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Supplementary Information for
Biaxial Stresses Controlled Three-dimensional Helical Crack
Li Wang†1,4, Xiang-Ying Ji†2, Nü Wang3, Jing Wu3, Hua Dong1,4, Jiexing Du3, Yong
Zhao*,1,3, Xi-Qiao Feng*,2 and Lei Jiang1,3
1 Beijing National Laboratory for Molecular Sciences (BNLMS), Key Laboratory of
Organic Solids, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P.
R. China
2 AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.
R. China
3 Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of
Education, School of Chemistry and Environment, Beihang University, Beijing 100191,
P. R. China
4 Graduate University of the Chinese Academy of Sciences, Beijing 100190, P. R. China
† These authors contributed equally to this work.
* Corresponding authors. E-mail: zhaoyong@iccas.ac.cn., fengxq@tsinghua.edu.cn.
Supplementary information files include a word file and two movie files. The word
file includes introductions of experimental materials, numerical simulation, a table,
six figures, references and instructions for movies.
1
Experimental Materials:
The Pluronic P123 (HO(CH2CH2O)20(CH2CH(CH3)O)70(CH2CH2O)20H, Mw ~5800)
was kindly donated by BASF corporation. Titanium (IV) butoxide (Ti(OBu)4, reagent
grade, 97%, Sigma); Aluminum chloride hexahydrate (AlCl3·H2O, crystallized, ≥99.0%,
Sigma); Orthosilicic acid tetraethyl ester (Si(C2H5O)4, Sigma); Ethanol (C2H5OH), 1-
Butanol (C4H9OH), HCl (~37%), acetic acid (CH3COOH), ferric nitrate and bismuth
nitrate were bought from Beijing Chemical Reagent Company. All chemicals were used
as received without further purification. Water was purified by a Milli-Q system (Millipore
Corporation). The glass microfibres (contain borate, Φ = 12.3 ± 0.5 m) were supplied by
Shangdong General Glassfibre Corporation (China) (Fig. S1).
Numerical simulation:The model is designed according to the real configuration of the specimen. The spindle
has a length of 76 microns and diameters changing from 12.6 microns at the ends to 20.0
microns in the middle. The material parameters of the inner cylinder core and the outer
shell used in the simulation are listed in Table S1. A “static, general” analysis is done with
61,446 C3D8R and 7,840 C3D4 elements under a temperature loading decreasing from
800 K to 300 K.
Table S1. Materials parameters
Materials Young’s modulus (MPa) Poisson’s ratio Thermal expansion coefficient (K-1)
Glass 72,000 [S1] 0.166 [S1] 3 × 10–6 [S2]
TiO2 282,760 [S1] 0.28 [S1] 8.6 × 10–6 [S3]
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Figure S1. SEM image of glass microfiber used as core material in the helical cracking
process. The fiber has a relatively uniform diameter and smooth surface.
Figure S2. SEM image of irregular cracks in the uniform core-shell column (titania layer
coated onto glass microfiber).
Figure S3. Magnified section image of Micro-XCT in the axial direction indicating a
spiral notch (dark region) aside the core (grey region) and shell (white region).
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10 m
Crack
Shell
Core
10 m
10 m
Figure S4. Helical angles statistics of cracks on the spindle-knots. The data are derived
from the measurement of SEM images. The helical angles range from 3° to 32° and
basically follow a normal distribution. Most cracks have a helical angle in the scope from
10° to 25°.
Figure S5. Intact spindle-knot shell appears when a soft fiber is used as the core.
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Figure S6. Helical cracks on spindle-knots of different materials. Some typical brittle
ceramic materials such as: (a) SiO2; (b) Al2O3; (c) Fe2O3 and (d) FeBiO3 are used as the
shell materials. The results verify that the proposed helical fracture mode relies mainly on
the different coefficients of expansion of the shell and core materials, rather than the
specific kinds of materials. It means that the fracture technique is general and effective for
a very broad variety of brittle materials. Scale bars, 20 m.
References
S1. Shackelford, J. F. Alexander, W. CRC Materials Science and Engineering Handbook
762–825 (CRC Press, Boca Raton, London, New York, Washington, D. C. 2001).
S2. Lima, M. M., Monteiro, R. Characterisation and thermal behaviour of a borosilicate
glass. Thermo chimica Acta, 373, 69–74 (2001).
S3. Shibata, T., Irie, H., Hashimoto, K. Enhancement of photoinduced highly hydrophilic
conversion on TiO2 thin films by introducing tensile stress. J. Phys. Chem. B, 107,
10696–10698 (2003).
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a
SiO2 Al2O3
Fe2O3 FeBiO3
b
dc
Instructions for Movies:
Movie S1: 2D sectional X-ray computerized tomography. The movie shows a spiral
cracking notch runs continuously around the column core when the spindle-knot is
scanned from one end to another.
Movie S2: 3D tomography of a spring-like helical crack.
The movies were derived from MicroXCT-200 (Xradia Inc. Concord).
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