Research ArticleMATERIALS SCIENCE

Nonlinear fracture toughness measurement and crack propagation resistance of functionalized graphene multilayers

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Science Advances  06 Apr 2018:
Vol. 4, no. 4, eaao7202
DOI: 10.1126/sciadv.aao7202
  • Fig. 1 In situ TEM setup for tensile test of precracked GO nanosheet.

    (A) MEMS-based in situ TEM/STEM/SEM (scanning electron microscopy) experimental setup. (B) MEMS device placed inside a custom-made TEM holder. (C) SEM image of the TEM-compatible monolithic MEMS device, as dash box in (B). (D) Higher magnification SEM image showing actuation shuttles with a ~2.5-μm gap [dash box in (C)]. (E) SEM image of pristine GO nanosheet suspended over the actuation shuttles in (D). (F) SEM image showing high-energy electron beam–irradiated GO nanosheet (34 nm; sample 3) in (E); a ~1.2-μm crack was introduced. (G) High-resolution SEM image of the artificial crack in (F). The entire experiment was conducted in STEM mode and Hitachi HF-3300 STEM/TEM, which has a secondary electron detector that allows capturing SEM images in STEM mode.

  • Fig. 2 Fracture behavior of GO nanosheet under tension.

    (A) Stress-strain response before subcritical crack propagation (captured during in situ TEM uniaxial tensile testing). Data were recorded for all the four tested samples of GO nanosheets with different thickness. Inset: Electron irradiated precracks of four different samples. (B) Representative snapshots of propagation of the artificial crack (34-nm-thick sample). The last image is a high-magnification image showing film overlap after load release.

  • Fig. 3 Fracture toughness analysis of GO nanosheet.

    (A) SEM image of a precracked GO nanosheet before loading (sample 1) for which J integral calculations were performed. (B) FE analysis stress contour (GPa) in the loading direction of sample 1 corresponding to the maximum experimentally measured far-field stress immediately before the propagation of the crack. (C) High magnification of the stress distribution near the crack tip in (B). The region colored orange experienced stress in the nonlinear stress-strain regime. (D) Stress as a function of distance from the crack tip. A nonlinear zone from the crack tip to 5.6 nm is shaded. (E) Variation of JIC along the crack front as a function of the number of contours considered for the domain integral method.

  • Fig. 4 Atomistic origin of enhanced fracture toughness of GO nanosheet.

    (A) The initial configuration of a layer in a precracked four-layered GO sample and the schematic of the constraints. (B to G) Snapshots of the distinct stages of fracture path through one of the layers in a precracked four-layered GO sample during uniaxial loading. Atoms in the precracked layer are colored on the basis of their shear strain magnitudes. For clarity, the functional groups are hidden in these images. Here, atomic strain is defined as the von Mises shear strain invariant of the atomic Green-Lagrangian strain tensor, which may be derived directly from the definition of the local deformation gradient. (H) Uniaxial stress-strain response of the layer and labels in stress-strain curve refer to MD snapshot panels in this figure. (I) Fracture pathways of constitutive layers in a four-layer GO sample. (J) MD simulations: Uniaxial stress-strain response of precracked monolayer and multilayer GO nanosheets subjected to uniaxial tensile loading. (K) Energy absorbed per unit volume by GO nanosheets of varying thicknesses during crack propagation. It is calculated as the area under the stress-strain curve in (J) from the point of fracture initiation to the 50% of their peak stress, where the sheet is considered to have failed completely.

  • Table 1 Summary of fracture toughness measurements.
    Sample number1234
    Thickness (nm)14.6 ± 0.121.1 ± 0.234.0 ± 0.3131.5 ± 0.2
    Number of layers~21~30~49~188
    Crack size (nm)416.7 ± 1818 ± 21244 ± 61279.6 ± 7
    Crack size/sample width12%16%10%11%
    Linear analysis (Griffith theory)
    Critical stress intensity factor KIC (MPa√m)4.4 ± 1.25.9 ± 2.44.9 ± 1.74.0 ± 0.5
    Critical stress energy release rate GIC (J/m2)*80–92140–167110–11576–262
    Nonlinear analysis (J integral)
    JIC (J/m2)34–3981

    *Critical strain energy release rate for each sample was reported as a range because it is Young’s modulus dependent; the lower bound value was obtained by using the modulus of monolayer GO in the study of Suk et al. (26), whereas the upper bound value was determined using the modulus of GO nanosheets [calculated by fitting the modulus versus thickness trend in the study of Cao et al. (14)]

    Supplementary Materials

    • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaao7202/DC1

      section S1. Hole-by-Hole crack creation via electron beam and additional experimental results

      section S2. Applying Griffith theory of brittle fracture to calculate fracture toughness

      section S3. Summary of sample geometry

      section S4. FE-based stress analysis and calculation of J

      section S5. Uniaxial tensile simulations of pristine multilayered GO

      section S6. Linear and nonlinear stress analysis

      section S7. J integral calculations

      section S8. MD simulations of fracture in multilayered GO

      fig. S1. Crack creation via electron beam and tensile testing of sample 4.

      fig. S2. Crack creation via electron beam and tensile testing of sample 1.

      fig. S3. FE models and mesh.

      fig. S4. MD simulation model.

      fig. S5. Nonlinear mechanical properties of GO nanosheets from MD simulations.

      fig. S6. Stress analysis ahead of the crack tip in sample 1 using FE simulations.

      fig. S7. Stress analysis ahead of the crack tip in sample 2 using FE simulations.

      fig. S8. Crackfront nodes and corresponding JIC values for sample 1.

      fig. S9. JIC for sample 2.

      fig. S10. Atomic configurations of cracked AB-stacked GO sheets.

      fig. S11. Stress-strain response for four-layer GO sheet.

      fig. S12. Fracture in four-layered graphene.

      table S1. Summary of sample geometry.

      movie S1. In situ TEM tensile test of functionalized graphene multilayers.

      References (4655)

    • Supplementary Materials

      This PDF file includes:

      • section S1. Hole-by-Hole crack creation via electron beam and additional experimental results
      • section S2. Applying Griffith theory of brittle fracture to calculate fracture toughness
      • section S3. Summary of sample geometry
      • section S4. FE-based stress analysis and calculation of J
      • section S5. Uniaxial tensile simulations of pristine multilayered GO
      • section S6. Linear and nonlinear stress analysis
      • section S7. J integral calculations
      • section S8. MD simulations of fracture in multilayered GO
      • fig. S1. Crack creation via electron beam and tensile testing of sample 4.
      • fig. S2. Crack creation via electron beam and tensile testing of sample 1.
      • fig. S3. FE models and mesh.
      • fig. S4. MD simulation model.
      • fig. S5. Nonlinear mechanical properties of GO nanosheets from MD simulations.
      • fig. S6. Stress analysis ahead of the crack tip in sample 1 using FE simulations.
      • fig. S7. Stress analysis ahead of the crack tip in sample 2 using FE simulations.
      • fig. S8. Crackfront nodes and corresponding JIC values for sample 1.
      • fig. S9. JIC for sample 2.
      • fig. S10. Atomic configurations of cracked AB-stacked GO sheets.
      • fig. S11. Stress-strain response for four-layer GO sheet.
      • fig. S12. Fracture in four-layered graphene.
      • table S1. Summary of sample geometry.
      • Legend for movie S1
      • References (46–55)

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      Other Supplementary Material for this manuscript includes the following:

      • movie S1 (.mp4 format). In situ TEM tensile test of functionalized graphene multilayers.

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