Research ArticleMATERIALS SCIENCE

Laser Speckle Strain Imaging reveals the origin of delayed fracture in a soft solid

See allHide authors and affiliations

Science Advances  04 May 2018:
Vol. 4, no. 5, eaar1926
DOI: 10.1126/sciadv.aar1926
  • Fig. 1 Imaging local prefracture deformations.

    (A) Macroscopic stress transient in a step-strained notched elastomer en route to delayed fracture (denoted by “×”). (B) Schematic illustration of forward-scatter LSSI used to visualize strain precursors within the solid. The elastomer is illuminated with a coherent plane light wave, which is multiply scattered from TiO2 nanoparticles embedded in the elastomer, giving rise to (C) speckle patterns on a camera on the opposite side. Spatiotemporal correlation of the speckle intensity fluctuations, using the d2 function (Eq. 1), is used to create image contrast, encoding the local dynamics. (D) The resulting mobility maps reveal a growing zone of nanoscopic deformations, culminating in (E) catastrophic failure and the nucleation of a brittle crack. The background is masked in all images.

  • Fig. 2 Setup sensitivity and strain quantification.

    (A) Comparison of the average nanoparticle mobility 〈d2〉 in a thin horizontal strip in four different samples: an elastomer strained by 25% at Δt = − 1 s (), an elastomer strained by 3% (▲), the same elastomer in its quiescent, unstrained, state (■), and a static opaque medium, that is, a piece of ground glass, in which no thermal speckle fluctuations occur (). The notch is located at Δx = 0. The angular brackets denote averaging over 40 pixels in the orthogonal direction. (B) Apparent local strain rate in the center of an elastomer strained at a constant macroscopic rate. The dashed line is a predicted linear fit to the data, validating our analysis procedure. Inset: Average d2(τ) curves from which Embedded Image is computed, here at τ = 5 ms marked by the dotted line. The error bars indicate the SD of time averaging d2 over 2 s.

  • Fig. 3 Localized growth of nanodeformations.

    (A and B) The local differential strain intensity Embedded Image increases exponentially toward the moment of crack nucleation Δt = 0, shown for an elastomer strained macroscopically by ϵ = 25% (A) and 30% (B) as a function of the distance to the locus of highest stress concentration: Δx = 0.1, 0.28, 0.4, 0.55, and 1.5 mm. The angular brackets denote averaging over 40 pixels in the orthogonal direction [see inset in (A)]. The expansion of the precursor zone is evidenced by the different starting points Δts of the Embedded Image curves. (C) Spatial dependence of Δts for a macroscopic strain of ϵ = 25% (, right ordinate) and 30% (, left ordinate). The initial linear growth is marked by the fitted solid lines, whose slopes reveal growth velocities of 0.17 and 5.6 mm/s, respectively. (D) Collapse of all transient Embedded Image profiles, illustrating universality, through rescaling of the time axis with the local strain acceleration rate constant k(ϵ, Δx) (see inset). Ten percent of all data points are shown.

  • Fig. 4 Spring network simulations of delayed fracture.

    (A to H) Time sequence of a fracture simulation at times t* ≃ 21.1 (A and E), 61.7 (B and F), 79.7 (C and G), and 104 (D and H) [corresponding state points are indicated in (I)]. In (A) to (D), bonds are color-coded according to the amount of local damage, from blue to red indicating little to much damage. In (E) to (H), springs whose deformation rate exceeds a threshold are colored green. (I) Total damage rate constant Rtot as a function of time, indicating different stages in the damage accumulation and rigidity loss that precipitate the macroscopic fracture. Inset: Center-of-mass position 〈Δxdam〉 of the damage zone showing its growth toward the bulk until a crack nucleates. (J) Local stiffness μbin as a function of time at different distances from the notch: Δx/l0 = 1.5, 4.5, 7.5, 10.5, 13.5, and 16.5. For these data, the simulation is parameterized as: ϵ = 25%, fthr = 0.35, rnotch = 20l0, nsoft = 20, α = 0.95, Nx × Ny = 200 × 100, and wx = 40l0 (see Materials and Methods and the Supplementary Materials for details).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/5/eaar1926/DC1

    Supplementary discussion of simulations

    fig. S1. Schematic top view of LSSI in the forward-scatter geometry.

    fig. S2. Spatial blurring in forward-scatter LSSI.

    fig. S3. Robustness of the fitting procedure of the Formula profiles.

    fig. S4. Simulation protocol and shape of damage zone.

    fig. S5. Tunability of the softening-breaking protocol.

    fig. S6. Simulations at different strains for various notch radii.

    movie S1. Speckle movie of the damage-induced deformations preceding delayed fracture of a 25% strained elastomer.

    movie S2. d2 movie of the growth of the prefracture deformation zone in a 25% strained elastomer.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary discussion of simulations
    • fig. S1. Schematic top view of LSSI in the forward-scatter geometry.
    • fig. S2. Spatial blurring in forward-scatter LSSI.
    • fig. S3. Robustness of the fitting procedure of the √f(U)(Δt) profiles.
    • fig. S4. Simulation protocol and shape of damage zone.
    • fig. S5. Tunability of the softening-breaking protocol.
    • fig. S6. Simulations at different strains for various notch radii.
    • Legends for movies S1 and S2

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mp4 format). Speckle movie of the damage-induced deformations preceding delayed fracture of a 25% strained elastomer.
    • movie S2 (.avi format). d2 movie of the growth of the prefracture deformation zone in a 25% strained elastomer.

    Files in this Data Supplement:

Navigate This Article