still be calculated to
validate the proper stress ratio on the primary reinforcement. If all reinforcement fibres are considered
structural in meeting demonstrated burst performance, then each reinforcement will be evaluated for
stress ratio compliance.
Type 4 designs hybridized with multiple reinforcements, having a primary structural fibre and
secondary non-structural reinforcement, the burst ratio will be corrected by the cross-sectional area of
the non-structural fibre within the lamina. This is considered by defining a reinforcement stiffness ratio.
EA
PP
Reinforcementstiffnessratio==RSR
EA +EA
PP SS
where
A is the cross-sectional area of the fibre in the lamina (primary or secondary as noted);
E is the elastic modulus of the fibre (primary or secondary as noted).
The minimum required demonstrated burst ratio for the cylinder is then calculated by
Burstratio =Burstratio *2−RSR
()
()MinimumdemonstratedS()inglereinforcemeent
For example, if the primary reinforcement is carbon fibre and it carries 90 percent of the structural
load, as calculated by the RSR, and the secondary reinforcement carries 10 percent, the minimum burst
ratio to be demonstrated = 2,25 * (2 – 0,9) = 2,25 * 1,1 = 2,475.
For Type 4 designs with multiple classes of reinforcement where all the fibres are used to demonstrate
minimum burst performance, all of the reinforcements will be evaluated for stress ratio compliance.
The reinforcement with the lowest strain to failure may be validated for an appropriate stress ratio
with the burst test of the cylinder. All other reinforcements require knowledge of the failure strain for
each reinforcement and the failure location. This may require separate cylinder burst tests for each
reinforcement to explicitly determine its expected failure strain in the application. In addition, an
analysis appropriate for the cylinder failure mode will need to be performed to determine the stress
field in the laminate.
6.4 Analysis of Type 2 and Type 3 designs
For Type 2 or Type 3 designs the interaction of the liner with the composite shell will be included to
develop an accurate understanding of the stress state of the reinforcement at any point in the pressure
history. This requires an advanced understanding of the composite design process but it is still
within the known state-of-the-art for good pressure vessel design practice. Generally, these advanced
technics are numerical methods which includes finite element analysis (FEA), but may include other
methodologies. The model will have sufficient capability and accuracy so as to yield acceptable results,
as confirmed by strain gages, and will have the ability to perform non-linear analysis in order to model
the yielding behavior of the metallic liner.
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It is necessary to know certain information in order to have an accurate and valid analysis. This
information includes:
— composite material properties, including elastic modulus in the principle directions and
Poisson’s ratio;
— composite strength in the principle directions;
— composite layer thicknesses;
— liner stress/strain behaviour over the full pressure range;
— liner thickness;
— cylinder inner diameter;
— autofrettage, test, working, and minimum burst pressures;
— inclusion of pre-stresses from winding tension, if significant.
A typical refinement in the cylinder model would be to investigate if internal (galvanic isolation) or
external (impact shield) protection layers disturb the stress ratio calculations. In some national
standards, these additive plies are limited to a total maximum load share at burst. This is a type of inter-
ply hybridization that requires advanced techniques if the analysis is solely used to validate regulatory
compliance. The generally recognized method to provide compliance is modeling the cylinder in a
commercially available FEA software package. The FEA model for the cylinder will need to account
for the varying liner and composite thickness, orientation of the fibres in the layers and the non-linear
response (yield) of the liner material if autofrettage is used in the fabrication process and as analysis is
done at the minimum burst pressure.
The designer needs to be able to evaluate the principle fibre and liner stresses at any point in the
cylinder and maintain an accounting of those stresses at (a) autofrettage, (b) zero after autofrettage,
(c) service, (d) test, and (e) burst pressure in the order (strain history) as they are accumulated in the
actual cylinder. This is because strain history of the liner material is an integral part of the autofrettage
process. The FEA also needs to have sufficient fidelity to model the failure mechanism and location
at burst pressure. For cylinders limited to a mid-cylinder burst a simple axisymmetric shell model
provides sufficient resolution. Where the failure location is part of the dome or port geometry then
the additional complexity of the dome will be included to properly evaluate the liner response and the
corresponding stress field of the composite.
Examples of studies conducted on Type 3 cylinders with metallic liners of increasing thickness and
varying autofrettage pressures are provided in Figures 4 through 8. The process for developing these
figures includes the following:
— Start with single fibre Type 4 design (no liner).
— Add liner (Composite ID maintained).
— Remove composite material to maintain common burst ratio with Type 4 design (step 1).
— Check new Type 3 design with varying levels of autofrettage pressure and calculate resulting fibre
stress ratio.
— Repeat steps 2-4 with various liner thicknesses.
— The chart is the plot of various Type 3 designs, designed with the same burst ratio (line 1) but with
different composite-to-liner thickness ratios.
— Each design has undergone a series of different autofrettage cycles and the subsequent stress ratio
at service pressure has been plotted (lines 3 through to 7).
— Additionally, a simple liner burst calculation has been included for reference (line 2).
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— The bottom horizontal axis shows the liner thickness of each design.
— The left vertical axis shows the stress ratio and the burst ratio of each design.
— The right vertical axis shows the composite thickness of each design.
— Every point along the bottom horizontal axis represents a new design with a different composite-
to-liner thickness ratios.
— The vertical column of each horizontal position (design) shows you:
— the design’s liner thickness (horizontal axis);
— the design’s composite thickness (line 8, plotted on the right vertical axis)
— the design’s burst ratio (line 1, plotted on the left vertical axis) of the tank;
— the design’s liner burst ratio (line 2, plotted on the left vertical axis) of the tank;
— the design’s stress ratio without an autofrettage cycle (line 3, plotted on the left vertical axis) of
the tank;
— the design’s stress ratio after different levels of autofrettage (lines 4 thru 7, plotted on the left
vertical axis) of the tank.
