Simulation and Burst Validation of 70 MPa Type IV Hydrogen Storage Vessel With Dome Reinforcement
Simulation and Burst Validation of 70 MPa Type IV Hydrogen Storage Vessel With Dome Reinforcement
Simulation and Burst Validation of 70 MPa Type IV Hydrogen Storage Vessel With Dome Reinforcement
ScienceDirect
Article history: The dome reinforcement (DR) technology was studied to reduce the amount of carbon fiber of
Received 18 January 2021 the type IV hydrogen storage vessel in this paper. Firstly, the influence of the angle and
Received in revised form thickness of the dome reinforcement part on the stress distribution of the dome section is
8 April 2021 studied by finite element analysis. Secondly, the weight reduction of carbon fiber composite
Accepted 28 April 2021 layer is studied based on the dome reinforcement model. The strain-based Hashin progressive
Available online 26 May 2021 damage model is used to predict the burst pressure and burst mode with user-defined material
subroutine (UMAT) of ABAQUS. Finally, the dome reinforcement technology is further verified
Keywords: in comparison with non-dome reinforcement by burst tests. The results show that the pro-
Hydrogen storage vessel gressive damage model can effectively represent matrix cracking and fiber fracture, and the
Optimization predicted burst pressure and mode is consistent with the test results. The fiber stress near the
Dome reinforcement (DR) equator of the dome section affects the burst mode, and the smaller the angle of dome rein-
Winding forcement parts, the better the reinforcing effect, and the dome reinforcement technology can
Hashin failure theory help to improve the fiber damage state at the dome, transfer the maximum stress to the cyl-
inder section of the vessel, and ensure the burst mode to be a safe mode. Also, it can help to
reduce the consumption of carbon fiber by up to 5.5% in composite material.
© 2021 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author.
E-mail address: meemhchen@nuaa.edu.cn (M. Chen).
https://doi.org/10.1016/j.ijhydene.2021.04.186
0360-3199/© 2021 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
23780 i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4
Netting theory
pR 1
Tc ¼ 2 tan2 a (2) As the fiber composites are anisotropic materials, the fiber
2sf k
direction will carry a large load. Therefore, the maximum
Eqs. (1) and (2) are Chen's optimized netting theory for- loading capacity of composite materials is determined by the
mulas, where, R- cylinder radius, a-the average angle of heli- angle between loading and the fiber direction. As shown in
cal winding, p- burst pressure, sf - fiber strength, k - stress Fig. 2, q means the angle of helical winding, when q > 60 , helical
balance coefficient, Ta - the thickness of helical layers, and Tc - wound fiber has enhanced contribution rate of hoop strength,
the thickness of hoop winding. When k ¼ 1 , Eqs. (1) and (2) when q < 60 , The circumferential strength is negligible.
become the traditional equilibrium conditional netting the- However, in order to strengthen the overall strength of the
ory, when k < 1 , the netting theory takes into account the dome, it is necessary to use small angle helical winding, which
whole section of the vessel including the dome section, and causes waste of fiber and increases the cost. Therefore, the DR
this theory has become popular for the design of filament technology of hydrogen storage vessel is studied this paper, by
winding cylinders, especially in thickness estimation. As strengthening the key position of the dome, the amount of
shown in Fig. 1, the strength of the dome determines the burst helical wound fiber is reduced and to achieve the purpose of
mode. When after burst test the dome and cylinder section are reducing costs.
still connected, which can be considered as safe mode;
otherwise, it is considered as unsafe mode.
Simulation
Dome reinforcement theory
Finite element model
It is necessary to strengthen the dome in order to keep a safe
mode, for winding process, only helical winding can enhance As shown in Fig. 3, the length of the inner liner is about
the strength of the dome section. According to the netting 855 mm, the diameter is 347 mm, and the height of the dome
theory, the smaller the stress balance coefficient k is, the section is 95 mm. Among them, the metal boss and the plastic
larger the helical wound thickness will be, and the burst mode liner are made of aluminum alloy (6061-T6) and nylon (PA),
tends to be safe. In the actual design process, the range of k is respectively. Both of them are connected by a sealing struc-
determined mainly through the burst mode, so as to increase ture, and the whole liner prevent hydrogen leakage, and acts
the thickness of helical and ensure the safe burst mode. as a mandrel to provide support for the composite winding.
