- Email: [email protected]
Lateral indentation of a reinforced braided tube with tunable stiffness
Thin–Walled Structures 149 (2020) 106608
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: http://www.elsevier.com/locate/tws
Full length article
Lateral indentation of a reinforced braided tube with tunable stiffness Zufeng Shang a, b, Jiayao Ma a, b, *, Zhong You b, c, Shuxin Wang a, b, ** a
Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China School of Mechanical Engineering, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China c Department of Engineering Science, University of Oxford, 17 Parks Road, Oxford, OX1 3PJ, UK b
A R T I C L E I N F O
A B S T R A C T
Keywords: Reinforced braided tube Lateral indentation Tunable stiffness Fiber-membrane interaction Negative pressure
In this paper, the lateral indentation of a newly proposed reinforced braided tube with tunable stiffness, which takes a braided tube as skeleton and is sealed by thin membranes, has been studied experimentally and numerically. It is found out that the radial stiffness could be increased by 290% compared with that of a standalone braided tube, through adjusting the negative pressure between the braided skeleton and the membranes. During deformation, the fibers in the reinforced tube are longitudinally restricted by friction, which increases the stiffness of the braided skeleton. In addition, friction dissipation due to sliding between fibers and membranes also contributes substantially to the load carrying capability of the reinforced tube, leading to a much stiffer structure than the summation of the constituents. A parametric analysis has also been conducted, from which the effects of the design parameters are obtained.
1. Introduction Fiber-reinforced composite is a combination of high-strength fibers and a matrix, where the former is embedded in or bonded to the latter with distinct interfaces [1]. In the composite, the fibers generally act as the principal load-carrying members, whereas the matrix functions as location, orientation, transmission and protection [2]. Thanks to the heterogeneous composition, it has superior mechanical properties and durability over the constituents alone [3]. As one type of fiber-reinforced composite, braided composite has attracted increasing interests with the development of modern braiding technology. It dis tinguishes from others with the interlacing of the fibers, leading to improved delamination toughness and impact resistance [4], as well as design versatility and manufacturing simplicity. The braided composite can be categorized into two groups. The first group is braided composite with closed configuration, in which the fibers are jammed and contact each other tightly [5,6] to achieve a high fiber volume fraction. Close braided composite is often used as structural components [7,8], espe cially in aerospace engineering [9–11], due to its lightweight and su perior mechanical strength/mass ratio. The second group has an open configuration, where the adjacent fibers are separated [5,6,12].
Compared with the closed composite, the open one exhibits a modest stiffness, but excellent bending flexibility [13]. With the features, it is widely used as air ducts [14], and medical catheters [15,16] and stents [17,18] in medicine which are required to pass through tortuous body orifices. In addition, energy absorption structures have also adopted such structure which is filled with crushable foam to prevent delami nation [19]. Recently, a reinforced braided tube with tunable stiffness, which had a braided skeleton sealed in thin membranes, was proposed [20]. It can switch between flexible and rigid states by adjusting the negative pressure between the skeleton and the membranes, making it suitable for biomedical engineering applications such as manipulators for mini mally invasive surgery [21,22]. When in operation, the structure could be subjected to localized lateral loading, which may cause denting and kinking, thus severely affecting its functionality [23,24]. Currently, research on the lateral indentation of composite tubes has been very limited, and most work focuses on the failure mechanism of filament-wound tubes [25–27]. In this work, the deformation mecha nism and radial stiffness of the reinforced braided tube with tunable stiffness are investigated both experimentally and numerically, with the aim of providing a design guidance for the new structure with suitable
* Corresponding author. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China. ** Corresponding author. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China. E-mail addresses: [email protected] (Z. Shang), [email protected] (J. Ma), [email protected] (Z. You), [email protected] (S. Wang). https://doi.org/10.1016/j.tws.2020.106608 Received 26 September 2019; Received in revised form 5 December 2019; Accepted 9 January 2020 Available online 12 February 2020 0263-8231/© 2020 Elsevier Ltd. All rights reserved.
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
stiffness upon request. The paper is organized as follows. In the material section 2, the geometry of the structure and the fabrication approach are introduced. Then the experimental setup and finite element modeling are presented in the methods section 3. Results and discussions are presented in section 4, in which the deformation mechanism of the structure and the effects of design parameters are shown. Section 5 gives the conclusion.
membrane with high tensile stiffness, were adopted to fabricate the reinforced tube. The braid was fabricated with a 3D braiding machine shown in Fig. 2. With the mandrel moving in the longitudinal direction, two groups of bobbins, eight in each group, rotated around the mandrel in clockwise and anticlockwise directions, respectively, to weave the fibers into a braid on the surface of the mandrel. The diameter of the braid D was determined by the mandrel diameter Dm and the fiber diameter d, and the relationship is expressed as
2. Materials 2.1. Geometry
The braiding angle β was determined by the take-up speed of the mandrel v and angular speed of the bobbins w through
The reinforced braided tube with tunable stiffness is composed of a braid and sealing membranes [20]. As shown in Fig. 1, the membranes cover both the inner and outer surfaces of the braid and forms a sealed cavity. The membranes and braid contacts loosely in the flexible state, where the whole structure functions virtually as a sole braid. In the rigid state, negative pressure is applied in the cavity. The membranes are compressed onto the braid by the air pressure, and both components deform interactively so as to improve the stiffness of the structure. The braid in the structure is formed by helical springs interwoven together as seen in Fig. 1 [13], and its geometry can be completely defined by L, D, n, β and d, which are tube length, tube diameter, number of fibers, braiding angle, and fiber diameter, respectively. The braid shrinks in the radial direction when elongated longitudinally, and the relationship between β, D and L was given by Jedwab and Clerc [28] as f
L’ ¼ L sin β’=sin β D’ ¼ D cos β’=cos β
(2)
D ¼ Dm þ 2d
(3)
β ¼ arctanð2v = wDÞ
Subsequently, the braid was heat treated at 100 � C for 1 hour on the mandrel, after which a stable tubular braid was obtained as shown in Fig. 3(a). Finally, tubular membranes with a slightly larger diameter than that of the braid was inserted into the braid, and then folded to cover the outer surface of the braid. The ends of the membranes were glued together so that the braid was sealed, and a reinforced braided tube shown in Fig. 3(b) was obtained [20]. In addition, a stand-alone braid in which the fibers could freely slide at intersection points as shown in Fig. 3(a) and a welded braid in which all the fiber intersection points were glued together as shown in Fig. 3(c) were also built for comparison purpose. All the three specimens have the same parameters listed in Table 1.
(1)
3. Methods
where each parameter of the deformed braid is denoted with a prime.
3.1. Experimental setup
2.2. Fabrication
The lateral indentation experiments of the physical specimens were carried out on an Instron 5982 testing machine. The reinforced braided tube was connected to a pump via an air duct to tune the negative pressure. A negative pressure P ¼80 kPa was applied to the specimen. The experimental setup shown in Fig. 4 was set as Kim et al. [13] sug gested, where a circular rod is used to compress the longitudinal midpoint of the braid to test the radial stiffness. During the experiment, the specimen was placed on a flat plate freely, and a 3D printed circular rod with a diameter of 18 mm moved downward to compress the midpoint of the specimen by 4.5 mm, about a quarter of its original diameter. To avoid dynamic effects, the indentation was conducted at a loading rate of 5 mm/min. Both force and displacement during each experiment were recorded automatically by the Instron.
