Winding path design based on mandrel profile updates of composite pressure vessels

Journal Pre-proofs Winding Path Design Based on Mandrel Profile Updates of Composite Pressure Vessels Lei Zu, Hui Xu, Xiaolong Jia, Qian Zhang, Huabi Wang, Bingzhan Zhang PII: DOI: Reference:

S0263-8223(19)33764-X https://doi.org/10.1016/j.compstruct.2019.111766 COST 111766

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Composite Structures

Received Date: Revised Date: Accepted Date:

4 October 2019 22 November 2019 30 November 2019

Please cite this article as: Zu, L., Xu, H., Jia, X., Zhang, Q., Wang, H., Zhang, B., Winding Path Design Based on Mandrel Profile Updates of Composite Pressure Vessels, Composite Structures (2019), doi: https://doi.org/10.1016/ j.compstruct.2019.111766

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© 2019 Published by Elsevier Ltd.

Winding Path Design Based on Mandrel Profile Updates of Composite Pressure Vessels Lei Zua, Hui Xua, Xiaolong Jiab,c,*, Qian Zhanga,*, Huabi Wanga, Bingzhan Zhanga a

Anhui Province Key Lab of Aerospace Structural Parts Forming Technology and Equipment, Hefei University of Technology, Hefei 230009, China b

Key Laboratory of Carbon Fiber and Functional Polymers, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China

c

State Key Laboratory of Organic-Inorganic Composites, College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China

Abstract: A novel design approach has been proposed to generate winding paths for composite pressure vessels with unequal dome parts. The experiments were carried out to obtain the mandrel profiles after each update of composite layers, and then the winding paths were generated to accommodate the updated profiles. To evaluate the effect of mandrel profiles updated by composite layers on the winding paths, the variety of winding angles and dome thickness distribution as well as the slippage coefficients corresponding to different winding paths were investigated. Further, the burst pressure was predicted using the progressive failure method, and the performance factors were calculated to evaluate the effect of the profile-update-based winding paths on the structural performance of the pressure vessels. The results illustrate that the winding angles have a significant change as the number of updated layers increases. The thickness accumulation on dome parts is reduced and the fiber stability is further improved, therefore, the precision of fiber paths is improved using updates of mandrel profiles. The improvement of the performance factor indicates that the present method is able to provide a useful tool for improving the performance of composite pressure vessels. Keywords: Composite material; Filament winding; Pressure vessel; Winding path design; Mandrel profile update *Corresponding author. E-mail address: [email protected] (X. Jia); [email protected] (Q. Zhang).

1. Introduction Filament winding is a technology for fabricating various composite products such as large storage tanks, piper lines, pressure vessels, rocket motor casings

[1-4].

During the

winding process fiber tows are wound onto the mandrel surface of a desired shape with designed winding patterns to keep fibers distribute uniformly, which is manipulated by a computer numerical control machine. The generation of winding path is one of the most key issues in the winding process since the fibers must be kept non-slip as well as non-bridged. In addition, the winding path should be continuous even at the ends of mandrel for turnaround operation. The previous investigations focus on the geodesic paths due to the fact that geodesic winding has the shortest paths and excellent stability on the supporting surface

[5-7].

Nevertheless, the geodesic paths have a major defect that the winding paths are entirely determined by the meridian profile and initial winding angle. In order to overcome this limitation to enlarge the design space, the non-geodesic paths that allow changes in the direction of the geodesic paths to a certain extent have attracted considerable research efforts. Zu et al. [8-9] studied pressure vessels with various shapes based on non-geodesic paths. Zhang et al. [10] proposed a method to generate non-geodesic paths for the composite elbows. Zhou et al.

[11]

developed an optimum design method for generating the winding paths of the dome

parts that are described by a hyperelliptic function. Paknahad et al.

[12]

designed the dome

shape of articulated pressure vessels based on non-geodesic winding patterns. However, these methods were not suitable for non- axisymmetric models or polygonal cross sections. Considering the limitation of geometrical shape, some investigations have been carried out to propose new methods suitable for irregular geometries. Fu et al.

[13]

presented a patch

winding method to generate winding paths applicable for axisymmetric and non-axisymmetric mandrels. Compared to the methods that need to calculate non-geodesic equations, this

method can directly generate winding paths according to the mesh nodes and is not restricted by the size and density of the mesh model. Vargas et al.

[14]

developed the non-geodesic

winding method to propose a unified approach suitable for complex shapes and the method has been validated by experiments. Li et al. [15] utilized the spline techniques to generate a new class of paths that have been employed to filament winding on non-axisymmetric mandrels. Fu et al.

