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Research Papers

Tensile Stress-Driven Surface Wrinkles on Cylindrical Core–Shell Soft Solids

[+] Author and Article Information
Shan Tang

College of Aerospace Engineering,
Chongqing University,
Chongqing 400017, China
e-mail: stang@cqu.edu.cn

Ying Li

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: yingli@u.northwestern.edu

Wing Kam Liu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: w-liu@northwestern.edu

Ning Hu

College of Aerospace Engineering,
Chongqing University,
Chongqing 400017, China
e-mail: ninghu@cqu.edu.cn

Xiang He Peng

College of Aerospace Engineering,
Chongqing University,
Chongqing 400017, China
e-mail: xhpeng@cqu.edu.cn

Zaoyang Guo

Institute of Solid Mechanics,
Beihang University,
Beijing 100191, China
e-mail: zyguo@buaa.edu.cn

1S. Tang and Y. Li contributed equally to this work.

2Present address: Distinguished Scientists Program Committee, King Abdulaziz University (KAU), Jeddah 21589, Saudi Arabia.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 28, 2015; final manuscript received August 3, 2015; published online September 10, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(12), 121002 (Sep 10, 2015) (17 pages) Paper No: JAM-15-1342; doi: 10.1115/1.4031244 History: Received June 28, 2015; Revised August 03, 2015

It has been experimentally observed that wrinkles formed on the surface of electrospun polymer nanofibers when they are under uniaxial tension (Appl. Phys. Lett., 91, p. 151901 (2007)). Molecular dynamics (MD) simulations, finite element analyses (FEA), and continuum theory calculations have been performed to understand this interesting phenomenon. The surface wrinkles are found to be induced by the cylindrical core–shell microstructure of polymer nanofibers, especially the mismatch of Poisson's ratio between the core and shell layers. Through the MD simulations, the polymer nanofiber is found to be composed of a glassy core embedded into a rubbery shell. The Poisson's ratios of the core and shell layers are close to that of the compressible (0.2) and incompressible (0.5) polymers, respectively. The core is twice stiffer than the shell, due to its highly packed polymer chains and large entanglement density. Based on this observation, a FEA model has been built to study surface instability of the cylindrical core–shell soft solids under uniaxial tension. The “polarization” mechanism at the interphase between the core and shell layers, induced by the mismatch of their Poisson's ratios, is identified as the key element to drive the surface wrinkles during the instability analysis. Through postbuckling analysis, the plastic deformation is also found to play an important role in this process. Without the plastic deformation, the initial imperfection cannot lead to surface wrinkles. The FEA model shows that the yielding stress (or strain rate) can greatly affect the onset and modes of surface wrinkles, which are in good agreement with experimental observations on electrospun polymer nanofibers. The deformation mechanism and critical condition for the surface wrinkles are further clarified through a simplified continuum theory. This study provides a new way to understand and control the surface morphology of cylindrical core–shell materials.

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Figures

Grahic Jump Location
Fig. 1

Experimental results on the surface morphology of polymer fiber during (a) electrospinning process and (b) uniaxial tension. (a) and (b) are reproduced with permission from Refs. [9] and [10], respectively.

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Fig. 2

(a) Molecular model of the polymer nanofiber: lateral (upper) and cross-sectional (bottom) views. The distributions of (b) number density, (c) radius of gyration, and (d) entanglement density within the nanofiber. The nanofiber is divided into 25 cylindrical layers of identical thickness along its radial direction. The layer numbers 1 and 25 represent the inner (core) and outermost (shell) layers of the nanofiber, respectively. All the results are given in the reduced LJ units, as given in the Appendix.

Grahic Jump Location
Fig. 3

Schematic of a cylindrical core–shell soft solid for the polymer fiber

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Fig. 4

Snapshots of the surface instability (the second, fourth, sixth, and eighth modes) of cylindrical core–shell soft solids with the length L0/R0=40 and E2/E1=0.5 (a) on the surface θ=π/2 ; (b) on the cylindrical surface R=Ro. Blue and red colors represent the smallest and largest perturbation displacement, respectively. (c) At the interphase between the shell and core layers, the polarization of the materials, alternating compressed and stretched along axial direction, can occur. Note that the core is stiffer than the shell.