Nylon PA66 fiber with good elasticity, great compliance to the mandrel and low heat treatment temperature, and polyethylene
Fig. 1. Design of the reinforce braided tube with tunable stiffness.
Fig. 2. The braiding machine. 2
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
diameters of the membranes were slightly different from that of the braid so as to avoid physical interference. For the welded braid, radial distribution of the helical fibers was ignored and the whole structure was modelled as a number of helical fibers merged together. Three-dimensional membrane elements, M3D4R, and beam elements, B31, were used to mesh the membranes and the braid, respectively. To model the indentation experiment setup, a plate and a circular rod shown in Fig. 5 were also built in Abaqus as rigid bodies. Two analysis steps were defined to model the loading process of the reinforced tube. In the first step, both the rod and the plate were fixed, and uniform pressure was applied to both membranes to model the negative pressure. In the second one, at the constant pressure, a pre scribed displacement was assigned to the free degree of freedom of the rod to compress the structure. Smooth amplitude definition built in Abaqus was adopted to control the indentation procedure. Hard contact was used to model the normal behaviour and penalty was chosen as the friction formulation with a coefficient of friction μ of 0.3 to capture the tangential behaviour. As for the stand-alone braid and the welded braid, only the second step was applied. The mesh density and analysis time were determined prior to the analysis. According to the convergence experiments, mesh sizes of 0.2 mm and 0.5 mm respectively for the braid and the membranes, and step times of 0.003s and 0.05s respectively for the two steps, were found to yield satisfactory results. The rigid plate was meshed with one element, a fine mesh with 100 nodes were applied to the lower end of the rod to capture its curved profile. Displacement and force of the rod were recorded during the analysis. The Young’s modulus of the Nylon PA66 fiber and the polythene membrane were respectively determined through tensile experiments as Ef ¼ 3.5 GPa and Em ¼ 291 MPa. And their Poission’s ratios were selected as 0.28 and 0.3, respectively. The membrane thickness b was 0.04 mm.
Fig. 3. Specimens of (a) a stand-alone braid, (b) a reinforced braided tube, and (c) a welded braid. Table 1 Design parameters of the specimens. Parameters
Values
Length L Diameter D Number of fibers n Braiding angle β Fiber diameter d
100.20 mm 19.34 mm 16 44.4� 1.07 mm
3.2. Finite element modeling
4. Results and discussions
To understand the deformation mechanism and radial stiffness of the reinforced braided tube in more details, numerical models were also established in Abaqus/Explicit [29]. The geometrical models of the braid were established in the pre-processor Matlab. Assumption of radial sinusoidal disturbance suggested by Alpyildiz [30] was adopted for staggering the helical fibers at the intersections, so that the fibers could slide during deformation. With the node and element information ac quired with Matlab, an orphan mesh part was established and imported into Abaqus. To form the tube shown in Fig. 5, inner and outer mem branes directly established in the Abaqus were added on the braid. The
4.1. Experimental results Lateral indentation experiments of the three structures are first presented. The deformed configurations are shown in Fig. 6(a–c), and the reaction force versus indentation displacement curves are drawn in Fig. 6(d). It can be seen that the stand-alone braid extends longitudinally upon compression, while the other two show negligible change in length. The reaction forces of the three structures increase mono tonically with compression displacement. In addition, the stand-alone braid and the welded braid exhibit the lowest and highest stiffness, respectively, whilst the reinforced tube is in between. The numerically obtained curves are also drawn in Fig. 6(d) for comparison. A good match between numerical and experimental results is achieved in all the three structures. The errors of at a displacement of 4.5 mm of the welded braid, the reinforced tube, and the stand-alone braid are only 9.1%, 8.0%, and 2.2%, respectively, thereby validating the accuracy of the numerical models. The slight differences between numerical and experimental results are mainly due to the limitation of the fabrication
Fig. 4. Experiment setup.
Fig. 5. Numerical modeling of the indentation experiments. 3
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 6. Experimental results: deformed configurations of (a) the stand-alone braid, (b) the reinforced braided tube, (c) the welded braid, and (d) reaction force versus indentation displacement curves.
maximum stress. The numerical results in Table 3 show that the elastic energy of the braided skeleton is 173.5% higher than that of the standalone braid. To further explain the deformation mechanism of the braided skel eton in the reinforced tube, a welded braid in which the fibers are rigidly joined at intersection is also built and analyzed. As can be seen in Fig. 7 (c), the deformation mode and stress distribution is similar to those of the braided skeleton. The only major difference is that the stress is higher due to the stronger constraint at the intersection points. In comparison with the stand-alone braid, the elastic energy is dramati cally increased by 789.7%. Having understood the contribution by the braided skeleton, next we will study the role played by the membranes. The Mises stress contour of the deformed outer membrane resembles that of the inner one, and is presented in Fig. 8(a). The stress is found to be mostly below 10 MPa and the elastic energy of the membrane as shown in Table 3 accounts for only 4.3% of the total energy in the reinforced tube. However, the membrane contributes to the radial stiffness of the reinforced tube in two ways. The first is to restrain rotation at the intersections of the braided skeleton, the effect of which has been demonstrated above. The second is through friction dissipation arising from sliding between fibers and membrane. Fig. 8(b) shows the contact shear force, i.e., the friction, on the mem brane. It can be seen that friction between the two constituents of the reinforced tube exists in the whole structure. And the area with friction is denser in the neighborhood of the loaded middle portion, indicating larger sliding between fibers and membrane. As seen in Table 3, the friction dissipation takes up 32% of the total energy, clearly demon strating the effect of friction. Moreover, different from ordinary com posites with a nearly perfect bonding between fibers and matrix, the friction serves two functions. First, it enables tunable stiffness of the structure, i.e., the larger the friction, the higher the radial stiffness. Second, it allows sliding between constituents during deformation, but the bonding interface is maintained by the negative pressure. As a result, the reinforced tube is expected to withstand larger deformation than ordinary composites without causing fiber-matrix debonding [24].
