Fig. 3: Apparent fracture energy and the crack tip opening displacement as a function of crack tip complexity.
From: Complexity of crack front geometry enhances toughness of brittle solids
a, CTOD data are evaluated for each z slice by varying the evaluation window \({{{\mathcal{W}}}}\) (inset) and fitting a parabola to the CTOD. Apparent fracture energies Γapp are then graphed as surfaces as a function of z and \({{{\mathcal{W}}}}\) for a simple (below) and complex (above) surface. In both cases, Γapp converges to the background value Gc. b, For various materials, the normalized critical strain energy release rate (Gc − Γpz)/Γ* increases in proportion with the crack tip complexity, measured by the normalized geodesic crack length \(\tilde{{{{\mathcal{L}}}}}\). The square and the inverted triangle for gel 1 represent sample thicknesses of 100 μm and 380 μm, respectively. The linear proportionality is explained by the energy partition depicted schematically in the inset. The strain energy release rate is partitioned between bond scission at the crack tip, Γ*, which scales with \(\tilde{{{{\mathcal{L}}}}}\), and a constant process zone fracture energy Γpz. The evaluation of Γ* and Γpz is described in Methods. Error bars are defined from n = 31 segmentations for \(\tilde{{{{\mathcal{L}}}}}\). The sample number for Gc is provided in the data repository48. Better segmentation achieved with the embedded fluorophore in gels 2–4 and the PDMS generates error bars comparable to the symbol size for \(\tilde{{{{\mathcal{L}}}}}\). Data are presented as mean values ± s.d. Due to the large CTOD, a tile acquisition was required for gels 2–4 and the PDMS sample; thus, no error bars are reported for these data.
