(Color online) SiNx islands on PI substrate stretched horizontally. Island thickness h and island size L are shown at the upper left corner of each micrograph. The substrate elongation is given at the lower left corner. For islands with h = 0.3 μm (a)–(c), debonding and cracking coexist when L = 20 μm. When L > 20 μm, only channel cracking occurs. For islands with h = 1 μm (d)–(f), debonding and cracking coexist when L = 40 μm. When L < 40 μm, only debonding occurs; when L > 40 μm, only cracking takes place.
(Color online) Summary of the failure modes for different island configurations. C—only cracking occurs. D—only debonding takes place. M—debonding and cracking coexist (the numbers indicate the proportion of cracked islands).
(Color online) The accumulated fraction of cracked islands is plotted as a function of the applied strain. The experimental observations are plotted as dots and the Weibull distributions are plotted as dashed lines. (a) Island size is varied with fixed island thickness (h = 500 nm). (b) Island thickness is varied with fixed island size (L = 40 μm). If cracking and debonding coexist, the curve cannot reach unity because debonded islands do not crack.
(Color online) The accumulated fraction of debonded islands is plotted as a function of the applied strain. The experimental observations are plotted as dots and the Weibull distributions are plotted as dashed lines. (a) h = 250 nm is fixed, island size is varied. (b) L = 20 μm is fixed, island thickness is varied. If cracking and debonding coexist, the curve cannot reach unity because cracked islands do not debond from the edge of the island.
(Color online) Schematics of the 3D finite element model of a unit cell: (a) top view and (b) side view. S/L = 1.5 is fixed in all the experiments and simulations. Due to the symmetry, only the shaded quarter in (a) is modeled. The maximum tensile strain is found at the root of the center of the edge, as marked by .
(Color online) (a) FEM results of normalized maximum strains in the island and (b) critical strain-to-rupture calculated by Eq. (4), as functions of island size with various island thicknesses.
(Color online) (a) FEM results of the normalized maximum energy release rate and (b) critical applied strain-to-debond calculated by Eq. (7), as a function of island size for various island thicknesses.
(Color online) Combining Figs. 6(b) and 7(b), the critical applied strains to debond or to rupture are plotted as functions of island size for various island thicknesses: (a) h = 250 nm, (b) h = 500 nm, and (c) h = 1000 nm. The measured strain-to-rupture and strain-to-debond are plotted as square and triangular symbols, respectively, to compare with the theoretical prediction. For a given island configuration, the failure mode with the lower critical applied strain is predicted to occur.
Critical local rupture strain, ɛ c , calculated from Eq. (4) using the measured strain-to-fracture, ɛ f , and Fig. 6(a) for various island configurations.
Interfacial toughness Γi, calculated from Eq. (7) using the measured strain-to-debond, ɛ d , and Fig. 7(a) for various island configurations.
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