0
Research Papers

A Computational Model for Surface Welding in Covalent Adaptable Networks Using Finite-Element Analysis

[+] Author and Article Information
Kai Yu

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Qian Shi, Tiejun Wang

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace Science,
Xian Jiaotong University,
Xian 710049, China

Martin L. Dunn

SUTD Digital Manufacturing
and Design (DManD) Centre,
Singapore University of Technology
and Design,
Singapore 138682, Singapore

H. Jerry Qi

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: qih@me.gatech.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 31, 2016; final manuscript received May 17, 2016; published online June 22, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(9), 091002 (Jun 22, 2016) (11 pages) Paper No: JAM-16-1163; doi: 10.1115/1.4033682 History: Received March 31, 2016; Revised May 17, 2016

Covalent adaptable network (CAN) polymers can rearrange their macromolecular network by bond exchange reactions (BERs), where an active unit attaches to and then replaces a unit in an existing bond and forms a new bond. When such macromolecular events occur on the interface, they can contribute to surface welding, self-healing, and recycling of thermosetting polymers. In this paper, we study the interfacial welding and failure of CANs involving both interfacial normal and shear stresses. To do this, we incorporate our recently developed multiscale model for surface welding of CANs with a cohesive zone modeling approach in finite-element method (FEM) simulation. The developed FEM paradigm involves a multiscale model predicting the interfacial chain density and fracture energy, which are transferred to a cohesive zone model to establish the surface traction-separation law. The simulations show good agreement with experimental results on the modulus and strength of welded samples. They also provide understanding of the interactions between surface welding and material malleability in determining the final mechanical properties of polymer structures. The developed FEM model can be applied to study other complex welding problems, such as polymer reprocessing with nonregular particle size and shape.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Billmeyer, F. W. , 1984, Textbook of Polymer Science, 3rd ed., Wiley, New York.
Ferry, J. D. , 1980, Viscoelastic Properties of Polymers, Wiley, New York.
Pickering, S. J. , 2006, “ Recycling Technologies for Thermoset Composite Materials—Current Status,” Composites, Part A, 37(8), pp. 1206–1215. [CrossRef]
Scott, T. , Schneider, A. , Cook, W. , and Bowman, C. , 2005, “ Photoinduced Plasticity in Cross-Linked Polymers,” Science, 308(5728), pp. 1615–1617. [CrossRef] [PubMed]
Amamoto, Y. , Kamada, J. , Otsuka, H. , Takahara, A. , and Matyjaszewski, K. , 2011, “ Repeatable Photoinduced Self-Healing of Covalently Cross-Linked Polymers Through Reshuffling of Trithiocarbonate Units,” Angew. Chem., 123(7), pp. 1698–1701. [CrossRef]
Canadell, J. , Goossens, H. , and Klumperman, B. , 2011, “ Self-Healing Materials Based on Disulfide Links,” Macromolecules, 44(8), pp. 2536–2541. [CrossRef]
Capelot, M. , Montarnal, D. , Tournilhac, F. , and Leibler, L. , 2012, “ Metal-Catalyzed Transesterification for Healing and Assembling of Thermosets,” J. Am. Chem. Soc., 134(18), pp. 7664–7667. [CrossRef] [PubMed]
Deng, G. H. , Tang, C. M. , Li, F. Y. , Jiang, H. F. , and Chen, Y. M. , 2010, “ Covalent Cross-Linked Polymer Gels With Reversible Sol-Gel Transition and Self-Healing Properties,” Macromolecules, 43(3), pp. 1191–1194. [CrossRef]
Zhang, Y. , Broekhuis, A. A. , and Picchioni, F. , 2009, “ Thermally Self-Healing Polymeric Materials: The Next Step to Recycling Thermoset Polymers?,” Macromolecules, 42(6), pp. 1906–1912. [CrossRef]
