90-degree peeling of elastic thin films from elastic soft substrates: Theoretical solutions and experimental verification

Peeling of thin films has been widely used in adhesion measurement, film transfer and bio-inspired design. Most previous studies focused on the peeling of thin films from rigid substrates, but soft substrates are common in practical applications. Herein, we propose a two-dimensional model based on the bilinear cohesive law to characterize the 90-degree peeling of elastic thin films from elastic soft substrates, and obtain theoretical solutions expressed in terms of the Chebyshev series. The theoretical solutions match well with the finite element method results, including the load-displacement curves and the bulging deformation of soft substrates. We find that with decreasing substrate modulus, the maximum peeling force ($P_{\text{max}}$) decreases but the steady-state peeling force remains unchanged. With the present solutions, the interfacial strength and fracture energy can be extracted simultaneously from the 90-degree peeling experiments of thin film/soft substrate systems, and then the experimentally measured $P_{\text{max}}$ for different film thicknesses can be well predicted. Furthermore, we obtain a new power scaling law of $P_{\text{max}}$, where the scaling exponent depends on substrate elasticity. These results can help us measure the interfacial properties of thin film/soft substrate systems via peel tests, and regulate their peeling behaviors by interface design.