On the peeling of elastic tapes from viscoelastic substrates: Designing materials for ultratough peeling
Introduction
In the last few years, the scientific community has devoted increasing attention to the study of adhesion between surfaces. Nature provides the most inspiring examples and great amount of biological species, such as many insects, spiders and lizards, which are able to adhere and quickly detach from several surfaces. This is why researchers, in the last decades, have tried to mimic such marvellous capacities, at first by deeply investigating the properties of the contacting surfaces. It was found that the mushroom-shaped pillars [1] exhibit very high adhesive performance, and several studies [[2], [3], [4]] have disclosed that the origin of such behavior lays in the shape of the terminal plate. Moreover, in some insects [5,6], the architecture of the pads enhances adhesion, therefore microwalls covered by a thin film have been proposed in some studies [7,8]. Attachment/detachment mechanisms of gecko spatula have been deeply investigated, through several peeling models [[9], [10], [11], [12], [13], [14], [15], [16]], as well as many experimental and theoretical studies have been carried out, aimed at calculating the peeling force required to detach thin films from rigid or compliant substrates [[17], [18], [19], [20], [21], [22], [23]]. This problem is crucial in many practical applications, such as in the adhesion of medical bands on human skin, which is a very compliant viscoelastic material [[24], [25], [26], [27], [28], [29], [30]]. In this context, the adherence of this kind of adhesives in contact with viscoelastic substrates has been extensively studied in the last years [[31], [32], [33], [34], [35], [36],52].
It is important to observe that the peeling phenomenon and more complex fracture problems are strictly related each other. Moreover, in a viscoelastic material the energy dissipation in the bulk makes the energy release rate not easily to be defined and the work of adhesion does not completely describe the crack growth process [37,38], since the entire process is related to different viscoelastic properties of the polymer [[39], [40], [41], [42], [43]].
In a so compelling research context, the authors in Ref. [44] proposed a new approach to investigate the interface crack propagation. In this paper, the theoretical study is extended to real-like viscoelastic substrates, by considering an increasing number of relaxation times in the Prony series, to correctly describe the response of the material. Moreover, the case of the peeling of an elastic tape from a PMMA (polymethyl methacrylate) substrate, whose viscoelastic response is characterized by relaxation times (Ref. [45]), is presented.
Section snippets
Peeling of an elastic thin tape from a viscoelastic substrate with more than one relaxation time
Here, we briefly recall the methodology developed in Ref. [44], at which the reader can refer for more details, by investigating the case of a viscoelastic substrate with a spectrum of relaxation times covering numerous decades. To this end, consider an elastic tape of width and thickness adhering on a viscoelastic substrate (Fig. 1) and peeled off by a constant vertical force . The thickness represents the only length of scale of the problem, therefore, we expect that interfacial
Results
In order to evaluate the influence of the spectrum of relaxation times characterizing the elastic modulus of the viscoelastic substrate, we first compare three ideal materials with , and relaxation times. For the first material we assume and . For the other two materials with three and five relaxation times, we take , with and , and and respectively. The real and imaginary parts of the viscoelastic
Conclusions
In this paper, we have investigated the effect of the viscoelastic damping in the substrate material on the peeling of elastic thin tapes. Specifically, by properly increasing the number of relaxation times in the viscoelastic modulus, it is possible to enlarge the frequency range in which material damping and energy dissipation occur. This condition gets adhesion ultratough, in the sense that stable peeling occurs at arbitrarily high loads. As a result, the detachment velocity of the tape can
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
L.A. and G.C. acknowledge support from the Italian Ministry of Education, University and Research (MIUR) under the program Department of Excellence" Legge 232/2016 (Grant No. CUP - D94I18000260001).
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