damaged element as positive definite matrix in a small in- strain is not along the fiber direction, the coordinate system
cremental step, which ensures the convergence of the whole transformation is needed ε0nþ1 ¼ T : εnþ1 , T is the trans-
solution. formation matrix. Then the above Hashin criterion is used to
The regularization damage value at the nþ1 increment determine the damage. If no damage occurs, the stress is
step can be expressed as directly calculated without stiffness attenuation, and the
stress is transformed into the calculation coordinate system
Dt h
dvx;nþ1 ¼ dx;nþ1 þ dv (7) in the finite element model by using the transformation
h þ Dt h þ Dt x;n
relation. If it is determined that the element has been
This paper is based on the implicit algorithm of ABAQUS damaged, the corresponding modulus is decreased. The cycle
2017 64-bit software, which can effectively connect UMAT continues until the incremental step is completed.
subroutines and integrate the new material model into them.
The used computer processor is the Xeon(R) GOLD 5118 with
256 GB of memory. Test
Newton's iterative method was adopted, with a conver-
gence threshold of 106, and the geometric nonlinearity Fabrication of DR parts
considered in the analysis. The strain output by ABAQUS was
logarithmic strain LE, which was the integral of the whole The DR part is made of composite materials, the fiber is the
strain path, as shown in Eq. (8). same as the external composite, which is T720SC produced by
Toray® Japan. The epoxy resin is produced by ALZChem®
Zln
dl ln Germany. The manufacturing process of DR part is shown in
ε¼ ¼ ln (8)
l l0 Fig. 5.
l0
First, a full size liner is set up on the winding machine, as
In the formula, l0 and ln represent the length before and shown in Fig. 5a. The shape of the molded dome is used to
after the change respectively, and ε represents the logarithmic ensure that the shape is consistent with the cylinder liner to
strain in the case of geometric nonlinearity. Logarithmic be produced. Due to the limitation of test conditions, only the
strain is used to avoid strain inaccuracy after large full size cylinder liner can be used, and sand mold can also be
deformation. used in the future to reduce costs. Next, wrap the fibers
How the subroutines work is shown in Fig. 4, Firstly, the around the liner as shown in Fig. 5b and c, and make the
cumulative total strain in current increment is calculated reinforcement parts with the specified thickness and angle.
εnþ1 ¼ εn þ Dε, Dε is strain increment. Since the calculated Since the hoop winding cannot provide reinforcement for the
Fig. 8 e a) deformation of the composite layer; b) stress along the fiber near the equator.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4 23787
occurs at large angle helical winding (e.g. 65 ), but the stress
with small angle helical winding (e.g. 20 ) is more complex,
with tensile stress inside but compressive stress outside.
Fig. 9 shows the stress along the fiber direction of the
innermost hoop and helical winding layer. It can be seen that
the stress in the direction of the helical winding fiber has a
small variation in the cylinder section and a large variation
near the equator under the pressure of 180 MPa without DR.
The stress increased near the equator in the direction of the
innermost helical layer, rising from 1166 MPa to 4661 MPa,
exceeding the limit value of the fiber stress, the main reason is
that the dome parameter b/a is less than 0.7, when the burst
pressure is loaded, the dome equatorial position will be
destroyed before the cylinder section.
Influence of DR angle
Non-damage model was used to simulate the cylinder stress
distribution of 20 , 45 and 60 DR parts, and the influence of
different angles on the cylinder stress distribution was stud-
ied. The equatorial thickness of all DR parts is 3 mm, and the
equatorial angle is 20 , 45 and 60 , respectively. The angle and
thickness distribution of the rest of DR parts are based on the
geodesic winding law. Fig. 10 lists the stress distribution along
the fiber direction innermost hoop winding and the innermost
Fig. 10 e Fiber stress distribution of DR @180 MPa. helical winding, it can be seen that at 180 MPa, with the
embedding of the DR part, the stress along fiber direction
presents a downward trend, which is mainly reflected in the
decrease of the stress along fiber direction in the helical
axis of ellipsoid, b: short axis of ellipsoid) is equal to 0.7, the wrapping of dome position, but the hoop fiber stress is almost
stress of circumferential near equator position is “000 , when not affected. Compare the stress distribution of different angle
the dome parameter b/a less than 0.7, the stress near equa- on the DR, it can be seen that the Dome-20 reinforcement has
torial position appear compressive, at the equator, the com- an obvious effect on reducing the stress of helical wound
posite shrinks inward, and the innermost layer of the along fiber direction, reduced from 4600 MPa without rein-
composite appears tensile stress under the action of bending forcement to 3000 MPa, which ensures the safety of the head.