Combinations of fibres, liners, and stress ratios (set at 5 % above nominal) evaluated include the
following:
— Figure 4, carbon fibre, aluminum liner 2,36 SR;
— Figure 5, carbon fibre, aluminum liner, 3,00 SR;
— Figure 6, glass fibre, aluminum liner, 3,68 SR;
— Figure 7, carbon fibre, steel liner, 2,36 SR;
— Figure 8, glass fibre, steel liner, 3,68 SR.
The material properties used are as follows:
Aluminum
68,95 GPa modulus of elasticity
0,33 Poisson’s ratio
200 MPa proportionality limit
240 MPa yield strength – 0,2 % offset
Steel
200 GPa modulus of elasticity
0,29 Poisson’s ratio
648 MPa proportionality limit
731 MPa yield strength – 0,2 % offset
Resin
3,17 GPa modulus of elasticity
0,35 Poisson’s ratio
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Carbon fibre
230 GPa modulus of elasticity
0,20 Poisson’s ratio
Glass fibre
82,7 GPA Modulus of elasticity
0,22 Poisson’s ratio
The given material properties have been used to show the basic behaviour of the given designs. Results
will vary when different properties, including yield strength, are used. The material properties will be
reflective of the actual materials used in order to get valid results for the actual designs being analysed.
Observe that in each of the Figures 4 through to 8, the designs operating with portions of lines 4 through
to 7 below line 1 indicating the burst ratio, are in fact operating below the intended stress ratio, and are
therefore at risk of rupturing during their lifetime (except in Figure 5, where the burst ratio for carbon
fibre is greater than normally required). This confirms that stress ratio and burst ratio are not the
same for Type 3 tanks, and that the stress ratio will be calculated to ensure that burst will not be at
high risk due to stress rupture.
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Key
1 vessel burst ratio
2 liner burst ratio
3 fibre stress ratio before autofrettage
4 fibre stress ratio after 1,50x autofrettage
5 fibre stress ratio after 1,67x autofrettage
6 fibre stress ratio after 1,83x autofrettage
7 fibre stress ratio after 2,00x autofrettage
8 composite thickness
X liner thickness (mm)
Y ratio (stress or burst)
Z composite thickness (mm)
Figure 4 — Carbon fibre, aluminum liner, 2,36 SR
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Key
1 vessel burst ratio
2 liner burst ratio
3 fibre stress ratio before autofrettage
4 fibre stress ratio after 1,50x autofrettage
5 fibre stress ratio after 1,67x autofrettage
6 fibre stress ratio after 1,83x autofrettage
7 fibre stress ratio after 2,00x autofrettage
8 composite thickness
X liner thickness (mm)
Y ratio (stress or burst)
Z composite thickness (mm)
Figure 5 — Carbon fibre, aluminum liner, 3,00 SR
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Key
1 vessel burst ratio
2 liner burst ratio
3 fibre stress ratio before autofrettage
4 fibre stress ratio after 1,50x autofrettage
5 fibre stress ratio after 1,83x autofrettage
6 fibre stress ratio after 2,17x autofrettage
7 fibre stress ratio after 2,50x autofrettage
8 composite thickness
X liner thickness (mm)
Y ratio (stress or burst)
Z composite thickness (mm)
Figure 6 — Glass fibre, aluminum liner, 3,68 SR
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Key
1 vessel burst ratio
2 liner burst ratio
3 fibre stress ratio before autofrettage
4 fibre stress ratio after 1,50x autofrettage
5 fibre stress ratio after 1,67x autofrettage
6 fibre stress ratio after 1,83x autofrettage
7 fibre stress ratio after 2,00x autofrettage
8 composite thickness
X liner thickness (mm)
Y ratio (stress or burst)
Z composite thickness (mm)
Figure 7 — Carbon fibre, steel liner, 2,36 SR
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Key
1 vessel burst ratio
2 liner burst ratio
3 fibre stress ratio before autofrettage
4 fibre stress ratio after 1,50x autofrettage
5 fibre stress ratio after 1,83x autofrettage
6 fibre stress ratio after 2,17x autofrettage
7 fibre stress ratio after 2,50x autofrettage
8 composite thickness
X liner thickness (mm)
Y ratio (stress or burst)
Z composite thickness (mm)
Figure 8 — Glass fibre, steel liner, 3,68 SR
There are other numerical methods, including closed form analysis that may require iteration to address
non-linear material properties, which may give suitable results as well. The information required to
conduct an accurate analysis includes the same values given above for finite element analysis, and the
requirements for calculated outputs would be the same.
Accurate modelling can reduce development risk in the design phase but it also can be used to point to
safe operational use of cylinders that might not be directly covered by published standards. This may
occur with novel materials, processes or applications within the literal scope of the standards but not
considered in the experience base of the industry at the time of publishing. In all cases, the designer is
responsible for providing for the safe application of the design.
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The key issue then becomes one of validating the calculated stress ratios within the fabricated cylinders.
This is necessary because of potential errors in modeling and need for an independent verification of
the design in performance based standards. Chief concern for a robust validation process is maintaining
operational safety to prevent stress rupture. Operational safety in a performance based standard can
be accomplished through several different approaches. As stated earlier for single reinforcing material
Type 4 cylinders the burst ratio is directly the stress ratio. For Type 2 and Type 3 cylinder designs
verification requires more knowledge of the cylinder’s performance.
It sho
...
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