process, including weaker gluing at the intersections of the welded braid and the additional effects caused by the membranes at the two ends in the reinforced tube. 4.2. Deformation mechanism In this subsection the numerical models that have been validated by experiments will be used to reveal more details during deformation of the structures. We start from the braids, the Mises stress contours of which are shown on the deformed configurations in Fig. 7(a–c). First the stand-alone braid is investigated. Upon compression, it accommodates the deformation easily because the fiber can rotate at the intersection points, leading to increased braiding angles. To demonstrate this feature, the change in braiding angle Δβ at five points along the middle cross section A-A, a~e, and six points along the longitudinal direction, c, f, g, h, j, k, are measured from the numerical model and respectively drawn in Fig. 7(d–e). It can be seen that a symmetric distribution about point a is obtained along the circumferential direction, leading to an elliptical middle cross section as shown in Fig. 7(a). Along the longitu dinal direction, on the other hand, the braiding angle variation di minishes from the middle section to the end, indicating the localized feature of the indentation. As shown in Eq. (1), increase in the braiding angle results in elongation of the stand-alone braid, which explains the change in the length by 7 mm in the numerical model. Moreover, the stress contour in Fig. 7(a) indicates that the compression load is main carried through bending of the fibers on the top side of the stand-alone braid, which are directly in contact with the rod. This is because the rod tends to straighten the originally curved fibers. Subsequently the braided skeleton in the reinforced tube is studied. In comparison with the stand-alone braid, the braided skeleton shows three different features. First, as seen in Fig. 7(d–e), the magnitude of braiding angle variation is much lower due to restriction provided by the membranes, leading to a slight elongation of only 1.2 mm. Second, at the middle cross section B-B, the braiding angles on top (point a) and bottom (point e) decrease, whereas those on the sides (points b, c, d) increase. As a result, a kind of oval shape with localized flattening on the top is obtained. This mode indicates that the membranes effectively bond the fibers and make them deform more simultaneously like a thin-walled cylinder with continuous surface. Finally, in the vicinity of the rod, apart from the top surface, the fibers at the two sides contribute greatly to the overall stiffness. With the restriction brought by the membranes, they tend to keep their original direction, which is roughly parallel to that of the load. As a result, they become the main load carriers instead of the contacting surface in the stand-alone braid, thereby presenting the
4.3. Effects of design parameters It has been shown from subsection 4.2 that the stiffness of the rein forced braided tube is affected not only by the stiffness of the braided skeleton and the membranes but also by their interaction through fric tion. In this subsection, the effects of those design parameters are analyzed through a series of models of the stand-alone braid and the reinforced tube. They have a length of 100 mm and a middle diameter of 4
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 7. Mises stress contours of the (a) stand-alone braid, (b) the braided skeleton in the reinforced tube, and (c) the welded braid; changes in braiding angle at intersection points in the (d) circumferential direction and (e) longitudinal direction for the stand-alone braid and the reinforced tube.
20 mm, and the other varied parameters are listed in Table 2. The re action forces at a compression of 5 mm were recorded and analyzed. First, we look at the effects of braided skeleton through model groups A-D. The radial forces of the reinforced tube against varying Young’s modulus of the fiber Ef, diameter of the fiber d, the number of fibers n, and the braiding angle β, are respectively drawn in Fig. 9(a–d). The radial forces of the stand-alone braid with identical parameters are also presented in the figures for comparison. It can be seen that the curves of the two structures present the same trend, further proving that a stiffer braided skeleton leads to a stiffer reinforced tube. In addition, the force of the reinforced tube increases with Ef, d4, and n in a roughly linear manner. The reason is that during indentation, the fibers can be regar ded as beams and mainly undergo bending. The bending stiffness of the fibers can be calculated as πEfd4/64, which is linear with Ef and d4. And the larger n, the more fibers are bent, leading to higher structural radial
stiffness. Furthermore, Fig. 9 (d) shows that a higher reaction force is obtained at a smaller β, and the relationship between the force and β is nonlinear. This is because the number of fiber coils contained in a length L can be calculated as coil ¼ L=πD tan β
(4)
At a smaller β, more fibers coils sustain the load, leading to a higher overall radial stiffness. Second, the effects of membrances are investigated with model groups E and F. Since they can only sustain tension, the membrance tensile stiffness Emb is considered in the investigation. The reaction forces of the reinforced tube with varying Emb are shown in Fig. 10(a). The force is found to increase mildly at a smaller membrane stiffness, but tends to reach a plateau when membrane stiffness is relativley large. 5
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 8. (a) Mises stress and (b) contact shear force contours of the membrane. Table 2 Parameters of the numerical models. Group
Ef/GPa
d/mm
n
β/deg
Em/MPa
b/mm
P/kPa
μ
A B C D E F G H
10–90 50 50 50 50 50 50 50
0.6 0.2–1.0 0.6 0.6 0.8 0.8 0.8 0.8
16 16 16–48 16 16 16 16 16
45 45 45 30–60 45 45 45 45
300 300 300 300 100–900 300 300 300
0.03 0.03 0.03 0.03 0.03 0.01–0.09 0.03 0.03
70 70 70 70 70 70 10–90 30
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.1–0.9
Finally, the friction between the constituents are studied with model groups G and H. The friction has a linear relationship with negative pressure P and friciton coefficent μ, and therefore the two parameters are considered collectively as Pμ. According to the result in Fig. 10(b), the force of the reinforced tube increases substantially with Pμ, indi cating that the stiffness of the reinforced tube can be widely tuned with negative pressure. Understanding the effects of design parameters can provide guidance in the design of reinforced tubes to satisfy engineering requirements. For instance, it can be a promising candidate as a manipulator for minimally invasive surgery. To this end, it should be compliant enough in the flexible state to facilitate insertion into body orifices. In addition, it needs to preserve a large radial stiffness in the rigid state to withstand the lateral contraction caused by narrow body orifices thus providing an intact passage for the operation tools. Based on the parametric analysis, the skeleton which contributes to most of the stiffness in the flexible state, should not be too stiff. Reducing fiber diameter, Young’s modulus and fiber number, as well as increasing braiding angle can achieve this. On the other hand, the stiffness in the rigid state should be improved. This can be achieved by a large membrane stiffness, friction, and negative pressure, without noticeably affecting the stiffness in the flex ible state.
constituents. It has been found out that the radial stiffness of the rein forced tube mainly arises from two deformation mechanisms. One is the restriction exerted on the braided skeleton by the membranes. It con strains the rotation of fibers at intersections and thus increases the stiffness of the skeleton. The other is the sliding between fibers and membranes, which leads to substantial friction dissipation in the struc ture. Such sliding allows for large deformation in the structure without causing failure in the fiber-matrix interface as in ordinary composites. A parametric analysis has also been conducted to investigate the effects of design parameters on the radial stiffness of the structure. The results show that a stiff braided skeleton with large Young’s modulus, diameter, number of fibers, but small braiding angle, a stiff membrane with large Young’s modulus and thickness, as well as large friction between them through high negative pressure and coefficient of friction, can lead to a reinforced tube with high resistance to lateral indentation. In the future, a theoretical model to estimate the radial stiffness of the reinforced tube and approaches to improve the tunable stiffness range will be pursued.
Table 3 Energy distribution in the structures.
5. Conclusion In this paper, the deformation mechanism and radial stiffness of a reinforced braided tube with tunable stiffness when subjected to lateral indentation have been studied experimentally and numerically. The structure is composed of a braided skeleton and sealing membranes, and the stiffness can be adjusted by applying negative pressure between the
Structure
Parameter
Value(mJ)
Stand-alone braid
Elastic energy Friction dissipation Elastic energy of skeleton Elastic energy of membrane Friction dissipation Elastic energy Friction dissipation
15.98 4.40 43.70 4.23 22.55 142.17 3.76
Reinforced tube Welded braid
6
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 9. Effects of the braid parameters on the stiffness: (a) Ef, (b) d, (c) n and (d) β
Fig. 10. Effects of (a) membrane stiffness and (b) friction.