load [31], and the deformation and stress state near the However, as the angle of DR increases, the coverage scope
equator with the dome parameter b/a ¼ 0.4 are shown in Fig. 8, decreases, for example, the coverage of the Dome-60 is the
as shown in Fig. 8a, the composite shrinks inward near the smallest among the three, covering only about 40% of the
equator. As shown in Fig. 8b, bending load and inward- dome area, and its effect on the stress reduction of helical
squeezing load occur at the equator, and compressive stress wound fiber is also the smallest. The stress of helical wound
23788 i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4
fiber fluctuates at the equator, but the stress level is around 1 mm, 3 mm and 5 mm under 180 MPa. It can be seen that with
4000 MPa. the increase in the thickness of the reinforcement, the fiber
On the whole, the reinforcement part of Dome-20 has the stress near the equator decreases gradually, while in the cyl-
most significant effect on reducing the stress of helical wound inder body increases gradually.
along fiber direction, and the stress level of helical wound is The stress distribution of cylinder section is shown in
reduced to about 2000 MPa. The peak of stress was transferred Fig. 13, where the maximum stress is marked, it can be seen
from the dome area to the cylinder section. This phenomenon that when the thickness of the DR is 1 mm, the stress along
occurs mainly because Dome-20 is located inside the com- fiber direction is 2605 MPa; when the thickness of the DR in-
posite layer. According to the membrane stress model anal- creases to 5 mm, the stress drops to 2585 MPa, 0.76% down
ysis, the fiber near the equator is affected by the bending compared with 1 mm. The stress state of the entire cylinder is
moment, the inner fiber is subjected to tensile stress, The in a safer state, which means that the burst pressure is higher.
Dome-20 has sufficient bending stiffness compared with According to the lay-up design shown in Fig. 3, the thick-
Dome 45 and Dome 60 to resist bending torque near the ness of the helical winding layer is about 10.0 mm, and the
equator, resulting in reduced stress levels at the dome. At the coefficient k in netting theory (Eqs. (1) and (2)) is less than 1 to
same time, the stress distribution along the thickness direc- ensure the safety mode of blasting, 10.0 mm thickness is close
tion in the middle of the cylinder section was monitored. As to the minimum allowable value of the helical winding layer,
shown in Fig. 11, it can be seen that the DR has almost no however, the strength of the helical winding layer is surplus at
influence on the stress of the cylinder section. the cylinder section. When the coefficient k ¼ 1, the pressure
vessel is simplified into a pipe by ignoring the strength of the
Influence of DR thickness dome and only considering the strength of the cylinder sec-
As shown in Fig. 12, a non-damage model was used to simu- tion. And the required helical winding thickness is about
late the stress distribution of the DR with the thickness of 5.6 mm, as shown in Fig. 14. The purpose of using DR parts is
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4 23789
to reduce the thickness of helical winding layer, so as to from which it can be predicted that the burst location should
reduce the weight of the cylinder. The remaining 4.4 mm be at the equator of the dome.
thickness in the dome section is the theoretical critical value In Fig. 16, for the pressure vessel with reinforcing parts,
of the thickness of the DR part. When exceed 4.4 mm, there is when the load is loaded into the 105 MPa, there is no damage,
residual strength in the dome section, and the fiber con- but the load to 192 MPa, fiber damage occurs at the dome
sumption is too large. Therefore, DR parts with a thickness of position, but no penetrating damage is formed. The hoop
3 mm are selected as the research object. winding layer fracture completely under 192 MPa, however,
no fiber breakage occurred in the helical wound layer of the
Weight optimized analysis and burst simulation cylinder body, combined with the damage analysis of the
From the above analysis, it can be concluded that the DR helps
to reduce the stress at the equator of the dome and may
transfer the maximum stress to the cylinder section. There-
fore, the weight of the wound layer of composite material can
be optimized to reduce the amount of carbon fiber with DR.
