ISO/TR 13086-3:2018

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 2018
© ISO 2018
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ii © ISO 2018 – All rights reserved

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
Foreword
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This document was prepared by Technical Committee ISO/TC 58, Gas cylinders, Subcommittee SC 3,
Cylinder design.
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iv © ISO 2018 – All rights reserved

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).
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 .
2 © ISO 2018 – All rights reserved

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.
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 behavi
...