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International Journal of Pressure Vessels and Piping 84 (2007) 451–459

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Determination of burst pressures and failure locations ofvehicle LPG cylinders

A. Kaptan, Y. Kisioglu�

Department of Mechanical Education, Kocaeli University, Umuttepe, 41380 Kocaeli, Turkey

Received 8 July 2006; received in revised form 9 February 2007; accepted 21 February 2007

Abstract

This study addresses the determination of the burst pressures (BP) and burst failure locations of vehicle liquefied petroleum gas (LPG)

fuel tanks using both experimental and finite element analysis (FEA). The experimental burst test investigations were carried out by

hydrostatic test in which the cylinders were internally pressurized with water. Two nonlinear FEA models, plane and shell, were

developed and evaluated under non-uniform and axisymmetric boundary conditions. The required drawn shell properties including weld

zone and shell thickness variations were investigated. The FEA BP and the burst failure locations are compared to the experimental ones.

The permanent volume expansions of the LPG tanks due to internal pressure were also examined based on the code regulations.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Burst pressures; Failure locations; Vehicle LPG cylinder; Nonlinear failure analysis; Non-uniform FEA model

1. Introduction

Liquefied petroleum gas (LPG) is commonly used as analternative fuel for internal combustions engines of vehiclesin Turkey and Europe. The LPG is stored and transportedbased on Turkish Standard Institute (TS) and EconomicCommission for Europe Regulation (ECE-R). In order tostore LPG in vehicles, the LPG cylinders known as LPGfuel tanks are commonly used and approved by theseregulations. About 75,000 of these tanks are designed andmanufactured annually, in Turkey, based on ECE-R67 inEurope [1] and TS 12095 in Turkey [2]. The LPG tanks,low-pressure cylinders since their service pressure is lowerthan 3.44MPa (500 psi) [3], can be commercially filled andused in the automobile industry. They are equipped with arefillable two-way hermetic valve, are produced as LPGcontainers and used in vehicles having water capacitiesranging from 35 to 80 l.

The primary aim of this study is to determine the burstpressures (BP) and the failure locations of LPG cylinderswhose service pressure (SP) and test pressures (TP) are

e front matter r 2007 Elsevier Ltd. All rights reserved.

vp.2007.02.004

ing author. Tel.: +90 262 303 2278; fax: +90 262 303 2203.

ess: ykisioglu@kou.edu.tr (Y. Kisioglu).

known by the definitions of the ECE-R67 and TS 12095rules. The SP is the working (operating) pressure where thecylinders are filled and used in industrial applications. TheTP is a given pressure that is applied and released afterwhich the permanent volume expansion of the cylindermust not exceed 10% of the initial measured volume [3].Finally, the BP is the maximum pressure a cylindrical tankcan withstand without bursting.In case of instability of cylindrical shells, analytical

formulations are available for ideal shells with perfectgeometry and specific boundary conditions [4–6]. These donot take into account the strain distribution, and non-homogeneous nonlinear material properties and geome-trical imperfections including thickness variations in thecylinder shell material. Kisioglu et al. [3] studied anddetermined the BP and failure locations for refrigerantcylinders using both experimental and FEA approaches.The prediction of the BP in filament wound compositevessels was studied using neural network acoustic emissiontesting by Hill et al. [7], and using the finite element methodby Sun et al. [8]. The BP of a vessel was estimated after asingle application of internal pressure using mathematicaland experimental models for tensile loading by Updike andKalnins [9]. The bursting of a large silo on a farm was

ARTICLE IN PRESSA. Kaptan, Y. Kisioglu / International Journal of Pressure Vessels and Piping 84 (2007) 451–459452

performed experimentally by filling up the silo repeatedlyover several months by Keiselbach [10]. Aksoley studiedexperimentally picnic-type portable LPG cylinders used inhome applications to identify the test parameters [11]. Theelimination of refrigerant cylinder instabilities by designingan optimum head are also studied by Kisioglu et al. [12]using both experimental and numerical approaches. Nosimilar body of knowledge appears to be available in thecurrent literature for the BP and the failure locations forLPG fuel tanks.