Leibler, L. , Rubinstein, M. , and Colby, R. H. , 1991, “ Dynamics of Reversible Networks,” Macromolecules, 24(16), pp. 4701–4707. [CrossRef]
Stukalin, E. B. , Cai, L. H. , Kumar, N. A. , Leibler, L. , and Rubinstein, M. , 2013, “ Self-Healing of Unentangled Polymer Networks With Reversible Bonds,” Macromolecules, 46(18), pp. 7525–7541. [CrossRef]
Smallenburg, F. , Leibler, L. , and Sciortino, F. , 2013, “ Patchy Particle Model for Vitrimers,” Phys. Rev. Lett., 111(18), p. 188002. [CrossRef] [PubMed]
Ma, J. , Mu, X. M. , Bowman, C. N. , Sun, Y. Y. , Dunn, M. L. , Qi, H. J. , and Fang, D. N. , 2014, “ A Photoviscoplastic Model for Photoactivated Covalent Adaptive Networks,” J. Mech. Phys. Solids, 70, pp. 84–103. [CrossRef]
Long, R. , Qi, H. J. , and Dunn, M. L. , 2013, “ Modeling the Mechanics of Covalently-Adaptable Polymer Networks With Temperature-Dependent Bond Exchange Reactions,” Soft Matter, 9(15), pp. 4083–4096. [CrossRef]
Yang, H. , Yu, K. , Mu, X. M. , Shi, X. H. , Wei, Y. J. , Guo, Y. F. , and Qi, H. J. , 2015, “ A Molecular Dynamics Study of Bond Exchange Reactions in Covalent Adaptable Networks,” Soft Matter, 11(31), pp. 6305–6317. [CrossRef] [PubMed]
Stukalin, E. B. , Cai, L.-H. , Kumar, N. A. , Leibler, L. , and Rubinstein, M. , 2013, “ Self-Healing of Unentangled Polymer Networks With Reversible Bonds,” Macromolecules, 46(18), pp. 7525–7541. [CrossRef]
Yang, H. , Yu, K. , Wei, Y. , Guo, Y. , and Qi, H. J. , 2016, “ Molecular Dynamics Studying on Welding Behavior in Thermoset Polymers Due to Bond Exchange Reactions,” RSC Adv., 6(27), pp. 22476–22487. [CrossRef]
Yu, K. , Shi, Q. , Li, H. , Jabour, J. , Yang, H. , Dunn, M. L. , Wang, T. , and Qi, H. J. , 2016, “ Interfacial Welding of Dynamic Covalent Network Polymers,” J. Mech. Phys. Solids, 94, pp. 1–17. [CrossRef]
Yu, K. , Taynton, P. , Zhang, W. , Dunn, M. L. , and Qi, H. J. , 2014, “ Reprocessing and Recycling of Thermosetting Polymers Based on Bond Exchange Reactions,” RSC Adv., 4(20), pp. 10108–10117. [CrossRef]
Mei, H. X. , Gowrishankar, S. , Liechti, K. M. , and Huang, R. , 2010, “ Initiation and Propagation of Interfacial Delamination in Integrated Thin-Film Structures,” 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Las Vegas, NV, June 2–5, pp. 1–8.
Hertzberg, R. W. , 1983, Deformation and Fracture Mechanics of Engineering Materials, 2nd ed., Wiley, New York.
Ungsuwarungsri, T. , and Knauss, W. G. , 1987, “ The Role of Damage-Softened Material Behavior in the Fracture of Composites and Adhesives,” Int. J. Fract., 35(3), pp. 221–241. [CrossRef]
Tvergaard, V. , and Hutchinson, J. W. , 1992, “ The Relation Between Crack-Growth Resistance and Fracture Process Parameters in Elastic Plastic Solids,” J. Mech. Phys. Solids, 40(6), pp. 1377–1397. [CrossRef]
Schellekens, J. C. J. , and Deborst, R. , 1993, “ On the Numerical-Integration of Interface Elements,” Int. J. Numer. Methods Eng., 36(1), pp. 43–66. [CrossRef]
Reedy, E. D. , Mello, F. J. , and Guess, T. R. , 1997, “ Modeling the Initiation and Growth of Delaminations in Composite Structures,” J. Compos. Mater., 31(8), pp. 812–831. [CrossRef]
Pietruszczak, S. , and Mroz, Z. , 1981, “ Finite-Element Analysis of Deformation of Strain-Softening Materials,” Int. J. Numer. Methods Eng., 17(3), pp. 327–334. [CrossRef]
Camacho, G. T. , and Ortiz, M. , 1996, “ Computational Modelling of Impact Damage in Brittle Materials,” Int. J. Solids Struct., 33(20–22), pp. 2899–2938. [CrossRef]
Montarnal, D. , Capelot, M. , Tournilhac, F. , and Leibler, L. , 2011, “ Silica-Like Malleable Materials From Permanent Organic Networks,” Science, 334(6058), pp. 965–968. [CrossRef] [PubMed]
Yu, K. , Taynton, P. , Zhang, W. , Dunn, M. L. , and Qi, H. J. , 2014, “ Influence of Stoichiometry on the Glass Transition and Bond Exchange Reactions in Epoxy Thermoset Polymers,” RSC Adv., 4(89), pp. 48682–48690. [CrossRef]