CRediT authorship contribution statement
Acknowledgement
Zufeng Shang: Methodology, Validation, Formal analysis, Data curation, Writing - original draft, Visualization. Jiayao Ma: Methodol ogy, Software, Investigation, Writing - review & editing, Supervision, Project administration, Funding acquisition, Conceptualization, Meth odology, Software. Zhong You: Methodology. Shuxin Wang: Concep tualization, Resources, Supervision, Project administration, Funding acquisition.
This work was supported by the National Natural Science Foundation of China (Grant 51575377), the National Key R&D Program of China (Grant No. 2017YFC0110401) and the National Natural Science Foun dation of China (Grant 51520105006 and Grant 51721003). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.tws.2020.106608. 7
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
References
[17] Q. Zou, W. Xue, J. Lin, Y. Fu, G. Guan, F. Wang, L. Wang, Mechanical characteristics of novel polyester/NiTi wires braided composite stent for the medical application, Results Phys 6 (2016) 440–446. [18] F. Zhao, F. Wang, M.W. King, L. Wang, Effect of dynamic and static loading during in vitro degradation of a braided composite bioresorbable cardiovascular stent, Mater. Lett. 250 (2019) 12–15. [19] A.M. Harte, N.A. Fleck, M.F. Ashby, Energy absorption of foam-filled circular tubes with braided composite walls, Eur. J. Mech. Solid. 19 (2000) 31–50. [20] Z. Shang, J. Ma, Z. You, S. Wang, A foldable manipulator with tunable stiffness based on braided structure, J. Biomed. Mater. Res. B (2019) 1–10. [21] S. Zuo, S. Wang, Current and emerging robotic assisted intervention for Notes, Expet Rev. Med. Dev. 13 (2016) 1095–1105. [22] D. Rattner, A. Kalloo, ASGE/SAGES working group on natural orifice translumenal endoscopic surgery, Surg. Endosc. 63 (2006) 199–203. [23] National orifice surgery consortium for assessment and research(NOSCARTM), Working group summary on development of a multitasking platform, Available from: http://www.noscar.org/presentations-2006/tasking-platform, 2006. (Accessed October 2006). [24] C.C. Thompson, M. Ryou, N.J. Soper, E.S. Hungess, R.I. Rothstein, L.L. Swanstrom, Evaluation of a manually driven, multitasking platform for complex endoluminal and natural orifice transluminal endoscopic surgery applications (with video), Gastrointest. Endosc. 70 (2009) 121–125. [25] J. Curtis, M.J. Hinton, S. Li, S.R. Reid, P.D. Soden, Damage, deformation and residual burst strength of filament-wound composite tubes subjected to impact or quasi-static indentation, Compos. B Eng. 31 (2000) 419–433. [26] F. Hafeez, F. Almaskari, Glass reinforced epoxy tubes subjected to indentation load: a study of scaling effects, Compos. Struct. 117 (2014) 433–444. [27] S. Li, S.R. Reid, P.D. Soden, M.J. Hinton, Modelling transverse cracking damage in thin, filament-wound tubes subjected to lateral indentation followed by internal pressure, Int. J. Mech. Sci. 47 (2005) 621–646. [28] M.R. Jedwab, C.O. Clerc, A study of the geometrical and mechanical properties of a self-expanding metallic stent - theory and experiment, J. Appl. Biomed. 4 (1993) 77–85. [29] Abaqus Analysisi User’s Manaul, Abaqus Documentation Version 6.14-1, 2014, dassault sys- tems SIMULA Corp. Providence, RI, USA. [30] T. Alpyildiz, 3D geometrical modelling of tubular braids, Textil. Res. J. 82 (2012) 443–453.
[1] M.M. Schwartz, Composite Materials, Volume I: Properties, Nondestructive Testing, and Repair, Prentice Hall PTR, New Jersey, 1997. [2] P.K. Mallick, Fiber-reinforced Composites: Materials, Manufacturing, and Design, CRC press, Boca Raton, 2007. [3] C.E. Bakis, L.C. Bank, V.L. Brown, E. Cosenza, J.F. Davalos, J.J. Lesko, A. Machida, S.H. Rizkalla, T.C. Triantafillou, Fiber-reinforced polymer composites for construction—state-of-the-art review, J. Compos. Construct. 6 (2002) 73–87. [4] J.P. Carey, Handbook of Advances in Braided Composite Materials: Theory, Production, Testing and Applications, Woodhead Publishing, Amsterdam, Netherlands, 2016. [5] F.K. Ko, C.M. Pastore, A.A. Head, Handbook of Industrial Braiding, Atkins and Pearce, Inc., Covington, KY, 1989. [6] D. Brunnschweiler, Braids and braiding, J Text I Proc 44 (1953) 666–686. [7] X.Y. Pei, J.L. Li, Research on fabricating technology of three dimensional integrated braided composite I beam, Adv. Mater. Res. 136 (2010) 59–63. [8] W. Zhang, B. Gu, B. Sun, Transverse impact behaviors of 3D braided composites Tbeam at elevated temperatures, J. Compos. Mater. 50 (2016) 3961–3971. [9] A. Saboktakin, 3D textile preforms and composites for aircraft structures: a review, Int J Aviation Aeronautics Aerospace 6 (2019) 2. [10] J.H. Eun, J.S. Lee, S.H. Park, D.H. Kim, J.S. Chon, H.W. Yoo, A study on the mechanical properties of braid composites for the manufacture of aircraft stringer, Compos Res 31 (2018) 293–298. [11] I. Dayyani, A.D. Shaw, E.I.S. Flores, M.I. Friswell, The mechanics of composite corrugated structures: a review with applications in morphing aircraft, Compos. Struct. 133 (2015) 358–380. [12] J. Ochola, B. Malengier, L. Daelemans, L. Van Langenhove, Finite element simulations to evaluate deformation of polyester tubular braided structures, Textil. Res. J. 87 (2017) 1275–1283. [13] J.H. Kim, T.J. Kang, W.R. Yu, Mechanical modeling of self-expandable stent fabricated using braiding technology, J. Biomech. 41 (2008) 3202–3212. [14] S. Li, J.S. Tsai, L.J. Lee, Preforming analysis of biaxial braided fabrics sleeving on pipes and ducts, J. Compos. Mater. 34 (2000) 479–501. [15] B. Wang, P. Zhang, W. Song, L. Zhao, C. He, Design and properties of a new braided poly lactic-co-glycolic acid catheter for peripheral nerve regeneration, Textil. Res. J. 85 (2015) 51–61. [16] J. Carey, A. Fahim, M. Munro, Design of braided composite cardiovascular catheters based on required axial, flexural, and torsional rigidities, J. Biomed. Mater. Res. B 70 (2004) 73–81.