[16]

proposed a novel method to generate the winding paths that approach

the major principal stress of complex mandrel shapes as closely as possible, which improves the structure strength. However, these methods did not consider the effect of composite layers update on the winding paths. One should be noted that the filament winding paths obtained by the current methods are generated based on the original mandrel profile. In fact, during filament winding process the mandrel profile changes as each composite layer is wound onto the mandrel surface. Therefore, the winding path is different corresponding to each layer. Moreover, with the composite layers increasing, the fibers along the original winding paths are easily slipping especially at the polar openings. In order to improve the precision of the winding paths in filament winding process, it is imperative to investigate the design of winding paths based on layers update of mandrel profiles. In this paper, a method was proposed to generate winding paths based on composite layers update. The coordinates of the original mandrel profile were obtained using the laser scanner and were then imported into the design program to generate the original winding paths and winding codes. The new mandrel profile is then obtained by winding new composite layers onto the mandrel surface, and the new winding paths are calculated according to the updated mandrel profiles. To evaluate the winding paths based on the layers update, the experiments of different layers update were implemented and the finite element simulation of a composite vessel were carried out to calculate the performance factor.

2. Design of filament winding paths Since winding paths change with composite layers, obtaining mandrel profiles after layers update is the key part of the winding paths design. In order to precisely obtain mandrel profiles, the laser scanner was used to scan the composite layers. It has the precision of 0.03mm, and displays the mandrel profiles in real time through the computer. To improve the efficiency of data transmission, the program was written to connect the laser scanner to the design software. The overall procedure of the presented method is shown in Fig.1. Firstly, the original mandrel is scanned by the laser scanner to obtain the coordinates of mandrel profiles so as to generate the original winding path. Secondly, the composite layers updates are implemented by experiments according to the winding paths based on the former mandrel profiles. Finally, the winding paths corresponding to updated layers are obtained until the end of experiments, and then the numerical simulations are carried out to evaluate the winding paths. The experimental design scheme for generating winding paths using layers updates of mandrel profiles is shown in Fig.2. To evaluate the method proposed in present study, the aluminum liner with unequal domes was used to implement experiments where the winding paths based on every two-layers updates and every-four layers updates of mandrel profiles were generated. Simultaneously, the variety of winding angles that were calculated using the mandrel-profile-updated method was investigated. In addition, the slippage coefficients corresponding to different winding paths were calculated to study the effect of mandrel profiles updates on the fiber stability. Considering the unequal domes of the composite pressure vessel in this study, the non-geodesic trajectories were employed. 3. Finite element models Aluminum Alloy 6061-T6 was here used as the liner of the pressure vessel and its mechanical properties were listed in Table. 1. It should be also remembered that the

aluminum liner will be in plastic state when its stress is greater than the yield strength. It is thus of importance to determine the non-linear stress-strain relation of the liner, as depicted in Fig.3. The material properties of the used T700 carbon fiber epoxy composite were given in Table. 2.

Table. 1. Mechanical properties of Aluminum Alloy 6061-T6 property

6061-T6

Elasticity modulus, GPa

74.12

Poisson's ratio

0.28

Tensile strength, MPa

340

Yield Strength, MPa

281

Ultimate Elongation

11.57 %

Density,

kg/m3

2700

Table. 2. Material properties of the used T700/epoxy composite Property

T700/epoxy composite

Extensional modulus in1- direction(E11)

134 GPa

Extensional modulus in 2- direction(E22)

7.42 GPa

Extensional modulus in 3- direction(E33)

7.42 GPa

Shear Modulus (G12)

3710 MPa

Shear Modulus (G23)

4790 MPa

Shear Modulus (G13)

3710 MPa

Poisson’s ratio (μ12)

0.28

Poisson’s ratio (μ23)

0.3

Poisson’s ratio (μ13)

0.28

Density

1680 kg/m3

Longitudinal tensile Strength (Xt)

2300 MPa

Longitudinal compressive Strength (Xc)

1250 MPa

Transverse Tensile Strength in (Yt)

74 MPa

Transverse compressive (Yc)

180 MPa

Shear Strength (S)

