skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Nonsteady fracture of transient networks: The case of vitrimer
We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number W 0 that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can “program” a specimen’s crack extension dynamics by tuning the loading history.  more » « less
Award ID(s):
1761918
PAR ID:
10295771
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
118
Issue:
29
ISSN:
0027-8424
Page Range / eLocation ID:
e2105974118
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. CO2-induced dynamic covalent polymer networks (DCPNs) have received significant attention due to their capability of sequestering CO2 to remodel material properties. Despite the promising success of carbon sequestration in the polymer, the mechanistic understanding of the CO2-induced polymer network is still at the very beginning. A theoretical framework to understand the CO2-induced formation of bulk networks and healing of interfacial cracks of DCPNs has not been established. Here, we build up a polymer-network-based theoretical model system that can mechanistically explain the constitutive behavior and crack healing of CO2-induced DCPNs. We assume that the DCPN consists of interpenetrating networks crosslinked by CO2-induced dynamic bonds which follow a force-dependent chemical kinetics. During the healing process, we consider the CO2 molecules diffuse from the surface to the crack interface to reform the polymer network for interfacial repair. Our theoretical framework can calculate the stress-strain behaviors of both original and healed DCPNs. We demonstrate that the theoretically calculated stress-strain responses of the original DCPNs across various CO2 concentrations, as well as those of healed DCPNs under different CO2 concentrations, consistently match the documented experimental results. We expect our model to become an invaluable tool for innovating, designing, understanding, and optimizing CO2-induced DCPNs. 
    more » « less
  2. null (Ed.)
    We investigate the rate-dependent fracture of vitrimers by conducting a tear test. Based on the relationship between the fracture energy and the thickness of vitrimer films, we, for the first time, obtain the intrinsic fracture energy and bulk dissipation of vitrimers during crack extension. The intrinsic fracture energy strongly depends on tear speed, and such dependence can be well explained by Eyring theory. In contrast, the bulk dissipation only weakly depends on tear speed, which is drastically different from observations on traditional viscoelastic polymers. We ascribe such a weak rate-dependence to the strong force-sensitivity of the exchange reaction of the dynamic covalent bond in the vitrimer. 
    more » « less
  3. Crack propagation in viscoelastic solids under cyclic loading is a fundamental problem underlying the fatigue fracture of elastomers. We present a continuum theory to determine the crack extension per loading cycle for various loading amplitudes, loading frequencies and viscoelastic properties. This is achieved by examining the energy dissipated through viscous effects and the energy available for driving crack growth. In particular, energy dissipation is controlled by an interplay of three time scales: the material relaxation time, the timescale associated with crack propagation (i.e., crack speed) and the loading frequency. By tracking the stress history of material points around the crack tip under concurrent crack propagation and cyclic loading, we derive an integral equation governing crack speed within a loading cycle. Comparisons between numerical solutions of our theory and finite element simulations demonstrate that our theory predicts the influence of material parameters and loading conditions on fatigue fracture at a much lower computational cost. 
    more » « less
  4. Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel. 
    more » « less
  5. null (Ed.)
    Abstract In the standard fracture test specimens, the crack-parallel normal stress is negligible. However, its effect can be strong, as revealed by a new type of experiment, briefly named the gap test. It consists of a simple modification of the standard three-point-bend test whose main idea is to use plastic pads with a near-perfect yield plateau to generate a constant crack-parallel compression and install the end supports with a gap that closes only when the pads yield. This way, the test beam transits from one statically determinate loading configuration to another, making evaluation unambiguous. For concrete, the gap test showed that moderate crack-parallel compressive stress can increase up to 1.8 times the Mode I (opening) fracture energy of concrete, and reduce it to almost zero on approach to the compressive stress limit. To model it, the fracture process zone must be characterized tensorially. We use computer simulations with crack-band microplane model, considering both in-plane and out-of-plane crack-parallel stresses for plain and fiber-reinforced concretes, and anisotropic shale. The results have broad implications for all quasibrittle materials, including shale, fiber composites, coarse ceramics, sea ice, foams, and fone. Except for negligible crack-parallel stress, the line crack models are shown to be inapplicable. Nevertheless, as an approximation ignoring stress tensor history, the crack-parallel stress effect may be introduced parametrically, by a formula. Finally we show that the standard tensorial strength models such as Drucker–Prager cannot reproduce these effects realistically. 
    more » « less