Research paperA chemo-mechanical fracture model for the welding interface of vitrimers
Introduction
Thermosetting polymers have been widely used as building blocks for structural components in the aircraft and automotive industries due to their excellent mechanical properties, thermal stability and chemical resistance. However, permanently crosslinked networks are difficult to reprocess, reshape and weld once they are synthesized; the ability to weld them is needed and is also a longstanding challenge in polymer science. To overcome the challenge, Leibler and coworkers (Montarnal et al., 2011; Capelot et al., 2012) introduced thermoactivated transesterification exchange reactions into epoxy-acid and epoxy-anhydride thermosetting polymers to achieve the welding and assembly of these two dynamic covalent polymers (also called vitrimers) by rearranging their topology while maintaining their network integrity and insolubility. More recently, in the interest of developing economical and environmentally friendly approaches, solvent-assisted bond exchange reactions have been exploited by Shi et al. (2016) and Yu et al., 2016a for the efficient welding of epoxy vitrimers. Further exploration of the rich potential of such a welding strategy requires fundamental understanding of the interfacial deformation and failure mechanisms. Uncovering the structure-property relationship is of particular significance for optimizing the mechanical performance of welding interfaces. To this end, herein, we develop a multilevel theoretical model to quantitatively study such a relationship.
As a classical topic in the fields of solid mechanics and polymer physics, considerable efforts have been dedicated to developing theoretical models to account for the fracture behavior of polymer interfaces over the past decades. For example, Hui and coworkers (Xu et al., 1991; Hui et al., 1992; Brown et al., 1994) and De Gennes and coworkers (Raphael and De Gennes, 1992; Ji and De Gennes, 1993) first proposed the fracture model for the interface of viscoelastic polymers by considering the chain pullout mechanism and stress fields in the interfacial cohesive zone. In addition, Chaudhury (1999) developed a rate-dependent fracture model based on the stress relaxation kinetics and density of bridged polymer chains. Recently, Yu et al., 2016b yielded a theoretical model capturing the chain density evolution across the welding interface and predicted the fracture energy of the heat-induced self-welding interface of adaptable network polymers by directly adopting the Chaudhury fracture model (Chaudhury, 1999). Yu et al. (2018) formulated a polymer-network-based model to characterize the constitutive behavior and interfacial self-healing behavior of polymer networks crosslinked by dynamic bonds. Diffusion-reaction theory was used in the model to simulate the diffusion of polymer chains across the healing interface. Although these works enable the prediction of the fracture behavior of a traditional polymer interface and the self-healing interface of an adaptive network polymer, how to correlate the fracture toughness with the polymer network structure and failure mode of the welding interface still remains elusive. How the network structure and fracture toughness of the welding interface are affected by the welding conditions, such as the welding time and temperature, also needs to be further explored.
Herein, we consider an ethylene glycol (EG)-assisted welding interface of fatty acid-epoxy vitrimers by using a vitrimer glue, i.e., a mixed solution consisting of a ring-opened epoxy and fatty acid-EG polymer (Shi et al., 2016; Yu et al., 2016a). The process of a typical welding experiment is shown in Fig. 1a. At high temperature, the vitrimer glue is polymerized via a transesterification exchange reaction. After evaporating the EG, the interfacial welding of the vitrimers is achieved, and the polymerized chains penetrate into the bulk vitrimers, forming a coupling crosslinked interface (Fig. 1b). In this paper, we establish a chemo-mechanical fracture model for a solvent-assisted welding interface that can capture the evolution of the interfacial vitrimer network microstructure and the interfacial fracture. The evolution of the crosslinked network microstructure is modeled by combining the diffusion of the polymer solutions with their transesterification reaction in the welding process. A microstructure-based fracture model of the welding interface is formulated by integrating the dissipated strain energy in the deformation and breaking of vitrimer networks within the cohesive region ahead of the interface crack (Fig. 1c), in which an exponential function is proposed to describe the elongation deformation of the vitrimer chain networks. Using the theoretical model, we study the effects of the welding temperature and time on the toughness of an EG-assisted welding interface with a fatty acid-epoxy vitrimer. We also predict the effects of the length and profile of the cohesive region on the interfacial fracture behavior. The theoretical predictions are consistent with the relevant experimental results. The theoretical model might aid in deciphering the welding and fracture behavior of vitrimers from the perspective of the interfacial network microstructure.