Grahic Jump Location
Fig. 5

Snapshots of the surface instability (the second, fourth, sixth, and eighth modes) of cylindrical core–shell soft solids with the length L0/R0=40 and E2/E1=2 on the surface θ=π/2. Note that the core is softer than the shell.

Grahic Jump Location
Fig. 6

Snapshots of the axisymmetric surface instability (the first and 16 modes) of cylindrical core–shell soft solids, with the length L0/R0=10, ν2=0.499 (nearly incompressible) and ν1=0.2 (compressible) for six different ratios of Young's moduli between the shell and core layers, under compression

Grahic Jump Location
Fig. 7

Snapshots of the axisymmetric surface instability (the first and 16 modes) of cylindrical core–shell soft solids with the length L0/R0=10, ν1=ν2=0.499 (nearly incompressible) with six different ratios of Young's moduli between the shell and core layers under compression

Grahic Jump Location
Fig. 8

(a) Critical compressive strain at the bifurcation for cylindrical core–shell soft solids as a function of mode number when the shell is nearly incompressible (ν2=0.499) and the core is compressible (ν1=0.2). Six different ratios of Young's moduli between the core and shell layers are considered. (b) Comparison of the critical compressive strain versus mode number between the case with nearly incompressible shell and compressible core and the one with both nearly incompressible shell and core at two different ratios of Young's moduli.

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Fig. 9

(a) Engineering stress normalized by E1 versus engineering strain for pure elastic layered soft solids with L0/Ro=40. (b) Snapshots of deformation at strain levels 50% and 100% on the surface θ=π/2.

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Fig. 10

(a) Engineering stress normalized by E1 versus engineering strain for three different values of yielding stress of polymer nanofibers with L0/Ro=40. Experimental results (scattered dots) are taken from Fig. 2 in Ref. [10] under three different loading rates. (b) Snapshots of deformation at several strain levels for case 1 with σ01/E1=0.05,σ02/E1=0.025, corresponding to strain rate 0.025 s−1 (the fastest rate); and case 2 with σ01/E1=0.1,σ02/E1=0.05, corresponding to strain rate 0.00025 s−1 (the slowest rate), on the surface θ=π/2. Note that the shell is softer than the core.

Grahic Jump Location
Fig. 11

(a) Engineering stress normalized by E1 versus engineering strain for three different values of yielding stress of polymeric nanofibers with L0/Ro=40. Experimental results (scattered dots) are taken from Fig. 2 in Ref. [10] under three different loading rates. (b) Snapshots of deformation at several strain levels for case 1 with σ01/E1=0.05,σ02/E1=0.1, corresponding to strain rate 0.025 s−1 (the fastest rate); and case 2 with σ01/E1=0.075,σ02/E1=0.15, corresponding to strain rate 0.00025 s−1 (the slowest rate), on the surface θ=π/2. Note that the shell is stiffer than the core.

Grahic Jump Location
Fig. 12

(a) Engineering stress normalized by E1 versus engineering strain for four different interphase thickness with L0/Ro=40. Snapshots of deformation for two different interfacial thicknesses (b) δ/R0=1/6 and (c) δ/R0=1/2 on the surface θ=π/2.

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Fig. 13

(a) Engineering stress normalized by E1 versus engineering strain for three different plastic hardening exponent with L0/Ro=40. (b) Snapshots of deformation at several strain levels for n = 0.4 and 0.5 on the surface θ=π/2.

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Fig. 14

Comparison of the theoretical results with FEA results for the critical buckling strain versus the ratio of Young's moduli E2/E1 (a) under tension and (b) under compression

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Fig. 15

Phase diagram for buckling status of a polymer nanofiber with L0/R0=10 and ν2=0.499 (the shell layer is nearly incompressible). Symbols ○, ◻, △, and × represent only tension instability, only compression instability, tension and compression instability and no instability, respectively. The symbols are predicted by FEA simulations, while the dashed lines are obtained through the simplified continuum theory.

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