50 MPa

The liner of the pressure vessel with unequal dome parts is shown in Fig. 4. The pressure

vessel was modeled based on the finite element method. A quarter of the model was applied to finite element analysis, as shown in Fig. 5. The liner was modeled as cubic solid element (C3D8R). The profiles of updated composite layers can be obtained with aid of the laser scanner after filament winding process, and they were used for constructing composite layers by the continuum shell. In dome parts, the winding angles constantly change with the fiber paths owing to the ellipsoidal shape; thus, the fiber angles are determined by the winding paths generated based on mandrel profiles updates. Fig. 5 shows that an internal pressure was applied on the internal surface of the liner and the axial displacement of the model was restricted. Due to the symmetry of the model, the cyclic symmetry was applied to improve compute efficiency. 3.1 Progressive damage model In order to precisely predict the burst pressure that was used to calculate the performance factor of the composite vessels, a progressive damage model was written in a FORTRAN code as the user-defined subroutine to predict the failure of composite layers in this work. The simulations of the damage process require the definition of a damage initiation criterion to determine the damage onset of composite materials, and a damage evolution law which controls the stiffness reduction of the materials. At present, the failure modes of composite laminates are generally classified to be fiber tension and compressive breakage, matrix tensile and compressive failure as well as delamination that occurs between neighbor plies. Hashin’s failure criteria

[17]

are widely used to predict damage onset in one layer of

composite laminates. In this work the three-dimensional Hashin’s criteria were employed, which include through-thickness normal stress component in matrix failure. Delamination that was applied to detect the damage between neighbor plies was proposed by Change failure modes are defined as: Fiber tensile failure (110)

[18].

The

2    2   2    11  13 12   1         S S X  T   12   13  

(1)

Fiber compressive failure (110) 2

  11    1  XC 

(2)

Matrix tensile failure (22+330) 2

2   22 + 33   122   132  23   22 33   1   2 S12 S232  YT 

(3)

Matrix compressive failure (22+330) 2 2  Y  2       22   33   122   132  23   22 33 C 22 33       1 1    2 2 2S YC S12 S23  2 S23   23  

(4)

Delamination caused by tensile (33>0) 2

2

2

  33    13    23     1     ZT   S13   S 23 

(5)

Delamination caused by compression (33<0) 2

2

2

  33    13    23        1  Z c   S13   S 23 

(6)

Shear failure (110) 2

2

  11    12    13      1    X C   S12   S13 

(7)

where ij (i,j=1, 2, 3) represent the effective stress tensor; XT and XC denote respectively the tensile and compressive strengths in the longitudinal direction; YT and YC stand for the tensile and compressive strengths in the transverse direction; ZT and ZC are the tensile and compressive strengths in the normal direction; 12 and 13 are the shear stress respectively; S12, S13 and S23 are the shear strengths,` respectively;  is shear failure coefficient employed to determine the contribution of shear stresses on the fiber tensile failure, which is here set as 1.

3.2 Constitutive matrix degradation As the stress increases, the damage of composite materials takes place locally, and the material properties will change as well, which ultimately leads to the stiffness reduction of matrix. Therefore, the stiffness degradation model should be applied to modify material properties. The stiffness degradation criteria are depicted in Table. 3 [19]. Table. 3. Stiffness degradation criterion of composite materials failure mode

stiffness degradation criterion

Matrix Cracking

E22=0.2 E22, G12=0.2 G12, G23=0.2 G23

Fiber tensile failure

E11=0.07E11,E22=0.07E22,E33=0.07E33, G12=0.07G12,G13=0.07G13,v12=0.07v12, μ23=0.07μ23, μ13=0.07 v13

Shear failure

G12=v12=0

Delamination caused by tensile

E33=G23=G13=μ23=μ13=0

Delamination caused by compression

E33=G23=G13=μ23=μ13=0

4. Results and discussion The experiments based on different layers update of mandrel profiles were carried out, as shown in Fig. 6 and Fig.7. Fig. The experimental results show that the mandrel profiles obtained by every-four layers update have a significant change especially on dome parts compared with that using every two-layers update. The winding paths illustrate that the winding angle, tangent points and thickness distribution especially on dome parts have been changed as the mandrel profiles update. 4.1 winding angles based on layers update of mandrel profiles The winding angles on dome parts are obtained by every two-layers updates and every four-layers updates of the mandrel profiles, respectively, as shown in Fig.8. and Fig. 9. Fig. 8 illustrates that the winding angles do not have a significant change with the coordinate in the range of 0-30mm as the layers increase; however, the winding angles that are closed to polar openings change significantly, which shows that fiber stacking on the polar openings leads to the apparent change of mandrel profiles.