The finite element model established by ABAQUS including
the damage model was used to predict the burst pressure. In
Fig. 15, it can be seen that, without DR, the fiber damage first
occurs at the equatorial position of the dome when the
loading load reaches 161 MPa, and no fiber damage occurs in
the cylinder body. In the process of loading to 187 MPa, the
fiber damage near equator of the dome is continuously accu-
mulated, and finally a penetrating damage zone is formed, Fig. 14 e Minimum thickness required for helical winding.
23790 i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4
dome fiber, it can be known that the thickness of the helical radial displacement with the reinforcement showed an
wound layer is surplus, and which can be reduced in weight. obvious mutation trend, indicating that the fiber damage had
Figs. 17 and 18 represent the fiber damage reduced by 2 produced a penetrating damage zone at the moment, and the
layers of helical winding, 2 helical layers and 4 hoop layers, predicted bursting pressure was 192 MPa.
respectively. The main fiber damage still occurs in the cylin- Table 4 shows the cylinder weight under different pro-
der body, and the predicted burst location is in the middle, and posals. It can be seen that the DR technology can reduce cyl-
the burst mode is a safe mode. inder weight, and the fiber composite material reduced by
Fig. 19 shows the relationship between burst pressure and about 6.3%.
axial (radial) displacement in the burst simulation. According
to report of Leh [32], the burst mode of gas cylinders can be Burst pressure and burst mode
predicted from them. As shown in Fig. 19, without dome
reinforcing, the axial displacement curve turns at 180 MPa, but Fig. 20 shows the actual burst mode of pressure vessel, to
the radial displacement shows no obvious trend, it showed verify the reproducibility of the test, three times of repeated
that the predicted burst pressure of simulation is 180 MPa. The tests were carried out for without DR parts, and two times of
axial displacement becomes larger and larger after 180 MPa, repeated tests were carried out for the DR parts (the third test
indicating that the blasting mode is unsafe, combined with failed to burst because of the leakage).
the damage simulation, the first location of fiber damage is at Fig. 20a shows the result of burst without DR and Fig. 20b
the equator of the dome, which indicates the feasibility of with DR (dome-20, With DR þ Lack 2 Helical & 4 Hoop). It can
blasting model prediction. be seen that after the burst test, the entire composite material
In the burst simulation with DR (Dome-20), it can be seen layer outside the cylinder has been damaged. However, in
that the axial displacement curve with the reinforcement is Fig. 20a, the dome section is almost separated from the cyl-
opposite to the curve without the DR, at the same time, the inder body, in Fig. 20b, the dome and cylinder body remain as
a whole, and the burst mode is consistent with the simulated
prediction results.
The actual burst pressure and the average actual weight
are shown in Fig. 20c, from which it can be seen that the
burst pressure are all exceed 175 MPa, meet the re-
quirements of design standards ISO19881. For cylinders
without DR, the burst pressure is high, and the burst mode
is not safe, but for cylinders with DR, the burst pressure can
also meet the requirements, and the burst mode is safe,
specially the weight is reduced by 5.5%. Roh [2] uses dome
reinforcing technology to save about 10% of composite
material weight. Consideration of defects such as pores will
lead to the degradation of composite properties in the actual
fiber winding process, the weight reduction ratio of the
technology studied in this paper is different from the results
of Roh [2], but the optimization trend is consistent, which
achieves the purpose of reducing the amount of carbon
Fig. 19 e Displacement burst pressure curve. fiber.
23792 i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4
the burst mode was studied. And the effects of thickness and
Conclusion angle of DR parts on burst pressure were also studied. The
reinforcement design scheme of the dome was optimized by
In this paper, the DR technology of Type IV hydrogen storage taking damage into account in composite material, and the
vessel is studied, including reducing the weight of carbon fiber blasting results of the reinforced parts and the non-
in hydrogen storage vessel and optimizing the burst mode. reinforcement were compared. The main finding was sum-
The effect of the fiber stress at the dome equatorial position on marized below.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 6 ( 2 0 2 1 ) 2 3 7 7 9 e2 3 7 9 4 23793
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Declaration of competing interest prevent collapse of plastic liners in composite pressure
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