Section snippets
Theoretical modeling
In this section, we establish a chemo-mechanical coupling model of the welding interface that describes the interfacial microstructure evolution and fracture formation.
Results and discussion
In this section, we study the fracture behavior of the EG-assisted welding interface for the vitrimers with the aid of Eqs. (18) and (30). We discuss the effects of catalyst concentration, welding time and temperature, and the length and profile of the cohesive region on the fracture toughness of the welding interface. We also compare the theoretical predictions of our model with the relevant experimental results (Shi et al., 2016).
Conclusions
In this work, we develop a chemo-mechanical fracture model to account for the toughness of the welding interface in vitrimers. We formulate the theoretical equation of the welding interface that correlates the interfacial vitrimer network structure with the initial polymer concentration and the welding temperature and time. Considering the energy dissipation mechanisms of the cohesive region ahead of interfacial crack, we derive an expression for the interfacial fracture toughness as a function
Declaration of competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
CRediT author statement
Qinghua Meng: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data Curation, Writing-Original Draft, Writing-Review & Editing, Visualization, Project administration, Funding acquisition.
Acknowledgements
This work was supported by the National Natural Science Foundation of China [grant numbers 11902242]; and the Natural Science Basic Research Plan in Shaanxi Province of China [grant number 2019JQ-023].
References (53)
- et al.
A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
J. Mech. Phys. Solids
(1993) - et al.
A theory of network alteration for the Mullins effect
J. Mech. Phys. Solids
(2002) - et al.
A multiscale crack-bridging model of cellulose nanopaper
J. Mech. Phys. Solids
(2017) - et al.
Effects of nanofiber orientations on the fracture toughness of cellulose nanopaper
Eng. Fract. Mech.
(2018) - et al.
On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers
J. Mech. Phys. Solids
(1993) - et al.
Mechanics of electrophoresis-induced reversible hydrogel adhesion
J. Mech. Phys. Solids
(2019) - et al.
A micromechanical model of crack growth along polymer interfaces
Mech. Mater.
(1991) - et al.
Interfacial welding of dynamic covalent network polymers
J. Mech. Phys. Solids
(2016) - et al.
Mechanics of self-healing polymer networks crosslinked by dynamic bonds
J. Mech. Phys. Solids
(2018) - et al.
Dissolution of covalent adaptable network polymers in organic solvent
J. Mech. Phys. Solids
(2017)
A theory for large deformation and damage of interpenetrating polymer networks
J. Mech. Phys. Solids
Constitutive models of rubber elasticity: a review
Rubber Chem. Technol.
The adhesion between polymers
Annu. Rev. Mater. Sci.
A molecular interpretation of the toughness of glassy polymers
Macromolecules
Effects of chain pull-out on adhesion of elastomers
Macromolecules
The adhesion of polymers: relations between properties of polymer chains and interface toughness
J. Adhes.
Interplay between intermolecular interactions and chain pullout in the adhesion of elastomer
Macromolecules
Metal-catalyzed transesterification for healing and assembling of thermosets
J. Am. Chem. Soc.
Rate-dependent fracture at adhesive interface
J. Phys. Chem. B
The Mathematics of Diffusion
Simple views on adhesion and fracture
Can. J. Phys.
Vitrimers: permanent organic networks with glass-like fluidity
Chem. Sci.
Network structure and the elastic properties of vulcanized rubber
Chem. Rev.
Statistical mechanics of cross-linked polymer networks I
Rubberlike elasticity. J. Chem. Phys.
Reaction-rate theory: fifty years after Kramers. Rev. Mod
Phys
A fracture model for a weak interface in a viscoelastic material (small scale yielding analysis)
J. Appl. Phys.
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