Fig. 9 shows the winding angles obtained by every-four layers update. With the composite layers increasing, the winding angles do not have a significant change with the coordinate in the range of 0-40mm; nevertheless, the winding angles approaching to the polar openings change significantly compared to that obtained using every-two layers update. In addition, as the number of updated layers increases, the fiber stacking on the polar openings has a significant effect on the mandrel profiles, as shown in Fig.7. In order to investigate the effect of composite layers updates on the winding angles on the cylindrical section, the comparison of the winding angles obtained by different layers update is shown in Table. 4. The winding angles on the cylindrical section do not have a significant change with the corresponding updated layers; However, as the number of updated layers increases, the winding angles gradually become larger. Compared to the winding angle based on the original mandrel profile, the winding angles increase due to the mandrel profiles updates. 4.2 Slippage coefficients In winding process the fiber paths of are generally constant, which leads to the fiber stacking around the polar openings. As the layers increase, the thickness accumulation in the same position results in instability of fibers to some extent. Due to the winding paths generated by the mandrel profiles updates, the fiber distribution on the dome parts is relevant uniformly, and the fiber stacking does not always occur in the same position through the entire winding process; the fiber stability is thus improved. On should be noted that the slippage coefficients can be used to evaluate the stability of winding paths, the slippage coefficients in present study were therefore calculated, as shown in Table.5. Table.5 shows the slippage coefficients corresponding to different winding paths that are generated by mandrel profiles updates. The slippage coefficients decrease as the update of mandrel profiles, illustrating that the stability of the winding paths is gradually improved.

Table.4. Winding angles for various layers-updates of mandrel profiles Mandrel profiles updated for every two layers Layers

1-2

3-4

5-6

7-8

9-10

11-12

Fiber angle at the equator (°)

13

13.1

13.2

13.3

13.5

13.5

Increase proportion (%)

0

0.7

1.5

2

3.8

3.8

Mandrel profiles updated for every four layers Layers

1-4

5-8

9-12

13-16

Fiber angle at the equator (°)

13

14

14.1

14.2

Increase proportion (%)

0

7.7

8.5

9

Table.5. Slippage coefficients for various layers-updates of mandrel profiles Mandrel profiles updated for every two layers Layers

1-2

3-4

5-6

7-8

9-10

11-12

Fiber angle at the equator (°)

13

13.1

13.2

13.3

13.5

13.5

Slippage coefficient

0.025

0.023

0.02

0.019

0.016

0.01

Mandrel profiles updated for every four layers Layers

1-4

5-8

9-12

13-16

Fiber angle at the equator (°)

13

14

14.1

14.2

Slippage coefficient

0.025

0.008

0.0065

0.0025

4.3 Thickness distribution of composite layers To evaluate the effect of winding paths generated by layers updates of mandrel profiles on the thickness distribution, the experiments based on the original mandrel profiles and on the different mandrel profiles updates were carried out, respectively. At the end of filament winding process, the composite thickness on the dome parts was obtained by scanning the surface of the whole composite vessel. Fig. 10 shows the composite thickness on the two dome parts of the cylindrical pressure vessel. It is demonstrated that the composite thickness becomes reduces especially on the polar openings using mandrel profiles updates; therefore, the winding paths design based on layers updates of mandrel profiles have a valuable reference for composite pressure vessels in term of reducing the thickness accumulation on the polar openings.

4.4 Performance factors of composite pressure vessels According to the experimental results, the composite thickness on dome parts and the winding angles obtained by every four-layers updates of the mandrel profiles change significantly compared to that computed using every two-layers updates of mandrel profiles. The mandrel profiles and the winding paths for every four-layer update of the mandrel profile were obtained and the results were compared to that based on the original mandrel profile. In order to evaluate the winding paths, the performance factors of composite pressure vessels were calculated using the progressive failure analysis. Fig.11 shows the results of the composite pressure vessel without update of mandrel profiles. As the internal pressure increases the matrix failure occurs (Fig.11-b) due to its lower capacity, and then the damage extends to fibers. When the internal pressure exceeds yield limit of fibers, the fiber failure occurs at cylindrical section, as shown in Fig.11-d. With the internal pressure increasing further, the fiber stress achieves the ultimate value, which leads to the burst of composite layers. Simultaneously, the liner bursts on account that stresses exceed the ultimate strength of the material, as shown in Fig.11-e. Fig.12 illustrates that the displacement on cylindrical part increases with time in the range of 0-0.7s. However, the displacement has a sharp increase at the time of 0.7s, which demonstrates the composite vessel failed at the burst pressure of 84MPa. Fig. 13 shows the results calculated by every-four layers updates of the mandrel profiles. the damage process is similar to that of the pressure vessel without update of mandrel profiles. The burst of the pressure vessel is also caused by the matrix failure (Fig.13-b) and the fiber failure (Fig.13-d). As can be seen from Figure. 14, the displacement on cylindrical part has a nearly line change with time in the range of 0-0.55s. Nevertheless, the displacement increases sharply at the step time of 0.55s, which shows that the burst pressure of the composite vessel is 88MPa.

