Self-Replicating Cracks: A Collaborative Fracture Mode in Thin Films

Straight cracks are observed in thin coatings under residual tensile stress, resulting into the classical network pattern observed in china crockery, old paintings, or dry mud. Here, we present a novel fracture mechanism where delamination and propagation occur simultaneously, leading to the spontaneous self-replication of an initial template. Surprisingly, this mechanism is active below the standard critical tensile load for channel cracks and selects a robust interaction length scale on the order of 30 times the film thickness. Depending on triggering mechanisms, crescent alleys, spirals, or long bands are generated over a wide range of experimental parameters. We describe with a simple physical model, the selection of the fracture path and provide a configuration diagram displaying the different failure modes.

Figure 1

Unusual cracks in thin film moderately adherent to a substrate (scale bar $100\mu \mathrm{m}$). Numerous nucleation spots lead to complex patterns (a). Self-replicating cracks triggered by scarce defects (see the supporting movies S1, S2, S3 in the Supplemental Material [12]): Archimedean spirals (b); regular alleys of crescents (c),(d); and parallel bands (e) follow an initial arch, loop, or line, at a fixed distance $W_1$. (f) Pairs of cracks simultaneously follow each other path leading to isolated bands.

Figure 2

(a) Width of the delaminating front in SOG films with different adhesion energies ${\mathrm{\Gamma }}_0$ (color coded) as a function of the thickness $h$ of the film for different morphologies: pitch of the spiral or wavelength of the crescent alleys ($W_1$, open symbols) and width of paired cracks ($W_2$, filled symbols). Lines correspond to linear fits of the data. (b) Generalization to a wider range of systems including data from the literature (other silicate films [13, 14, 15, 20], metal films [17, 18, 19]) and macroscopic measurements on varnish or paint.

Figure 3

(a) Delaminated symmetric band with imperfect release of stress ${\sigma }_{yy}$ close to the debonding front. (b) The spontaneous tilt of the band releases stresses ${\sigma }_{xx}$ ahead of the debonded zone. (c)–(e) Comparison of experimental crack paths with the prediction from energy minimization with ($\alpha =0.0251$, $\beta =1.26$) starting from an initial crack represented by a thick black line. The debonding front is drawn in dashed blue line.

Figure 4

Experimental observations of patterns in the ($\gamma e/G_c$, $e/{\mathrm{\Gamma }}_0$) plane: cracks following a previous cut (open circle, spiral or crescent) and paired cracks leading to self peeling strip (solid square). Two borders $\gamma e/G_c\ge 0.5$ (pink line) and $e/{\mathrm{\Gamma }}_0\ge 1$ (yellow line) classically define the regions where isolated channel cracks and delamination are, respectively, impossible. However, collaborative delamination cracks are observed within the light pink domain. The different patterns are observed for ${\mathrm{\Gamma }}_2>{\mathrm{\Gamma }}_0$ (paired cracks above the brown curve), ${\mathrm{\Gamma }}_1>{\mathrm{\Gamma }}_0$ (spirals and oscillating crescents above the black limit). Different patterns are observed for the same range of physical parameters, depending on nucleation geometries. We observe crescent patterns with larger amplitude closer to the black limit.