The purpose of this work is to investigate the BP andfailure locations of LPG fuel tanks using both experimentalburst tests and FEA. To predict the BP and the failurelocation using computer modeling, the actual shell andweld zone material properties (MPs) including thicknessvariations are investigated from the LPG tanks. Theseproperties are used in the FEA to approximate the BPvalues obtained experimentally. Two different types oftwo-dimensional (2D) nonlinear FEA models, plane

and shell, are developed under axisymmetric boundaryconditions.

2. Design of LPG cylinders

Guidelines for the design of cylindrical shells can befound in many international codes such as BS-5500 (BritishStandard) and the ASME codes (Section VIII, Division 1)[3]. These rules are restricted mostly to the load carryingcapacity under internal pressure. However, these LPGcylinders are designed and manufactured according to therestrictions of the ECE-R67 and TS 12095 codes,

Table 1

The cylindrical LPG fuel tank specifications

Cylinder

ID (mm)

Wall

thickness, t

(mm)

Service

pressure

(MPa)

Test

pressure

(MPa)

Water

capacity

(l)

310 2–3 1.75 3.00 35–80

Fig. 1. The vehicle LPG fuel tan

considering the SP and TP of the LPG cylinders. Basedon the regulations, the minimum BP is 9/4 times the TP,which is set at between 1.2 and 2 times the SP [1,2]. Thepressure specifications of the most commonly manufac-tured cylinders of 310-mm inner diameter used in industrialapplications are given as an example in Table 1. Thesecylinders are equipped with a valve system and a labelwelded to the shell body, as shown in Fig. 1.Cylindrical LPG tanks are usually manufactured within

four different groups, which are classified by their watercapacities: 35, 45, 60, and 80 l. Each group of cylinders hasa different wall thickness ranging from 2 to 3mm. In thepresent study, the BP and failure locations of the mostcommonly used three groups (35, 60, and 80 l) ofcylindrical LPG tanks having 2.5mm wall thickness areinvestigated. These tanks consist of three main parts: onecylindrical shell and two torispherical end closures asshown in Fig. 1. The cylindrical shell is folded up andwelded longitudinally and the two torispherical drawn endclosures are welded circumferentially at the ends of theshell (see Fig. 1). Also in the figure, some design parametersare shown such as inner diameter (ID), minimum wallthickness (t), knuckle radius (Rk), crown radius (Rc), andlength of the cylindrical shell (L).The LPG tanks are constructed from Erdemir-6842 steel

using the welding process for the shell body and the deepdrawing process for the end closures. The Erdemir-6842 isa hot rolled steel with 0.18% carbon content and is aductile material suitable for the cold forming process usedto construct the LPG tanks. The deep drawing processchanges the material properties (MPs) and thicknessvariations. After completing all manufacturing and weldingprocesses, these tank have been subjected to a heattreatment process before service.

3. The experimental burst tests

The experimental setup is shown in Fig. 2, with testing atroom temperature. The cylinder specimens, randomly

k and its design parameters.

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Fig. 2. (a) The experimental setup and equipment, (b) the burst cylinders.

Fig. 3. The BP results of three groups of LPG tanks.

A. Kaptan, Y. Kisioglu / International Journal of Pressure Vessels and Piping 84 (2007) 451–459 453

selected from the manufacturing stacks, were completelyfilled with water, and the pressure was controlled by meansof a single-acting hydraulic pump. The tanks were placedhorizontally during the experiments and air was ventedduring filling as seen in Fig. 2(a).

For the burst experiments, 64 35, 62 60, and 51 80 lcylinders having an ID of 310mm and an approximate wallthickness of 2.5mm were randomly selected. A group ofburst cylinders; one from each group is shown in Fig. 2(b).The BP distribution of the 177 tanks is shown as a functionof test frequency in Fig. 3. The wall thickness was variabledue to the thickness tolerances for the blank sheet. As canbe seen from the figure, the BP ranged from a minimum of7.40MPa to a maximum of 9.36MPa. The mean BP valuesobtained are about 7.76, 8.52, 9.07MPa for the LPG tankgroups, 35, 60, 80 l, respectively.

4. Computer-aided FEA modeling

The FEA were carried out using the ANSYS finite elementcomputer code to predict the BP and the failure location foreach type of LPG cylinder. Two different non-linear FEA

models, plane and shell, were developed using 2D axisym-metric finite plane and shell elements, respectively. To createthese FEA models and simulate the experimental burst tests,first shell MPs and thickness variations due to themanufacturing processes of the LPG tanks were investigatedto provide input to the computer modeling process.Additionally, after selecting the loading and boundaryconditions and appropriate finite elements, the nonlinearaxisymmetric 2D FEA models are generated and simulatedin non-uniform and non-homogeneous conditions.

