Influence of the shape of cohesive zone models on the peeling of stiff film/soft substrate systems: A theoretical perspective

Abstract

Peel tests have been widely used to measure the interfacial properties of thin film/substrate systems. With the emergence of soft materials and structures, there is a growing need to characterize the interface of stiff film/soft substrate systems. The accurate prediction of their peeling behaviors relies on cohesive zone models (CZMs), but the influence of the shape of CZMs remains unclear. Herein, we propose a theoretical model based on the trapezoidal CZM to characterize the 90-degree peeling of stiff film/soft substrate systems, and this model can degenerate into those based on Dugdale’s and bilinear CZMs. We validate the theoretical solutions for different shapes of CZMs by finite element simulations, and reveal that the maximum peeling force ($P_{\max }$) and the corresponding cohesive zone length ($l_{\text{CZ}}^{\max }$) are significantly affected by the shape of CZMs. We further obtain the unified power scaling laws of $P_{\max }$ and $l_{\text{CZ}}^{\max }$ for different shapes of CZMs, where the scaling exponents depend on substrate elasticity and the shape of CZMs. By a simple extension of the present model, we find that the presence of a small initial interfacial crack can lead to a significant decrease of $P_{\max }$. When the initial interfacial crack is long, the influences of the substrate modulus, the shape of CZMs and the interfacial strength on $P_{\max }$ can be ignored, and the peeling is governed by the interfacial fracture energy. With the present theoretical solutions, the interfacial strength and fracture energy of stiff film/soft substrate systems can be extracted simultaneously via 90-degree peel tests as long as the shape of CZMs is given and the initial interfacial crack is not very long. We expect that the present model can be extended to the case of arbitrary multi-linear CZMs, which can approximate arbitrarily shaped CZMs. These results can help us measure the interfacial properties of stiff film/soft substrate systems via peel tests, and understand the influence of the shape of CZMs on the interfacial fracture from a theoretical perspective.