Real-Time Early Detection of Crack Propagation Precursors in Delayed Fracture of Soft Elastomers

The fracture of materials can take place below the critical failure condition via the slow accumulation of internal damage followed by fast crack propagation. While failure due to subcritical fracture accounts for most of the structural failures in use, it is theoretically challenging to bridge the gap between molecular damage and fracture mechanics, not to mention predicting the occurrence of sudden fracture, due to the lack of current nondestructive detection methods with suitable resolution. Here, we investigate the fracture of elastomers by using simultaneously space- and time-resolved multispeckle diffusing wave spectroscopy (MSDWS) and molecular damage mapping by mechanophore. We identify a fracture precursor that accelerates the strain-rate field over a large area (${\mathrm{cm}}^2$ scale), at considerably long times (up to thousands of seconds) before macroscopic fracture occurs. By combining deformation or damage mapping and finite-element simulations of the crack-tip strain field, we unambiguously attribute the macroscopic response in elastic deformation to highly localized molecular damage that occurs over a sample area of about $0.01{\mathrm{mm}}^2$. By unveiling this mechanism of interaction between the microscopic molecular damage and the minute but long-ranged elastic deformation field, we are able to develop MSDWS as a flexible, well-controlled tool to characterize and predict microscopic damage well before it becomes critical. Tested using ordinary imaging and simple image processing, MSDWS predictions are proven applicable for unlabeled and even opaque samples under different fracture conditions.

Popular Summary

In everyday life and in industrial applications, fractures of soft materials normally occur via a local accumulation of undetectable damages that suddenly and unexpectedly transition to catastrophic failure. The prediction of this failure ahead of time would significantly reduce the safety margins currently required in shaping soft materials for applications. However, suitable methods to detect and characterize the early stages of fracture formation and what role local damage plays are still lacking. Here, by combining two existing tools, we investigate the formation of a fracture in a soft elastic polymer, or elastomer.

Recently, elastomers labeled with force-sensitive fluorescent molecules have been used to detect localized molecular damage occurring in front of cracks. Meanwhile, in separate experiments, a time-resolved optical method known as “multiple speckle diffusing wave spectroscopy” (MSDWS) has been used to detect nanoscale motion a few centimeters ahead of cracks. We use both methods simultaneously in a polydimethyl siloxane elastomer, demonstrating that the elastic response to localized molecular damage directly causes nanoscale motion on large areas of the sample.

Our work sheds light on the details of the fracture mechanism and demonstrates that MSDWS can detect nanoscale motion due to molecular damage significantly before any detectable macroscopic change. By performing experiments under several loading conditions and for various materials, we demonstrate the general applicability of MSDWS to better estimate product lifetime and maximum loading before failure.

Figure 1

(a) Setup for simultaneous MSDWS and confocal microscopy. A single edge notched sample (width 9 mm, length 15 mm, thickness 2 mm, and notch length 1 mm, cut with a fresh razor blade) is tested under uniaxial tension simultaneously mechanically, by MSDWS, and by confocal microscopy. (b) Three-dimensional image of bonds breaking around the crack tip during tensile testing of a notched PDMS sample. Four image slices ($1.4\mathrm{mm}\times 1.4\mathrm{mm}$ in plane with detection thickness $150\mathrm{\mu }\mathrm{m}$) scanning a depth of $750\mathrm{\mu }\mathrm{m}$ around the midplane of the sample are collected for a single 3D image. Images are labeled by the imposed strain.

Figure 2

(a) Main plot: black, averaged intensity $\overline{I}$ of mechanophore activation, in the region with $I>2I_{\mathrm{bulk}}$ (defining activated fluorescence after deformation), renormalized by the bulk intensity $I_{\mathrm{bulk}}$. Blue: crack propagation length $\mathrm{\Delta }s$. Insets: 2D mechanophore maps at $400\mathrm{\mu }\mathrm{m}$ deep from the sample surface. For images at the onset of macroscopic propagation (15.502% and 15.503%), a confocal microscope cannot capture the images due to its low time resolution, so raw images from the MSDWS camera are shown instead. (b) Main plot: averaged value of the normalized relaxation rate ${\overline{\nu }}_0/{\nu }_{0T}$ (red) measured by MSDWS in the region ${\nu }_0>2{\nu }_{0T}$. Inset: ${\nu }_0$ maps at different ${ϵ}_N$. Note that the field of view in MSDWS is about 20 times wider than in confocal microscopy.

Figure 3

Maps of the relaxation rate ${\nu }_0$ calculated from MSDWS (a) and DIC (b) at different times before fracture for two distinct samples stretched at ${\dot{ϵ}}_N=1.25\times {10}^{-4}{\mathrm{s}}^{-1}$.

Figure 4

(a) ${\mathit{D}}_{xx}$ component of the rate of deformation tensor as a function of distance $y$ from the crack tip, for $x=0$ [see the definition of axes $x$ and $y$ in the inset of (a)], as obtained by DIC (symbols, experiments) and FEM (lines, simulations). In panel (a), FEM data were obtained assuming that the crack tip does not move. (b) Same as in panel (a) but focusing on the late stages of the tests and implementing crack-tip propagation in FEM, at various propagation speeds $\dot{c}$, as indicated by the labels.

