Fig. 3: Grain-size controls the tensile properties of methane hydrate.
a, b Stress–strain data under monotonic loading to failure, for several points in typical samples. Straight lines in a are axial elastic constants E = 0.8, 1.6 and 4.9 GPa at supercoolings ΔT = 21.8, 33.8 and 40.3 K; c Thickening of the shell at different supercoolings ΔT. Solid lines: w(t) ∝ tγ with γ = 0.35, 0.4 and 0.35 at ΔT = 21.8, 33.8 and 40.3 K. Dashed lines: fits to γ = 1/2; d Grain size evolves with both annealing time ta and supercooling, ΔT. Scale bar: 50 μm; e The rigidochrome fluorescent dye DASPI marks grain boundaries in a maturing halo (ΔT = 40.3 K): left transmission images (T), right fluorescence (F). Scale bar 20 μm; f Dependence of the von Mises tensile strength on shell thickness, as determined by the supercooling (colour coded pink through ice- to deep blue ΔT = 21.8, 38.3, 33.8 and 40.3 K, and by the annealing time, ta (symbol size); g Situation of the present data (grey box) in a log-log plot of tensile strength vs. grain-size, g, (or shell thickness at failure), with respect to experimental (large symbols) and simulated data (small symbols) on methane hydrate (circles refs. 21,24) and ice (triangles, refs. 25,34). Supercooling of all data colour coded as in part f. Dotted line: slope β = −1/2 for a standard Hall-Petch relation, Eq. (8); Solid line: size-effect Eq. (9) with σ∞ = 0.2 MPa, Y = 11 GPa64 and K = 0.13; dashed line: predicted extension of the size effect into the range of grain sizes observed in marine sediments (pink box, refs. 33,76).
