Figure 1

(Color online) Optical microscope images of wavy cracks with (a) large area and the wavy cracks with different wavelength ranging from (b) several microns to [(c) and (d)] several tens of microns. The arrows in (a) indicate the secondary cracks initiated perpendicular to the first crack path. Rectangles indicate the wavy cracks with different dimensions near to each other.Reuse & Permissions

Figure 2

(Color online) (a) An AFM microscope image of a wavy crack on silicon substrate, marked with the wavelength and the amplitude. IDZ stands for the interface debonded zone, one of which is denoted by dashed line. The gap between the two crack edges is indicated by yellow arrows. (b) The corresponding curvature changes along the crack path, where arrows indicate the kinks and the dashed line indicates the $\text{C}=0.25$ line.Reuse & Permissions

Figure 3

(Color online) The anticipate deformation and shift of the serration leaves along the wavy crack. The orange and green arrows indicate the deformation shift of the two adjacent crack leaves. Different places have different shift, indicating different dynamic process. $G_{1–3}$ stands for three gaps with different widths.Reuse & Permissions

Figure 4

(Color online) (a) An AFM microscope image shows the uncompleted crack tip with the stress region formed after the second crack and the different width of the crack gap. (b) The model illustrating the crack propagation process and the stress zone evolution in the wavy cracks. $K_{1\sim 3}$ stands for the kinks. Dashed lines indicate the suppositional process, arrows indicate the propagation directions.Reuse & Permissions

Figure 5

(Color online) The infinite element model of the crack in thin film deposited on substrate. (a) Right part: plane view of a crack in film deposited on substrate, and left part: cross-sectional view of the unit ahead (upper part) and below (lower part) the crack tip. (b) Plane view of a crack with extended debonded part of the film, which indicates that the propagate velocity ratio of the interface debonding and film crack is larger with respect to that in the situation shown in figure (a). Red circles stand for the debonded units with the substrate, dashed lines with a red cross are the bonds broken, and blue lines at the crack tip are the stressed bonds. The arrows denoted on the units at the crack tip show the forces or partial forces which have the similar meaning with that shown in (a).Reuse & Permissions

Figure 6

(Color online) Optical microscopy image shows a slightly curved straight crack with the debonded area around the crack line. Dashed line indicates one of the debonded areas.Reuse & Permissions

Figure 7

(Color online) The log-log plot of the amplitude versus wavelength, which suggests the scaling rule. This figure includes totally 448 pairs datum obtained from the digitalized wavy patterns; and dashed line is the best linear fit performed with a least standard deviation method. In order to separate the data points obtained from different samples, some of the data points corresponding to the cracks in the same sample are appeared as the same marks. Typically, the filled pink rectangle and the hollow yellow triangle corresponding to cracks in two samples, which have “special points” that is evidently deviated from the fitting line. As both the special points and the “normal points” are presented in the same sample, we suggest that the deviated points are not caused by the different film thickness, but are more favored to be related with the properties of the crack itself.Reuse & Permissions