Figure 5

(a) Prototype test of the predictive capability of MSDWS. Letters corresponding to maps taken at different stages of the experiment are indicated in the strain-time curve. For both stretching ramps, the strain rate is ${\dot{ϵ}}_N=5\times {10}^{-5}{\mathrm{s}}^{-1}$. (b) Real-time DAM obtained at ${ϵ}_N=22.3\%={ϵ}_p$, using ${\tau }_{\mathrm{MSDWS}}=0.75\mathrm{s}$. The DAM reveals the formation of a dynamic precursor localized ahead of notch V. (c) Mechanophore mapping after unloading: notches III (for which the DAMs showed no enhanced dynamics) and V (for which the DAMs showed enhanced dynamics) after the first stretching ramp (${ϵ}_N={ϵ}_p$), compared to the pristine sample (${ϵ}_N=0$) as a reference. The sample was slightly opened (much less than ${ϵ}_p$) for a better visualization of activation. (d) Final fracture during the second loading ramp, at a strain ${ϵ}_f\sim {ϵ}_p+2\%$. [See horizontal dashed lines in panel (a).]

Figure 6

(a) DAMs obtained by plotting $C_I$ values from MSDWS at different waiting times $t_w$, with a fixed ${\tau }_{\mathrm{MSDWS}}=40\mathrm{s}$. (b) Time evolution of precursors of failure inferred from MSDWS (top), mechanophore signal (middle), and crack imaging (bottom), respectively. Top: area in the DAM where the dynamics are much faster than in the bulk (see text for definition). Middle: renormalized fluorescence intensity due to mechanophore activation $I/I_{\mathrm{bulk}}$. Bottom: propagation length of the crack as a function of $t_w$. Inset of the middle panel: 2D confocal images showing the mechanophore signal at 1680 s and 2820 s, respectively.

Figure 7

(a) DAM obtained for an un-notched PDMS sample submitted to a series of strain steps, 20 s after imposing the seventh step (${ϵ}_N=23.1\%$). The DAM is obtained using ${\tau }_{\mathrm{MSDWS}}=10\mathrm{s}$. (b) Speckle image taken during fast crack propagation, which occurred 910 s after the DAM shown in panel (a). Note that the crack starts from the bottom-left corner of the sample, where the DAM revealed faster dynamics almost 1000 s before. (c) Mean-squared displacement $⟨\mathrm{\Delta }{r}^2⟩$ over a time delay ${\tau }_{\mathrm{MSDWS}}=10\mathrm{s}$, averaged over the leftmost, the central, and the rightmost column of the DAM shown in panel (a), as a function of time before failure. For the sake of clarity, only relaxation phases 4 to 7 are shown. Failure occurs at $t=0$ in the figure, about 900 s after the seventh relaxation phase.

Figure 8

Prediction of “sideway” propagation in natural rubber.

Figure 9

Raw images and DAMs during the propagation of a piece of notched tagliatelle pasta (with egg).

Figure 10

(a) Material composition of PDMS with the addition of mechanophore cross-linker and nanoparticles. (The schematic is not to scale since the ${\mathrm{TiO}}_2$ nanoparticle should be significantly larger than the mesh size.) (b) Fluorescence mechanism of mechanophore cross-linker in polymer under tension.

Figure 11

The ${\mathit{L}}_{22}^{\mathrm{ncg}}$ (to be identified with $D_{xx,\mathrm{FEM}}$ in the main text) and $\dot{a}/a$ at different ${ϵ}_N$ plotted in a double logarithmic scale.

Figure 12

Imaging of a poly (ethyl acrylate) sample after stretched to ${ϵ}_N=15\%$. (a) Mechanophore maps around the tip, measured by confocal microscopy and averaged over 50 s. (b) DAM during the crack propagation, with ${\tau }_{\mathrm{MSDWS}}$ fitted from the reference rectangular region. Each DAM is labeled by the corresponding $t_w$ value.

Figure 13

Relaxation time ${\tau }_0$ obtained by fitting Eq. (a2) to the MSDWS data in the reference bulk region indicated in Fig. 12 as a function of $t_w$.

Figure 14

Propagation length $\mathrm{\Delta }c$ as a function of $t_w$.

Figure 15

Relaxation time ${\tau }_0$ in the bulk region of PDMS in Fig. 6 as a function of $t_w$.

Figure 16

Propagation length $\mathrm{\Delta }c$ as a function of $t_w$ for the PDMS experiment of Fig. 6.

Figure 17

Fracture strain ${ϵ}_f$ and modulus as a function of curing agent concentrations $\mathrm{\Phi }$.

Figure 18

DAM of single edge notched PDMS samples prepared with $0.0625<\mathrm{\Phi }<0.25$ (as indicated above each panel), with moduli as shown in Fig. 17. The DAM is taken 20 s before fracture occurs, using ${\tau }_{\mathrm{MSDWS}}=0.24\mathrm{s}$.