Quantifying Rate- and Temperature-Dependent Molecular Damage in Elastomer Fracture

Elastomers are highly valued soft materials finding many applications in the engineering and biomedical fields for their ability to stretch reversibly to large deformations. Yet their maximum extensibility is limited by the occurrence of fracture, which is currently still poorly understood. Because of a lack of experimental evidence, current physical models of elastomer fracture describe the rate and temperature dependence of the fracture energy as being solely due to viscoelastic friction, with chemical bond scission at the crack tip assumed to remain constant. Here, by coupling new fluorogenic mechanochemistry with quantitative confocal microscopy mapping, we are able to quantitatively detect, with high spatial resolution and sensitivity, the scission of covalent bonds as ordinary elastomers fracture at different strain rates and temperatures. Our measurements reveal that, in simple networks, bond scission, far from being restricted to a constant level near the crack plane, can both be delocalized over up to hundreds of micrometers and increase by a factor of 100, depending on the temperature and stretch rate. These observations, permitted by the high fluorescence and stability of the mechanophore, point to an intricate coupling between strain-rate-dependent viscous dissipation and strain-dependent irreversible network scission. These findings paint an entirely novel picture of fracture in soft materials, where energy dissipated by covalent bond scission accounts for a much larger fraction of the total fracture energy than previously believed. Our results pioneer the sensitive, quantitative, and spatially resolved detection of bond scission to assess material damage in a variety of soft materials and their applications.

Popular Summary

When rubbery materials (elastomers) are stretched, they typically extend elastically and spring back to their original shape. However, if stretched too far, they break into two pieces by the formation and propagation of a crack. Understanding why increasing the temperature or decreasing the rate at which the elastomer is deformed leads to a significant decrease of the stretch at which it breaks has been a challenge for the last 50 years, partly because the picture of molecular bond breakage was missing. To address this missing element, we use novel force-sensitive fluorescent molecules incorporated in an elastomer network to visualize, quantify, and map the breakage of chemical bonds accompanying macroscopic fracture.

To our surprise, we find that the number of broken bonds near a crack is very strongly and almost linearly correlated to the level of molecular friction in the material. Increasing the temperature sharply decreases the number of broken bonds, showing that the mechanical coupling between friction and bond scission controls macroscopic fracture and not the intrinsic strength of the molecular bond.

These results will likely stimulate new physics-based molecular models of elastomer fracture and guide the design of better fracture-resistant elastomers.

Figure 1

Macroscopic fracture propagation in elastomers. (a) Image of a notched sample during a fracture test. The scale bar is 1 mm. Inset: Geometry of the fracture test, with a notched sample in uniaxial extension submitted with a constant stretch rate $\dot{\lambda }$ to an increasing stress $\sigma$ until a crack propagates at speed $v_{\mathrm{crack}}$. (b) Stress-strain curves for notched PMA-DA-0.4 elastomer samples at temperature $T=25$, 40, 60, and $80°\mathrm{C}$ (from light blue to purple). (c) Variation of the fracture energy ${\mathrm{\Gamma }}_c$ as a function of rescaled crack velocity $a_T.v_{\mathrm{crack}}$. Squares correspond to samples fractured at different temperatures and constant stretch rate $\dot{\lambda }=3\times {10}^{-3}{\mathrm{s}}^{-1}$ and circles to samples fractured at $25°\mathrm{C}$ and varying stretch rates $\dot{\lambda }=[3\times {10}^{-4};3\times {10}^{-3};3\times {10}^{-2}]{\mathrm{s}}^{-1}$.

Figure 2

Strategy for mechanophore incorporation and quantification of the activation. (a) Incorporation of mechanophores at cross-link points in the elastomer network. (b) Mechanophore activation reports for strand scission. (i) Nonfluorescent form of the DA mechanophore, connected to a strand under tension. (ii) Irreversible scission of the mechanophore (retro DA reaction), leading to the release of a fluorescent anthracene moiety, reporting for strand breakage (orange). Dashed bonds show connectivity to the network.

Figure 3

Postmortem damage quantification through confocal imaging. (a) Postmortem image of fluorescence activation in a poly(methyl acrylate) sample (PMA-DA-0.4, Table 1) measured by confocal fluorescence microscopy. Samples are fractured at $\dot{\lambda }=3\times {10}^{-3}{\mathrm{s}}^{-1}$, respectively, in conditions of (i) low and (ii) high viscoelasticity, at (i) $T=80°\mathrm{C}$ and (ii) $T=25°\mathrm{C}$. Pixel size is $1.63\mu \mathrm{m}$. The scale bar is $100\mu \mathrm{m}$. The direction of crack propagation is along the $x$ direction (vertical). (b) Schematic of the confocal imaging plane (in red), perpendicular to the crack surface (shown in orange). The direction of crack propagation is along the $x$ direction, the stretch direction along $y$, and sample thickness along $z$. (c) Average spatial damage profile $\varphi$ for conditions (i) and (ii), with damage $\varphi$ defined as the fraction of broken strands in the material, equal to the fraction of activated mechanophores. The inset shows the profiles in lin-log scale, with $L_{(\mathrm{ii})}$ characterizing the spatial extension of damage for condition (ii).