Persson, B. N. J. , 2002, “ Adhesion Between an Elastic Body and a Randomly Rough Hard Surface,” Eur. Phys. J. E, 8(4), pp. 385–401. [CrossRef]
Persson, B. N. J. , Albohr, O. , Creton, C. , and Peveri, V. , 2004, “ Contact Area Between a Viscoelastic Solid and a Hard, Randomly Rough, Substrate,” J. Chem. Phys., 120(18), pp. 8779–8793. [CrossRef] [PubMed]
Needleman, A. , 1987, “ A Continuum Model for Void Nucleation by Inclusion Debonding,” ASME J. Appl. Mech., 54(3), pp. 525–531. [CrossRef]
Needleman, A. , 1990, “ An Analysis of Tensile Decohesion Along an Interface,” J. Mech. Phys. Solids, 38(3), pp. 289–324. [CrossRef]
Hillerborg, A. , Modeer, M. , and Petersson, P. E. , 1976, “ Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cem. Concr. Res., 6(6), pp. 773–782. [CrossRef]
Ouyang, Z. Y. , and Li, G. Q. , 2009, “ Local Damage Evolution of Double Cantilever Beam Specimens During Crack Initiation Process: A Natural Boundary Condition Based Method,” ASME J. Appl. Mech., 76(5), p. 051003. [CrossRef]
Ouyang, Z. Y. , and Li, G. Q. , 2009, “ Nonlinear Interface Shear Fracture of End Notched Flexure Specimens,” Int. J. Solids Struct., 46(13), pp. 2659–2668. [CrossRef]
Ji, G. F. , Ouyang, Z. Y. , and Li, G. Q. , 2012, “ On the Interfacial Constitutive Laws of Mixed Mode Fracture With Various Adhesive Thicknesses,” Mech. Mater., 47, pp. 24–32. [CrossRef]
Dugdale, D. S. , 1960, “ Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids, 8(2), pp. 100–104. [CrossRef]
Xu, X. P. , and Needleman, A. , 1994, “ Numerical Simulations of Fast Crack-Growth in Brittle Solids,” J. Mech. Phys. Solids, 42(9), pp. 1397–1434. [CrossRef]
Barenblatt, G. I. , 1959, “ The Formation of Equilibrium Cracks During Brittle Fracture. General Ideas and Hypothesis. Axisymmetrical Cracks,” J. Appl. Math. Mech., 23(3), pp. 622–636. [CrossRef]
Mi, Y. , Crisfield, M. A. , Davies, G. A. O. , and Hellweg, H. B. , 1998, “ Progressive Delamination Using Interface Elements,” J. Compos. Mater., 32(14), pp. 1246–1272. [CrossRef]
Aoki, Y. , and Suemasu, H. , 2003, “ Damage Analysis in Composite Laminates by Using an Interface Element,” Adv. Compos. Mater., 12(1), pp. 13–21. [CrossRef]
Alfano, G. , and Crisfield, M. A. , 2001, “ Finite Element Interface Models for the Delamination Analysis of Laminated Composites: Mechanical and Computational Issues,” Int. J. Numer. Methods Eng., 50(7), pp. 1701–1736. [CrossRef]
Camanho, P. P. , Davila, C. G. , and de Moura, M. F. , 2003, “ Numerical Simulation of Mixed-Mode Progressive Crack in Composite Materials,” J. Compos. Mater., 37(16), pp. 1415–1418. [CrossRef]
Xie, D. , and Waas, A. M. , 2006, “ Discrete Cohesive Zone Model for Mixed-Mode Fracture Using Finite Element Analysis,” Eng. Fract. Mech., 73(13), pp. 1783–1796. [CrossRef]
Turon, A. , Davika, C. G. , Camanho, P. P. , and Costa, J. , 2005, “ An Engineering Solution for Using Coarse Meshes in the Simulation of Delamination With Cohesive Zone Model,” NASA Langley Research Center; Hampton, VA, Report No. NASA/TM-2005-213547.
Song, S. J. , and Waas, A. M. , 1995, “ Energy-Based Mechanical Model for Mixed-Mode Failure of Laminated Composites,” AIAA J., 33(4), pp. 739–745. [CrossRef]
Song, S. J. , and Waas, A. M. , 1994, “ Mode-I Failure of Laminated Polymeric Composites,” Eng. Fract. Mech., 49(1), pp. 17–27. [CrossRef]
Song, S. J. , and Waas, A. M. , 1994, “ A Spring Foundation Model for Mode-I Failure of Laminated Composites Based on an Energy Criterion,” ASME J. Eng. Mater. Technol., 116(4), pp. 512–516. [CrossRef]
Shahwan, K. W. , and Waas, A. M. , 1997, “ Non-Self-Similar Decohesion Along a Finite Interface of Unilaterally Constrained Delaminations,” Proc. R. Soc. A, 453(1958), pp. 515–550. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