4.1. Investigation of material properties

The LPG tank is divided into three regions, shell, weld,and end-closure, as seen in Fig. 1. From each region, tensiletest specimens A–E were cut out in the directions shown inFig. 4, and the corresponding engineering stress–strain(ESS) data were obtained. These ESS data are convertedusing well-known equations [13] to give the true stress–strain (TSS) data, as shown in Fig. 4.Tensile test specimens were cut from both the cylindrical

shell and the torispherical end in both the longitudinal and

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Fig. 4. Orientations of tensile test specimens and their true stress–strain curves.

Table 2

Mechanical properties of the cylindrical LPG fuel tanks

Tensile

specimens

Elasticlik

modulus

(GPa)

Yield

strength

(MPa)

Tensile

strength

(MPa)

Tensile

strain

(%)

Elongation

(%)

A 104 310 495 14 18.42

B 18.5 194 477 18.2 28

E 9.44 355 484 23.3 13.21

Fig. 5. Thickness variation of the drawn cylindrical shell.

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circumferential directions about the principal axis. Thematerial strength of the cylindrical shell in the longitudinaldirection (specimen C) due to rolling was higher than in thecircumferential direction (specimen B) (Fig. 4). As the hoopstress is about twice the longitudinal stress [5,6], the dataobtained from the specimens tested in the circumferentialdirection (specimen B) are considered in the analyses. Onthe other hand, the MPs in the spherical (crown) regionincluding most of the knuckle region exhibit almost thesame characteristics in all directions (specimens D and E).To investigate the weld zone properties, a few tensile testspecimens were taken from the welded region of theassembled cylinders. Tensile specimens were cut outlongitudinally about the weld line shown with specimen‘‘A’’ in Fig. 4. The MPs of these regions are represented bytheir true stress–strain data converted from correspondingESS data as illustrated in Fig. 4.

The mechanical properties of the tank materials can bedefined considering the tensile test data (ESS data) as seenin Table 2. For the plastic region of the TSS curve (Fig. 4),the relationship between true stress (st) and true strain (et)can be defined as st ¼ K�n

t , where K and n are the strainhardening coefficient and the strain hardening exponent,respectively [13,14]. The constant K can be obtained byextending the plastic stress–strain line until it intersects anordinate through �t ¼ 1 (log �t ¼ 0). The height of thisordinate is (logK). The n value can then be specified for thetank materials using the values in Table 2.

4.2. Thickness variation

The shell thickness variation was investigated both‘‘point-by-point’’ and ‘‘by-sliding’’ a micrometer with aprecision of 0.001mm on the surface of the full cross

section, Fig. 1. The measured thickness was very close tothe nominal thickness of Erdemir 6842 steel-sheet betweenpoints ‘‘a’’ and ‘‘c’’ except in the weld zone. In fact, theErdemir 6842 steel is manufactured within the sametolerances of the sheet thickness as well. However, fourslightly different thicknesses were measured between points‘‘c’’ and ‘‘d’’ (see Fig. 1).The thickness variation of the cylindrical LPG tank is

shown as a function of shell regions in Fig. 5. As can beseen, the wall thickness is altered mostly in both knuckleand crown regions of the end closure. It was also observedthat the maximum thickness change of about 20%occurred in the ‘‘knuckle’’ region, and the minimumthickness change of about 5% occurred in both flange

ARTICLE IN PRESSA. Kaptan, Y. Kisioglu / International Journal of Pressure Vessels and Piping 84 (2007) 451–459 455

and top of the crown regions (Fig. 5). On the other hand,the weld deposits are generally formed quite uniformly.The average value of the nominal weld zone dimensionmeasured was about 6.35mm.