8
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: http://www.elsevier.com/locate/tws
Full length article
Lateral indentation of a reinforced braided tube with tunable stiffness Zufeng Shang a, b, Jiayao Ma a, b, *, Zhong You b, c, Shuxin Wang a, b, ** a
Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China School of Mechanical Engineering, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China c Department of Engineering Science, University of Oxford, 17 Parks Road, Oxford, OX1 3PJ, UK b
A R T I C L E I N F O
A B S T R A C T
Keywords: Reinforced braided tube Lateral indentation Tunable stiffness Fiber-membrane interaction Negative pressure
In this paper, the lateral indentation of a newly proposed reinforced braided tube with tunable stiffness, which takes a braided tube as skeleton and is sealed by thin membranes, has been studied experimentally and numerically. It is found out that the radial stiffness could be increased by 290% compared with that of a standalone braided tube, through adjusting the negative pressure between the braided skeleton and the membranes. During deformation, the fibers in the reinforced tube are longitudinally restricted by friction, which increases the stiffness of the braided skeleton. In addition, friction dissipation due to sliding between fibers and membranes also contributes substantially to the load carrying capability of the reinforced tube, leading to a much stiffer structure than the summation of the constituents. A parametric analysis has also been conducted, from which the effects of the design parameters are obtained.
1. Introduction Fiber-reinforced composite is a combination of high-strength fibers and a matrix, where the former is embedded in or bonded to the latter with distinct interfaces [1]. In the composite, the fibers generally act as the principal load-carrying members, whereas the matrix functions as location, orientation, transmission and protection [2]. Thanks to the heterogeneous composition, it has superior mechanical properties and durability over the constituents alone [3]. As one type of fiber-reinforced composite, braided composite has attracted increasing interests with the development of modern braiding technology. It dis tinguishes from others with the interlacing of the fibers, leading to improved delamination toughness and impact resistance [4], as well as design versatility and manufacturing simplicity. The braided composite can be categorized into two groups. The first group is braided composite with closed configuration, in which the fibers are jammed and contact each other tightly [5,6] to achieve a high fiber volume fraction. Close braided composite is often used as structural components [7,8], espe cially in aerospace engineering [9–11], due to its lightweight and su perior mechanical strength/mass ratio. The second group has an open configuration, where the adjacent fibers are separated [5,6,12].
Compared with the closed composite, the open one exhibits a modest stiffness, but excellent bending flexibility [13]. With the features, it is widely used as air ducts [14], and medical catheters [15,16] and stents [17,18] in medicine which are required to pass through tortuous body orifices. In addition, energy absorption structures have also adopted such structure which is filled with crushable foam to prevent delami nation [19]. Recently, a reinforced braided tube with tunable stiffness, which had a braided skeleton sealed in thin membranes, was proposed [20]. It can switch between flexible and rigid states by adjusting the negative pressure between the skeleton and the membranes, making it suitable for biomedical engineering applications such as manipulators for mini mally invasive surgery [21,22]. When in operation, the structure could be subjected to localized lateral loading, which may cause denting and kinking, thus severely affecting its functionality [23,24]. Currently, research on the lateral indentation of composite tubes has been very limited, and most work focuses on the failure mechanism of filament-wound tubes [25–27]. In this work, the deformation mecha nism and radial stiffness of the reinforced braided tube with tunable stiffness are investigated both experimentally and numerically, with the aim of providing a design guidance for the new structure with suitable
* Corresponding author. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China. ** Corresponding author. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China. E-mail addresses: [email protected] (Z. Shang), [email protected] (J. Ma), [email protected] (Z. You), [email protected] (S. Wang). https://doi.org/10.1016/j.tws.2020.106608 Received 26 September 2019; Received in revised form 5 December 2019; Accepted 9 January 2020 Available online 12 February 2020 0263-8231/© 2020 Elsevier Ltd. All rights reserved.
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
stiffness upon request. The paper is organized as follows. In the material section 2, the geometry of the structure and the fabrication approach are introduced. Then the experimental setup and finite element modeling are presented in the methods section 3. Results and discussions are presented in section 4, in which the deformation mechanism of the structure and the effects of design parameters are shown. Section 5 gives the conclusion.
membrane with high tensile stiffness, were adopted to fabricate the reinforced tube. The braid was fabricated with a 3D braiding machine shown in Fig. 2. With the mandrel moving in the longitudinal direction, two groups of bobbins, eight in each group, rotated around the mandrel in clockwise and anticlockwise directions, respectively, to weave the fibers into a braid on the surface of the mandrel. The diameter of the braid D was determined by the mandrel diameter Dm and the fiber diameter d, and the relationship is expressed as
2. Materials 2.1. Geometry
The braiding angle β was determined by the take-up speed of the mandrel v and angular speed of the bobbins w through
The reinforced braided tube with tunable stiffness is composed of a braid and sealing membranes [20]. As shown in Fig. 1, the membranes cover both the inner and outer surfaces of the braid and forms a sealed cavity. The membranes and braid contacts loosely in the flexible state, where the whole structure functions virtually as a sole braid. In the rigid state, negative pressure is applied in the cavity. The membranes are compressed onto the braid by the air pressure, and both components deform interactively so as to improve the stiffness of the structure. The braid in the structure is formed by helical springs interwoven together as seen in Fig. 1 [13], and its geometry can be completely defined by L, D, n, β and d, which are tube length, tube diameter, number of fibers, braiding angle, and fiber diameter, respectively. The braid shrinks in the radial direction when elongated longitudinally, and the relationship between β, D and L was given by Jedwab and Clerc [28] as f
L’ ¼ L sin β’=sin β D’ ¼ D cos β’=cos β
(2)
D ¼ Dm þ 2d
(3)
β ¼ arctanð2v = wDÞ
Subsequently, the braid was heat treated at 100 � C for 1 hour on the mandrel, after which a stable tubular braid was obtained as shown in Fig. 3(a). Finally, tubular membranes with a slightly larger diameter than that of the braid was inserted into the braid, and then folded to cover the outer surface of the braid. The ends of the membranes were glued together so that the braid was sealed, and a reinforced braided tube shown in Fig. 3(b) was obtained [20]. In addition, a stand-alone braid in which the fibers could freely slide at intersection points as shown in Fig. 3(a) and a welded braid in which all the fiber intersection points were glued together as shown in Fig. 3(c) were also built for comparison purpose. All the three specimens have the same parameters listed in Table 1.
(1)
3. Methods
where each parameter of the deformed braid is denoted with a prime.
3.1. Experimental setup
2.2. Fabrication
The lateral indentation experiments of the physical specimens were carried out on an Instron 5982 testing machine. The reinforced braided tube was connected to a pump via an air duct to tune the negative pressure. A negative pressure P ¼80 kPa was applied to the specimen. The experimental setup shown in Fig. 4 was set as Kim et al. [13] sug gested, where a circular rod is used to compress the longitudinal midpoint of the braid to test the radial stiffness. During the experiment, the specimen was placed on a flat plate freely, and a 3D printed circular rod with a diameter of 18 mm moved downward to compress the midpoint of the specimen by 4.5 mm, about a quarter of its original diameter. To avoid dynamic effects, the indentation was conducted at a loading rate of 5 mm/min. Both force and displacement during each experiment were recorded automatically by the Instron.
