Effect of bending stiffness on the peeling behavior of an elastic thin film on a rigid substrate

Inspired by the experimental observation that the maximum peeling force of elastic films on rigid substrates does not always emerge at the steady-state peeling stage, but sometimes at the initial one, a theoretical model is established in this paper, in which not only the effect of the film's bending stiffness on the peeling force is considered, but also the whole peeling process, from the initiation of debonding to the steady-state stage, is characterized. Typical peeling force-displacement curves and deformed profiles of the film reappear for the whole peeling process. For the case of a film with relatively large bending stiffness, the maximum peeling force is found arising at the initial peeling stage and the larger the stiffness of the film, the larger the maximum peeling force is. With the peeling distance increasing, the peeling force is reduced from the maximum to a constant at the steady-state stage. For the case of a film with relatively small stiffness, the peeling force increases monotonically at the initial stage and then achieves a constant as the maximum at the steady-state stage. Furthermore, the peeling forces in the steady-state stage are compared with those of the classical Kendall model. All the theoretical predictions agree well with the existing experimental and numerical observations, from which the maximum peeling force can be predicted precisely no matter what the stiffness of the film is. The results in this paper should be very helpful in the design and assessment of the film-substrate interface.

Figure 1

Schematic of an elastic thin film with a length $L$ peeling from a rigid substrate with a peeling force $F$ and a peeling angle ${\theta }_F$ at the right end of the film. A curvilinear coordinate $(s,\theta )$ and a rectangular one $(x,y)$ are attached to the film-substrate system with the origin $o$ at the left end of the film. (a) The initial peeling state and (b) an intermediate state.

Figure 2

Comparison between the generalized peeling model and the simplified one with the same peeling angle ${\theta }_F={90}^{\circ }$ and adhesion energy $\Delta \gamma =3.84\mathrm{J}/{\mathrm{m}}^2$.

Figure 3

Peeling force varying with the peeling distance of the film with different bending stiffness for (a) ${\theta }_F={60}^{\circ }$, (b) ${\theta }_F={75}^{\circ }$, and (c) ${\theta }_F={90}^{\circ }$. Labels of (i) in (a) and (c) denote different peeling moments, which will be used to compare with the corresponding snapshots in Figs. 5 and 6, respectively.

Figure 4

Comparison between the peeling force of the generalized model in the steady-state stage and that of Kendall's model with the same adhesion energy and Young's modulus.

Figure 5

Profiles of the deformed film during different peeling moments with determined interface adhesion energy $W=10\mathrm{J}/{\mathrm{m}}^2$ and peeling angle ${\theta }_F={60}^{\circ }$ for (a) $Eh/W=200$ and (b) $Eh/W=1000$. Labels on each profile correspond to those in Fig. 3.

Figure 6

Profiles of the deformed film during different peeling moments with determined interface adhesion energy $W=10\mathrm{J}/{\mathrm{m}}^2$ and peeling angle ${\theta }_F={90}^{\circ }$ for (a) $Eh/W=200$ and (b) $Eh/W=1000$. Labels on each profile correspond to those in Fig. 3.

Figure 7

Peeling force varying with the peeling distance considering the effect of the adhesion energy with determined bending stiffness at ${\theta }_F={90}^{\circ }$.