4.3. Development of the non-uniform non-homogeneous

model

The non-uniform FEA model is constructed using thethickness variation (see Fig. 5) applied to relevant zones asillustrated in Fig. 6(a). To apply non-uniform wallthickness concepts in the modeling process, the wedgefunction procedure [3] is applied. In addition, differentMPs are applied non homogeneously to relevant regions tocreate the non-homogeneous FEA model as shown inFig. 6(b). Therefore, the non-homogenous model consistsof three different types of MPs, shell, weld, and end closure(see in Fig. 4) which are applied to both plane and shellFEA models in Fig. 6.

4.4. FEA modeling using axisymmetry

The LPG cylinders considered here are axisymmetricwith respect to the main axis of the cylinder geometry andwith respect to the applied load. The 2D axisymmetricFEA model was developed by using quarter symmetrywithout the valve slot. Initially, it was assumed that thevalve hole located at the cylinder body has no effect on theBP values and the failure locations.

In the 2D shell model, the mid-surface of the wallthickness is considered to create the LPG tank geometry asshown in Fig. 6(a). Preliminary investigations were carriedout to select the most suitable shell element from theANSYS element library, and the SHELL51 element wasused. This element has two nodes and four degrees offreedom at each node; three nodal translations are in the

Fig. 6. (a) Non-uniform (shell) and (b) no

x-, y- and z-axis and one nodal rotation is about the z-axis[15]. In contrast, to create the 2D plane model, the LPGcylinder is generated as a full section of the tank using itsquarter axisymmetry. A suitable 2D plane element,PLANE2, is selected to create the computer-aided LPGtank model. This element has six nodes and two degrees offreedom at each node, which are nodal translations in the x

and y-axis [15].

4.5. Selection of axisymmetric boundary and loading

conditions

To determine the BP, the internal pressure is appliedincrementally and linearly increased by 0.1MPa per step.The loading increment is applied as a function of a nominalloading time and gradually increased up to the step (point‘‘a’’) as shown in Fig. 7. When the loading reaches thatpoint, a bifurcation state takes place and then the loadingincrement is decreased to the step (point ‘‘b’’), where thecylinder is burst as illustrated in Fig. 7. The point ‘‘b’’represents burst of the LPG tanks. In addition, axisym-metric boundary conditions were applied on the x- andy-axis of the FEA model as shown in Fig. 8(a).

4.6. Burst failure analysis and failure locations

Several methods are available to determine the BP andthe failure location from the FEA simulations beside theloading conditions explained above. One way is that thestructural behavior of the cylinder can be plotted as afunction of time to determine the BP. To illustrate this,some nodes are selected from critical places of the model asseen in Fig. 8(b). These critical places were represented withnodes including N1, N146, N1660, and N3010. The nodaldeflections for the selected points of the plane model areplotted as a function of loading increment in both x- and

n-homogeneous (plane) FEA models.

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Fig. 7. Loading conditions and max displacements of the entire model.

Fig. 8. (a) FEA model and boundary conditions, (b) the burst location and selected nodes (35 l).

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y-directions, in Fig. 9. It is evident, the nodal displacementschange suddenly from 3.02-mm (point a) to 34.82mm(point b) as the pressure approaches the BP. In addition, todetermine the BP, it was noted that the stress valuesreduced suddenly especially at the burst point andultimately the FEA does not converge.

Another way to analyze the burst failure is to examinethe nonlinear equivalent plastic strain results. The non-linear equivalent plastic strain is compared to the cylindermaterial property. The maximum total equivalent (vonMises) strain is obtained as about 0.241865 at the instant of

burst, and this is higher than the given strain of the shellmaterial which was about 0.24, in Fig. 4. The burst failurecan also be predicted from the maximum displacement ofthe model as illustrated in Fig. 7. The maximum displace-ment shown with the curve ‘‘Max Disp’’, is reached atpoint ‘‘d’’ after the burst (point ‘‘b’’) as seen in Fig. 7.The burst location of the LPG cylinders is well known

from the experimental burst tests (see Fig. 2(b)). Burstfracture occurs at the middle point of the cylindrical shellat point ‘‘a’’ as shown in Fig. 1. This point defined as theburst failure location of the LPG fuel tanks is also shown

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Fig. 9. Nodal deflection of selected nodes of the LPG tanks.

Fig. 10. (a) The permanent volume expansions and (b) the measurement distributions.

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by the node number ‘‘N1’’ of the FEA model in Fig. 8(b).In the experimental studies, the cylinder specimensfractured in such a way that the burst crack continueslongitudinally as illustrated in Figs. 2(b) and 8(b).