Nylon PA66 fiber with good elasticity, great compliance to the mandrel and low heat treatment temperature, and polyethylene
Fig. 1. Design of the reinforce braided tube with tunable stiffness.
Fig. 2. The braiding machine. 2
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
diameters of the membranes were slightly different from that of the braid so as to avoid physical interference. For the welded braid, radial distribution of the helical fibers was ignored and the whole structure was modelled as a number of helical fibers merged together. Three-dimensional membrane elements, M3D4R, and beam elements, B31, were used to mesh the membranes and the braid, respectively. To model the indentation experiment setup, a plate and a circular rod shown in Fig. 5 were also built in Abaqus as rigid bodies. Two analysis steps were defined to model the loading process of the reinforced tube. In the first step, both the rod and the plate were fixed, and uniform pressure was applied to both membranes to model the negative pressure. In the second one, at the constant pressure, a pre scribed displacement was assigned to the free degree of freedom of the rod to compress the structure. Smooth amplitude definition built in Abaqus was adopted to control the indentation procedure. Hard contact was used to model the normal behaviour and penalty was chosen as the friction formulation with a coefficient of friction μ of 0.3 to capture the tangential behaviour. As for the stand-alone braid and the welded braid, only the second step was applied. The mesh density and analysis time were determined prior to the analysis. According to the convergence experiments, mesh sizes of 0.2 mm and 0.5 mm respectively for the braid and the membranes, and step times of 0.003s and 0.05s respectively for the two steps, were found to yield satisfactory results. The rigid plate was meshed with one element, a fine mesh with 100 nodes were applied to the lower end of the rod to capture its curved profile. Displacement and force of the rod were recorded during the analysis. The Young’s modulus of the Nylon PA66 fiber and the polythene membrane were respectively determined through tensile experiments as Ef ¼ 3.5 GPa and Em ¼ 291 MPa. And their Poission’s ratios were selected as 0.28 and 0.3, respectively. The membrane thickness b was 0.04 mm.
Fig. 3. Specimens of (a) a stand-alone braid, (b) a reinforced braided tube, and (c) a welded braid. Table 1 Design parameters of the specimens. Parameters
Values
Length L Diameter D Number of fibers n Braiding angle β Fiber diameter d
100.20 mm 19.34 mm 16 44.4� 1.07 mm
3.2. Finite element modeling
4. Results and discussions
To understand the deformation mechanism and radial stiffness of the reinforced braided tube in more details, numerical models were also established in Abaqus/Explicit [29]. The geometrical models of the braid were established in the pre-processor Matlab. Assumption of radial sinusoidal disturbance suggested by Alpyildiz [30] was adopted for staggering the helical fibers at the intersections, so that the fibers could slide during deformation. With the node and element information ac quired with Matlab, an orphan mesh part was established and imported into Abaqus. To form the tube shown in Fig. 5, inner and outer mem branes directly established in the Abaqus were added on the braid. The
4.1. Experimental results Lateral indentation experiments of the three structures are first presented. The deformed configurations are shown in Fig. 6(a–c), and the reaction force versus indentation displacement curves are drawn in Fig. 6(d). It can be seen that the stand-alone braid extends longitudinally upon compression, while the other two show negligible change in length. The reaction forces of the three structures increase mono tonically with compression displacement. In addition, the stand-alone braid and the welded braid exhibit the lowest and highest stiffness, respectively, whilst the reinforced tube is in between. The numerically obtained curves are also drawn in Fig. 6(d) for comparison. A good match between numerical and experimental results is achieved in all the three structures. The errors of at a displacement of 4.5 mm of the welded braid, the reinforced tube, and the stand-alone braid are only 9.1%, 8.0%, and 2.2%, respectively, thereby validating the accuracy of the numerical models. The slight differences between numerical and experimental results are mainly due to the limitation of the fabrication
Fig. 4. Experiment setup.
Fig. 5. Numerical modeling of the indentation experiments. 3
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 6. Experimental results: deformed configurations of (a) the stand-alone braid, (b) the reinforced braided tube, (c) the welded braid, and (d) reaction force versus indentation displacement curves.
maximum stress. The numerical results in Table 3 show that the elastic energy of the braided skeleton is 173.5% higher than that of the standalone braid. To further explain the deformation mechanism of the braided skel eton in the reinforced tube, a welded braid in which the fibers are rigidly joined at intersection is also built and analyzed. As can be seen in Fig. 7 (c), the deformation mode and stress distribution is similar to those of the braided skeleton. The only major difference is that the stress is higher due to the stronger constraint at the intersection points. In comparison with the stand-alone braid, the elastic energy is dramati cally increased by 789.7%. Having understood the contribution by the braided skeleton, next we will study the role played by the membranes. The Mises stress contour of the deformed outer membrane resembles that of the inner one, and is presented in Fig. 8(a). The stress is found to be mostly below 10 MPa and the elastic energy of the membrane as shown in Table 3 accounts for only 4.3% of the total energy in the reinforced tube. However, the membrane contributes to the radial stiffness of the reinforced tube in two ways. The first is to restrain rotation at the intersections of the braided skeleton, the effect of which has been demonstrated above. The second is through friction dissipation arising from sliding between fibers and membrane. Fig. 8(b) shows the contact shear force, i.e., the friction, on the mem brane. It can be seen that friction between the two constituents of the reinforced tube exists in the whole structure. And the area with friction is denser in the neighborhood of the loaded middle portion, indicating larger sliding between fibers and membrane. As seen in Table 3, the friction dissipation takes up 32% of the total energy, clearly demon strating the effect of friction. Moreover, different from ordinary com posites with a nearly perfect bonding between fibers and matrix, the friction serves two functions. First, it enables tunable stiffness of the structure, i.e., the larger the friction, the higher the radial stiffness. Second, it allows sliding between constituents during deformation, but the bonding interface is maintained by the negative pressure. As a result, the reinforced tube is expected to withstand larger deformation than ordinary composites without causing fiber-matrix debonding [24].