To calculate the performance factors of the composite pressure vessel, the mass of composite layers, the volume of the liner and the comparison between the two types of vessels are shown in Table.6. Table .6 demonstrates that the burst pressure calculated by every-four layers updates of mandrel profiles is improved compared to that obtained without update of mandrel profiles. It can be concluded that the winding paths generated by layers updates of mandrel profiles are significant in term of improvement of performance factors. Table.6. Comparison of performance factors between the two composite pressure vessels Burst pressure

Volume

Mass

PV/W

Increase

(MPa)

(L)

(Kg)

(Km)

(%)

Design without profile update

84

6.8

2.932

19.48

Design with profile update

88

6.8

2.92

20.49

5.18

5. Conclusions The aim goal of this paper is to outline a method for generating the winding paths based on layers update of mandrel profiles, and to evaluate the effect of the winding paths on the structural performance of composite pressure vessels. The experiments were implemented to obtain the updated mandrel profiles that were used to generate winding paths with the aid of the design software. The comparison between experimental results that were obtained based on different layers update of mandrel profiles was completed. With the aid of the three-dimensional Hashin’s criteria, the progressive damage model was established in order to predict the burst pressure that was used to calculate the performance factors. It is concluded that the winding angles have a significant change as the number of updated layers increases. By comparison with the thickness obtained by employing not-updated method, the thickness accumulation around polar openings is significantly reduced using mandrel-profile-updated method. The fiber stability is improved as the mandrel profiles update, which indicates that the precision of winding paths is further improved. Moreover, the burst pressure is improved using the method proposed in this study owing to

the reason that the variety of winding angles on the cylindrical part enhance the load carrying ability in circumferential direction. According to the comparison of the structural performance of composite vessels, the method presented in this paper improves the performance factors. Additionally, in order to improve the burst pressure prediction, the hydrostatic tests will be implemented to obtain more accurate results. However, it is believed that the present approach based on layers update of mandrel profiles could prove very useful in the design stage of pressure vessels.

Author Contribution Statement

Xiaolong Jia planned the project and provided financial support for this research activity. Qian Zhang formulated overarching research goals and aims. Lei Zu developed methodology and created models and participated in drafting the manuscript. Hui Xu implemented the numerical simulation and experiments and participated in drafting the manuscript. Huabi Wang validated the formulations and participated in drafting the manuscript. Bingzhan Zhang helped to perform the experiments and edit the manuscript.

Acknowledgements This research is supported by the National Natural Science Foundation of China (Grant No. 51875159), the Key Research and Development Program of Anhui Province (Grant No. 201904d07020013), and the Fundamental Research Funds for the Central Universities (Grant No. JD2019JGPY0017).

Data Availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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List of Figures Fig. 1. Overall procedure of the proposed method. Fig.2. Experimental process based on layers update of mandrel profiles. Fig.3 Non-linear stress-strain relation of the aluminum liner. Fig.4. Geometry of an aluminum liner. Fig.5. Finite element model and its boundary conditions. Fig.6. Winding paths based on (a) original mandrel profile and updated profiles for every (b) two layers; (c) four layers; (d) six layers; (e) eight layers; (f) ten layers. Fig.7. Winding paths based on (a) original mandrel profile and updated profiles for every (b) four layers; (c) eight layers; (d) twelve layers. Fig.8. Variety of the winding angle at dome parts based on every two layers update: (a) winding angle at dome part 1 and (b) winding angle at dome part 2.

Fig.9. Variety of the winding angle at dome parts based on every four layers update: (a) winding angle at dome part 1 and (b) winding angle at dome part 2. Fig.10. Comparison of thickness distribution based on different winding paths at (a) dome part 1 and (b) dome part 2. Fig.11. Failure analysis for non-updated mandrel profiles: (a) shear failure, (b) matrix failure in the transverse direction, (c) matrix failure in the normal direction, (d) fiber failure and (e) MISES stresses of the liner. Fig.12. Displacement of the cylindrical section for non-updated mandrel profiles. Fig.13. Failure analysis for updated mandrel profiles (every four layers): (a) shear failure, (b) matrix failure in the transverse direction, (c) matrix failure in the normal direction, (d) fiber failure and (e) MISES stresses of the liner. Fig. 14. Displacement of the cylindrical section for updated mandrel profiles (every four layers).