A schematic of the developed multiple length scale constitutive model for the surface welding effect of CANs. (a) ABER occurs on a macromolecular chain, (b) this event can occur within a network and at the interface where macromolecular chains cross the interface, (c) the welding occurs when the two surfaces are in contact, and (d) two samples are welded together[4].

Grahic Jump Location
Fig. 2

Mechanical properties of welded samples. (a) Experimental procedure to weld two pieces of epoxy sample. (b) Typical stress–strain curves of the thermosetting samples after being welded for different time periods. Inset view shows the appearance of the welded sample during experiment. The welding temperature is 180 °C, and the applied pressure is 40 kPa.

Grahic Jump Location
Fig. 3

(a) Experimental procedure to welded three epoxy cylinders and (b) typical force–displacement curves as a function of welding time. The welding temperature is 180 °C.

Grahic Jump Location
Fig. 4

Schematic view of the linear traction separation law

Grahic Jump Location
Fig. 5

Schematic view of the DCZM

Grahic Jump Location
Fig. 6

FEM simulations on the surface welding of flat interface. (a) Comparison of experimental and simulated stress–strain curves as a function of welding time. (b) The crack propagation in both simulation (top figure) and experiment (bottom figure). States ① and ② correspond to the data point ① and ② in (a). (c) Interfacial normal stress and shear stress distribution at different states of crack propagation. The black line indicates the state right before the break of the first contact pair. A positive normal stress indicates stretching. (d) Summary of the strength of a welded sample as a function of welding time and temperature. For (a)–(c), the welding temperature is 180 °C, and the welding pressure is 40 kPa. For (d), the welding temperature is 180 °C or 160 °C, and the welding pressure is 40 kPa.

Grahic Jump Location
Fig. 7

Analysis of the mechanical properties of welded polymer structure. (a) Snap shots during the simulation and experiment. (b) Interfacial normal and shear stress distribution before and after unloading step. The welding time is 60 min. (c) Interfacial normal and shear stress distribution after unloading as a function of welding time. (d) Summary of maximum stretching force and shape fixity as a function of welding time in both experiments and simulation.

Grahic Jump Location
Fig. 8

(a) FEM simulations of the welding enabled polymer reprocessing. The welding pressure is 90 kPa, and the welding time is 60 min. (b) The porosity and Mises stress distribution in the unloaded structure with different welding time and pressure applied.

Grahic Jump Location
Fig. 9

Normalized stretch ability of reprocessed sample in both experiment and simulation

Grahic Jump Location
Fig. 10

(a) Normalized stretch ability as a function of reprocessing pressure and time. (b) Porosity of reprocessed sample and the maximum interfacial residual stress as a function of reprocessing pressure and time. The maximum residual stress is located on the end points of interface.

Grahic Jump Location
Fig. 11

The simulated stress–strain curves of welded CANs with different sizes of imperfection

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In