process, including weaker gluing at the intersections of the welded braid and the additional effects caused by the membranes at the two ends in the reinforced tube. 4.2. Deformation mechanism In this subsection the numerical models that have been validated by experiments will be used to reveal more details during deformation of the structures. We start from the braids, the Mises stress contours of which are shown on the deformed configurations in Fig. 7(a–c). First the stand-alone braid is investigated. Upon compression, it accommodates the deformation easily because the fiber can rotate at the intersection points, leading to increased braiding angles. To demonstrate this feature, the change in braiding angle Δβ at five points along the middle cross section A-A, a~e, and six points along the longitudinal direction, c, f, g, h, j, k, are measured from the numerical model and respectively drawn in Fig. 7(d–e). It can be seen that a symmetric distribution about point a is obtained along the circumferential direction, leading to an elliptical middle cross section as shown in Fig. 7(a). Along the longitu dinal direction, on the other hand, the braiding angle variation di minishes from the middle section to the end, indicating the localized feature of the indentation. As shown in Eq. (1), increase in the braiding angle results in elongation of the stand-alone braid, which explains the change in the length by 7 mm in the numerical model. Moreover, the stress contour in Fig. 7(a) indicates that the compression load is main carried through bending of the fibers on the top side of the stand-alone braid, which are directly in contact with the rod. This is because the rod tends to straighten the originally curved fibers. Subsequently the braided skeleton in the reinforced tube is studied. In comparison with the stand-alone braid, the braided skeleton shows three different features. First, as seen in Fig. 7(d–e), the magnitude of braiding angle variation is much lower due to restriction provided by the membranes, leading to a slight elongation of only 1.2 mm. Second, at the middle cross section B-B, the braiding angles on top (point a) and bottom (point e) decrease, whereas those on the sides (points b, c, d) increase. As a result, a kind of oval shape with localized flattening on the top is obtained. This mode indicates that the membranes effectively bond the fibers and make them deform more simultaneously like a thin-walled cylinder with continuous surface. Finally, in the vicinity of the rod, apart from the top surface, the fibers at the two sides contribute greatly to the overall stiffness. With the restriction brought by the membranes, they tend to keep their original direction, which is roughly parallel to that of the load. As a result, they become the main load carriers instead of the contacting surface in the stand-alone braid, thereby presenting the
4.3. Effects of design parameters It has been shown from subsection 4.2 that the stiffness of the rein forced braided tube is affected not only by the stiffness of the braided skeleton and the membranes but also by their interaction through fric tion. In this subsection, the effects of those design parameters are analyzed through a series of models of the stand-alone braid and the reinforced tube. They have a length of 100 mm and a middle diameter of 4
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 7. Mises stress contours of the (a) stand-alone braid, (b) the braided skeleton in the reinforced tube, and (c) the welded braid; changes in braiding angle at intersection points in the (d) circumferential direction and (e) longitudinal direction for the stand-alone braid and the reinforced tube.
20 mm, and the other varied parameters are listed in Table 2. The re action forces at a compression of 5 mm were recorded and analyzed. First, we look at the effects of braided skeleton through model groups A-D. The radial forces of the reinforced tube against varying Young’s modulus of the fiber Ef, diameter of the fiber d, the number of fibers n, and the braiding angle β, are respectively drawn in Fig. 9(a–d). The radial forces of the stand-alone braid with identical parameters are also presented in the figures for comparison. It can be seen that the curves of the two structures present the same trend, further proving that a stiffer braided skeleton leads to a stiffer reinforced tube. In addition, the force of the reinforced tube increases with Ef, d4, and n in a roughly linear manner. The reason is that during indentation, the fibers can be regar ded as beams and mainly undergo bending. The bending stiffness of the fibers can be calculated as πEfd4/64, which is linear with Ef and d4. And the larger n, the more fibers are bent, leading to higher structural radial
stiffness. Furthermore, Fig. 9 (d) shows that a higher reaction force is obtained at a smaller β, and the relationship between the force and β is nonlinear. This is because the number of fiber coils contained in a length L can be calculated as coil ¼ L=πD tan β
(4)
At a smaller β, more fibers coils sustain the load, leading to a higher overall radial stiffness. Second, the effects of membrances are investigated with model groups E and F. Since they can only sustain tension, the membrance tensile stiffness Emb is considered in the investigation. The reaction forces of the reinforced tube with varying Emb are shown in Fig. 10(a). The force is found to increase mildly at a smaller membrane stiffness, but tends to reach a plateau when membrane stiffness is relativley large. 5
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 8. (a) Mises stress and (b) contact shear force contours of the membrane. Table 2 Parameters of the numerical models. Group
Ef/GPa
d/mm
n
β/deg
Em/MPa
b/mm
P/kPa
μ
A B C D E F G H
10–90 50 50 50 50 50 50 50
0.6 0.2–1.0 0.6 0.6 0.8 0.8 0.8 0.8
16 16 16–48 16 16 16 16 16
45 45 45 30–60 45 45 45 45
300 300 300 300 100–900 300 300 300
0.03 0.03 0.03 0.03 0.03 0.01–0.09 0.03 0.03
70 70 70 70 70 70 10–90 30
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.1–0.9
Finally, the friction between the constituents are studied with model groups G and H. The friction has a linear relationship with negative pressure P and friciton coefficent μ, and therefore the two parameters are considered collectively as Pμ. According to the result in Fig. 10(b), the force of the reinforced tube increases substantially with Pμ, indi cating that the stiffness of the reinforced tube can be widely tuned with negative pressure. Understanding the effects of design parameters can provide guidance in the design of reinforced tubes to satisfy engineering requirements. For instance, it can be a promising candidate as a manipulator for minimally invasive surgery. To this end, it should be compliant enough in the flexible state to facilitate insertion into body orifices. In addition, it needs to preserve a large radial stiffness in the rigid state to withstand the lateral contraction caused by narrow body orifices thus providing an intact passage for the operation tools. Based on the parametric analysis, the skeleton which contributes to most of the stiffness in the flexible state, should not be too stiff. Reducing fiber diameter, Young’s modulus and fiber number, as well as increasing braiding angle can achieve this. On the other hand, the stiffness in the rigid state should be improved. This can be achieved by a large membrane stiffness, friction, and negative pressure, without noticeably affecting the stiffness in the flex ible state.
constituents. It has been found out that the radial stiffness of the rein forced tube mainly arises from two deformation mechanisms. One is the restriction exerted on the braided skeleton by the membranes. It con strains the rotation of fibers at intersections and thus increases the stiffness of the skeleton. The other is the sliding between fibers and membranes, which leads to substantial friction dissipation in the struc ture. Such sliding allows for large deformation in the structure without causing failure in the fiber-matrix interface as in ordinary composites. A parametric analysis has also been conducted to investigate the effects of design parameters on the radial stiffness of the structure. The results show that a stiff braided skeleton with large Young’s modulus, diameter, number of fibers, but small braiding angle, a stiff membrane with large Young’s modulus and thickness, as well as large friction between them through high negative pressure and coefficient of friction, can lead to a reinforced tube with high resistance to lateral indentation. In the future, a theoretical model to estimate the radial stiffness of the reinforced tube and approaches to improve the tunable stiffness range will be pursued.
Table 3 Energy distribution in the structures.
5. Conclusion In this paper, the deformation mechanism and radial stiffness of a reinforced braided tube with tunable stiffness when subjected to lateral indentation have been studied experimentally and numerically. The structure is composed of a braided skeleton and sealing membranes, and the stiffness can be adjusted by applying negative pressure between the
Structure
Parameter
Value(mJ)
Stand-alone braid
Elastic energy Friction dissipation Elastic energy of skeleton Elastic energy of membrane Friction dissipation Elastic energy Friction dissipation
15.98 4.40 43.70 4.23 22.55 142.17 3.76
Reinforced tube Welded braid
6
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
Fig. 9. Effects of the braid parameters on the stiffness: (a) Ef, (b) d, (c) n and (d) β
Fig. 10. Effects of (a) membrane stiffness and (b) friction.
