Elsevier

Mechanics of Materials

Volume 148, September 2020, 103516
Mechanics of Materials

Research paper
A chemo-mechanical fracture model for the welding interface of vitrimers

https://doi.org/10.1016/j.mechmat.2020.103516Get rights and content

Highlights

  • Chemo-mechanical fracture model accounting for the vitrimer welding interface.

  • Network structure evolution by combining polymer diffusion with chemical reaction.

  • Fracture toughness obtaining by integrating dissipated energy in the cohesive region.

  • Exponential shape function representing stretching profile of polymer chain network.

Abstract

The welding of thermosetting polymers is a longstanding challenge in polymer science and engineering. Recently, developed dynamic covalent polymers (also known as vitrimers) provide a promising strategy for achieving interface welding. An understanding of the fundamental physical mechanisms underlying interfacial welding and fracture behavior is critically required to thoroughly explore the full potential of this technique. To this end, in this paper, we develop a chemo-mechanical fracture model to account for the toughness of the welding interface in vitrimers. The evolution of the interfacial vitrimer network microstructure in the welding is modeled by using a bamboo joint-like structural model. Based on the evolution of the network structure, the fracture toughness of the welding interface is formulated by integrating the dissipated strain energy in the cohesive region ahead of the interfacial crack, in which a shape function with an exponential form is proposed to describe the strain profile of the vitrimer networks. Our theoretical model also correlates interfacial fracture toughness with welding temperature and time. An optimal range of welding temperature to time is identified to achieve a higher toughness of the welding interface. We show that a larger cohesive region induced by enhancing the vitrimer network structure results in an elevated interfacial fracture energy. The results predicted by our model are in good agreement with the relevant experimental measurements. This work might help to decipher the toughening mechanisms 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].

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