On the theory of mechanically induced chemiluminescence in multiple network elastomers

Abstract

Mechanophores, force-sensitive molecules, can be covalently linked into polymer networks to reveal the damage properties of polymeric materials under deformation. Recent works have introduced bis-adamantyl dioxetane (Ad) into multiple network elastomers. These mechanoluminescent cross-linking molecules can emit luminescence as they break. The experimental results can directly visualize the damage behaviors of multiple network elastomers and reveal the damage mechanism of these materials during deformation. In this work, we develop a constitutive model to describe the complex mechanical behaviors of multiple network elastomers based on observations from mechano-chemiluminescent experiments. The free energy density consists of the contributions from the filler network, the matrix network, and the entangled network. A new type of single-chain model is developed for the filler network, while the classic eight-chain mapping is adopted for the micro–macro transition. The chains in the filler network are progressively damaged under deformation to explain the stress-softening behaviors observed in the small and median strain regions of multiple network elastomers. The entangled network is rooted in individual fragments of the damaged filler network, which can be further damaged in the large deformation regime. The model can comprehensively capture the complex mechanical responses of multiple network elastomers with different values of the prestretching ratio of the filler network, including linear response, necking instability, and re-hardening phenomena in quadruple networks. By assuming that the luminescence intensity of the materials is proportional to the total percentage of damage from both filler and entangled networks, we quantify the relationship between damage and the luminescence intensity from mechanophores, which is further validated in quantifying luminescence intensity against different sets of experimental data on the uniaxial tension of multiple network elastomers. The model is further implemented for finite element analysis, demonstrating the ability to visualize and characterize the damage behaviors around a crack.