CRediT authorship contribution statement
Acknowledgement
Zufeng Shang: Methodology, Validation, Formal analysis, Data curation, Writing - original draft, Visualization. Jiayao Ma: Methodol ogy, Software, Investigation, Writing - review & editing, Supervision, Project administration, Funding acquisition, Conceptualization, Meth odology, Software. Zhong You: Methodology. Shuxin Wang: Concep tualization, Resources, Supervision, Project administration, Funding acquisition.
This work was supported by the National Natural Science Foundation of China (Grant 51575377), the National Key R&D Program of China (Grant No. 2017YFC0110401) and the National Natural Science Foun dation of China (Grant 51520105006 and Grant 51721003). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.tws.2020.106608. 7
Z. Shang et al.
Thin-Walled Structures 149 (2020) 106608
References
[17] Q. Zou, W. Xue, J. Lin, Y. Fu, G. Guan, F. Wang, L. Wang, Mechanical characteristics of novel polyester/NiTi wires braided composite stent for the medical application, Results Phys 6 (2016) 440–446. [18] F. Zhao, F. Wang, M.W. King, L. Wang, Effect of dynamic and static loading during in vitro degradation of a braided composite bioresorbable cardiovascular stent, Mater. Lett. 250 (2019) 12–15. [19] A.M. Harte, N.A. Fleck, M.F. Ashby, Energy absorption of foam-filled circular tubes with braided composite walls, Eur. J. Mech. Solid. 19 (2000) 31–50. [20] Z. Shang, J. Ma, Z. You, S. Wang, A foldable manipulator with tunable stiffness based on braided structure, J. Biomed. Mater. Res. B (2019) 1–10. [21] S. Zuo, S. Wang, Current and emerging robotic assisted intervention for Notes, Expet Rev. Med. Dev. 13 (2016) 1095–1105. [22] D. Rattner, A. Kalloo, ASGE/SAGES working group on natural orifice translumenal endoscopic surgery, Surg. Endosc. 63 (2006) 199–203. [23] National orifice surgery consortium for assessment and research(NOSCARTM), Working group summary on development of a multitasking platform, Available from: http://www.noscar.org/presentations-2006/tasking-platform, 2006. (Accessed October 2006). [24] C.C. Thompson, M. Ryou, N.J. Soper, E.S. Hungess, R.I. Rothstein, L.L. Swanstrom, Evaluation of a manually driven, multitasking platform for complex endoluminal and natural orifice transluminal endoscopic surgery applications (with video), Gastrointest. Endosc. 70 (2009) 121–125. [25] J. Curtis, M.J. Hinton, S. Li, S.R. Reid, P.D. Soden, Damage, deformation and residual burst strength of filament-wound composite tubes subjected to impact or quasi-static indentation, Compos. B Eng. 31 (2000) 419–433. [26] F. Hafeez, F. Almaskari, Glass reinforced epoxy tubes subjected to indentation load: a study of scaling effects, Compos. Struct. 117 (2014) 433–444. [27] S. Li, S.R. Reid, P.D. Soden, M.J. Hinton, Modelling transverse cracking damage in thin, filament-wound tubes subjected to lateral indentation followed by internal pressure, Int. J. Mech. Sci. 47 (2005) 621–646. [28] M.R. Jedwab, C.O. Clerc, A study of the geometrical and mechanical properties of a self-expanding metallic stent - theory and experiment, J. Appl. Biomed. 4 (1993) 77–85. [29] Abaqus Analysisi User’s Manaul, Abaqus Documentation Version 6.14-1, 2014, dassault sys- tems SIMULA Corp. Providence, RI, USA. [30] T. Alpyildiz, 3D geometrical modelling of tubular braids, Textil. Res. J. 82 (2012) 443–453.
[1] M.M. Schwartz, Composite Materials, Volume I: Properties, Nondestructive Testing, and Repair, Prentice Hall PTR, New Jersey, 1997. [2] P.K. Mallick, Fiber-reinforced Composites: Materials, Manufacturing, and Design, CRC press, Boca Raton, 2007. [3] C.E. Bakis, L.C. Bank, V.L. Brown, E. Cosenza, J.F. Davalos, J.J. Lesko, A. Machida, S.H. Rizkalla, T.C. Triantafillou, Fiber-reinforced polymer composites for construction—state-of-the-art review, J. Compos. Construct. 6 (2002) 73–87. [4] J.P. Carey, Handbook of Advances in Braided Composite Materials: Theory, Production, Testing and Applications, Woodhead Publishing, Amsterdam, Netherlands, 2016. [5] F.K. Ko, C.M. Pastore, A.A. Head, Handbook of Industrial Braiding, Atkins and Pearce, Inc., Covington, KY, 1989. [6] D. Brunnschweiler, Braids and braiding, J Text I Proc 44 (1953) 666–686. [7] X.Y. Pei, J.L. Li, Research on fabricating technology of three dimensional integrated braided composite I beam, Adv. Mater. Res. 136 (2010) 59–63. [8] W. Zhang, B. Gu, B. Sun, Transverse impact behaviors of 3D braided composites Tbeam at elevated temperatures, J. Compos. Mater. 50 (2016) 3961–3971. [9] A. Saboktakin, 3D textile preforms and composites for aircraft structures: a review, Int J Aviation Aeronautics Aerospace 6 (2019) 2. [10] J.H. Eun, J.S. Lee, S.H. Park, D.H. Kim, J.S. Chon, H.W. Yoo, A study on the mechanical properties of braid composites for the manufacture of aircraft stringer, Compos Res 31 (2018) 293–298. [11] I. Dayyani, A.D. Shaw, E.I.S. Flores, M.I. Friswell, The mechanics of composite corrugated structures: a review with applications in morphing aircraft, Compos. Struct. 133 (2015) 358–380. [12] J. Ochola, B. Malengier, L. Daelemans, L. Van Langenhove, Finite element simulations to evaluate deformation of polyester tubular braided structures, Textil. Res. J. 87 (2017) 1275–1283. [13] J.H. Kim, T.J. Kang, W.R. Yu, Mechanical modeling of self-expandable stent fabricated using braiding technology, J. Biomech. 41 (2008) 3202–3212. [14] S. Li, J.S. Tsai, L.J. Lee, Preforming analysis of biaxial braided fabrics sleeving on pipes and ducts, J. Compos. Mater. 34 (2000) 479–501. [15] B. Wang, P. Zhang, W. Song, L. Zhao, C. He, Design and properties of a new braided poly lactic-co-glycolic acid catheter for peripheral nerve regeneration, Textil. Res. J. 85 (2015) 51–61. [16] J. Carey, A. Fahim, M. Munro, Design of braided composite cardiovascular catheters based on required axial, flexural, and torsional rigidities, J. Biomed. Mater. Res. B 70 (2004) 73–81.
8