Figure 4

Coupling of damage with viscoelastic dissipation in the material. (a) Fracture energy ${\mathrm{\Gamma }}_c$ as a function of rescaled crack velocity $a_T.v_{\mathrm{crack}}$, for the PMA-DA-0.4 (blue squares and circles) and PEA-DA-0.5 samples (black stars). The reference temperature is taken at $25°\mathrm{C}$ for the PMA sample (see Fig. S7 [24]). At a low rescaled crack speed, ${\mathrm{\Gamma }}_c$ becomes less dependent on crack speed for PEA. The blue square corresponds to samples fractured at stretch rate $\dot{\lambda }=3\times {10}^{-3}{\mathrm{s}}^{-1}$ and different temperature and blue circles to samples fractured at $25°\mathrm{C}$ and stretch rates $\dot{\lambda }=[3\times {10}^{-4};3\times {10}^{-3};3\times {10}^{-2}]{\mathrm{s}}^{-1}$. (b) Normalized areal density of broken strands as a function of the rescaled crack velocity. The horizontal line corresponds to the Lake-Thomas prediction $\mathrm{\Sigma }/{\mathrm{\Sigma }}_{\mathrm{LT}}=1$. (c) Damage length $L$ as a function of the rescaled crack velocity. Error bars in (b) and (c) show the standard deviation based on four local confocal measurements on each fractured sample.

Figure 5

Effect of molecular structure and contribution of bond scission to the fracture energy. (a) Fracture energy as a function of the rescaled velocity for two PMA samples with distinct cross-link densities (see Table 1). Dashed lines show the power-law fit. (b) Absolute number of cleaved strands per unit area as a function of the rescaled velocities for the two samples. Dashed lines show power-law fits. (c) Rescaled fracture energy due to bond scission ${\mathrm{\Gamma }}_{\mathrm{damage}}/U_B=\mathrm{\Sigma }.N_x$ as a function of the total fracture energy ${\mathrm{\Gamma }}_C$. Dashed lines are power-law fits with power $\beta =0.95$, 0.72, and 0.54, respectively for PEA-DA-0.5, PMA-DA-0.4, and PMA-DA-0.2. The gray area represents $({\mathrm{\Gamma }}_0/U_B)={\mathrm{\Sigma }}_{\mathrm{LT}}.N_x$, the Lake-Thomas threshold for the three materials. Error bars in (b) and (c) show the standard deviation based on four local confocal measurements on each fractured sample. (d) Ratio ${\mathrm{\Gamma }}_{\mathrm{damage}}/{\mathrm{\Gamma }}_c$ of the energy ${\mathrm{\Gamma }}_{\mathrm{damage}}$ dissipated by bond scission, over the total fracture energy ${\mathrm{\Gamma }}_c$, as a function of the reduced crack speed $a_T{v}_{\mathrm{crack}}$. The energy ${\mathrm{\Gamma }}_{\mathrm{damage}}$ is estimated assuming $U_B=60\mathrm{kJ}.{\mathrm{mol}}^{-1}$. (e) Schematic coupling between viscoelasticity (blue domain) and strand breakage (red domain) at the crack tip. The enlarged region shows the occurrence of bond scission (yellow stars) in the elastomer network. Bond scission and viscoelastic dissipation are strongly coupled, with a joint increase in bond scission and viscoelastic dissipation between the low viscoelasticity (i) and large viscoelasticity regimes (ii). $\delta$ represents the crack tip opening displacement and $L$ the characteristic spatial extension of bond scission at the crack tip.

Figure 6

Calibration of fluorescence intensity with mechanophore concentration. Typical calibration curve, showing the linear relation between fluorescence intensity and concentration of calibration molecule.

Figure 7

Damage profile extraction. Intensity normal to the crack profile. The horizontal dashed line shows the background level in the material.

Figure 8

Linear dependence of fluorescence intensity with mechanophore concentration. (a) Linear dependence of activated mechanophore per unit area as a function of the molar fraction of mechanophore. (b) Absolute damage profiles $\varphi (z)$ for various molar fractions of mechanophore.

Figure 9

Intrinsic activation of mechanophore as a function of the stretch rate and temperature. Bulk fraction of activated mechanophore in the triple network, as a function of the stretch $\lambda ·{\lambda }_0$ on the first network for (a) various stretch rates and (b) temperatures.