5. Permanent volume expansions

When the tanks are pressurized hydrostatically, theyballoon permanently in both the x- and y- directions asseen in Fig. 10(a). The permanent volume expansions of theLPG fuel tanks are measured from both the experimentaltests and the FEA simulations, to verify the computermodeling and comply with code definitions. Based on theregulations [1,2], the permanent volume expansions of

these tanks before burst must exceed 20% of the initialvolume. The magnitudes of the circumferential and long-itudinal expansions are shown with ‘‘a’’ and ‘‘b’’,respectively, in Fig. 10(a). The magnitudes of ‘‘a’’ areobtained from FEA simulations as about 34.05 and38.62mm for the 35 and 60 l tanks (see Fig. 8(b) for 35 ltank), respectively. Similarly, the magnitudes of ‘‘b’’ areobtained as 18.14 and 18.69mm for the 35 and 60 l,respectively, as illustrated in Fig. 10.The magnitudes of ‘‘a’’ and ‘‘b’’ shown in Fig. 10(a) are

also measured manually from the LPG tanks after burstexperiments. For the measurement process, 15 LPG tankseach of 35 and 60 l are measured before and after the bursttests to obtain the expansions. Half the magnitudes of the

ARTICLE IN PRESSA. Kaptan, Y. Kisioglu / International Journal of Pressure Vessels and Piping 84 (2007) 451–459458

measurements in both ‘‘a’’ and ‘‘b’’ directions are takeninto account to compare the results obtained with the FEAsimulations. Distributions of the experimental measure-ments of the volume expansion in both directions of 35 and60 l LPG tanks are shown in Fig. 10(b). Based on thesemeasurements, the permanent volume expansions wereexceeded about 24% of the initial volume of the tanks thatcomply with the code requirements.

6. The BP results

The BP values are obtained for three groups ofcylindrical LPG tanks having constant wall thickness.The results obtained from the FEA simulations arecompared with corresponding experimental values inTable 3. The BP results from the simulations are veryclose to the experimental results. The BP values of LPGtanks having variable wall thickness are also investigatedusing the same FEA modeling processes. These BP resultsare plotted as a function of the nominal wall thickness (t)of the LPG fuel tanks, in Fig. 11. The figure has threecurves representing the BP values of three LPG tankgroups with the name of the group as: 35, 60 and 80 l. Theexperimental BP values are also placed in this figure withthe legend of ‘‘Experm’’, to compare with the FEA results.Not only were the BPs of the LPG cylinders obtained from

Table 3

The BP results of the cylindrical LPG tanks

Tank capacity

(1)

Nominal

thickness

(mm)

Burst pressures

Experimentals

(MPa)

FEA modeling

(MPa)

35 2.50 9.07 9.68

60 2.50 8.52 8.57

80 2.50 7.72 7.94

Fig. 11. The burst pressures of th

the axisymmetric FEA modeling process, but the burstfailure locations were found and coordinated with theexperimental results.

7. Conclusions

A series of thin-walled cylindrical LGP fuel tanks underinternal pressure, to determine the BP and burst failurelocation, was studied using both experimental and compu-ter-aided FEA approaches. The FEA models use 2Daxisymmetric elements and simulate non-uniform geometryand non-homogeneous material property conditions in anonlinear field. Based on the generated results, goodagreement between the measured BP in the experimentsand the corresponding non-linear axisymmetric FEAmodel values was found for all of the tank models (seeTable 3 and Fig. 11). Good experimental and FEAsimulation agreement was also found for the burst failurelocation of the LPG tanks when considering non-uniformnon-homogeneous axisymmetric FEA modeling condi-tions. In addition, the permanent volume expansionmeasurements obtained from both experiments and simu-lations verified each other as shown in Fig. 10 andcomplied with the code definitions.

Acknowledgments

The authors thank Karadeniz Tupgaz (Samcelik) Co. inOrdu, Turkey, for their financial and R&D facilitiessupports to perform these tests and prepare this material.Special appreciation is expressed to Umit Pekdemir,Engineering and Manufacturing Director. However, anyopinions, findings, conclusions or recommendations ex-pressed herein are those of the authors and do notnecessarily reflect the views of the Manufacturer.

e cylindrical LPG fuel tanks.

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